The traffic was dominated by Facebook and Twitter. Early leads from usual suspects (Hacker News, Reddit) within hours became a rounding error. Social media was sending a torrent of traffic, reaching almost 50,000 a day in total. Mainstream press, while lending a lot of credibility to the material (thank you!), was relatively small source in comparison.
С большим удовольствием, ну и грустью конечно, прочитал вашу статью на AIN и просто не могу согласиться больше – под каждым словом подпишусь.
Roman
Thank you for your honest article and clear vision. Even in the U.S., it takes the courage to express yourself so freely about the Russian mafia regime and ruthless KGB. Oksana
To a professional expert in social apps that sent one clear signal: it was all happening thanks to people individual effort to share. It resonated in a profound way with a lot of people. It resonated personally; it resonated emotionally. They were reposting, reposting and reposting on any social channel they could reach. That was classic, cascadegrowth viral distribution.
твоя статья! хотела просто сказать, что согласна с каждым твоим словом. Спасибо!!! Я чувствую ровно то же самое!
Anya
Max, that was a powerful blog posting you wrote about Russia. Thank you.
It touched something that people felt they just had to share, they had to restate that message, they had to do something about it. They did. They shared. The result was explosive.
– Thank you for your post “norussian” – it made my day!
– Все так. До запятой.”
I think better approach is to stop calling Putin and his cabal Russians – Lubyankans or Soviets or something similar would fit better….
Большое спасибо вам за эту попытку объяснить происходящее в России … Я вижу, что люди на Западе совсем не понимают российской ситуации и как она сформировалась. И очень много какихто плоских стереотипов о русских, еще времен Холодной Войны. Тут, в Европе я постоянно слышу наивные вопросы как европейцев, так и американцев вроде “если вам так не нравится ваше правительство и президент, то почему вы их не переизберете?”, они не знают как ущемляются гражданские права людей и как ведется бизнес (“ой, какие ужасы! А почему вы в суд на них не подаете?”), или они совершенно не понимают размеры экономики РФ (“Как работать негде? Как так правительство уничтожает средний и мелкий бизнес? Это же основа экономики!”) итд.
Anna
Умно, хорошо, понятно,правдиво..
Russians “thank you” notes were a flood. A pain long held and suppressed, finally finding an outlet, finally getting a release. At last they had an answer they did not know they were looking for. That was their stake in the ground, the demarcation line they can define, a clear definition of “us” versus “them”.
Хорошая статья !
Отличная статья. Неприятная для многих правда. Слава правде, позор лжи.
The decision to separate is never easy. By human nature we prefer to collaborate, to find common things, to emphasize what unites us. Going the opposite way is hard. Going against your own national identity is very hard. You prefer not to. You wait it out and hope it just you. Yet at some point pain becomes too great. You had waited too long. A simplest trigger can set off a chain reaction.
They found that trigger. The small blue “Share” button was all it took to start the catharsis. Given number of translations to different languages, number of mainstream sites running their own coverage I think there might have been up to a MILLION people by now who had seen the story in one way or the other. The original article just put few right words on the page. It’s the Russian people who spread that message around the planet.
“Я хоть и не программист и работаю в другой отрасли, но живу в Силиконовой Долине уже больше 20 лет. … тут же приезжают толпы новых из России. Вы не представляете, сколько здесь сейчас русских. 20 лет назад и даже 10 лет назад столько не было. И всё едут и едут. И я не преувеличиваю нисколько. … Сейчас у нас тут, куда ни пойди, везде слышится русская речь. И вот эти люди – тот самый креативный класс, о котором автор написал. И все они работают на Америку. И даже многие из тех, кто ещё в России и не уехал ещё, тоже на Америку работают в амер. … Я это не из злорадства пишу, а просто констатирую факт. Если комуто не нравится и хочется думать, что это не так, то это ваше право, конечно. Всегда приятнее выдавать желаемое за действительное, правда ?”
“Great article! But I must say that difference between Russians and Ukrainians is not “cosmetic”. The main difference is Ukrainian individualism vs. Russian collectivism. Therefore, Ukrainians HATE tyranny, they never accepted it, any Ukrainian statebuilding efforts have always been democratic. While Russians seem to adore their dictators (Putin is not the first). Victoria”
Ukrainian side, deservedly, had a lot of critique for calling Ukrainians “ethnic Russians”. It was interpreted as usual Russian chauvinism rejecting Ukrainian identity, language and rights as a sovereign nation. Ouch.
My apologies to Ukrainians. From a historical perspective I was referring to, the article would be unchanged if I were to say “Russia is populated by ethnic Ukrainians from KievlanRus“. inosmi.ru did astute and very subtle translation as “Russich”, which precisely the meaning I was trying to convey. Keep in mind, there is no English word I know for “Russich”, and if one exists, I’m sure last person around here who knew it left after he locked gates at Fort Ross after himself.
There is no doubt about modern Ukraine national identify. I’m only making the point it is fairly similar culture to Russian one, when contrasted with sharp differences with, say, Chinese, Indian or LatinAmerican cultures.
“И отдельное вам спасибо за последний параграф с призывом к действию. Я сейчас сама ищу работу вне России и знаю, насколько трудно быть русской сейчас. Если бы у меня были возможности, то я бы постарались вывезти из РФ как можно больше людей. Причем не только креативный класс, но и простых рабочих, мастеров, учителей, медработников и тд. Как Шиндлер из фильма “Список Шиндлера”. Я исколесила всю Россию вдоль и поперек, работала в Сибири и я очень люблю и уважаю русских людей, которые реально работают. А они работают и очень много. Не смотря и вопреки. Надеюсь, на моей новой работе у меня получится нанимать людей из России. Еще раз спасибо! Anna”
As a person who went through the full immigration process, I know first hand how hard it is. Relocating is hard, learning new language is very hard. Working in a different culture requires a big adjustment, especially for the older people. The immigration systems and work visa programs of other countries (and especially United States) are borderline stupid, almost designed to keep best and brightest away. The sad truth is that H1B visas and asylum applications do not have the capacity to save entire creative population of the country. Its far too many people numerically.
At the same time, make no mistake: current Russian’s regime is ruthless, efficient and fully in control. It not going to change soon, especially with 81% popularity rating. It has no obvious weaknesses besides potential economic collapse from sanctions (and still would take 10 to 20 months and resulting political change that might not be for the better at all). The ruling elite is not considering Russia their homeland: it is occupied territory with captive native population to be exploited for monetary gain which is to be squirreled away overseas. If country and it’s people would be irrevocably ruined by the process so be it: the elite and their children will just permanently move their European residences.
That is the key problem that makes sanctions such a blunt and imprecise weapon: until they include all extended families of the corrupt Russian governmentindustrial complex officials they are toothless. If they do include them (and assets registered in the name of *all* their relatives) it will have big negative impact on EU/UK economy, and it becomes equivalent of nuclear weapon against Russian ruling class: they will have absolutely nothing to loose, the whole purpose of their life (Western wealth) would be wiped out in an instant. In general, it is not a smart move to put a nucleararmed power in that position.
That leaves us is with a huge population of extremely talented people totally captive and unable to realize their potential under current regime. It is no accident that of 5 dominant giants of high tech – Apple, Google, Amazon, Facebook, Microsoft – one founder is Russian in and another is halfSyrian Arab. The fact that that majority of people in these cultures are suppressed is not a tragedy just for them, its tragic loss for the whole planet bereft of that amazing talent. Until recently I did not see any constructive solution to the problem.
Ukranian revolution, in my opinion, changes all that for the Russian culture (or to mark the progressive part of it: EuroSlavic). Assuming Ukrainian people preserve their freedom and don’t fall under the rule of corrupt oligarchs again (enlightened oligarchs who would engage in nation building are quite all right) it presents a unique opportunity.
Kiev is a cosmopolitan European capital with good climate and great people. Unlike Moscow, it much less infected with toxic poison of oil and gas revenues – here you got to work to make your fortune. I observed many times that when it comes to cutting edge technologies Ukranian and Kiev teams are far ahead of Russia as whole – and Russia is a pretty big place! The reason is simple: Kiev teams already compete, learn and grown on the world level – they wouldn’t get any contracts otherwise. Russian teams always have a fallback to easy lowcompetency contracts driven by oil and gas: they have much less pressure to become exceptionally good. That how global technology competition works.
Russia’s 10% of best and brightest will now try to leave the country at all cost. Many of course will come our way to Silicon Valley or New York or other world capital, where they will be extremely welcome. However, they have to pay a heavy price: adoption and hard adjustment to Englishlanguage Western culture.
Free Ukraine represents a unique opportunity: a land culturally close to Russia, yet under no oppressive rule. Kiev should look at this 10% as very precious resource Putin’s Russia is squandering away like a drunken sailor. They are squandering their own country future; it would be invaluable gain for Ukraine future growth to pick up that talent. Consider special programs, similar to that of Singapore, promoting easy immigration path for STEMs for talented Russians to join or start a business in Kiev. Obviously, given current extremely emotionally charged situation between two countries that might be a hard thing to do.
I will leave you with the following thought: 20 years ago, I was making similar choice, and Silicon Valley was an obvious destination. Somebody younger, smarter and more energetic than me is making that choice right now in Moscow or another Russian city. He is miserable from the avalanche of propaganda washing over him, from the atrocities majority of his countryman seem to approve and celebrate. He wants to get out. Obviously, he can learn English and join me here in the Silicon Valley (as a matter of fact do send me your resume if this applies to you!)
Yet, for an Ukrainian, do you want for him to feel at home in Kiev instead, and build next international giant like Google or Facebook headquartered in Kiev?
When writing original post I was not expecting any audience larger than few hundred Silicon Valley geeks who read my blog. Hence the grim analogy of “No Russian” would be apparent to them. For the larger audience here is what it means.
“No Russian” is a level in 2009 firstperson shooter game “Call of Duty”. In this part of the story a deranged Russian psychopath, Makarov, and his terrorist group slaughter a helpless, unarmed crowd of Russians, Ukrainians and other fellow slavic travelers at Moscow airport – with the sole purpose to plant the blame on Americans for the massacre. Killing your own brothers and sisters just to make Americans look bad is a good deal for Makarov. Activision game designers were going for the shock effect with this level, yet even they thought to make the story to something borderline on “this is insane, yet very remotely possible”. So to keep it real, Makarov is just a fringe lunatic, a terrorist leader, fighting against and deceiving Russian government among other world governments. In the story arc that follows Makarov actually kidnaps Russian president and his daughter, Alena. Then he proceeds to blackmail him for nuclear launch codes while threatening to torture Alena.
Let’s compare a real world Russia in 2014 with what game designers considered unrealistic shockjock dark fantasy just a few years ago. Russian weapons are killing Ukrainian brothers and sisters with tanks and heavy missile fire. The only threat to president daughter is a Twitter apology (?!) from Netherlands city mayor who just received (first) 40 coffins of his fellow countryman killed by Russian weapons. And nuclear launch codes are safe and sound in the hands of the maniac for the time being.
The scariest part: this is not a game.
]]>
The mass murder of passengers & crew of Malaysia Airlines Flight 17 using Russian’s weapons and (most likely) by hands of Russian military squad exposed to the world that Russia is now complicit in committing crimes against humanity. That was quite a journey for a country that just six months ago were considered a full member of the global community, even if notoriously ornery one. How was it possible for things to collapse so far and so fast?
“How did you go bankrupt?”
“Two ways, gradually and then suddenly”
Ernest Hemingway
To understand Russia’s lighting fast descend into the abyss one has to understand a simple truth that many (myself included) suspect all along: Russia was and is a failed state. What is seen from the outside is just a facade imitating a functional country and government. High oil prices, residual infrastructure of USSR and internal mass propaganda machine maintained the illusion for more than a decade.
Silicon Valley is far removed from that part of the world (Russia is nonentity when it comes to startups and innovation, besides being inexhaustible source of great engineers, we will come back to that), so let’s review some basic facts about Russia.
In simple terms, Russia is a mafia state. All the way from Moscow to regions and to small towns, everything is controlled by various mafia gangs. Police and judiciary are parts of most powerful gangs. They usually assist in extortion or theft of property earned by local small and medium size businessmen. Big business is subject to federal mafia clan wars.
The mafiastate formation is logical consequence of Russian economy: it is totally dominated by oil and gas revenues. Oil, gas and derivatives provide meaningful employment to about 1M people. Russian population is about 150M. How do they survive? The majority depends on various forms of government handouts.
With russianstyle oil production you don’t have to think, innovate or even hire smart people. All you have to do is to cash the check. Gazprom is ranked as one of the most grossly inefficient enterprises in the world. So what happens when a small, totally incompetent minority controls countrywide oil rent while the rest of 149 million people are a burden? The answer is obvious: that 1M would create a mafia state to keep the rest of 149M in check by means of police and judiciary abuse and mass propaganda.
Russian propaganda machine is vast, it now exceeds the one of Soviet Union. Official TV propaganda lies professionally and constantly. There are no independent TV channels; everything is controlled by government stooges. The “news” teams employ special teams that do video editing and fabrications to present absolutely falsified accounts for TV transmission. Then these fabrications are broadcast to brainwash captive population.
The population at large is, statistically speaking, not very bright. Many are deranged from overuse of alcohol or drugs. A big number are simply aging elderly rooted in USSRcentric mindset who never adjusted to the modern world. Most of them do not “work” in the sense we understand fulltime employment here: they occupy placeholder positions sponsored by the government. Being dependent their whole life on government help, they are psychologically unable even to think government can do something wrong.
The families, wives, children of Russian elite (think top 1% of that 1M strong oil & gas service clan) doesn’t live in the country. They actually despise Russia and it’s people. All of the live in the west, many in London: Russian’s oligarch family spending is major contributing factor to London overall economy. They have absolutely no long term interest in Russian country or population survival.
Corruption and theft are endemic. Recent Olympic games ended up most expensive in history of the planet not because they were so well built: it was because it gave an excuse to a huge number of mafia clans to steal on a gigantic scale.
Modern Russia is not a weaker version of Soviet Union “empire of evil.” This capability is, thankfully, long gone. Russia is “cargo cult” of Soviet empire. It lacks competent professionals, leaders and minimal work ethics to accomplish anything on that scale. It just have enough capacity to cover everything in a blanket of lies, and as long as it works on captive domestic population that is all that it’s leaders need to keep channeling profits from Russia to London accounts.
The best way to understand modern Russia is to imagine a steep pyramid. At the very top there is a clique of KGBaffiliated oligarchs, who manage barelycompetent class of middlemanagers (which can and do steal a fraction of everything they touch) which in turn sit on top of largely brainwashed and deranged mass population living on lifelong government welfare.
Needless to say this is most toxic environment imaginable to incubate a startup ecosystem.
