
John Conway - bindidwodtj
https://terrytao.wordpress.com/2020/04/12/john-conway/
======
areoform
Conway'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.

~~~
dbmueller
To 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
They 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.

~~~
dbmueller
It's not necessarily about becoming famous. If you're good enough, you can
just work on what you enjoy doing, and it will probably yield something
research worthy anyway, and your bosses will be happy, etc. Otherwise, you
might end up simply having fun on dead-end stuff, which are harder to sell,
academically.

But that's just my impression… mind sharing your story?

------
trombonechamp
It'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
I 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

------
comex
> 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
Perhaps 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
In "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)

~~~
jiofih
How do you reconcile this idea with the fact that light bounces around in 3D
space? How would you “see”?

~~~
buo
Interesting. A 2-D being in flatland would consider the inside of a closed,
empty circle to be "dark", but from 3-D we can still see inside it. Maybe one
could postulate a 4-D source of light.

------
red_admiral
In 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
and 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.

------
gautamcgoel
Terry 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.

------
ijidak
On a side note, this is mind-blowing:
[https://conwaylife.com/forums/viewtopic.php?f=2&t=2561#p3742...](https://conwaylife.com/forums/viewtopic.php?f=2&t=2561#p37428)

------
nixpulvis
I 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)

~~~
schoen
Thanks!

Your implementation currently misspells "Wednesday".

~~~
nixpulvis
Should be fixed now. Always bad at spelling am I.

------
kzrdude
I 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)

------
Alkhwarizmi
Definitely one of the true “poly maths” to ever grace the mathematics
world...RIP Dr. Conway

------
erex78
TLDR: “Conway was arguably an extreme point in the convex hull of all
mathematicians. He will very much be missed.”

~~~
hanche
NTL:DR (Not _that_ long: Do read!)

~~~
erex78
Agreed! I just thought this was such a powerful line.

~~~
vladislav
Indeed such a good one when you really think about it, but it's above most
readers heads.

~~~
hanche
So 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
I don't think it was meant so literally. just an interesting way of calling
someone a unique mathematician

------
raister
And 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
He did — in an edit.

