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Lessons by 3blue1brown

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Re: Lessons by 3blue1brown

#91

Post by [deleted] »

jameshart wrote: post #74
beambot wrote: post #61

Earlier quoted context omitted.

I think I get what you are trying to say... but the intuition about "this moment in time" is perfectly reasonable for a spectrum analyzer, since it's actually doing a DFT (not continuous from +-infinity) with the last sample (i.e. "now") defining the end of the window.

The thing that makes a DFT discrete is that it is over individual samples rather than a continuous function - not that it is over a finite domain. A Fourier transform applied to a brief window of an underlying continuous function is called a ‘short-time Fourier transform’. And the frequency information a STFT can pick up is bounded on the low end (think, like the opposite of the Nyquist limit) by the length of the wi…

[deleted]

Re: Lessons by 3blue1brown

#92

Post by beambot »

jameshart wrote: post #85
beambot wrote: post #84

Earlier quoted context omitted.

Respectfully, your characterization of a DFT's infinite domain conflicts with the definition of the DFT -- it is defined as a finite sequence, and that's how it's used in common industry usage. Case in point: https://en.wikipedia.org/wiki/Discrete_Fourier_transform > In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of e…

In practice it’s hard to store an infinite number of discrete samples, let alone process them. So I assume that’s why people don’t try. A spectrogram remains a visualization of a short time Fourier transform at a number of points in time . In practice usually produced using a DFT because discrete samples are what you have to work with.

You're describing the DTFT (discrete-time Fourier transform), not the DFT.

https://en.wikipedia.org/wiki/Discrete-time_Fourier_transfor...

Pedantics aside: Spectrum analyzers are computing DFTs over a finite window, and it's perfectly reasonable to think of these as (an approximation of) power spectral density changing over time.

Re: Lessons by 3blue1brown

#93

Post by SkyBelow »

geokon wrote: post #88
pdpi wrote: post #19

Earlier quoted context omitted.

My "ten minutes to understand something I never quite got" moment was his video on Fourier Transforms.

This probably won't be a very popular take.. but to me Fourier Transforms are the perfect example of the opposite problem - where the educators are so hellbound on constructing a visual explanation that they end up brain damaging the students. I've seen this come up several times in my math education. For the Fourier transform there are primarily two issue: 1. The "complex plane" - this tries to make complex numbers…

I think there is a special trick that happens many places in math. When you are given a visual, and then some integral or derivative is applied to it, you need to pause and make sure to truly include that in the mental model. Often I find math videos go far too fast through this section and I have to re-watch that specific spot and even pause and just ponder on how does the integral or derivative change what I was working with.

Re: Lessons by 3blue1brown

#94

Post by Nifty3929 »

haberman wrote: post #38

I would love it if some of these educational YouTube videos came with exercises. I watch a lot of educational YouTube videos. But I've come to see them as more entertainment than education. Not in terms of the quality of the videos (which is often excellent), but in terms of what I retain. Sometimes I come across YouTube videos that YouTube claims I have watched, and I don't remember the first thing about them. I thi…

Pável did a great job of this with his linear algebra videos and Lem.ma

Re: Lessons by 3blue1brown

#95

Post by bertil »

haberman wrote: post #38

I would love it if some of these educational YouTube videos came with exercises. I watch a lot of educational YouTube videos. But I've come to see them as more entertainment than education. Not in terms of the quality of the videos (which is often excellent), but in terms of what I retain. Sometimes I come across YouTube videos that YouTube claims I have watched, and I don't remember the first thing about them. I thi…

Grant Sanderson (the author) has repeatedly mentioned in his videos that he is very much _for_ active learning and doesn’t think passive viewing offers more than some insights and entertainment. He tirelessly asks his viewers to explore actively. If he weren’t the kindest and most earnest person on the internet, it would be jarring to hear him criticize so plainly what are admittedly the best videos out there.

I’m convinced that he would welcome and likely support any effort. I’m assuming he has something in mind or underworks, either building something himself or working with Brillant (the de-facto leader in active learning and a sponsor for all science education channels, including 3b1b).

There was an effort in that direction with last years’ _Summer of math_, where he asked students to make their own video.

Sabine Hossenfelder (physicist, of Science News fame) has made content for Brillant, branded under her name, so it could be an option to host it there. I suspect Grant having a website is a precursor to a homegrown option.

Either way, I’m assuming he has all the encouragement and the unlimited support of anyone here —— he certainly has mine.

Re: Lessons by 3blue1brown

#96

Post by Silverback_VII »

LordDragonfang wrote: post #80
Silverback_VII wrote: post #28

Earlier quoted context omitted.

