Search found 706 matches

by Macbi
December 8th, 2019, 6:03 am
Forum: Patterns
Topic: 16 in 16: Efficient 16-bit Synthesis Project
Replies: 282
Views: 199686

Re: 16 in 16: Efficient 16-bit Synthesis Project

Kazyan wrote:
December 7th, 2019, 3:13 pm
Or maybe an aggressive 5G search to find the three 10-bit still lifes that still require 6 gliders (very long hook with tail, tub with long long tail, and the remarkably long snake).
Is there any hope for getting the two remaining 9-bitters in 4?
by Macbi
December 3rd, 2019, 6:32 am
Forum: Patterns
Topic: orphan pattern / garden of eden
Replies: 27
Views: 14897

Re: orphan pattern / garden of eden

The problem of deciding whether a given finite-population pattern is a GoE has been rattling about in my brain for the last couple of years. So when I saw a mathoverflow question asking for " Decision problems for which it is unknown whether they are decidable " I quickly posted it as an example of ...
by Macbi
November 18th, 2019, 2:20 pm
Forum: Patterns
Topic: 16 in 16: Efficient 16-bit Synthesis Project
Replies: 282
Views: 199686

Re: 16 in 16: Efficient 16-bit Synthesis Project

Congrats! Here's the current state of the art: Population Max Cost 9 5 10 6 11 7 12 8 13 9 14 11 15 12 16 14 17 16 18 38 19 infinity Every still life <9 cells can be done in 4 or less, which is known to be optimal since we've checked all the 3 glider collisions.
by Macbi
November 13th, 2019, 6:24 pm
Forum: The Sandbox
Topic: Introductions
Replies: 84
Views: 58338

Re: Introductions

It sounds natural to me.
by Macbi
November 7th, 2019, 11:14 am
Forum: Website Discussion
Topic: Cross topic search reqiest
Replies: 6
Views: 2377

Re: Cross topic search reqiest

Google wasn't indexing all the posts before the forum update either.
by Macbi
October 26th, 2019, 7:14 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 165
Views: 3979

Re: Ordinals in googology

What is the cardinality of the set of: 1) all ordinals; 2) all countable ordinals; 3) all computable ordinals. 3) ℵ_0 That does not make sense; you can infinitely exponentiate w and add them together (this is further enlargened by the branching possibilities of each exponent and coefficient), so un...
by Macbi
October 25th, 2019, 7:45 am
Forum: The Sandbox
Topic: Ordinals in googology
Replies: 165
Views: 3979

Re: Ordinals in googology

testitemqlstudop wrote:
October 25th, 2019, 7:34 am
What is the cardinality of the set of:

1) all ordinals;
2) all countable ordinals;
3) all computable ordinals.
1) There is no set of all ordinals, just like there is no set of all sets.
2) ℵ_1
3) ℵ_0
by Macbi
October 5th, 2019, 6:38 am
Forum: The Sandbox
Topic: Largest total computable function competition
Replies: 155
Views: 15955

Re: Largest total computable function competition

I believe the fastest growing known computable functions are of the following form: n ↦ The combined running time of all Turing machines (with no input) such that there exists a proof that they halt in second-order PA using fewer than n symbols FIrst order set theory is much stronger, and you might...
by Macbi
October 3rd, 2019, 10:12 am
Forum: Website Discussion
Topic: Updating website
Replies: 45
Views: 1678

Re: Updating website

If I'm going to be quite honest, it seems a bit jarring in terms of color compared to the rest of the wiki, and also feels like it gets in the way to an extent. Maybe the links could be moved to the left sidebar? Honestly I kind of agree. I'll leave it up for at least a day though to see if anyone ...
by Macbi
October 3rd, 2019, 4:07 am
Forum: Website Discussion
Topic: Like button in forum request
Replies: 33
Views: 10818

Re: Like button in forum request

All of the original comments raised good points. It would be nice to be able to congratulate people without having to comment. (I'm thinking in particular of Nick Gotts' work, which I find amazing but don't always have anything interesting to add.) But it would be bad if the like buttons turned the ...
by Macbi
October 2nd, 2019, 9:08 am
Forum: Website Discussion
Topic: Updating website
Replies: 45
Views: 1678

Re: Updating website

Nathaniel wrote:
October 2nd, 2019, 8:42 am
Gamedziner wrote:
October 2nd, 2019, 8:28 am
Pages in the updated forums seem to load a lot slower.
Anyone else having this problem? Seems fine to me.

