The second conclusion set out by Duhring from this is the “Law of Determinate Number”. He says,
“the accumulation of identities of any actual species of independent things is only conceivable as forming a determinate number”. Not only must the number of celestial bodies existing at any point of time be in itself determinate, the total number of all the tiniest independent particles of matter existing in the universe must also be determinate. This latter requisite is the real reason why no combination can be conceived without atoms. Every actual state of being divided invariably has finite determination, and must do so if the contradiction of the counted uncountable is to be avoided. For the same reason, not only must the number of the earth's revolutions round the sun up to the present time be finite though unstatable, but all periodical processes of nature must have had some beginning, and all differentiation, all the successive manifold elements of nature must have their roots in one self-identical state. This state may have existed from eternity without contradiction; but even this idea would be excluded if time in itself were composed of real parts and instead of being merely arbitrarily divided up by our minds through the positioning of possibilities.” (p 59)
To give Duhring his due, this is set out by him 50 years before Einstein described space-time in terms of a fabric of space, and nearly a century before the Big Bang theory similarly posited a counting back to an initial beginning of that space-time. He continues,
“The case is quite different with the real, and intrinsically differentiated content of time; this real filling of time with differentiable facts of a certain kind and the forms of being of this sphere are countable precisely because of their differentiation. If we imagine a state in which no change occurs and which in its self-identity offers no differences whatever in the order of succession, the more specialised idea of time is transformed into the more general idea of being. What the accumulation of empty duration would mean is quite unimaginable.” (p 59)
What neither Duhring nor Engels could conceive, at this point, is the role of Quantum Mechanics, and the reality that what appears as a steady state, at the macro-level, is a seething flux of instability at a sub-atomic level. Even Einstein could not accept the existence of uncertainty based on probability at the quantum level, famously saying, “God does not play dice with the Universe.”, and yet not only has Quantum Theory been proven over the last century, without it, almost the whole of modern electronics would be impossible without it. We now have the development of the first Quantum Computers, in which the bits rather than being either zeros or ones, are both simultaneously.
But, as Engels notes, although Duhring takes credit for these discoveries that “deepened”, and “sharpened” the understanding of space and time, the ideas had, in fact, been taken, line for line, from the work of Kant, in 1781, in The Critique of Pure Reason. Einstein is usually credited with overturning elements of Newtonian Physics, in his Theory of Relativity, for example, in relation to gravity, but Kant had begun his career by resolving the problems involved in Newton's steady-state model, by proposing the idea of an evolution of the Universe from an initial impulse, into the development of stars and galaxies etc.
“So that Herr Dühring's fame rests solely on his having tacked on the name — Law of Determinate Number — to an idea expressed by Kant, and on having made the discovery that there was once a time when as yet there was no time, though there was a world.” (p 60-61)
Kant, however, also set out, on the same basis, the opposite conclusion, that there is no beginning or end to space and time,
“and it is precisely in this that he finds the antinomy, the insoluble contradiction, that the one is just as demonstrable as the other. People of smaller calibre might perhaps fuel a little doubt here on account of “a Kant” having found an insoluble difficulty. But not so our valiant fabricator of “fundamentally original conclusions and views”; he cheerfully copies down as much of Kant’s antinomy as suits his purpose, and throws the rest aside.” (p 61)
The point, here, is not whether the one conclusion of Kant was right and the other wrong, as subsequent observation of the Universe has confirmed, but that no conclusion could be demonstrated true or false, purely on the basis of pure reason. It required observation of the real world to make that determination.
“The problem itself has a very simple solution. Eternity in time, infinity in space, signify from the start, and in the simple meaning of the words, that there is no end in any direction neither forwards nor backwards, upwards or downwards, to the right or to the left. This infinity is something quite different from that of an infinite series, for the latter always starts from one, with a first term. The inapplicability of this idea of series to our object becomes clear directly we apply it to space.” (p 61)
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