THEREFORE I WILL SCREAM ABOUT IT HERE MULTIPLE TIMESHunting wrote:PEOPLE TENDS TO IGNORE MY RULES FOR EXAMPLE THE NEW RULE I POSTED IN THE UNRECOGNIZED THREAD
Random posts
Re: Random posts
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
TREE(3) bottles of root beer on the wall,
We’ll never have time to get to them all.
Take one down, pass it around,
TREE(3)-1 bottles of root beer on the wall!
TREE(3)-1 bottles of root beer on the wall,
We’ll never have time to get to them all.
Take graham’s number down, pass them all around,
TREE(3)-G-1 bottles of root beer on the wall!
TREE(3)-G-1 bottles of root beer on the wall,
We’ll never have time to get to them all.
Take hydra(a googol) down, pass them all around,
TREE(3)-hydra(googol)-G-1 bottles of root beer on the wall...
We’ll never have time to get to them all.
Take one down, pass it around,
TREE(3)-1 bottles of root beer on the wall!
TREE(3)-1 bottles of root beer on the wall,
We’ll never have time to get to them all.
Take graham’s number down, pass them all around,
TREE(3)-G-1 bottles of root beer on the wall!
TREE(3)-G-1 bottles of root beer on the wall,
We’ll never have time to get to them all.
Take hydra(a googol) down, pass them all around,
TREE(3)-hydra(googol)-G-1 bottles of root beer on the wall...
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
I remember Dani posted something like this before:
I think it was like "is 58 a number"
I feel that "easy to get out of clothes" should have been more popular a search than "edible"
Is mud edible?
It depend on what's in it, but it wouldn’t be terribly pleasant a meal. It's like eating really wet dirt. With probably a lot of insects, weeds, maybe some fungi, and other stuff. I’d say if you had to eat mud don’t do it near buildings or lawns since those may be full of fungicides/herbicides/insecticides.
I think it was like "is 58 a number"
- Why is "edible" more popular than the one below?
- 942DF183-0BA8-4F6C-BB36-3C279677F103.jpeg (378.17 KiB) Viewed 7258 times
Is mud edible?
It depend on what's in it, but it wouldn’t be terribly pleasant a meal. It's like eating really wet dirt. With probably a lot of insects, weeds, maybe some fungi, and other stuff. I’d say if you had to eat mud don’t do it near buildings or lawns since those may be full of fungicides/herbicides/insecticides.
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
for the "saka" of simplicity
heh heh
heh heh
Last edited by Gustone on July 14th, 2019, 11:22 am, edited 1 time in total.
Re: Random posts
check out my new profile picture
Re: Random posts
When does this stabilize?
Code: Select all
x = 9, y = 1, rule = AbsoluteTurmite_0N21S10E00S01W11N2
B7.B!
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
Turing machine 123456 is a c/3 ship.
http://m.wolframalpha.com/input/?i=evolve+TM+123456
(I’m using wolfram alpha cuz that’s easier to quickly shuffle through TMs on)
C/7:
http://m.wolframalpha.com/input/?i=evolve+TM+192837465
2c/6:
http://m.wolframalpha.com/input/?i=evol ... 0000000000
Challenge: find a pattern on a finite tape that does not stabilize the same way as this in this rule: http://m.wolframalpha.com/input/?i=evol ... andom+tape
http://m.wolframalpha.com/input/?i=evolve+TM+123456
(I’m using wolfram alpha cuz that’s easier to quickly shuffle through TMs on)
C/7:
http://m.wolframalpha.com/input/?i=evolve+TM+192837465
2c/6:
http://m.wolframalpha.com/input/?i=evol ... 0000000000
Challenge: find a pattern on a finite tape that does not stabilize the same way as this in this rule: http://m.wolframalpha.com/input/?i=evol ... andom+tape
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
f(3,1,4)=
Which is big, but not THAT big.
ggç_3,3,3(3,3,3) is much much much larger (~f_w^3(3) as opposed to a petite tetration of something), so it far exceeds something petite like f(3,1,4). To be fair it also exceeds, say, g_64 or σM(2).
