Ep Null: In the beginning...Ø (
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- Опубликовано: 9 окт 2022
- What a surreal foundation may look like, and the beginning of why...
Looking ahead: Complex, Quaternion, and Octonion numbers, oh my!
DISCLAIMER: I editorialize throughout these explications (don’t we all), yet editorializing occasionally departs from standard opinion, which I try to make obvious. Whenever in doubt, leave questions in the comments to signal where I should improve clarity, and include any other constructive criticism- puns always intended.
ACKNOWLEDGEMENTS:
Thank you to my family and friends for their support and encouragement or else none of this would be possible. Thanks to Curt Jaimungal and his fantastic @TheoriesofEverythingProject (ruclips.net/p/PLZ..., as well as his Physics and Consciousness Explication Contest (#PaCE1 • Physics & Consciousnes... ), modeled after @3blue1brown’s #SoME, which was the nudge I needed to start this channel! Thanks to the Blender software community and the 3b1b/manim community for their lessons (wishing I could have taken them on with more finesse!) Thanks to Guillaume Jacquenot for openly sharing his Pythagoras tree, or else our “Persistence of Memory-esque” surreal landscape on Day Omega might have been a bit sparser. For content, I take the blame for any errors, but what good you find here should be credited to my many great teachers, both living and not.
ADDITIONAL LINKS:
For more on the Surreals…
From Don Knuth & @numberphile: • Surreal Numbers (writi...
Musings from the man himself: • John Conway: Surreal N...
Also check out Conway’s book for a fulsome, unadulterated version: g.co/kgs/XucnHz
For a lighter but still rigorous version, check out Knuth’s book: g.co/kgs/B2BT9i
Causal Set Theory (CST) is based on an excellent set of premises that make it one of the most exciting programs in quantum gravity. Check out the amazing Helen Fay Dowker’s quick and accessible summary here: • Helen Fay Dowker - Cau...
We will continue to unpack questions here over whether CST’s mathematical formulation may have promising alternatives, and actually whether much of physics may have promising foundational alternatives, drawing connections to other alternative theories of quantum gravity in development, not just the usual suspects of string theory and loop quantum gravity.
Re. Surreal Matroids: for the closest, best, and actually one of the only existing works I can find on this idea thus far, check out:
arxiv.org/abs/1810.04521
(while not precisely where we’re headed, at least ideas like these are not absent from the aether... please let me know what else I am missing in the comments!)
And if you don’t already know, matroids in and of themselves are awesome, so check out Oxley’s: g.co/kgs/rqbVh3
…or a variety of other books and online lectures to learn more about them. I would love to see more matroid explainer videos, given their unlimited application potential (but they are a challenging concept to grasp). Great job to everyone giving it a go thus far! We’ll keep digging into them here too.
For background on some of the future mathematical directions we are headed in, check out @cohlfurey8766’s excellent work, and references therein:
arxiv.org/abs/1611.09182
And she has some great blackboard explainer videos herself:
• C. Furey - Division al...
(this one is for general audiences, but many of her others are technical)
These @surrealphysics videos take time to create, so while I have the next 6+ episodes written, a dozen planned, and even some related technical papers in draft, please be patient for more renderings here.
We take heart in our program from none other than Albert Einstein (doesn’t everyone?):
“...it seems to me that the alternative continuum-discontinuum is a genuine alternative; i.e. there is no compromise here. In [a discontinuum] theory there cannot be space and time, only numbers... It will be especially difficult to elicit something like a spatio-temporal quasi-order from such a schema. I can not picture to myself how the axiomatic framework of such a physics could look... But I hold it as altogether possible that developments will lead there...”
- Einstein, in his letter to H.S. Joachim, August 14, 1954
This is an entry for a contest of @TheoriesofEverything of Everything with Curt Jaimungal: / theoriesofeverything (specific video for the contest is • Physics & Consciousnes... ) 
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Wow - definitely one of our new favorite channels! Frankly, we were blown away by this. Although we haven't managed to quite wrap our heads around the concept of the surreal number, we were otherwise mesmerized from start to finish by this production. The animation with its flowing, hypnotic, seductive, vibrant whirlwind style was simply Hollywood-worthy... the narration was poetic and alluring, a scintillating feat of dazzling intellectual virtuoso. Your reverence, deep-learning and love for the topic blazed forth electrically across every frame. And you kept the topic grounded with an appropriate dose of satire and humor for the rest of us. Immediately subbed and proceeded to watch all the sequels.
Oh my goodness, I don't know what to say besides thank you so very much! You've definitely made my day! And also don't worry... It took me quite a while before I started to even get some first inklings of understanding about the Surreals, and I know I have much further to go. So if you keep at it, I hope you enjoy the ride as much as I have, if not more! Thanks again for letting me know the specifics of your enjoyment--- appreciated!!
@@surrealphysics Definitely will be reading up on some of the material you've linked! Keep at it and looking forward to your future videos!
Hello Dialect, who measures distance quite well. Your video submitted to Curt was also absolutely wonderful. I watched it right before this video. 🎉thanks to you and the astoundingly beautiful work of surreal physics , i am very inspired, and happy for what it is worth. Thank you both for your brilliance and and thanks to curt jaimungal . :)
Finally, a representation of theoretical mathematics for the profundity that it is. Enlightening 🙏
Thank you so much, Lyam. That means so much to hear 💗
Somehow it took RUclips almost two months to recommend this video and channel to me, despite me being subscribed to 3Blue1Brown and Mathologer, as well as several physics channels, for years. Very well done! Looking forward to more... which might already exist; I haven't checked the channel page yet.
Yes, the RUclips algorithm is clearly careful with us newcomers! I highly appreciate that you enjoyed and also went searching for more! The next one is well underway, hopefully done soon, and many more written for after that, so I hope you stay tuned!
Conway and Don would be proud. Amazing video and editing. Also your voice is perfect for these kind of videos I'm my opinion. Awesome work!
Oh wow, thanks for making my day!
Donald Knuth is alive
what the heck, this is an absolutely top tier content!
Thank you so much! I've got the next one nearly finished and a dozen more written to come!!
I am in love. Please do not stop!
Thank you so much! I do not plan on stopping before at least a dozen episodes!
“Complex, Quaternion, Octonion numbers, oh my!” Love it! ^.^
Thanks and sorry this ended up mostly being in episode -1 :-) it's on its way ASAP!!
Not so sure about Octonions. They're not even associative, so they don't fit in with most other math like group theory. Transformations like what the complex numbers and quaternions describe are trivially associative..
That's not too say you can't have 8 dimensional qualities that describe transformations in 4 dimensions. They just require a different approach to reach. The simplest version with basic rotation requires 3 distinct types of bases rather than 2, which is in fact intimately connected with the concept of 4D double rotations. 1 scalar for the amount to stay put, 6 imaginary components to define the plane in which to rotate, and 1 other component to describe when the rotation doesn't have just one (planar because 4D) axis.
