The search for the biggest shape in the universe.
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- Опубликовано: 10 сен 2024
- Love Triangle sweepstakes are open until Monday August 19th: sites.prh.com/...
Details on where you can pre-order/buy Love Triangle: bit.ly/3wCTesR
Or if you just want it from Amazon, this is my affiliate link: amzn.to/4fy30Ph
For people in Europe, signed UK copies are still available on Maths Gear: mathsgear.co.u...
“Search For Largest Polyhedra” by Donald Grace
www.ams.org/jo...
Thanks to Bill Hedges at Cosmic Films Studio in Nebraska, USA for having us to film our sci-fi adventure. Check out Bill’s Cosmic Cat series: / @williamhedges1519
Thanks to Laura Taalman for 3D printing the fantastic shapes for me. She's a Professor of Mathematics at James Madison University. mathgrrl.com/
Thanks to Roger Antonsen, for testing the local maxima of the Grace shape for this video. Roger sadly passed away earlier this year. His department at the University of Oslo have published a memorial page to celebrate him: www.mn.uio.no/...
Geogebra model of the Grace's Shape made by Sam Hartburn.
Much appreciation to Donald's children who talked to me about late nights spent with their father watching a computer crunch away at some math.
Huge thanks to my Patreon supporters. I could maximise the occupancy of a unit sphere with my gratitude. / standupmaths
CORRECTIONS
- 00:23 I say "August 22" which is wrong: this Tuesday is August 20. Please don't tell my publishers I got that wrong.
- At 16:50 I say "eight times" which is completely wrong and not part of the formula. No idea what was going on there. The onscreen value (and everything else I say) is correct.
- Let me know if you spot anything else!
Filming and editing by Alex Genn-Bash
Additional footage by Bill Hedges
Written and performed by Matt Parker
Voiceover by Gemma Arrowsmith
Produced by Nicole Jacobus
Music by Howard Carter
Design by Simon Wright and Adam Robinson
On-set entertainment by Cosmic Cat (and kittens)
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
To bodly go where no mathematician has gone before...
Star Trig!
Aboard the USS Enterprism!
Incidentally the dilithium crystals have this very shape.
Where's the cosmic cat link?
Okay, i finished feeding my cats and I found it, if you Google William Hedges Cosmic Cat you'll find it.
His ongoing mission: to explore strange new shapes, to seek out new sums and new divisions....
@@iteerrex8166 Hmm, I thought they were rhombic dodecahedra....
Matt has himself found something truly remarkable: a reason to go to Nebraska.
Ouch
bruh. true
Not just Nebraska, but Lyons, NE which is a blink and you'll miss it going down the highway sort of town.
It's not the first place I'd expect would be the location of... well, anything.
@@vigilantcosmicpenguin8721 Maybe a missile silo or a Warren Buffet tourist attraction
Between Bill and friendly horse guy, its nice to see non-mathematicians find love and joy from math and computing in their lives and hobbies
And that guy who discovered the einstein tile! Can’t believe that paper hasn’t been peer reviewed yet.
@@ferretyluv I suspect it's because his peers don't have the credentials to appropriately review it, while the one who do are not his peers. They should review it, though.
@@jorgelotr3752 He did hook up with a legit mathematician to publish it on arXiv. So there’s no reason they can’t find a peer review for it.
I got to speak with friendly horse guy just yesterday! He is indeed quite friendly (as are his horses!)
it's*
This just makes me wish Matt had a kids' show about maths. If this is any indication, he'd do it very well and be the maths equivalent of Bill Nye for the new generation.
I think Bec Hill should have the Show and Matt is just like the special guest math character. Triangle Guy
I had the same (similar?) thought, that this is like a math kids show for adults haha
What do you think stand up maths is?
I'm getting Space Teens vibes, from How I met your Mother.
He is in at least one talk, maybe more, in the "Christmas lectures" series aimed at children on @TheRoyalInstitution.
