# Translating english into mathematical equations

1. May 27, 2010

### cs23

I heard that doing physics is basically translating english into mathematical equations, Could someone elaborate on this, and provide an example?

thanks"

2. May 27, 2010

### fasterthanjoao

I'm really not sure what you're looking for... I guess the person that said this is making the observation that physics is the mathematics of the universe. For an example, think about the fact that the Earth moves around the Sun, with a period of 1 year. Physics contains the mathematics necessary to describe this, allowing you to predict where the Earth will be in the future. Anything you can think of really can be covered by your question, consider: a cup of tea will take maybe 10 minutes to cool down? Differential equations in heat transfer will allow you to estimate the amount of heat leaving the tea, and give a much better estimate - thus helping you to make the optimal cup of tea!

I'm not sure if that's what you were asking.. otherwise, have a look at the definition of 'physics' on wikipedia.

3. May 27, 2010

### cs23

sorry i was confusing.

I meant to say. When solving physics problems, you need to translate the statement into mathematical equations in order to solve the problem

4. May 27, 2010

### fasterthanjoao

I don't really see how this is any different..? A question will describe the problem - "how long does it take for this cup of tea to cool down?" and you use a model of second order differential equations to work it out.

It isn't a case of 'translating' the problem so much as understanding the mathematics that will help you solve it. With practice, when someone asks a question you will be able to think of the equations that would be relevant in tackling such an issue.

5. May 27, 2010

### jgm340

Physics is not really a matter of "translating english into mathematical equations".

English and Mathematics are both languages used to describe phenomena studied in physics. Mathematics tends to be used more often because it is able to communicate complicated concepts very concisely and unambiguously.

As an example, I'll translate an equation into English:

EQUATION: velocity = displacement / time

TRANSLATION: If an object is moving in a straight line, and it is not speeding up or slowing down, then a quantity called "velocity" is fixed. At any point in time, if we measure it's "displacement" from a starting point (the straight line distance from the starting point to it's current location, along with an associated direction) and we divide this by the amount of time which has elapsed since the object was at the starting point (we call this quantity "time"), we will find that this equals the fixed quantity "velocity".

You can see, however, that even my translation references mathematical concepts. My English explanation still covers only a small bit of what is meant by the equation above! If I were to give a complete explanation, I would have to say how this also implies that if I allow an object moving at a uniform velocity to travel for double the amount of time, it will go twice as far. I would have to make many such statements to completely convey what is represented by the equation.

You can see that a simple statement like v=d/t actually has a lot of assumptions built into it. When you study physics, you need to be aware of and understand all these assumptions, and all the implications of the relationships implied by the equations.

Now, when learning physics, you will often face word problems written in mixed English/math. You will have to interpret statements in English and understand their meanings in the same way you understand a mathematical statement. Most of the time, the English statements are merely statements that certain assumptions can be made, which in turn allow you to use certain equations. For example, "frictionless inclined plane" allows you to know that the object is traveling in a straight line, and that there is no friction. This allows you to use certain equations specific to these cases.

The reason you are often given problems like these while learning physics is because physics is NOT math. Physics is an appropriate application of math to understanding our world, and to understand physics, one must be able to describe phenomenon in the language of mathematics, not merely solve equations. The study of physics is, in it's most basic sense, the study of assumptions about our world.

(On a side note, mathematics is the study of the implications of assumptions, and so physics and math go hand in hand, but there is a very clear distinction between the two.)

6. May 27, 2010

### Sean1218

I was actually sort of wondering the same thing. How does math tell you, for example, that everything is actually made of little strings? I don't really get how you get to that conclusion from numbers.

Last edited: May 27, 2010
7. May 27, 2010

### jgm340

It doesn't. At least not directly.

In most aspects, physics is a hard science. This means that claims are supported by "observation". I put "observation" in quotes, because what it actually means is "prediction". It's gotten to the point where all observations are performed so indirectly that it's almost hard to call them observations anymore (Ex: No one has seen an electron). We accept a claim in physics only if it accurately predicts the results of experiments.

Historically, we have seen that despite all its complexity, the physical world is predictable enough to be modeled by mathematics. Now, a mathematical model is useful in physics so far as it remains true. For most purposes Newtonian models are perfectly sufficient, but they fail at high speeds, and at small scales. A lot of the work in physics, then, is testing the limits of a theory: is it still true in this case, or in that one?

The thing is there are an infinite number of potential ways to model the world. One potential way to explain the world is to say that some omnipotent being dictates every occurrence. However, physicists typically stick to the rule that "simpler is better". That is, if we can find a few equations from which we can predict ANY known phenomena, then that's a better explanation than a whole bunch of equations. If we can find only a few fundamental forces, then that's better than a whole bunch. If we can find only a few basic particles, then that's better than a whole bunch (although that's getting into chemistry).

[Aside: it may seem arbitrary or even unscientific to rely on the idea of "simpler is better", especially since our human preference for simplicity biases us so much towards accepting simpler explanations more readily. However, the majority of the body of work in physics has not to do with developing theories, but with testing "laws". A theory is an explanation, but a law is merely a description of the outcome of experimentation. For example, look at "F=ma". While it could be thought of as a theory, it actually represents a series of experiments which physicists have conducted over centuries. Perhaps there aren't naturally such quantities as "mass", "acceleration" and "force", but even still the measured outcomes experimentally fit exactly with the equation, and so we call it a law. In this sense, whether or not we represent our experimental data as a giant chart with the results and conditions of all experiments or just as a simple equation, the basis of physics is entirely scientific. In other words, physics is always asking "How?", but it rests on the scientific foundation of "What Happens?"]

So, physicists are trying to find a single, simple model that explains all known phenomena. String theory is that attempt. Different physicists/mathematicians have been trying to find mathematical models which accurately predict all known phenomenon. The idea is that once a model checks out mathematically (by which I mean that all known laws can be derived from it), then we will try to go about testing it by trying to reproduce a phenomenon yet to be observed which the model predicts ought to be possible.

If a new model accurately predicts all known phenomena and more, then it is accepted as being the best explanation as to how things work. However, physics never actually scientifically proves that there ARE tiny little strings. It can't even prove that there are such things as atoms! It can't even prove there is such thing as "matter" in our usual conception! All it proves (or is trying to prove) is that if we imagine that there are little strings that behave a certain way, then we can predict phenomena.