@@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".
@@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.
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 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.
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!
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.
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.
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.
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
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°
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)
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.
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. 💐
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.
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!
@@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.
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!
…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.
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.
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.
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
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!? 🫠
@@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! 🫠
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?
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!
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.
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!
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.
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.
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
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.
@@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.
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.
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!
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?
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.
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.
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.
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.
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.
T̶h̶e̶ ̶s̶e̶a̶R̶C̶H̶ ̶f̶o̶R̶ ̶t̶h̶E̶ ̶b̶i̶g̶g̶E̶S̶t̶ ̶S̶h̶a̶P̶e̶ ̶i̶N̶ ̶t̶H̶E̶ ̶u̶N̶I̶V̶e̶r̶s̶E̶ The search for the biggest 8-cornered polyhedron in a unit sphere.
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. :)
Dear Matt, I love how much fun you have with your vids. I cannot imagine your face when you were given free roaming within the studio! I could see you trying not to crack a huge grin as you walked off stage left towards the end. Honestly, send this in to ABC Australia and they'll nab you for Play School in a heart beat. You could earn some more multi coloured money papers again!
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.
You have outdone yourself. You have a talent for making math interesting and put a lot of time and effort into these videos. Absolutely brilliant work. Thank you!
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.
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.
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?
@@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 😁
@@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 😁)
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.
@@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.
The mix between the Jupiter 2 from Lost in Space, and the Seaview from Voyage to the Bottom of the Sea in the opener, I mean, it's just incredible. Bill definitely has a love for Irwin Allen Sci-fi with the Cosmic Films Studio. It's so accurate to how Lost in Space, Time Tunnel, Land of the Giants, and Voyage to the Bottom of the Sea look. Absolutely wonderful.
At 4:46, the volume of the double hexagonal pyramid is approximately 1.73, but at 15:23 the local maximum examples have a volume of approximately 1.63 and "are both bigger than the back-to-back hexagonal pyramids". Am I mistaken or is this some sort of Parker inequality I don't know about?
Wait a minute. 4:50 Cube is 8/9 of square root of three and the double piramid is square root of three... That's not 1/8 bigger, that's 1/9 bigger... or am I wrong? Edit: am indeed a dumdum. Doesn't surprise me in the slightest
If the cube is 8/9 of the volume of the double pyramid, then the pyramid is 9/8 the volume of the cube. That's why it's 1/8 bigger than the cube. On the other hand, the cube is 1/9 smaller than the double pyramid. You can also check with the numbers: 1.7320508 / 1.5396007 = 1.1250; 1.5396007 / 1.7320508 = 0.8888...
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....
@@iTeerRex Hmm, I thought they were rhombic dodecahedra....
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.
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.
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
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'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.
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!
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
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?
And if you define the torus In terms of non-overlapping planar convex pentagon. What would the minimum number be?
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!
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
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 :(
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 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.
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. 💐
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.
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.
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!
"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
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 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? 😉
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.
Bill is the geeky uncle almost none of us had but almost all of us wanted.
Three cheers for Bill!
hip, hip!
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!
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?
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!
the production values of this video are through the roof.
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.
That set is absolutely beautiful and well-kept, they were probably very happy to have it used.
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!
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 😄
"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)
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.
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
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.
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.
Really cool to see where math, computing, and film and television collide.
5:00 this is INCREDIBLE original series Trek energy. i love you, matt, and also the studio who let you use their stuff
7:00 wait is this ACTUALLY the star trek set? oh my gosh, this is a whole new level of awesome
"Oh I can use this studio?" Then precedes to use every inch possible, almost like the subject of the video! 🤭
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!
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?
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
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.
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.
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.
Matt Parker, forgot to put it in park.
He forgot to put it in the Parker square
Matt Driver
Parker parking
Production quality was just out of this world, wow. Thanks Matt, helps a lot!
Ah yes, my favorite RUclipsr, Matt Forget-To-Parker.
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.
