Earlier quoted context omitted.
How was Gauss so productive with 6 children?
That's 30 more fingers he could count with.
30? Did they only count on one hand back then?
The unreasonable effectiveness of the Fourier transform
141–150 of 167 posts
Re: The unreasonable effectiveness of the Fourier transform
#142Earlier quoted context omitted.
There is a saying about Gauss: when another mathematician came to show him a new result, Gauss would remark that he had already worked on it, open a drawer in his desk, and pull out a pile of papers on the same topic.
One of the things I admire about many top mathematicians today like Terence Tao is that they are clearly excellent mentors to a long list of smart graduate students and are able to advance mathematics through their students as well as on their own. You can imagine a half-formed thought Terence Tao has while driving to work becoming a whole dissertation or series of papers if he throws it to the right person to work o…
not sharing something you had no time to properly check is entirely understandable
Re: The unreasonable effectiveness of the Fourier transform
#143Earlier quoted context omitted.
> as he would simply end up in his father's shadow as he deemed it utterly Impossible to surpass his brilliance in maths Definitely true but also bad parenting. Gauss was somewhat of a freak of nature when it came to math. Him and Euler are two of the most unreasonably productive mathematicians of all time.
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?
Not wanting your child to be permanently compared to you for their entire career is entirely understandable
Re: The unreasonable effectiveness of the Fourier transform
#144A 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,…
Another example: ears are excellent at breaking down the frequency of sounds, but are imprecise about where the sound is coming from; whereas eyes are excellent at telling you where light is coming from, but imprecise about how its frequencies break down.
that's mostly due to light waves being FAR shorter and many orders of magnitude more "sensors"
Ears are essentially 2 "pixels" of sound sensing; and for that limitation they are ABSOLUTELY AMAZING at pointing out the sound source.
Re: The unreasonable effectiveness of the Fourier transform
#145A 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,…
The self loading dishwasher would be the greatest marriage saving invention since car navigation systems.
you just need to go "if you want it loaded your way, you do it" and all is solved
And if loading dishwasher is on top of your marital issues you're probably in very happy marriage.
The constant small degree of conflict and strife is key to happiness, people can't be permanently happy, they just find ways to sabotage when they do
Re: The unreasonable effectiveness of the Fourier transform
#146Earlier quoted context omitted.
You're correct that the culture of mathematics has changed a lot, and has become much more collaborative. The rise of the modern doctoral training system in Germany later in the 19th century is also relevant. So really Gauss's example points primarily to how much mathematics has changed. But at the same time, I think you could reasonably take Gauss to task even applying the standards of his own era - compare him with…
There's also this notion of holding themselves to their own standards. They, Newton included, would often feel that their work was not good enough, that it was not completed and perfected yet and therefore would be ammunition for conflict and ridicule. Gauss did not publicize his work on complex numbers because he thought he would attacked for it. To us that may seem weird, but there is no dearth of examples of peopl…
Weird typo in what I wrote. It's past the edit window. This is what I had meant to type:
There's joy in figuring things out, but the process of communicating what has been so figured can be tedious and full of drama -- the kind of drama that one maybe tempted to do without.
Re: The unreasonable effectiveness of the Fourier transform
#147My biggest missing feature for Grafana is that I want a Fourier transform that can identify epicycles in spikes of traffic. Like the first Monday of the month, or noon on tuesdays.
I had a couple charts that showed a trend line of the last n days until someone in OPs noticed that three charts were fully half of our daily burn rate for Grafana. Oops. So I started showing a -7 days line instead, which helped me but confused everyone else.
Re: The unreasonable effectiveness of the Fourier transform
#148Earlier quoted context omitted.
There is a saying about Gauss: when another mathematician came to show him a new result, Gauss would remark that he had already worked on it, open a drawer in his desk, and pull out a pile of papers on the same topic.
One of the things I admire about many top mathematicians today like Terence Tao is that they are clearly excellent mentors to a long list of smart graduate students and are able to advance mathematics through their students as well as on their own. You can imagine a half-formed thought Terence Tao has while driving to work becoming a whole dissertation or series of papers if he throws it to the right person to work o…
Someone blew my mind by convincing me to read Bush’s “As we may think” which was published in 1945. Then I started digging into him and discovered he was also the second president of the ACM, was instrumental in shaping the formation of the National Science foundation (mainly by critiquing their initial plans as unworkable) and also Claude Shannon’s doctoral advisor. Because of course he was.
Re: The unreasonable effectiveness of the Fourier transform
#149Earlier quoted context omitted.
I don't think pulsing skin (due to blood flow) is visible from a webcam though.
MIT was able to reconstruct voice by filming a bag of chips on a 60FPS camera. I would hesitate to say how much information can leak through. https://news.mit.edu/2014/algorithm-recovers-speech-from-vib...
I befriended the guy in high school who built a Tesla coil. For his next trick he was building a laser to read sound off of plate glass. The decoder was basically an AM radio. Which high school me found slightly disappointing.
Re: The unreasonable effectiveness of the Fourier transform
#150Earlier quoted context omitted.
All these transforms are switching to an eigenbasis of some differential operator (that usually corresponds to a differential equation of interest). Spherical harmonics, Bessel and Henkel functions, which are the radial versions of sines/cosines and complex exponential, respectively, and on and on. The next big jumps were to collections of functions not parameterized by subsets of R^n. Wavelets use a tree shapes para…
You may well be right about neural networks. Sometimes models that seem nonlinear turns linear if those nonlinearities are pushed into the basis functions, so one can still hope. For GPT like models, I see sentences as trajectories in the embedded space. These trajectories look quite complicated and no obvious from their geometrical stand point. My hope is that if we get the coordinate system right, we may see someth…
> Sometimes models that seem nonlinear turns linear if those nonlinearities are pushed into the basis functions, so one can still hope.
That idea was pushed to its limit by the Koopman operator theory. The argument sounds quite good at first, but unfortunately it can’t really work for all cases in its current formulation [1].