Code: Select all
6f(6,0,4)
144f(4,6,3)
144*(4!*4!!*4!!!*4!!!!*4!!!!!*4!!!!!!)f(4!!!!!!,0,3)
864*(4!*4!!*4!!!*4!!!!*4!!!!!*4!!!!!!)f(3,4!!!!!!,2)
864*(4!*4!!*4!!!*4!!!!*4!!!!!*4!!!!!!)*(3!*3!!*3!!!...3!!!!!!!!... where the last one has 4!!!!!! !s)f(fact^4!!!!!!(3),0,2)
1728*(4!*4!!*4!!!*4!!!!*4!!!!!*4!!!!!!)*(3!*3!!*3!!!...fact^4!!!!!!(3))f(2,fact^4!!!!!!(3),1)
1728*(4!*4!!*4!!!*4!!!!*4!!!!!*4!!!!!!)*(3!*3!!*3!!!...fact^4!!!!!!(3))2^(fact^4!!!!!!(3))ggç_3,3,3(3,3,3) is much much much larger (~f_w^3(3) as opposed to a petite tetration of something), so it far exceeds something petite like f(3,1,4). To be fair it also exceeds, say, g_64 or σM(2).
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
Define CAboundingmethuselah(a,b) as the longest lifespan of any a x a stabilizing pattern in any b-state, range-b or smaller (it doesn't have any restrictions beyond that) rule.
It's provable that
1: CAboundingmethuselah(a,b) is uncomputable since it is essentially a generalized version of the maximum shifts function.
2: CAboundingmethuselah(1,b+2) >= max_shifts(b) since TMs are a subset of CAs. CAboundingmethuselah(1,b+2) > max_shifts(b) if there is at least one time before stabilization where the TM doesn't change state.
2: CAboundingmethuselah(a,2) is strictly less than CAboundingmethuselah(a,3) for all a if the winner would not be a B0 rule since in the worst case you can always use that state 2 as a state 1 parent, meaning that you can add 1 to the lifespan. This can be generalized to show that CAboundingmethuselah(a,n+1) < CAboundingmethuselah(a,2n+1) if the winner would not have any birth without neighbors.
Are there any other upper/lower bounds for CAboundingmethuselah(a,b)? CAboundingmethuselah(3,2) >= the lifespan of the R-pentomino by definition, since the R-pentomino is a 3x3 object in a 2-state rule (actually there are quite a few methuselahs lasting longer than that but whatever.)
CAboundingmethuselah(a,b) must be finite for all natural number inputs >0 for a and >1 for b.
There are finitely many patterns fitting in an n-by-n bounding box for finite n and there are finitely many n-state CAs for finite n-- thus there are finitely many n-by-n objects in m-state rules for finite n and m, thus there are finitely many that stabilize, thus the maximum time to stabilization is defined and finite. (Unlike with population, where at latest it becomes undefine at n >= 35)
It's provable that
1: CAboundingmethuselah(a,b) is uncomputable since it is essentially a generalized version of the maximum shifts function.
2: CAboundingmethuselah(1,b+2) >= max_shifts(b) since TMs are a subset of CAs. CAboundingmethuselah(1,b+2) > max_shifts(b) if there is at least one time before stabilization where the TM doesn't change state.
2: CAboundingmethuselah(a,2) is strictly less than CAboundingmethuselah(a,3) for all a if the winner would not be a B0 rule since in the worst case you can always use that state 2 as a state 1 parent, meaning that you can add 1 to the lifespan. This can be generalized to show that CAboundingmethuselah(a,n+1) < CAboundingmethuselah(a,2n+1) if the winner would not have any birth without neighbors.
Are there any other upper/lower bounds for CAboundingmethuselah(a,b)? CAboundingmethuselah(3,2) >= the lifespan of the R-pentomino by definition, since the R-pentomino is a 3x3 object in a 2-state rule (actually there are quite a few methuselahs lasting longer than that but whatever.)
CAboundingmethuselah(a,b) must be finite for all natural number inputs >0 for a and >1 for b.
There are finitely many patterns fitting in an n-by-n bounding box for finite n and there are finitely many n-state CAs for finite n-- thus there are finitely many n-by-n objects in m-state rules for finite n and m, thus there are finitely many that stabilize, thus the maximum time to stabilization is defined and finite. (Unlike with population, where at latest it becomes undefine at n >= 35)
Last edited by Moosey on July 16th, 2019, 8:12 am, edited 1 time in total.
