Spaceship speed limits

For general discussion about Conway's Game of Life.
Macbi
Posts: 735
Joined: March 29th, 2009, 4:58 am

Spaceship speed limits

Is the proof that spaceships can't go faster than c/2 on the net somewhere? I can't find it.
Last edited by Macbi on April 24th, 2010, 6:06 am, edited 1 time in total.

dvgrn
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> I[s] the proof that spaceships can't go faster than c/2 on the net somewhere?

You're right, the actual c/2 and c/4 speed limit proofs seem harder to find than they should be. Here's something written by John Conway on 24 Mar 1994, summarizing the original result from much longer ago -- the proofs are mentioned but not quoted in the original October 1970 Mathematical Games article (http://www.ibiblio.org/lifepatterns/october1970.html).

I've reformatted the text slightly... what should I use instead of "code" tags to get a fixed-width font, anyway?

---begin quote---

JHC> Here's my old proof of the speed limit results:

Suppose we are initially below the diagonal line abcde... in the figure I'll soon draw, at time 0. Then for x to be born at time 2, we'd need u and v to have been born at time 1, and c to be alive at time 1.

However, for u and v to be born at time 1, we'd need b, m, c, n, d all to be alive at time 0, and that means that c would die of overcrowding, so wouldn't be alive at time 1.

Code: Select all

``````        a
bux
mcv
nd
e
f
``````
This shows that if a configuration is behind a diagonal line at time 0, it's necessarily behind the next such line at time 1, and so on, which restricts the speed in diagonal directions to c/4.

If you're below two diagonal lines at time 0:

Code: Select all

``````               m
l n
k   o
j     p
i       q
h         r
...
``````
then you're below the ones just above them at time 1. So this "bow shock" can travel vertically at at most c/2.

The glider attains c/4 in diagonal directions, and the spaceships attain c/2 in orthogonal ones, so they move as fast as is possible for finite configurations.

---end quote---

Elithrion
Posts: 100
Joined: February 3rd, 2009, 4:02 pm
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Re: Spaceship speed limits

Hmm... I wonder if this proof idea could be emulated for other rules. Some of them clearly have higher speed limits, and others presumably have lower.
Vi veri veniversum vivus vici.

Nathaniel
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Joined: December 10th, 2008, 3:48 pm
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Re: Spaceship speed limits

Elithrion wrote:Hmm... I wonder if this proof idea could be emulated for other rules. Some of them clearly have higher speed limits, and others presumably have lower.
I was wondering the same thing. The proof only seems to rely on the fact that "3" is a birth condition, "0", "1" and "2" are not a birth conditions, and "4" is not a survival condition, so any rule of the form B3(45678)/S(01235678), where numbers in brackets are optional, should have those upper bounds (and maybe tighter upper bounds in some cases as well).

Clearly you can't go faster than c orthogonally, but for some reason c/3 seems to be the magically upper limit for diagonal spaceships in weird rules (example), and I'm not sure why.

Edit: Sorry, c/2 seems to be the upper diagonal limit for arbitrary rules, which seems like it shouldn't be hard to prove. c/3 seems to be the upper diagonal limit for rules without "2" in the birth list, and I'm not sure why *that* is.

dvgrn
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Joined: May 17th, 2009, 11:00 pm
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Re: Spaceship speed limits

Elithrion wrote:Hmm... I wonder if this proof idea could be emulated for other rules. Some of them clearly have higher speed limits, and others presumably have lower.
And if you want to dodge the spaceship speed limit even in plain old Conway's Life, all you have to do is relax the condition about travelling through a vacuum. The 2c/3 and lightspeed "negative spaceships" through an infinite stripes agar were a wonderful find (see the bottom of Gabriel Nivasch's lightspeed signals page -- RLE link).

I wonder how many other kinds of "ocean" in Conway's Life it will turn out to be possible to swim through...? There are probably a number of other surprises out there on the same order as the 2c/3-to-anywhere-in-the-Universe bombshell.

H. V. McIntosh
Posts: 49
Joined: June 20th, 2009, 5:26 pm
Location: Mexico

Re: Spaceship speed limits

Macbi wrote:If the proof that spaceships can't go faster than c/2 on the net somewhere? I can't find it.

By now, that's been answered, both here and via Google. However, I have a related question, for which searching doesn't reveal much of anything: In the Wiki "Rotor" entry we find
Under the standard Conway rules any rotor cell must be adjacent to another rotor cell., but ... .
Lexicon says it is "easy to see," but not for me. Offhand it would seem that one would need to scan all 32M 5x5 neighborhoods to find which ones had a 3x3 central core in which both the center cell and at least one of the others did not change.

