Maths vs Physics

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I feel like I'm missing the point of this discussion but to me, math is the fundamental building block of physics. And math can exist without physics but physics can not exist without math.

Imaginary numbers and infinity are prime examples. Both do not exist in the physical world but are mathematical concepts that are used to describe physical things indirectly. A simple example is limits in calculus which uses the concept of infinity and in-doing so calculus describes everything from velocity and acceleration to magnetic flux. Imaginary numbers are also useful in describing various physical phenomena such as electrical voltage in AC circuits and certain themes in fluid dynamics.

As to the genesis of maths and physics? I would say maths ultimately "descended" from physical objects. Rudimentary counting systems were probably based on fingers and toes as any linguist can tell you based on the roots of ancient number names.

 

[MorkandMindy]

Surely without maths you can't have physics.

The definition of physics is pretty much that it is a quantitative theory describing the Universe around us, so if 'quantitative' is part of the definition then maths is an indispensable part of physics.

But what about the indispensibility thesis thing (was it Quine?). If maths does not refer us to facts, then physics that depends on maths cannot be true of the factual world.

If by the term 'fundamental' you mean it relies on no other human thought structure, and therefore only on the world around us and the way the human brain works, then both physics and maths are fundamental.

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I think we get our concepts of mathematics from experience, and they are an implication of our powers of abstraction.

eudaimonia,

Mark

Yes, experiments with very young babies showed they did simple adding and subtracting instinctively.


I would also comment that the claim of being 'fundamental' is supported by the involvement of the Ancient Greeks in both mathematics and science. The philosophical basis for both was also debated; Plato was a champion of rationalism and Aristotle of empiricism, mathematics fits into rationalism, and physics is empirical although the speculation is a rational endeavour based on existing empirical knowledge.

So although both are fundamental, they are in a sense rivals as well as complementary.