• Computing,  Logic,  Mathematics,  Philosophy,  Physics

    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…

  • Biology,  Computing,  Logic,  Mathematics

    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…

  • Computing,  Logic,  Mathematics,  Philosophy

    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…

  • Computing,  Linguistics

    The Problem of Meaning in Artificial Intelligence

    Since the 1960s, when computers first appeared,  a machine that can think just like humans was claimed to be just a few years away. This idea has been called Artificial Intelligence (AI) and it reappears every few years in a new form, the latest being the brouhaha around “Machine Learning”, “Deep Learning”, etc. The algorithms and techniques underlying these trends have existed for a few decades, and their limitations are also well-known. However, even with growing computational power we are only able to get closer to the boundaries of what is possible, rather than cross into what is impossible. This post discusses the problems which cannot be solved by AI in…

  • Computing,  Mathematics,  Overview,  Philosophy,  Physics

    Computers and the Mind – What’s the Difference?

    This post discusses the widespread notion that the mind is some kind of computer; that the computer is able to represent knowledge, and this knowledge can be about the world. As we shall see, this notion is quite silly, although people—who are either not physicists, mathematicians, or computer engineers, or just happen to have an academic title without an understanding of these subjects—tend to profess it over and over. This post explores the multiple and successive levels at which this notion is flawed, and why fixing it has proven so hard so far. The post ends by commenting on whether it can ever be fixed.

  • Biology,  Computing,  Mathematics,  Physics

    Evolution and Mechanism – Are They Compatible?

    A computer is a canonical example of a machine. Every machine can be described by a mathematical theory, and every mathematical theory can be automated on a computer. Therefore if you could describe something mathematically, you could also automate it in a computer. People often suppose that this means if we had a mathematical description of nature, that description could also be automated on a machine. In the case of living beings, such an automation would mean that we too are automatons—machines. This post examines the issues in this argument, highlighting the holes in it.

  • Biology,  Computing,  Research

    Evolution’s Halting Problem

    This post describes a problem in Evolutionary Theory that arises when we consider why all living beings eventually die. I will compare the death of a living being to a computer program that halts after completing execution. The issue of program halting is problematic in computing theory because current computing models do not incorporate meanings. A similar problem exists for living beings too. If living beings are evolving by random mutation and natural selection, then there is no physical process of selection that will produce finitely lived living beings. In fact, if the selection process is just as Evolutionary Theory describes it, then we must find living beings that live…

  • Computing,  Mathematics,  Philosophy,  Research

    The Scientific Method – Does it Deliver Truth?

    The below is a modified version of a response I wrote recently on Google+ in response to a question about the conflict between reason and faith. The response is also detailed in my recent book Uncommon Wisdom. This essay will argue that the manner in which science has construed the use of reason (and experience) – i.e., the path to discovery – cannot deliver truth. There is, however, another notion about reason which works in conjunction with faith to verify rather than discover the truth. Faith and reason are contradictory when reason is defined as the method of truth discovery. But they are not contradictory when reason is used for verifying the truth. In this…