Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries | Lex Fridman Podcast

[@lexfridman]

Here are the timestamps. Please check out our sponsors to support this podcast. 0:00 - Introduction & sponsor mentions: - Secret Sauce: wondery.com/shows/secret-sauce/ - ExpressVPN: expressvpn.com/lexpod and use code LexPod to get 3 months free - Blinkist: blinkist.com/lex and use code LEX to get 25% off premium - Indeed: indeed.com/lex to get $75 credit 1:01 - Mathematical thinking 4:38 - Geometry 9:15 - Symmetry 19:46 - Math and science in the Soviet Union 27:26 - Topology 42:15 - Do we live in many more than 4 dimensions? 46:45 - How many holes does a straw have 56:11 - 3Blue1Brown 1:01:57 - Will AI ever win a Fields Medal? 1:10:22 - Fermat's last theorem 1:27:41 - Reality cannot be explained simply 1:33:25 - Prime numbers 1:54:54 - John Conway's Game of Life 2:06:46 - Group theory 2:10:03 - Gauge theory 2:18:05 - Grigori Perelman and the Poincare Conjecture 2:28:17 - How to learn math 2:35:26 - Advice for young people 2:37:31 - Meaning of life

[@Random_qubit]

Would love to see u interview Terrence Tao and Ed Witten

[@worldshaper1723]

Lex I love you and your podcast. But control the length you talk. Sometimes you explain why you ask questions for too long. Please think about this. Very grateful for your podcast and the amount of work you put into it.

[@HarrySManback]

@LightSound Geometry d

[@robmorgan1214]

I do math via feeling and dreams. It's not visual or linguistic for me.

[@ElanaBatshalom]

Lex, you might want to check out this new math - Klein, M. and Maimon, O. (Forthcoming, 2021). “Fundamental of soft logic” accepted for publication, New mathematics and natural computation journal. Klein, M. and Maimon, O, (2020). “The Dynamics in the Soft Number Coordinate System“, The journal Advance in Mathematics. Vol 18 Klein, M. and Maimon, O, (2019) “Axioms of Soft Logic”, p-Adic Numbers, Ultrametric Analysis and Applications, Volume 11(3): 205-215

[@EsaelPaggin024]

Lex, I'll say it again like a broken record.. You have *the* best podcast on KZbin.

[@eduardotijerina3930]

You forgot “by far”

[@mousquetaire86]

Are there better podcasts, outside of KZbin?

[@qwerpasdf]

@@mousquetaire86 hardcore history is amazing but you've probably heard of that since lex talks about it quite a bit. Sam harris podcast is good too. I used to like the freakonomics podcast a lot a few years ago but I haven't listened to them much recently. Also S Town is a great story but that's just a seven episode narrative type podcast.

[@mousquetaire86]

@@qwerpasdf Thanks. I hadn't heard of S Town. (I had heard of all the others.)

[@willd4686]

KZbin doesn't have podcasts

[@awsomenesscaleb]

More mathematicians please. I love this kind of stuff.

[@jwbeats1]

^

[@qwerpasdf]

Perfect timing. Always when I'm bored something good from Lex pops up.

[@Michael_Angle]

facts my friend

[@michaeltalpas]

Oh wow.. I'm one of the rare ones.. I immediately thought that the straw has no holes in it, because it is a tube. A tube doesn't have a hole in it, it is just round. The fact that the straw is slender and tall, doesn't make it any less a round piece of plastic. Therefor, it has no holes.

[@nicolasisaksson1175]

Lex had to work hard to get the answer to what is the Poincare conjecture. Lol

[@eugeneyakshin3199]

**sipping milk though a hole in my pants** awesome episode, thank you! I like the width and depth of it.

[@ballardmallard2138]

The rhythm of smart people talk : speak fast then take a long pause before quickly finishing your sentence and starting the next one.

[@goyonman9655]

Musk

[@kras2255]

1 second in. “So If the brain is a cake...”

