Can you read math?

[Robert]

You may wish to read my starting post in the neuroscience forum for some background information to this post.

I'm curious about something. When I read in my primary language, English, I have no problem. I don't have to think about the words, the figures of speech, the gramatical structure of the sentence, etc. I just read it and the story, ideas, facts, etc just flow into my brain. I don't stop and think about how to read, it just happens on its own. Like riding a bike, after a while you don't think about how to do it, you just do it.

When I look at math, I can figure out the simple stuff, but I have to remember my trigonometry, my rules of algebra, how to integrate and I'll have to go to reference books to help me out. But I don't do math full time and haven't been trained in math beyond the engineering classes I took in college. But to someone trained extensively in math who does math full time, can math become like riding a bike. Do the better mathematicians read math without thinking so much about it. Do the equations form mental images, tell stories, give knowledge like the words do in a book.

[mkirkpatrick]

Not being a mathamatian either full time or part time,I do not know the answer to this
question Robert,but to hazard a guess I would think,that those who lived maths daily
and were spending hours regulary accessing numbers and equations,would read maths
much like you or me would read the newspaper.
Practise at anything makes perfect,maths is no exeption.

BTW Robert it is good to see you posting more,please keep it up.


regards michael.

[neutralino]

I've been flicking through the maths forum, and found this rather old thread. I hope no-one minds me reopening the discussion!

I think this topic is a really interesting one to discuss. There are, at least I think anyway, analogies that can be drawn between the english language and the language of mathematics. In fact one of my housemates a few years ago, who wasn't a mathematician, stumbled upon some of my notes that I'd left lying around and said to me "this is like a different language!" I think the analogy extends to the fact that, even if one knows what the symbols mean in a mathematical expression, there's nothing to say that he will know what the expression is saying. I compare this to one knowing what the words mean in a sentence, but not being able to understand what the sentence is trying to describe.

To answer some of the questions in the thread starter-- Do the equations form mental images, tell stories, give knowledge like the words do in a book.-- I'd say that the analogy breaks when asking whether mathematics forms mental images. Of course, some mathematical expressions do provoke mental images; for example a mathematician would see the equation [imath]y=x^2[/imath] and immediately think of a parabola; or the equation [imath]x^2+y^2=1[/imath] and think of the unit circle. However, much of mathematics is very abstract, and so direct mental images are impossible to construct. I'm also not sure that it would be correct to say that mathematical equations tell a story in all cases. However, if you think of a proof of some theorem, then I think it is quite like a story, in that we usually start with an equation at the beginning, and then continue with mathematics until we have the proven result at the end.

Mathematics definitely gives us knowledge; however instead of comparing equations to words, I would compare an equation to a sentence, for the reasons I've mentioned above.

Finally, I think it is like "riding a bike" in some sense. For example, we don't have to convince ourselves why we can use the formula [imath]\sin(2x)=2\sin(x)\cos(x)[/imath] everytime we use it, in a way that we do not need to convince ourselves that it is safe to take our feet off the floor, and start riding a bike. However, I can assure you that all mathematicians looks things up in books, since there is no way that anyone can hold that much knowledge inside their mind. In this sense, I think that it is a weak analogy; but still somewhat there.

[Profpat]

Hi Neutralino;

Can you give me a mental image of E=mc2.

I keep on imagining that mass, say my computer laptop explodes into a giant circle or perhaps sphere of tiny energy particles.

Any help on a description of this event would be helpful.

Best,

Pat

[neutralino]

That's a tough one to actually picture, Pat. I guess I just see the equation as saying that mass and energy are equivalent in relativity. More precisely, it says that the rest mass of every body has an associated energy; namely the rest-mass energy.

I don't particular picture anything when I look at that equation, however.

[Profpat]

Thanks Neutralino;

I would like to expand on this just a bit.

Photons, if I'm not mistaken, are TWO (2)dimensional transverse waves. Being tranverse it does have a 3 dimensional or particle effect, having the qualities of L, W, and H.

And so I equate energy as a 2 dimensional entity.

I also speculate that the photon does have the smallest quanity of mass. I believe this has been addressed before in physics, with no evidence of this , but still a possibilty that they may have an immeasurable minute mass.

Now a second question is there such a thing as conservation of gravity?

Thanks for your help,

Pat

[neutralino]

I also speculate that the photon does have the smallest quanity of mass. I believe this has been addressed before in physics, with no evidence of this , but still a possibilty that they may have an immeasurable minute mass.

A photon does not have rest mass according to current theory. This is because a photon is never at rest; that is, it always travels at the speed of light; and so it cannot have a rest mass. Of course, I'm not saying that we will ever be able to measure the mass of a photon to be zero, but theory says it is, and we have no reason to doubt the theory. See here
for more info.

Now a second question is there such a thing as conservation of gravity?

I'm not entirely sure what you mean by this, but I'd say no, such a thing does not exist.

[N0B0DY]

Would the helicity of the photon be in the form of a tube or beads? Perhaps the surface of the photons constitute their mass, and since there is no evidence for a perfect conversion, the conservation of gravity would be in the form of that minute mass.

Any thoughts on G=mc^2, Neutralino?

[neutralino]

Any thoughts on G=mc^2, Neutralino?

G is a constant; as is c. So, this equation says that the mass of every body is equal to some constant. That is, I have the same mass as an electron...

[N0B0DY]

Could you explain a little more how the constants are set, neutralino? For instance, what is it that limits "c" to approx. 300,000 km/s in the vacuum?