I’m a second-year engineering student, and I’m starting to believe that our use of symbols causes more trouble than it could possibly be worth. How many different things does the letter ‘k’ stand for? Or the greek letter Sigma? Shoot, there are cases where ‘v’ is used to mean two different things in the same equation! I’m honestly contemplating starting my own set of symbols where no symbol will refer to two different concepts. What are your opinions on the matter? Does such a system already exist?
It’s all about context. If this really bothers you, change your major to Mathematics, where purity of thought will be your friend.
My favorite thing is how electrical engineers use j to represent the imaginary component of complex numbers, rather than i (since that is current).
Wait till you start with Maxwell’s equations (which can be expressed in complex notation), where you have j representing the displacement current. Then it gets fun.
I read somewhere (can’t remember if it was here or somewhere else), that one mathematics lecturer started using runes, because he’d run out of symbols.
Personally, I prefer Greek squiggle 1 and Greek squiggle 2. 
Yours is not a new observation. There’s a wonderful article written in 1958 by Nicholas Vanserg called Mathmanship (reprinted in the collection, A Stress Analysis of a Strapless Evening Gown, Prentice Hall Press, 1963) where he argues that “since most concepts of science are relatively simple (once you understand them), any ambitious scientist must, in self-preservation, prevent his colleagues from discovering that his ideas are simple, too”. Vanserg goes on from that premise to discuss all the ways to use mathematical obscurity to make one’s work look impressively impenetrable.
Most of the techniques he discusses (e.g., “the proof is left as an exercise for the reader”) will be familiar to almost any engineering student. A good part of the article is devoted to “The Pi-Throwing Contest or Humpty-Dumpty Dodge”, referring to the creative use of symbols to mean anything except what the reader will naturally expect (e.g., introduce the Greek letter Pi to stand for anything except 3.14159…). “If you are careful not to warn him, this one is good for a delay of about an hour and a half”.
You want symbols? Take a look at this unicode site:
http://www.unicode.org/charts/
I’ve wondered what the symbol was for the artist earlier called the artist originally referred to as Prince.
I think we need to go the opposite direction - divorce ourselves from the idea that a certain variable always means a certain thing. Because then what if you need two? Subscripts are ugly and hard to read, especially when they’re on something inconvenient, like a limit of integration. I hate having to integrate from lambda[sub]i[/sub] to lambda[sub]j[/sub], but heaven forbid wavelength be called anything different!
Hmm… But its all a matter of consistency (or so I tell my students who complain about this!). If I say lambda=2m, then most physicists will instantly know what we’re talking about. And when you’re integrating, consider the case where you may be doing a multiple integral; then having your wavelength limits as lambda[sub]i[/sub] and lambda[sub]j[/sub] makes a lot more sense than having your limits going from lambda to psi say.
Look at the bright side. As a physics guy who ended up working with a lot of engineering guys, it often seemed that they used what I called the “Theory of Random Knowledge”: just start writing down equations until it looks like something fits. Variables with multiple definitions makes this a lot easier, and more fun, too.
Of course, if you’re trying to make yourself understood, then the best course of action is to explicitly say what all of your symbols mean. For instance, “F = ma, where F is the force applied to an object, m is the mass of the object, and a is the acceleration of the object”, or at least “F = ma, where F is force, m is mass, and a is acceleration”
Anyone who thinks we’ve run out of symbols has never studied formal logic.
Heh. Sounds like my end of first year viva, when the examiner asked me to write down Maxwell’s equations. I put down random letters and symbols hoping and praying that it looked right, oh and put everything into “natural” units, so I didn’t have to bother with factors of epsilon and mu.
I passed the viva.
There have been attempts in the past to create a perfect universal language where every single concept is assigned a unique integer. Google “Descartes perfect language” or pick up the book by Umberto Eco on the same topic.
That’s probably a bit more ambitious than what you’re thinking of, though.
I think Cantor had it right when he used the Hebrew letter Aleph for his set theory. Why limit ourselves to Greek and Latin? With all the symbols in Cyrillic, Amharic, Devangari, Linear A, etc. there should be no reason to overlap.
Ummm, professor, I don’t understand how you derived the final equation, sine of two ex squared over five omicron is equal to seven backward-el raised to the four pi smiley-face all over the natural log of two thirds eyeball plus the square root of six em minus star-of-david.
Ah, I left out the substitution of three register-mark to the power of six cat-whiskers over nine phone-handset for eleven radical men’s-room.
Ah notation. Well, we could all learn Kanji, I suppose, with some 6,000 characters in more or less regular use (and up to 100,000 a Japanese claimed to me, mostly archaic).
Seriously, though, what is a poor mathematician to do. There are hundreds or thousands of useful constants and variables abound. For example, many of you might think that pi is used for only one thing, but in fact, depending on the context, there are unlimitedly many things it might be used for. I have probably used in dozens of different things in various publications. And while an eigenvalue (i.e. frequency) is generally denoted by lambda, lambda is not usually used to denote an eigenvalue since you cannot reserve 1/24 of the Greek alphabet for just one concept. I am reminded of what the Russian mathematician Matyusevich mentioned in a talk. He discovered an integer form (a polynomial in many variables with integer coefficients, all terms of the same total degree) whose positive values, when you substituted integers for the variables, produced all and only primes, thereby solving Hilbert’s tenth problem. (The kicker is that nearly any substitution produces a negative value, so it is actually useless.) His first solution had thirty odd variables and he was very pleased when he reduced it 26 since then he could use the letters of the Roman alphabet without subscripts. I might add that from what I have seen of Russian papers, they never use Cyrillic characters for symbols.
The only thing to be careful of is to always say what each symbol means. Oh yes, while a letter might be used with two different meanings in the same equation, it will be in different–usually quite different–fonts. So a slant, a bold, and a script letter can represent three different things and it is sometimes quite appropriate that they do so, especially if the variation is used in a systematic way.
You know what Greek letter gets underused? Omicron.
Not always! Check this out. It’s been three years now since I informed this site that they use a to mean the expansion parameter in Eq. 1-8, 16-17, and a to mean the Stefan-Boltzmann constant in Eq. 9-15. And in Eq. 18 they have both. Since the whole point was to eliminate a, and there’s an a left over at the end, it has real potential to confuse!
The one symbol problem that I have encountered the most is v(nu?) and v. Old schoolers use the greek v for frequency, which many times is around or in equations with v, for velocity. What was wrong with f? It makes too much sense.
For some reason when thinking of tons of symbols I think of my mechanics book (Symon). In the back was an index of symbols which gave the symbol, a short possible explanation of what it might be, and then a page number where it supposedly appeared. I just looked at it, there are nine pages of them. Nine pages of columns of symbols.
And I STILL get asked why I majored in history! When math gets back to using numbers, I’ll study it again. I just don’t understand this stuff. :smack:
And I thought biology was for people who don’t have the maths for real science.