@@angeldude101 They sound almost magical in that case. ^.^
@@TheMemesofDestruction Quite the contrary. There's a very simple way to extend this to arbitrary dimensions. In an N dimensional vector space, the space of all possible rotations can be described in 2^(N-1) components. That's 1 in 1D (since the only "rotation" is mirroring across the origin), 2 in 2D (complex numbers), 4 in 3D (quaternions), 8 in 4D, 16 in 5D, and so on.
Things work even better when you use the full powerset of all basis vectors, allowing for distinct basis elements for every combination of basis vectors. Here, the rotations are generated by the basis elements formed from an even number of basis vectors.
If you really want something magical, extend _all the way_ to _infinite_ dimensions. There are also ways to represent different kinds of geometric spaces, letting you effectively perform rotations, translations, and hyperbolic rotations all at once.
This doesn't quite encompass the full tensor algebra, which seems to include practically every conceivable way to have an associative product, but it does provide a much more concrete geometric picture.
This is all very apropos to the next couple of episodes, so to not spoil too much, I'll say (1) yes, no one's ever too sure about the Octonions and I think there might be a really good reason for that (2) you will see a sparkly particle portrait of Moufang (3) we'll take an extra look anywhere we smell magic (4) while power-associativity may be off to the races, some critical structures have fascinating finite limits that are worth not abstracting away too quickly, and we must mind the choices involved. That is all :-) ... for now... but more ASAP! This is kind of making me consider releasing the audios as podcasts as it takes so long to finish the full visual cut. But then that takes time too... Alas!
This channel is like a fever dream of all the things that confuse me. I love it.
Thank you? 😊 Ha. I mean thank you 💗 I can't promise things get less confusing in a hurry though. 😬 hopefully, eventually...
@@surrealphysics sometimes it's fun to wallow in what we don't know. Eventually something will stick.
Thanks for all your hard work.
@@dugger0 I very much agree. It's delightful to wallow
Absolutely enchanting
Thank you!
New subscriber here. This was beautiful - the way a song is beautiful. One doesnt have to know the chord progression or even why a chord progression is interesting in the first place to know you just love a song. love this video, in that way. You have accomplished art in the science space. Bravo and thanks. 🥹 ( and thanks Curt for the introduction.)
Oh wow! Thank you for making my day 🥹 greatly appreciate your comment. I'm nearly done with a primer to help explain the notes and chords here more simply, but I'll keep the two series separate. We will keep pushing through with our deep-end sciencey art in the main episodes. 😊 Thanks again!
Wow! So happy to read this response! Please continue expressing these spectacular ideas. 🤩👏⭐️ This effort is very appreciated . 📚🫶
Thank you so much for your submission! (final video announcement with winners / runner ups out now, by the way)
Thank you! It was such an honor to be there along with the many great submissions. Again, it was the catalyst I needed to get this channel going. Thank you for sharing your platform with your community in such an engaging way. 💗
Amazing job!
The production quality is excellent, and the concept are brilliant.
I highly encourage you to continue with this journey.
Thank you so much! I will!!
So much beauty and mesmerizing ideas in one video, I’m instantly subscribed ! Thank you !
Thank you for making this. It was almost a spiritual experience. I cried from the beauty. Deep insight into the nature of reality conveyed in such an intuitive way
Oh wow, Benjamin: that means so much to me, thank you for sharing! It is fascinating how so many people who immerse into the Surreals come away with these deep spiritual feelings. Conway and Knuth are both on the record with something like that. I know that's how I've felt.
Amazint channel! I love yboth your style and the quality of information of your presentation. Thank you!!!
Thank you so much! 💗💗💗🎉
Interesting presentation and perspective
Thanks... It will actually get much more "interesting" than this, if you stay tuned. Hopefully not in the bad way for folks, but the perspectives will continue to be non-standard!
I think it's grand. I'm not downgrading your work. It's a very beautiful way of presenting math.
Thank you so much!
Mmmm... proper mathematics presented with artistic flourish, A good start. RUclips is finally starting to grow up.
Thank you!! Greatly appreciated!
Nice comment. If only the Finitists agreed it was "proper". But I guess they're a healthy part of the ecosystem.
Great! Looking forward to going through this
Thank you so much!! I really appreciate the listen! If you are who I think you are, then I very much appreciate all I've been able to listen to from you!! Thanks again.
Thanks Dialect for introduce this great and promising channel!
💗💗💗💗
I am so happy I stumbled upon your channel. Everything about this is incredible. I can’t wait to dive through all your videos. Instant fan. Thank you so much for this amazing series!!!!
Thank you so much for making my day! 💗💗💗💗 I do put in some effort here in hopes that I'm not the only one who gets anything out of it. ☺️ Much more on the way, hopefully ever better--- also as someone who appreciates a good odyssey, I appreciate your name here. Thanks again! 💕
The surreal class of numbers has insufficient cardinality to describe the brilliance of this you tube series. Un-f*ing-believable. It will make you feel smarter, then dumber, then confused, then amazed, then fractured, then whole, then wanting eagerly to watch the next. There are no words, but that's the best I could do.
Oh wow. Thank you so very much! I really appreciate that it sounds like it was an experience for you, as that's what I very much aim and hope for, but of course can't quite expect! Your words are quite sufficient to make my day. 🎉 Thanks again for engaging and sharing!
Wow, this video is just extraordinary! I am so grateful that RUclips recommended this channel to me
Thanks, Nate! I greatly appreciate your comment!
Thanks. I'm on board; let's all take a surreal ride. tavi.
I created the surreal numbers in python, where only the greatest left and least right numbers are used. Then I used these number inside a Cayley DIckson calculator. And then I multiplied two complex surreal numbers to complete a surcomplex multiplication.
Excellent! Are you exploring these forms or do you have specific applications in mind? I'll note that it was sequences of game values that inspired me most to take these surreal forms as a main event rather than a curious curiosity. Enjoy!!
this is my new favorite math/physics channel
Wow, thank you! Hopefully I will get the new episode out any day now!!
It's really confusing. Thank god I knew what you talked about but I dare to imagine how confused some newcomer would be. looks cool though . I'm intrigued so I'll continue through this
Thanks for the feedback. Yes, these are not meant to be self-contained. Those not already familiar with the basics of the material are encouraged to learn in whatever way they learn best, if they are so inspired, and then hopefully come back for a new layer or two of meaning if they wish. I certainly acknowledge this is niche--- not meant to be the standard intro explainers, of which there are many great options.
Yo, these visuals are off the chain
Thank you!! 💗💗💗
Great video
Thanks!
Your videos are so beautiful animated! May I ask how you make them?
Two free and open source ways that I'm very grateful exist: Blender and manim (community edition), the latter being a python library, but you can hook into Blender with python as well. It's all pretty hand-crafted, whatever that means in the digital animation sense (well a lot of manual implementation), but it's a romantic labor of aesthetics, especially as I sense we're at the end of an era, and stuff like this will be increasingly automated by AIs looking ahead. That's a mixed sentiment because it'll be great to enable people who have no interest in that part of it to still tell visually pleasing stories, without great expense. But with all we inevitably gain, we inevitably lose as well in that ruthless push onward.