I have to say Matt I've never seen you so well or evenly lighted.
It's what professional studio does!
He is indeed a clean and well-lighted face.
Lit
@@simatbirch "lighted
/ˈlīdəd/
adjective
1. provided with light or lighting; illuminated."
Both "lit" and "lighted" are acceptable, with the more common choice depending where you're from. But even in America, where "lit" is more common, author Ernest Hemingway wrote "A Clean, Well-Lighted Place".
@@KBRoller it’s still lit.
From squaring the circle to cubing the sphere.
octagoning the sphere?
dodecahedron-ing the sphere
Almost sphering the sphere
@@Emma-i9x octagons are flat not 3D, youd put an octagon in a circle not in a sphere
free Ireland!
So, what shape is it? Does it have a name? Does it have other properties that make it interesting? etc. I feel you skipped the most interesting part of this whole thing, the shape is what I was hoping to learn more about...
Yeah, Matt! What is the shape? You can’t explain to us the construction of even the locally maximal shapes and then vanish into space without a word about the shape that we were searching for the entire video!
With all equilateral triangles it would be a snub disphenoid, one of the Johnson Solids. So irregular snub disphenoid could be a name for it. en.wikipedia.org/wiki/Snub_disphenoid
copy of my answer to another comment:
You know the two parts of a tennis ball? Put four points along the longer center line of each part, equally spaced. That's your eight points.
-> The optimal shape has the same symmetry as a tennis ball ;)
PS the spacing is 2*arccos(sqrt((15+sqrt(145))/40)) = 69.4°
Thank you!
@@deinauge7894 0.4 degrees past true glory :(
Did I miss seeing the shape up close in the video? Matt showed a lot of other shapes close up both physically and rendered on the computer but I didn’t see where he showed a nice, close up view from different angles of the final shape.
Nope, he just didn't show the shape. I hope he makes a follow-up to expand on the topic, maybe share the proof of the shape's absolute maxima property
@@chilldo5982 I agree. I'd even like to see this shape available on mathsgear.co.uk
Here are the vertices of the shape. You can paste them into Desmos 3D graphing calculator to see what it looks like:
(0.9700, 0.0000, -0.2432)
(0.5692, 0.0000, 0.8222)
(-0.5692, 0.0000, 0.8222)
(-0.9700, 0.0000, -0.2432)
(0.0000, -0.9700, 0.2432)
(0.0000, -0.5692, -0.8222)
(0.0000, 0.5692, -0.8222)
(0.0000, 0.9700, 0.2432)
Agreed. He had good diagrams and verbal descriptions of the local maxima, but not the best shape. I don’t really understand the final shape or why it would be the best. But I do know it’s a weird square root of a fraction with a square root.
What is the minimum number of points necessary to define a torus?
I wish this had included a description of the shape itself
Vertices were 6 points along the equator and two opposing points. But yeah no name given or description of its other possible properties... or whether there is a function for x number of vertices to maximise volume within a sphere.
@@Hesnotoneofus, please doublle check your result. I make out four vertices at which five faces meet and four vertices at which four faces meet. I think that implies there is no coplanar set of six vertices. I agree with @Jellylamps in wishing for a more exact description of the shape.
Here are the vertices. You can paste them into Desmos 3D graphing calculator to see what the shape looks like
(0.9700, 0.0000, -0.2432)
(0.5692, 0.0000, 0.8222)
(-0.5692, 0.0000, 0.8222)
(-0.9700, 0.0000, -0.2432)
(0.0000, -0.9700, 0.2432)
(0.0000, -0.5692, -0.8222)
(0.0000, 0.5692, -0.8222)
(0.0000, 0.9700, 0.2432)
@@Hesnotoneofus Matt said 5 at the equator
@@stevechrisman3185 I think thAt was one of the local maximum, no? 5 on equator, 2 above, 1 opposite.
