# Did Feynman really use his own trig notations?

• Icebreaker
Which is what they are: complex ones, but still column vectors. The only advantage of the Dirac notation is that it saves a bit of space, but it does so at the expense of logical order and clarity.In summary, Feynman is known for using his own set of trigonometry notations because he found the traditional notations to be ambiguous. He replaced "sin x" with a sigma stretched over the x like a square root, "cos x" with a gamma-like symbol, and "tan x" with a tau with the top extended. He also had a unique notation for the inverse sine. However, some people find his notations unnecessary and prefer the traditional symbols.

#### 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?

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."

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

Daniel.

Sounds like pretty good ideas, actually!

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.

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

HallsofIvy said:
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.

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:

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

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.

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.

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?

Zurtex said:
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?

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 that's nonsense and actually,
lim_{x>0} sinx/x = sin

-- AI

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 ?

Richard Feynman said:
"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."[/I]
Just ridiculous, whatever his name was.

Curious3141 said:
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 ?

We bow to him and surrender our possessions.

It appears, then, as if Feynman 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.

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

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.

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) don't 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

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:
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".

HallsofIvy said:
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.

I've met Feynman and can say that is an unfair characterization. He loved to talk with people about any subject. He never assumed a person to be a fool. But if you were "talking through your hat" or, IOW, expressing an opinion that you had not thought through, he would find you out in short order.

arildno said:
Another thing is that "Bra"&"Ket" are stupid and childish names. :grumpy:
A strange thing to say. In physics, math is utilitarian. Names, like symbols are either helpful or not. I found Bra and Ket quite helpful in kick-starting my learning of QM.

matt grime said:
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)).
I agree with Feynman's objections, but LaTeX gets around this problem by using different fonts for such functions. However, most newbies to LaTeX don't use this feature. Hence, sin x is correctly
$$\sin (x)$$
while most people on this forum incorrectly use
$$sin (x)$$
In the latter expression, LaTeX treats sin as s times i times n. Click each symbol to see how it's done; it's simply an extra backslash.

krab said:
A strange thing to say. In physics, math is utilitarian. Names, like symbols are either helpful or not. I found Bra and Ket quite helpful in kick-starting my learning of QM.
Well, why not, for example, use R&L as in "right"&"left"? (there are many choices..).
This is at least as visual and utilitarian, and avoids splitting up a perfectly nice English word into two faintly amusing ones.

arildno said:
This is at least as visual and utilitarian, and avoids splitting up a perfectly nice English word into two faintly amusing ones.
Well, OK, I admit physicists tend toward faintly amusing names. Hence "Charm" and "Strange" etc. for quarks.

Those ("Charm" and "Strange") are fun and amusing (and hence, cool), not only "faintly amusing"..

Sinus of "x" is correctly

$$\sin x$$

and not bracketed in any way.

Daniel.

dextercioby said:
Sinus of "x" is correctly

$$\sin x$$

and not bracketed in any way.

Daniel.
That depends on which convention you've happened to elevate to the status of correctness.

krab said:
I agree with Feynman's objections, but LaTeX gets around this problem by using different fonts for such functions. However, most newbies to LaTeX don't use this feature. Hence, sin x is correctly
$$\sin (x)$$
while most people on this forum incorrectly use
$$sin (x)$$
In the latter expression, LaTeX treats sin as s times i times n. Click each symbol to see how it's done; it's simply an extra backslash.

That isn't the point I was making at all. I have no idea why you'd think that I was getting at the sin as variables versus functions argument. I was pointing out the inconsistent use of powers.

krab said:
A strange thing to say. In physics, math is utilitarian. Names, like symbols are either helpful or not. I found Bra and Ket quite helpful in kick-starting my learning of QM.

But to an Englishman Bras and Kets sound like underwear. This is not amusing; it is silly.

Mathematically though it simply glosses over the 'natural' embedding of a vector space in its double dual and presents it as some mystical overly notated symbols. You found them helpful; I found them completely pointless and unnecessary. You are a physicisist (guess); I am a mathematician who knew about dual spaces and such long before QM. I ought to clarify that it is only as someone looking back on something I ought to ahve done before that I find the notation stupid. As I never learned it "from first principles" I find it only serves ot overly complicate something. But that is just the way *I* think as someone trying to read literature where it is assumed that knowledge of Bras ans Kets is basic and universal: it isn't.

Last edited:
krab said:
I agree with Feynman's objections, but LaTeX gets around this problem by using different fonts for such functions. However, most newbies to LaTeX don't use this feature. Hence, sin x is correctly
$$\sin (x)$$
while most people on this forum incorrectly use
$$sin (x)$$
In the latter expression, LaTeX treats sin as s times i times n. Click each symbol to see how it's done; it's simply an extra backslash.
LaTeX doesn't treat it as anything, it's not a programming language, it's just a way of displaying symbols.

dextercioby said:
Sinus of "x" is correctly

$$\sin x$$

and not bracketed in any way.

Daniel.
Yes, that's usually the convention I use. But I was making a comparison. A newbie tends not to write "sin x" in LaTeX, because it looks like
$$sin x$$
(with no space) and I was guessing they tend to correct it by putting brackets round the x rather than cluing into the backslash.

A newbie writes sin and not \sin because they are a newbie and not aware that \sin exists. It is nothing to do with their mathematical skills. If they care they will use \text{sin} first then learn about\ \sin

Sometimes things get beyond hands and i had a feeling it would be so. (Hmm ESP? or is it just Murphy's Law in action). Anyways, i do agree with the inverse sin problem and some years back i found a neat solution. Now i use asin or arcsin and my problem is solved. (uh-oh, is this one of the "my way of writing inverse sin" syndrome? :tongue:)

-- AI

Now i use asin or arcsin and my problem is solved.

I have for many years used "asin". But for me, the "a" does not stand for "arc". I read asin(x) as : "the angle whose sine is x".

The inverse sine of x is much harder for me to think about for some reason, then the angle whose sine is x.