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 billion-dollar 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 .

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pipboyWelcome, startup wanderer! This is my personal blog where you will find essays about startups, angel & venture  investing and other stories from the Silicon Valley. If  you are curious to learn more about my background take a look at my  bio.

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P90X by Tony Horton

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 low-tech 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.

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This is mathematical section of the parent essay Gödel Incompleteness for Startups

Gödel Numbering

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 ASCII-compatible 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:

  • Number 0 exists ⇔ 7811710998101114324832101120105115116115
  • Each number has a successor that is a number ⇔ 6997991043211011710998101114321049711532973211511 7999910111511511111432116104971163210511532973211 011710998101114

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.

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In the classic book “Founders at Work” the founders of many high tech startups repeatedly return to the subject of failure and how they recovered from it. One of the popular conferences in San Francisco is FailCon.  Failure is regular subject of panel discussions at high tech conferences. That may sound strange to an external observer. Isn’t Silicon Valley all about innovation and success stories? Why such fascination with failure?

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. Read more…