I'm a little upset we didn't get to hear more details about the shape, I barely even know that it looks like! (Pink, presumably)
same, esp since the 2nd best down was interesting
We know it's not round...
@@tiagotiagotwe also know it’s…what were we talking about again?
It's a snub disphenoid ( en.wikipedia.org/wiki/Snub_disphenoid ), squashed a bit so it fits in a sphere
I assume it's just the shape with the largest angle possible between all points, and all points being all equally spaced from all adjacent points. Maybe that's not possible, but it will be close.
It hurts my brain that it's not more elegantly symmetrical. I feel like Pythagoras would have killed a man if they told him about this shape.
It has the same symmetry as a tennis ball. Sort of a helical radial symmetry. It does have one curve of symmetry, just not a line of symmetry.
I just finished my PhD in computer architecture a couple weeks ago, and seeing a computer I actually read about on this channel has made me unexpectedly giddy. Matt, you made my day.
I don't have PhD in any subject, but I adore old computers. The best fact about them is that during that era the US government published yearly reports with not only total amount of computers in the US, but also how many of each model there were! And the sad fact is that Soviet secrecy hid even the number of computers in the USSR. Luckily there were not so many Soviet computer models, so we at least can estimate. For example, my research (I used several approaches, and all gave similar results) shows that in 1975 there were about 10 000 computers in the USSR, while the US had almost 20 times more!
@@saszab That's amazing! I'll have to go take a look into that when I get a chance!
Thank you Bill for keeping these old sci-fi (and mathematical) oddities alive!
I wish there was a bit in the video where you had a closer look at what the shape actually looks like. Or gave us the name of the shape, so we could look at it on our own time. Something like that.
It's called Jimbo's shape
"Let's show a 3D model of a few other shapes, but not the best shape"
Parker presentation: Tell us a solution exists, have a 3d model made, but never explain it.
Agreed. I was really interested to at least get the proof paper about the shape, but nothing even in the description! Cool either way that this was done by a computer, I enjoyed the watch, but disappointed that the shape wasn't elaborated
Yeah, even tho the title suggests that it’s the first shape duscovered by a computer, it’s in a maths channel so i want to know more about the shape, not about the computer
The later Burroughs are interesting because it is not Vonn Neumann architecture but , it had what we would call a hypervisor built into the hardware and would switch between processes to provide symmetric multiprocessing - you could not elevate your privileges to the level of Hypervisor. It was a stack machine with virtual memory and 48bit word size. In 1961!
I don't remember the model, but I read about a Burroughs computer that allowed user micro coding. You could even choose the number of bits in a word.
Yupp. And they had an interesting file system implementation too.
@@johnbennett1465 Maybe you're thinking of the B774. It had "Nano Memory," "S Memory," and "Micro Memory" As I recall, you could design your own op-codes, though I learned to fix it, not to program it. TBH, it was always a mystery to me and I thank my lucky stars that the one I was (partly) responsible for never broke down. The part I did like about it was that there were signal names like "True Blue," and "Stupid," in the diagrams.
@@HSkraekelig I don't see how you would ever be able to do your own opcodes because those correspond to physical toggles. I suppose you could make up all sorts of "illegal" opcodes since it was a stack machine and therefore most of your operations wouldn't need an address at all. You'd instead just send a postfix operation to tell the ALU what you wanted it to do and it would just do that operation on whatever is on top of the stack.
Rumor has it that skilled users of the Boroughs 220 console now posses the more modern skill of being able to read QR codes at a glance.
Ah, the lost thrill of booting your code oby setting a bank of toggle switches on the front of the console. "Booting" the code? Reading the first punch card in a deck with the JCL for the rest of it.
It's 4 bit BCD, not really hard to read as it is a decimal computer.
@@swankeepersdoubtful the Burroughs had JCL 😂
That'd be a fun build, an old-timey computer with flashy lights that just generates QR codes to the actual data.
"Used a motor-driven cam for the blinking lights"...can't get more anti-digital than that.
Analog still rules.
