Well, not having ever taken the time to compute ƒ(meow) I couldn’t tell you how close the approximation in the graphic really is, but it’s plausible. (Damn WordPress doesn’t have a decent Fourier transform operator symbol…)
Source: http://blogs.scientificamerican.com/cocktail-party-physics/2011/09/29/love-among-the-equations/
Believe me when I say that the Fourier transform of my morbidly obese cat Jilly is the kindest and thinnest way I think we’ll ever witness her.
Below is the continuous Fourier transform in the general Euler form rather than the cosine/sine variation for even/odd functions that are initially easier to look at when trying to make sense of the whole thing. If you took the transform of Jilly in the very most flattering light (basically a roundish DC signal) you’ll get a delta at zero frequency – razor thin. She’s actually more of a long-ish single rectangular pulse so her transform will be sort of a central peak – but kind of spread out and lumpy, so I guess you could say she’s already been transformed.
Note: Euler knew what he was doing even if that e to the imaginary phase thing looks weird as all get out.
Note #2: But by gum it works and it holds water after all this time. Euler is one of my heroes, right behind Feynman. Ask Cruel Wife, she’ll tell you. Granddad was #1.
She could be a Gaussian and not know it, LK! Remember that the transform of a Gaussian is always a Gaussian, IIRC.
…and it would be just soooo like her, wouldn’t it?
BTW: Nice integral sign! But where’s the limits (+- infinity in this case)?
Yeah, that whole “I’m not pretentious, I’m a Gaussian” BS vibe I got from so many gaussians annoyed me to no end. It made lots of optics problems easier so I didn’t rock the boat too much.
In meatspace, if that cat is a gaussian she’s a big ol’ fat happy gaussian. It would indeed be like her to do that just to f*ck with me.
I stole the integral sign – and hereby hang my head in shame. Just as I did not do a proper F for the transform itself. I haven’t been doing much else besides watch Big Bang Theory (and laughed my ass silly, I admit).
So we’re going to have to just squint our eyes really tightly and imagine infinity as the de-facto bounds of the integral. At least it’s not like leaving out dt or π or some silly thing like that.
Oh, I’ll give you the limits. Its a swell integral sign.
You know – your cat might be the embodiment of the ol’ “finger function” – sin(x)/x.
I was stunned when my 5th grade teacher Mrs. Hurd referred to it as such.
Are you saying my katt is not normalized?
As tubby as she is, I find it hard to believe that what she needs is two pi’s.
Sinc(x) does indeed look like the f***ya finger, doesn’t it?
Would you belief for a brief few very juvenile hours we went around saying “Sinc(you)”?
Yes! The Finger Function, otherwise known as the Frilled D*ldo.
Next thing is to integrate it, and you eventually get ….Si(x).
Ok, is it me, or is the blog acting funny?
When I’m at a post, everything in the sidebar is where it should be. But when I’m at the front page, the sidebar falls under the posts, and the two posts prior to the last one are in the sidebar.
This is the only WP blog I have seen doing this, too.
I’d noticed those too, Aggie. Probably the result of all the damned gaussians and Fourier transforms the Lemur King’s slinging around.
It was some WEIRD HTML burp from WordPress. That whole post behaved strangely.
Lemur, at what level of math does one encounter Fourier transforms and gaussians?
I greatly enjoyed the math classes I took in college, and wanted to take more, and one of these days I will, when there’s more time in my schedule.
Depending on your degree, I would say it’s generally a 400 level class but if it is applied to any one thing it could be higher – such as fourier analysis of optical systems. You certainly saw it in DiffEq’s along with convolution, autocorrelation, etc.
Gaussians, heck you can’t walk around an optics department without stubbing your toe on a dead one (optics people are forgetful and don’t always feed ’em), or having one throw poo in your hair. They’re out of control.
Don’t get me started about Top Hats and Solitons.
At least evanescent waves are cool and just kind of flow and gradually fall away.
Evanescent fields mean never having to say “separation anxiety”.