Despite all that titanic effort, modern technology is far more powerful than any attempts by a backward medieval government to hold it back. Internet, web and mobile formed so called “creative class” in Russia. In general, these folk are young, smart, energetic, totally in tune how to leverage modern technology to find out the truth or to achieve their goals. They were the spearhead and main organizers of December 2011 protests against Putin’s mafia state. When you see smart young Russian engineer in Silicon Valley, most likely, you are talking with a member of this creative class.
Yet, Macbook Pro Retina is a poor weapon when fighting AKwielding government thugs. Mass propaganda and intimidation do work at mass scale. It is much easier to be dumb and “patriotic” than smart and inquisitive ( even US population had to learn that lesson the hard way after Iraq invasion ).
Creative class was a minority in modern day Russia and there is a strong emergent behaviour that draining their numbers. That is a class of people with the skills most in demand in Europe and USA. During “peaceful” decade of Putin’s rule over two million people emigrated from Russia: this is a number higher then immigration after communist revolution and civil war.
By my estimate there is probably few hundreds of thousands of people in the creative class in Russia. This vocal, yet very small group so far never succeeded at thwarting russian mafia state at anything. Then, recently everything had changed.
The differences between “Ukrainian” and “Russian” people are cosmetic. The distance between Kiev and Moscow is about same as Sacramento to San Diego. Even today, after all that happened, the most likely language you will hear on the streets of Kiev is Russian. So why Kremlin was so enraged about recent Ukrainian revolution? After all Ukraine has no natural gas or oil, there were no riches to divide, what was the fuss all about?
What happened is that first time in history, large group of ethnic “Russians” had overthrown a mafia clan in a popular uprising. Until then, Ukraine was a satellite state, and exactly because it had no natural oil and gas, much larger portion of the population had to develop “creative class” skills rather than going to work for oil company or police enforcement. Then suddenly this social group had enough heft and popular power to overthrow local mafia don.
You can imagine the amount of terror it produced in the gang occupying Kremlin right now. If was and still is an extensional threat to them, hence they pulled out all the stops to overthrow or destabilize a new government in Kiev, and at the same time whip out xenophobic masshysteria in a local population.
At this moment, Kremlin can not really stop. If Kiev government survives, it will fairly quickly unlock economic benefits of nonmafia, free economy. The large parasitic class living by bribes and extortion will be displaced: it will have the same effect as if base tax rate would suddenly drop by a double digit percentage. Next door, progressive Russians would quickly notice and spread information about growing prosperity and opportunity in a city next door. What was half million Euroleaning progressives, would become a million, then few million: before long you can picture a Gaddafistyle demise for the Kremlin gang.
Kremlin is fighting for its own survival: supplying weapon system and military crew to a roaming criminal gangs is nothing for them in big scheme of things.
This situation will get worse before it gets better. Kremlin will fight to the last: we will yet see the massive flood of lies and deceit they will unleash to mitigate the anger of their recent mass murder. Very unfortunately everything they do will be branded with the words Russia or Russian. Can’t say the rest of the country is blameless: Putin got a stratospheric 71% support level after annexation of Crimea. Many in creative class would do the logical thing: give up the hopeless fight and emigrate. We are probably going to see another, supermassive wave of immigration coming from Russia in next few years.
I think we came to the end of the line with regards to Russia as a name, culture, a global brand. For the time being the country future is destroyed, police state is wellentrenched and the narrative for the brainwashed locals would be xenophobic tale of struggle with the “West”.
Here is what it all means for Silicon Valley:
Personally, I’m thinking to start calling myself EuroSlavic instead of “Russian”. It’s a flimsy defense, yet Russian brand, after already being tainted with gulag and the rest of its toxic legacy, is now synonymous with mass murder of innocent civilians. There is nothing of value left to recover.
Updates & Coverage
Bloomberg
The Village
VOA
Euroslavic translation by AIN:
Ukrainian translation
Interview with Espreso.TV: Part 1  Part 2  Part 3
The story continues in Part 2
]]>P90X is a home fitness program developed by Tony Horton & Beachbody. You can do P90X at home with simple exercise equipment, since it is just a big set of DVDs with different workout sessions. Over the years, it became widely popular – sales are rumored to be close to a billion dollars a year. On the surface, P90X may look like many other lowtech video exercise programs. However, on a deeper level, P90X shows a brilliant social design; a design so successful that many Silicon Valley startups would envy it even today, a full decade after P90X launch. This essay will explain how P90X ingeniously hacks human behavior to help people get healthier, seemingly against their own will.
Positive facts about healthy exercise are so well known that it feels almost awkward to restate them one more time. Working out every day is good for you. The benefits are not just burned calories, toned muscle and increased stamina: a workout also increases your metabolism, which will last for many hours and give you extra energy throughout the day. Working out will release neurochemicals that will elevate your mood, make you alert and proactive. You can instantly make yourself happier and energetic just by including 3060 minutes of exercise in your day. Given such a wide range of benefits for a small time investment, it should be an easy decision for everybody.
Of course, this is almost the opposite of our day to day reality. The obesity epidemic shows no signs of slowing down despite our having a gym on almost every corner, myriad yoga studios and uncountable New Year’s resolutions. Like everybody else, I tried to solve this on my own: top tier gym memberships, extreme dieting, thousands of dollars worth of expensive exercise equipment, all of which were a total waste of time and money. After short bursts of activity, what always followed was the same lifestyle of a constant time crunch with too much bad food and too little physical activity. All I got from all these expensive experiments was a few occasional workouts and a quick regression to the past patterns. What I did not get was a real longterm result: a habit of healthy living.
When the summer 2012 presidential campaign brought P90X into the national spotlight, I decided to give it a try. Even after just a week the results were nothing short of amazing.
The mechanics of P90X are deceptively simple. Every day of the week you set aside an hour to workout in front of your TV. Every day you use different DVD to do a different workout. You keep the same weekly routine for 4 weeks, and then you switch to more advanced DVD set, and 4 weeks later to yet another one. P90X certainly packs a lot of content in that DVD box. Yet let’s not spend too much time on the low level specifics of P90X; what we want to understand is, why is P90X so successful at what it does?
The first key to P90X’s secret formula is that you are very likely to complete the first week’s of training; there is an important reason why the first week is so sticky, which I will explain later. For now, just assume once you try the first P90X DVD you are very likely to complete the full weekly set. What happens next?
Well, after you exercise intensively for one hour, day after day, the results are selfexplanatory: you effectively have just became an athlete. Your muscle mass begins to grow. You rapidly progress along all athletic parameters. It is surprising how quickly the biological mechanisms kick in to reinforce your newfound good habits. Your body shape changes within the first ten days; it has been optimized for exactly that kind of physical activity by hundreds of thousands years of evolution. You start noticing muscles where you never knew they existed. A week or two later you feel as if some sort of powerful alien machinery has taken over your body: the brain is still used to your old body, and it is not yet used to the power that appeared literally out of nowhere. All of us possess so much growth potential hidden inside, that it takes just a few days to kick all that machinery into action.
So if you do an intensive workout every day, you will become a healthy athlete with a totally different lifestyle and energy level. If you do not do it – you will not. You can do P90X, you can do yoga, you can do regular morning runs, yet at its very core, it boils down to simple binary question: are you intensively working out every day, at least half an hour or more? The only valid answers are “yes” or “no”.
P90X works, and it works amazingly well. Tony Horton and his team certainly spent plenty of effort to figure out the right workout sessions, the nutrition plan and other critical details of P90X’s mechanics. Yet the most profound question to understand is why P90X makes so many people actually do the exercise every day, considering most of them did not make that hard choice before? Tony Horton and the merry crew at Beachbody did not invent the idea of a healthy exercise video & infomercial – there were many others before them. Why is P90X the one that won big and not the other fitness programs? Why not these “8 minute something” videos? Somehow P90X managed to persuade millions to include workouts in their busy modern lifestyle, and to do so every day: that is impressive. That level of massive modification of people’s permanent habits sounds just impossible knowing what we know about ourselves. Yet P90X did it, repeatedly and at massive scale.
The real brilliance of P90X is not limited to showing us how to exercise smart. Workouts are the healthproducing payload delivered by ingenious P90X social design, they are only the visible tip of P90X iceberg. What’s really going on is that P90X hacks your behavior to make you subtly yet surely change your habits. P90X is brilliant at it from the very first session. After a new initiate makes it past his first week, he will find the process becoming progressively easier. He will keep exercising, he will keep becoming more of an athlete, his performance will spike through the roof, and all the while he will be raving to all his friends about how amazing P90X is. They will buy more DVDs, and the viral loop will repeat itself in high gear. To understand what really drives P90X, we need to understand how P90X permanently changes people behavior.
If you ask Dr. BJ Fogg of Stanford University how to change personal behavior, he will consider it an easy challenge. After all, he has been studying this area for many years. One of his findings is the Fogg Behavior Grid: a matrix that helps determine realistic pathways to change person’s behavior. In a nutshell BJ advocates a few simple ways to change our behavior, like picking up a healthy habit (fitness) or stopping a bad habit (unhealthy foods)
Here are a few takeaways from Dr. Fogg’s studies:
That’s where most traditional workout regimens and gym memberships fail: they expect us to go from zero “unfamiliar new behavior” to full strength “permanent repeatable behavior”, while all we are realistically capable on the first day is to do something just once, and strive to repeat it a few times later.
With that knowledge at hand, let’s take a detailed look at the P90X process.
Looking at P90X as a social product, it is easy for the professional eye to notice key components that make it so successful when compared to other health video products. Nowadays these components are wellknown in communities that design new social and gaming products. Yet many years ahead of the modern explosion of social networks, P90X pioneered many of the techniques we used in digital products years later. Lets start from the very beginning.
All startup founders know the initial “activation funnel” is one of the most critical components of a social product. The activation funnel is a process of converting an “unknown” user visiting your website for the first time to a registered user and hopefully a regular visitor. You never ever give users a reason to leave your website during the activation process. You try to find the minimum number of questions to ask, such as “what is your name?”, “what is your email?” and move the user as fast as you can to something she actually wants to do.
P90X is treats new user in the same way. Tony immediately goes after everything you can use as an excuse to NOT exercise and throws it out the window. The P90X activation funnel is superbly clean.
Lets see, what has prevented us from doing regular workouts in the past? There are so many convenient denials we keep telling ourselves to avoid exercise:
The list can go on and on. What you notice as soon as you start P90X is how few reasons you have to NOT do it. All exercises and equipment are carefully designed to be easy and accessible in a confined space. P90X goes to extreme lengths to make its program requirements very low. If you have extra space you can use a set of dumbbells, yet if you do not Tony specially provisions every weightlifting session with rubber bands – much more compact and travelfriendly device than dumbbells. Tony Horton spent two years trying to find the best combination of exercise and equipment, and it clearly paid off big time in ease of access.
The accessibility of P90X makes it very easy to start. In startup terminology, this moves us past the “Activation Phase” into the next stage: “Retention”. We made our “user” exercise once or twice, but how we make him do it over and over? How are we going to go from doing something once to doing something a number of times within a given period, as a recommended pathway on Dr. Fogg’s behavior grid?
At this moment, P90X unleashes the next component of its delivery mechanism: diversity. P90X comes on 12 DVDs. It’s a lot of videos. In fact, it is so much content that Tony is not going to use it all on you right away: the first 4 weeks will be a particular set of DVDs, with about 7 hours of total exercise time. That is still quite a lot of airtime for you to watch and actively participate in for a single week.
As everybody knows, working out is not much of a problem by itself. It is the mindless repetition over time that leads to boredom and ultimately prevents us from forming a healthy new habit. Traditional exercise programs give you the boring routine they want you to follow and just leave you running in a moribund loop until you give up from the boredom.
P90X leaves you no chance to get bored in the first few weeks. The first week is an overwhelming rush of new workouts, names, positions and techniques. The program diversity is astonishing: different forms of weight lifting, pullups, pushups, jump training, yoga and even a form of karate. Every day you learn something new.
Your curiosity and sense of adventure are running high: what is going to be in store for me today? What is going to happen tomorrow? Instead of finding ways to avoid workouts, now you proactively move other activities around to satisfy your curiosity for the new bag of tricks Tony will unleash on you next time.
At the end of the first week, your mind is totally overwhelmed by the new things you are learning. Your body is a painful wreck of muscles sore and strained by nonstop daily routine, yet boredom is last thing on your mind. You jump into the second week determined to figure out and master all these techniques you just discovered over the past week, and go over these again with at least minimal familiarity and do them better. The second week passes before you know it.
Congratulations, new initiate. You just crossed over to the 2nd square on Dr. Fogg’s behavioral grid: going from the first workout to repeating same activity over the period of a few weeks. You just formed a new mild habit, had a blast doing it, and did not notice what was actually going on. P90X just delivered the second part of its ingenious payload.
By the 3rd and 4th weeks you more or less know what you are doing. Routines became familiar. At that moment, Tony will use another technique to cement your newfound healthy habits.
After week 4, you switch to the (much needed) recovery phase, which means: new DVDs! Great, you just unlocked the prize. Now you have new toys to watch and master. By design, the recovery phase contains lighter exercises, and you feel like an overachieving superman blasting through workouts. Excellent, you just unlocked another prize. By the end of the recovery phase, you have to start a new rotation, which again means more DVDs! Fantastic, you just unlocked your 3rd achievement. The virtuous circle begins again: curiosity, exploration, improvements and, finally, mastery.
Many factors are now working in parallel to reinforce your new habits. Your body has begun to change for the better; you feel more energetic than you’ve ever been in your life. What used to be fat increasingly starts to become muscle. Since you already spent weeks figuring out how to include workouts in every day of your life, now your schedule is semiadjusted for that activity; you know what tradeoffs you need to make to keep doing your daily fitness routine.
At each workout, Tony drives home the need to write down your reps and weights. What initially looks like columns of confusing numbers after a few weeks become an eyeopening testimony of how far you can progress in so little time. 3 pullups become 10, then 20, and then you start thinking about 3040 as the new normal. And that is when Tony resets the board again with hard new routines, like onehand pushups in yet another DVD. Looking at the scorecard becomes a big point of pride and a powerful motivator: can I beat last week’s numbers today? How about an extra challenge, can I beat them by 34 rather than just one?
What a social design expert will instantly recognize is that many years before social gaming, P90X had all the elements of an addictive health game, with its own scoreboard, achievements and unlocks leading to new game content. These well known behavioral hooks are working hand in hand to cement the new reality of your life: you are working out every day doing intensive training and really enjoying it.
Good products rarely fit neatly into easy top down or bottom up model. It’s always a lattice of overlapping and interconnected factors, all supporting each other. So far we have reviewed social design techniques used in P90X. What is impossible to reduce to a design component is Tony Horton himself, a critical and perhaps even the dominant factor in P90X’s success.
His onscreen persona is superb. He is your buddy; he is here to help your exercise and find the routine that works for you. Somehow he always guesses exactly the right moment you are ready to give up, your muscles are burning, and tells you from the screen the thing you need to hear: “hey, don’t be a hero, take a midset break and then finish it”, “do it like this, that will make it easier on yourself”. The level of joyous hilarity he brings into the workout is impossible to overstate.
