The Axiom of Choice

 

The Oracle and Neo, The Matrix Reloaded

“We can never see past the choices we don’t understand.” — The Oracle

Ricardo Anguiano, my friend and former colleague, recently expressed frustration over the fact that life wasn’t long enough to be good at everything. What sort of cruel universe would deny him the ability to play scratch golf, perform as a concert violinist, and serve on the City Council, all while excelling at his job? Why should he have to choose?

I recently met an obviously talented entrepreneur (lets call him Albert) and asked him about his goals for his nascent business. Was he looking to make an adequate living with more control of his day-to-day existence than he’d have if he took a job for a big company? Would he prefer to have a business that steadily provided him a $1M/yr. annuity for life, or would he rather forgo the income stream for a chance to be a multibillionaire icon like Bill Gates, Jeff Bezos, or Mark Zuckerberg? His answer was that he’d like the chance to go big, but he wouldn’t want to endanger the business to do it. When I asked whether he had plans to raise a larger VC round after the initial angel round, he said he wasn’t sure; he thought an angel round would allow the company to reach break-even, at which point he could re-evaluate his options. In other words, he didn’t want to make a choice.

In mathematics, the Axiom of Choice is a mildly controversial principle of modern set theory that says that you can simultaneously choose elements out of any collection (even an infinite collection) of non-empty sets. But, my version of the Axiom of Choice is simpler: you always have to choose.

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