02 Apr

The Paradox of Natural Laws and Its Resolution

In an earlier post, I described the problem of computing in nature, namely that scientific laws employ mathematical formulae, but it is not clear how these formulae are being calculated in nature. The reasons for this are historical and date back to Newton’s formulation of the three laws of motion. While Newton had produced a mechanics, he had not himself envisioned machines. He was only trying to describe celestial and terrestrial motion, and his laws were later used to create machines. As a result, the components of reality in Newton’s mechanics (particles and properties) are unrelated to the components of a Turing Machine that can calculate the formulae. This post discusses how the separation of motion and computation leads to a paradox in which the computer that calculates the natural laws for a single finite universe must be infinite in space or time.

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28 Mar

Reasoning and Semantic Computation

Since the advent of computers, it has been widely believed that the human mind is just like a computer. I have previously described why this is a false analogy due to two problems: (1) the problem of meaning, and (2) the problem of choice. I have also discussed the problem of meaning in computing theory in the book Gödel’s Mistake. However, all these critiques are inadequate without an understanding of how nature itself computes. For example, if nature is governed by some natural laws, then these laws have to be computed on some machine to obtain a prediction. How is nature computing these predictions? Even otherwise, living beings are constantly involved in decision making—i.e. what next steps must I take to achieve my goals?—which is also a computational problem. This post discusses a proposal on how this problem should be tackled, and the relation between Sāńkhya and computational theory.

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22 Mar

Sāńkhya, Reductionism, and New Science

Many people believe modern science is reductionist and an alternative anti-reductionist science must replace it. This post discusses why Sāńkhya is reductionist—because it reduces everything to only three modes of nature (sattva, rajas, and tamas). It also discusses why Sāńkhya is anti-reductionist—because the first mode of nature in this reductionist theory (sattva) represents the whole, which precedes the contradictory parts (rajas and tamas). Sāńkhya becomes anti-reductionist because the whole precedes the parts. And yet it remains reductionist because there are only three states in nature. The post discusses Gödel’s Incompleteness and how incompleteness arises from the problem of opposites. It then argues why the Sāńkhya anti-reductionist model of reduction can be made to work—because the opposition between rajas and tamas is a feature of the logical system, not a bug. In the process, we can see how a shift from bi-stable to tri-stable logic changes science so fundamentally. This shift (in logic itself) constitutes the essence of what we might call “Vedic science”: it is not pseudo-science, and it is not just philosophy; it is science in every sense of the word, just based on a different kind of logic. Just as binary logic is the basis of all modern science (because any law of modern science can be computed on a binary digit computer), “Vedic science” is based on a ternary logic computation.

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