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Long-lived methuselahs

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Re: Long-lived methuselahs

Postby danny » January 31st, 2019, 1:30 pm

testitemqlstudop wrote:2->2->3->6 * 4

How many digits does that number have? Just so I can wrap my head around it a bit.
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Re: Long-lived methuselahs

Postby Moosey » January 31st, 2019, 1:46 pm

Can you put that in knuth arrows?
For reference, the way Wikipedia puts it, p→q→r = p↑ʳq and p→q = p^q
So I imagine (2->(2->3->6))*4 is (2^(2^^^^^^3))*4. = 4*2^(2^^^^^(2^^^^^2)) = 4*2^(2^^^^^4)
danny wrote:How many digits does that number have?

If I’m understanding Conway chained arrow notation correctly, ~log(4*2^(2^^^^^(2^^^^^2)), (no, I’m not calculating pLifespan. That’s a tilde) so I bet that that is still a large number (i.e. How many digits does that number have)
Though in the way it was provided, I would evaluate to 4*4, so 2 digits is your answer.
EDIT: the number of digits in a number x (base n) is (log base n of x) + 1, rounded down.
So if that answers your question, Dani, log(4*2^(2^^^^^4))+1, rounded down.
EDIT2: based on the more accurate lifespan estimate, >digits(2^^9)
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Re: Long-lived methuselahs

Postby testitemqlstudop » January 31st, 2019, 2:04 pm

Whoops, guess I used chained-arrow notation wrong.

Anyways, it takes
on the order of 2^^^^^^^(2^^^^^^(2^^^^^(2^^^^(2^^^(2^^(2^n))))))

to get the glider to the spacefiller, which is only 1/4 of the total evolution time. Then, the tear in the agar propogates through the spacefiller, and after 4x as much time, it destroys the three corners. Now it would probably take much more time to have the triangle completely stabilize, and if it spawns a natural replicator, :shock:
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Re: Long-lived methuselahs

Postby Moosey » January 31st, 2019, 2:06 pm

testitemqlstudop wrote:Whoops, guess I used chained-arrow notation wrong.

Anyways, it takes
on the order of 2^^^^^^^(2^^^^^^(2^^^^^(2^^^^(2^^^(2^^(2^n))))))

to get the glider to the spacefiller, which is only 1/4 of the total evolution time. Then, the tear in the agar propogates through the spacefiller, and after 4x as much time, it destroys the three corners. Now it would probably take much more time to have the triangle completely stabilize, and if it spawns a natural replicator, :shock:

I really don’t know that well about Conway chained arrow notation, so you’re probably right.
It would probably become periodic, but maybe it wouldn’t. I hope it releases a couple sir robins, possibly with new Tagalongs.
Actually, 2->2->(doesn’t matter) =4, and that thing doesn’t stabilize in 4 generations, so you used Conway chained arrow notation wrong.
But regardless, that probably lasts on the order of 2^(2^(2^(2^(2^(2^(2^n)))))) (your estimate, likely more accurate, but those arrows are misleading. It's just 2^2^2^2^2^2^2^2... because those are chained log growths. Apologies If i'm wrong) or (2^(2^^^^^4))*4 (my estimate, based on your Conway chained arrows and a generous helping of assumed parentheses), and that is bigger than
13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096
(From Wikipedia, 4->3->2). That number was only 4^256, while our numbers are 2^(Almost infinitely larger than 512)
EDIT:
The important question is whether that pattern is a methuselah in the classical sense.
It has an enormous MCPS.
It was engineered.
Anyone who can recognize log(log(log(log(log...)))))) growth can tell it's got a long life.
However, Its lifespan is enormous, So we should call it a methuselah anyways.
According to the forum rules, Methuselahs larger than 20*20 in bounding box are uninteresting. However, in the case of a pattern with lifespan on the order of 2^(2^^^^^4)) it might be okay to make an exception.
EDIT:
As Dani says below, This kind of pattern could be referred to as an engineered methuselah. I guess they could be notable if they last a VERY VERY VERY long time, or if they have an unusual mechanism.
This variety runs on a mechanism that delays self destruction for a long long time.
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Re: Long-lived methuselahs

Postby danny » January 31st, 2019, 7:38 pm

I would use the term 'engineered methuselah' to refer to things like that. Kind of like engineered vs natural spaceships. Once loafer or one of the c/4s becomes natural we can call it natural...
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Re: Long-lived methuselahs

Postby Moosey » January 31st, 2019, 7:50 pm

danny wrote:I would use the term 'engineered methuselah' to refer to things like that. Kind of like engineered vs natural spaceships. Once loafer or one of the c/4s becomes natural we can call it natural...

