How to Make a Human Being: A Body of Evidence. Christopher Potter
George Eliot, Daniel Deronda
16 | There is something circular about our physical descriptions of the universe. We suspect the universe might well be infinite beyond the horizon of the visible universe, and yet the laws of nature that underpin that understanding are derived precisely out of the limit of how far we can see. The finite speed of light, the fixed amount of time that has passed since the Big Bang, and the set number of particles out of which the contents of this region of the universe are fashioned obey laws that we only understand in the form that we understand them because we cannot see further than we do. If we could see further, we might discover, for instance, that the speed of light is not a constant after all.
Nor would the laws of physics as we understand them necessarily apply to universes with different numbers of particles in them. Nothing could be predicted if the universe had only a few particles in it. Even the so-called laws of nature have something statistical about them. The laws of nature, as we understand them to be, are what we uncover in a universe of this kind, with this many particles in it, seen from this perspective.
17 | We have forged our idea of reality out of what we can see. Nature crooks a finger and draws us on, and we follow in the hope of finding out things truer than those we knew before; revelation follows revelation, curtain after curtain is pulled aside – this, then this, then this – but there is no inner sanctum. There are days, most days, when I believe that the universe will not be outrun, not by the scientific method, imagination, moral intuition, religious insight, nor any methods or combinations of methods of truth-seeking available to us.
We never get to the bottom of our understanding of the universe; there is always something more universal, more encompassing. We reach out to things truer but never arrive at the truth because there is no final destination. The starting conditions of the universe hold within them everything we don’t know about the physical universe moved to the edges of time and space.
18 | It requires a certain kind of stubbornness not to see, in the fine measurements that science makes, confirmation of the existence of an external reality. But there are days when I find that I am that stubborn. How can we be separate from reality? Reach out and you reach into the Big Bang everywhere about you. The universe and we its observers have grown up together from the one stuff. What could we be separate as?
Evidence for the existence of an external world
1 | That science works – it creates what we mean by progress – is proof and evidence enough for most of us that there is a world out there, separate from us and full of things that have separate existences. And then there is mathematics, the strongest evidence of all.
2 | For the philosopher René Descartes the only certainties were mathematics and theology.
The mathematics appear to be there in the behaviour of physical things and not merely imposed by us.
Roger Penrose, mathematical physicist and philosopher
3 | Roger Penrose believes that mathematics has real existence in a kind of Platonic world parallel – but somehow connected (by what mechanism is not known) – to our world of experience.
I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our ‘creations’, are simply our notes of our observations.
G.H. Hardy, A Mathematician’s Apology
Pure mathematics … seems to me a rock on which all idealism founders: 317 is a prime, not because we think it is, or because our minds are shaped in one way rather than another, but because it is, because mathematical reality is built that way.
Ibid.
4 | If we can believe with G.H. Hardy, Roger Penrose and others that mathematics is out there, and not intertwined with our own perspective on the world, then materialists may claim, as some do, that one day we will be able to write down, in the language of mathematics, laws that fully describe the physical world. Mathematics appears to be proof that the world can be transcended. Processes are real because they can be described by mathematics, which is itself real. Mathematics looks like proof that there is an external world, and that science is an investigation of its nature and substance.
Mathematics is the only religion that has proved itself a religion.1
F. de Sua, mathematician
The unreasonable effectiveness of mathematics.
Unattributed
The equation is smarter than I am.
The theoretical physicist Paul Dirac (1902–84), on his equation that predicted the existence of antiparticles
5 | Deeper descriptions of the universe require more and more sophisticated mathematical formalisms. Einstein took ten years to find the mathematical language in which to write his general theory of relativity. Unusually, the mathematical formalism that quantum mechanics is written in came first, and its interpretation – still argued over – came afterwards.
It is only the unsophisticated outsider who imagines mathematicians make discoveries by turning the handle of some miraculous machine.
G.H. Hardy, reminding us that mathematics is carried out by human beings, not machines
There is no sort of agreement about the nature of mathematical reality among either mathematicians or philosophers. Some hold that it is ‘mental’ and that in some sense we construct it, others that it is outside and independent of us. A man who could give a convincing account of mathematical reality would have solved very many of the most difficult problems of metaphysics. If he could include physical reality in his account, he would have solved them all.
G.H. Hardy
6 | Mathematical truths seem to have been out there waiting out the ages, to be discovered or not, by whoever or whatever.2 It looks as if idealism founders on the rocks of mathematics. Not quite. There are loopholes. The philosopher Immanuel Kant (1724–1804) argues that science is an exploration of the co-evolution of humans and the universe; the doll and the dolls’ house are inextricably entangled. Science is an exploration of that entanglement. Even mathematics, Kant believed, is not outside us: it is as much in our brains as in the outside world; yet it is less a mental construct than a product of the co-evolution of everything together, there being no meaningful separation between inside and outside. For Kant science is access to one kind of truth, another path being our sense of morality.
Two things fill the heart with renewed and increasing awe and reverence the more often and the more steadily that they are meditated on: the starry skies above me and the moral law inside me.
Immanuel Kant, Critique of Practical Reason
7 | Roger Penrose writes that mathematical models describe reality with ‘a precision enormously exceeding that of any description free of mathematics’. Clearly this is true but somewhat circular. Physics does precision, poetry does metaphor. They are incommensurate. Biology cares for decimal points only somewhat; poetry not at all.
Neither physicists nor philosophers have ever given any convincing account of what ‘physical reality’ is, or of how the physicist passes, from the confused mass of fact or sensation with which he starts, to the construction of the objects which he calls ‘real’. Thus we cannot be said to know what the subject matter of physics is; but this need not prevent us from understanding roughly what a physicist is trying to do. It is plain that he is trying to correlate the incoherent body of crude fact confronting him with some definite and orderly scheme of abstract relations, the kind of scheme he can borrow only from mathematics.
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