[@woodandwandco]

7:44 This podcast summarized in 2 words.

[@trimbotee4653]

Great listen. Looking forward to hearing more from Jordan Ellenberg!

[@pinnedyllmboxrp5933]

Thanks for watching For more tips on how to grow your portfolio Send a direct msg right away Whatsapp.

[@pinnedyllmboxrp5933]

+ 𝟣 𝟥 𝟣 𝟧 𝟤 𝟪 𝟢 𝟧 𝟢 𝟪 𝟦

[@rjb1172]

interview Ed Frenkel. Come on Lex. This one is a no brainer and you should know someone at MIT that has his number. Soviet born brother, mathematician and wonderful guy. This should have happened already.

[@pinnedyllmboxrp5933]

Send me a direct msg right away on WhatsApp.

[@pinnedyllmboxrp5933]

＋ １ ３ １ ５ ２ ８ ０ ５ ０ ８ ４

[@masonart4950]

Language is different from visual proofs in that language must illicit concepts that exist outside of the language itself. The whole is more than the parts. The visual proof is complete and self contained as its own concept, even though we can begin to further extrapolate it through language.

[@grahamhenry9368]

Its a tragic loss to all of us that Lex Fridman wasn't around for the vast majority of human history. We've lost insightful interviews with Plato, Newton and Galileo. Einstein, Godel and DaVinci. If we ever construct a time machine, I think Lex deserves the first seat

[@Tagraff]

The configuration of morphological state with hole: Flatten, Entry points, Inside-Out (whole, polarity), Outter-Lip vs Inner-Lip, Insertion (Single vs Loop), Sleeve (In/Out), Shifting Skin (freedom of moving surface), Density topological (tropical denses, thick skin, light skin), Balloon (Inflate/Deflate)

[@wade8518]

Omgggg! Go lex luther

[@ApePostle]

Amazing Podcast Lex, can you try to get Yau on the podcast? He is a behemoth in the field of geometry (from the analytical perspective as opposed to the algebraic perspective).

[@Hexanitrobenzene]

2:30:08 This story can be summed up in 3 words: Goal, Relevance, Practice.

[@stanstarygin6622]

"You can't visualize the mug while living inside the mug"? Some would argue that's a big part of what physics is.

[@abelmerol]

Fuck yeah,Lex time!

[@gettingthroughlife3860]

Reality can be communicated and simulated through cos and sine wave x

[@shoopinc]

The one scandal with Poincare was his beef with Cantor. Poincare was more of an intuitionist so he never accepted infinite sets.

[@tigershark4238]

deep thought

[@lexfridman2549]

Thanks for your comment, will introduce you to something quite profitable ............. ᴡ=ʜ=ᴀ=ᴛ=ꜱ=ᴀ=ᴘ=ᴘ.+][1][8][3][2][9][5][3][1][9][5][7][📞]...

[@kyuubimitch]

Where’s the Charles Hoskins podcast at tho?

[@georgedotjohnston]

Ok so how could you not have Andrés Gómez Emilsson on here after this

[@smelliestdank21]

Can i please sit in your class! No degree, just want to theorrize

[@thomasturnbull9509]

Hey, this guy was my Discrete Mathematics professor! He was awesome!

[@AA-gl1dr]

Wow you’re very lucky

[@losboston]

Sounds tough and not much fun if no math indiscretions allowed.

[@nate9952]

Oh man, I’m taking that this fall. Wish this guy was my prof.

[@joelomangino4577]

Not very discrete of you to put that on the inter webs

[@Mdautkreix]

Idky but your avi makes me confident enough to bet you got the A.

[@burkebaby]

Lex, I'll say it again like a broken record.. You have the best podcast on KZbin.

[@NicksReviews]

"We'll together walk along the path of curiosity." -Lex Fridman If that's not a slogan for a talkshow I don't know what is.