I don't know what I was expecting to make the lights blink. Maybe some rat's nest of a circuit board. Can't argue with the classics, though.
@@Veylon I was half expecting him to say 'an arduino'
…no, that's still digital - it's using discrete "digits" (the lights can still be interpreted as 1s and 0s).
Even Babbage's analytical engine (had it been completed) would've been a digital computer, despite being completely mechanical, since it would work with numbers as digits, not as, say, a position on a dial, like a speedometer.
lights turn on and off so its output is still digital
I love the still Matt chose during the mini-add for his book. His expression and the hands are awesome, this guy does not take himself too seriously.
@@FLPhotoCatcher what
@@FLPhotoCatcher JK? What? 😉
On a set, and he is still totally being himself 🤣🤣
"Oops, gotta put the ship in park" 🤣🤣
Yes he is, but he didn't put a Cosmic Cat link in the description as yet and there seem to be quite a few cosmic cats on the internets. We'll go off and find it in a while but just wanted to note this so maybe somebody else will paste in the link since I have to go feed my cats.
Could that be a reference to Capt. Pike asking: "Did you remember to release the parking brake?" After which Mr. Spok clarifies for the pilot: External inertial dampers. Yes I actually watched that movie.
@@2ndfloorsongs It's in the description now, he must have just added it.
Missed a massive trick though. "Forgot to put it in parkER"
@@trimetaI'm not normally so impatient, but my cats were pressing me hard to feed them. And yeah, it's there, cool.
I actually did my PhD in math in this exact topic, Super-shapes, hyper-sizes, etc and how it relates in Reimannian Geometry and spacetime. It was so challenging especially when trying to explain to people not in the know. My proudest moment was when I co-authored the paper discovering the largest shape ever was your mom.
Edit: I spelled Riemannian wrong. Sue me. Some of you have the biggest shape in the universe stuck up your asses lol
Thank you!
If you can describe something, even if very complicated, to the layman then you know you really understand it! If you're unable to do that maybe you don't!? 🫠
@@jeffknott1975 1. It’s a joke. 2. You’re loosely quoting Feynman. 3. It’s a joke. How’s that explanation?
@@ruckingrugger6365 not good enough no and I'm not sure I believe you, you're gonna have to do a lot more persuading than that! A 100 word essay? Maybe affidavits from friends and family confirming you have a sense of humour? Videos of funny quips or humorous situations you've been in will help! 🫠
Thanks, Mom!
I'm from Eastern Nebraska, and I love computing history. I'm sure I've driven through that town dozens of times and would have never imagined that this gem was right under my nose!
I catch myself drifting away from what he's saying and going, "Man, he's sweaty....oh, wait, that's the design on the shirt." It's just the right, or just the wrong combinations of shades of grey. Amusing.
The shape of the implosive lens (the boundary of the two different explosives) needed to produce a spherical shock was attacked by punch card machines in the 40's. The Navier Stokes equations were literally what the first digital computers were built to solve. They were all about shapes. Folded wave guide horns are another early example. Nozzles of all types were investigated. Orbital mechanics and trajectories were studied by human computers. Michells integral solution to the free surface wake of an actual ship was computed by hand in 1898.
From what I can tell from some quick web searching, the 220 had nine (9) registers with 44 bit words, and a very basic instruction set (even by early RISC standards). Pretty impressive that people managed to program this machine to find a new shape given those constraints.
I'm usually the type of person who just listens to videos, but Holy Mackerel! This set is so beautiful that it would be a crime to miss out on the visuals!
to everyone complaining about the shape not getting more screen time: while I agree a few extra second was due, this was really more about the application of a generic method (gradient ascent) to a specific problem (volume maximization) than the final result. The appeal of the technique is that you don't have to have an analytical understanding of the problem, just an idea of how to start, and a way to measure how much improvement you have. Yes, it's proto machine learning.