His whole team is clearly is having a blast recording the workout. Tony is like a busy conductor orchestrating things: his own moves, his teammates, the forms they are showing, the invisible viewer presumed (correctly) to be in some stage of his muscleinduced agony. Tony manages to pull it all off effortlessly without a hint of the show being staged or scripted. The truth becomes obvious as you watch: there’s no staging – it’s just a great group workout with your new buddies.
Tony manages to pull off one of the hardest tricks: he is not pushing you to watch the health fitness program. Instead, he makes you an avid viewer of a funny new TV series “The Tony Horton Show” that airs every day at the time of your choosing. You just have to watch the next episode. The level of personal charm and attraction it generates is impossible to overstate. If smart social techniques & great workout content are the hard steel framework of the P90X building, Tony Horton’s personality is what makes it so warm and welcoming inside.
Given P90X’s brilliant application of the best modern social techniques, it is easy to forget how old the product actually is. It’s been over a decade since its inception in 2002. Its age is almost unnoticeable today, aside from the few rare moments when the helpful voice reminds you to insert an “Internet Support Disk” bringing back memories of a forgotten era.
P90X remains widely popular. The sequel, P90X2, was launched in 2011. A few weeks ago the brand new P90X3 became available. I haven’t played with it yet; however, I’m sure Tony gives another amazing performance in these new sets.
Yet all current P90X versions share one common weakness – the dependence on most common denominator technology of the past decade: the DVD disc. What would be possible for P90X if we redesign it from the ground up to leverage all the power of modern web, social and mobile platforms? There are innumerable ways how P90X can benefit from all these technological advances.
DVDs have been on the way out for a long while. With all videos already moving to the cloud storage in a few years we probably won’t even have devices to accept physical media. In fact, the first thing I did with my P90X disks was to run them trough HandBrake to easily stream the videos to various networked Apple TVs around the house. Today such a house wiring might be typical only for Silicon Valley geeks, but in a few years it will be prevalent for all households.
P90X will migrate to cloud hosting and stream content directly to any device owned by the subscriber. P90X will cease to be a physical product; it will become a destination portal that will merge all aspects of the program: delivering workouts, tracking progress, and sharing your achievements with a likeminded community. Every morning you will be able to login into your P90X dashboard that will know what day of the rotation you are on, what track sheet you need to use today, what videos are sequenced for today’s session.
One of the startups experimenting in that direction is FitStar: it requires only an iPad as the single piece of equipment for your home workouts.
P90X is pretty modular to begin with. “Abs Ripper X” is a plugin that is attached to the end of main workouts. Some segments include “bonus” parts if you feel particularly energetic or have extra time that day. The extra long “Yoga X” is effectively 3 yoga workouts combined into one.
After monolithic DVD disks are split into small online modules, each with very specific workout profile, we can create products with finegrained control of intensity and scheduling. As a simple solution, we can just give that control to the user via an online dashboard. An even more intriguing option would be to engineer a “fitness AI” that would understand user progress and then create a specific sequence of workouts for each day to get best results and maximize the variety.
The P90X habit forming is profound, yet physical media puts a hard limit on its diversity. No matter how many clever rotations, DVD switches and variations Tony packs in that DVD box, by the 3rd month of the program there is just not enough content left to keep the same sense of curiosity you had in the beginning. Streaming P90X via modular segments can nicely solve that problem.
What we all want later in the program is additional variety. We want more Tony, more “pterodactyl sounds” and more content. The same workouts recorded in different sessions with different groups would be a welcome change after the first segment’s routine sets in. Add to that a number of bonus segments to be unlocked based on your progress and seasonal specials (think Halloween or Xmas themed workouts), and the program variety would explode in a combinatorial manner. Just a few hours of extra footage would create a very welcome prize for the champions many months into the program.
Speaking of which, lets talk more about the prizes.
Game design is not hard to master: there are only a few wellknown basic mechanics powering most online games. Every year, the gaming industry generates a huge amount of new content by packaging and repackaging these timetested constructs.
P90X already has all the required ingredients of a successful online game. It’s easy to start and hard to master. It has a clear roadmap from easy early achievements (chair pullup) to hard “end game” challenges (corncob). There is a scoreboard tracking your progress. In the social environment of an online community, your personal reps score can become a big motivator. Huge amounts of video content are dedicated to the key component of any game: feedback on how to improve and reach a higher score next time. After earning enough achievements you unlock more content to play with.
The only thing left to do is to tie in all these components into one digital product. Let people publish their personal P90X profile to share their achievements or to challenge each other in joint workout sessions. Offer bonus segments to unlock as users progress through the program. Give achievement badges for every small and significant milestone: first 10 pullups, first 5 onehand pushups, 4 weeks with not a single day of exercise missed, etc. There are endless possibilities to create engaged online community by opening the system to peer pressure, awarding achievements, unlocking prizes and hidden content.
Social motivation is a very powerful force yet it is largely absent from P90X today. For social motivation to work we must expose user workout activities to each other, which leads to explore “user generated content”, or UGC for short.
P90X has been motivating users to create their own content for years in the form of “before & after photos” that have proven to many how well P90X works (hat tip to Sandi MacPherson for reminding me)
The wellknown rule of UGC is that the majority of UGC is very bad and would not hold a candle to professionally produced content – like P90X itself. What usually makes it work is a dynamic system that constantly surfaces to the broader public the top 0.1% content that is entertaining to watch. That in turn requires a huge audience to create a sufficient mass of raw content so that crowd rankings can put the best material on the top.
P90X certainly has an audience and the numbers to make such an approach work. Enabling members to share webcam streams of their workouts to join fitness groups would ferment social ties and build new friendships. Ratings of user streams should help to surface the best UGC and can become an additional source of content to add variety to users’ daily routines. A usercreated library of workout videos can become a very powerful complementary source of content for P90X’s online portal. Real time streaming coupled with a dynamic organization of workout groups would be an engaging center of activity on top of P90X’s static segments.
One company that is taking the social motivation factor to the extreme is FitMob (disclaimer: I’m one of the advisors). The company is very young yet it’s already making big waves in San Francisco’s fitness scene. FitMob delivers unique workouts with top trainers in your local neighborhood: the city itself becomes your social gym when you join this fun fitness community.
Completing P90X is certainly a transformational experience. P90X’s brilliant design solves the biggest problem of how to permanently change people’s habits to live healthier lifestyles on a massive scale. Needless to say, if you haven’t found the fitness system that works for you go ahead and try P90X to see if it changes your habits for the better.
For product designers, it offers another powerful lesson: you do not need the greatest & latest technology platform to transform the lives of millions. All you need is a brilliant concept, lots of hard work to finetune the details, and a pack of old school DVDs.
Many thanks to Raj Kapoor, Kevin Gao, Sami Inkinen, Elliott Wolf, Sizhao Yang for reading the draft of this essay and valuable feedback. And of course very special thanks to Tony Horton for coming up with the whole shebang.
]]>Every year a few thousand startups are incubated in Silicon Valley. Few of them will succeed; the rest will decay or outright fail. Yet there always seems to be room for one more billiondollar company. Besides appearing seemingly out of nowhere, the most radically successful startups are also the most unpredictable ones. What force seems to create these massive sources of wealth that initially look like “bad ideas” to everybody beside their founders?
You may be tempted to say “Black Swan,” and you would be correct; however, beside simple acceptance of extraordinarily rare random events, there is deeper mathematical influence over a process that constantly spawns new opportunities. Understanding that influence will help any startup founder or investor to improve his business insights. To understand these concepts better we will make a long journey that will touch upon very foundations of logic and mathematics .
I usually find time to look at about two hundred startups every year. Referrals arrive from other investors, startup founders I mentor or via the massive firehose of demo days at YCombinator & 500 Startups. As you can imagine, this creates an overwhelming supply of startups and innovative ideas to look into. Every startup presents the ultimate question: Is it worth it to invest your time and money? Or is it a waste of both? There is never enough time to dig deep enough into any single startup to understand it fully. Making an investment is not an easy or obvious decision. Yet, over the years, I started to notice certain metapatterns common to all startups, the patterns that give a tantalizing premonitions on their chances of success or failure. The specifics of an industry or investment cycle might change, yet these patterns remain the same in every decade. I see them as two big groups of patterns: human patterns and mathematical patterns.
Human patterns emerge from our personal traits. Weather a startup will overcome its humanrelated challenge is determined by what a person or a team can succeed or fail at. The telltale sign is when the outcome will be determined by quality or quantity of personal efforts. What you typically read in Silicon Valley startup blogs would be all about such human patterns. It will be hundreds of topics covering which software language to use, how to pick founders, how to operate the company, how to build a product, how to build software, what is company culture etc. It’s all good content, yet it only addresses patterns driven by human traits, and thus is only half of the equation.
What you rarely hear about is “mathematical” patterns. These patterns emerge from objective nature of the reality where a startup must operate. The market dynamics, the ecosystem of industries they find themselves in, the governing trends of technological progress. As soon as a startup starts operating in the real world, the vast majority of factors will be outside of a startup direct control or even influence, while having absolutely dominating impact on that startup eventual outcome. Beside now legendary Black Swan^{1} making big waves since 2006, there is almost no information on the mathematical fundamentals of startup formation and investing. Usually all you get is a nonactionable statement like “90% of all startups fail” after which the author promptly moves back to human factors, which are much easier to understand and analyze.
To help develop our mathematical intuition we will turn to one of the most profound mathematical results, provided by the legendary Kurt Gödel: The First Incompleteness Theorem. To most it is a seemingly dry statement on the completeness and consistency of formal systems. On a deeper level, however, there is an interesting commonality between the mathematics of incompleteness and startup disruption. It’s critical to understanding the dynamics how startups get born, get big or fail, and finally how the few survivors become legacy companies. Showing this deep connection between mathematics of incompleteness of formal systems and startups will be the purpose of this essay.
“[My] own work no longer means much, I came to the Institute merely…to have the privilege of walking home with Gödel.”
Albert Einstein
It is surprising that Gödel’s famous theorem is all but unknown in the startup world. Thinking of all the mathematical knowledge that has direct impact on computer science, software and startups I would be hard pressed to come up with anything more powerful than Gödel’s Incompleteness Theorem.
Y Combinator is famously named after Y Combinator, one of the bestknown fixedpoint combinators used to construct certain recursive functions. Yet who was the first to define and use a recursive functions? Gödel. Further, the proof that fixed points exist at all is a side effect implicit of his work. Y Combinator is direct descendant^{2} of Gödel’s proof.
Consider another cornerstone of computer science, such as Alan Turing’s Halting Problem. He created that theorem when working at Princeton, right at the time when discussions about Gödel recent results dominated the institute mathematical debates. Turing’s proof is a continuation of Gödel’s work^{3}. Kleene, Turing and Shannon were all standing on the shoulders of the giant – gnome sized Gödel – when they were following his groundbreaking proof and inventing modern computer science. We will review Halting Problem in more details later in this essay.
When you truly grasp the implications of what Gödel actually proved, it will be like opening a Pandora’s box of wonderful insights. The implications of the theorem go far beyond just logic and math. Answers to the most sought after questions such as: Why can everything be made better? Why are so many startups possible and will always be possible? Why things we build tend to get more complex over time? Why does civilization always has room to improve?
To answers these questions, and see how all these things are connected mathematically you need to understand Gödel incompleteness.
Naturally, there is a reason why Gödel theorem is still relatively unknown outside of mathematical circles. There are few big problems. First of all, Gödel’s proof is hard. Not “learn new computer language” hard, not “make an iPhone game” hard, really, really, really hard. Gödel did not make the task of understanding his theorems easy. Being famously introverted, he preferred the logic of his proofs to do all his speaking for him. Even mathematical education is not much help here. For example, Gödel offers the following preview, a “sketch proof”, what he called an “an intuition” for the real proof to follow.
We will define a class K of natural numbers as follows: K = { n ∈ IN  ¬ provable(R_{n}(n)) } (where provable(x) means x is a provable formula). K is the set of numbers n where the formula R_{n}(n) that you get when you insert n into its own formula R_{n} is improvable. Since all the concepts used for this definition are themselves definable in PM, so is the compound concept K, i.e. there is a classsign S such that the formula S(n) states that n∈K. As a classsign, S is identical with a specific R_{q}, i.e. we have S ⇔ R_{q} for a specific natural number q. We will now prove that the theorem R_{q}(q) is undecidable within PM. We can understand this by simply plugging in the definitions: R_{q}(q) ⇔ S(q) ⇔q ∈ K⇔ ¬(R_{q}(q)), in other words, R_{q}(q) states “I am improvable.“
Unless you are an active mathematician, reading and intuitively understanding his proof would be next to impossible. Just in case here is the proof again in case you enjoy sharpening your mathematical teeth against this amazing whetstone of logic^{4}.
The second, even bigger problem is that understanding the proof will not help you much. Gödel’s logic is so alien, so strange that even understanding the formal deductions won’t help you understand all the implications of that phenomenon. Gödel’s proof is like a map with “X marks the spot”, yet on that map every border connecting it with our reality is torn away. You have no idea what particular area that map refers to. X is there, treasure is certainly there, but how the heck do you practically use it? In ironic selfreferential selfvalidation Gödel’s formal proof cannot be understood formally. It requires an intuition leap that will unlock its secrets. And after you make that leap your perspective on everything related to startups and innovations will change. That is the insight we will try to develop^{5}.
Gödel’s theorem is rapidly becoming accepted as being the fundamental contribution to the foundation of mathematics – probably the most fundamental ever to be found.
What exactly has Gödel proving? In modern language, simplified statement will be the following:
Any … formal system capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, … formal system that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in theory
Let’s work our way through that, since most of the concepts here are actually fairly easy to understand.
Formal systems are simple things. They are just collections of axioms and rules on how to manipulate them. For example, lets make a few axioms about numbers:
If we continue writing down such “self evident” axioms, we can arrive at certain set of axioms, called Peano axioms. These axioms and few rules of manipulations would constitute the simple arithmetic you learned in kindergarten if not earlier.
Axioms and rules about how axioms can be manipulated to produce derived statements is what constitute a formal system. Systems can be very different from each other. You can have just few rules about the numbers and stop at that – then you just get basic arithmetic. Or you can keep adding rules and axioms as long as they don’t make the system inconsistent. Gödel’s proof will apply to all systems that are complicated enough to include that kindergartenlevel arithmetic. Most systems you encounter in real world and in your work will be much more complicated than arithmetic and thus fall under domain of Gödel’s proof.