[@LE0NSKA]

"am I allowed to cuss on this podcast?" "uh, fuck yes." lmao. 7:40

[@PrashantMaurice]

I can empathise with that square flatlander as that's exactly how i feel everytime I watch lex's episodes.

[@dalitshiv834]

What you do? Prashant

[@InkaHacker]

I remember the feeling when I managed to proof some simple theorems. Crazy, is like the universe telling you that order is the underlying principle of the cosmos. I loved it

[@user-pd9sb8ov7d]

My favorite episode. The discussion on homology is fantastic. Amazing to introduce such important concepts which are significant artistic and scientific achievements. Bring on more math!!!

[@dalitshiv834]

**Topology

[@jacobsmith7285]

Fuck, I guess this is what Im gonna spend all night thinking about instead of sleeping. Thanks Lex, keeping the great content coming. You inspire me as a floundering student to keep moving towards the goal, and to stay curious.

[@surpleg]

Thank you Lex. Your format is so refreshing, your curiosity and quality of guests are outstanding. Not to mention your intellect and credibility. I love your podcast, I can't wait to see what else is in store for you!

[@bennguyen1313]

I recommend Sabine Hossenfelder many videos where she talks about how we have *NO* evidence to suggest that there exists simple, beautiful unified theories that explain reality.. and therefore spending limited resources to find such theories/particles needs to be scrutinized. And, for example, even if CERN were to have discovered something new that led to deriving the 3 standard model forces from a GUT, it wouldn't have give us any new insights or make any new predictions that is lacking in our standard model. Regarding multiple dimensions / topology, Sabine also has a recent video ("2+2 Doesn't Always Equal 4") on how the universe isn't expanding into anything (flat embedding space).. and describes how measurements can be done from within the object you are trying to measure, like ants on a ball, to prove that it's growing. Finally, regarding Grant Sanderson's channel (3blue1brown) on learning math, I recommend the Freakonomics episode #391, where Steve Levitt talks about how the math curriculum needs to be re-balanced, with less emphasis on calculus and other tasks best accomplished with computers, and instead, adding (modern) statistics, linear-algebra, and data science. See Salman Khan interview on the People I (Mostly) Admire Podcast Ep. 22)

[@ոakedsquirtle]

I'm so early that it's mathematically guaranteed that 0% of the people who commented watched the podcast all the way through 😄

[@PerfectlyNormalBeast]

What if they are super minds that downloaded it and watched at high speed? I'm only being pedantic because you said 0% :)

[@proddreamatnight]

Let's goooo who would have thought 10 years out of high school i would actually enjoy math

[@frontbattles8090]

When will you upload the cardano meeting?

[@frontbattles8090]

@@KinokoCardano thanks

[@marcuss5115]

2021-06-16 at about 15:39 UTC

[@frontbattles8090]

@@marcuss5115 yep saw it after the first min of release hehe thanks

[@psycho42069]

I've never been so compelled to sit and listen to people talk about things far above my understanding as I am with your podcast, Lex. Although many of the people you have and the topics you discuss are totally foreign to me, you have a way of discussing them that I both enjoy listening to and make me excited to learn new things!

[@carlostapia2822]

I resonate with the first 9 minutes I was pretty good with Algebra and equations, but when I took Geometry I did not understand why we had to work on proofs and why the proof was more important than the fact that I was looking at a square and could prove with a number why it was a square. Needless to say, I passed the class with a C+ and I did not enjoy my teacher.

[@robertwallace5498]

This is my favorite Lex podcast yet. I love it when you go back and forth with the guest. You made a lot of great points. I have been saying the thing about infinity too for a while lol

[@Zeratul1005]

You've been knocking it out of the park with your recent podcasts! I thought this was going to be a boring dry podcast about math but this episode was really rich with both fascinating ideas and questions and hilarious moments of jokes.