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
Today's fun fact:
The first earliest record of written (old) Javanese is an ancient "No fishing." sign.
[Source]
The first earliest record of written (old) Javanese is an ancient "No fishing." sign.
[Source]
jarring cyan
Re: Random posts
I vote that an ordinal Calcyman mentioned once (n such that Xi(x) ~= fgh_n(x)) should be called "a whack" since a = w_a^ck vaguely resembles that.
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
I only half believed that until I clicked the link.Saka wrote:Today's fun fact:
The first earliest record of written (old) Javanese is an ancient "No fishing." sign.
[Source]
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
In a few miles, take a u-turn.2718281828 wrote:A fun oscillator:Code: Select all
x = 12, y = 8, rule = B3-q4jw6-in7/S2n3-ky4aeknrty5y678 b3o$ob2o4bo$8obo$10o$ob10o$b3ob5o$8b2o$7b2o!
In a few miles, take a u-turn.
...
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
You are neglecting neighbourhood. If there are no restrictions on the CA rule other than that it has b-states then there are infinitely many of them.Moosey wrote:Define CAboundingmethuselah(a,b) as the longest lifespan of any a x a stabilizing pattern in any b-state (it doesn't have any restrictions beyond that) rule.
<snip>
Are there any other upper/lower bounds for CAboundingmethuselah(a,b)? <snip>
CAboundingmethuselah(a,b) must be finite for all natural number inputs >0 for a and >1 for b.
There are finitely many patterns fitting in an n-by-n bounding box for finite n and there are finitely many n-state CAs for finite n-- <snip>
The 5S project (Smallest Spaceships Supporting Specific Speeds) is now maintained by AforAmpere. The latest collection is hosted on GitHub and contains well over 1,000,000 spaceships.
Semi-active here - recovering from a severe case of LWTDS.
Semi-active here - recovering from a severe case of LWTDS.
Re: Random posts
Edited.wildmyron wrote:You are neglecting neighbourhood. If there are no restrictions on the CA rule other than that it has b-states then there are infinitely many of them.Moosey wrote:Define CAboundingmethuselah(a,b) as the longest lifespan of any a x a stabilizing pattern in any b-state (it doesn't have any restrictions beyond that) rule.
<snip>
Are there any other upper/lower bounds for CAboundingmethuselah(a,b)? <snip>
CAboundingmethuselah(a,b) must be finite for all natural number inputs >0 for a and >1 for b.
There are finitely many patterns fitting in an n-by-n bounding box for finite n and there are finitely many n-state CAs for finite n-- <snip>
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
Me too.Saka wrote:i like coleslaw
I like cabbage a lot, especially when you can get Probably_Not_Super_Healthy dressing on it.
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
Yeah, red cabbage is infinitely superior to green cabbage for some reason.Saka wrote:yeah especially the purple crunchy ones
Also whoever named red cabbage clearly never heard the word purple.
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
Cthulhu wrote:A̶̱͂̇̋ñ̶̹͍ḋ̵̖̈́̋ ̵̟̖̃ṇ̸͑̇̚o̶̭̗͓̒̔͌w̸̟̭̒̏ ̴̰͇́w̷̗̹̃ẽ̵͙̜̝ ̶̮̗͒͠s̷̹̼̫̈́́h̷̡̡͂̋̚a̶̘̘̅̀̾ļ̸͌̃ĺ̴̳̓̄ ̴͈̪̦̓͆̈t̷͈͑a̷̧̲͘l̷̤̃k̷̨͔̂ ̶̬͌̚a̴̢͓͇̓b̴̗̙̐̏̾ó̸̢̼u̶͎̓̄̑ẗ̸̤͖̺ ̸͕͕̇f̶̮͓́͜ư̵̘̲̱z̸̰̱̲̓͌̔z̵̮̋̄y̴͙̾͋ ̸͇͕͒k̴͎̼̈́̓i̵͕̬̗̓ṯ̴̪́t̶̲̮͇̿͛̄e̶̹̭̅̄͘n̷̺̙̈s̵̱̈́.̶̣̱̰̌
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ
Re: Random posts
κ is measurable iff there is a nontrivial elementary embedding j:V→M (M transitive) with critical point κ