Formal systems can be consistent or inconsistent. Inconsistent systems are practically useless, since in such a system anything can be proven about anything. In real world most of the formal systems you are dealing with are consistent or at least strive to be consistent. The consistency is important, since it means the system cannot at the same time prove mutually exclusive statements and therefore form contradictions. For example if my formal system deals with weather forecasting, it will be a sign of inconsistent system if it proves both “its going to rain tomorrow” and “its not going to rain tomorrow” at the same time^{6}. Formal system can be constructed that give such contradictory predictions, but obviously its not going to be useful at all to us to actually predict is it going to rain tomorrow or not. If we construct a system that is consistent, then proving “it’s going to rain tomorrow” will also prove that “its NOT going to NOT rain tomorrow” – all deductions of such system will be consistent with each other^{7}.
For example, how you make decisions about paid marketing campaigns in your startup? Well, you probably have few axioms (usually written on stone tablets by your CFO) and some rules how to interpret data from previous campaign: how to AB test, how to make deductions based on that data, what to do next. The whole civilization we live in is full of systems that strive (with various degree of success) to be formal and consistent. Investment funds use complex financial trading systems, governments issue complicated regulations, the list of mankind attempts to formalize the universe around them is nearly endless: consider even the Bible with its famous ten axioms. Everything around you is collection of deductive rules and “self evident” axioms that remain largely unquestioned.
The premise of every formal system is that by using initial axioms of the system and using its deduction rules you will arrive to new true statements. You can then take these results, use rules and axioms on them again to arrive to yet more deductions. Your goal obviously will be to make a list of all true statements that can be deduced in the given system. If you want to create a formal system that is a new business model you incorporate axioms of arithmetic to describe how money works. Expanding your business model further, you will start deriving additional true statements like “User acquisition campaign will have positive arbitrage if lifetime value of average user is higher than average user acquisition cost”.
Finally, we would certainly want our system complete. That means for every statement in the system you can either prove it or disprove it, and then keep the list of all true statements. Thus you would learn everything that there is possible to learn from given system. If your business plan includes an axiom “All actions should increase lifetime profit” you can then try to derive all true statementsabout how to make more money. Obviously we would want to get a complete system: if there are some ways to make money, we certainly would want to derive them from our axioms and know about them!
Yet look again at what Gödel has proven:
“Any formal system capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent formal system, there is an statement that is true, but not provable in the theory”
That means that no matter how hard we try to derive all the results of a given theory, there will always be MORE true statements, more results that we can’t reach within our formal system. These statements, called Gödel statements or Gstatements, will be out there, totally true and correct, floating in the abstract, yet totally improvable by deductions of our given formal theory.
Real world is far too messy and chaotic to resemble nice, clean logic of pure mathematical formal system. Yet we always have that optimistic hope that if we just work hard enough, if we are just diligent to account for all the details, if we do what it takes: get right education, find the right partners, use great methodology; and after all that great effort we can deterministically find next big breakthrough. We hope there is that one system we could use to mechanize our success in business or in life. Gödel demonstrated this to be completely false hope. No system will be ideal: even under best imaginable circumstances, when your industry can be reduced to pure mathematical formal system (which in reality is almost never possible), you still will be denied its full knowledge.The full implications of that result are staggering when you realize their full extent. Let me give you one quick example.
Imagine an Ultimate Monopolist, who wants to find all possible ways to extract money and value from the global marketplace and keep them inside his business empire. He is Bill Gates on steroids. What would be his “formal system” of economics & business? Whatever he wishes. Library of Congress? Done. Every single issue of the “Economist” since 2000 BC, clay tablet edition? Delivered to his office in giftwrap. He can have formal systems as long and as expressive as he wants, and he is careful to avoid adding axioms that lead to contradictions. We will also throw in a full Googleplex or Gogolplex (your choice!) of computers to parse and analyze all that data, that will give him the list of all possible true statements derived from that system^{8}: all the ways how to make money, create new profitable startups, all the ways to generate value. Furthermore he has money and manpower to immediately staff these startups and make them operational businesses. It’s a pretty cool gig to be an Ultimate Monopolist.
In other words our Ultimate Monopolist will stop at nothing to grab any promising business idea for himself, and throw his almost unlimited resources at the opportunity. That description is not far from reality when you think about modern Apple, Google, Facebook & Amazon. These companies had built amazing semiformal^{9} systems over the years and decades. Their systems are optimized for one thing – how to extract maximum value from marketplace of technology innovation. Their systems are immense – computer source code, marketing guidelines, “playbooks”, hiring guides and countless other printed and digital documents. That is the system their collective employees use in their daily work that’s how they train new ones. And on top of that, they have the tens of billions dollars in the bank necessary to bring about any conclusion of their semiformal systems.
Yet despite all that might of formalized knowledge, again and again innovative startups appear out of nowhere. They constantly catch incumbents blindsided and make them pay billions to acquire the new discoveries. Be that Google or Facebook, anyone would love to jump on such ideas first and capture all the upside of new innovation for themselves, instead of paying billions to acquire a disruptive startup. So why can’t they? What is stopping trilliondollar capitalization might of our technology cabal is the same: Gödel.
Gödel had proven that any kind of “Ultimate Monopolist” is still going to lose. There are true statements in his system – in other words there are new ideas and startup business models – that never can be proven in his formal system. No matter how many libraries of knowledge he will keep adding, how many more resources or computers he is going to add to his formal system of discovery, he still will never ever discovery every true statement (i.e. every profitable model) of his formal system of business. Ultimate Monopolist will always loose in the end because he cannot cover every statement, he cannot make his moneymaking empire complete.
We are getting closer to answering the big questions posed at the beginning of this essay. We are almost ready to apply mathematical insights to our familiar world of startups, business models and innovation. However it would be a grave disservice to the amazing elegance of Gödel’s proof to omit the mathematical details. For those of you who would like to see the glimpse of the math involved I created the [special section] that includes a lightweight walkthrough. In that section we will also cover to basics of Turing Halting Problem and Cantor Diagonal Proof, which will be very important for us later. Feel free to read Gödel, Turing and Cantor: The Math first or just continue with our main narrative.
In mathematical section we just reviewed the technical details of the Gödel Incompleteness Theorem, the famous Cantor Diagonal proof and the Turing Halting Problem. Lets quickly recap what we learned for our readers who join us without reading up the mathematical details.
Cantor proof deals with nature of infinity. It shows that even between any two small real numbers, for example 1.1 and 1.2 there is an infinity so dense that even infinity of all natural numbers (which are numbers like 1, 2, 3, etc.) won’t be enough to count them all. The infinity of real numbers, so called infinity of continuum is more “powerful” then an infinity of all countable natural numbers.
Gödel told us that no matter how long and complicated the formal systems we construct, there always will be true yet improvable statements. If we keep expanding our formal systems and make them bigger, that will only create more of such “true yet unprovable” Gödel statements.
Turing told us that you couldn’t capture infinite complexity with finite software code. Software itself cannot be bound or predicted by other software. With very simple software you can create very complex behavior, and the only way to see the result of such complex behavior is to let such software run, which might require an infinite amount of time.
There is clearly something hiding behind all these proofs. Something so powerful that it keeps breaking the chains we are trying to put on it. Something out there is saying: You want to pick a few rules that will cover me in the net of deductions to know all about me? You can’t. You want to write software that will do all the hard work for you? You will never know if your software will ever finish working. And yet, what lies behind all these proofs is the true nature of continuum infinity. Infinity will always be far too rich, far too dense, far too big to be chained by anything countable – formal systems, software, and finite proofs. Better systems, better software can grab bigger chunks from infinity. Yet by expanding themselves they are no closer to fully capturing the potential variety hidden in continuum infinity. They just moved the boundary between “knowledge” and “unkown” further out.
Lets try to understand what that means visually. Every system we use roughly will have three distinct areas. There will be an area of proven true statements, the “knowledge” of such system. This is what we can deduct in a given system, we can write it down and actually prove its true.
Then we will have an area full of true yet unprovable Gstatements that belongs to that system. That is something that we can still express and write down in systems syntax, but we cannot prove. It may have a very clear pattern of actually being true like Goldbach’s conjecture yet we still are unable to write a hard proof.
And finally there is endless infinity of totally unknown space, that cannot be even expressed in a given system until more axioms are introduced.
That’s ok for first approximation, yet it misses a few important points. First of all – lets remember Cantor’s proof. Even between real numbers like 1.1 and 1.2 there is an uncountable infinity of other numbers. Similar to that imagine that between any two points of our “knowledge space” or “ideaspace” there might be infinity of new proofs and true deductions.
The system doesn’t represent one solid whole with sharp boundaries between known and unknown. It is more like a head of cheese riddled with holes, holes within the holes, etc. It is a much more complicated structure then what we can draw on paper. Formal system create certain grids over what we are trying to learn. Between the cells of that grid whole infinities might lie undiscovered. Each circle in our illustration should be riddled with infinity of small and large holes.
Finally, the biggest misrepresentation created by such picture is a sense of scale. The following would still massively overstate the coverage of our formal system against an infinity of unknown:
Just like the following will overstate it again:
Remember, this dot in the center will represent all the knowledge, all of the proofs of any given formal system. You can consider the biggest formal system of all – the totality of all recorded writings of human civilization since its inception. All that still will be just an infinitesimal dot comparing to the continuum infinity.
The history of human civilization is a process of creation of formal systems serving a specific purpose^{10}. From the earliest legal codes to modern data centers with terabytes of information we are trying to bring order and predictability to the chaos of infinite continuum. Creating formal systems is finding the balance between the “good enough” simplifications of infinite variety while preserving enough complexity of a given domain. The only way to go around our daily lives is to massively simplifying the world around us. The rules, conventions, labels, best known practices, mental models and myriad other ways humanity has developed over the years solve the single purpose – chain the infinite complexity in some manageable, finite form we can deal with. Do something to create a practical shortcuts so that our simple brains can deal with that finite, countable and limited model of reality rather then infinitely dense reality itself.
What Gödel, Cantor and Turing have proven so decisively is that no system will be ideal. All systems will be rough approximations that will never capture full variety of infinite possibilities of the continuum^{11}. There will always be gaps in our nets, imperfect labels, misinformation and missed knowledge just because we rely on the crutches of formal systems. The infinite reality of continuum doesn’t care where we draw our lines of given formalization. The very act of drawing lines will make certain knowledge hidden from us, the gist of Gödel’s proof.
The most brilliant minds already know pretty well about deficiency of any given formal system. The legendary Charlie Munger stresses the discipline of developing multiple overlapping mental models when developing his own formal system for investment. He understands no single system no matter how complex will give him the full truth^{16}. But at least using multiple independent systems he can check if this or that idea is worth trying out. What is ambiguous within one mental model might be easily provable using deduction in another, and can be empirically verifiable in a third one. There is the risk of relying on formal system composed from other formal systems, yet Charlie greatly increases his predictive powers by knowing the limitations of each^{12}. That might explain why he is one of the richest people on the world.
Despite their limitations, we cannot get away from formal systems. Our brains can hold only simple, short & easily countable sets of axiom and rules, that’s how we operate. Yet the first step to avoid the worst mistakes is to be fully aware of natural limitations of formal systemss – that they are never full or nor complete model of reality they are trying to represent.
Now that we have better insight in interplay between formal systems we must use, and the infinite reality hidden behind them, we turn our attention to world of startups, innovations and the way our civilization propels itself forward.
Every startup is formed with a dream to become a bigger company. As Steve Blank aptly put “A startup is an temporary organization formed to search for a repeatable and scalable business model”. And what happens after such scalable business model is found? What, fundamentally, is a company?
A company is a semiformal system to extract money from the marketplace. Startups may skip the revenuemaking part for a few years, but sooner or later what’s going to differentiate winners from losers is the ability to drive sustainable revenue from a business model they discover. To put things in perspective, here is one well known (at least among startups) example of the simplest formal business system.
As you can see, the system of South Park Gnomes consists of three rules. “Collect underpants” clearly implies a countable set of objects, meaning the system is compatible with Peano Axioms. That makes Gnomes business plan complex enough to “expressing elementary arithmetic” and it will be subject of Gödel theorem.
Next part of their system is “?”. That most likely is a free variable, the one that would accept a another system as its input. Gnomes is shrewdly using a metasystem so that they can change the specifics of business model depending on changing market conditions.
Finally, an axiom “Profits” which means the consistency of the system will be preserved if and only if all previous steps generate profit. A strong move obviously driven by Gnomes racial heritage.
If we remove Gnome specific “underpants” rules, the formal system of “? => Profits” would correctly describe pretty much every corporation in the planet. However corporations would need something more actionable then that.
Lets review that on few practical examples. To get things started lets look at Microsoft in the late 1990’s.
By end of the millennium Microsoft was almost a monopoly over the technology field with unmatched power and influence. The rules and combined knowledge of that business empire would probably fill thousands and thousands pages. How you sell software to OEM partners? How you control pricing? How do you leverage strength in Office suite of products to keep competing operating systems out of the marketplace? How you leverage ubiquity of Windows installations to get favorable pricing from OEM partners? Myriad details, big and small.
The complexity of such formal system would be mindboggling. At same time that system did require formalization. You need employee guidelines in every division. You need a system to train new employees. You need a system to pass knowledge when one executive replaces another. Over the years of transitions and employee rotations the intangibles will be lost, only formalized knowledge will be preserved. With tens of thousands of rules, Microsoft was in a unique position to extract amazing margins from its dominant positions in operating systems and office software.
Let’s imagine, for a second, a time traveler from the future appears in front of Bill Gates in 1999 and utters something like:
“I’m from the future! You should sell keywords to match search queries!”
What would Bill do with such a traveler? The syntax of his request is familiar – he knows what web search is and what keywords are. But everything else makes no sense whatsoever. There are few web search companies out there, AltaVista, Lycos. Their whole capitalization was less than Microsoft’s soda budget. They are troubled companies, far from being in great shape financially. Why on earth sell keywords for search?!
Bill can consult his experts, and dig into these thousands of documents on Microsoft servers representing their semiformal system of value extraction. But there is very little there about search or keywords. The statement about selling keywords might be true yet having everything Bill has at his disposal, it’s utterly unprovable.
As an important side note, lets consider if time travelers move deeper into the past, to pitch Henry Ford or Nikola Tesla. However in this case the whole syntax of his proposition makes no sense. Computers do not exist, web and internet does not exist, everything he is saying is meaningless on a syntactical level. His statements belong to total unknowns for inventors of past centuries. Yet for Bill Gates, it represents a true yet unprovable statement.
Even if Microsoft knew in advance about keyword search, their formal system lacked any predictive powers to really evaluate that opportunity. Their systems were about software, OEM sales, computers and hardware. Google’s model just couldn’t be analyzed with it and therefore acted upon even with advance knowledge.
Thus it falls to Larry Page and Sergey Brin to formalize the system about web search and selling the keywords. The founders start with almost pure imagination, almost a dream: to “organize the world’s information”. Since it turned turned out that such statement is very profitable one the cascading process of formalization of that domain rapidly followed. The new terms and axioms were added based on that purely empirical truth. The formal system of modern technological knowledge was expanded, and it generated its own new “true yet unprovable” massive opportunities. Nowadays when you call one of many Google satellite offices where hundreds of sales reps share with you thousands of tips and tricks how exactly to optimize search keyword campaigns for your small business you see directly the results of such formalization.