[@bartholomewbaltech5622]

@Lex Fridman WTF, Lex? lmao

[@KaliFissure]

I was very lucky and in middle school in the 70s came across the work of Charles Howard Hinton. Changed my life and view of universe. But I'm pretty sure we can describe this one using only 3 physical dimensions and compactified time. This allows every point in the universe to be in contact via infinitesimal NOW. Which also allows and explains entanglement. Kaluza Klein for 3 dimensions and compact time down there in the corner.

[@peterdentice5725]

59:15 The Golden Ratio through the song Lateralus by Tool.

[@miaodu1695]

Nice timing! Just finished his book "Shape" ^__^

[@EugeneSeidel]

Non-math person here. Was hoping for more talk on dimensions above three. I believe in string theory the extra dimensions are "compactified" -- too tiny for us to detect? And that most of the gravitational force, which is inexplicably weak in our 3D, lives there? What about the extra dimensions used by -- is it electrical engineers? -- to solve real-world problems -- these would seem to be entirely different conceptually from compactified extra dims? And if there is a 4D (5D, 6D ...) world of which our 3D world is but a subset, would that be yet another incongruous definition of extra dimension(s)? If we cannot perceive such a higher dimension directly, then can we infer it from effects on our world that could not be explained otherwise?

[@jamieg2427]

something peculiar: b is twice as big as a. written algebraically, usually you'd see b = 2a. but if a = 0, then b = 0 too, and b would no longer be twice as big as a anymore. zero is such an odd number . . . but zero's an even number as well (:

[@WHEATSFPV]

Nothing like getting home after a short day of work and seeing a new Lex Fridman podcast. I feel smarter after listening to these.

[@thezebraherd8275]

I recently finished my Freshman year at the University of Wisconsin and am from Wisconsin. It's nice to see Wisconsin represented.

[@akhiljindal5450]

53:06 "I'm right there with you" I felt that

[@annikolako]

Hey Lex! Regarding visualisations and topology you should definitely check out the work of Robert Ghrist. His Applied Topology book is full of them! In general, it would be nice to have him in your podcast some time! He seems to be quite the character! :)

[@sortof3337]

This was absolute delight to listen to. As someone who is absolutely fascinated by geometry and lie algebra, enlightening as well. :D

[@bobodka]

Lie Algebra i.e. an algebra full of lies??? :-). To the mathematicians, I know Lie Algebra is a thing btw, this is in jest.

[@sortof3337]

Its pronounced as Lee I think, at least that's how our professor did it.

[@MultiAndAnd]

There is a letter of Perelman where he explained that he turned down the prize because he says that he just put together ideas of others. That's it. Also. More than the Fields, which is a prize for young researchers, the Wolf prize or the Abel prize are more suitable analogues for the Nobel.

[@Lucasvoz]

I honestly don't know much about math and geometry, but I try to understand this stuff so that psychedelics might make more sense to me. Also the pyramids seem to contain super complex geometry which is another reason I'd love to learn. This life is very short however, maybe in the next one I'll learn form an early age.

[@Israel2.3.2]

Jordan studied under Barry Mazur, should be an insightful conversation.

[@skittleharbor]

Who is Barry Mazur?

[@tonytanner3048]

@@skittleharbor Cool guy who found some interesting links between number theory and topology a long with many other things.

[@samanthaqiu3416]

most interesting thing that mathematicians have in common with vampires? the mathematicians they studied with become a meta-ancestry, a kind of meta-genealogic tree of inheritance of knowledge

[@7hBruh7]

LEX... HEDERA HASHGRAPH should be the next topic covered. The blockchain alternative that’s delivered what blockchain hasn’t, while avoiding the crypto hype.

[@chyldstudios]

I initially was going to watch about 10 minutes. I ended up watching the whole video.