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
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. :)
1:45 "(...) sorry, forgot to put it in park"
Can't let that happen, after all he's a Parker.
Dear Matt, I love how much fun you have with your vids. I cannot imagine your face when you were given free roaming within the studio! I could see you trying not to crack a huge grin as you walked off stage left towards the end.
Honestly, send this in to ABC Australia and they'll nab you for Play School in a heart beat. You could earn some more multi coloured money papers again!
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.
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.
You have outdone yourself. You have a talent for making math interesting and put a lot of time and effort into these videos. Absolutely brilliant work. Thank you!
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. 😂
I love stories like that - about people with passion and everything that goes with it
What a cool video. I love when happenstance leads to some additional content like this.
I love how Matt travels to world for these videos.
You showed the two local maxima in detail, but not the one shape we all came here to see!
Production value here is absolutely aces!!
What a beautiful video Matt, thanks for all your incredible work! Regards from Argentina
Excellent. That computer should be featured in a Top-Shelf magazine.
Very attractive. x
@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.
This is incredible! So awesome that you got to film on these sets, what an awesome video
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)
Feels like I got a whole preview of this video at the An Evening of Unnecessary Detail event!
Rest in peace, Roger 😢
I love how much fun you had making this!
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.
That set is fantastic! What an amazing piece of history he has there.
Nebraska! Make sure to get some footage of that triple landlocked place!
The Antikythera mechanism from 100 BC was used to calculate astronomical positions
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.
There were many things on the list of things I expected to see today, and this was NOT one of them.
Wow, absolutely amazing!
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 😁)
The music, the set, just everything is amazing. Great video!
What a positive way of stating Cunningham's law
Cunningham's Law: "Anything that can go wrong will go wrong."
This is the second or the third time Matt has ended up in nebraska. Finally putting us, nebraska, on the map.
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.
I wanted to say, I absolutely hated math in schools but have always enjoyed real-world applications of it. You are fantastic!
You need to keep that new theme song!
This video, quality and appearance, was incredible. How fun.
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
"You can use our sets, which one would you like to use?"
Matt: "Yes"
The mix between the Jupiter 2 from Lost in Space, and the Seaview from Voyage to the Bottom of the Sea in the opener, I mean, it's just incredible. Bill definitely has a love for Irwin Allen Sci-fi with the Cosmic Films Studio. It's so accurate to how Lost in Space, Time Tunnel, Land of the Giants, and Voyage to the Bottom of the Sea look. Absolutely wonderful.
@UsagiElectric enters the chat...
At 4:46, the volume of the double hexagonal pyramid is approximately 1.73, but at 15:23 the local maximum examples have a volume of approximately 1.63 and "are both bigger than the back-to-back hexagonal pyramids". Am I mistaken or is this some sort of Parker inequality I don't know about?
Dude. This is one of the best stories I've ever seen. I just kept saying "awesome", over and over again.
This was such a fun episode! What a creative idea, and fortuitous coincidence! 😊
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
"More on that shape after these important messages." *an actual ad roll begins*
Postulate a spherical universe...
And in vacuum...
On a frictionless plane...
Of unit radius...
What an absolutely wonderful location.
Wait a minute. 4:50 Cube is 8/9 of square root of three and the double piramid is square root of three... That's not 1/8 bigger, that's 1/9 bigger... or am I wrong?
Edit: am indeed a dumdum. Doesn't surprise me in the slightest
Just about to comment the same thing!
That's what I thought but was to scared to put my own comment and have people call me an idiot.
Maybe he meant 1/8th better as in 12.5% better
If the cube is 8/9 of the volume of the double pyramid, then the pyramid is 9/8 the volume of the cube. That's why it's 1/8 bigger than the cube. On the other hand, the cube is 1/9 smaller than the double pyramid.
You can also check with the numbers: 1.7320508 / 1.5396007 = 1.1250; 1.5396007 / 1.7320508 = 0.8888...
1/9 of the large shape is 1/8 of the cube….
He’s got such a historic monument that he should be worried about the British museum stealing it