In a vacuum, a single live cell can change without any other change. But it's not an oscillator, so that must be important. A beacon or the test tube babies have coupled adjacent pairs, which works well enough. Babbling brooks &c depend on this. Does someone have either a reference or an explanation?
-hvm

calcyman
Posts: 2199
Joined: June 1st, 2009, 4:32 pm

Re: Spaceship speed limits

Lexicon says it is "easy to see," but not for me.
Every rotor cell is alive in some phase(s) of the oscillator, and dead in others. Now consider a dead cell directly before it becomes alive. It must, by definition, be surrounded by three live cells. If these cells are stator cells, not rotor cells, then the isolated rotor cell will continue to have three live neighbours permanently. Such a cell is a stator cell, not a rotor cell. Reductio ad absurdum.
What do you do with ill crystallographers? Take them to the mono-clinic!

H. V. McIntosh
Posts: 49
Joined: June 20th, 2009, 5:26 pm
Location: Mexico

Re: Spaceship speed limits

So it seems that the oscillator part is essential, otherwise we never return to that first cell. Actually, it seems that I misread or misunderstood the whole definition, since I expected an immediate reaction. Which one has, when the period is 2. However the connected string doesn't have to go very far, as in the beacon, test tube babies, and so on. That is probably why there are so few babbling brooks, although there do seem to be oscillators with lots of cells which are pure rotor.

Anyway I'm glad to have that cleared up. In a way, it's just common sense, since a changed cell implies a changed neighborhood unless you have a rule in which the same neighborhood just bounces its cell back and forth.
-hvm

H. V. McIntosh
Posts: 49
Joined: June 20th, 2009, 5:26 pm
Location: Mexico

Re: Spaceship speed limits

So, space ships have their speed limits, but extended structures can behave differently, especially with respect to superluminal movement. What if the structure is not extended? A recent example was the reasonable explanation in the LifeWiki that the stargate was an optical illusion, but that leads to the interesting question of whether the stargate needs a steady stream of space ships to generate the boost, or if it can be done on demand? Probably not because that would imply rapid movement of information, but it does raise the question of the extent to which widely separated activities can be considered to be correlated.

In that direction, I have been wondering about the electric fence, which absorbs and releases ants from a finite stream. Either edge could be removed to obtain matching wicks, but there are further possibilities.

1) trivially, two separated terminators could be used to create a gap in the ant stream, absorb two oppositely directed ant streams or conversely to emit them. Could these two separate terminators be coalesced into a single object?

2) the ant stream is symmetric about its axis of propagation, but the terminators are not. Is there any reason why they couldn't be? As it stands, each has a distinct mirror image which would function equally well; the choice between them may be historical, or it could be just to adjust the size of the bounding box.

3) There are varieties of ants. Does each have a corresponding terminator, again subject to the foregoing questions.

4) can an ant stream be turned 90 degrees, preferably by setting matching terminators at right angles? It is hard to turn space ships, probably equally so for ants.

All this probably calls for a search program, of which I do not have one handy.
-hvm

PM 2Ring
Posts: 152
Joined: March 26th, 2009, 11:18 am

Re: Spaceship speed limits

A recent example was the reasonable explanation in the LifeWiki that the stargate was an optical illusion, but that leads to the interesting question of whether the stargate needs a steady stream of space ships to generate the boost, or if it can be done on demand?
The stargate is a p60 device, and it accelerates any p60 LWSS stream you feed it, assuming the stream is in synch with the stargate. A glider or (other) space ship accelerator that used stable technology and had a fast recovery time would be very interesting!

H. V. McIntosh
Posts: 49
Joined: June 20th, 2009, 5:26 pm
Location: Mexico

Re: Spaceship speed limits

PM 2Ring wrote:..... The stargate is a p60 device, and it accelerates any p60 LWSS stream you feed it, assuming the stream is in synch with the stargate. .....
Yes, this much can be found via Internet, and concretely, in the LifeWiki. However, I wonder if this description is truly worthy of the reference source which we are trying to work up. For example, without going after Golly or some similar program, I still don't know whether "in synch with the stargate" means that the glider stream must be continuous, or whether it can have gaps. Presumably the latter, since the fast forward mechanism ignores a missing space ship, while promoting one which is physically present. It would be reassuring to have this spelled out, particularly given the complexity of the stargate. I mean, as written the sentence seems to be totally correct, but the problem is really to get the reader to understand and believe it.

