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John Conway
- Alkhwarizmi 7y agoDefinitely one of the true “poly maths” to ever grace the mathematics world...RIP Dr. Conway
- gautamcgoel 7y agoTerry always amazes me with his gift of graceful and insightful writing. This post was much more interesting and meaningful to me than 90% of the Conway tribute posts I've come across.
- comex 7y ago> I also recall Conway spending several weeks trying to construct a strange periscope-type device to try to help him visualize four-dimensional objects by giving his eyes vertical parallax in addition to the usual horizontal parallax, although he later told me that the only thing the device made him experience was a headache. I'm quite curious what exactly Conway was trying to do here. The parallax we use for depth sensing is indeed horizontal in terms of the axes of the image we see, because our two eyes are separated horizontally. With a periscope you might be able to simulate two eyes separated diagonally or vertically. But how does that help you visualize four-dimensional objects?
- Normal_gaussian 7y agoPerhaps by splitting each eye's vision in two or four. Sure, in a single instant you can only be looking in one pair, but vision has significant hysteresis effects. I suspect something like this really requires you to grow up with it.
- wallflower 7y agoIn "Death's End" of the Three Body Problem trilogy by Liu Cixin, there is a fantastical description of 4D space. > kranner on Aug 4, 2018 | parent | favorite | on: 4D toys This passage from Death's End by Cixin Liu really gave me pause to stop and wonder about what the experience of seeing extra dimensions might be like (here translated to English by Ken Liu): -- A person looking back upon the three-dimensional world from four-dimensional space for the first time realized this right away: He had never seen the world while he was in it. If the three-dimensional world were likened to a picture, all he had seen before was just a narrow view from the side: a line. Only from four-dimensional space could he see the picture as a whole. He would describe it this way: Nothing blocked whatever was placed behind it. Even the interiors of sealed spaces were laid open. This seemed a simple change, but when the world was displayed this way, the visual effect was utterly stunning. When all barriers and concealments were stripped away, and everything was exposed, the amount of information entering the viewer’s eyes was hundreds of millions times greater than when he was in three-dimensional space. The brain could not even process so much information right away. In Morovich and Guan’s eyes, Blue Space was a magnificent, immense painting that had just been unrolled. They could see all the way to the stern, and all the way to the bow; they could see the inside of every cabin and every sealed container in the ship; they could see the liquid flowing through the maze of tubes, and the fiery ball of fusion in the reactor at the stern.... Of course, the rules of perspective remained in operation, and objects far away appeared indistinct, but everything was visible. Given this description, those who had never experienced four-dimensional space might get the wrong impression that they were seeing everything “through” the hull. But no, they were not seeing “through” anything. Everything was laid out in the open, just like when we look at a circle drawn on a piece of paper, we can see the inside of the circle without looking “through” anything. This kind of openness extended to every level, and the hardest part was describing how it applied to solid objects. One could see the interior of solids, such as the bulkheads or a piece of metal or a rock—one could see all the cross sections at once! Morovich and Guan were drowning in a sea of information—all the details of the universe were gathered around them and fighting for their attention in vivid colors. Morovich and Guan had to learn to deal with an entirely novel visual phenomenon: unlimited details. In three-dimensional space, the human visual system dealt with limited details. No matter how complicated the environment or the object, the visible elements were limited. Given enough time, it was always possible to take in most of the details one by one. But when one viewed the three-dimensional world from four-dimensional space, all concealed and hidden details were revealed simultaneously, since three-dimensional objects were laid open at every level. Take a sealed container as an example: One could see not only what was inside, but also the interiors of the objects inside. This boundless disclosure and exposure led to the unlimited details on display. Everything in the ship lay exposed before Morovich and Guan, but even when observing some specific object, such as a cup or a pen, they saw infinite details, and the information received by their visual systems was incalculable. Even a lifetime would not be enough to take in the shape of any one of these objects in four-dimensional space. When an object was revealed at all levels in four-dimensional space, it created in the viewer a vertigo-inducing sensation of depth, like a set of Russian nesting dolls that went on without end. Bounded in a nutshell but counting oneself a king of infinite space was no longer merely a metaphor. https://news.ycombinator.com/item?id=17686464 https://news.ycombinator.com/item?id=17686464
- EchoAce 7y agoI just read this! Gave me chills..
- tly_alex 7y agoWhen read "three body" at the time, I was also amazed by the description. Always wondering how a multi dimention world would looks like as a kid.