Well said. It’s an interesting dichotomy of technological advancement and loss/lack of skill. (The simplest example being that calculators substitute our need for performing arithmetic.) However, I think the time saved from arduous work is worth the opportunity cost of rigorous skill. The benefit being that humans will have more time to construct great things.
I hope so, and I hope we can find a good way to keep society healthy and everyone taken care of
Animations do look good, but I didn't understand anything at all. Neither what's the point in surreals nor what they even are.
So you said that you'll use surreals to construct all the numbers, and then at 7:48 "If L and R are 2 sets of numbers". What numbers? We haven't constructed them yet. The first number only appears at 8:54.
Do L and R contain natural numbers? I guess so, because it'd be kinda stupid to use complex numbers to construct complex numbers. But you really need to specify it.
Okay, so we don't have natural numbers yet, but L and R already contain them. Cool. What's next?
7:53 So if no numbers in L are greater than any number in R, then there exists a number LR. What? What on earth is the number LR? What does this { | } thingy even mean? Why does everything in L need to be smaller than everything in R?
8:04 I don't understand what these numbers are, but I guess they can be ordered? Okay?
8:32 Not obvious at all, just circular.
8:54 Okay, so nothing on both sides is 0, makes sense. Then {0|∅} is 1 and {∅|0} is -1. Why not the other way around? Then {01|∅} is 2 for some reason, is it a mistake? If not, you need to specify why. Then there's ±1/2, and then ±1/4, ±3/4, ±3/2 and so on. I have no idea why there are these specific numbers. There are obviously some rules, but you don't tell what rules are these.
10:12 "You come back to find such inconceivably large and small numbers, and you decide to call these omega". So is omega a very large number or a very small number? Or maybe both? And infinity is its inverse somehow? Normally, infinity isn't a number at all, but maybe here it is, i don't know.
I recognize your questions and skepticism as I experienced them myself at first! (Well... and honestly still do from time to time.) Actually I think asking all of these questions, and I believe yours are the right kinds to be asking, is ultimately how we gain new intuition for concepts like these relativistic numbers. Some see the definition as obvious, some see it as circular. There really is no magic... Just iterative circularity. Perhaps not obvious, and when things seem obvious I think it's a sign we should ask deeper questions, like it seems you are.
The hardest yet coolest thing to grasp I think is how L and R start out as nothing. They don't contain anything. Yet somehow, working through this exercise of building games allows us to name new numbers that have the properties we expect them to have. In Episode zero we go through addition and multiplication definitions which reinforce the numerals arriving as their intended numbers, in more consistent circularity. We take Gödel at his word here, not necessarily his or others' interpretations.
It's not for two episodes we actually step back and look at all combinatorial games and at the same time ask this extremely good question you are asking, which is why do the numbers arrive as they do. E.g. why is {0,1,2|} = 3 rather than 4, say. I know you were asking about them even before that particular example, but this one may give you some further insight. I hope to give just enough to entice people to wrestle through it on their own. I think it's the only way to really learn something like math, as much good education that watching videos can provide. And I don't mean that (or any of this) sarcastically!
Conway treats omega like a number, but not full and improper infinity, which he rather sees in the Surreal gaps. That will take three more episodes to really get to, but omega as the "simplest" infinite ordinal he does treat as a number. I made a supplement tour of the surreal window that gives a bit more detail on these ordinals and beyond, at least what's possible in several minutes. But he instructs that as a game, once the "players" L and R start playing options, it actually becomes a finite game, as a first move must be chosen, although I remain suspicious of this as it smells like the axiom of choice, even if it technically could be formalized another way. Even if we can think of omega and similar "infinite numbers" as numbers, I see no clear evidence they actually instantiate in the universe. I do hope you continue to wrestle with these ideas, and please remain ever skeptical, my friend! It's not easy, but the world needs skeptics!
I should have also mentioned that while we start out with some explicit (and implicit!) rules, and assumptions more generally, we will eventually see how many of these we can melt away.
Great work! I've been studying these topics for quite some time and this was a good overview.
Using nebulous animations may overcomplicate and sensationalize your content to the point of inscrutability for some viewers. Not to say this is worrisome, I quite enjoy this art style. However, you may find that as time goes on here on RUclips you will be rewarded to create more flashy content, slowly losing sight of the reason you began to do this in the first place.
It is a very difficult balancing act, where people new to this kind of mathematics are attracted by the animations, but won't necessarily understand what you're talking about. You are rewarded to explain to them, but these explanations only reinforce your understanding, they don't necessarily bring you closer to any solution. You may just be re-hashing another's explanation. For some videos you make, only viewers who have studied these subjects will understand, leaving those who don't, the bulk of your audience, confused.
In summary, you may find that viewership on RUclips is inversely proportional to the amount of technical content and clarifications a videos has.
Good Luck! I'm looking forward to more :)
Many thanks for your thoughts and advice. I suppose it's worth clarifying these are not made to be educationally self-contained, but I want to highly encourage anyone who watches to dig more into the great many (amazingly free!) educational resources that do exist on any/all of these subjects. Apparently like your channel, which I'd not come across before, so thanks for this new awareness! It's really an awesome time to be a nerd.
I'm attempting something fairly foolhardy, which is to get useful questions into the minds of anyone who might watch, imagining the flavor of question will depend on the journey they are on. There are specific ideas I'm driving at, but in hoping for the reward of the playful, Socratic arrival, I give up any semblance of assurance.
I know trying to make things work on many levels is pretty much a balance recipe for impossible. But that's where the artist in me is ok with a certain amount of interpretation that is different from my intentions, including the kind of confusion that doesn't lead to much. My optimist lives in hope that may some day bear fruit. And the scientist in me actually geeks out this is extremely layered and complex relativity in action, as no amount of the most straightforward communication will perfectly safeguard against misinterpretation. The realist in me is ok with that, but the idealist in me hopes as many as possible hear the very serious ideas I'm trying to tell a story about in my own strange way.
All that said, I will certainly heed your clearest advice, which is to try to not lose sight of why one starts something.
I couldn't have asked for a better reply. I'm glad you're thinking about these things
This is very hard to watch.
I already understood the surreal, so that helped me understand the video. The visuals certainly dazzle, but it makes it to hard to see.
For example:
1:04 - The Dirac Equation surrounded in orbs of light. These orbs of light obscure the equation, making it hard to read.
5:20 - A Go Board, filled with sparkling light that don't appear to have any obvious significance. At 5:24, we rapidly flip away from the board only to end up back where we started - which is serious whiplash for seemingly no reason.
5:53 - we see the go board on its side (for some reason), the screen goes blurry. It makes it hard to see if the board, lights or blur have any significance.
The whole video is constantly moving, flickering, strobing, warping and rotating. I am getting motion sick.
6:53 - the game tree, a good way of representing the idea of how surreals are made, nice!
7:03 - why are we floating around, getting blurry, flipping upside-down? I'm trying to focus on the game tree, this is very difficult to do.