Also, I'll be updating to PHP 7.2 in a day or two, which should speed up the whole site somewhat.
Seems fine to me too.
by Macbi
October 1st, 2019, 10:54 am
Forum: The Sandbox
Topic: Thread for your ridiculously absurd questions
Replies: 51
Views: 1691

Re: Thread for your ridiculously absurd questions

Then what would be the best way to affect the spin of the Earth that we can do currently? Say the entire human race's goal is to affect the Earth's spin as much as possible. What's the most effective way with today's technology? Perhaps adjust the orbit of an asteroid so that it falls out of the be...
by Macbi
October 1st, 2019, 7:27 am
Forum: The Sandbox
Topic: Thread for your ridiculously absurd questions
Replies: 51
Views: 1691

Re: Thread for your ridiculously absurd questions

What if we attached a massive light sail, say the diameter of the moon, to the equator? Assume the light sail and the supports and attachments etc. are indestructible and ignore the logistics and things to actually make said light sail (Lets say it suddenly appeared out of nowhere.). Would it affec...
by Macbi
September 23rd, 2019, 8:06 am
Forum: General Discussion
Topic: Golly with Python 3?
Replies: 5
Views: 565

Re: Golly with Python 3?

I think the current status is that there are no plans to migrate Golly to Python 3. It was Andrew Trevorrow who implemented Python 2 originally, but he much prefers Lua to Python 3 and has no plans to continue working on Python support (see his message here ). But he's happy for Golly to have Python...
by Macbi
September 21st, 2019, 11:59 am
Forum: The Sandbox
Topic: Thread for Non-CA Academic Questions
Replies: 308
Views: 74073

Re: Thread for Non-CA Academic Questions

Is it possible to define an infinite sequence of ordinals such that for all o less than w_1, you have only gone past a finite amount of ordinals in the sequence? Formally: Is ∃(A)∀(o|o<|(w_1))∀(B|[∀n|n<o,n∈A⇒n∈B]∧[∄(C|C⊂B∧[∀n|n<o,n∈A⇒n∈B])])(|B|<w∧|A|>=w) a true statement? I think in your formalisa...
by Macbi
September 19th, 2019, 10:25 am
Forum: Patterns
Topic: Systematic survey of small patterns
Replies: 38
Views: 31454

Re: Systematic survey of small patterns

Nice progress! My search has also (as it should) found Paul Callahan's 10-cell single-cluster pattern producing a block-laying switch engine, together with 5 trivial variants: x = 50008, y = 50007, rule = B3/S23 bo$2obo$bobo$3bo$5bobo$5bo9995$10001bo$10000b2obo$10001bobo$10003bo$ 10005bo$10005bobo99...
by Macbi
September 19th, 2019, 9:20 am
Forum: General Discussion
Topic: Thread for basic questions
Replies: 1686
Views: 451192

Re: Thread for basic questions

That would be xq0_2702072 That implies that it's a period 0 spaceship (whatever that would be)--as it turns out, x0_2702072 is a perfectly valid apgcode A period 0 spaceship is a pattern that returns to its original state (up to a translation) whenever the generation number is a multiple of 0. So t...
by Macbi
September 13th, 2019, 3:52 am
Forum: General Discussion
Topic: Is every spaceship edible?
Replies: 8
Views: 1332

Re: Is every spaceship edible?