As for the complexity, why can't a force field simply lay in wait for a space ship, and kick
it along if one shows up (with all due respect for the phase)? Presumably a stargate has to set up several force field generators to handle more than one at a time, leading to the
question of designing one to handle several at one go. I've been looking at the stargate image trying to pick out the individual generators, but there are a lot of them and the resolution isn't wonderful.

Assuming for the moment that the gate will handle sparse streams, we have something like the situation in experimental quantum mechanics wherein a diffraction experiment is performed at such a low density that only one electron is loose in the video camera at any one time. Nevertheless, by waiting, a perfectly convincing diffraction pattern will evolve. Transferring this idea to Life, set up a sequence of stargates into which a single space ship is launched at a precise phase from a given place. Somewhat later look at the far end of
its track, to find that it has arrived somewhat sooner that predicted by the velocity of light. Or not; implying a transmission of information.

Somehow that seems to be a real effect, and not just an optical illusion.
-hvm

calcyman
Posts: 2199
Joined: June 1st, 2009, 4:32 pm

Re: Spaceship speed limits

Somehow that seems to be a real effect, and not just an optical illusion.

No, because the reactions cannot be compacted close enough together to propagate information faster than lightspeed. Indeed, it is simple to prove that information cannot travel at superluminal speeds, due to the fact that the rules of Life only update a cell based on its Moore-connected neighbours after one generation.

If you're still not convinced, then construct such a pattern for yourself. You'll find that it either functions below lightspeed, explodes, or otherwise detects the 'ghost' LWSSes as being actual ones, and emits a spaceship regardless of whether a spaceship actually entered the device.
What do you do with ill crystallographers? Take them to the mono-clinic!

PM 2Ring
Posts: 152
Joined: March 26th, 2009, 11:18 am

Re: Spaceship speed limits

H. V. McIntosh wrote:
PM 2Ring wrote:..... The stargate is a p60 device, and it accelerates any p60 LWSS stream you feed it, assuming the stream is in synch with the stargate. .....
Yes, this much can be found via Internet, and concretely, in the LifeWiki. However, I wonder if this description is truly worthy of the reference source which we are trying to work up. For example, without going after Golly or some similar program, I still don't know whether "in synch with the stargate" means that the glider stream must be continuous, or whether it can have gaps. Presumably the latter, since the fast forward mechanism ignores a missing space ship, while promoting one which is physically present. It would be reassuring to have this spelled out, particularly given the complexity of the stargate. I mean, as written the sentence seems to be totally correct, but the problem is really to get the reader to understand and believe it.
Yes, the LWSS stream can have gaps in it. For example, see here for a pattern I built last August, using a modified form of Calcyman's LWSS fanout device (LWSS duplicator). It feeds the fanout device with an intermittent stream of LWSSs and uses 4 copies of the stargate to accelerate the output LWSS stream to synchronize it vertically with the input LWSS stream.

It's not easy to describe complex patterns. It's hard to know what level of detail to go down to, and which reactions need to be explained in detail. Also, after working with a pattern for a while, the sub-patterns & reactions tend to seem obvious, and so one may not realize that they need explaining. But this is a topic for another thread.
As for the complexity, why can't a force field simply lay in wait for a space ship, and kick
it along if one shows up (with all due respect for the phase)? Presumably a stargate has to set up several force field generators to handle more than one at a time, leading to the
question of designing one to handle several at one go. I've been looking at the stargate image trying to pick out the individual generators, but there are a lot of them and the resolution isn't wonderful.
A new pair of force field reactions occur every 60 steps. Roughly speaking, the force field reaction eats a LWSS at its left end while synthesizing a new LWSS at its right. But if the LWSS at the left fails to appear, the LWSS on the right is killed by the sparks from the left.

While the whole stargate pattern may appear daunting at first glance, most of its bulk is in its glider guns. The forcefield reaction itself is remarkably compact in space & time:

The output LWSS appears at step 6, the debris is clear by step 28 if the output LWSS escapes, or by step 39 if it gets destroyed.

Here are two copies of the forcefield in a row, as used in the stargate. Using two of them restores the LWSS phase.

Code: Select all

``````x = 39, y = 18, rule = B3/S23
21bo5bobo\$19bobo6b2o\$20b2o6bo3\$7bo6bo\$8bo6b2o\$2b2o2b3o5b2o\$2ob2o\$4o9bo
\$b2o9b2o\$12bobo4\$37b2o\$36b2o\$38bo!
``````
Somehow that seems to be a real effect, and not just an optical illusion.
Is it reality or an optical illusion? I'm still not sure. I shall have to build my own stargate tunnel & contemplate this question...