7:12 - why the flashing lights?
7:51 - this is very nice math, very understandable, and no large flips, blurs, or stars get in the way. Do more of this, please!
9:24 - again, flipping, rotating, bright spots. It's not adding anything other than spectacle, and it actively hinders people from learning.
10:10 - A turing machine is not needed here. it may work, but it's entirely unrelated. But the visuals here are simple. nice!
10:30 - the infinite ordinals are defined after an infinite time with this process. I wouldn't call it hubris then, but that is just an opinion.
10:51 - please stop flipping me upside down - this is a math video, not a roller coaster
10:54 - Please stop blurring the video
11:40 - Please please stop blurring the video when I'm trying to read. It hurts.
13:43 - It is very hard to work through the ideas you're presenting when you're flashing unrelated things on screen.
15:41 - Please Please Please stop blurring the video.
I am very curious as to what surreal physics may look like, but please stop presenting it this way. I am getting seriously motion sick.
I'm afraid overall it seems my authentic aesthetic is not your cup of tea, at least not in these more swirling, blurring, and disorienting sequences. I'm doing it all for a reason, but that doesn't mean it's enjoyed! You join others who have shared similar sentiments, which I acknowledge and appreciate. Maybe the others who gel with it are ultimately in the minority with me, but like with everything I only see what filters through survivorship bias, so again, your words are appreciated.
My style is not something I can easily change, and I'm not sure I should stray too far from what I'm artistically trying to accomplish along with the math and physics storytelling, but not all is lost! For one, the more artistic visuals will increasingly settle down as the story clarifies, but it's not going to be a linear journey, by any means, and it will never be the glory and practical perfection that is 3b1b. You may ultimately prefer to skip out on the Surreal Physics journey episodes until the end when I'll finally do the soberest, most straight-forward pedagogy I can muster to summarize it all. This is not because I'm choosing to hold out on you until the end, but rather I'm not sure I'll be able to do that kind of clean and pure summary until the end of this finite series. In the meantime I hope anyone watching any episode can get something out of each, but I hold no illusions that it will be perfectly understandable and completely enjoyable for everyone. I just hope something about it makes it worthwhile viewing for any viewer, no matter where they are in their own journey, and I especially value anything anyone shares here. Thank you for taking the time to share these points! Hopefully the above makes sense.
On your more specific points not already covered:
We are working our way to Dirac's brilliance through the arguably obscuring nature of particle models;
The Go board reoccurs because Conway was watching games of Go when he saw how the numbers are constructed from within the full class of Combinatorial games--- I'm artistically trying to convey an aspect of this---however the true experience of this realization is something everyone finds for themselves in their own way. It would be interesting if you like the way the Surreal Primer (part I) goes through the material more than the main episodes, which will continue to rehash these core points, but warning it has more imagery of the Go board swirling around, which you should close your eyes for!
It is a wonder that we are all not constantly motion sick and disoriented all the time and worth pondering what all makes this so, whether or not our eyes are open or closed---we'll keep picking at this;
None of this material is straightforward pedagogy, and I was wrong to say viewers would all be ready for each equation, implying this upon first watch without supplemental material, but I'm going for a different kind of experience arriving at what beauty math reveals than the standard math video on RUclips--- I am largely relying on introductory and other intermediate sources to do best practices teaching, with the learning of course only done by the unique mind. Rather I want you to get a sense of story and come away with an experience as well as a curiosity to learn more if something doesn't make sense or is not familiar. It's a hard balance, and I know I'm failing at perfection;
A turing machine brings a familiar model of computation to the surreal picture, and we are not done playing with all these concepts together and beyond; it is more related than you might at first suspect;
The day omega written over the tape is like an absurd surreal joke more than an opinion;
Ha! I'm sorry, but this is kind of a roller coaster, and you will be flipped a finite number more times if you keep watching--- maybe I can do a calm cut of everything at some point because I do worry about those sensitive to lights and flashes. But I'll say too this is a physics and philosophy series as much as a set of math videos 😊;
There will continue to be the odd bit of blurring, but less and less... Again, even as we calm down into more details, you may ultimately just not like the artsier side of my style here, and I'm sure it is yours that is the more refined taste. Thanks again for all the feedback!
@@surrealphysics Thanks! Then I will come back later and take a look
This sort of content is valuable in ways you probably cannot imagine. It is hard to be a mathematician these days, it is so incredibly overwhelming, especially for a generalist. The poetry is indispensable, even more jewel-like when accompanied by the theory. It is the poetry and art that can help us stay sane and avoid the tragic fates of past geniuses who were ignored and went mad, or died young (William Kingdon Clifford, Cantor, Galois, &c.). At the outer limits of geometric algebra (beyond Hestenes and Cohl Furey) have a look at Bill Pezzaglia and this psycho called Berndt Schmeikal. I try to make head & tail of it, but I'm involved in macroeconomic justice work (employ all mathematicians!), so it's a strain.
... and I am willing to bet my lunch geometric algebra is a key to one method of proof of the Riemann Hypothesis.
Also, discrete versus continuum are a false dichotomy in physics I reckon. It's not one or the other. Discrete structure exists with non-trivial spacetime topology. The fact this implies closed timelike curves have to occur (and can be "quarantined" naturally to the Planck scale) is a feature, not a bug, if you think about it. I saw you are a Casual Set fan, but give other ideas a bit of room too, you might get delighted.
Thanks! But perhaps I imagine a semi-consistent incompleteness, at least, of the value I attempt to deliver here. :-) As much as I am a mere late instantiation of the intuitive math artist who cannot help ponder these things that drive us to the edges. I wish you well on your journey, my friend! Thanks for commenting!
I'd say these "false dichotomies" have a way of creating interesting structures within compositions. I agree that the Reimann Zeta Function appears to be all about geometric algebra, or algebraic geometry, depending on the goggles... with topology implied, of course, always creeping in the background. :-) What may appear as closed timelike curves may not mean what we might presume they could mean, but I aim to tackle these complex threads more fulsomely here in time. Continued comment welcome! And yes, I'm trying to work my way through the variously developed theories of quantum gravity... Delighted at least by how many there are now and how they interestingly reflect each other, sometimes as duals, trialities, or even otherwise.
It felt like reading a page of Hegel.
Thanks! I think? Hegel was notoriously long-winded, which I'll admit to battling as my episodes stretch ever-longer. And Hegel is perhaps the most misunderstood of great philosophers, e.g., his meaning of dialectic approach. I merely stand on the shoulders of two more centuries of greatness, and sign up to misunderstanding when insisting on playful socratics. I also admit to a rather Hegelian relativism that is not the typical philosopher's, but rather Noether's and Einstein's, and of course Conway's.
You may continue to notice some very Hegelian sentiments, even as we depart in more ways than one. But through totally Hegelian goggles, it might all look pretty similar: afterall, the Surreals as contradictions surmount to the ultimate contradiction: Thought-- which we cannot completely transcend-- we can only become more aware of it as clicks of time tick on.
