# Feynman's trig notations

1. Jun 5, 2005

### Icebreaker

A friend told me that Feynman used his own set of trig notations because he found "sin x" ambiguous. Apparantly he replaced it with a $$\sigma$$ stretched over the x like a square root. He did similar things for the other trig notations as well, but I can't find any of this info anywhere. Anyone know if this is true?

2. Jun 5, 2005

### Pyrrhus

According to the book, "Surely You're joking, Mr. Feynman", it states

"While I was doing all this trigonometry, I didn't like the symbols for sine, cosine, tangent, and so on. To me, "sin f" looked like s times i times n
times f! So I invented another symbol, like a square root sign, that was a sigma with a long arm sticking out of it, and I put the f underneath. For the
tangent it was a tau with the top of the tau extended, and for the cosine I made a kind of gamma, but it looked a little bit like the square root sign.
Now the inverse sine was the same sigma, but left -to-right reflected so that it started with the horizontal line with the value underneath, and then
the sigma. That was the inverse sine, NOT sink f--that was crazy! They had that in books! To me, sin_i meant i/sine, the reciprocal. So my symbols
were better."

3. Jun 6, 2005

### dextercioby

Feynman is famous for the slash notation.That is really useful.

Daniel.

4. Jun 6, 2005

### Icebreaker

Sounds like pretty good ideas, actually!

5. Jun 6, 2005

### HallsofIvy

Staff Emeritus
Feynman was clearly a brilliant physicist but reading some of his non-math writing (especially "Surely you're joking, Mr. Feynman", he was more than a little wacky. And quite ready to assume that anyone who disagreed with him, even on non-physics subjects, was a fool.

6. Jun 6, 2005

### z-component

Of course if anyone non-famous were to come up with a new notation, it wouldn't seem so brilliant.

7. Jun 6, 2005

### Pyrrhus

Yes, Halls, i agree, he was an interesting fellow. Did you like the $e^x$ series chapter? i found it very entertaining how Feynman played with logs to trick those poor math students :rofl:

8. Jun 6, 2005

### Icebreaker

Well even with Feynman's reputation I doubt the math community's going to change.

Seriously, though, what happens if I have the variable s, i, n, c, o, t or a and I need to use the trig functions? Ambiguity.

9. Jun 6, 2005

### dextercioby

That's nonsense.We've got "x","y" & "z" as the traditional notation for real variable.And for the arguments of circular trigonometrical functions we've got the greek letters...

Daniel.

10. Jun 7, 2005

### Zurtex

Erm that's why we have standard use of parenthesis so we can see what are functions and what are not as well as just using out intelligence and realising it's common use to write a function in any particular way it's most common to write it. I see where Feynman is coming from, however does it not seem painful to come up with a special symbol for every highly used function and have to remember them all?

11. Jun 7, 2005

### TenaliRaman

Not only that, but a standardised set of notations which are readable, form **that** special integral part of communicating things to others. If i developed a set of notations that only i can understand, then i would have to attach a new thread on this board, ask ppl to look into those notations before i could even ask a simple problem such as
why is lim_{x>0} sinx/x = 1 ??

Ofcourse according to feynman thats nonsense and actually,
lim_{x>0} sinx/x = sin

-- AI

12. Jun 7, 2005

### Curious3141

Dear me. If he objected to trig notations, what did he think of $\frac{dy}{dx}, \int ydx, \log x$, and really so many other notations that any normal person would consider fairly unambiguous ?

13. Jun 7, 2005

### arildno

Just ridiculous, whatever his name was.

14. Jun 7, 2005

### Icebreaker

We bow to him and surrender our possessions.

15. Jun 7, 2005

### matt grime

It appears, then, as if Feynmann thought "symbolically", perhaps influenced by Dirac's Bra and Ket idea. I mean, he wishes to have the inverse of sin to be the symbol reflected in a horizontal line. Intuitive but only to those who think, or who have been taught to think, in a certain way.

Personally I loathe such things as Bra and Ket as they make stuff unnecessarily complicated. In fact for a long time I failed to understand any quantum mechanical literature I happened across until someone pointed out that the Bra could be simply thought of as an element of the dual space, which perhaps reflects my education. It may seem obvious to people who like to assign too much meaning to a symbol, but not to me. Seems like physicists like reinventing the wheel though.

16. Jun 7, 2005

### arildno

Another thing is that "Bra"&"Ket" are stupid and childish names. :grumpy:

17. Jun 7, 2005

### matt grime

Yep, they are, and stupid names for a special case of a more general phenomenon that happens to have a particularly nice interpretation for a reflexive hilbert space.

18. Jun 7, 2005

### TenaliRaman

Just a special note :

I just hope that none of Mr. Feynman fans here get irritated due to this conversation. Its just that, I (and few other members of the forum) dont think that Mr. Feynman's criticism of standard notations is justified. This conversation in no way undermines Mr Feynman's credentials as one of the greatest physicist to have born on earth. I am Feynman fan myself and whatever physics i know came from Feynman (and Resnick & Halliday). I have read "Surely you are joking Mr. Feynman" and i adore the way he dedicates himself to whatever work he takes up (be it picking locks or making sketches). I just thought let me post this up before someone starts a flamefest.

-- AI

19. Jun 7, 2005

### matt grime

Well, in English English bra is female underwear and kex or kegs are male underwear, so when I say I think they are silly names I genuilenly mean they are silly because if the (unintentional?) p[artial homophonic double entendre, and they aren't Feynman's invention anyway.

In any case far too much mathematics is hidden under unnecessarily complicated notation, and adding yet more unnecessary notation to the already unnecessary stuff that exists should be frowned upon. As we all know, the hardest thing in mathematics is getting good notation.

This shouldn't detract from the argument that in this cases there is good cause to be annoyed at $\sin^{-1}$ being used for inverse sin if we are to use the convention that $sin^2(x)$ is not going to be sin(sin(x)).

Last edited: Jun 7, 2005
20. Jun 7, 2005

### HallsofIvy

Staff Emeritus
Perhaps we should explain to anyone reading this who is not familiar with Dirac's notation that "bra" and "ket" are actually from the word "bracket": < | > being broken into the "bra" < | and "ket" | >. I will leave you to ponder why he left out the "c".