- jdkee 7y agoGreg Egan has some fantastic writing on considering extra-dimensional space. See Wang's Carpets as the basis for https://en.wikipedia.org/wiki/Diaspora_(novel) https://en.wikipedia.org/wiki/Diaspora_(novel)
- andai 7y ago> they were not seeing “through” anything. Everything was laid out in the open, just like when we look at a circle drawn on a piece of paper, we can see the inside of the circle without looking “through” anything. Brilliant, I had always imagined it as a sort of fuzzy MRI, but of course that's not how it would be at all. I'm surprised by the next part though. My visual field already presents me with infinitely nested detail, which doesn't seem to depend on the dimensionality of the input. After all there are 1D, 2D, 3D fractals (and beyond!)
- kitd 7y agoThis is fantastic, but one thing it seems to be missing is a projection of how objects change and interact over time, eg how revolving bodies form a helix in 4D, etc. Or is that described elsewhere? I've not read the book (one more for the quarantine list!)
- bla3 7y agoI believe this is about 4 space-like dimensions, not spacetime. Imagine perceiving a 2d image from within the plane: you'd only see width, not height, and lines would be hidden behind other lines. Only if you're in 3d, you can look at the plane from atop and see everything. Similar for looking at a 3d scene from 4 dimensions.
- zamadatix 7y agoI think he was aiming to get a simultaneous perspective of an entire 3d object. A bit like taking a 3d viewing perspective of a gD shadow being better at helping understand the 3d shape than a viewing pespective of the same shadow from the 2d plane it rests on.
- mulberryprism 7y agoIt's discussed in this PDF: https://archive.bridgesmathart.org/2015/bridges2015-317.pdf https://archive.bridgesmathart.org/2015/bridges2015-317.pdf
- erex78 7y agoTLDR: “Conway was arguably an extreme point in the convex hull of all mathematicians. He will very much be missed.”
- hanche 7y agoNTL:DR (Not that long: Do read!)
- erex78 7y agoAgreed! I just thought this was such a powerful line.
- vladislav 7y agoIndeed such a good one when you really think about it, but it's above most readers heads.
- hanche 7y agoSo the analogy with the Krein–Milman theorem would be this: Any proof is (approximately, at least) a combination of the extreme proofs of the same result? Now I have to go read the paper referred to.
- vladislav 7y agoI don't think it was meant so literally. just an interesting way of calling someone a unique mathematician
- kzrdude 7y agoIt was a good line also because it referred back to a point earlier in the text
- raister 7y agoAnd Sir, you win the Internet for not mentioning GOL there. Kudos well deserved, Conway was a great mathematician (among other 'skills'). He'll be missed.
- petters 7y agoHe did — in an edit.
- nixpulvis 7y agoI had a pretty interesting time reading up on his Doomsday, algorithm. I've coded it up (in Rust), if anyone is interested. https://github.com/nixpulvis/doomsday https://github.com/nixpulvis/doomsday
- ijidak 7y agoOn a side note, this is mind-blowing: https://conwaylife.com/forums/viewtopic.php?f=2&t=2561#p37428 https://conwaylife.com/forums/viewtopic.php?f=2&t=2561#p3742...
- etrabroline 7y agoIt's ironic how the misleading graph advocating the "flatten the curve/herd immunity" strategy at the top of tao's blog is what lead to the high number of cases in the UK, including John Conway's. People tend to think that high intelligence or expertise in a particular field makes one's opinions carry more weight, but that is, perhaps unfortunately, often not the case.
- mehrdadn 7y agoIf you're going to be so disparaging of someone with such great contributions and intellect, it'd be nice if you could at least get the facts straight and not muddy everything in your response. It's pretty impossible to comprehend what you're talking about and what's been so "misleading" about Tao's image, especially considering the "herd immunity" strategy (UK) is in many ways the diametric opposite of the "flattening the curve" approach (that of much of the rest of the world).
- schoen 7y agoI'm also confused about the notion of John Conway's COVID-19 case being a UK case. Although Conway was originally from the UK, the press and Wikipedia reports refer to his getting sick and dying in New Jersey, where he was a professor at Princeton.
- etrabroline 7y agoHere is an explanation of why the graph used by Tao on his blog is highly misleading: https://medium.com/@joschabach/flattening-the-curve-is-a-deadly-delusion-eea324fe9727 https://medium.com/@joschabach/flattening-the-curve-is-a-dea... A few days after Joshua Bach posted the above critique, the original "flatten the curve" blogger, Thomas Pueyo, basically echoed Bach's points and called it "the hammer and the dance." https://medium.com/@tomaspueyo/coronavirus-the-hammer-and-the-dance-be9337092b56 https://medium.com/@tomaspueyo/coronavirus-the-hammer-and-th... The damage and confusion done by Pueyo's original graph is moot at this point, but it's been interesting to see how the FTC phrase has lived on. https://miro.medium.com/max/1340/1*PZesaMfoPxgYJBoQVtpmjQ.gif https://miro.medium.com/max/1340/1*PZesaMfoPxgYJBoQVtpmjQ.gi...
