Concrete way of doing abstract maths?

[tgt]

Much of the physics in 'Beyond the Standard Model' use a lot of abstract mathematics. So I was just wondering is doing this type of physics a unique way of doing concrete abstract maths, if that makes any sense?

In other words being able to do abstract maths in a very concrete manner. Have a vote and discuss.

 

[cristo]

Define "doing abstract maths in a concrete manner."

 

[Demystifier]

Tgt, can you rephrase your question? I have no idea what exactly you are asking.

 

[marcus]

Much of the physics in 'Beyond the Standard Model' use a lot of abstract mathematics. So I was just wondering is doing [this?] type of physics a [unique?] way of doing concrete abstract maths, if that makes any sense?
...

Not just this type but ALL kinds of physics offer instances where abstract mathematical models and relationships are concretely realized. Think of the minimal surface shapes of soap films (bubbles on wire frame) or hanging chain (catenary) curves or patterns of mechanical vibration. orbits and trajectories. All kinds of physics shows cases of doing abstract math in concrete manner.

So I would question your seeming to restrict it to THIS type, namely Loop Quantum Gravity, Causal Triangulations, String etc. that we discuss in this forum. And I question your saying UNIQUE. Representations of mathematics are normally not unique. You may find in nature several different processes that obey the same differential equation.

What I'm saying is I question some minor details in how you worded things. But your basic idea has an element of truth in it. All mathematics is abstract---including calculus. You may think calculus is not abstract simply because you have gotten used to it, but abstraction is at the heart of all math (whether easy or hard, old or new). And many kinds of physics do indeed provide wonderful ways of concretely representing mathematics----the delight people find in this is one of the root motivations of physics ever since Kepler and Galileo.

 

[arivero]

I suposse it is abstract when you have not shown a model. In principle, every consistent set of axioms has a model; consistency implies existence.