Is there any hope for getting the two remaining 9-bitters in 4?

## Search found 706 matches

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

- 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 ...

- 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.

- November 13th, 2019, 6:24 pm
- Forum: The Sandbox
- Topic: Introductions
- Replies:
**84** - Views:
**58338**

### Re: Introductions

It sounds natural to me.

- 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.

- 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...

- October 25th, 2019, 7:45 am
- Forum: The Sandbox
- Topic: Ordinals in googology
- Replies:
**165** - Views:
**3979**

### Re: Ordinals in googology

1) There is no set of all ordinals, just like there is no set of all sets.testitemqlstudop wrote: ↑October 25th, 2019, 7:34 amWhat is the cardinality of the set of:

1) all ordinals;

2) all countable ordinals;

3) all computable ordinals.

2) ℵ_1

3) ℵ_0

- 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...

- 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 ...

- 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 ...

- October 2nd, 2019, 9:08 am
- Forum: Website Discussion
- Topic: Updating website
- Replies:
**45** - Views:
**1678**

### Re: Updating website

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

Also, I'll be updating to PHP 7.2 in a day or two, which should speed up the whole site somewhat.

- 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...

- 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...

- 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...

- 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...

- 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...

- 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...

- 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.

- 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!
```

- 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...

- 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

Right, but more specifically the joke is thattestitemqlstudop wrote:Oh you forgot /s?

*Kellyanne*Conway does work for Trump.

- 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

Good point.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

- 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 ...

- 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

I think that's a record!Saka wrote:A slope 107 (1,107) oneCode: Select all

`x = 5, y = 4, rule = B2-ak3y4aeijrz5aky6-n7e8/S12ek3qry4-cjz5-j6-in7 2b2o$3obo$b3o$bo!`

- 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...