Yes, but literally he spent significant time showing detailed comprehensive renderings of two local maxima shapes. If he spent merely that on the final solution, (almost) no one would be complaining.
"Out this Tuesday August 22nd" Neat trick, considering this Tuesday is the 20th
I propose this was actually filmed last year, or in 2028.
he noted in the description that it was a mistake
That's because they're in the UK, time zones and stuff
It's called a Parker date...
what if matt really committed to the 1960's bit and he's referring to tuesday, august 22nd, 1961 (or 1967)
That set is absolutely beautiful and well-kept, they were probably very happy to have it used.
Those of us who were computer nerds in the 60's and 70's may remember that Burroughs was quite popular among banks because of their greater speed for their purposes than GE, Honeywell, Sperry, or IBM. NCR tried it's hand in the market, too.
RIP Roger. Nothing I can say will do him justice, he was such a generous person and incredible teacher. Roger inspired me to apply to university when I was still in high school and he taught the logic courses that shaped my thinking to this day. Thank you, Roger, for everything. You will always be my hero. 💐
Dude. This is one of the best stories I've ever seen. I just kept saying "awesome", over and over again.
T̶h̶e̶ ̶s̶e̶a̶R̶C̶H̶ ̶f̶o̶R̶ ̶t̶h̶E̶ ̶b̶i̶g̶g̶E̶S̶t̶ ̶S̶h̶a̶P̶e̶ ̶i̶N̶ ̶t̶H̶E̶ ̶u̶N̶I̶V̶e̶r̶s̶E̶
The search for the biggest 8-cornered polyhedron in a unit sphere.
Protip: You can strike through text by putting dashes on either side instead of copying special characters
-like this-
@@katakana1 -oh i didn't know that-
-cool-
@@RhombicTriacontahedron-really?- -wow cool-
With all 8 vertices lying on the sphere
annoying that he didn't explain the shape. he went into details about those suboptimal shapes, and yet not the one that actually made it
I think Matt forgot! Oh well, sometimes Matt gets over excited. 😂
1:45 "(...) sorry, forgot to put it in park"
Can't let that happen, after all he's a Parker.
@17:43: "...there's no better way to find out you're wrong than to put something on the Internet..." 😂
A corollary to Cunningham's Law.
Bill is the geeky uncle almost none of us had but almost all of us wanted.
Three cheers for Bill!
hip, hip!
I love these little historical contingencies, like the designer of this computer's console could never have predicted that they would have been forming the basis of the western world's aesthetic of retro-futurism decades later.
Could they really not have anticipated that? The industrial designers who (presumably) designed the outside (since getting engineers to do that is rarely a good idea!), must have been inspired by science fiction works at the time, surely? The writings of Isaac Asimov and others? Take films for instance, a flat screen display appears in "Things to Come" (1936) and a tablet computer appears in 2001: A Space Odyssey (1968). I can't imagine that industrial designers of those later items weren't inspired by the arts departments of these earlier films?
Matt Parker, forgot to put it in park.
He forgot to put it in the Parker square
Matt Driver
Parker parking
Lovely Burroughs computer! The Batcomputer in the Adam West Batman tv-series was also a Burroughs computer of some kind. I collect mechanical calculators, and have a couple of Burroughs machines, including a unique pink calculator that was made especially for Princess Anne.
.. & BigClive ;)
Jaap is in the house! I’ve got a hunch Chris Staecker and Stephen Freeborn may be lurking in these comments as well 😄
the production values of this video are through the roof.
fun fact: we still use gradient ascent (and descent) all the time today. It's even behind the training method for chatGTP style neural networks. Which might mean it's actually the most commonly performed mathematic computation that's more complex than simple arithmetic (I realize that's a bit hand-wavy but still, with the amount of gen-ai training going on these days there's *a lot* of gradient descent computations happening every millisecond.
What is the name of the shape? What are its properties? Looks like a shape of triangles? Is there a picture of it, that explains it's properties? Also is there an explanation, why it is the larges volume in the sphere or even a proof?