Time passes. Our time traveler appears in front of Larry & Sergey in 2003 and utters the words of prophecy:
“I’m from the future! You should organize social friends graph between all people!”
Larry consults his formal system – it has thousands of documents about search engines, optimizations, ranking connections, etc. He can easily access public Microsoft servers and read about the smaller formal system of nineties OEM sales, software, cutting oxygen supply to competitors. Unfortunately neither old systems nor newly expanded ones like the one Larry helped create has knowledge about building social graphs or maintaining friend connections. There are a few companies out there – Friendster and Myspace, their whole capitalization is less then Google’s sushi budget. Larry is perplexed – he understands the syntax of suggestion, but he totally lacks the tools to prove or disprove its profitability.
It falls to Mark Zuckerberg to formalize the system about building social graphs and optimal ways to extract value from it.
We can continue same narrative forever. Time traveler will appear to Mark, and give advice on say mobile photosharing. The formal system will be totally inadequate to prove the potential of the new idea. Only after somebody practically and decisively proves its potential by actually doing it, the previous unprovable model becomes part of the current business model.
Successful huge startups are rare, unprovable, unique and disruptive. To be successful they must first discover new “true yet unprovable” idea in a system of a given industry or marketplace. This is very hard because these “Gödel statements” they need to find are so rare. After they find it, they must build a new, expanded formal system to extract all value from the domain they discovered.
Failed startups fail for myriad of different reasons, since the precious “true yet unprovable” statements are hidden amidst the infinite sea of false statements. They might build the model around unprovable yet false statement. That means even after years of efforts, there could be no profitable enterprise at the other end of the rainbow. Or they discover a Gödel statement with very small potential, which will be minimally working, but not well enough to feed and grow a VCfunded startup. And even if they succeed with all of the above, the formalization of new domain no one understood previously is no small achievement. Many startups may stumble on such a domain first (say Friendster) yet fail to build efficient formalization around it, thus letting others capture most value the new domain offers.
At each step of startup lifecycle there is different interplay between unpredictable complexity of the world and formalization effort to rein in and manage that complexity.
Inception: A tiny team of founders embark to test an idea. Rationally, it is impossible to prove such idea has big business potential. Yet we are human, and we are not perfectly rational. We are not robots that can only follow 100% logical deductions of existing formal systems. What will drive these founders might be an irrational intuition passion about a specific domain, or just the desire to build things just because they like to build things. Existing formal systems with all their benefits and all their limitations are thrown overboard, and founders are largely free to do whatever they wish in totally unchartered waters.
Discovery: The product or service the team builds is released to the real world. Real world complexity is continuum infinity, it’s not bound by any formal systems. What market “wisdom”, startup mentors, university professors, and plain old “common sense” knows is irrelevant – that’s formalization of reality, not the reality itself.
Usually the first product has next to zero probability to find the right spot for a new Gödel statement. Founders will be extraordinarily lucky even to land close enough to such statement on their intuition alone. Hitting exactly the right idea and right execution with all its myriads of tiny details is impossible. Continuum infinity of the real world demands an infinity of small details that needs to be adjusted to find exactly the right implementation.
Startups can’t adjust infinite number of details at once. The only way they can proceed further is to maximize their discovery process if they work traditional “startup hours” to create maximum number of iterations possible in incredibly short timeframes. That process of frantic search generates the empirically observed startup curve. The iterations create the initial wiggles on the graph. If the startup zeroes in on the right point in ideaspace of new Gödel statement they will move on to the growth phase. Otherwise they will die off as another failed startup in “false statements” area. The culture of fast iterations and pivots are natural consequence of free form search each startup runs in ideaspace.
Unfortunately there are absolutely no solid predictions we can do about this stage. At the end of the day the startup just has to be lucky enough to start close enough and navigate optimally enough to hit its first discovery before company disintegrates from lack of funding or team morale. The process can be as fast as few months or as long as a decade.
Human patterns are playing huge role too at this stage. The “startup hours” and total lack of personal life is not easy on anyone involved. Startup is racing against complexity of continuum infinity while leveraging whatever formal system they have at their disposal. Increasing number of experiments, increasing speed of “experiment, feedback, next experiment” cycle greatly increases their probability of tuning all the dials to exactly the right value. It takes human leadership, human craftsmanship, team spirit to survive the rigors of this long process and to keep everyone motivated: that may sound trivial in the first month, but is an entirely different story by the 10^{th} month. Startups that can manage both sets of patterns: motivated, highly productive top quality team churning out experiments month after month while doing rigorous search process in ideaspace without succumbing to infighting, demoralization, degradation of quality – would be the big winners of that phase. Everybody else would churn out and die as a failed startup.
Proof: Finally, if the biz model founders choose or pivoted into after many experiments represents a true statement of value^{17} extraction, they will immediately see explosive results that their model is working – very often much to founders surprise at the scale of their own success.
Formalization: Now the startup’s challenge is to transition from early product, often held together by duct tape to professional system of extracting value from marketplace. We usually call that stage “explosive growth”. Startup goes into overdrive trying to both operate what they built and formalize the space it finds itself in. Be that Google ranking algorithms or pinboards^{18} at Pinterest, in every case the teams are working around the clock to understand better their new found domain, put software, processes, and training around all new discoveries, and explore new opportunities these effort brings. That is the most stressful yet incredibly exciting period for any startup.
Today creating software is one of the most powerful and scalable ways to formalize newly discovered domain. Software is eating the world is an unstoppable phenomena because the human world is nothing more then a huge collection of formal systems. Software is the best tool so far to create most efficient and powerful formal systems for any purpose.
The process of formalization can take decades. As long as a startup has growth, especially nonlinear growth driven by new products, the formalization is never finished. Yet sooner or later the process of formalization of any big discovery must end. Facebook will add the last unsigned user and will be permanently bound by birth rate. Everybody will own some version of the iPhone. Amazon’s catalog will carry every single item manufactured on the planet. The new expanded system that includes newly discovered true model might be big, yet it’s still a formal system, it’s still finite.
Sequential Gs: The greatest companies you hear about in the press are rarely singleG discovery products. To create truly massive company from a startup requires finding multiple independent Gödelstatements of increasing size. Perfect example of such would be Apple after Jobs return. Finding the company near bankruptcy, Jobs first bet was on relatively modest project of iMacs – a computer with focus on personal convenience and simplicity of use. That unquestionably was an idea from the domain of totally “unknown and unprovable” in the world dominated by the likes of Microsoft and Dell^{19}. The success of iMacs created resources to find another unproven and unprecedented Gstatement about music devices: the iPod. The success of iPods allowed for revolutionizing mobile phone business; and finally there was the breakthrough of formalizing whole new “unkown” domain of tablet computing.
This story is inspiring yet incredibly rare. Most startups would be lucky just to find one or two disruptive Gödelstatements to build their new business model around. Besides being lucky enough to find such sequential new models, the size of each new discovery must be much bigger to the previous one.
In the world of gaming, Zynga was a good example of relentless discovery of new disruptive properties. Starting few years ago from an online poker game, every year Zynga reached for new heights. Thanks to identifying and optimizing key new genre every year – such as Mafia Wars, Farmvile, and Citiville properties – it grew at unprecedented rate for the gaming industry. Every new genre it has discovered^{20} led to bigger and bigger domains of value to be exploited every year. Yet, since by the nature of the gaming business the staying power of these disruptions is much more limited then say Apple inventions, the demand for new discoveries is much higher. Now after suffering a catastrophic stock crash, Zynga is poised at yet another Gödeltest of its existence. Either they will find their next disruptive and unpredictable business model^{21} that will dwarf everything they have previously built, or their discovery will only yield a succession of false positives, and the slow transition into legacy company will settle in.
Legacy: If company stops innovating and loses capacity to proactively search for new Gödel statements first the nonlinear explosive growth of formalizing new ideaspace will slow down. Years later it will start bumping into objective limits of that new area that the startup discovered.
The process of formalization is complete. It brings its own unique benefits – new employees can be easily trained. The model can be transplanted to other countries with relatively little effort – unless cultures are radically different the formalization developed in birth country will be good enough as starting point in the rest of the world. The business becomes predictable and from the view of startup founders fairly boring.
At that stage startups resemble little of their wild beginnings. Making risky bets in early days would always pay off – it was rich undiscovered space ripe with possibility. The job of employees now is to simply execute the formal system developed during preceding years. Lack of risktaking is not just driven by “big company bureaucracy” or lazy “95” corporate employees mindset. It’s driven because most of the potential and opportunities that were hidden undiscovered around original proof point, original Gödel statement that gave birth to the company are now tapped out^{22}. The new expanded formal system is now well formalized and has little surprises left. New explosive discoveries can be made only by venturing far into unknown yet again. The big company can either try to facilitate that behavior (isolated labs, venture arms) or simply buy innovations via startup acquisitions.
The Company now becomes a permanent part of tech landscape. Its role is to continue operating the value extracting system and perhaps optimize a few things here and there to increase performance year after year. Apple was founded to upset IBM. Microsoft had stolen the personal computing torch from Apple. Google was formed to avoid the domain where Microsoft ruled supreme. Facebook leapfrogged Google’s dominance. And after all that cascading warfare you would expect just scorched earth and pile of bodies, yet what happens is exactly the opposite.IBM is still around, doing “ok”, and mindblowingly is still selling mainframes! Microsoft still sells Windows and Office while tearing their hair out trying to find ways to be relevant. Tech companies rarely die unless extremely badly mismanaged, they just move deeper and deeper into legacy part of the stack, as new formal systems keep being added to the outer shell.
Now we have reviewed the major life cycles of startup, let’s run down key attributes of Gödel’s model and see what deductions we can come up with for the startup domain.
Self evident from the nature of the startup space of ideas. The space of false statements is much larger than few points of undiscovered true statements. Every startup must go out there to total wilderness of not just unproven ideas, but ideas that cannot be proven in advance, and experiment based on blind faith to find such “true yet unprovable” ideas. Naturally most of such wild guesses would be wrong. In fact the 90% ratio was probably driven mostly by what used to be expensive and slow process of creating startups in the past. Right now the cost of starting a startup has collapsed to almost zero. Nowadays there are hundreds times more startups being incubated, while the relative density of Gödelstatements in the space have stayed the same. The failure ratio might become even more extreme like 99% or 99.9%. The fact that there are more startups doing experiments doesn’t change the extreme rarity of Gödel statements in the space of undiscovered business models.
Closely correlated to the previous observation. Most of wild guesses about new Gödelstatement will be wrong. Very few will be extremely good. Paul Graham empirically classified these as “good ideas that look like bad ideas initially”. From Gödel’s model we can draw even more precise distinction. These ideas look “bad” because they are unprovable ideas in composite formal system “everything we know so far”. Bad ideas that are actually bad are usually provably bad even in current system. Discerning between the two is key skill for an investor and startup founder. If you start thinking about all the indicators of “provable bad” ideas, it will make it much easier to filter out the “unprovable” ones that you really ought to pay attention to.
When looking at new startups you should take special note when you hear something that is unanalytical, something that makes your mental gears skip turns since they suddenly lack axioms and rules to analyze the proposition. The usual reaction to that uncomfortable feeling is to think the idea is “bad”. Try instead what Gödel does in his proof. Can you prove that idea is bad? Can you prove the negation of the idea (antiidea so to speak) is good? Can you use any of Charlie Munger style overlapping mental models to prove either? If your mind keeps drawing a blank no matter what approach you use it’s a strong indication you might be dealing with an unprovable statement in a given system. It doesn’t make it true, and is likely not true. Yet it certainly deserves a second look, you shouldn’t dismiss it just because its “unprovable” – it just might be a new Gödel statement.
Self evident from the nature of a given startup Gödel statement. Disruption means a totally unexpected way to do business in the marketplace – that is just a restatement that new startup business model is unprovable in the previous formal system. Disruption happens from the “truth” of newly discovered business models and its vast size makes it impossible to ignore.
Paul Graham also defined “Startup = Growth”. That is natural consequence of formalization of newly discovered domain. Startup initial product is never complex enough or extensive enough to cover all potential hiddens in the domain around newly discovered Gödelstatements of its product or business model. The initial Gödel statement is that swing of pickaxe that sends the first gold nugget flying. All that potential is out there, surrounding initial point of contact, waiting to be formalized and therefore exploited. Growth means totally disproportional rewards for founder’s efforts. That disproportion happens because founders are mostly unlocking the value in domain they had found rather then directly creating value themselves. The formalization stage is a proactive exploration and mining of the new domain that the first strike located. The “gold” produced (might be revenue, might be users, might be investors) immediately goes back to powering even more effort to find the full extent of the newfound domain, increasing the extraction rate in the chain reaction. That leads to exponential growth Paul mentions in his empirical observations.
Obviously a bad idea. If you and your direct competitor are in same formal system, whoever formalized that system first got all the advantages. The business model is extracting value from marketplace, and they formalized far more efficient systems for far longer than small startup can afford or create^{23}. The new Gödelstatement is the one and only weapon startups have. It must leave the domain of the known and formalized to find its new domain of opportunity.
Every few years we usually get a new popular strategy of incubating or running startups. Crossing the Chasm, Blue Ocean, The Four Steps to Epiphany and most recently Lean Startup. The books are good reads that will certainly help you. Yet it’s important to understand their intrinsic limitations. As we know new Gödel statements cannot be found by using any formal system. The strategies are valuable as long as they related to “human” patterns: “talk with your customers”. Yet all these systems become next to useless as soon as they delve into territory of mathematical reality of startup ideaspace. When doing exactly the opposite of recent “Lean Startup” strategy led to the creation of newest multibillion dollar company^{24}, is very telling example of the huge potential for misdirection these strategies contain. There were certainly some startups^{25} that benefited from following Lean Startup or some other strategy. Yet the fact that some startups benefited from following it, and some benefited from following the opposite the opposite shows that startup success is independent from any such “startup system”. Obviously the danger is exactly the same to consider this essay some sort of “Gödel strategy” for startup incubation. Avoid the temptation.
The best approach to avoid these fallacies is to keep limitations of formal systems in your mind. No strategy will tell you which idea is good or bad. There is no software that will tell you if your idea is next billion dollar opportunity (HALT) or a fluke (loop forever): you must deploy the idea in the world to see if it “HALTs”. You cannot fake any part of that proof by using a system you picked up from the book. Therefore you have the right to override with your intuition everything and anything these systems tell you. As soon as these popular books leave the domain of humanrelated matters you are totally on your own.
Most startups become so called “zombies”. They growth stops too early, and they have trouble realizing potential investors were hoping for. Yet they make some revenues, usually can keep few dozen people on staff, and continue doing what they are doing for many years. “Second Life” would be a good example of startup that seemed to have huge potential early on as new social platform yet ended up with relatively small user base and was driven to nearirrelevance by the rise of Facebook.