- 7y ago
- areoform 7y agoConway's meditations on life are beautiful, "You know in my early twenties, let's say, people always thought that I would, you know, be a great mathematician. And be good at various things and so on. And in my late twenties, I hadn't achieved any of the things that people were predicting, and so I call it my black period. I started to wonder you know whether it was all nonsense. Whether I was not a good mathematician after all and so on, and then I made a certain discovery and was shot into international prominence. As a mathematician when you become a prominent mathematician, in that sense, it doesn't mean that many people know your name. It means that many mathematicians know your name, and there aren't many mathematicians in the world anyway, you know. So it doesn't count very much, but it suddenly released me from feeling that I had to live up to my promise. You know, I had lived up to my promise. I sort of made a vow to myself. It was so nice not worrying anymore that I thought I'm not going to worry anymore ever again, I was going to study whatever I thought was interesting and not worry whether this was serious enough. And most of the time I've kept to that." Life, Death and the Monster (John Conway) - Numberphile https://www.youtube.com/watch?v=xOCe5HUObD4 https://www.youtube.com/watch?v=xOCe5HUObD4 I take great solace from these words.
- physicles 7y agoI think a lot of us here will recognize this as the exact same sentiment that Feynman expressed pretty early in his career. It seems that while some great people got there by being hell-bent on greatness from early on (Schwarzenegger comes to mind), for others it’s ironically the release of that pressure that unlocks the capacity for greatness.
- dbmueller 7y agoTo me, the question that springs to mind then is: does that kind of attitude work as well for “lesser” mathematicians/people? (I'm not sure it does)
- tehwalrus 7y agoThey may not become famous in their fields, but they're not going to be worrying about that stuff anyway, so will probably be happier. Which, it turned out for me, was a better goal all along.
- red_admiral 7y agoIn Conway's game of Life, if you start with a cross as the symbol of death (5x7 grid 00100/00100/11111/00100/00100/00100/00100), you get first a "gravestone", then an egg which is traditional symbol of new life and rebirth. The egg stays around forever, unchanging, perhaps waiting for the right moment (or for you to set one of the two interior pixels). R.I.P. John Conway.
- pietroppeter 7y agoand if you then fill in the top cell inside the egg you get a (small) exploder that will create four eggs. And if you fill in again the top egg (and only the top egg), you will get a more complex pattern result in a four gliders walking off scene.
- deleted 7y ago[deleted]
- kzrdude 7y agoI know this is tangential, and related to Life, but the life wiki is ridiculously deep, the detailed exploration of life has been pretty wild. Here's one interesting overview page, about speed: https://www.conwaylife.com/wiki/Speed https://www.conwaylife.com/wiki/Speed
- trombonechamp 7y agoIt's a bit tragic that he is remembered for something he himself wasn't very fond of. From his biography: "Do you know something? I hate the Life game. I've really realized that I hate the damned Life game. ... I'm scared of the following thing happening. I'm scared of it becoming another one of these, 'John Conway, inventor of the celebrated Game of Life...' I told you, every time I turn to a book, a new math book, I look up the sacred name and it says: 'Conway, Game of life, pages 34 to 38.' And that's roughly all it says. And how can I say it---it's not character assassination, exactly, it's quality assassination. I regard Life as trash, and frankly. I mean, it was a real part of my life to have discovered it and so on. And I don't think it should be totally removed. But it seems to be all that I'm known for, among the general public. ... This was never a big deal as far as we were concerned. This was just a recreation, a game we played. Somehow it became a bit more important later on, or at least it did in the eyes of other people. I never thought of it as very important, I just thought of it as a bit of fun. In fact, in a way, I felt ashamed of it. I don't think it counts in the mathematical community, or at least in the serious mathematical community. I don't think any of my Princeton colleagues think this Life game is of any importance. I don't know. In a way it doesn't count for me." Apparently his favorite work was on the surreal numbers: https://en.wikipedia.org/wiki/Surreal_number https://en.wikipedia.org/wiki/Surreal_number
- vikramkr 7y agoI listened to the numberphile podcast on it yesterday where Brady interviewed Conway's biographer, and it looks like conway had come around to liking the game of life by the end. The real tragedy is that he never figured out the monster group
- jimbokun 7y agoSounds kind of like Alec Guinness becoming best known for playing Obi Wan Kenobi.