Infinity is a concept full of contradictions, such as that it is, itself, composed of purely finite terms. But, these finite terms are, themselves, mathematical constructs, which, in reality, are only approximations, required for purposes of categorisation and delineation, in order to calculate. In the real world, there is no such clear delineation, but rather fuzziness at the boundaries, where quantity turns into quality, and where uncertainty and probability reign supreme. One test of whether we live in a computer simulation, it has been suggested, is that, any such simulation, based upon mathematics, would require, at the most minute scale, to be comprised of discrete segments, rather than being continuous. At the boundary of these discrete segments, there would be detectable breaks, and jumps.
“The limited nature of the material world leads no less to contradictions than its unlimited nature, and every attempt to eliminate these contradictions leads, as we have seen, to new and worse contradictions. It is just because infinity is a contradiction that it is an infinite process, unrolling endlessly in time and in space. The removal of the contradiction would be the end of infinity. Hegel already understood this quite correctly, and for that reason treated the gentlemen who chop logic over this contradiction with well-merited contempt.” (p 63-4)
In Duhring's argument, time has a beginning, the equivalent to 1 in a numerical sequence, and as noted, our current space-time, likewise, has a beginning, the Big Bang. However,
“The subject at issue is not the concept of time, but real time, which Herr Dühring will by no means rid himself of so cheaply. In the second place, however much the concept of time may be converted into the more general idea of being, this takes us not one step further. For the basic forms of all being are space and time, and being out of time is just as gross an absurdity as being out of space.” (p 64)
The only modification that the concepts of space-time, which is itself incorporated in Engels' statement, here, long before it was theorised by Einstein, necessitates, is this distinction between our current space-time, i.e. post Big Bang, as against what preceded it, and what follows it. Engels is wrong when he says of our present space-time,
“time, does not in itself consist of real parts” (p 64)
After Einstein, we know that time, as space-time, can be stretched like a fabric, along with space. But, this does not undermine the substance and significance of Engels argument.
“According to Herr Dühring time exists only through change; and change does not exist in and through time. Just because time is different from change, is independent it is possible to measure it by change, for measuring always requires something different what is to be measured. And time in which no recognisable changes occur is very far removed from not being time at all; rather it is pure time, untouched by any foreign admixtures, that is, real time, time as such. In fact, if we want to grasp the idea of time in all its purity, divorced from all foreign and improper admixtures, we are compelled to put aside, as not being relevant here, all the various events which occur simultaneously or successively in time, and in this way to imagine a time in which nothing happens. In this way, we have not let the concept of time be submerged in the general idea of being, but have thereby for the first time arrived at the pure concept of time.” (p 65)
In other words, it is time as an abstraction from any specific manifestation, such as our current space-time, just as Marx, in arriving at the concept of labour, as the essence of value, sets out that it is labour in the abstract, not any specific manifestation of labour, such as wage-labour, slave-labour, or corvee-labour, and so on.
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