When I first saw the stargate, I just assumed it worked by magic. Although I was interested in Life in the early 1970s, much of its development passed me by, and when I discovered all the incredible patterns that had been built by the mid 90s, I was amazed and rather overwhelmed. I thought I'd never understand how things like glider gun puffers worked. And so I didn't delve into the details of these fancy patterns for several years. But eventually curiosity got the better of me, and I felt the desire to try & build some glider based circuits myself. I'm more comfortable with complex constructions these days, but I don't know if I really understand a lot of the reactions I use, I've just become more familiar with them.

calcyman
Posts: 2199
Joined: June 1st, 2009, 4:32 pm

Re: Spaceship speed limits

Is it reality or an optical illusion? I'm still not sure. I shall have to build my own stargate tunnel & contemplate this question...

I can demonstrate the invalidity of the stargate reaction:

First, observe this pattern, which accelerates a LWSS at 15c/14, overtaking a lightspeed signal:

Code: Select all

``````x = 430, y = 176, rule = B3/S23
bob4o4boobboo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo\$obboboo4boobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbo\$bob4o4boobboo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo3boo3\$12bo\$\$12bo\$\$12bo\$\$12bo\$\$12bo\$\$12bo255bo6bo\$269bo6boo\$12bo254b
3o5boo\$\$12bo244bo5bobo\$255bobo6boo\$12bo243boo6bo\$245bo6bo\$12bo233bo6b
oo\$244b3o5boo\$12bo\$234bo5bobo\$12bo219bobo6boo\$233boo6bo\$12bo209bo6bo\$
223bo6boo\$12bo208b3o5boo\$\$12bo198bo5bobo\$209bobo6boo\$12bo197boo6bo\$
199bo6bo\$12bo187bo6boo\$198b3o5boo\$12bo\$188bo5bobo\$12bo173bobo6boo\$187b
oo6bo\$12bo163bo6bo\$177bo6boo\$12bo162b3o5boo\$\$12bo152bo5bobo\$163bobo6b
oo\$12bo151boo6bo\$153bo6bo\$12bo141bo6boo\$152b3o5boo\$12bo\$142bo5bobo\$12b
o127bobo6boo\$141boo6bo\$12bo117bo6bo\$131bo6boo\$12bo116b3o5boo\$\$12bo106b
o5bobo\$117bobo6boo\$12bo105boo6bo\$107bo6bo\$12bo95bo6boo\$106b3o5boo\$12bo
\$96bo5bobo\$12bo81bobo6boo\$95boo6bo\$12bo71bo6bo\$85bo6boo\$12bo70b3o5boo
\$\$12bo60bo5bobo\$71bobo6boo\$12bo59boo6bo\$61bo6bo\$12bo49bo6boo\$60b3o5boo
\$12bo\$50bo5bobo\$12bo35bobo6boo\$49boo6bo\$12bo25bo6bo\$39bo6boo\$12bo24b3o
5boo\$\$12bo14bo5bobo\$25bobo6boo\$12bo13boo6bo\$15bo6bo\$16bo6boo\$10boobb3o
5boo\$8booboo\$8b4o9bo\$9boo9boo\$20bobo\$\$39boo\$38boo\$40bo\$58bo\$57boo\$57bo
bo\$\$76boo\$75boo\$77bo\$95bo\$94boo\$94bobo\$\$113boo\$112boo\$114bo\$132bo\$131b
oo\$131bobo\$\$150boo\$149boo\$151bo\$169bo\$168boo\$168bobo\$\$187boo\$186boo\$
188bo\$206bo\$205boo\$205bobo\$\$224boo\$223boo\$225bo\$243bo\$242boo\$242bobo\$\$
261boo\$260boo\$262bo\$280bo\$279boo\$279bobo\$\$298boo\$297boo\$299bo\$317bo\$
316boo\$316bobo\$\$335boo\$334boo\$336bo\$354bo\$353boo\$353bobo\$\$372boo\$371b
oo\$373bo\$391bo\$390boo\$390bobo\$\$409boo\$408boo\$410bo\$428bo\$427boo\$427bob
o!``````

That seems quite genuine at first, doesn't it? The stargate reaction _does_ accelerate the LWSS to a superluminal speed -- 15c/14.

Now delete the LWSS:

Code: Select all

