Surreal Window Tour (Ep Ø Bonus)

[@AbulAmm]

Thank you for creating and sharing. I feel intellectually curious in a way that I have not since long ago.

[@surrealphysics]

That warms my heart and makes my day! I strongly encourage you to pursue your curiosities to the extent you may find ways to--- if/when you hit a wall, you've got the creativity to find a way

[@ijcurtis]

Bruh, these animations are insane. Seriously, you gotta keep this up!

[@surrealphysics]

Thank you, Friend! It may look like I've been quiet for a few months, but I'm actually working away, very hard, on the next "season"... It takes so long!

[@ijcurtis]

@@surrealphysics I look forward to it

[@ebog4841]

THE KZbin COMPRESSION ALGORITHM ABSOLUTELY DESTROYS THIS VIDEO... dag nabbit!

[@surrealphysics]

Hopefully you can watch in HD, but if not, then it is extra bad, and actually it's not just KZbin-- in general things that look like "confetti" or "glitter" are pretty lossy with the standard compression algorithms! Technically I knew that going in, but, you know, I couldn't not with the sparkly "particles"... afterall they are one of the main "characters" in this story, even if they end up a bit vacuous! They are still not so flat as characters! ☺️

[@APaleDot]

​@@surrealphysics Hey, if you upload a video in 1440p (even if the clips in the video are lower resolution) the artifacts will be much less when users select that resolution.

[@TheMemesofDestruction]

5:43 - Anybody know what this construction represents?

[@surrealphysics]

Conway's semi-informal continued exponential expressions. (Ref. P. 35-36 On Numbers and Games, or ONAG) He's gisting the expressiveness of the Surreals in what I can only call the mind-blowing vernacular of infinite numbers.

[@surrealphysics]

I should have specified those are page numbers for the second edition, my friend!

[@TheMemesofDestruction]

@@surrealphysics Thank you. ^.^

[@TheMemesofDestruction]

@@surrealphysics I showed my Physicist Friend your Videos and this totally blew his mind! :-)

[@worldnotworld]

Beautiful. Makes you start thinking about God again.

[@surrealphysics]

Oh that is so lovely to hear 💞 thank you for sharing 💗

[@account1307]

Hey! Random math question - If supremum can be thought of as a "set union limit" can infimum be thought of as a "set intersection limit"? Also can you point me to further reading on this topic? Edit: you just mentioned further reading on the video so I'll check that out- thanks!

[@surrealphysics]

This is a really great question, and "knowing" the surreals to the extent I do, which still honestly feels like grasping for some out of reach lower bound as the birthdays roll on, you probably can find numbers that work like this although you'll need to mind the birthdays and it certainly won't always work. For instance I wasn't perfectly clear, the supremum will not always exist either, ultimately due to the surreal gaps, which we are working our way towards in this series... Eventually :-) I think Conway mostly addresses the full gamut of game values and the equivalent concepts in so many words by the end of On Numbers and Games, but if that doesn't ultimately address what you're after (or Siegel's text), and you pursue this question further, would love to hear what you find! My intuition says that because the supremum and infimum concepts ultimately fail in the surreals for the general case, there's better dual concepts for given birthdays--- ultimately I think this has to do with how we confuse gaps and numbers in lone set specifications. Grains of salt, because this is intuition, but the wandering gaps of the surreals make "capturing" ultimate limits a truly infinite, mind-melting spectrum of games. Transcendental values get really interesting precise definitions, for instance over the nimbers / modular fields which emerge from the games, so you can actually end up saying more with this construction than with the lone frame.

[@account1307]

This is such an amazing video

[@surrealphysics]

Thank you!

[@thereiffodyssey2000]

These videos and the animations and everything that goes into really are so brilliant! I’m gonna have to work hard to get a grasp on all this as I’m just a crazy math fan. Music is my trade! I wonder if there’s any applications/ connections for any of this stuff in the world of music…

[@surrealphysics]

Oh man, I actually had a segment in Episode 2 on music that I had to move to a future episode for timing considerations. I might even pull it into its own piece. It's really just the beginnings of thinking how this construction (not just numbers but more general values) can inform some aspects of music theory and our experience of music that are otherwise a bit mysterious. It's speculative, ultimately pushing on what we know about qualia. But be warned! I'm a music person too who found a resonance in math they really loved, and I'm now hopelessly hooked! You may turn out to be a mathematician too, not just a "fan"! ☺️ At least that's how the slippery slope worked for quite a few musicians I've known. For me, even if something gets demystified, at least in part, it just makes the experience richer and fuller. Ultimately we can't be 100% confident we've really figured something out, but studying games and their surreals clarifies for me like never before how the building up of waves and their gaps, from simplest to more and more complex, might ultimately be boundless in creative potential. It informs why our continual experience of time unfolds as it does. But also, even through all that novelty, the base forms are shared, so that unreasonable coherence we find connecting with each other through music starts to make a little more sense, as a beautiful way we celebrate being aware in the universe.

