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Innovation through incompleteness

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This piece on incompleteness for startups is the sort of thing I love to see: a mapping from one discipline’s problem to another’s, which thereby brings an idea from the first discipline available to the second as a novel result. In this case, the mapping is from the axioms of mathematics to the rules-of-thumb that govern businesses. If the latter constitute a complete formal system then, according to Gödel, they must be inconsistent, meaning there are some assertions which these rules-of-thumb are unable to evaluate. If we take “assertions” in this context to mean “business plans”, and “true assertions” to mean “profitable business plans”, then voila - out falls the innovator’s dilemma.

That’s not quite the formulation, but it’s close enough. Also perhaps the danger of these sorts of reductions - after such a lengthy exposition, it appears that we’ve arrived at a conclusion some 15 years old at the time of the blog post’s writing. Business leaders for industry incumbents often don’t see the next challenger on the horizon, what of it?

There is another result in this discussion which bears some mention, the problem of a technology before its time. Edison could not possibly have succeeded with Google’s business plan, and so forth. To even make sense of it he’d have to derive a host of new axioms from the ones with which he was familiar. In the study of innovation this sort of problem is well known and much discussed.

The reduction itself is a little suspect, because rules-of-thumb in business are actually very different from mathematical axioms. In particular, the former are not complete and no one claims they are. I’ve never heard of a business leader who has full confidence that her business model is somehow universal or indeed even correct. For the most part it seems that businesses are just figuring it out as they go along. Moreover, truth and profitability are very different properties. “One follows zero” is entirely falsifiable according to certain axioms, but “monetizing internet search results” may be profitable in some ways, not profitable in others, or perhaps it is so only within certain regions, etc. Obviously it has been for quite some time, but that could certainly change for a number of reasons.

One might conclude that this blog post and its conceptual model is rather overdone and wrong, or perhaps just right by accident. It seems to me that even with its flaws, it’s valuable nonetheless. To begin with, the reduction itself is interesting and thought-provoking, even if imperfect. More than that, this reduction helps us to connect the innovator’s dilemma with the invention-before-its-time problem: according to this theory the only difference between them is a slightly different set of axioms. Indeed there is even the hint of a continuum of these kinds of problems: for every set of axioms, at any point in time or geography, there is some new invention which confounds those axioms. That is in fact the promise of this blog post: to import Gödel’s surprising proof into the world of business strategy.

Strictly speaking the blog post fails, in that it’s not a precise reduction or a rigorous mathematic proof. No matter! Some insights are a little imprecise and even incorrect. That is not entirely harmless - in fact history is riddled with shockingly harmful reductions. It’s also bursting with really useful ones. Ultimately that is why I’m so fond of these kinds of ideas - they are so potent, and they carry such promise. This particular one certainly is clever, and deserves a read.