Can mathematics disagree with the real world?

[phinds]

That only shows a circle doesn't exist when a "point" fails to represent matter. It doesn't deal with situations when a "point" represents some other aspect of the real world. As I said before, the question of whether a mathematical object exists is only a specific question when we define particular ways of mapping mathematical concepts to things in the real world. You are selecting one particular way of associating mathematical concepts with something in the real world. That creates an example where a mathematical object doesn't exist in the context of using that association. It doesn't eliminate the possibility that there are other ways of doing associations where the mathematical object does exist.

Fair enough. I'm an engineer and think in simple concrete terms so perhaps this is beyond me.

 

[fresh_42]

Can't we define circles in a nonflat space? I don't see a reason why we can't. They just won't satisfy the usual properties we're used to.

Of course. But that leaves us alone with a flat circle that cannot be found elsewhere. But even in a perfect flat space there is still a difference between the mathematical imagination of a circle and some imaginary curve in space. I think there can't even be a precise radius. But that's probably another discussion about the Planck length. And whether there is actually such a border or not, I believe there is a border beyond which we cannot measure or define anything.
But I confess guilty for being a Platonist.

 

[ehild]

Do we know what real world is? We can feel, see, smell, hear and touch different things and we call these real world. We have tools to extend our observations, and we say these non-direct observations also belong to the real world, but do they really?
On the other hand, I exist, I am real, so I belong to the real world. I do not know if my observations are real or not. Maybe all of them are shadows on the wall of the cave I live in, like in Plato's cave.
On the other hand, if I am real, my brain is real, and my thoughts really exist for me. I imagine a circle with my real brain. A circle is real for me, as set of points on a plane all at equal distance from the centre. If somebody tries to make that circle, it will not be perfect. It will be only a model of my circle.
And I can imagine a sphere in 3-dimensional space. And spheres in 4, 5, ...N dimensions. I even can derive their volume ( I can not now, I forgot what I had learned about it) . I can use my N-dimensional spheres to model gases, and derive their properties. And my observations about gases support these derivations. So are N-dimensional spheres not real? What we call real world at all?

 

[rootone]

I think if you were to drop a 10kg weight on your foot, you would come to the conclusion that kilograms are real.

 

[chiro]

You can quantize continuous objects in language just like discrete objects.

The only difference is what the information maps to and the basis for the language.

One can represent objects that have continuity and analyticity (analytic being based on complex variable calculus) with a finite number of symbols.

Just because information is quantized does not mean it has to correspond to some fixed discrete system representation.

 

[jack476]

Are there "things" mathematics describes that can't exist in the real world; things mathematics says can exist but are actually impossible to ever exist in the world we live in?

Also, are there things that do exist in our world that mathematics says can't exist? The obvious answer to me is no, but I am far from informed on any of this.

Your insights are greatly valued, to me.

Well, does math "exist" in the universe at all?

And yes, of course you can mathematically construct things that do not correspond directly to the real world. See for instance the physics engine of any video game.

And as for physics describing things that can't be mathematically explained, at least with current tools, that's pretty much the summary of the entire history of theoretical physics.

 

[lavinia]

It's hard to answer the question "Does math describe things that can't exist in the real world?" because math is one thing; the real world is another.

Strip the mathematical form completely out of the "real world" including our perceptions which are intrinsically geometrical - what is left over to be called the "real world"?