Yeah, after all that, I would have liked a closer look, a deeper dive. You have time for the history of stage props, but not to show us the whole objective? We don't know what it was called or even got a good look. Why not at least paint the sides different colors or color the edges? Why not talk about the shapes of the faces? All that build up and then we don't get what we really want.
en.wikipedia.org/wiki/Snub_disphenoid but irregular.
@@ksjazzguitaryt Yeah, the even lighting of the studio he's so excited about actually completely flattened out the shape visually, he didn't give us any closeups anyway, but even zooming in on it I couldn't really grasp what I was looking at.
You showed the two local maxima in detail, but not the one shape we all came here to see!
I love how this might be the earliest shape discovered by computer, but it also might be the local minimum for the earliest shape discovered by computer. So meta
Why didn't you show a diagram of the biggest shape or even a close up of it. After watching the video, I know a lot more about the "almost biggest" shapes than I know about the actual biggest shape.
Really cool to see where math, computing, and film and television collide.
Ah yes, my favorite RUclipsr, Matt Forget-To-Parker.
I absolutely love how you stumbled upon this really cool studio. I imagine he started this as a project a long time ago and he’s built it into this in retirement. I aspire to have that kind of hobby and drive into retirement! Really cool!
"Oh I can use this studio?" Then precedes to use every inch possible, almost like the subject of the video! 🤭
Not exactly a shape discovered by a computer, but this might be interesting too.
The Strandbeest by Theo Jansen is a walking art installation with many three-segemented legs. The artists has said that he found the optimal 3-segements lengths (so with the largest forward step distance) by running a simple basic program on his Atari ST. He let the program run overnight which tried many random combinations of lengths. Then he took the best results found so far for the next run, and so on. Iirc he mentioned that the ratio of lengths he found this way, back in the 80s, was in fact optimal.
This shape is highly relevant to EVE Online players, as it also represents the optimal scanner probe arrangement. I'm glad I worked out the square anti-prism on my own (the one on the right at 15:30 ), but I'll be sure to rearrange my probes if/when I log into EVE again.
Is your profile pic supposed to be part of LSD? Because it's missing the double bond in the pyramidine ring if so. Otherwise all we can see is 6-methylergoline.
@@jwnomad It's deliberately not supposed to be part of LSD. It's from a paper about the structure-activity relationships of LSD derivatives and it was only titled "compound 11" (IIRC, they didn't actually make or test it). The closest existing analog with literature would be a compound called RU-28306, if you want a point of reference. It should be very active at 5HT2a, and possibly dopamine receptors and/or 5HT/DA reuptake as well. Unlike ergoline, it lacks that 4th ring, making it easier to synthesize, in theory. Also it's not prohibited by any laws so people can have fun until regulators catch on.
The proof that it's the global maximum sounds much more interesting than the search for it in the first place. How were they able to prove such a thing?
My instant response to the video's title is, "How did it manage to outline your mom!?"
Yes, I'm 13 years old and have been for almost 34 years straight now.
I love that he's uploading so regularly, so often I find myself saying "man is there another Matt video I haven't watched yet? not really" and then he uploads in a day or two.
Parker’s shapes are friends, but they aren’t platonic.
"I'm in love with the shape of you"
I actually used my phone while watching on TV to say that this filmmaking is awesome.
If you search for the digits of the number in 16:40, namely 1,8,1,5,7,1,6 in the OEIS (Online Encyclopedia of Integer Sequences), then you will get a result that cites Berman and Hane's paper.
This is the second or the third time Matt has ended up in nebraska. Finally putting us, nebraska, on the map.
I love stories like that - about people with passion and everything that goes with it
Some of the earliest uses of digital computers were things like crystallography and aerodynamics, and identifying molecular structures or optimising airfoils could be "finding shapes". The fourth significant computer lab in the UK was a crystallography laboratory at Birkbeck College, London where pioneers like Kathleen (invented the first assembly language) and Andrew (invented Booth's multiplication algorithm) Booth both worked; they had machines working on X-ray crystallography in the late 1940s and early 1950s.
