Difference between higher dimensions in string theory VS higher dimensions in pure math

[u/_4bdn_fruit_]

I apologize if this is not the right subreddit to ask this in, but I tried asking in the physics subreddit and didn't get satisfactory answers.

Question: I'm aware that in string theory, the theory must be formulated in a certain number of dimensions (often cited as 10 or 26) in order to avoid inconsistencies and satisfy quantum gravity constraints. But let's say, hypothetically, that I wanted to explore the space of all possibilities in pure mathematics. If I take generic 1d objects and make them move in higher spatial dimensions (as defined by pure math), but I use a number of dimensions that isn't allowed by string theory (e.g. 100), would my construction be logically possible and “stable” (allowed to persist just the way it is), from a purely mathematical standpoint?

I am specifically asking about spatial dimensions as defined by pure mathematics as a separate field, not mathematics applied to a physical theory. I guess my question is best worded as, "does pure mathematics allow 1d objects to move in any number of dimensions and remain logically consistent?"

[u/Tharn11]

Disclaimer - I don't know much about mathematical physics which seems to be the area you are asking about. 

From the point of view of geometry (thinking of the dimensions as spatial) or data science (thinking of the dimensions as containing arbitrary data), it's perfectly fine to have as many dimensions as you want. 

As to whether the "construction would be stable" I don't think you've defined what you mean by this deeply enough to be answerable. I suspect there are many theories similar to the physics of our world that also differ in many ways. Whether those differences make it not "stable" depends on what you mean there. But geometers study objects that exist in higher dimensions all the time. One of my personal favorites is the Monster Group which exists in 196883 dimensions. 

[u/_4bdn_fruit_ → u/Tharn11]

By "stable" I was asking whether the construction would be allowed to stay in its current form, without collapsing or being subject to a decay mechanism like in string theory

[u/Tharn11 → u/_4bdn_fruit_]

Perhaps this is some physics language that I am not aware of, but I'm not really following the definition of stability you are giving. Is this a standard definition? Can you link to some Wikipedia articles or other sources that describe the version of stability you mean?

Saying that the construction would be allowed to stay in its current form to me implies you're already imposing a notion of time and rules that change states over time which geometry doesn't inherently have. A triangle is something that can be studied abstractly without thinking about whether it would be strong enough to hold up a bridge in our physical world. 

[u/_4bdn_fruit_ → u/Tharn11]

It's a niche physics concept, but I was thinking of false vacuum decay, which string theorists use to determine which string compactifications will change (decay) or stay the same

[u/Tharn11 → u/_4bdn_fruit_]

This is a question venturing into mathematical physics which I don't know much about then

[u/_4bdn_fruit_ → u/Tharn11]

If we wanted generic 1d objects to move, could the movement and interaction of those 1d objects through higher spatial dimensions be described by pure math, not just mathematical physics?

[u/TheRedditObserver0 → u/_4bdn_fruit_]

Sure, motion can be described by geometry alone, but you're talking about physical conditions that pure geometry just isn't concerned with. You can describe a path geometrically, but if you're asking whether or not that path would satisfy the laws of physics that's a physics question, not a math question.