@@surrealphysics I meant it as a compliment! I've been thinking about your video lately and, without claiming to grasp the ideas you are talking about, I would like to contribute a few vague thoughts in the (naive?) spirit of generalizing the attitude of Conway under the concept of "Game", which to me is another word for "Dialectics".
It looks as if in every one-million-dollar question that human thought faces whenever it goes to its limit, e.g. "How the Political arises from the Natural?", "How does Language emerge?", "How the development of organisms can be seen as an abstract, geometrical Physics problem/ how Physics and Biology can be married?", "How thought and matter can be grasped as expression of one substance?", "Does society constitute of subjects or are subjects essentially social beings?", "How does the 'Outer'-world reconcile to the 'Inner'-world?", "How Order arises from Chaos?", and, finally and most importantly, "How Being comes from non-Being?", it seems that "Game" always emerges as an answer...
It is interesting to me, for example, that the pre-Socratic Heraclitus in fragment #52 states "Time is a child at play, moving pieces in a board game; the kingly power is a child's." or that the Pythagoreans reconcile the movements of 'inanimate' beings with the movement of an 'animate' being through 'Music', which maybe is just a game.
Do you see any point in correlating these ostensibly different aspects (anthropological, linguistic, psychoanalytic, metaphysical, physical) of human thought under "Game"? And, if there is some truth in it, which two things does "Game" reconcile in Conway's idea? Discontinuous structure with continuous structure?
Oh wow-- you are zeroing in on many reasons I started this channel, and the related journey from well before! Excellent.
To shorten what will already be a very long comment, my fuller thoughts with supporting arguments will unfold with the episodes and linked papers. But it's hard to resist jumping to a few punchlines (I'm already winking with them in the episodes already out): my take is that Surreal structure does reconcile (to the incomplete extent possible) the quantized with the continuous (your discontinuous|continuous)-- but also even more fundamentally: something and nothing. That these concepts irreducibly must be held together.
A delightful physical picture of this is what I am working my way towards here, and I can't spoil any further because like any good game or story, timing is everything.
Which is the next major (counter-)point it seems you share: Time is critical to the Surreal structure, indeed it is the core of dependency upon which all other structures branch from and find their coherence (i.e. as space(s)). Some structure plays as music, some as noise. Some create numbers, but all structure is relativistic play, where we can't help but pick a side and a few other critical details, but none are generally preferred.
It's amazing how much is captured by just letting all the games play, and imagining what it must be like to play them. I truly thought they were silly to seriously study, even a year or two ago, but now I see I was silly. They have taught me that value doesn't necessarily come as a number. They've taught me intuition of superposition like I never understood from even the best quantum physics textbooks.
I see how they enable information to roll up from its substrate into layers of abstraction, and how both numerical and computational complexity roll right into decideability, as Turing would remind us too, critical to the consistency trifecta-- always incomplete. These are critical threads in the story on why abstract concepts can couple across layers where the flow is not always bottom up. And that likely much more than human thought and decision are what arises from the play of combinatorial games.
Whether we call them games or dialectics or relativistic frames of reference, I see no end to the extraordinarily rich structure generated from their interplay, which is importantly not a blank canvas, nor a continuous smear of flat possibility to infinity in all possible directions. Surreal structure looks like actual, natural structure. Thus it's awfully tempting to think this could be the unifying mathematical trick of the universe. All of it. We wouldn't be the first to suspect this. But such suspicions require extraordinary arguments and evidence, and a good bit of fleshing out to the bones considered thus far. For as ancient as these ideas are as forms, somehow the formal journey has only just begun. I'll continue to bring what details I can resolve here.
@@surrealphysics I deeply appreciate your extended respond! I would like to diverge a bit from your last remark though. It seems to me that this is larger than any particular activity, even larger than the activity of Mathematics. The fact that this Game-attitude will eventually dominate over an attitude of imposing general, universal, timeless structures upon the "world", doesn't tell us more about the World than it tells us about ourselves endeavoring to decipher the World/Phenomena. It seems to me that Bohr's quote "It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we can say about Nature." is just a forerunner of this attitude. And the reason I'm so preoccupied with these thoughts is that, I believe, that if this is the case (and with the presupposition that the "experts" of the fields are able to see beyond their "expertise") this will have cultural and political extensions in the sense of revision and reflection over 'practical' questions like "how should young people be educated?", "how many hours should we work?", "who should take the decisions in a state/community/company ?", "what is a meaningful life and what does it mean for a citizen to be 'free'?", "Is Art just an asset or an integral part of a 'meaningful' life?", "Is there a way to break free from a utilitarian and profite-oriented organizing of priorities?" etc... which are questions the answers of which can never be guaranteed by any mathematical proof (I think).
After all Math may be just a game and, hence, we shouldn't take it so 'seriously' :)
I apologize for 'drifting away' from this channel's interests and please excuse my vague, 'primitive' way of writing (in a Math video) but your video has been an inspiration. Keep up the amazing work!
p.s. I'm not prejudiced against Math/Physics. My background is in Physics.
@@DoDoRaC10 You are not drifting away at all--- and I was perhaps not explicit enough earlier, but the incompleteness of math and thus formal physics ideas in any sense of "proof" is indeed support for this deeply relativistic composition that the games reflect in dialectical structures. It is a mere formal reflection of the incapturable fullness of whatever produces the universe that we observe.
I think of math and science as types of arts, defined by sets of rule conventions or languages with which we share perspectives of experience, rules which can be broken in context. But none can be complete pictures, in and of themselves. We all just reach towards an impossible completeness as individual conscious minds in collective and dynamic efforts composed in cultural phenomena where languages develop, maths being but some of the many. There will probably be congruent arts of other species as well, just naturally tailored to their natural biases, like the ones we find so difficult to escape.
But since we all grasp at the elephant (perhaps even the room itself, if that analogy holds) there will be duals in trialities to unite across the gaps in all forms of arts from any remotely aware collections of generative minds. Hence my use of just as much visual and auditory art to communicate as math and more traditional physics artforms. Historical perspectives and the wisdom traditions have a lot to say about all these things as well.
Indeed the games are just one possible approach to telling a relatively simple story of our recovery from modernism and that one impossible perspective to rule them all.
14:57 - Reminds me of a bifurcation. :-)
There is both a shallow and deep way to interpret this comment, so I'll of course give you the benefit of the doubt (doesn't everyone do that on the Internet?) and say that this is a profound insight, my friend. I hope you will not be disappointed in where this is all going :-)
This needs more views.
Thank you, my friend! ☺️
make 2h versions of it, so it can be watched on nerd-birthdays as a "math-thriller"
Ha! That's a great idea, to compile a feature length version of the whole story once I'm done with the series. I also planned to make a much shorter and sober version for cleaner aesthetic tastes, once the sequence finds its endgame, but so much will be missing from that--- I'll personally definitely prefer the mystery of the original storyline, simply condensed! I hope we get there before too long 😅
This is like, the best video I've ever seen! It is so good, so inspirative, so interesting, so... I think I've run out of possible definitions😅
P.S. At 8:43 - 9:27 you've made a mistake by putting the REVERSED null symbol on the screen instead of the original null symbol, so please tell me was that an unnoticed mistake or did you made it on purpose, and if you made it on purpose please tell me why because that really confused me.