Other early computers worked on the development of nuclear weapons and may have been used to discover or refine some very particular shapes...
I wish he would have shown/explained the proof that it is an absolute maximum. I also wonder what the curve looks like if you add more vertices to the shape.
Feels like I got a whole preview of this video at the An Evening of Unnecessary Detail event!
August 22nd is Thursday, Matt. You can thank @singingbanana for that.
This is what I get for recording a voice over late at night! I’ve added a correction. Please don’t tell my publishers I got that wrong.
@@standupmaths 🤣🤣🤣
@@standupmaths No, see, it’s the Twenty-Second, so it’s TWOsday! It was obviously an intentional joke! (Just roll with it)
He’s got such a historic monument that he should be worried about the British museum stealing it
You could have explained how the resulting shape is...
how it is what? a shape?
@@jwnomad Like how explained that another local maximum was 5 on one axis, a perpendicular point and two on the other side, I want the explanation for the actual maximum
@@MortalMercury It's just a medial complex with four valence 4 vertices and four valence 5 vertices. The fact that the solution has no simple polar or cartesian coordinates is kind of the point of the video.
@@jwnomad it's just a fkn what? That might have made sense to you but to most of us it's too advanced to understand intuitively. An explanation of what you just said is exactly what would have improved this video.
@@dielaughing73 It's a slightly pointy thing that fits inside a sphere
"More on that shape after these important messages." *an actual ad roll begins*
What a cool video. I love when happenstance leads to some additional content like this.
Man, I love that set! Reminds me of the old sci-fi shows I watched in reruns when I was a kid. They were obviously fake but had some kind of magical alien quality to them. It's hard to describe, but awesome!
15:17 "These two shapes have a volume of 1.626288. They are both bigger than the back-to-back hexagonal pyramid."
Are they Matt? Pretty sure that 1.626288 is less than sqrt(3)
The 3rd shape shown here is also still smaller than the double hexagonal pyramid.
I had the same question.
maybe he meant bigger than the cube?
16:39 He then says it's 1.815716, which is finally bigger than √3
lmao you can tell matt is having so much fun on these sets
Matt i love your books and i always buy them but i also feel like if i wait long enough the entire book comes out in amazing high production quality videos like this one.
Not complaining at all. Seeing the information in two different formats helps retention a lot. :)
Matt walks out of the Jupiter 2 space ship onto an alien planet. Danger Matt Parker Danger!!
Rest in peace, Roger 😢
"There's no better way to find out you're wrong than to put something on the Internet."
What a positive way of stating Cunningham's law
Cunningham's Law: "Anything that can go wrong will go wrong."
This might be something for the LOST MEDIA crowd: Years ago I have seen an old documentary on RUclips about geometrical discoveries, that also included this exact finding. The documentary was probably from the 60s or 70s and it had amazing animations and models. I remember it to be very entertaining and informative at the same time. If someone knows more about it or knows a link where I can watch it please let me know. Thanks!
What a beautiful video Matt, thanks for all your incredible work! Regards from Argentina
We found him. The man that made the lights blink IN sequence!
"You can use our sets, which one would you like to use?"
Matt: "Yes"
For a moment, when he almost forgot about being in "Park". He was just Matt 'er.
@UsagiElectric enters the chat...
If you call that spaceship a Matt, then this makes Matt Parker a Matt Parker
1:46 The true Parker
You need to keep that new theme song!
I love how Matt travels to world for these videos.
Nebraska! Make sure to get some footage of that triple landlocked place!
I love how in the 60’s “surfing culture” music was so popular that it made its way into tv show and movie music, from futuristic space themed programs to “horror” type shows and movies like “The Munsters.” There are a ton of spooky Halloween songs with surfing sound. It’s a strange mix, but it blends well in my opinion.
