Why do theorys need mathmatics?

[cameron marical]

I dont see a necessity for theorys to have mathmatics to back them up, i dont even see how math can back up a theory an any way other than helping to show what the theory explains.

 

Im probably really wrong, and i dont mean to sound stupid, i was just wondering.

 

Thanks.

[iNow]

So, if you predict that when you kick a ball... how will you describe the force imparted to it and how far it will go and where it will land?

 

I'm gonna kick it "hard."

Okay... what does that mean?

 

It's gonna go "far."

Okay... what does that mean?

 

It's gonna go "that way."

Okay... where's it going to land, though?

 

It will take a "little while" to get there.

Okay... how much is a "little while?"

 

 

 

Math allows you to be precise. I'm going to impart X force to the ball at N vector and it will land at Z location in T seconds...

 

It's about precision. Words fail you since we all have fuzzy meanings when we interpret words. Math... well... that is consistent no matter who you are or what you're doing...

[Mr Skeptic]

For the same reason you need math to see.

[ajb]

In physics the theory is used synonymously with mathematical model. In practice theories have to use mathematics as they are mathematical constructs.

 

I think your meaning of theory is the physical interpretation of what is usually meant by a theory. Really this is a "wordy" description of the mathematics and how it relates to observations of nature.

[Severian]

Theories don't need mathematics.

 

Mathematics is just a language. The logical implications embedded within mathematics are very very useful in using physical theories to make predictions. You would really struggle to make these predictions without mathematics, but in principle it could be done.

 

You would really handicap yourself without using mathematics though.

[Bob_for_short]

I dont see a necessity for theorys to have mathmatics to back them up, i dont even see how math can back up a theory an any way other than helping to show what the theory explains.

 

Im probably really wrong, and i dont mean to sound stupid, i was just wondering.

 

Thanks.

 

In physics many things resemble accounting: between objects there are exchanges with energy, momentum, angular momentum, for example. Math helps do this bookkeeping, if you like.

 

Bob.

[GDG]

I dont see a necessity for theorys to have mathmatics to back them up, i dont even see how math can back up a theory an any way other than helping to show what the theory explains.

 

Im probably really wrong, and i dont mean to sound stupid, i was just wondering.

 

Thanks.

 

Nothing wrong with your question: questions like yours sometimes force us to reconsider our assumptions, which can be a profitable thing to do

 

Theories do not universally require math. For example, you might hypothesize that the world is round, and that therefore when you watch ships sailing away out to sea, the lower part of the ship will disappear from view before the top of the mast, as the ship sails past the horizon. No math required. (OK, perhaps we are dealing with geometry even here...)

 

However, most scientific theories concern things about which we already have some understanding. If your theory is to succeed and be accepted, it will need to make predictions that (a) differ from the prevailing view, and (b) are confirmed by experiment. Sometimes those differences may be qualitative, but most of the time they're going to be quantitative, e.g., your theory predicts a measurement of X+0.00067 instead of the X given by currently-accepted theory. In such cases, mathematics are almost essential (and often, lots and lots of very detailed calculations) to prove your point.

 

And then, of course, you get to cosmology and particle physics, where mathematics seems to drive the theories, for example, M-theory which seems to be based on elegant (but difficult) mathematical and topological arguments -- perhaps inevitable due to the difficulty of performing confirmatory experiments...

[Mokele]

Technically, not all theories *need* mathematics, though it can enhance their utility.

 

Consider the Germ Theory of Disease. Or the theory that birds evolved from dinosaurs.

 

Evolution, when first proposed, didn't rely on math at all (it was later found to be useful, once we discovered genes).

[ljogle]

Since I am a neophyte to not only the forum, but to the world of inventing, I can see both sides of this question clearly. I have a vision, I can document that vision, but without math I cannot prove the theories which support the vision. Therefore my visions require math for proof and my math requires that I hire someone who understands the language to aid with my visions.

[north]

I dont see a necessity for theorys to have mathmatics to back them up, i dont even see how math can back up a theory an any way other than helping to show what the theory explains.

 

Im probably really wrong, and i dont mean to sound stupid, i was just wondering.

 

Thanks.

 

hmm...

 

a theory needs imagination

 

mathematics is guided by the imagination

[ajb]

Technically, not all theories *need* mathematics, though it can enhance their utility.

 

Consider the Germ Theory of Disease. Or the theory that birds evolved from dinosaurs.

 

Evolution, when first proposed, didn't rely on math at all (it was later found to be useful, once we discovered genes).

 

This can be a big source of confusion.

 

The notion of a theory in physics is different to the notion of a theory in biology and indeed mathematics. As this post is in general physics I assume (maybe incorrectly) that cameron marical is asking about theories of physics. In physics there quite a blur between the mathematical and observational aspects of a theory. By this a mean a physical theory is usually taken to mean a mathematical model, the question is then how to relate this to observation/experiments. I think one should take the attitude that the only thing "real" in a theory is what can be measured. Everything else is mathematics and not physical.

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hmm...

 

a theory needs imagination

 

mathematics is guided by the imagination

 

I think even more poignant is that mathematics can also guide the imagination, and then the physical theories.

 

I find the opening passage of Geroch's book quite appropriate at this stage...

 

 

 

“One sometimes hears expressed the view that some sort of uncertainty principle operates in the interaction between mathematics and physics: the greater the mathematical care used to formulate a concept, the less physical insight to be gained from the formulation. It is not difficult to imagine how such a viewpoint could become popular. It is often the case that the essential physical ideas of a discussion are smothered by mathematics through excessive definitions, concern over irrelevant generality, etc. Nonetheless, one can make a case that mathematics as mathematics, if used thoughtfully, is almost always useful–and occasionally essential–to progress in theoretical physics.”

 

Robert Geroch, Mathematical Physics, Chicago Lectures in Physics, (1985) 351p