Zombie startups represent small Gödelstatements. They are the small dots in the 3area chart we used above. Gödel’s theorem only proves they exist – it doesn’t prove anything about their size or distribution. There will be Gödel statement for $100 opportunities just like there would be a few for $1B ones. Zombie startups unfortunately have stumbled upon such a statement that does generate revenue or users, yet the limit of that newly discovered domain is far too small. Instead of having decades to grow into that newfound space, startup hits the walls far too early and is now limited to much smaller revenue streams and overall potential.
The best advice to give to startups that find itself in such situation is to treat early product as source of free cashflow and find a way to aggressively experiment in surrounding areas to find new Gödel statement of much higher volume.
Why are some startups bought preproduct, pretraction? At that stage it’s purely domain of “human” patterns. The team background, simple charisma of team leader, the desire to invigorate a stale corporate workforce, or myriad other reasons may lead to a vote for or against such deal. From perspective of formal analysis there is no hard data yet to make any sort of conclusion.
That the type of deal most corporate development officers are looking for, especially if they can get the team at relatively low price comparing the the future value of the domain they are actively unlocking. Now everybody sees hard proof that new model is actually working, the only risk remaining is what is the ultimate size and potential of such domain? Instagram purchase by Facebook falls exactly into this category of deals. Where would Instagram growth stop if it was left to fare on its own: $10B, $100B? We will never know since now all the benefits of formalizing this new domain of picturedriven social experience will belong to Facebook.
Its often puzzling to the newcomers to the tech industry why some companies like Instagram can get a x1000 multiplier of their revenues in deal valuation, while another company with huge revenue stream will get x3x5 at best? The reason is company position on the timeline of unlocking all the potential from the new domain. As your startup starts to accumulate years of operational history, these years will serve as an indirect indicator of your startup future potential. Everybody will assume if you generated certain revenue after operating for say 5 years, it’s very unlikely you will generate ten times bigger revenue in year 6. Such statement would be incorrect for any pretraction and earlytraction startups. They are exactly in the ground zero of Gödeldisruption – for them everything is potentially possible. Yet that is no longer true for a startup who is past formalization stage of a new domain. As years pass corporate officers will assume whatever potential for disruption it had its now behind it, and a startup is bound by the gravity again. Their growth becomes more predictable, more linear, big surprises are becoming almost impossible. Since its future upside potential is now limited, it is reflected in valuation multiplier.
These are the first few observations we can make from applying Gödel Incompleteness model to the domain of startups. As you consider all phenomena you encounter in startup world our new formal system is there to help your mental modeling. As we know all too well now our list of deductions about startups will always be incomplete. Yet even if goal of completeness will be forever out of our reach, let’s try to make that list as comprehensive as we can. Ask all the questions you want to be reviewed from Gödel perspective in the comments, or add your own analytical observations! I will be updating this essay with your best contributions.
It’s impossible to write about Gödel Incompleteness without mentioning Black Swan book that achieved a cult following in Silicon Valley since its release in 2006. The book is incredibly deep and it will be a disservice to simplify all its ideas for the purpose of a blog post. Therefore we will address this part to the readers who already are very familiar with the book and we will direct others to experience it first hand.
In our terminology Black Swan events would be instantiation of Gödelstatements in any existing social or economical system. The original book deals mostly with negative Black Swans – undecidable statements inherent in the system that satisfies the attribute of system collapse. The positive Black Swans are mentioned exactly in the context of the startup world. In this essay we have concentrated on such positive Black Swan events that led to value creation provided by startups. Over time these positive Black Swans lead to the progress of civilization: ongoing process of formalization of larger and larger domain of continuum infinity.
The source of negative Black Swans that can topple financial systems, countries, and governments is exactly the same as the source of positive Black Swans that lead to growth, new opportunities and progress. The source is Gödel Incompleteness. Every formal system by virtue of existing will contain both the seeds of its own potential destruction and seeds of its own possibilities of expansion. Both of these will be unprovable and therefore unpredictable. There is a very deep connection between Black Swan events and Gödel statements.
Disruptive startups springing into existence out of nowhere might look like random positive Black Swans. Yet what makes their formation not only possible, yet outright inevitable, are fundamental dynamics similar to Gödel Incompleteness. Just like strict formal systems of pure math will always contain proof of their own incompleteness, so the very act of formalization of reality undertaken by big established corporations will always contain within itself the seeds of its future disruption: true yet currently unprovable statements of the successful startups of the future. Every startup will start in a totally unprovable, unpredictable new domain they can discover only empirically, by building and launching something with no assurances of success.
It’s inspiring to know at any moment in time there is an infinite number of true statements for new startups to discover and further expand our collective system. Gödel’s theorem is not really about our limits: it’s about possibilities always waiting to be discovered. The process is certainly hard and alien to us. Out there, outside the comforts of the “known” there will be no formal systems to help us as we grow so accustomed to throughout our lives. All systems of meaning, convenient assumptions and well known predictions will be rendered useless. New startup cannot be invented in the library of our past knowledge and existing systems. It will always require an intuitive leap of faith or passion to cross the chasm of unknown and unprovable. Yet, as we know, every year dozens of startups and their triumphant teams cross that chasm to start formalizing domains previously unreachable to human thought and ingenuity. The mathematical reality of these domains ensures that this process will never stop; the expansion of our formalized knowledge will never cease. The human intuition unbound by limitations of pure formality will always push forward, find new domains, and leverage the amazing powers of software formalization to bring the fruits of new knowledge to the rest of the civilization. Your intuition just like your powers of formal deduction is all you need to join in.
Big huge thanks to the amazing team of reviewers who helped so much to improve this essay. Author is indebted to Elliott Wolf, Jeremy Carr, Igor Shoifot, Kamal Ravikant and Tim Hanson for reviewing this text and contributing a number of valuable suggestions. Doug Lee as always provided a number of great design insights.
It’s impossible to overstate the effort of my dear editor Laura Ochoa, who was tirelessly reviewing draft after draft of these writings. One might be tempted to say there exists a formal system proving that fashion models cannot review mathematical treatises, only to be decidedly routed once more by the demigod of logic himself, who famously married to cabaret dancer Adele.
If the statement is false, then I am not a liar and tell the truth all the time. But I told you I was a liar. Either way you go, you get a contradiction.
Both this and the statement Goedel constructed (“I am not a theorem”) are selfreferential paradoxes, many of which have yielded alternative proofs of incompleteness.↵
A formal system is just a collection of axioms and rules. Just like we did before we can record axioms in plain English like “Number 0 exists”.
Can we associate axioms and rules with natural numbers? As you know everything you read on computer, is actually encoded into numbers. Inside the computer letter “N” is 78, letter “u” is 117, etc. What is word “Number” for us, is just 7811710998101114 for the computer – just one long number. Why is it that “N” is 78 and not 87, or 8787? No reason, its arbitrary arrangement, called encoding standard. That specific standard called ASCII which states that all computers who want to be ASCIIcompatible must assign “N” to 78 and vise versa.
But here is an interesting part, a key to Gödel’s proof: Our axiom “Number 0 exists” is first axiom in a system that defines existence of numbers and simple arithmetic. At same time we can encode “Number 0 exists” using ASCII encoding, or any other encoding we choose and get a number that represents that axiom (or a rule) about numbers themselves. You will get something like the following:
That number is awfully long, yet it’s still just a number. And then we do the same for rest of your initial axioms and rules. Then you can start encoding your first deductions about the formal system, deductions of deductions, etc. In the end any axiom or sequence of deductions will be just a long arithmetical number.
Something interesting happens here. On one hand we define a formal system that describes basic properties of natural numbers. On the other hand because of the encoding these very axioms and rules are also numbers themselves! We can go back and forth as we want. We can deal with axioms as plain English text. Or we can switch them into pure, even if very long, numbers, and deal with them as just a set of numbers. The system becomes selfreferential: axioms and rules describe what numbers are and at same time are just numbers themselves.
In reality English is very long and inefficient way to describe formal systems. Logicians developed much more compact syntax to describe such systems. Also, ASCII encoding is good for computers, but it lacks certain properties critical for Gödel’s proof. Gödel come up with his own totally unique encoding, which is called Gödelnumbering. Remarkably, he came up with such numbering decades before computers or anything like ASCII existed. That encoding uses prime numbers, which thanks to absolutely fundamental Prime Factorization Theorem gives such encoding important properties that are critical for next steps of the proof. That type of encoding ensures that each unique sequence of logical symbols – axioms, rules, and deductions – have one and only one unique Gödelnumber. And one can always move back and forth between Gödelnumbers and original sequences of symbols that originated them^{1}.
Now we can write down logical statements of any length using standard symbols of logic, and then convert them to Gödel numbers. We describe the axioms and rules of formal system about natural numbers (or more complex formal system) and thanks to the magic of Gödel numbering these statements at same time will be just big natural numbers. From the shortest axiom to complicated long chains of deductions that may end up stating something like “User acquisition campaign will have positive arbitrage if lifetime value of average user is higher then average user acquisition cost” – everything in the end can be associated with just a number. And we can deal with these numbers like regular math: prove theorems about them, and show which properties and relationships with each other they have like all numbers do.
Instead of dealing with very complicated matters of the infinite number of all possible proofs within given logical system, Gödel effectively is saying to us:
You know, we don’t have to deal with all that insane complexity. Let me show you a unique way how any proof can become just a big number, and how any such number can be converted back to exactly same proof. Any proof you produce, be that a 10 page proof or 1000 page proof, is just one unique number fully representing your proof. And that’s true for all and any possible proofs. From now on, we can just deal and prove theorems about numbers and functions of numbers. That is a much simpler task.
What Gödel does next would be familiar to modern software developer – never mind that he did it many decades before such concepts entered our technical lexicon. He would develop his own personal library of functions, in fact almost a domainspecific language required to solve the problem he set out to solve. And as mere side effect he invents modern recursion. Speaking again in modern terms he diligently proves that all functions he constructs are computable – that they can deliver specific answer in finite (even if may be large) number of discrete steps. The hints of future Turing Machine are floating in the air of his definition of primitive recursion.
The first function is almost trivial: he defines what it means “x is divisible by y”. In modern logical language it would be written down as
1. y  x ⇔ ∃z ≤ x . x = y ∙ z
In plain English says “x is divisible by y if there exists such z that is smaller or equal to x and x is equal to that z multiplied by y” Well, that makes sense: that’s exactly is definition of division.
Afterward definitions start to make use of previous ones like a function calls of modern software library. That allows Gödel to quickly build up complexity of his deductions. Next he defines what is prime number:
2. isPrime(x) ⇔ ￢(∃z ≤ x . ( z≠1 ⋀ z≠x ⋀ zx)) ⋀ (x>1)
As you can see logical syntax allow you to make more complicated deductions if you follow the rules of the system to create longer statements. That particular statement says “x is a prime number if there are no such number z that is smaller then x, where z is not 1, nor z is equal to x and x is divisible by z. Also x must be larger then 1”. That’s just very explicit statement that x is divisible only by itself or by 1. There is no other numbers that x is divisible by – which is definition of a prime number.
And so on Gödel continues to build logical scaffolding of his library. Starting from Peano axioms he keeps deducing more and more elaborate functions. What is the purpose of that library he is building? Gödel goal is ingenious: he actually wants to describe a function that checks what is provable, what is correct deduction in any logical system.
Gödelnumbering allows us to encode the syntax of logical statements. However that tells us nothing about content of such statements. I can say “For any x it’s always x+1=5” which obviously is completely wrong (false for all values of x other then 4) yet nonetheless I can easily write it down. Logical syntax allows us to write down any sort of statement – incomplete, meaningless and false – as well as few statements that are actually true provable deductions of the system. How to differentiate between nonsensical statements and actual proofs?
When I was writing that wrong statement above, I had broken certain rules of deduction in our logical system. To be a real proof I need to start from axioms, build immediate consequence of these axioms, and finally after correct use of all rules of inherence arrive at whatever statement I’m trying to prove. True proof cannot be just written down as lone statement. It’s always a strict sequence going all way back to initial axioms of the system. Turns out all the steps to verify that specific sequence is a real correct proof can be checked and verified by purely mathematical function! With no less then 45 intermediate results Gödel arrives at that function number 46: provable(x)^{2}
provable(x) is similar to an English teacher grading papers. When writing in English (just like in logical syntax) you can write any sort of nonsense, texts full of misspellings and grammatical mistakes – A Good teacher will have none of it. Wellwritten texts will get passing grades, while texts with nonsense or mistakes will be rejected. provable(x) does the same for proofs written in syntax of logic. If “x” is correct sequence of logical deductions, in which all axioms and rules are properly followed, provable(x) will confirm that such (x) is a valid proof. If x is instead nonsense or a wrong proof it will get rejected. Obviously provable(x) relies heavily on every single other function Gödel defined in steps 1 to 45. It is a massive amount of work of mindbending complexity. Yet all that complexity is expressed and encoded in pure symbols of mathematical logic.
The selfreferential nature of any logical system is becoming exposed again. From pure mathematical perspective provable(x) is just a function like any other. Its certainly a very complicated function, yet beside the requirement of doing many complicated steps to arrive at the result there is nothing “magical” about it on the surface. It takes one argument and returns certain result. It’s like any other function you can find in a math reference book. Yet at same time the purpose of that one function is certainly “magical” for the formal system it belongs to. That very formula describes what can and cannot be proven in that very system. That function gives the system a voice, and system starts to speak about itself to tells us what is possible inside it. Things certainly are getting “curiouser” and “curiouser”.
Einstein, Gödel & The Constitution of the United States
Like many of us in Silicon Valley Gödel was an immigrant and had to prepare for a citizenship test. Naturally when this mastermind of logic started to study the Constitution of the United States it wasn’t long before he spotted a problem. According to Gödel, he found an inconsistency in the Constitution that would allow democracy to deteriorate to the tyranny. Gödel’s friends, knowing full well that no social protocol would ever stop Gödel from speaking against perceived logical violations, decided to dispatch handlers to make sure Gödel actually passes his citizenship exam. One of the handlers was Albert Einstein himself. Despite handlers best effort to distract Gödel he still managed to present his findings to the judge officiating the ceremony. Thankfully it was the same judge who administered the oath to Einstein few years earlier and Gödel passed his exam without an incident. Not bad having Einstein as your sidekick when you decide to tell the judge you had found a logical error in nation’s ultimate legal document!
Here is unavoidable yet very simple math. Diagonal lemma wasn’t initially part of the proof; using his sheer brainpower Gödel just implicitly worked it out inside his overall proof. The lemma states that in given system of Gödelnumbering there always will be at least one number f for any logical formula F that f = GödelNumber (F(f)).
Intuitively such proof can be grasped that if we start graphing such y=GödelNumber (F(x)) on a piece of paper starting from x=0, x=1, x=2 and putting dots where we get corresponding Gnumbers. We keep increasing x and keep moving along the axis to the right. The lemma proves that sooner or later that graph will intersect the diagonal where y=x. Therefore^{3} we get at least one number that remains itself when it passes through function F and result is converted to final Gnumber.
