Concrete way of doing abstract maths?

In summary, the conversation discusses the use of abstract mathematics in physics, specifically in the context of 'Beyond the Standard Model'. The question is raised whether doing this type of physics is a unique way of concretely representing abstract maths. The response points out that all kinds of physics can offer instances of representing abstract mathematics concretely, and questions the restriction to only certain types of physics as well as the use of the word "unique". It is also mentioned that abstraction is at the heart of all mathematics, and physics provides ways of concretely representing abstract concepts.

Is it a conrete way of doing abstract maths?

  • Yes

    Votes: 1 100.0%

  • No

    Votes: 0 0.0%
  • Total voters
    1
  • #1
tgt
522
2
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.
 
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  • #2
Define "doing abstract maths in a concrete manner."
 
  • #3
Tgt, can you rephrase your question? I have no idea what exactly you are asking. :confused:
 
  • #4
tgt said:
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.
 
  • #5
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.
 

Related to Concrete way of doing abstract maths?

1. What is the concrete way of doing abstract maths?

The concrete way of doing abstract maths is using real-life examples or physical objects to explain abstract mathematical concepts. This approach helps students to understand complex mathematical ideas by connecting them to something tangible or familiar.

2. How does the concrete way of doing abstract maths benefit students?

The concrete way of doing abstract maths can benefit students in several ways. It can help them to visualize abstract concepts, develop problem-solving skills, and improve their understanding of mathematical principles. It also makes learning more engaging and enjoyable for students.

3. Can the concrete way of doing abstract maths be used in all levels of education?

Yes, the concrete way of doing abstract maths can be used in all levels of education, from elementary school to university. It is a versatile approach that can be adapted to suit the needs and abilities of different students.

4. Are there any limitations to the concrete way of doing abstract maths?

While the concrete way of doing abstract maths is a useful tool, it may not be suitable for every mathematical concept. Some concepts may be too complex or abstract to be explained using physical objects. In such cases, a combination of concrete and abstract methods may be more effective.

5. How can teachers incorporate the concrete way of doing abstract maths in their lessons?

Teachers can incorporate the concrete way of doing abstract maths in their lessons by using manipulatives, real-life examples, or interactive activities. They can also encourage students to use their imagination and create their own concrete representations of abstract concepts.

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