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The unreasonable effectiveness of the Fourier transform

joshuawise.com

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Re: The unreasonable effectiveness of the Fourier transform

#81
post #75

Earlier quoted context omitted.

But what he deemed being posited as true, was this really bad parenting? It could be to head off competition or it could be brutal realism to head off future depression. Nepotism existed since time immemorial but for a mathematical genius, what was the nepotistic deliverable for the child? A sinecure placement at university?

It’s unusual to tell others not to do something because you’re projecting they’re secretly doing it to compete with you, or that they’ll be depressed when they don’t do what you did. Doubly so when the rationale is “I’m so fucking awesome” Triply so when it’s something you’re passionate about, presumably inherently. Quadruply so when it’s your child. Its tough as a kid hearing your parents come up with elongated excu…

I posit Gauss knew he was a GOAT and had ego. But I also posit he loved his children.

So, a nepotistic delivery was beneficial for his family, and advising his son to seek excellence outside the shadow cast by Gauss himself wasn't stamping on dreams (in my view) it was seeking the happiest outcome.

Without overdoing it, the suicide rate for rich kids with famous parents isn't nothing. There are positive examples, Stella McCartney comes to mind. She isn't wings.

Re: The unreasonable effectiveness of the Fourier transform

#82

Earlier quoted context omitted.

Don’t let unreasonable effectiveness become the enemy of reasonable effectiveness.

A closer look at unreasonable effectivenessness.

A rigorous study of the "unreasonable effectiveness" method.

Re: The unreasonable effectiveness of the Fourier transform

#83
post #58

A signal cannot be both time and frequency band limited. Many years ago I was amazed when I read that this fact I learned in my undergraduate is equivalent to the Uncertainty Principle! On a more mundane note: my wife and I always argue whose method of loading the dishwasher is better: she goes slow and meticulously while I do it fast. It occurred to me we were optimizing for frequency and time domains, respectively,…

It’s literally the Heisenberg uncertainty principle, applied to signal processing.

Re: The unreasonable effectiveness of the Fourier transform

#84
post #58

A signal cannot be both time and frequency band limited. Many years ago I was amazed when I read that this fact I learned in my undergraduate is equivalent to the Uncertainty Principle! On a more mundane note: my wife and I always argue whose method of loading the dishwasher is better: she goes slow and meticulously while I do it fast. It occurred to me we were optimizing for frequency and time domains, respectively,…

Signals can be approximately frequency and time bandlimited, though, meaning the set of values such that the absolute value exceeds any epsilon is compact in both domains. A Gaussian function is one example.

Re: The unreasonable effectiveness of the Fourier transform

#86

I dont like the Fourier Transform. It is infinite which makes it coarse and rough and it it gets everywhere.

Not sure if an oblaque tomb raider reference or math metaphor.

It's both a math metaphor and a Star Wars prequel reference.

Re: The unreasonable effectiveness of the Fourier transform

#87

My favorite story about the Fourier Transform is that Carl Friedrich Gauss stumbled upon the algorithm for the Fast Fourier Algorthim over a century before Cooley and Tukey’s publication in 1965 (which itself revolutionized digital signal processing).[1] He was apparently studying the motion of the asteroids Pallas and Juno and wrote the algorithm down in his notes but it never made it into public knowledge. [1] http…

How was Gauss so productive with 6 children?

That's 30 more fingers he could count with.

Re: The unreasonable effectiveness of the Fourier transform

#88
post #58

A signal cannot be both time and frequency band limited. Many years ago I was amazed when I read that this fact I learned in my undergraduate is equivalent to the Uncertainty Principle! On a more mundane note: my wife and I always argue whose method of loading the dishwasher is better: she goes slow and meticulously while I do it fast. It occurred to me we were optimizing for frequency and time domains, respectively,…

> I was minimizing time so spent while she was minimizing number of washes I'm probably just slow, but I'm not following. Do you mean because you went fast, you had to run another cycle to clean everything properly? If you haven't already, you should watch the Technology Connections series on dishwashers. https://www.youtube.com/watch?v=jHP942Livy0

Since I’m rushing to load it as fast as possible the packing is not as good as hers so some dishes are left out. Overall this leads to more loads.

Re: The unreasonable effectiveness of the Fourier transform

#89
post #54

Earlier quoted context omitted.

I don't think pulsing skin (due to blood flow) is visible from a webcam though.

You will be surprised of The Unreasonable Effectiveness of opencv.calcOpticalFlowPyrLK

Which is a special case of mathematics.

Re: The unreasonable effectiveness of the Fourier transform

#90
post #58

A signal cannot be both time and frequency band limited. Many years ago I was amazed when I read that this fact I learned in my undergraduate is equivalent to the Uncertainty Principle! On a more mundane note: my wife and I always argue whose method of loading the dishwasher is better: she goes slow and meticulously while I do it fast. It occurred to me we were optimizing for frequency and time domains, respectively,…

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