ConwayLife.com

This is my page everyone, so let's start with two amazing feats:
1. When I was 11, I learned calculus!
2. At the same age, I learned quantum physics!
And it's TRUE!
This page is mostly about my life from now on.
Quantize away!

Monthly Anniversary! Also exactly 50 posts (including this one)! And today I saw two Mysterious Pendulums! One is contradictory to the other!

dvgrn wrote: October 21st, 2022, 11:08 am Size is a slippery slope for methuselahs.

What's a slippery slope? Does it mean hard to measure?

If f denotes the function of longest lifespan devided by size, then f prime would grow very large very fast, which means f is a very slippery slope indeed. (My guess only)

yujh wrote: October 22nd, 2022, 2:41 pm If f denotes the function of longest lifespan devided by size, then f prime would grow very large very fast, which means f is a very slippery slope indeed. (My guess only)

The way it's used here seems more like an idiom than a mathematical statement.

Greetings !

And Welcome to Our Community !

AND Congratulations on learning subjects that I have not gotten around to yet !

( and I am 70 years young... )

I use Cellular Automata ( C.A. ) and particularly Conway's Game of Life ( CGoL )

to attempt to derive useful analogies that may assist my ongoing efforts

to understand The Universe I live in and The People I live with...

I have a feeling you will be a very interesting person

ALL people are VIPs ( V.I.P. = Very Interesting Persons ) -

because everyone is Unique, One-Of-A-Kind, and especially

has their very own UNIQUE point-of-view

SO

what do you like about C.A. and CGoL ?

Cheers !

A neat little puzzle:
Fill in the blank to make the third statement true (assuming the first two are true):
This sentence was typed on a computer.
The above sentence isn't identical to this one.
The above sentence ____ identical to this one. (is/isn't)

otismo wrote: October 31st, 2022, 12:27 pm ...
what do you like about C.A. and CGoL ?
...

Well, I first encountered it 3 or 4 years back while seeing something on whether life can exist in two dimensions. I played with Life for a while but soon dismissed it as a mere encounter.

Then last year I saw something on math and its flaw and it mentioned Life again! Besides, I think that was the video that left the most impact on me even now as I've been working to fix that flaw ever since! (though I admit it wasn't a good idea in the first place but I was not on good terms with the flaw) So I started playing with life a year back. Soon, I discovered the Lifewiki, and it took a while but I found the forums too.

At first I was only a passive observer of the forums (I am a very privacy-conscious person which is why there is very little information about me here) Then I discovered this century-eater block thing which I so wanted the community to know (though I didn't know it was already known 10 years back) that I became a member of the forums!

About Life, I think it's amazing. I think of it as an entire universe of itself! Has very simple rules, with bring the big bang for the Life universe. I don't run scripts, everything is done by hand (it's a bug in my system). So I think my discoveries are very original (unless already known, of course).

Proof that everything can be described in 10 words:
Suppose the above sentence isn't true.
Then there must be a simplest thing that cannot be described in 10 words.
It can be described like so:
" The simplest thing that cannot be described in ten words."
But we just described it in 10 words.
Therefore, its a contradiction.
Therefore, everything can be described in 10 words. Q.E.D. (Even this proof, I realize, if we knew how!)

(deleted)

100 posts including this one!

qqd wrote: November 9th, 2022, 11:32 am Proof that everything can be described in 10 words:
Suppose the above sentence isn't true.
Then there must be a simplest thing that cannot be described in 10 words.
It can be described like so:
" The simplest thing that cannot be described in ten words."
But we just described it in 10 words.
Therefore, its a contradiction.
Therefore, everything can be described in 10 words. Q.E.D. (Even this proof, I realize, if we knew how!)

See https://en.m.wikipedia.org/wiki/Berry_paradox

Conway Life Book wrote: Given that the definition of a pseudo still life involves being able to partition the still life into 2 or more component still lifes, it seems natural to ask whether or not there really are cases that can be decomposed into (for example) 3 still lifes but not 2. Still lifes with this property are indeed known. Similarly, there are pseudo still lifes that can be decomposed into 4 still lifes, but not 2 or 3. Somewhat surprisingly, this pattern does not continue: there does not exist a pseudo still life that can only be partitioned into 5 or more still lifes.

This reminded me of the 4 color theorem, which was a similar partitioning problem and with the same upper bound of 4, so it wasn't surprising to see that the proof of the above statement uses it.

qqd wrote: October 9th, 2022, 1:12 pm 2. At the same age, I learned quantum physics!

Solve the Schrodinger Equation for the hydrogen atom in front of me.

pzq_alex wrote: May 19th, 2023, 11:56 pm Solve the Schrodinger Equation for the hydrogen atom in front of me.

You must know that at the time, I only learned the basics of quantum mechanics, like the quantum spin and the quantized energy levels of the harmonic oscillator. After that, I did not find much sources so I could learn more about the subject, and the only ways I did new things was to use 'toy models' of particles in a system. Finding the Hamiltonian was pretty much guesswork (certainly of the form 1/2mv^2+V(x), but then the potential energy function had to be made, and that was usually done by experiments, which isn't very much of my spirit.), but guesswork was really unsatisfying in some cases.

The real reason I become interested in quantum mechanics at the time was to actually find some mathematics involved in a scientific discipline, and quantum mechanics seems to the simplest area of physics which I could actually learn the basics of. (Linear algebra is a LOT more easier than integral calculus, which, for my part, become too complicated in classical physics than what I usually do.) My main interest in my entire life was mathematics, and so I naturally learned more advanced mathematics like calculus and linear algebra after the things I learned at school became 'too simple and uninteresting'. Nevertheless, I have found many things to be easier to understand after learning the basics of quantum mechanics, but for now your question is beyond the scope of what I have learned.

The minimum population required for linear growth (O(x^1)) is 10 cells. For quadratic growth (O(x^2)), it's twice that number, 20 cells. Moreover, you need 3 gliders to make linear growth, and twice that (6 gliders) for quadratic growth. Hmm, is there a connection?