Yeah, I was thinking along those lines.
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Re: Long-lived methuselahs

Postby 77topaz » January 31st, 2019, 10:38 pm

By removing all but one of the delay structures, I managed to, after something like 10^20 generations, see a glider hitting the spacefiller. The spreading chaos showed an interesting periodic rake-like structure propagating along the edge between vacuum and the agar, periodically sending out gliders. However, trying to copy a selection large enough to show this (it was about 10000x10000, which is large but microscopic compared to the whole pattern at that point) caused Golly to freeze entirely.
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Re: Long-lived methuselahs

Postby Moosey » February 1st, 2019, 9:34 am

77topaz wrote:By removing all but one of the delay structures, I managed to, after something like 10^20 generations, see a glider hitting the spacefiller. The spreading chaos showed an interesting periodic rake-like structure propagating along the edge between vacuum and the agar, periodically sending out gliders. However, trying to copy a selection large enough to show this (it was about 10000x10000, which is large but microscopic compared to the whole pattern at that point) caused Golly to freeze entirely.

So it likely becomes periodic?
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Re: Long-lived methuselahs

Postby 77topaz » February 1st, 2019, 5:36 pm

The rake-like crawler (I'm not entirely sure what the right terminology would be) I saw moving along the side of the agar did indeed to be periodic, as it released gliders at regular intervals.

The pattern as a whole would also eventually become periodic (with the stipulation that each "eventually" will take an extremely long time): a glider eventually passes through the delay systems and hits the spacefiller's agar, causing the agar to break down. The disturbances propagate at light speed, and so eventually catch up to the corners of the spacefiller, causing its expansion to cease; the area covered by the spacefiller will then eventually settle down to regular CGoL ash.
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Re: Long-lived methuselahs

Postby Moosey » February 1st, 2019, 6:18 pm

77topaz wrote:The rake-like crawler (I'm not entirely sure what the right terminology would be) I saw moving along the side of the agar did indeed to be periodic, as it released gliders at regular intervals.

The pattern as a whole would also eventually become periodic (with the stipulation that each "eventually" will take an extremely long time): a glider eventually passes through the delay systems and hits the spacefiller's agar, causing the agar to break down. The disturbances propagate at light speed, and so eventually catch up to the corners of the spacefiller, causing its expansion to cease; the area covered by the spacefiller will then eventually settle down to regular CGoL ash.


I’ve seen something like that rake-crawler happen on (smaller) spacefillers.
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Re: Long-lived methuselahs

