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Lessons by 3blue1brown

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Re: Lessons by 3blue1brown

#81

Post by campground »

eimrine wrote: post #33
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.

Just listen to some music with spectrum visualization, this is a Fourier transform of what you are listening right now.

That’s a good place to start building intuition, but it can also distract you actual understanding. What that visualization really is is a bunch of arbitrarily bounded Fourier transforms of little windowed slices of a piece of music. The true Fourier transform of a time bounded piece of music is a single unbounded function over an infinite frequency spectrum.

Re: Lessons by 3blue1brown

#82

Post by [deleted] »

locusofself wrote: post #69
gumby wrote: post #24

Earlier quoted context omitted.

> CLEARLY superior to the instruction I received at a tier 1 research institution. It was pretty clear at the R1 institution I attended (MIT) that it is really a huge research lab with a small school attached, and that the educational part, for undergrads at least, was definitely not a priority. The continuing stream of advertising (err, alumni updates) that I’ve received over the subsequent decades don’t seem to con…

I've been watching some MIT lectures online recently, most of which are about 10 years old. Do they still use those huge a chalkboards?

[deleted]

Re: Lessons by 3blue1brown

#83

Post by jerf »

jackphilson wrote: post #77
dingosity wrote: post #7

2b1b does a video on how you raise e to a matrix (hint: raising something to e is converted into another function where it's not nonsensical to do such a thing.) In about 10 minutes he explains something my math methods instructor struggled with over two weeks (4 classes). I was resistant to the view that YouTube could host "decent" instructional content for a long time. That video was one of the first that was CLEAR…

perhaps we should remodel our educational system towards content that had a great deal of time spent creating it rather than a slideshow created last night. if only there was this medium that allowed information to be duplicated all over the world instantly so that every professor doesn't need to create their own content

I'm actually some combination of flabberghasted and annoyed that we're in 2023 and computers have still not been terribly successfully deployed into any educational setting.

I suppose the idea that we should look to the results rather than some Ivory Tower education professor's ideas about what constitutes good teaching is just too foreign for the establishment as a whole. I've got armies of PhDs A-B testing whether they can extract .001 cent more per ad from me, but it's too much to ask of society as a whole to check into the question of what curriculum works better. Grant shouldn't have to be all but forcing his way uphill into this space.

Re: Lessons by 3blue1brown

#84

Post by beambot »

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…

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 equally-spaced samples [...]

Related: Showing energy content (i.e. DFT) versus time -- aka spectrograms: https://en.wikipedia.org/wiki/Spectrogram

Re: Lessons by 3blue1brown

#85

Post by jameshart »

beambot wrote: post #84
jameshart wrote: post #74

Earlier quoted context omitted.

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…

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.

Re: Lessons by 3blue1brown

#86

Post by viburnum »

jackling wrote: post #2

I'm likely in the minority, but I found 3blue1brown videos difficult to understand and they usually give me a worse intuition about a concept than I previously had. I wonder why that is. Seems like most people I know swear by his videos.

What usually happens to me is 2/3rds of the way through he rushes through seem keep points and it goes from feeling like a clear explanation to feeling like a magic trick.

Re: Lessons by 3blue1brown

#87

Post by ChuckMcM »

gumby wrote: post #24
dingosity wrote: post #7

2b1b does a video on how you raise e to a matrix (hint: raising something to e is converted into another function where it's not nonsensical to do such a thing.) In about 10 minutes he explains something my math methods instructor struggled with over two weeks (4 classes). I was resistant to the view that YouTube could host "decent" instructional content for a long time. That video was one of the first that was CLEAR…

> CLEARLY superior to the instruction I received at a tier 1 research institution. It was pretty clear at the R1 institution I attended (MIT) that it is really a huge research lab with a small school attached, and that the educational part, for undergrads at least, was definitely not a priority. The continuing stream of advertising (err, alumni updates) that I’ve received over the subsequent decades don’t seem to con…

Interesting that we both saw the same thing. I visited MIT as it was on my list of schools I wanted to attend out of HS and realized after that visit that all the "action" there was in research/postgrad so it was a better graduate school candidate than undergrad.

Re: Lessons by 3blue1brown

#88

Post by geokon »

pdpi wrote: post #19
dingosity wrote: post #7

2b1b does a video on how you raise e to a matrix (hint: raising something to e is converted into another function where it's not nonsensical to do such a thing.) In about 10 minutes he explains something my math methods instructor struggled with over two weeks (4 classes). I was resistant to the view that YouTube could host "decent" instructional content for a long time. That video was one of the first that was CLEAR…

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 somehow less scary and more intuitive? But it's actually a useless crutch that gives people a false sense of understanding. The core issue is that you can multiply two complex numbers and get another complex number. If I give you two vectors or two points on a map and tell you to multiply them.. you can't - b/c that is not a defined operation. We have no intuition about how to multiple 2D numbers (you might think, oh dot products and cross products! but those are something unfortunately unrelated)

2. "Frequency Space" and an the constant suggestion that your signal is somehow being broken up into it's magical innate hidden frequencies. This is also very deceptive (or doesn't hold up in the discrete case). The basis is selected to be mathematically convenient (ie. orthogonal) and is based on your sampling window and properties of complex numbers. These may correspond to some underlying natural frequency that's occurring - or it may not. But it's not helpful to try to confound the two

If you instead approach the whole problem from a purely mathematical perspective of projection on an orthogonal basis and how to construct complex values that are convenient - then the whole setup is less "fun" but it actually becomes a lot more understandable. You can then move on from there and start asking yourself much more interesting questions about aliasing, ringing, fm/am, phase etc.

I feel it took be ~5 attempts of learning Fourier Analysis to unwire my brain and unlearn these bad visual intuitions that send you down the wrong path

Re: Lessons by 3blue1brown

#90

Post by aaur0 »

3Blue1Brown videos really transformed my view on math. If only I had something like this while learning the basics! I've been supporting him on Patreon because I believe he's making a big difference for students all over the world.
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