[@surrealphysics]

And I meant to also say, thank you again for your comment! 💗

[@thereiffodyssey2000]

@@surrealphysics thanks so so much for your detailed response! Well I really can’t wait for any of the music videos you plan on posting! And yes, your journey into math as a music person sounds similar to what I’ve been going through recently. I almost see music as a higher way for humans to understand mathematics. Like with harmony, we’re decoding often complex relationships of waveforms and the fractions they produce, in real time, but not in a logical “heady” manner, but naturally interpreting them in an intuitive emotional response. Studying the wonders of math really reaffirms my position as musician in a beautifully harmonious way. I’m really glad there’s other people such as yourself with similar resonances :)

[@thereiffodyssey2000]

And I meant to ask, do you create all the music for these videos yourself?

[@surrealphysics]

@@thereiffodyssey2000 yes, I agree about music, that it is a very full kind of embodied awareness, and at some level we've probably solved all types of important problems and conjectures in its complexity. At least in a relative sense, but I suspect we can do no better, even in our most general expressions. The artful discipline of math is trying to linearize all this complexity into coherent strings to tell these complex stories, true to form. For instance, we've probably connected representations of Galois groups with automorphic functions in all kinds of novel ways for the Langlands program in the forms of music that we've yet to reduce into the poetic formalism of mathematics.

[@tothm129]

Hello. So I am confused by this consept of e0 (subscript). my original assumption was that would equal w^^w (tetration) and then go on =w^^^w (pentation) then go on to hexation heptation w-ation, then go into idk BEAF notation and even further. are we just like e0 is bigger than all even if its not formally written down.

[@surrealphysics]

Great question and I think this thread should help: math.stackexchange.com/questions/2313576/ordinal-tetration-the-issue-of-epsilon-0-omega

[@alexanderjenkins7929]

With all positive numbers and their inverse born alongside, infinity is always balanced at 0. Is this how 0=♾?

[@surrealphysics]

It might be that in some games this could be, that a "hot-temperatured" and "infinite" game is confused with zero, yet still finite once the first move is chosen (as long as there are no infinite loops). But here is where you can come up with situations where infinite sets of values can get confused in games, but the numbers of zero and omega are in an abstract and isolated sense, as constructs, unique and distinct.

[@pacificll8762]

What do you think about the book Infinity and the mind that gives a good introduction to surreal numbers ?

[@surrealphysics]

Somehow I've never read it, but now I must! Thanks so much for the recommendation!

[@laurenpinschannels]

the swarm of moving dots to represent a tree feels like a pretty confusing visualization to me

[@surrealphysics]

I'd agree if there were only numbers as game values, but there are also non-numeric values which are formally "fuzzy" or "confused" with numeric game values--- this is slowly getting revealed in the series

[@laurenpinschannels]

@@surrealphysics have you seen "HACKENBUSH: a window to a new world of math"? I thought that video did a nice job of visualizing things as it introduced them. my concern is that the dynamics of the moving dots give a visual intuition that the behavior of the non-numeric values is fuzzy *in the way that the percept of the moving dot is fuzzy*, which would confuse my intuition if I were just first learning these concepts.

[@surrealphysics]

@@laurenpinschannels yes, I'm not doing straightforward pedagogy here. I actually honor the maker of the video you mention, Owen Maitzen, at the end of my Surreal Primer Part I video, and recommend everyone go watch his. I'm not trying to do what he brilliantly did, but it's complementary. Have you found you're thinking more (than you might otherwise have perhaps thought) about what the sequence of games might dynamically do as they extend in structural sequences? That question is not rhetorical, I'm very honestly curious if you are finding my style problematic in a way that might have a silver lining.

[@surrealphysics]

@@laurenpinschannels I meant to also say thank you so much for reaching out with your thoughts and comments! ❤️

[@luciwaves]

WOW. Mind blown.

[@surrealphysics]

Thanks, Luci! Yes, this stuff melts my mind too!

[@ebog4841]

SO MANY PARTICLES

[@surrealphysics]

Ha! 🫠☺️ Yes, can't help it!

[@uh2998]

thanks for your video. I've used your video to make mine kzbin.info/www/bejne/aqS5dWqZes51a6s