Postby 77topaz » February 1st, 2019, 7:19 pm

Hm. It doesn't seem like just colliding a glider with the orthogonal edge of Halfmax is necessarily sufficient to get such a structure to appear:
x = 181, y = 670, rule = B3/S23
bo$2bo$3o588$147b2ob2o$146bobobobo$146bobobobo$144b2obo2bob2o$143bobo
4bo$142bo3bobobob2o$142b3obobobo2bo$145bo2bo2b2o$142b2o$141bo2b3o3b3o$
141bobo9bobo$142bobob2ob2obob2o$144bob2ob2obo$144bobo3bobo$145bo5bo2$
143b11o$143bo2bobobo2bo2$140b2o6bo6b2o$140bobo3b5o3bobo$138bobob3o7b3o
bobo$137bobobobo9bobobobo$137bobobobob2o3b2obobobobo$138bo3bob2obobob
2obo3bo$146b2ob2o$126b2o8bo10bobo10bo8b2o$125b2o3bo4b2o7b4ob4o7b2o4bo
3b2o$124b2o2b2o4bo3b3o3bo7bo3b3o3bo4b2o2b2o$125bo4b5obo4bo3b3ob3o3bo4b
ob5o4bo$129bo4bobo23bobo4bo$126b2o3b2ob2obo7b3ob3o7bob2ob2o3b2o$129b2o
4bo25bo4b2o$119b5o3b2o5bo6b2o2b2o3b2o2b2o6bo5b2o3b5o$119bo4b2obo2bo10b
2o2b3ob3o2b2o10bo2bob2o4bo$119bo6bo18bobobobo18bo6bo$120bo5b2obo17bobo
17bob2o5bo$122b2o2bo3b2o11b4obob4o11b2o3bo2b2o$125bo17b2o3bo3b2o17bo$
123b3o20b2ob2o20b3o$122bo8bo5bo5b3obobob3o5bo5bo8bo$122bo4bobo2b2o4b2o
7bobo7b2o4b2o2bobo4bo$122bo3b2o2bob2ob2ob2ob5obobob5ob2ob2ob2obo2b2o3b
o$123bo21bobobobo21bo$124b21o3bo3b21o2$126b21o3b21o$125bo21bobo21bo$
124bo3b20ob20o3bo$121bobo2bo2bo37bo2bo2bobo$120bo2bobo4b37o4bobo2bo$
119b2o10bo33bo10b2o$118bo13b33o13bo$117b4o12bo29bo12b4o$116bo4bo12b29o
12bo4bo$116bo2bo15bo25bo15bo2bo$116bo2bo16b25o16bo2bo$117bo19bo21bo19b
o$118b4obo14b21o14bob4o$119bo3bo15bo17bo15bo3bo$120bo19b17o19bo$120bob
o18bo13bo18bobo$142b13o$119b3o21bo9bo21b3o$119b2o23b9o23b2o$119b3o26bo
26b3o$145b3ob3o$120bobo23bo3bo23bobo$120bo24bobobobo24bo$119bo3bo21bob
obobo21bo3bo$118b4obo20bo7bo20bob4o$117bo26bo7bo26bo$116bo2bo24bo2bobo
2bo24bo2bo$116bo2bo24b3o3b3o24bo2bo$116bo4bo53bo4bo$117b4o55b4o$118bo
59bo$119b2o55b2o$120bo2bo49bo2bo$121bobo49bobo!


It's likely that a different, specific phase alignment between the incoming glider and the wick that stabilises the orthogonal edge is required.
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Re: Long-lived methuselahs

Postby testitemqlstudop » February 1st, 2019, 7:30 pm

77topaz wrote:The rake-like crawler (I'm not entirely sure what the right terminology would be) I saw moving along the side of the agar did indeed to be periodic, as it released gliders at regular intervals.

The pattern as a whole would also eventually become periodic (with the stipulation that each "eventually" will take an extremely long time): a glider eventually passes through the delay systems and hits the spacefiller's agar, causing the agar to break down. The disturbances propagate at light speed, and so eventually catch up to the corners of the spacefiller, causing its expansion to cease; the area covered by the spacefiller will then eventually settle down to regular CGoL ash.


I'm not sure, but it actually propgates at 2c/3 vertically and c horizontally.
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Re: Long-lived methuselahs

Postby Moosey » February 1st, 2019, 7:41 pm

testitemqlstudop wrote:
77topaz wrote:The rake-like crawler (I'm not entirely sure what the right terminology would be) I saw moving along the side of the agar did indeed to be periodic, as it released gliders at regular intervals.

The pattern as a whole would also eventually become periodic (with the stipulation that each "eventually" will take an extremely long time): a glider eventually passes through the delay systems and hits the spacefiller's agar, causing the agar to break down. The disturbances propagate at light speed, and so eventually catch up to the corners of the spacefiller, causing its expansion to cease; the area covered by the spacefiller will then eventually settle down to regular CGoL ash.


I'm not sure, but it actually propgates at 2c/3 vertically and c horizontally.

Huh. Weird nonuniform speeds. But this makes sense, because with the grain negative spaceships go at c and against the grain negative spaceships travel at 2c/3
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Re: Long-lived methuselahs

Postby Macbi » February 1st, 2019, 7:51 pm

Moosey wrote:Huh. Weird nonuniform speeds. But this makes sense, because with the grain negative spaceships go at c and against the grain negative spaceships travel at 2c/3
I think it's the other way around. Those are the speeds people searched for ships because they observed that those were the speeds at which the agar collapsed.
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Re: Long-lived methuselahs

Postby Moosey » February 1st, 2019, 8:16 pm

Macbi wrote:
Moosey wrote:Huh. Weird nonuniform speeds. But this makes sense, because with the grain negative spaceships go at c and against the grain negative spaceships travel at 2c/3
I think it's the other way around. Those are the speeds people searched for ships because they observed that those were the speeds at which the agar collapsed.

Oh, that makes sense. But still, I guess you could argue that it makes sense because the negative spaceships go at those speeds because the agar decays at those speeds.
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