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/
How and why to take a logarithm of an image [video]
41–50 of 71 posts
Re: How and why to take a logarithm of an image [video]
#42Earlier quoted context omitted.
> How (and why) to take a logarithm of an image I watched it a few days ago and this descriptive title was part of the reason I clicked. I generally trust 3B1B anyway but normally a title like "This picture broke my brain" would put me off.
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!
Re: How and why to take a logarithm of an image [video]
#43Earlier quoted context omitted.
> How (and why) to take a logarithm of an image I watched it a few days ago and this descriptive title was part of the reason I clicked. I generally trust 3B1B anyway but normally a title like "This picture broke my brain" would put me off.
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…
perhaps a bit inappropriate of me to say so here as it is off-topic, but i am going to take the opportunity anyways:
big thanks for all of your work making math both enjoyable and accessible. my kids (and i) love your videos. your positive impact extends far and wide.
Re: How and why to take a logarithm of an image [video]
#44Makes me wonder how this would look/feel interactively if a game world was rendered like this
Re: How and why to take a logarithm of an image [video]
#45Re: How and why to take a logarithm of an image [video]
#46Makes me wonder how this would look/feel interactively if a game world was rendered like this
Manifold Garden isn't far off.
Re: How and why to take a logarithm of an image [video]
#47Re: How and why to take a logarithm of an image [video]
#48I love 3B1B but generally don't have time to watch long videos. Can anyone sum up the punchline?
One of Dutch artist M.C. Escher's works is a man is admiring a piece of art that itself depicts the building the (very same) man is in [0]. Escher left out the middle bit of the painting, probably since it's fairly complicated, putting his signature there instead. The video itself is about the complex analysis used to fill in that missing middle, based on a paper ~20 years ago. [0] https://en.wikipedia.org/wiki/Print…
Hm, since I can't edit my comment: link to paper [0]
[0] https://pub.math.leidenuniv.nl/~smitbde/papers/2003-de_smit-...
Re: How and why to take a logarithm of an image [video]
#49Earlier 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.
And video performance = ad revenue.
Re: How and why to take a logarithm of an image [video]
#50Earlier quoted context omitted.
YouTube has A/B testing features that allow videos to have multiple titles and/or thumbnails.
I'm sorry, what? Can people now see different titles? Insanity, if true.
Oh yes. Some channels cycle through many different ones as they test them. Veritasium is notorious for this.