This is the kind of thing which we suspect is true, but which no one has ever thought of a way to prove.
by Macbi
September 1st, 2019, 7:16 am
Forum: Patterns
Topic: 17 in 17: Efficient 17-bit synthesis project
Replies: 315
Views: 95391

Re: 17 in 17: Efficient 17-bit synthesis project

chris_c wrote:There might be a way to do cleanup in one less glider.

Code: Select all

x = 27, y = 39, rule = B3/S23
5bo$o4bobo11bo$b2o2b2o12bobo$2o17b2o2$23bo$8bo12b2o$7bo14b2o$7b3o5$18b
obo$18b2o$19bo2$6b2o$5bo2bo$5bob2o$2b2obo$o2bobo$2o2bo9$24b3o$24bo$25b
o3$14b3o$14bo$15bo!
by Macbi
September 1st, 2019, 5:58 am
Forum: Other Cellular Automata
Topic: The Single Rotation Rule
Replies: 41
Views: 20275

Re: The Single Rotation Rule

This variant was suggested in the comments to the original post: x = 16, y = 16, rule = M0,4,1,3,8,5,6,11,2,9,10,14,12,7,13,15 obobob2o2b2obobobo2b5o2bobo$b2ob4o4b3o2bobo4b2o2bobo$o2bo3b3ob2o2b3ob 4ob8o$3b6obobobo3b2o4b3ob3o$o7b2o2b3o4bobobo3bobo$2obo3b5o4b6o5b2o$o2b obo2b2obobo4bo2bob2o3b2obo$3ob2o...
by Macbi
August 28th, 2019, 6:49 am
Forum: Patterns
Topic: 17 in 17: Efficient 17-bit synthesis project
Replies: 315
Views: 95391

Re: 17 in 17: Efficient 17-bit synthesis project

testitemqlstudop wrote:Oh you forgot /s?
Right, but more specifically the joke is that Kellyanne Conway does work for Trump.
by Macbi
August 11th, 2019, 11:15 am
Forum: The Sandbox
Topic: Thread for Non-CA Academic Questions
Replies: 308
Views: 74073

Re: Thread for Non-CA Academic Questions

calcyman wrote:This is all true, but I'd make a minor terminology change: s/large cardinal/strongly inaccessible cardinal/

'Large cardinal' is a more general (and less precise) term: https://en.wikipedia.org/wiki/List_of_l ... properties
Good point.
by Macbi
August 10th, 2019, 11:20 am
Forum: The Sandbox
Topic: Thread for Non-CA Academic Questions
Replies: 308
Views: 74073

Re: Thread for Non-CA Academic Questions

There's a thing called a "large cardinal" which means that it's so large that it can't be reached from anything below it using the operations that are well defined in ZFC. In particular a cardinal C is one such that if A is smaller than C then the power set of A is also larger than C, and such that ...
by Macbi
July 28th, 2019, 2:34 am
Forum: Other Cellular Automata
Topic: Smallest Spaceships Supporting Specific Speeds (5s) Project
Replies: 820
Views: 158367

Re: Smallest Spaceships Supporting Specific Speeds (5s) Project

Saka wrote:A slope 107 (1,107) one

Code: Select all

x = 5, y = 4, rule = B2-ak3y4aeijrz5aky6-n7e8/S12ek3qry4-cjz5-j6-in7
2b2o$3obo$b3o$bo!
I think that's a record!
by Macbi
July 25th, 2019, 12:13 pm
Forum: Other Cellular Automata
Topic: Miscellaneous Discoveries in Other Cellular Automata
Replies: 1484
Views: 299702

Re: Miscellaneous Discoveries in Other Cellular Automata

In one of Moosey's rules are tons of really long lasting methuselahs, and this one lasts 27,871,939,396,739,043,039,106 gens: x = 54, y = 46, rule = B2a3jry4iy5y/S 52b2o$52b2o41$b2obo$o3bo$o$b2o! It actually lasts 28,336,471,720,019,104,108,483 gens, until the vertical line boops the bit at the bot...