[@Hexanitrobenzene]

Grant Sanderson (3Blue1Brown) created his own podcast and invited Steven Strogatz, an expert in dynamical systems and chaos theory, also a great lecturer and textbook author. They talked at length about how to make presentation of mathematical ideas more intuitive and a lot more. Highly recommended: kzbin.info/www/bejne/iYawfX6tmqt0j80

[@joshua3171]

"1,2,3.....man this is so hard"-the universe

[@viaMac]

Lex's description of finitism and ultrafinitism were off. Both reject the infinite set of all natural numbers.

[@jeschr3462]

The universe is a hyper-dimensional manifold of some sort I believe.

[@DanielGomez-qg8vd]

You're a better version of Joe Rogan

[@carlkligerman1981]

Language is algebra. Derrida’s Grammatology is mandatory reading, for anybody interested in any type of math or science as far as I am concerned.

[@lexfridman2549]

Thanks for commenting, Get to me directly for more guidance and Information.. W•h•a•t•s•A•p•p +•1•8•3•2•9•5•3•1•9•5•7.

[@ascii1]

Reminds me of Manolis Kellis, he sounds so enthusiastic talking about math, both of these guests have a way of encapsulating you into what they're talking about. Hope you have Jordan on again!

[@Yamikaiba123]

Language is all surface and manipulation of symbols. It has no inherent meaning, but is nothing but pointing to that which is sensible.

[@lexfridman2549]

Thanks for your comment, will introduce you to something quite profitable ............. ᴡ=ʜ=ᴀ=ᴛ=ꜱ=ᴀ=ᴘ=ᴘ.+][1][8][3][2][9][5][3][1][9][5][7][📞]...

[@calebbarnes5452]

I love you Lex.

[@dbitely01]

i dont smoke weed *or any really but it feels like it* lmfao 13:15

[@ekszentrik]

Re Flatland: I think the 2D creatures, in their conception of the world, can be interpreted as non-sapient creatures or naive but intelligent pre-science creatures. The 3D creatures would be equivalent to humans able to perceive something beyond the "natural world" (the 2D plane), which is things like math/logic/science/philosophy -- immaterial, imperceptible things, but (arguably) still real. These 3D beings don't live in 3D space, as the 2D landscape represents actual, material reality. Rather, attaining sapience/intelligence or applying the correct Enlightenment methods has enabled these beings to grasp a new dimension, one of mind/reason, completely orthogonal to the physical plane. And the 4D creature would be, at least from a 3D perspective, something beyond even rational understanding. True understanding, not merely intellectual acknowledgment like us performing n-dimensional math. I am talking about perceiving it as it truly, wholly is, like we can with 3D objects. And the 4D creature would obviously something metaphysical -- god.

[@columbasaint465]

I got clean from coffee over a year ago but this guy's enthusiasm makes me think I should get back on it.

[@Snezana81]

I just thought of this little creative writing idea while listening to your show i can write about * today*. And tomorrow I'll write about tomorrow. And so on. Then, i will extract my comments and put it all together. Why is it so difficult to extract and connect all the notes you have everywhere (on your phone, thru different apps, pc, different folders, etc) so since we are on a topic of mathematical dimensional shapes ( i think thats the title of the show) i want to share a perfect song ive discovered recently. It's called "the grey" by teserract. I am terrible at math. I am not sure why. Another thing i dont even remember studying is physics, so i wonder who erased my memory about these important things. Why do i have to connect everything and be an observer. I'm not sure why i have a difficult frequency to get in touch with or why am i not getting any signals from outherspace, which is yet to be discovered. I had this thought about people getting visions, just like from the movie Bruce Almighty when they hear people trying to reach them, and there are just moments when you hear people, and it gets strange, you kind of get confused. So i imagine all of those amazing scientists who are getting improtant information from the knowledge field. They have to tune into that frequency somehow. Be open to it. At least for the moment. Thats why they say they have sometimes a strange behavior. Once Lex mentioned, what would happen if some scientists didn't discover nuclear power or electrical power or law of physics? The knowledge would be available to the person who tunes into that frequency. We are just names. The future is outhere. You know what i mean. That's all for today. ❤ P.S. This is my first comment. I have to write 400 and some.

