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Rhombic wrote: January 10th, 2020, 6:56 pm A philosophical question...

If a still life only has itself as a predecessor, clearly it is its only father, its only grandfather, its only great-grandfather and so on. Does that mean that it would be a Garden of Eden, by induction?

A philosophical answer:

If so Garden of Eden would be pretty overcrowded with still lifes. Absolutely no space anymore for apple trees, animals, galaxies and such...

Rhombic wrote: January 10th, 2020, 6:56 pm A philosophical question...

If a still life only has itself as a predecessor, clearly it is its only father, its only grandfather, its only great-grandfather and so on. Does that mean that it would be a Garden of Eden, by induction?

No; a still life is its own predecessor and therefore has a predecessor and therefore is not a garden of eden
Though if it is its only predecessor, it is a near GoE.

Moosey wrote: January 23rd, 2020, 7:39 pm No; a still life is its own predecessor and therefore has a predecessor and therefore is not a garden of eden
Though if it is its only predecessor, it is a near GoE.

Oh, there are lots and lots and lots of unproven conjectures out there which only philosophers care much about.

BTW: Pleased to post you again, @Moosey!

With each generation you usually have, digitally spoken,

1 father
10 grandfathers
100 great grandfathers
1000 great great grandfathers
10000 great great great grandfathers
100000 (great^100) grandfathers
1000000 (great^101) grandfathers
10000000 (great^(100^1)) grandfathe
100000000 (great^(100^10)) grandfathers
etc pp.

According to Gottfried Wilhelm Leibniz, at least.
See -> https://wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz

Hubi1857 wrote: January 23rd, 2020, 8:49 pm With each generation you usually have, digitally spoken,

1 father
10 grandfathers
100 great grandfathers
1000 great great grandfathers
10000 great great great grandfathers
100000 (great^100) grandfathers
1000000 (great^101) grandfathers
10000000 (great^(100^1)) grandfathe
100000000 (great^(100^10)) grandfathers
etc pp.

According to Gottfried Wilhelm Leibniz, at least.
See -> https://wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz

That seems kind of off-topic...
Also that reminds me of the Goodstein sequence

Moosey wrote: January 23rd, 2020, 9:24 pm That seems kind of off-topic...
Also that reminds me of the Goldstein sequence

Strictly speaking it was the reply of Hubi1857 to this philosophical question about grandfathers and the Garden of Eden:

Rhombic wrote: January 10th, 2020, 6:56 pm A philosophical question...

If a still life only has itself as a predecessor, clearly it is its only father, its only grandfather, its only great-grandfather and so on. Does that mean that it would be a Garden of Eden, by induction?

And your reply to Rhombic:

Moosey wrote: January 23rd, 2020, 7:39 pm

Rhombic wrote: January 10th, 2020, 6:56 pm A philosophical question...

If a still life only has itself as a predecessor, clearly it is its only father, its only grandfather, its only great-grandfather and so on. Does that mean that it would be a Garden of Eden, by induction?

No; a still life is its own predecessor and therefore has a predecessor and therefore is not a garden of eden
Though if it is its only predecessor, it is a near GoE.

BTW: the Goldstein sequence is completely irrelevant and useless to skillful theoretical and mathematical physicists like me!

I meant goodstein

Moosey wrote: January 24th, 2020, 12:53 pm I meant goodstein

Your misspelling got the whole thread demoted to Sandbox. Shame on you!

pcallahan wrote: January 24th, 2020, 1:04 pm

Moosey wrote: January 24th, 2020, 12:53 pm I meant goodstein

Your misspelling got the whole thread demoted to Sandbox. Shame on you!

Actually it was just the off topic posts by Hubi and me
Not sure why this went to the sandbox since it was on topic

Moosey wrote: January 24th, 2020, 2:01 pmNot sure why this went to the sandbox since it was on topic

There were some further off-topic replies to your message, so it seemed less confusing to just split the thread at the point where it went off the rails. There were already a couple of on-topic replies that addressed the same point, but mostly your post was an unintended casualty; feel free to re-post if you want.

Well, "unproven conjectures" means conjectures about CGOL and this is backed up by the first post:

Are there any interesting unproven conjectures in the Game of Life?

So I think it is off-topic unless it is at least about cellular automata. (Never mind, I just followed Moosey's "this" link and I agree it's on topic)

dvgrn wrote: January 24th, 2020, 2:35 pm There were already a couple of on-topic replies that addressed the same point, but mostly your post was an unintended casualty; feel free to re-post if you want.

And this is https://wikipedia.org/wiki/Goodstein%27s_theorem

Just in case you can afford a few minutes to waste, of course, or simply do not know what Goodsteins theorem is all about, feel free to read it thoroughly...

Entity Valkyrie 2 wrote: January 28th, 2020, 3:35 am I nominate the P7 pipsquirter variants

And here all digital P011 pipsquirter variants:

Variant 000 = P{sunday, paradise, Garden of Eden, The Big Bang} is still mysteriously only conjectured so far and thus needs a proof urgently before the apocalypse strucks and it doesn't matter anymore.

The rest of the set is perfectly well known and widely accepted amongs each and every possible scientific community an average mathematician is able to imagine.

So here they are:

variant 001 = monday
variant 011 = tuesday
variant 011 = wednesday
variant 100 = thursday
variant 101 = friday
variant 110 = saturday
variant 111 = sunday