/sci/ - Science & Math » Thread #11143641

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Anonymous Wed 13 Nov 21:31:43 2019 No.11143641 View Reply Original Report

Quoted By:

>be me
>engineering retard trying to understand convolution
>trying to grasp a decent intuition
>find a stackexchange answer
>think to myself how bad this answer is and how it didnt answer anything
>scroll down
>someone says "to elaborate on what terrance tao said"
>start sweating
>scroll back up
>the answer i called retarded was terrance fucking taos
>Terrance basically just says he "understood" what convolution was in grad school by settling for a tenuous, declarative description
what hope do i even have? how am i supposed to fucking understand anything? am i supposed to just use tools like a monkey without understanding them?

Anonymous

Anonymous Wed 13 Nov 2019 21:42:38 No.11143678 Report

Quoted By: >>11143688

Daily reminder he was in grad school at 14

Anonymous

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Anonymous Wed 13 Nov 2019 21:46:53 No.11143688 Report

Quoted By: >>11143697

>>11143678
>try to ask a question about something i genuinely understand
>"well 15 years ago when i was a teenager i basically just knew what convolution was by what it did when you used it"
wow, thanks terry! im so glad you responded with your irrelevant personal anecdote

Anonymous

Anonymous Wed 13 Nov 2019 21:48:16 No.11143695 Report

Quoted By: >>11143728 >>11143731

i don't think trying to 'understand' something far beyond what is immediately necessary is very helpful, without any application you'll forget it anyway. i believe prof. tao knew the definition before he learned of the 'physical' explanation, but anyways definition and intuition behind a concept are complementary, it can't be said that one always goes before the other.

anyways, what prof. tao wrote is of course correct. basically if you convolve with a bump function or other similarly shaped, you're replacing the value of the function at any particular point with the weighted average of the values in a region around that point, as broad as the bump is. so the effect is that any non-uniform features become 'smeared'. this is true for many cores and in fact is the only usage of convolution i've encountered so far, though i'm not involved with signal processing in any way.

Anonymous

Anonymous Wed 13 Nov 2019 21:48:32 No.11143697 Report

Quoted By:

>>11143688
genuinely dont understand*

Anonymous

Anonymous Wed 13 Nov 2019 21:54:18 No.11143722 Report

Quoted By:

Convolution in 1d with a "small" filter:
Imagine you have an array of numbers. Every number is replaced with a new number computed from the numbers that are "close by" in the array. Specifically it's computed as a linear combination of them. The same linear combination is used at all positions of the array.

Convolution in 2d with a "small" filter
Now instead of just a few numbers before and after, you take a whole rectangle around your number. Again you weight the numbers together according to a fixed set of weights.

Convolution can be seen as multiplication in fourierspace (frequency space)

Anonymous

Anonymous Wed 13 Nov 2019 21:56:02 No.11143728 Report

Quoted By:

>>11143695
>i don't think trying to 'understand' something far beyond what is immediately necessary is very helpful,
so when i ask a question its appropriate to give a complete non-answer anecdote that doesnt explain the thing at all

convolution is used in all of signal processing period, when i use it im not trying to "blur" a function as a means to an end, i'm using it to find the output of an LTI system given the input and impulse response. blurring isnt even relevant here, it's just a weird interpretation of the result of the output

Anonymous

Anonymous Wed 13 Nov 2019 21:57:26 No.11143731 Report

Quoted By:

>>11143695
You can use it for other stuff too! Like sharpening, edge detection, spot detection.

They are of course used in "convolutional neural networks"

You can even use convolution to multiply numbers!

Anonymous

Anonymous Wed 13 Nov 2019 22:09:03 No.11143762 Report

Quoted By:

I wouldn't overrate Tao's undergrad ideas (or his current ideas, for that matter).
At the same time, using some rough physical intuition to understand math isn't an exotic idea either, so I don't get your story, really.

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