John Conway
terrytao.wordpress.com
terrytao.wordpress.com
"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
I take great solace from these words.
(I'm not sure it does)
But that's just my impression… mind sharing your story?
My grades shot upwards when I stopped caring about them and decided to focus on what interested me (i.e. I like subject X and want to learn it well and will not use the grade as a metric of how well I learned it).
If work means to live a happy and meaningful life- absolutely.
If work means to gain the prestige of a man like Conway- probably not. But I can rest assured that I likely wouldnt achieve that with other attitudes either
At 15 I said ”Welp, not gonna be a music prodigy, that’s okay”
At 25 I was like ”Damn, not a comp sci prodigy either that sucks”
Then at 30 it was ”Well crap, anything I achieve now will just be considered normal”
Pressure is still there but it feels lessened. I’m not gonna be famous for achieving great things before the curve. But I can still gain notoriety for doing cool things at a normal pace.
The key is to let the ego motivate but not crush you, I guess.
"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
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?
I suspect something like this really requires you to grow up with it.
> 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.
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!)
Or is that described elsewhere? I've not read the book (one more for the quarantine list!)
R.I.P. John Conway.
Your implementation currently misspells "Wednesday".
Here's one interesting overview page, about speed: https://www.conwaylife.com/wiki/Speed
Now I have to go read the paper referred to.