Yes, I’m babbling. Again.
Yes, you are babbling again. Time to increase the meds.
Interesting conversation on this posting…Math drove me crazy in college, part of the reason it took 30 years to get my degree.
If only Mitchell would speak up. I’m hard of hearing these days. Nice that he’s joining the conversation, as well as the other 15 or so.
And where’s veeshir? Still boycotting?
Time to decrease the meds. I’m sick to death of the meds. Fix the damn problem and let me get back to living, I say.
I need to put more math-y stuff on here – if it generates the interesting comments I’ve seen today, it’s more fun than a barrel of monkeys with jock itch.
If you want to take more math, may I suggest statistics at any level and linear algebra? That is, if you plan on using them for engineering and whatnot. I kick myself even now for not having focused on those more. I’ve gotten ahold of some really good texts on them and am slowwwwly working through them again. I seem to have forgotten more than I ever knew.
I have taken Statistics. When I have the time to do so, I want to learn up through Calculus and maybe higher.
Mostly for my own knowledge. I couldn’t stand math in high school, but years later, when I started college, something just clicked and I found myself greatly enjoying it.
One of the things I want to learn is the math involved with chaos theory.
Mumble.
What’s that? You gotta speak up, Mitchell… blogs are noisy places.
I didn’t really have anything to contribute but wanted to be part of the conversation.
Statistics is…odd.
Well, as one of almost fifteen readers of this blog, showing up counts the most.
CF – if you stopped just short of calculus then I can assure you you were at the friggin’ door of the disco! – where all the hot babes dance with anyone and everyone (and do them strange favors)!! , but you didn’t go in!!!
Its in beginning and intermediate levels of integral calculus and differential eq that you run into Transforms (Fourier, Laplace, Hilbert, etc), learn to integrate sin(x)/x the easy way, and run into functions that – when rotated to form a volume – can be easily filled with a finite quantity of paint but whose inside walls require an infinite amount to cover!
If as you say “something clicked” then you should breeze through calculus – there is a lot there to be amused by! Its also where all those pesky formulas came from – like L=2*pi*r, A=pi*r^2, and V=(4/3)*pi*r^3.
I loved calculus like no other math course(s).
I think, ooGcM, that Fourier and Convolution are probably two of my favoritest mathy things, period, except for fractals of the self-similar replicating geometry type.
For fun I once wrote code for a calculating a serpinski tetrahedral, recursing to the point where there were millions of tetras, and then took the output and did a raytrace of the result – it was using POV-Ray way back in 1992, I believe. It was absolutely fantastically fun to watch the thing crank out line by line the raytraced image over the span of three days.
It was similar to this (duh) but I will have to see if I can dig it up.
It is buried here somewhere. I raytraced a great number of fractals in 3D back in those days. [mutters like Mitchell and shuffles through folders]
Don’t feel bad Mitchell. I don’t understand this post, either.
*goes off to read trashy novel*
We had just gotten done watching several hours of Big Bang Theory so I was feeling pretty nerdy.
LC – I just finished re-reading Pauline’s – The Memoirs Of A Madam On Clay Street.
Its kind of a dated (written in the 70’s) autobiography about Pauline Tabor – the madam of a famous upscale whorehouse that used to be on Clay street in Bowling Green, KY.
She has a number of wise – and extraordinarily non-PC – things to say on various subjects.
I’d read it in college, and wanted to see if my viewpoint of the book changed over the past 40 years. It did.
For the better, or for the worse?
The worse – but only because in the intervening decades I’ve gotten way more critical of author writing skills. Also, although I agree with much of her philosophy, I think she did a poor job (or no job at all) of justifying or rationalizing her positions.
I read it when I was in my late teens/early twenties and REMEMBERED it and even remarked upon it from time to time over the years.
I think if this had been my first reading recently, my response would have been simply ‘meh’, and in a year I’d have forgotten I even read it.
But I’ll never forget her line: “The great thing about prostitution is that – ya got it. Ya sell it. Ya STILL got it. You can sell it again!”