@@Math_Duo 🎉 Thank you!! You are so kind, and I really appreciate you sharing, including the second part!💗💗💗💗
But I do have a question for you first, why did you assume it was a mistake, when I keep flipping the camera framing around, and even twirl the empty set symbol a few times (along the other axis) in that very same construction scene? 😉
@@surrealphysics But at 8:43 - 9:27 you showed the symbol ⦰ instead of the symbol ∅ for representing the empty set
@@Math_Duo yes, and maybe my topological interpretations of games are all wrong, but it seems that nontrivial configurations are necessary in unambiguous construction of forms like numbers. I go back and forth as to whether I should have only flipped one side in this scene, having the empty set flip flop across the slashes, etc. But we are viewing the construction from the camera's frame too, and so along some axis, if we could "see" the empty set, it would appear flipped in projection (but then I don't flip the labels we are putting on configurations of the empty set, since those are "ours" anyway). I don't continue to play at this symbolism in this way, because you're right, it's a fine line between confusing and suggestive.
And probably what I've written above sounds absolutely mad, but I have more episodes written and planned that will hopefully explain better. There's actually proper math behind this, it's not just intuitive poetry! 🙃 The episode 2 preprint podcasts will give you much of the idea in intuitive language though, if you are interested.
Thank you again for asking about this! I think you are the first one to have said something, if I'm not mistaken (and of course, despite this instance of intention, I often am mistaken and greatly appreciate folks pointing out anything they see that doesn't look right/left! The ambiguity of art cuts in all the ways!)
@@surrealphysics So, it was a mistake by putting the symbol ⦰ insted of the symbol ∅ at 8:43 - 9:27?
@@Math_Duo if I'm wrong, then I shouldn't have done it (a mistake), but if I'm right then it wasn't a mistake. I intended to show you a playful empty set and make you scratch your head about why it seemed so active in the construction and appear in perspective. It's a topological hint if I'm "correct," but it's confusing art if I'm incorrect. I'm just trying to be a bit more humble than saying "no, it wasn't a mistake," and giving a quick explanation as to why. Apologies that it is literally not a straightforward matter and my previous explanation needed further clarification. 🙃
I get vihart vibes from this but much more impressive!
Oh wow, thank you so much! Vi Hart is amazing so I'm very touched. I know they call themselves a recreational mathematician, but it might turn out that's the most serious kind. ☺️ Thanks again, to the moon! 🌙 💗💗💗
@@surrealphysics Well you are amazing too! This was absolutely beautiful and I need more!
@@kasugaryuichi9767 I'm working away on it! 🌤️🌒😅 Thank you again for your kind words and encouragement!
@surrealphysics It's my pleasure, really! I know making something like this is extremely hard, but please don't ever stop making videos, even if it takes a long time between them.
@@kasugaryuichi9767 I take this deeply to heart 💗 thank you so much
math ?
...or maths, if you prefer? More physics is coming, I promise.
Is the size of the set of surreals the same as the size of the set of reals? (I'm guessing yes because elements of each can be represented by infinitely long strings of digits, but the surreals do "feel" a lot bigger...)
I love your question and it shows your good thinking, but there are some quite mind bending issues to gawk at here (at least that's what I do, but I wouldn't be surprised if you gazed upon them with more equanimity). Surreals are a proper Class, meaning amongst other aspects, they do not form one set, even though they are composed of very very many sets. So I know what you mean that it seems like they would be the size of the reals, while in the depth of Conway-esque study, they are somehow infinitely larger, at least(!) I begin to think of this as "dimensions," even though they are totally ordered and so it seems like there shouldn't be "more dimensions" to uncountably bleed into the one we're already working out, yet the Surreal forms show otherwise, including how they begin to create infinite echelons of values that are totally ordered yet not ordinals, the deltas, in addition to the epsilon numbers, and so on (!!!)
@@surrealphysics I think I have some ZF to learn.
@@surrealphysics I don't know enough to know whether this question makes sense. It seems like the lebesgue measure (e.g.) is rooted in the reals, but if the reals aren't enough to actually cover the whole number line, would things look different if we started from the ground up with the surreals? For example, a real number added to itself infinite times can only yield 0 or infinity, but I think there are surreals you can do this with that yield finite non-zero values (for some value of infinity).
@@balijosu Yes, everything I've read seems to base Lebesgue integration on the Reals (or some straightforward generalization of them) as the standard part of real analysis that it is... but maybe there are some less obviously real measures that are still "classical"? But I'm not convinced that even the wildest ideas from Grothendieck can remedy the ubiquitous standard (or even "standard non-standard") Real roots of the usual spaces, and improve upon what natural structure the Surreals and games more generally shed light on. When we lose the empty root, I think it does become a game of nonsense that requires re-rooting to make any sense of (but then we can't be quite sure where we landed).
Basically, I haven't seen definitive proof that we can resolve much of the structure you're mentioning, including its gaps, otherwise plainly seen with only a little patience all laid before us out of game construction. At least my brain is able to better follow what it sees as relatively simpler arguments in the latter.
@4:40 is definitely "getting ahead". You cannot call such platonic ideals "generators" of anything. Not even platonically. For any math a whole formal language is necessary first. It's like, "Who ordered that?"
The source of any or all generator(s) is perhaps another way of asking what creates something from nothing. This whole exercise could be telling us something... of "nothing." A few episodes from now will tackle this more head-on.
This universe was brought to you by the "number" { }.
Ha! Yes! Both the University and the Impropriety! Lol and thanks!
@@surrealphysics,
I'm really excited about your channel. You are off to a fantastic start. Keep up the good work!
A partial answer to your question, if there was any question: is it Lattice?
P.S. i'm enjoying the monolith you've gifted us with in this medium 🙏❤️
P.P.S. you have my sincere appreciation for regarding "physics" as the "foundation" of our mathematical knowledge. This might come off wrong in many directions-e.g. those "boo, that's not physics, it's just math" guys, which i'm not in their gang-but i hope you know what i meant by that.
Oh, i was mistaken? Ahh, such is game of life.. :)
I appreciate your use of language and insight! An extremely interesting lattice does form from this, which we'll keep unpacking. Thanks so much for appreciating my non-standard medium as fairly extended poetry. ☺️ And I really hover between those valences as to whether the foundation is more mathematical or scientific, but then depending on which way I'm listing I'm usually having to recast their conventions somewhat, so everyone...loses? 😅 Well, I think I know what you meant, and resonate with the sentiment, especially how our wrongness is potentially just a product of whatever ruleset we have adopted! 😁 oh how we torture ourselves with rulesets! They are one way to make progress. ❤️🙏
@@surrealphysics a pleasure! great to hear that lattice is also haunting, in an exciting way, the reality of another fellow natural philosophy* enthusiast 😊 now that you painted a glimpse of your world, i'd like to add that what i appreciate the most in your concerti, if i may use such an analogy, is your authentic representation of the maps between fundamental metaphors of reality; i.e. science, art, literature, etc. to quote late Yuri Manin, "metaphor helps a human being to breathe in this rarefied atmosphere of Gods." somebody asked about my own world? i'm glad you asked. i consider myself a metamythaphorian 😅 anyway, may your shining never halts! 🤞❤️
*a label for any countable union of the non-empty sets of reality diggers.
