"Moore's Law" (about steady increase to the power of transistors) has nothing to do with machine language. Transistors are used to have logical gates be set up; they don't change the machine language. Consider that machine language existed even before the transistor.
It's like saying that humans will develop wings because the life-expectancy will rise.
Maths isn't another word for physics, they differ very crucially in that math doesn't require sensory pick-up of a phenomenon. Secondly, that some being on earth - and more importantly humans - can pick up stuff in a certain way, doesn't have anything to do with how the stuff being translated thus by this special receiving intellect (human) is itself (in philosophy this argument is known as "the thing-in-itself").
That we pick up physical phenomena and for us they do get tied to rules which work as interpretations, has nothing to do with what those phenomena are and therefore also nothing to do with how a very different alien might pick up some or any of them.
Consider a few examples:
If a being has feet and can walk, it can move instinctively. It can also examine the physics of various types of movement.
If a being had feet but lost it, it can move by using some tech. Some sense of isomorphism may be sought (eg create mechanical feet).
If a being never had feet, it might be able to move in another way. Isomorphism to movement of something with legs may be lacking or worse.
If a being doesn't even have a sense of what movement is, no isomorphism is possible.
Now consider that, by definition, the same laws apply. One easily concludes that they will be picked up (if at all) only in a special manner, depending on the nature of the being itself. This is why a plea to "the same laws of x in the universe" isn't a good argument.
It's like saying that humans will develop wings because the life-expectancy will rise.
Maths isn't another word for physics, they differ very crucially in that math doesn't require sensory pick-up of a phenomenon. Secondly, that some being on earth - and more importantly humans - can pick up stuff in a certain way, doesn't have anything to do with how the stuff being translated thus by this special receiving intellect (human) is itself (in philosophy this argument is known as "the thing-in-itself").
That we pick up physical phenomena and for us they do get tied to rules which work as interpretations, has nothing to do with what those phenomena are and therefore also nothing to do with how a very different alien might pick up some or any of them.
Consider a few examples:
If a being has feet and can walk, it can move instinctively. It can also examine the physics of various types of movement.
If a being had feet but lost it, it can move by using some tech. Some sense of isomorphism may be sought (eg create mechanical feet).
If a being never had feet, it might be able to move in another way. Isomorphism to movement of something with legs may be lacking or worse.
If a being doesn't even have a sense of what movement is, no isomorphism is possible.
Now consider that, by definition, the same laws apply. One easily concludes that they will be picked up (if at all) only in a special manner, depending on the nature of the being itself. This is why a plea to "the same laws of x in the universe" isn't a good argument.
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) to position philosophy versus math.Moreover it took roughly 2000 years for that axiomatization to be reproached - the result of that was a huge crisis in math, the study of non-euclidian geometries and - ultimately - the attempt to find another basis for all math, this time not in geometry but formal logic (this attempt seems to also have failed, due to the limitative theorems).