The problem is that you can learn many things, but time is limited. Learning and understanding abstract concepts won't make you more successful, increase your SMV and give you access to better mating opportunities. What's the use of arcane knowledge about prime numbers if you are not mathematician, and even then, one should question its importance? Time is often better spent learning about crucial factors of success…

As a counterpoint to what you've said, doing things to increase your understanding of the language of the universe can lead to a more fulfilling life than a myopic focus on your... "sexual market value".

This is the language of the universe. To clarify, I am not opposed to marveling at the patterns of fractals or questioning our reality after seeing a mountain composed of polygons and normal maps, wondering whether we live in a simulation. However, let's consider who truly apprecates a better version of the universe: the individual captivated by the curves of a strange prime number arrangement on his computer screen, or the one in the company of three attractive women in a bubbling jacuzzi, also admiring curves.

Re: Lessons by 3blue1brown

#97

Post by 9erdelta »

geokon wrote: post #88
pdpi wrote: post #19

Earlier quoted context omitted.

My "ten minutes to understand something I never quite got" moment was his video on Fourier Transforms.

This probably won't be a very popular take.. but to me Fourier Transforms are the perfect example of the opposite problem - where the educators are so hellbound on constructing a visual explanation that they end up brain damaging the students. I've seen this come up several times in my math education. For the Fourier transform there are primarily two issue: 1. The "complex plane" - this tries to make complex numbers…

Can't speak to Fourier specifically -- but heartily agree that a lot of times in math, teachers try to make it "easy" and provide visuals that are actually a hindrance. Instead of understanding _the material_ you understand the _crutch_.

Re: Lessons by 3blue1brown

#98

Post by jameshart »

beambot wrote: post #92
jameshart wrote: post #85

Earlier quoted context omitted.

In practice it’s hard to store an infinite number of discrete samples, let alone process them. So I assume that’s why people don’t try. A spectrogram remains a visualization of a short time Fourier transform at a number of points in time . In practice usually produced using a DFT because discrete samples are what you have to work with.

You're describing the DTFT (discrete-time Fourier transform), not the DFT. https://en.wikipedia.org/wiki/Discrete-time_Fourier_transfor... Pedantics aside: Spectrum analyzers are computing DFTs over a finite window, and it's perfectly reasonable to think of these as (an approximation of) power spectral density changing over time.

Right. But if you think Fourier transforms produce a function of ‘power spectral density over time’ you are on a road to misunderstanding. Or even if you think that it makes sense to talk about the Fourier transform ‘at a moment in time’.

The thing I am railing against here is the idea that you can just look at a spectrogram to grasp Fourier. You can’t. It is an advanced application of Fourier transforms that creates a visualization of power spectral density over time but it is not a (simple) Fourier transform of the underlying data.

Re: Lessons by 3blue1brown

#99

Post by jhncls »

armchairhacker wrote: post #9

3b1b is doing everyone a huge favor with these lessons. Teaching is certainly a lot different today. Decreased attention spans, underfunded schools, and ChatGPT make it a lot harder, but online modules and tutorials like these make it a lot easier.

A really strong point is how Grant manages to explain the basic concepts, that most viewers already know in some way, in such a way that it doesn't sound like repeated general knowledge. Every time he adds in lesser known facts. A concept gets defined, but in that definition starts a roller coaster of related facts. Sometimes a little history gets mixed in, and almost magically an entertaining story is created.

Re: Lessons by 3blue1brown

#100

Post by hpcjoe »

geokon wrote: post #88
pdpi wrote: post #19

Earlier quoted context omitted.

My "ten minutes to understand something I never quite got" moment was his video on Fourier Transforms.

This probably won't be a very popular take.. but to me Fourier Transforms are the perfect example of the opposite problem - where the educators are so hellbound on constructing a visual explanation that they end up brain damaging the students. I've seen this come up several times in my math education. For the Fourier transform there are primarily two issue: 1. The "complex plane" - this tries to make complex numbers…

I gotta say I disagree. I got the space change bit quickly (piece-wise linear space into frequency space). Complex plane's aren't a crutch, really they are the firm theoretical basis in which to express the detailed discussion properly.

You could always just switch to the Fourier sine and cosine forms, and avoid all of the other theoretical basis baggage. Sort of like physics for poets (I'm a computational theoretical physicist by training), leaving out the more detailed derivations and background, for a more straightforward approach.

Moreover, the DFT is not the FT. In the limit as your sampled points get very large, it will approach FT. There's a great book covering lots of these things in depth[1], with a pragmatic as well as theoretical approach. I think I gave my daughter this one (math phd student) last year.

FTs aren't merely a change of basis, there is quite a bit more to them than that. For DFT you can look at the process as a sequence of operator applications, but in the FT case this becomes a continuous sequence. Hence the space bits.

[1] https://epubs.siam.org/doi/book/10.1137/1.9781611971514 I highly recommend this book.

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