Now Gödel has all pieces of puzzle together to bring biggest surprise in history of mathematics. The “Theorem VI” in his paper is very complicated. Here is the sketch proof that is traditionally used to describe its key finding.
As we discussed provable(x) is designed in many complicated steps to be a function that checks if x is provable statement. We can define another function, NP(x) = NOT provable(x). “NOT” is simple operation of logic. It reverses what’s given to it. provable(x) can be only true or false – either x is the proof or it is not. “NOT” will reverse true to false and vice versa. Since NP(x) is also a function of a single number we can use diagonal lemma on that particular function. Thus there must exist such number g such that g = GödelNumber (NP(g)). So far it’s pretty straightforward. We plot NP(x) as a function, find where it will intersect diagonal line of its yx plot, and mark the number g of that intersection.
Lets construct a logical statement G = NOT provable(g). In this case G is no longer a function – since we plugged in specific number g –now it’s just very long logical expression expanded according to the complicated logical syntax contents of provable(x) – where our specific number g takes place of free variable x. Is that specific logical statement true and can it be proven?
Lets think about this for a moment. provable(x) is designed so that it can tell us “true” or “false” about any given x. Therefore NOT provable(x) can only be true or false as well. Now we take that specific number g and need to figure out what would be G = NOT provable(g) evaluates to? There are only two answers: true or false, which one it’s going to be?
Lets consider what happens if G is false. Well, we defined G as “NOT provable(g)”. If G is false, then provable(g) is true. Because we used diagonal lemma to figure out value of number g, we know that g = GödelNumber(NP(g)) = GödelNumber(G). That means that provable(g)=true describes proof “encoded” in GödelNumber g and that proof is correct! We got correct proof g of false statement G. Kaboom! The whole consistency of our system just went down in big nuclear explosion: we got specific proof of G that actually is a false statement! Your system just became inconsistent: you can prove a false statement, meaning you can prove anything and everything. Not good. Not good at all.
Ok, so making G false is not a good move, which immediately leads to an inconsistent system. Then lets consider what happens if G is true. We obviously would prefer our system to remain consistent – otherwise it utterly useless – so our only option left is to assume G is true. Back to definition G=NOT provable(g). If G is true, then provable(g) is false. Our strict logical bookkeeper that lives inside provable(x) tells us “g doesn’t not contain any sequence I would accept as valid proof. Among all possible proofs you can encode in your system, g is just not one of them”. Therefore there is no such sequence of logical deductions; there is no text that can be put on paper that will prove G.
G is true. And at same time there is no proof of G. G is unprovable in our logical system. If proofs are villages in big network of roads, then all roads leading from our initial axioms will never arrive at G. G exits and its apparently true – yet there is just no logical road on our map that will start at axioms and arrive to the point G. All deductions you can make about your system wont include G, so your system will be incomplete.
And that’s exactly what Gödel is telling you: “Any … formal system capable of expressing elementary arithmetic cannot be both consistent and complete”
If you want to keep consistency of your system you will have to accept there are such Gstatements that are true yet unprovable in your system – your system will always be incomplete. Or you can insist on making them provable, which will immediately make such system inconsistent. You can take one or the other, but you cannot have both at same time for any formal system rich enough to express simplest axioms of arithmetic^{4}.
There is something very amazing about Gödel proof. We used to think about logical systems as dry and boring sequence of strange symbols written on paper. Yet suddenly it’s as if these symbols got a life of their own. As if the system itself got intelligence and started to describe to us what is its own axiom, what is the correct deduction of a theorem, what is provable statement. And finally the mindbending Gstatement is constructed showing there are true statements that can be written down … yet they will never be proven inside that system. The truth is out there… and totally out of your reach!
How much of that hidden knowledge is out there? Apparently an infinity. Here is why. Gödel made his proof even harder then necessary because he wanted to demonstrate one interesting consequence. What if we add G as a new axiom to our system? After all we know its true, since otherwise the system would be inconsistent. Would it make our system complete? It turns out that adding a new axiom to the system, changes the system! Remember all the steps to define provable(x) ? Since now we added new axiom to list of all original axioms, we would need to retrace our steps we took in defining provable(x) to account for the new axiom we just added. So now we are dealing with a new system, in which it will be new function provable’(x) that in turn will create new statement G’. And G’ is a different statement then the first G we already added as an axiom. So now you have a second unprovable statement for an expanded system. You can repeat same process to get G’’, then G’’’ and get an infinity of true yet unprovable statements for a sequence of ever expanding formal systems.
If some of you are totally confused at that point, I wont blame you. Gstatement is a highly abstract construct. So all formal systems are incomplete, but how can we practically use that fact? For all its unrivaled mathematical brilliance Gödel’s proof leaves us pretty much where we started.
Before making our own deductions about real world applications, let’s actually build out more insights about that strange world of formal systems. Just like billiard balls hitting each other at an angle to go into different directions, to understand the full implications of Gödel’s result lets review a few other important mathematical results closely related to his work. The first of these is Turing’s Halting Problem.
Turning’s famous Halting Problem is well known by software developers. In simple language Halting Problem states the following:
Let suppose I will give you the source code of a computer program. I will also give you all the data used by that program, files, hard drives or DVDs it will process. Can you tell me if that program will eventually print some sort of results we expect it to produce and HALT having accomplished its job, or it will run forever unable to finish it? In other words by looking at program and its data can you give me quick “yes/no” answer will it ever stop?
Turing had proven decisively that Halting Problem is impossible to solve. It’s impossible to write software that will take a look at source code of another program and make a determination if such program will ever stop running (halt) or will be running forever. It’s a restatement of Gödel proof for more specific domain of software. The proof is largely the same as Godel’s just easier to grasp it can be formulated as simple software code rather then mindbending functions operating on syntax of logic^{5}. Halting’s Problem proof is very easy to understand for software developers and not very useful for everyone else so we will not cover it here unless you want to read it on your own.
Instead of providing a dry proof, lets demonstrate it with a practical example. Say I ask you to give me your prediction: will such program ever halt and stop working?
Start at x=4. Get me first prime number p that is less then x. Check if xp is prime number too. If yes, increase x by 2 and repeat. If not, make p the next smaller prime and check again. Repeat that until you check for p=2. If xp is still not prime number,print out x and then HALT
This description is not very complicated and would be trivial in any modern computer language. Assuming we do not know the Halting Problem it would be tempting to think such a simple program would be certainly easy to predict.
The trick here is that I did not specify just any random program. The statements above describe famous Goldbach’s conjecture that have been utterly impossible to prove for almost 300 years. The software above just checks if the statement “Every even integer greater than 2 can be expressed as the sum of two primes” is true, and then moves on to the next even integer. The conjecture is totally true for all first 4 000 000 000 000 000 000 numbers checked so far, yet what we don’t have is hard mathematical proof.
The key insight here is that knowing if these few simple lines of computer code will ever halt is equivalent to having proof of Goldbach’s conjecture! If the conjecture is true the software will never halt, it will check all numbers to the infinity, never finding one that breaks the rule. If conjecture is wrong then software will stop as soon as it finds the first number that breaks the rule.
Something very interesting is going on. Software obviously is just another way to write down syntax of logical formal systems. We could use English or software code or even go low level with pure Gödelstyle logical operators if we wish. Yet fundamentally in just few lines we can write down a statement that represents one of most fundamental problem of mathematics. Knowing when such program will halt – gives us the result we want to know – is the same as having proof of that incredibly hard problem. We can even rewrite the software above as Gödel recursive function and make a statement “will it be true that such function will halt on at least one number?” Yet again proving that statement is the same as proving Goldbach’s conjecture.
Goldbach’s conjecture is currently considered one of the big unsolved problems in math. Maybe someday someone will actually find the proof; but it is just as likely someone will prove that conjecture is undecidable without additional axioms. Such proofs are incredibly hard, yet such things have been proven before.
Even the simplest expressions in a formal systems, such as a few lines of software code, can represent incredibly hard statements, some of which will be undecidable with all our current mathematical knowledge. Software cannot be “bound” by another software. Software is so universal^{6} that its behavior can be totally unpredictable. Another piece of software can not tell you “in advance” what’s going to be the result. The only way to obtain the result is to run original software for as long as needed – it could be a few hours till “halt”, or it might be an infinity of time.
The Halting problem shows the other side of the same coin. If a statement is undecidable you cannot “cheat”, and just write software that will test that statement for you. Software can easily express that statement, but it might take infinite time for that software to finish working. And as long as you don’t have the proof of the statement neither can you prove if such software will ever stop working. There is infinitely more knowledge out there, more proofs: yet all this knowledge is unreachable to you as long as you are bound by the limits of your current system.
Since we are dealing with infinities now, its time to understand them better. Almost 40 years before Gödel made his entrance, another brilliant mind was analyzing first problems related to infinity.
When we think about infinity, the first thing that comes to mind is infinity of numbers. Yet it turns out that infinity is much more interesting that a simple every increasing row of numbers. Lets look at difference between natural numbers and real numbers. As we know natural numbers are simple numbers like 1, 2, 3 etc. that we use to count things. Real numbers are what we use to measure elements of the real world—i.e., the distance between two points is 1.23 miles. There is obviously an infinity of natural numbers like 1, 2, 3, 4, 5 and as obviously there is an infinity of real numbers like 1.23, 2.345, 3.123 etc.
Georg Cantor proved astonishing result – called Cantor’s Diagonal proof – even when using an infinite number of natural numbers you still can not count even infinite number of real numbers! Somehow infinity of natural numbers is just not “infinite” enough! There are different types of infinities; Infinity consisting of real numbers is more “powerful” then an infinity consisting of simple natural numbers. The proof is actually surprisingly simple.
1  ⇔  1.1000… 
2  ⇔  1.2000… 
3  ⇔  1.3000… 
…


10  ⇔  1.01000… 
11  ⇔  1.11000… 
12  ⇔  1.21000 
… later in the sequence …


123  ⇔  1.321000… 
… much later in the sequence …


12345678910  ⇔  1.01987654321 
… infinity later …


Infinitely long
row of 9 
⇔  1.999…(infinite 9) 
Lets pretend the truth is actually the opposite: that we in fact can count all the real numbers. Lets start with counting all real numbers between 1 and 2. To make matters even simpler, we will count just by moving the increasing natural number to the right after “1.” and reversing the order of natural number digits^{7}. You will get something like table on the left.
Whew, we are done. That table is obviously infinitely long, but now we used 100% of all natural numbers and got a corresponding real number. Now, did we actually count all the real numbers just between 1 and 2?
Lets construct the following number: we will go along the diagonal of our table and construct a number where each digit is +1 higher then what we see in the table. If digit to increase is 9 we will make it 0. I will mark the diagonal digit in color and and then we pick each digit and increase it by 1:
1  ⇔  1.1000… 
2  ⇔  1.2000… 
3  ⇔  1.3000… 
4  ⇔  1.4000… 
5  ⇔  1.50000… 
…

New Real Number = 1.211… (infinitely more digits)
So do we already have that “new number” in our table, is that a duplicate? Obviously not – since we specifically constructed it to be different in at least one digit from every single line in the table. This number doesn’t match any of our real numbers directly associated with natural numbers. But the table is naturalnumbersinfinity long! We are out of natural numbers at this point – every natural number we could use is already in the table and associated with certain real number. We just constructed a new real number and have no space (among natural numbers) to associate it with.
Let me offer another example, which might help you grasp why infinity of real numbers, is called “continuum” it is so much more dense and powerful then infinity of countable numbers. Pick any two numbers you think are very close, much closer then our example of range from 1 to 2.
Lets pick 1.001 and 1.002. We made the range 1000 times smaller. Or we could have made it million times smaller. Then repeat the argument above trying to count all the real numbers in between. Obviously you would start with 1.0011, then 1.0012, 1.0013, etc. Your final number will be 1.001999…(infinity of 9), which actually rounds up to 1.002. So have you counted all the real numbers between 1.001 and 1.002? And you can repeat same diagonal argument to construct a new number between 1.001 and 1.002 that was not counted since it differs in at least one digit from all other numbers. Apparently even tiny segments between two real numbers have “more” infinity between them then all the infinity of natural numbers!
Apparently continuum infinity is very powerful. That’s the infinity that belongs to the real world around us – everything in our world is described by a real number. Yet we never know any of these real numbers exactly right. We are always limited by error of our instruments. At certain point our measuring tools will round up the result, and infinite sequence of digits of real number will be truncated. If you measuring distances with say tunneling microscope, you will round up the measurement to the nearest atom size. Such precision may create an illusion the world is fully measurable using scientific instruments. That is not true: rounded up final measurement no matter how precise, even if it’s to the limit of atomic sizes, is just simpler rational number. These rational numbers are countable with our familiar infinity of natural numbers. Yet the real world remains a continuum infinity never fully reachable to our tools.
That concludes our mathematical session. Now lets apply that hard earned knowledge to practical matters of startups & innovation. Lets return to our main essay.
This site is styled with imagery from the alternative universe of ‘Fallout‘. One of main themes of Fallout is bringing futuristic technology to a primitive world. Being inside of Silicon Valley has a similar feeling of an isolated Vault full of tech wonders too powerful or too arcane when compared to the rest of the normal world outside. That can lead to both positive and negative outcomes; however, spending over a decade inside such technological Vault certainly have been incredibly interesting experience.
I hope you will find these writings entertaining and may be even useful in our startup adventures. Naturally, the views and opinions expressed on this site are my own alone and do not represent the official view of my fund.
]]>In truth, the popular perception of the Valley as a magical conveyor belt that churns out billion dollar companies from startups is just a trivial case of survivor bias. The Valley creates thousands of failed startups that go away without notice during same time it creates a couple of Netscapes, Googles, and Facebooks. The latter get all the press and attention while the former disappear in the dark. This creates an illusion of an unbroken string of successes. If one looks at the actual time spent by entrepreneurs, as a distinctively different class of people than salaried employees of successful startups, they spend the most of their time and effort creating, enduring, and recovering from failure rather then creating success.
The very first company I started failed with a great bang. The second one failed a little bit less, but still failed. The third one, you know, proper failed, but it was kind of okay. I recovered quickly. Number four almost didn’t fail. It still didn’t really feel great, but it did okay. Number five was PayPal.
Max Levchin (Cofounder, PayPal)
The real machinery of Silicon Valley creation resembles a complex chemical factory. Raw ideas and visions are funneled into it, and undergo multiple transitions from one stage to another in a high pressure startup environment. 9095% break down and fail, and their raw materials recycle right back into furnace. The rest emerges from the silo years later as winners we all know today. One of Silicon Valley’s many secrets is the system of managing and dealing with systematic and constant failure of individual startups, while creating almost guaranteed small percentage of winners in the end. Lets take a closer look at how this refinery of massive failures actually converts a few ideas into real successes.
