Ask the Game of Life Guru one question!

[Extrementhusiast]

Legends tell of the Game of Life Guru living on top of a snow-capped mountain, who knows all pertaining to Conway's Game of Life. After a multi-day journey of braving the elements, fighting gravity, and testing your physical limits, you have successfully scaled this particular mountain and have encountered the Game of Life Guru. However, you are only allowed to ask one yes/no question of the Guru, who will answer truthfully using their omniscience in B3/S23. What question do you ask?

Personally, I would probably ask them something along the lines of, "Does there exist a stable 90-degree type-preserving signal turner for either 2c/3 single, 2c/3 double, or 5c/9 signals, with minimum repeat time at most 19, which fits within a 12x12 box (defining "fits within" to mean "all births/deaths outside of this box come from unmodified signals"), such that four copies of this turner plus any length of straight signal wire can create a closed loop for signals of the appropriate type?" I think this question strikes a balance between the implications of a 'yes' answer, the likelihood of a 'yes' answer, the search space required by a 'yes' answer, and the search space eliminated by a 'no' answer.

[calcyman]

I'd take the Yedidia-Aaronson Turing machine (which halts if and only if a certain extension of ZFC is inconsistent), convert it to a GoL pattern, and ask 'is this an infinite-growth pattern'?

https://www.scottaaronson.com/busybeaver.pdf

[C28]

is there an orthogonal speed (less than c/2) such that no elementary spaceships with said speed can exist in b3/s23?

[dvgrn]

I'd take the Yedidia-Aaronson Turing machine (which halts if and only if a certain extension of ZFC is inconsistent), convert it to a GoL pattern, and ask 'is this an infinite-growth pattern'?

https://www.scottaaronson.com/busybeaver.pdf

Well, that might be a nice thing to know, but it's not very publishable -- your only data point is "I got the Game of Life Guru to tell me", so then you'd probably have to deal with all kinds of guru-deniers until you came up with a proper proof.

Similar to Extrementhusiast, I think I'd pick a search space that's just barely within reach of an exhaustive enumeration by a distributed search. So I'd ask something like "are there any spaceships where some phase fits into a 7x8 bounding box (or whatever size) that are not on this list?", or "Are there any constellations of Spartan still lifes with at least two blank cells between any two of them, that fit inside 16x16 and can reflect a glider 90 degrees without sustaining permanent damage?"

If the answer was "No", I'd be sadder but wiser, but if the answer was "Yes", at least I would know a good search project to set up.!

[praosylen]

is there an orthogonal speed (less than c/2) such that no elementary spaceships with said speed can exist in b3/s23?

I believe the answer is no, if high-period examples of that speed count — at least I would assume there's some way to make a "speed orthogonoid" that would be able to achieve every speed strictly less than c/2 using puffers and fuses... If you need your ship to be true-period then it's a fascinating question, for sure.


I've thought of a couple options that might give some good directions for future search efforts:

• Does the smallest spaceship by population of an as-yet-undiscovered simplified velocity require less time (on average) to discover via running apgsearch at the peak weekly rate of Catagolue soup submission ever so far seen for the symmetry in which it's quickly findable or via running any other single existing search program (without modifications, or inputs giving meaningful information about the ship's shape beyond its global symmetry and width/height on some axes) on the most powerful computer (or set of computing resources) a single currently active Lifenthusiast currently has access to practically and ethically at a cost less than that person is willing to pay to find it?
• On average, will some single dr search with a random search order starting from the known 2c/3d signal (with some multiplicity or time offset between halves) or the known 5c/9d signal, with no additional parameters beyond some values of c/h/w and the aforementioned ones, encounter a period-19 oscillator or a loopable signal turn after less than a year when run on the aforementioned computer?

Or if asking about program runtimes isn't something the guru can respond to,

• Do the (period minus displacement) and (width along some axis, by Euclidean distance across if not an orthogonal axis) of the smallest spaceship or half-spaceship (if the full spaceship is symmetrical) by population of an as-yet-undiscovered simplified velocity multiply to less than 90? (Or some number in that ballpark.)

[GUYTU6J]

Related to this article on structures resistant to attacking gliders:
For a stable configuration, define its single-glider-proof ratio to be "the number of input glider lanes that allow a complete recovery, divided by the total number of input lanes that affect the object in any way". Is the highest possible (asymptotic) single-glider-proof ratio 4/9, which is attained in the following eater 2 chain?

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[wwei47]

Related to this article on structures resistant to attacking gliders:
For a stable configuration, define its single-glider-proof ratio to be "the number of input glider lanes that allow a complete recovery, divided by the total number of input lanes that affect the object in any way". Is the highest possible (asymptotic) single-glider-proof ratio 4/9, which is attained in the following eater 2 chain?

I don't think so.

Code: Select all

x = 50, y = 43, rule = B3/S23
b2o$b2o3bo$5bobo$6bobo$8bo$2o6b2o$bo$bobo$2bobo6b2o$3bo3b2o2b2o3bo$7b
2o6bobo$16bobo$18bo$10b2o6b2o$11bo$11bobo$12bobo6b2o$13bo3b2o2b2o3bo$
17b2o6bobo$26bobo$28bo$20b2o6b2o$21bo$21bobo$22bobo6b2o$23bo3b2o2b2o3b
o$27b2o6bobo$36bobo$38bo$30b2o6b2o$31bo$31bobo$32bobo6b2o$33bo3b2o2b2o
3bo$37b2o6bobo$46bobo$48bo$40b2o6b2o$41bo$41bobo$42bobo$43bo3b2o$47b2o
!

[dvgrn]

I don't think so.

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[chain of eater5s]

That doesn't work too well. If we were concerned only about gliders coming from one direction (NW or SE), this would have a safety rating of 1/2. But gliders from the NE or SW destroy things 17/18ths of the time, which brings the total asymptotic rating down far below 4/9.

For the gliders-from-one-direction problem, we might as well stack highway robbers similar to this stack of eater5s, and then we really could get arbitrarily close to a 100% rating for Glider Proofness From One Direction Only (or From Two Opposite Directions), right? The ends are fixed width, so cap them with eater2 chains or whatever, but a double-sided stack of highway robbers would absorb one more lane from each direction every time you add a pair of them, so the ratio would keep creeping up indefinitely.

[calcyman]

We can get arbitrarily close to 100% for the omnidirectional problem using highway robbers.

In particular, if you want to create a 99%-resistant omnidirectional eater, then make a 99.5%-resistant bidirectional eater by stacking lots of highway robbers, and then stack *this* many many times in the perpendicular direction.