How to Make a Human Being: A Body of Evidence. Christopher Potter
working with his own mathematical reality.
G.H. Hardy
8 | Einstein called mathematics the poetry of logical ideas.
9 | In the 1920s an attempt was made to make mathematical logic the sole means of advancing philosophical knowledge, and so rid the scientific method of metaphysics once and for all. The methodology was called logical positivism, and assumed experience as the sole source of knowledge. Logical positivists wanted to admit as meaningful only those sentences that can be independently verified, ultimately by mathematics.
Logical positivism is the idea that a sentence or another fragment – something you can put in a computer file – means something in a freestanding way that doesn’t require invoking the subjectivity of a human reader. Or, to put it in nerd-speak: ‘The meaning of a sentence is the instruction to verify it.’
Jaron Lanier, computer scientist and virtual-reality pioneer
Logical positivism is a form of solipsism. If you say physics is only about predicting the outcomes of experiments, you can only really say it’s about experiments that you personally do, because to you any other person is just another thing you’re observing. But solipsism is a dead-end philosophy and when it comes to science it’s a poison.
David Deutsch
10 | At the laboratory in Lagado, the capital city of the nation Balnibarbi, there is a great machine that manipulates all the words of the language of the people. Scientists hope to extract knowledge out of the random generation of words. Where three or four words are found together that might make part of a sentence, they are dictated and transcribed into a ‘large Folio already collated, of broken sentences’. Out of this process it is ‘intended to piece together, and out of [these] rich materials to give the World a complete Body of all Arts and Sciences …’ At the Mathematical School in the same city, formulae are written in ink on wafers and eaten, in the belief that the ink with its message will eventually reach the brain, where the information will be processed. Other scientists have attempted to reduce the nation’s language entirely to nouns, since in reality ‘all things imaginable are but Nouns’. Instead of speaking, language is reduced to pointing at things. The disadvantage is that it means carrying around a large number of things to point at. The women of the country rebelled and sought ‘the Liberty to speak with their Tongues, after the manner of their Ancestors; Such constant irreconcilable Enemies to Science are the Common People.’
The quotes are from Gulliver’s Travels by Jonathan Swift (1667–1745).
11 | Some materialists believe that out of enough data, meaning is self-generated. And so logical positivism creeps back into fashion. Larry Page, one of the founders of Google, believes that the internet will come alive at some point. The futurist George Dyson believes that it already has. Other futurists, Ray Kurzweil notably, predict that a moment will come when machines will outsmart humans. It is predicted that this singular event will occur in the twenty-first century.
12 | Kurt Gödel’s incompleteness theorem of 1931 (published when he was only twenty-five years old) presented the logical positivists’ programme in a new light. Gödel’s Theorem is often misstated. It does not show that mathematics is incomplete, but that mathematics is incomplete within any particular mathematical formalism, which is crucially different. It means, for example, that there are mathematical problems that can be written in the language of, for instance, arithmetic (an example of one kind of mathematical formalism), but cannot be proved in arithmetic. But arithmetic can be made complete within a more encompassing formalism, say, geometry; yet geometry is itself incomplete, and so on. Mathematics is a series of nesting formalisms, one inside another like a Russian doll. Our physical understanding of the universe – written as it is in mathematics – may be like this too.3
Gödel’s theory is useful when we think about computers or any mechanical device that works in some formal way. It tells us that there are mathematical truths that cannot be proved by any computer or mechanical device, no matter how sophisticated that device may be. If our minds are formal in the way computers are, then there will always be some mathematics that is beyond our reach, and so also some understanding of the physical world that is beyond our reach. Alternatively, as Gödel pointed out, if humans can always delve deeper into mathematical reality, then they cannot be machines. We are left with two possibilities: humans are machines and their understanding of the world has a limit, or they are not machines and are free to explore the physical world forever. Either way the world is more mysterious than we are.
If we accept that mathematics is the strongest evidence we have of an externally existing world, Gödel’s theorem throws a spanner in the works when we move on to consider the manufacture of our human doll. If human beings are not machines, then how can we make one? On the other hand, if they are machines, Gödel’s theorem casts doubt on the possibility that humans themselves could ever construct a machine of equal complexity. We must hope that out of the scientific method we can create machines that are intelligent enough to evolve, and in that way eventually transcend the intelligence of their makers.
Evidence against the existence of an external world
1 | Until the 1920s scientists believed in an independent reality that could be measured. But then from the 1920s there was quantum mechanics.
I think I can safely say that nobody understands quantum mechanics.
Richard Feynman
2 | The physicist Niels Bohr once said that quantum mechanics only makes sense if you change the meaning of the word ‘understand’.
3 | Quantum mechanics tells us that the world is best described by a wave of superimposed probabilities. The most famous wave formulation is the Schrödinger equation. It is a linear superposition of different states of reality that evolves smoothly in time. Each possible observed reality has a certain probability attached to it.
4 | From the perspective of a molecule, nature is a single quantum wave of probability. From the perspective of a human being there are separate things, and particular events occurring at particular moments. The fundamental problem of quantum mechanics is how a reality that is described by a smooth wave also describes the world that we witness at our human scale. How are these two different perspectives commensurate?
5 | Various mechanisms have been put forward to explain how the sinuousness of the quantum world, in which everything is entangled in probability, becomes a world of separate things that actually happen, or appear to happen (the appearance being what we take to be the actual), but each is problematic.
6 | The Copenhagen interpretation, the most famous interpretation of quantum mechanics, devised largely by Niels Bohr and Werner Heisenberg in the 1920s, argued that quantum mechanics does not describe a physical reality but probabilities attached to the act of measuring itself. The wave of possibility collapses when a measurement is made, and we find ourselves in that world out of the many possible worlds contained within the wave. All the other possible worlds disappear.
7 | Light is both wave and particle. Light is made out of photons that in particle physics are understood to be particles. But light diffracts when it passes around the edges of a slit (or more evidently when it passes through a double slit). Light behaves as if it is a wave: troughs of light coincide to make the bands of darkness of a diffraction pattern. Even when the light is thinned so that single photon particles pass through the slits one at a time the diffraction pattern remains. It is as if each particle knows that it is part of the pattern. But how can a single particle know where to go? Follow the particle with a detector to see exactly when and where it decides which slit to pass through and the diffraction pattern disappears. The Copenhagen interpretation of quantum mechanics claims that it is the measurement itself that changes reality.
8 | The Copenhagen interpretation raises problems about what defines a measurement.