Reality and representations

[TillEulenspiegel]

I am in a few discussions on various boards and I wonder what the general outlook is here regarding mathematical descriptions of real physical phenomena. Do you view mathematical descriptions of real systems, objects and behaviors to forever be defined as axiomatic ( the catholic definition ) , or is there a basis to view them as an attempt to define real world objects, Etc. ( I.E. where the case gives rise to the description rather then the other way around)?

The two are not necessarily mutually exclusive , but I view certain theorem rather then the postulate giving rise to the reality as coupled to real world phenomenon as descriptions of the reality , such as universal constants , Pythagorean theorem, etc.. With all apologies to the QM folks , I think that is an example a fishing expedition where the proponents are trying to define the reality by the model.

Thoughts?

 

[Badly Shaved Monkey]

I've asked this before and I think it is unknowable.

Is the Universe some kind of embodiment of mathematics or are our mathematical models always separate from the thing called reality? Might we asymptotically approach reality with our modelling, but never bridge the last gap or would a sufficiently detailed model itself induce creation of a reality?

Me dunno. Me just kick homeopaths.

 

[sorgoth]

I've asked this before and I think it is unknowable.

Is the Universe some kind of embodiment of mathematics or are our mathematical models always separate from the thing called reality?

Why can't the mathematics describe our universe while being part of it?

We give everything in the universe a number. We invented the numbers themselves, but what they describe is very real.
In a sense, our perception of red is simply our brain showing us whatever nanometer wavelengths (Anyone know the range for red?), as sound is just wavelengths of air. Our brain processes these things as senses, while we process them as numbers.

 

[rppa]

I am in a few discussions on various boards and I wonder what the general outlook is here regarding mathematical descriptions of real physical phenomena. Do you view mathematical descriptions of real systems, objects and behaviors to forever be defined as axiomatic ( the catholic definition ) , or is there a basis to view them as an attempt to define real world objects, Etc. ( I.E. where the case gives rise to the description rather then the other way around)?

Why would you expect there to be a general outlook? Certainly this depends at least partly on training.

My training is in physics. As such, I regard mathematical representations of nature as (at best imperfect) descriptions. Certainly they aren't axiomatic. They are hypotheses that fit the best known data, and at any moment they could be changed by new data.

The two are not necessarily mutually exclusive , but I view certain theorem rather then the postulate giving rise to the reality as coupled to real world phenomenon as descriptions of the reality , such as universal constants , Pythagorean theorem, etc..

You seem to be treating mathematics and physics interchangeably. They're not the same thing. Mathematics starts with its own axiomatic system and builds up from there. By necessity it is self-consistent. We don't know what the axioms of the universe are, so physics is stuck with trying to guess them.

There's no such thing as an experiment which can rule the Pythagorean theorem invalid within the axiomatic system where it is built.

With all apologies to the QM folks , I think that is an example a fishing expedition where the proponents are trying to define the reality by the model.

With all apologies to you, I have no idea what you're trying to say about QM, but I suspect that your view of QM bears very little resemblance to actual QM.

"QM folks", like any other physics folks, are people who write down a set of equations, use them to predict results of experiments, then see if the experiments match the predictions. So far, they do. That's all we ask of any physical theory, and all we can ask.

 

[Zombified]

My personal view: mathematics is a language for reasoning. The quantities and concepts in mathematics are abstractions that are helpful for reasoning, but they aren't necessarily "real things".

When applied to quantities in physics or another science, what you are doing is,

(a) defining a procedure for extracting a set of numbers from a situation (operational measurements)

(b) implicitly hypothesizing that those measurements do in fact correspond to numbers and therefore the rules of arithmetic etc. apply,

(c) postulating a set of rules for relating measurements to one another (e.g. your theory)

(d) making quantitative predictions about measurements based on logical conclusions that necessarily follow from (c)

(e) testing those predictions

If your tests fail then either you've got an inappropriate definition of the quantity or the rules you've chosen for your theory are wrong or incomplete.

For your theory (c) it's helpful, for understanding and communicating, if it's a nice, easily visualized model, but it's not strictly speaking necessary. You can pick whatever mathematical system you want to make the theory work. For example, Newtonian mechanics "chooses" Euclidean geometry, whereas general relativity "chooses" a more general geometry. Neither geometry is "true," it's just that they are applicable to certain theories, and those theories work or don't work, as the case may be.