[@jonarmani8654]

"Off-By-One Error" Simply yearning for Simple meaning by basics Since never before

[@kartech6938]

Nice

[@runvnc208]

Its so interesting for me because for my simple "computer vision" experiment right now I am literally grouping lines with the same angle using a Python dictionary and then combining them into one line. I mean when Lex points out this stuff is fundamental to AI, I hope other people feel the same way. Because I believe that we will actually get to a place where many real-world scenes and dynamics can be "understood" by AI using this type of fundamental. Especially when you think about it in terms of for example man-made environments that are often filled with regular shapes, machines with simple functions, etc. I will admit that I cheated by using a state-of-the-art neural network edge detection library to get to the point where I could break anything down like that though.

[@calebcreates8555]

I love your podcast dude. Thanks.

[@Orlyy]

When you come to this not being interested in the topics listed, but know Lex is gonna ask about the meaning of life 🤣

[@yuelwar4426]

Dear young brother Professor Lex Fridman. Our research and working motto to share for all : "ita lex scripta and scriptura non pose non picare. Ubi bene ibi patria." God bless you. No time for hiphocratism to learn and working.

[@benitomandelbrot1157]

2:27:48 That sounds like a juicy story

[@IUT-e8x]

Interesting part is people don't realize Ellenberg is one of the most intelligent people alive today, objectively his pre-1980 SAT is 1600 which is extremely g-loaded and accepted pretty much as a professional golden IQ test.

[@benharris6732]

How long till charles lex I've been checking every 10 mins for 2 days lol

[@Danny-hj2qg]

Another software tool for higher-level algebraic math is GAP, (Groups Algorithms & Programming)

[@CREATE-oo8xg]

Can someone describe to me how a 4 or 5d human being would look like?

[@frankdaze2353]

Omg I hit like out of habit and then looked to see 889 likes... my bad yo 8888 is more symmetrical anyway. Get to it

[@zoltanczesznak976]

Terence Tao pleaaase!

[@pinnedyllmboxrp5933]

Thanks for watching For more tips on how to grow your portfolio Send a direct msg right away Whatsapp.

[@willnutter1194]

Lol when you said “there is a humor in it” around 1:37:00, drawing a parallel between the prime joke and the simplicity of explanation of something. Felt like some shade thrown but in a subtle and humble way. Gave me a chuckle. :)

[@gena8414]

yeah I spotted that too. there is some truth in it😂😂

[@GBuckne]

..the human brain is not wired to accept infinity, how can something come from nothing and "nothing" is 0. If nothingness had boundaries it would then be "something", whether extremely large or extremely small, the equation is simple, but may pose a deep metaphysical problem for some...you can ask a question, does nothingness exist? It doesn't. That which doesn't exist is not limited by size, it doesn't exist...

[@joshgrant6290]

A straw clearly has no hole. The problem for me is in the production. For a straw to be made, they dont produce cylinders and then punch a hole. For a bottle to have an additional hole in the bottom, is against its intended form and so thats two holes

[@phaniram5012]

hey @Lex I give you an open challenge: can you interview Grigori Perelman in next 1 year? do you have will power to sign up?

[@stuarthys9879]

On “heavy metal bands explains mathematical concepts”. I request an episode on mathrock and/or the connection between music and mathematics. I don’t know who would be best to discuss this though.

[@DutchCrunch333]

Lex is a stoner, I'm convinced...my people💨💨☺ this was my favorite conversation. Love geometry, AI, mathematics and deep diving !!! This was deelish

[@woodandwandco]

1-hole people.

