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How and why to take a logarithm of an image [video]

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Re: How and why to take a logarithm of an image [video]

#61

Post by 3b1b »

cromulent2 wrote: post #42
3b1b wrote: post #40

Earlier quoted context omitted.

In case you're curious, when I ran that title/thumbnail AB test, the option "This picture broke my brain" did end up winning. I was a bit disappointed, because I didn't really _want_ it to win, but I did include it out of curiosity. Ultimately, I changed it to the other title, mostly because I like it better, and the margin was small. I was genuinely torn about how to title this, because one of my aims is that it sta…

That makes me wonder: do you see a difference in when viewers drop off between using a more math-y title versus a more accessible one? The "broke my brain" title originally put me off from watching. I caved after a few days; I think the video is one of your best!

That level of granularity would be interesting. For what it's worth, the metric they go by is not click-through rate; it's expected total watch time. For example, if you have two thumbnails, A and B, and for every 100 impressions of A, there are 51 total minutes of watch time, and for every 100 impressions of B, there are 49 total, then what you'd see in the dashboard is "51% A, 49% B". More total clicks with less engagement will not necessarily win out.

I generally agree that it's a pretty wild choice to just let creators put up multiple titles. That said, it's hard not to play with the shiny toy when it's sitting right there, especially if you know it may mean the lesson reaches more people. In this case, I genuinely don't know what the "right" title is, even setting engagement aside. Is it fundamentally about analyzing an Escher piece? Is it fundamentally a lesson on complex analysis, and complex logs in particular? It's both, but you don't always want to cram two stories into one title. This becomes all the more challenging when titles are, inescapably, marketing.

Re: How and why to take a logarithm of an image [video]

#62

Post by toxik »

pierrec wrote: post #41

This kind of technique can be used in 3D space as well! The analysis here represents Escher's techniques as conformal maps in the complex plane. Conformal maps are also possible, though more limited, in R^3. This is something that I explored some years ago and wrote an article about it, though it focuses more on graphics than math: https://www.osar.fr/notes/logspherical/

So to do this same Droste effect in 3D you would need a self-similar volume? Though since we can't really see 3D, we could never have that "one circle zooms in" effect.

Or could you walk around in such a world? That would be a very cool concept for a game.

Re: How and why to take a logarithm of an image [video]

#64

Post by pierrec »

toxik wrote: post #62
pierrec wrote: post #41

This kind of technique can be used in 3D space as well! The analysis here represents Escher's techniques as conformal maps in the complex plane. Conformal maps are also possible, though more limited, in R^3. This is something that I explored some years ago and wrote an article about it, though it focuses more on graphics than math: https://www.osar.fr/notes/logspherical/

So to do this same Droste effect in 3D you would need a self-similar volume? Though since we can't really see 3D, we could never have that "one circle zooms in" effect. Or could you walk around in such a world? That would be a very cool concept for a game.

Though since we can't really see 3D, we could never have that "one circle zooms in" effect.

Well, the 3D structure just needs to be sufficiently "holey" for the effect to become apparent. For example a cage-like structure, or a house with no roof (when seen from above).

Re: How and why to take a logarithm of an image [video]

#65

Post by db48x »

toxik wrote: post #63

So in other words you can take any Droste image and make an Escher zooming spiral effect. Neat. Also curious what happens if you take Escher's painting and undo the effect. Probably not great since it wasn't in the video. What a cool video.

It was in the video, actually.

Re: How and why to take a logarithm of an image [video]

#66

Post by db48x »

Lerc wrote: post #39
Jeff_Brown wrote: post #7

I love 3B1B but generally don't have time to watch long videos. Can anyone sum up the punchline?

Awᶜ This kind of risks obscuring what's actually going on.

Obscurity indeed. This morning shortly after I woke up I read your message and could only think that you were referring to Awk somehow. That didn’t make much sense to me. Now, hours later and after finally eating something, it does make sense! You really do have to have your faculties about you.

Re: How and why to take a logarithm of an image [video]

#67

Post by manudaro »

john_strinlai wrote: post #34
manudaro wrote: post #30

I've been loking into how 3B1B builds their rendering pipeline, and it's honestly mind blowing. They use Python along with custom OpenGl shaders to handle most of geometric transformations, shich seems to be what creates those "brain breaking" visual effects.It's fascinating how our visual cortex tries to interpret overlapping geometric patterns and ends up producing such counterintuitive perceptions. Shat I still ca…

there is at least one video, if not a series of videos, where he explains his process in detail, showing the coding process and everything. it is a collaboration with another person where, if i recall, he is teaching them. i will see if i can find it. edit: "How I animate 3Blue1Brown | A Manim demo with Ben Sparks" https://www.youtube.com/watch?v=rbu7Zu5X1zI more on workflow: https://github.com/3b1b/videos?tab=readme…

This is great, thanks for digging these up. The workflow doc on Github is exactly what I wat looking for - didn't realize they had that level of documentation publicly available.

Re: How and why to take a logarithm of an image [video]

#69

Post by TeMPOraL »

zacmps wrote: post #38
hidroto wrote: post #36

Earlier quoted context omitted.

It has been that way for a while now. I see Veritasium video titles and thumbnails change quite often, it can be quite annoying as it sometimes gives the appearance of it being a whole new video. A/B testing a title feels wrong to me, its almost as bad as A/B testing a UUID. Just pick a title and stick to it unless you need to fix a factual error.

Titles and thumbnails have a huge impact on video performance, and when it's your main income it seems reasonable to try to marginalise the impact.

Right, but then there's this thing called "shared reality" and once you break it, all kinds of bad consequences happen.

This is even worse, as it also breaks temporal continuity for individual reality. E.g. I expect that if I saw a video titled X today, I'll be able to find it under title X tomorrow, and if I can't, it's one of the rare/marginal cases when it got banned/deleted/retitled, or I just misremembered. Titles becoming unstable in the general case is a bad situation.

Re: How and why to take a logarithm of an image [video]

#70

Post by dandanua »

TeMPOraL wrote: post #69
zacmps wrote: post #38

Earlier quoted context omitted.

Titles and thumbnails have a huge impact on video performance, and when it's your main income it seems reasonable to try to marginalise the impact.

Right, but then there's this thing called "shared reality" and once you break it, all kinds of bad consequences happen. This is even worse, as it also breaks temporal continuity for individual reality. E.g. I expect that if I saw a video titled X today, I'll be able to find it under title X tomorrow, and if I can't, it's one of the rare/marginal cases when it got banned/deleted/retitled, or I just misremembered. Titl…

Gaslighting is now a government policy
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