One of the topics high tech pundits like to discuss is relative importance in startup destiny between initial idea, founding team, and the market. The answer usually puts lowest priority to an idea and splits the reminder of the importance between the team and the market, often putting more emphasis on the team. Something like 55% team, 35% market and 10% original idea. Such analysis has some merits and is helpful for founders to maintain healthy state of mind while assailing huge odds stacked against them. However, after observing Valley life for 15 years this author realistic estimate would along the following figures: 70% market, 29% team, 1% original idea.
Lets start with simple example. Microsoft was floundering tiny company from 1975 till 1982. There is a rumor Microsoft was on verge of bankruptcy when 25,000$ check from then roaring Apple Computer for BASIC license saved the day. Things changed for the better when IBM deal revenues started to come in 1982 and the rest was history. Yet think on this timeframe. Its full 7 years. Google went from nothing to 23,000,000,000$ IPO in 6 years. It took Bill Gates himself to work like crazy for 7 years to just survive as tiny obscure startup.
What changed between ’75 and 82’? Did team get radically better? Did Bill Gates suddenly get much smarter? In reality all that changed was market. Instead of serving hobby market of selling BASIC and other niche software to early computer enthusiasts company changed its market – which was delivered to them on silver platter by IBM – to what would become most mass produced computing platform in history. Then the very same teams vent on to create unimaginable amount of wealth, which Google is yet to beat after 12 years of trying.
We can go on and on about this. Say Steve Jobs returning to Apple and reinventing the company. He does this by not trying to beat the markets Apple already lost to Wintel platform by late 90ties. Instead, he went to find new markets: highend laptops, portable music players, smart phones where Apple unmatched design and elegance allowed them to dominate.
What this short excursion into history shows is that even the absolutely best of the best leaders of technology companies are:
Trick question: do you think founders of Silicon Valley startups are better or worse then Bill Gates or Steve Jobs to evaluate, pick and enter correct market when they just create first outline of their company? And what happens when they enter wrong markets? Simple – their company most likely will fail.
There is one little caveat to that whole marketplace discussion. We easily and confidently discuss metrics and timeframes of markets determined many years ago. The problem is we have some (not great) visibility into the past and virtually no visibility into the future.
Here is typical example from personal experience. Today we all know of multibillion companies like Zynga formed on Facebook application platform. Yet how things looked when the platform was just opened up in summer of 2007? Back then we had no visibility whatsoever on platform future. Facebook was fairly small network, much smaller then dominant Myspace at that time. Nobody ever saw anything like app platform on social network, thus no industry record to compare it with. Recalling many conversations with I had with entrepreneurs and investors at that time opinions ranged from treating it as small curiosity not worth investing much time into (opinion of highly experienced VC who generated $800,000,000 returns from his investments) to guarded optimism it could be a good helper tool to bring audience to existing standalone websites.
The prediction that there will be its own vertical industry with dozen of companies, doing nothing but building facebook apps which will bring hundreds of millions in revenue and have market capitalization in billions of dollars was so out of the realm of conceivable reality nobody came even remotely close to predicting that. As we know now from many interviews of the Facebook insiders they also had no clue what was coming! Their thinking was it would be a nice side addition to the Facebook product to bring incremental growth for their user base. The platform explosive growth caught them completely by surprise, unprepared and lacking resources in many areas, thus creating very interesting experience for everybody who was on the Facebook platform the first year.
Lets look at this again. We have collective wisdom of Silicon Valley best and brightest estimating new high tech product (Facebook platform) and completely missing its importance and impact. The Facebook team and their venerated young founder completely missed the scale of their own product. So who the heck knows the answer?
The hard truth any Valley founder realizes sooner or later is that answer to such question is: nobody. Future is practically unpredictable and therefore markets are impossible to predict as well.
No amount of past experience or industry standing helps much to predict what is the best market or the best product to enter the next year. While bigger companies can deploy (barely useful) the tools like focus groups and market research initiatives, a typical startup won’t have even these dubious tools at their disposal. The only option remaining to them is to take a completely blind guess. 90%+ of time such blind guess will be wrong, and startup will either fail or – a very important option! – pivot to something new.
Market miss is probably the biggest and the most important factor in startup death rate. It is also practically unavoidable. Founders can be inhumanly smart or hard working, they can hire best team on the planet, and still fare no better then Bill Gates during ’7582 or preiPod Steve Jobs.
Systematic failure is an irremovable part of startup ecosystem. Silicon Valley has naturally structured itself around constructive integration of such failure. Yet missing the market is not the only way in which startup can fail.
A reader may get surprised at this point in our story. Did not we argue just recently how important is talent and how one must follow all these cardinal talent rules? Yet now author goes on to saying markets are everything, and team is almost an afterthought.
Not so simple. In that complex multilayer refinery of startup lifecycle team does play a huge role. It just plays it later. The negative of being in wrong market are obvious – there are not that many customers, or not that much money, or there is no growth and momentum. Best team can blunt its pickaxe trying to make startup biz model work, and still most likely fail no matter how hard their try. However, what happens if they actually guessed correctly and find themselves in hot market?
Exploding new market has certain feel to it, it is like a digital Klondike. Nobody yet knows the future, but few prospects already have stricken rich gold veins (revenues, customers or growth) and there is a frenzy to grab the best parts of the market. That is where the team expertise and quality comes to the forefront. That is where “startup mode” of 24/7 nonstop marathon becomes typical, and the quality of people who can survive such inhuman wear and tear while keeping reliability to produce stellar results . I recall our own experiences during such supernova periods of startup life, and the most telling attribute that changes is one perception of time . Day of the week and time of the day largely loose meaning, and you start to think about the events in terms of “deliver +2 hrs from now”, “meetup +10hr from now”, “deploy +18hr from now”. The whole lifestyle becomes how to cram the absolutely most events in activities in the shortest timeframe and grabbing some sleep when you see a few hours not showered with the upcoming inner events. Sufficient to say very few people can survive such mode of operation for long, and one needs the whole team of them to run a successful startup.
There is one big caveat to all that. Remember Youtube sale to Google for 1,700,000,000$ ? Good outcome for #1 player in web video market. Quick, how much #2 fetched? Frankly, I have no idea. Probably you don’t either. The difference between #1 and #2 in such market, especially in consumerfacing industries is not just huge, it is astronomical. Sometimes #2 is good enough to get “just” 1020 times less then #1 player. Most often #2, #3, …., #10 get all about the same amount – next to nothing. #1 takes the majority of the market and huge share of proceeds. Just ask Microsoft about their search revenue versus Google. Or their mobile share vs iPhone.
If you’re growing at 50 percent a year, and your competitor is growing at 100 percent a year, it takes only eight years before your competitor is 10 times bigger than you. And when it’s 10 times bigger than you, it can buy 10 times as much advertising and do 10 times as many projects and have meetings with 10 times as many customers. And you begin to disappear.
What differentiates #1 from #2, #3,…#10 players is the team. What is ironic they did not even have to work twice or ten times better. 10% difference could be all it takes. The team works just slightly better and faster, customers flock to its product faster then they flock to competitors, that attracts more investors, more creative talent, success breads success, and before you know it such startup gets x 1,000 times better outcome.
Needless to say that fate of these #2, #3,…#10 players in the market is the same: absolute or relative failure. Guessing hot marketing is not enough. One got to build best team comparing to all others who guessed the same market. Yet even that is not the final story.
What about our tiny little 1% importance of the initial idea in startup? Why not make it 0% and say its completely irrelevant? The reason is that initial idea has significant yet indirect influence on both resulting market and team.
Imagine yourself in big dark forest in darkest hour of the night. Think of starting idea as very weak flashlight in very dark forest of big trees of unknowns: market, industry and overall future. You can sort of see where you going to make your next few steps next week. The future picture is quickly becoming blurry and fuzzy, just some projections and schedules. Anything more then half year out is very dark, only few very big shapes (big vendor platform plans, broad trends) are visible in ray of that weak flashlight of initial planing. Starting idea is the direction where founders point that flashlight initially. Hence based on shapes and predictions that they recognize in the dark they make decisions about market they enter and team they recruit.
So all these predictions are unlikely to be true. So what do founders do when the first few steps with flashlight show an unpenetratable wall or an unexpected object right on their projected path? They pivot and start moving flashlight slightly away trying to find the way around it. The initial idea starts to morph and change the shape. Paypal negotiated a big funding round as a payment system for the early Palm handhelds, and then a few days later pivoted into the web payments. Microsoft started with BASIC for Altair and then pivoted into operating systems.
By the time we had our first board meeting a month later, we had already realized that wasn’t going to to work…We started the board meeting basically saying “Hi, John. Hi, Pete” – the new VC guys – “We changed our business plan.” And these guys were like, “What?” They just put down $4 million to see something happen, and we said, “Sorry, we’re not going to do that; we going to do this.”
Max Levchin (Cofounder, PayPal)
The key understanding of pivot is that a startup cannot change its course completely. The existing team, existing products or prototypes if there is any, general expertise and knowledge of founders limit such freedom. That flashlight can only move to directions adjacent to the initial idea, and the speed of such transition is fairly slow. Even in extremely high energy startup environment people don’t like to give up something they worked months or even years on. It is harder to change existing habits even of a 6 months old startup than to create entirely new ones on a blank slate of a new startup.
Here we come to the main bottleneck of startup life, and therefore the main reason of such astonishingly high rate of startup failure. Look how all components are coming together. Founders no matter how experienced they are have very little chance of predicting and guessing future markets. All they have is tiny flashlight showing just where they putting their feet next few weeks or months. Initial idea realistically is just an excuse to form a team and find investment in general lightcone of that flashlight. The real most important event in startup life will happen when absolutely unpredictable opportunity in absolutely unpredictable market opens up and then it because death race for #1 stop against few other teams who also ended up in right place at right time.
Imagine an professional race runner who is training all his life to be fastest athlete on the planet. He is not just good, great or best. He is inhumanly good, his extra “supplements” are borderline to illegal substances to make his muscle work beyond any limit. There is no silver or bronze medal. It is #1 or nothing. Furthermore, he cannot just train on background and wait for Olympics. Instead, he must tire himself to death everyday working on his initial idea. And here is the clincher: At some random unpredictable moment at time, at some unpredictable market (with luck) adjacent to our Olympic runner initial idea will create an opportunity of allornothing potentially huge win. The Olympic Games between all teams is officially on… yet nobody even gets the signal the games are started! Nobody will even signal clearly thats it is time to morph initial idea and pivot with all speed toward the Olympic Games. Spending extra 36 months working on originally designed product – “oh, we just got to ship it, and then we will see what is up with that new little windows/web/facebook ” – could be all the difference between #1 and #2 (if not #10).
Having an idea in a largely right general direction is not enough. Building and recruiting the best team in that market is not enough. Just being lucky of recognizing the right market is not enough. One has to have an incredible luck of having the perfect timing while having all other requirements lined up to succeed in order to finish line and claim #1 prize.
Successful startup is such an improbable event, that it is even astounding we have only 90% failure rate, instead of much more comprehendable 99.999%.
The formation of the Valley culture took many decades. All that time market forces outlined above were fully active. Incidents built upon incidents to form the knowledge. Or perhaps more exact term would be metaknowledge. Nobody could predict next market hit, yet VCs started to learn how many startups would fail even with the best proven founders as helm, although they could never know exactly which ones of them. Rockstar employees going from startup to startup saw how many best ideas backed by the best effort would fare and evolve. First pioneers passed some of these lessons to the next generations, which learned or relearned them anew. Good habits sometimes helped startups to survive and these habits were more likely to end up in minds of founders and executives who made it big, and thus their lessons and speeches were eagerly learned by growing youngsters. Bad habits inescapably led to failed startups and had harder time to be replicated. It was Darwinian selection with metaknowledge of running and operating startups evolving for more then 50 years and seeing many generations of investors and entrepreneurs. While good habits did not guarantee success at all, bad habits certainly led to failure. One way or another almost all of these bits of knowledge were connected with dealing with failure.
Lets take a broad look at ecology formed by living and breathing in 90%+ failure atmosphere:
America threw off the old world’s hostility to failed businessmen along with British rule. Back in the 1830s one of the things that most struck Alexis de Tocqueville about the country was “the strange indulgence which is shown to bankrupts”, which, he said, diverged “not only from the nations of Europe, but from all the commercial nations of our time”.
Silicon Valley undoubtedly got it start due to the great leniency USA was traditionally showing to its failed businesses. After half a century of future development, that culture is amplified and focused many hundreds times more then it ever was before. The benefits of such approach impressive such as they are, are staggering when one considers compound interests of multigeneration selections of leaders and top talent such breding grounds reliably produces.
This lesson may be hard to learn for international community who is envious of Silicon Valley success. It is not just a method of operations that few enlightened executives can agree to adopt. It requires a broad acceptance by investors, government, employees, and to a degree by a larger public and especially media. European culture traditionally puts a high price on failure.
One common theme recurring in publications of international investors and goverment officials is that this or that country X desperately lacks entrepreneurs and startupfriendly talent. Lets take a look at that from perspective of young brilliant graduate of some international top institute. He is just beginning his professional carrier and has roughly two options. Join established company; say a bank or an oil company. He will get a great compensation, a full job security and a good carrier. However, he understands such choice will result in fairly boring and routine job. He is excited about the possibilities of doing a startup and researches the option further. Being brilliant, he quickly realizes that startup is a very chancy proposition. Even if in a great and remote Silicon Valley 9 out of 10 startups fail! Yet he is still willing to take even that chance. Then he finds out that the whole system is stacked up against him. Investors insist on grandiose topdown plans to validate the investment, which they actively meddle in and micromanage. Furthermore, they are very unfriendly to loosing money, with few founders even being afraid of criminal charges in case of failure. Society as whole is not tolerant to failure. While our young graduate will try and fail, his peers will be making good money in legacy industries and steadily climb corporate ladders. Estimating what is going to happen in the next few years our graduate realizes he runs a very real risk to be stigmatized by society, permanently harm his carrier and potentially even make some enemies just by trying a risky startup. Being brilliant he does the rational thing: he joins a big company.
In meantime, life in Silicon Valley goes on. In given cohort 10 startups start, and 9 fail. One winner captures everybody attention and international investors & governments are yet again amazed at the Silicon Valley creativity. Yet the main product created in that cohort goes unnoticed by the external world. These 9 failed startups with 510 person each, had just created 50100 people tempered and experienced by the failure. Reinvigorated by Silicon Valley community these people will now jump back into fray, some to join other startups, some to start their own. The real full production of 10 startups was one winning startup and 100 high quality people. While representing the loss of individual investors (from which they are of course protected by portfolio system), it’s a big win for the Valley as whole. These people will bring new ideas, experiences and most importantly even higher tolerances to failure to any startup or company they join.
In Silicon Valley failure is constantly refined into materials of future success, and it is one of the most important components of the Silicon Valley system.
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