Yes, I did ask! (in not enough words for someone who uses too many!) So thank you so much for sharing! And what a fabulous word to describe oneself-- I wish you many beautiful mythologically epic metaphors and metamorphoses on your clearly most excellent adventure. 💗
@@surrealphysics thanks a lot*! Wishing you colorful wishes, isomorphic to yours 😊 in the mean time, i'll try to ponder your other explorations, bit by bit 💗
*O(aleph_1) 😁
I got nothing... 😂still empty set
Hey i tried... At least
🤣
😍
Amaaazing work! Please keep it up
@@marcusfromsweden thank you! I will!!
What is logic, what is thinking?
Exactly. Two topics not altogether different, but not the same. Certainly worth sitting with, in long and awkward pauses, while they stare back at you with their ephemeral and illusive maws.
nothing creates "almost" everything. Math is amazing and weird at the same time.
I'm subscribed for sure. Editing and visuals are amazing. However... I came hoping that I would learn how sureal numbers are constructed. The definitions are there in the video, but the bottom line is that I still don't know how to construct surreal numbers. Take, for example, Veritasium video on the incompleteness theorem. He takes the viewer step by step... you're rushing too fast through the technical details... I hope this helps..
Honestly thanks so much for this earnest feedback. I am definitely thinking about doing another supplemental explainer as a kind of very slow pre-req on Surreal basics for the series. Just because there aren't tons of videos on them out there already. But this channel is meant to complement all the amazing science education RUclips moving slowly through basics. Rather here I'm working to tell a story of intermediate material, pulling together a bunch of concepts from across disciplines, which hopefully all remains interesting for those who don't have all the content basics. I am still trying to ensure anyone watching would get something worthwhile out of it, even if it's just a vague sense of why they might want to sit with the material a bit longer until it clicks. And then hoping they might want to return for a new layer or two. I'm trying to make them rich enough to have rewatch power.
But you know, even with all the great books, it still took me months to feel like I really "got" the Surreals. It doesn't seem to just be me. They are so simple, yet so profound, it's not necessarily easy to really feel like you understand them, and I'm definitely still on the journey. So while I'm happy to take any blame of moving too fast through material, I actually don't expect even the slowest and best explanations to provide instant understanding over the course of a video. Surreals really take some working through, which I'll actually try to make happen in real time for an engaged watcher on this basics explainer I'm percolating on, but that's probably the only one I'll do quite like that. Again, that part of RUclips is very well established, and I don't feel like I could add as much there. Thanks again!
@Surreal Physics keep up the good work. A supplementary will do the trick! Thanks
Whoever strummed that game into life, I mean I know that requires infinite energy, man! Where would the Universe get its initial momentum? God was for sure the first musician ever who strummed us to existence! Thank you, God!
This is a ride towards infinity, folks! Buckle up!
Ha! But the question is... will we ever get there??? (Boundlessness seems truly unfathomable, but I am a mere mortal... I guess it doesn't stop us from pining away though, right?)
@@surrealphysics You're mortal because you've always wanted to play the game. ;)
@@surrealphysics you mentioned out here that seems infinite possibilites came out from Null throught this game choice that doesn't defy any logic, it's imperative that this is a ride towards infinity from now on. Self does't exist, yet our individuality's illusion is infinitely surreal! Wooo, it's an honor to be me and honored to meet you. Thanks for doing these awesome videos and doing your purpose for humanity. May you get what you've ever set to take in this lifetime! :)
@@needheartranken it's my honor! I hope you have or find deep joy! Thanks for your uplifting comments! Even if we are forever seeking, it sure is a fun ride.
ASMathR? Seems good, it kinda sexy, whisperious lecture/reflections
I'm honestly not trying for that and find myself re-recording parts that are too much and thus possibly distracting-- But I'm not here to judge either! And I always thought @3blue1brown was Platonic ASMathR myself
@@surrealphysics well, I'm not complaing about it, at all. I assumed that is your tone of voice. But, I think it would be nice to tweak the mic configurations, maybe, to enhance the understanding. Specially for non-native english speakers like me. Aside from that, thanks for the response and continue your good job on scientific divulgation!
Infinities Snowflakes don’t repeat. Looking for the things that repeat is also infinite.
What is it when the relationships aren't binary, but say, like cells in a pentachoron, unfolding from itself.. now there's a visualization
Yes, a minimum of two but ultimately boundless... It does sometimes get challenging to maintain coherence with more and more players depending on the ruleset, but here is where topology and algebraic geometry / geometric algebra weave into games... If only our visualizations of nature weren't so lossy, I think it must be utterly stunning at levels beyond our current tech... as gorgeous as what we do see is... But we make progress every day!
@@surrealphysics I'm trying to wrap my head around irreducible's , because they don't seem to follow the tree back to the null source.. sets who's beginning start with three or more members.
I was hoping you could clarify some of that for me as you obviously have extreme lucidity in that department.
My perception or interpretation could be completely wrong as I've never made it into advanced math.
@@surrealphysics from what I can imagine the triangular (and their higher dimensional counterparts) make the most detailed fractal textures.. I should really get back into computer stuff, machines are actually capable of what I can visualize now.
Do you mean the reduced games/numbers?
Math is invented to describe the relations between things which is discovered.
Colors don't exist but they describe wavelengths which do
This seems to be a popular default interpretation of things, especially amongst scientists. Perhaps we'd call it the Newtonian view, and in part also the Einsteinian view, as he believed in the relations between bodies as the strict physics with all the math formalisms as mere tools, implying their invented status. I don't know what he thought of color. But what if I were to believe in a physical existence of your thoughts of color as you see them (not the wavelengths, which also exist), perhaps not quite like I see the colors in my mind, but why wouldn't those senses instantiate in your brain in some physical way? I'm not a dualist, despite all the L/R talk and playing with inverted involution. If colors do not exist, what does it mean that they supposedly don't exist but still fill anyone's mind with sensation, whether or not the person has the rods and cones or eyes functioning as per the textbooks even? If you want to believe in the physical brain, but not the mind or its thoughts, which is all we experience, then how might we ultimately square this logic?
@@surrealphysics i believe in the mind, but I view it as analogous to an operating system. Yes video files exist, but it's just data. The video file looks very different from the monitor than it does from looking at the transistors which makes up the file data.
@@surrealphysics I never even considered the description of the surreal numbers having a basis in two players would be relevant to dualism but I see how you got there.