[@kevinmorgan2818]

If reality is a high dimensional projection, surely it must come from a lower or higher dimensional source. Arguably sandwiched between both lower and higher dimensions above and below. )0( The dot at the centre of the axis could otherwise be perceived as the centre of X, which is ultimately deduced down to it's smallest denominator, a dot, but the dot always had the higher dimensions of a perfect Geometry capable of refracting the highest Geometry such as from a cube you can convert the enerrgy/math into another order/state of matter as the square undergoes transmorphism to become a rectangle. From the perspective of a bird we are 2d, until close enough or at an angle other than directly above to see our shadows change shape around us as we become observable in our higher dimensional state.

[@DrDeuteron]

2:12:00 Saying Lorentz contraction is an illusion will cause confusion. While it is true that you don't contract when someone else sees you moving (that would cause real problems), rather they see your space and time differently, and according to them: you *are* contracted.

[@stargazer8718]

If you live on a "line", and the line is all the existing space, you can't know it's a line. Imagine you're in a boat on a water planet 10 times larger than earth, and nothing else is there. Just you and the boat. There's no way to tell/prove you're on a sphere.

[@HiveGod-k2d]

47:44 Its almost as if there's some underlying force that keeps everything, even opinions, balanced 😉😉

[@MIKE_THE_BRUMMIE]

I think the universe itself is a super structure that can only be observed like the proverbial orange 🍊 in 2D space where you only see a point and ever increasing cross-sections of said orange till it is a point again. Maybe the universe before the big band was that starting point of a super structure moving through 3D space and time as the 4th demention that allows it to express itself in the 3rd. So the big bang is actually just the ever increasing cross-section of this super structure.

[@honey-py9pj]

It's like Lex reads quanta magazine

[@kevinmorgan2818]

If the centre of the universe was perceived as a bubble being popped, a big pop, the expansion of the universe could be perceived as the big pop still occurring, and the air contained inside the bubble is still emerging outwards like water against a beach, whilst the initial shockwave of the pop expanded faster than the air, so powerful it created a vacuum that is directed towards the shockwave at the edge of the universe. The space inside the bubble is the initial driving pressure, whilst the secondary pressure is the shockwave, the third being the residual energies expansion, the fourth being the vacuum of the shockwave itself, and the 5th being a host of resisting forces and everything inbetween other force connected, taking the energy transformations a long, finite, interconnected series of energy exchanges. Like a dot in the centre of a circle, the dot is the origin that produces the larger circle, whilst the lower dimensional circle is like a magnetic field that repeatedly grows in power to jump to a point that helps sustain it's field like a self sustaining forcefield capable of drawing power from itself and replenishing itself like a form of perpetual energy driven by a loop of creating and collapsing fields to create mini pops, spanks or resistance at point of convergence and field expansion direction, hence the expansion in all directions, starting with the path of least resistance. Think of this like a pair of magnets coming together at an accelerating pace the nearer they are together to converge, snapping together and collapsing the field inbetween that forces an energy exchange of the new unified field that displaces it according to it's field. The increased speed as the magnetic fields attract eachother are essentially creating more energy than put in. This could be perceived as something from nothing, or deposits of energy, masses created by the collapse of the field, comparable to pinching a finger that leaves you with a black mark. The black mark could be perceived as an antimatter deposit, a black hole mass with its own additional smaller field, or even a wormhole. The influence of the deposit (like a carbon deposit after burning fossil fuels in conventional combustion engines).

[@FAK_CHEKR]

Are there really three dimensions, or is ‘dimension’ only a concept that helps us do the math? Why? Because there is no such thing as a two dimensional object. If you shrink one dimension of an object to zero, the object does not exist. So, in a sense, each set of two dimensions is entirely dependent upon the other one. They are not separate, distinct things. We hear so much talk about ‘extra dimensions’. I question whether there are any ‘dimensions’ other than in the math that we invent. Three dimensions may be the best way we have at present to describe space, but a better description is out there somewhere.

[@wade8518]

It's funny how Kepler was able to put this into two-dimensional graphs 300 years ago😊

[@2894031]

Getting Grisha in your podcast would definitely be the biggest sensation ever