35. Chaos

In no other case than the right-angled triangle towards the mathematician is the human being towards the mathematical thinker. A mathematical thinker is too inclined to overlook this. He easily believes that he can talk about the world problem as if it were a mathematical problem. Paul Mongré falls into this error. An example. He puts forward the following idea, which has already been asserted elsewhere: "Because of the relativity of our measurement, the absolute dimensions of the spatial formations do not fall into our consciousness - we would not notice anything if the universe suddenly increased or decreased its real dimensions a hundredfold, since both the objects to be measured and our scales participate in this overall change. Does this mean that the universe is really, in the transcendentally realistic sense, a rubber ball that swells or shrinks at will? No, but only that beyond our relative perception of size, the concept of spatial size becomes irrelevant." That is mathematical thinking. But suppose someone were to go further and draw the conclusion from this undoubtedly true thought: if everything outside our consciousness loses its validity in the same way as the determinations of size seem to do, then it could also be correct that within our consciousness we rightly regard ourselves as descended from lower organisms; outside, however, a demon could be at work that apes human formations. For mathematical thinking there is no objection to drawing such a conclusion. If it were valid, then I would only ever be dealing with conclusions, with truths that apply to me - within my consciousness; outside of it would lie endless possibility - for me chaos, about which I know nothing, about which I am not even allowed to talk without having to make it clear to myself that I am going beyond what I am allowed to assert. Two things would then be certain. I would have truths; these would apply to me. But they apply to nothing but me. I seek the laws according to which the things that are spread out before my senses work; I seek the laws of my own working. But apart from me, none of this could be as it appears to me. Instead of the laws of light, there could be a demon at work, instead of my psychological and physiological laws, according to which I direct my foot to move forward, there could be a demon pushing it forward. That is one thing. The other is: I know the limits to which my truths extend. I build a lawful world for myself within these limits. And yet I say: this far and no further. The mathematician says: I measure things. They have this certain size in relation to my scale. If everything and therefore my scale grows, then I am at the end. I can't go any further. And for me, we are at a crucial point. Is there any point in talking about size if we can't measure it? What does it mean to say that the universe is getting bigger if nothing retains its former size? Has the universe really become larger if nothing has retained its original size? Does a size exist at all without being compared with another? But if it makes no sense to talk of increasing size where there is no measurement, does it not also make sense to allow measurement to apply unconditionally where there is measurement? Or, from a broader perspective: if it makes no sense to speak of an animal descent of man outside our world, is it not also correct to say that it makes absolute sense within this world and cannot be otherwise?