@@codatheseus5060 agreed that hardware and software "look" really different in the universe, but software exists, doesn't it? Software can affect hardware in non-trivial ways, as of course hardware affects software. These layers of information in existence seem to have different, but still real, existences (to my understanding). Appreciating these points are helping physicists disentangle long standing mysteries that are ultimately about information, entropy, energy, and the lack of a free lunch.
@@codatheseus5060 yes, even useful abstractions are tied to some physical substrate where they are implemented, even if they are such a common idea that they would be rediscovered over and over again... Concepts we might call mathematical. The infinite constructions are where the line starts to blur for me between invention and discovery, in more ways than one. But it seems we aren't the only systems that hold a flexible and adaptive kind of software which perceives of infinite forms (incompletely at least). Which is kind of cool, or really cool, depending on how you look at it 🙃
@3:50 a chaotic void is nice poetry, but true nothingness cannot be chaotic in the physics lingo! Not even satanic, haha. Nice metaphor though for the quantum vacuum. Build the numbers out of nothing. I just wish the amateur philosophy nerds would realise the physics vacuum is definitely not ∅.
Ha! yes, we are definitely not done contemplating the poetry of the empty set. :-) all flavors of philosophers are very welcome to keep contemplating here :-)
Instasub.
Thanks, Luke!
Most beautiful edited vedio. I'm research student, I'm looking for research collaboration. My topic is representing number using different digits also for polynomial. It's included prime number, square free number, prime number theorem, Matrix, group, sum of power, r fold summation. Please inform me of you are interested.
Thank you so much! Your chosen topics are very salient to surreal numbers and Combinatorial Game Theory more generally, so it would be very cool if your thesis touches on this, at least, in addition to the more conventional approaches to understanding those topics (which is important to still become an expert in for many respects, in addition to less common ones like this). As you see from the linked roadmap on my about page, I have my work completely cut out for me in applying this alternative foundation to physics (what you are hearing the beginnings of in the episodes thus far, after this one). You can also find my email there, and you're welcome to keep in touch, but I encourage you to rather share thoughts and ideas of your research and any connections you think of to these ideas more publicly, here or elsewhere. I'm afraid I won't be able to collaborate on pure math for awhile, something I wish I could live out in many lives in many worlds, but suspect it doesn't work like that! Either way, please don't be a stranger here, and please keep us updated about how your research and studies go! Very exciting!
You've called your channel 'Surreal Physics', but you'd better had called it 'Insane Math', because there is no physics here at all.
In physics, infinities do not exist.
"In physics, infinites do not exist"... Part of me wishes your wishful thinking was right, but modern physics is riddled with uncountable infinities in the form of continuous fields, tensors of real numbers, and all kinds of infinitesimals fancied as physical. Rather these probably only exist in our minds, but we too often forget they are extremely powerful tools, confusing them with the universe itself. Paying attention to the word choice in this and future episodes, you might find surreal physics is actually a pretty fitting title.
@@surrealphysics Thank you very much for your reply, S.P.
I give you the benifit of the doubt since I cannot judge the videos that are yet to come, but I can assure you that when we encounter one or more infinities or singularities in physics, we try to get rid of them ASAP, because they prevent us from getting any further, so we have to work our way around them.
I'm looking foreward to your next video, and I wish you a lot of creativity while making it.
Maybe not directly about the subject, but this is a video that shows the professors discussing physics in a web-session:
A video from the Quantum Engineering Grenoble channel, called:
Discussion on Non-Locality (with Tim Maudlin, Carlo Rovelli, Lev Vaidman)
Bye Miss.
Thanks for your further thoughts, JW: while the big infinities in physics are often identified as singularities and bad (although actually a lot of still large infinites are employed if they are "well behaved") the sneakier infinities that riddle nearly every subfield of physics are the infinitesimals and continua... These are also infinities that most physicists seem happy to imagine are physical. We will keep digging into this issue as the series progresses. We seem to agree on one thing for sure: to be highly suspicious of infinities in physical theories! :-)
@@surrealphysics A famous example of infinities in physics is the Ultraviolet Catastrophe, and there are quite a few RUclips videos about it.
One example from math is that 0.9999... = 1
Everybody knows it is true, but for physicists it is mathematically wrong because mathematicians ignor the time factor, like there is always time involved in physics.
Everyone who doesn't understand this, should write the number down without using the shorthand notation.
In physics, we also realise that our equipment still isn't sensitive enough to detect the smallest particles, and that we have a long way to go.
Some neutral particles can only be detected when they decay, but maybe we can detect infinite small charges in the future, who knows.
Take care, S.P.
I'm definitely familiar with the UV catastrophe, 😁 all kinds of interesting things to say there... But before I say more, to clarify, are you saying you are comfortable with infinitely small changes and a/the continuum?
despite all the great 3d work and animation this is more like a shitpost
ha! this piece is the beginning of a lengthy introduction, so I can see the analogy, but it is no joke! whatever farce that's here is authentically delivered!
No matter if you're a male or a female, I want to slap everyone talking about this stupid game of Life again
Ha! You are like the spirit of Conway, at least before he made peace with that overly appreciated game towards the end. But if you stay tuned you will almost certainly hear very little about that game, if at all... the play of games more generally is so much more interesting than any one particular game, with all of its assumptions and biased interpretations, impartial or otherwise.
@@surrealphysics that origins of Conway's idea (I didn't even know it was deeper than "some simple rules can produce a sophisticated megastructure") were the most interesting part in this video, I've watched it all. I have the same views, I almost got jealous, but then, here's smth u can do: describe why 0! (it's 0!) and what's sets vs spaces - of which these sets are, OK? there's an inherent 'metric' of alignment of two moments for changes to get measured for time to flow etc etc, I'm publishing soon, there are >2000 books in my head finely tuned to >20 illegal drugs and perfect visions I had to explain - and I have done it, and pretty much all physics, as close to human (and any living being's, incl. that of Particles on some level) experience, too
Sorry, but this is too much empty mumbo-jumbo for me. Surreal numbers are fascinating, but please without the menacing undertone.
Oh no! My mystery tone may unintentionally run menacing, so I'll keep that in mind, thanks! But you may not love the next episode, which definitely spends more time digging into the empty mumbo-jumbo! Some mysteries are perhaps worth some silly sounding ponderings and questions. Perhaps to reveal them as all the less menacing. Anyway, we'll keep unfolding fascinating aspects of the combinational games and their surreal numbers, if you decide to stick around!
If a circle represents an infinite amount of verticies what happens if you erase half of it?
You are moving towards the Banach-Tarski Paradox with this question! Which maybe you knew already: en.m.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox This is part of the reasoning behind my comments (and of course many many before me) that perfect circles and fully-completed infinities are not possible to completely instantiate in the physical universe, because they include our imagined ideas of completed boundlessness (a bizarre paradox that we can somehow make strange proofs and statements about with mathematical tools using infinity concepts). This turns out to not be that strange though, because so much in the universe approaches these infinite forms...trillium, large gravitating bodies like planets and stars, anything with the golden ratio as part of it's construction, which is all over nature... Etc.