Postulate a spherical universe...
And in vacuum...
On a frictionless plane...
Of unit radius...
4:07 That's the old 8sqrt(3)/9. How refreshing! (The long diagonal is sqrt(3) times the side, and since it's inscribed in a unit sphere with diameter 2, the long diagonal is 2, and the side is 2sqrt(3)/3. Cube the side to get the volume. Whatever the long diagonal is, the volume is (d^3)sqrt(3)/9. Such a nice number too.
So what's the biggest shape like this with 9 vertexes? 10? Do we have an efficient way to find them for arbitrary N vertexes, besides just stochastic gradient descent? And can we reverse that question, and find the shape with the fewest number of vertexes for which the volume is at least some given percentage of the unit sphere?
Sorry to be That Guy but the plural's _vertices._
@@hugobouma They're both acceptable plurals. I mostly heard "vertices" in school, but over the years I've also heard "vertexes". Cambridge Dictionary includes both, and there are plenty of examples of either being used in real-world language.
Most importantly, though, is that language is descriptive, not prescriptive, as long as communication is clear; and I don't think anyone is struggling to understand what "vertexes" means 😁
@@KBRoller _Linguistics,_ the study of language, strives to be descriptive. Languages themselves have rules.
@@hugobouma Yes... descriptive, not prescriptive. The rules arise organically and change over time. Linguistics just describes what they are currently, it doesn't decide what they should or must be. So as I said... both are currently acceptable, and either way, the communicated idea is clear irregardless of which is used.
(...yes, I did say "irregardless" to be snarky 😁)
Watching him have nerdy fun on the set is just wonderful. Lol
What if we asked about the shape with largest volume with 6 faces? That's gotta be the cube right?... Right?
12 faces should be dodecahedron, 20 faces icosahedron. Would be interesting to compare to the "buckeyball".
@@yudasgoat2000 I think 12 vertices should be the icosahedron
Excellent. That computer should be featured in a Top-Shelf magazine.
Very attractive. x
Haven’t watched the video yet but I drew a pretty big circle once I bet this shape wasn’t bigger than that
Turns out that no, it probably isn’t (dimensional inconsistencies aside)
When i was in school (HS), we had a mini-computer (an HP2100, a PDP 11 clone). For an open house, we programmed it's front panel to flash random patterns (normally the lights changed so quickly as to be constant) so it would appear like people would expect from popular media. That was fun to do.
Episode 3.14... I see what you did there ;)
Yes! It's half tau
Should've done episode 6.28 honestly
@@TheMysteriousQui That will be the sequel.
The Antikythera mechanism from 100 BC was used to calculate astronomical positions
With great filming gear, comes great responsibilities, and Matt's aced it.
No spare parts to be found, but would it be possible to remake the parts? I'll admit, that if the machine wasn't popular, then the schematics probably wasn't worth conservation, but one can hope.
Weren't these computers hideously expensive in period (not surprising given the sheer size of them, same for transistorised computers too before the cheap & cheerful integrated circuit)? Unless it's only a small number of boards or components that are being remade, I can't see how it would be cost-effective for hobbyists (even if all the basic tubes and other base parts are available)? Online it says the Borroughs 220 was $30,000 USD in 1960 dollars (about six Cadillacs at the time), which is about $315,000 USD in 2024 dollars.
Should let Bill Hedges hold onto that 3D printed... thing. Then he can have the computer *and* the shape it found.
Matt did actually leave it for me, I have it at the studio.
How's the hunt going for a 3-sided coin?
Heads; tails; the edge
@@RB-bd5tz quite a while ago Matt asked how thick does a coin need to be before landing on the edge is equally as likely as either heads or tales. He was working on a model (3d printed a bunch and "rolled" them) but that was largely inconclusive.
@@MrMaelstrom07 I know from experience that a round pill, if dropped, invariably lands on its edge and rolls to the most inaccessible part of the countertop, table, or floor.