'The Peculiar Math That Could Underlie the Laws of Nature'

[Stranger]

No it's just a statement that happens to be true.

How do you know?

[Walt Zingmatilder]

How does my statement that we use maths as a tool to describe the physical world mean that all maths has to describe the physical world?

Maths can be used as a tool to describe the physical world, that doesn't mean it can't be used for other things or even that its primary purpose is to describe the physical world.

what you have written is the qualification and clarification I think I can agree on now that you have agreed maths has a wider role.

Physics though seems to dependent on maths in a way maths is not dependent on physics by dint that maths can be used for other things and the physical world might not,as you suggest, be it's primary purpose.

[Walt Zingmatilder]

How do you know?

Good question.

[jeremyp]

How do you know?

The physical world is not made of maths. Maths is about abstract concepts and we are just lucky that the physical world can be represented (approximately) by abstract mathematical concepts. For example, there is an equation that describes an electron, but an electron is not that equation and one day we may discover that it doesn't always obey the equation.

[jeremyp]

Physics though seems to dependent on maths

If by "physics" you mean the scientific subject invented by humans, I would agree with you. Maths is the language we use to describe the physical world and make predictions about it.

If you mean the physical world, I would disagree with you. Maths is its description, not its prescription.

[Stranger]

The physical world is not made of maths. Maths is about abstract concepts and we are just lucky that the physical world can be represented (approximately) by abstract mathematical concepts. For example, there is an equation that describes an electron, but an electron is not that equation and one day we may discover that it doesn't always obey the equation.

That's just a further statement of your view, not how you know it to be true. I'm not saying you're wrong but I don't see how you can rule out the idea that what you are calling 'lucky' doesn't have a greater significance. How do you know that the ideas of (for example) Tegmark are wrong?

[Walt Zingmatilder]

If by "physics" you mean the scientific subject invented by humans, I would agree with you. Maths is the language we use to describe the physical world and make predictions about it.

If you mean the physical world, I would disagree with you. Maths is its description, not its prescription.

I mean the physical world. Several physicists and others would disagree with you. Maths has arisen which is not dependent on physical observation. On the other hand no physics or observation of the physical has been made that does not conform to mathematical principles and indeed much of the physical has been predicted by pure mathematics.


I don't think you have grasped the significance of the maths which is not descriptive if anything in the physical world eg the maths used to model simulated universes. Also there is the independence of maths from physics.... a suitable machine calculating the graph of a quadratic equation would yield the same result whether in a freezer or a furnace.


Because of these properties of maths Tegmark et al question a simple defining of maths as a tool or description of the observable.

[jeremyp]

On the other hand no physics or observation of the physical has been made that does not conform to mathematical principles and indeed much of the physical has been predicted by pure mathematics.

What mathematical principle does the orbit of the Earth around theSun "conform to"? 150 years ago, people would have said it conforms to Newton's gravitational equation but then Einstein came up with a better theory. Does the Earth's orbit conform to general relativity? OR is general relativity a description of that the Earth does? It would be a brave person who would say GR will never be superseded by a better description. Maybe the real Universe cannot be modelled accurately by maths at all. Perhaps we can only find better and better but ultimately wrong approximations.

I don't think you have grasped the significance of the maths which is not descriptive if anything in the physical world eg the maths used to model simulated universes. Also there is the independence of maths from physics.... a suitable machine calculating the graph of a quadratic equation would yield the same result whether in a freezer or a furnace.

I don't think you grasp the fact that you offered up a false dichotomy.

[Stranger]

Maybe the real Universe cannot be modelled accurately by maths at all. Perhaps we can only find better and better but ultimately wrong approximations.

Maybe so, but equally maybe there is a mathematical theory of everything and maybe what you referred to as "lucky" in #28 isn't luck at all and is indicative of some necessary relationship between mathematics and the physical universe.

How are you so sure?

[jeremyp]

Maybe so, but equally maybe there is a mathematical theory of everything and maybe what you referred to as "lucky" in #28 isn't luck at all and is indicative of some necessary relationship between mathematics and the physical universe.

How are you so sure?

The theory of everything wouldn’t actually be everything, it would just describe everything, perhaps perfectly, but we’ll never know.

[Stranger]

The theory of everything wouldn’t actually be everything, it would just describe everything, perhaps perfectly, but we’ll never know.

I agree we could never know but this is really just another restatement of your position, not the reason(s) why you are so sure.

The relationship between mathematics and the physical universe has been debated for millennia, yet you seem confident enough to proclaim the matter settled.

[jeremyp]

I agree we could never know but this is really just another restatement of your position, not the reason(s) why you are so sure.

The relationship between mathematics and the physical universe has been debated for millennia, yet you seem confident enough to proclaim the matter settled.

Maths is a language for describing abstract objects. It's not "stuff" in the sense that the Universe is stuff. It's as nonsensical to say the Universe is made of mathematics as to say that this cup of coffee is made of the English language.

[SusanDoris]

Maths is a language for describing abstract objects. It's not "stuff" in the sense that the Universe is stuff. It's as nonsensical to say the Universe is made of mathematics as to say that this cup of coffee is made of the English language.

I'm going to put that statement in a safe place - and try to remember where it is - so that I can quote it when appropriate.

[Stranger]

Maths is a language for describing abstract objects. It's not "stuff" in the sense that the Universe is stuff. It's as nonsensical to say the Universe is made of mathematics as to say that this cup of coffee is made of the English language.

Another restatement of your position. The problem is that we have no idea what 'stuff' is and, more specifically, we don't know why there seems to be a close relationship between 'stuff' and mathematics, which have led may people, over the course of millennia, to speculate about some necessary connection or even identity (Tegmark). Many mathematician feel that mathematics is discovered rather than invented, so we would then have two 'systems' we are discovering with a very close correspondence.

I still have no idea where you get the confidence to dismiss all that and call the relationship between the physical world and mathematics 'lucky'.