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Carlos E. Perez

@IntuitMachine

Sep 22

https://twitter.com/saranormous/status/1572791179636518913

When I wrote my book "Deep Learning Playbook" in 2017, most AI companies were working on AI infrastructure (i.e., tools and hardware). Now there are a lot more companies implementing applications.

https://twitter.com/saranormous/status/1572791179636518913

A business based on applications can only build a moat against the competition when there emerges a critical mass of methods that one can uniquely combine. Thus one's secret sauce is a recipe and not just a sauce.

Just to illustrate this, Figma created a graphic design tool in 2012. This is decades after vector drawing technology was introduced. Yet 10 years later, they could exit through an enormous acquisition. Why? en.wikipedia.org/wiki/Figma_(so…

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Carlos E. Perez

@IntuitMachine

Sep 21

It's not obvious why C.S.Peirce's triadic thinking has utility. The ordering of concepts in firstness, secondness, and thirdness explains how existing systems may have evolved. But existing systems exist in their thirdness, so their history does not lend to prediction.

The utility of triadic thinking is in design. This is because it tells you the first principles one needs to establish in one's vocabulary.

Humans are naturally dyadic thinkers, and we traffic in analogy-making. But analogy-making has its limits in that it can't discern first principles. It's important to know what comes first so as to design new ways of thinking.

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Carlos E. Perez

@IntuitMachine

Sep 20

Calculus is a language that connects our intuition about linear shapes with that of curvature and change. Similarly, one cannot speak about cognition without semiotics. Semiotics is the language of meaning as calculus is the language of change.

C.S.Peirce divides all of science into discovery, review and practicality. He divides the science of discovery into mathematics, philosophy and idioscopy. Math he further divides into logic, discrete series, continua, and pseudo-continua. Where does semiotics fit?

Semiotics is under "logic", where he defines 3 categories: speculative grammar, logical critic, and speculative rhetoric. What we know of logic today is under "logical critic". The analysis of signs and their combination is under "speculative grammar."

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Carlos E. Perez

@IntuitMachine

Sep 20

It's odd that calculus and deep learning are at the core based on the same principles, yet we claim the former leads to understanding yet many say the latter does not. How do we reconcile this difference in opinion?

We can argue that deep learning is analogous to an automated proof system. In an automated proof system proof can be laboriously long that it is infeasible to be surveyed by humans. Seemingly, the integration process of deep learning is equally intractable.

So the question is, are proof systems and deep learning aware of the results of their own computations? Don't proof system employ intermediate theorems to find subsequent proofs? Do deep learning systems employ pre-trained networks for downstream recognition?

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Carlos E. Perez

@IntuitMachine

Sep 19

If we accept process metaphysics instead of the predominant substance metaphysics, then we must accept that numbers are actually processes and not real things. arxiv.org/abs/2002.01653

In calculus, the symbol rewrite rules are discovered as a consequence of proofs of convergence of an infinite series of calculations. However, not all infinite series are known to converge. Furthermore, numbers like π become infinitesimally more precise the longer the computation

But no universal algorithm can find a proof that an infinite series will converge (i.e. halting problem). The lack of a proof doesn't imply that a series of computations does not converge. There are plenty of systems in reality that converge to recurrent patterns.

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Carlos E. Perez

@IntuitMachine

Sep 19

Let's explore the meaning of "understanding" that gets thrown around liberally in cognitive science. Let's look at two mechanical systems: proof systems and AlphaZero, which exist in a regime that is beyond our intuitive understanding of understanding.

The Four Color theorem in mathematics has a proof formulated by a computer-assisted proof system that humans find to lack any insight. Mathematicians call these kinds of proofs "Non-Surveyable". That is infeasible for a human to verify. en.wikipedia.org/wiki/Non-surve…

The intuition as to why these non-surveyable proofs can't be understood is the sheer number of steps involved in the proof. Too many steps that are infeasible for a human to follow and thus understand. This is despite humans being able to program the said steps!

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