``````x = 430, y = 176, rule = B3/S23
bob4o4boobboo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo\$obboboo4boobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbob
obbo\$bob4o4boobboo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo
3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3b
oo3boo3\$12bo\$\$12bo\$\$12bo\$\$12bo\$\$12bo\$\$12bo255bo6bo\$269bo6boo\$12bo254b
3o5boo\$\$12bo244bo5bobo\$255bobo6boo\$12bo243boo6bo\$245bo6bo\$12bo233bo6b
oo\$244b3o5boo\$12bo\$234bo5bobo\$12bo219bobo6boo\$233boo6bo\$12bo209bo6bo\$
223bo6boo\$12bo208b3o5boo\$\$12bo198bo5bobo\$209bobo6boo\$12bo197boo6bo\$
199bo6bo\$12bo187bo6boo\$198b3o5boo\$12bo\$188bo5bobo\$12bo173bobo6boo\$187b
oo6bo\$12bo163bo6bo\$177bo6boo\$12bo162b3o5boo\$\$12bo152bo5bobo\$163bobo6b
oo\$12bo151boo6bo\$153bo6bo\$12bo141bo6boo\$152b3o5boo\$12bo\$142bo5bobo\$12b
o127bobo6boo\$141boo6bo\$12bo117bo6bo\$131bo6boo\$12bo116b3o5boo\$\$12bo106b
o5bobo\$117bobo6boo\$12bo105boo6bo\$107bo6bo\$12bo95bo6boo\$106b3o5boo\$12bo
\$96bo5bobo\$12bo81bobo6boo\$95boo6bo\$12bo71bo6bo\$85bo6boo\$12bo70b3o5boo
\$\$12bo60bo5bobo\$71bobo6boo\$12bo59boo6bo\$61bo6bo\$12bo49bo6boo\$60b3o5boo
\$12bo\$50bo5bobo\$12bo35bobo6boo\$49boo6bo\$12bo25bo6bo\$39bo6boo\$12bo24b3o
5boo\$\$12bo14bo5bobo\$25bobo6boo\$12bo13boo6bo\$15bo6bo\$16bo6boo\$14b3o5boo
\$\$21bo\$20boo\$20bobo\$\$39boo\$38boo\$40bo\$58bo\$57boo\$57bobo\$\$76boo\$75boo\$
77bo\$95bo\$94boo\$94bobo\$\$113boo\$112boo\$114bo\$132bo\$131boo\$131bobo\$\$150b
oo\$149boo\$151bo\$169bo\$168boo\$168bobo\$\$187boo\$186boo\$188bo\$206bo\$205boo
\$205bobo\$\$224boo\$223boo\$225bo\$243bo\$242boo\$242bobo\$\$261boo\$260boo\$262b
o\$280bo\$279boo\$279bobo\$\$298boo\$297boo\$299bo\$317bo\$316boo\$316bobo\$\$335b
oo\$334boo\$336bo\$354bo\$353boo\$353bobo\$\$372boo\$371boo\$373bo\$391bo\$390boo
\$390bobo\$\$409boo\$408boo\$410bo\$428bo\$427boo\$427bobo!``````
The right-hand-side of the pattern still receives the LWSS, even though it was not initially present. This is because the 4F reactions must be separated in order to work, at which point they become subluminal.

Quod erat demonstrandum.
What do you do with ill crystallographers? Take them to the mono-clinic!

PM 2Ring
Posts: 152
Joined: March 26th, 2009, 11:18 am

Re: Spaceship speed limits

I spent some time last night playing with patterns like the ones Calcyman posted above, but with enough separation to allow the reactions to work properly. I now agree that the stargate's fast forward reaction (FFR) is an optical illusion.

At step 6, the FFR produces a LWSS displaced 11 cells to the right of the input LWSS at step 0. This is the source of the apparent superluminal movement. However, the minimum repeat time (aka compression) of the FFR is 22 steps, and of course over the other 16 steps the LWSS moves the expected 8 cells. So during the 22 step cycle, the LWSS appears to move a total of 19 cells, yielding a mean speed of 19c/22 ~= 0.8636c, which is still a lot faster than the usual LWSS speed of 0.5c, but it's hardly superluminal. However, if we "cheat" & measure the speed over a 28 step period we get (11 + 8 + 11)c / (6 + 16 + 6) = 30c/28 ~= 1.0714c.

If we chain multiple copies of the FFR together, the mean speed reduces. If we use n copies, the best speed we can achieve is (19*n + 11)/(22*n + 6) , as illustrated in the following table:

Code: Select all

``````0:  11/  6 = 1.833333    10:  201/ 226 = 0.889381
1:  30/ 28 = 1.071429    20:  391/ 446 = 0.876682
2:  49/ 50 = 0.980000    30:  581/ 666 = 0.872372
3:  68/ 72 = 0.944444    40:  771/ 886 = 0.870203
4:  87/ 94 = 0.925532    50:  961/1106 = 0.868897
5: 106/116 = 0.913793    60: 1151/1326 = 0.868024
6: 125/138 = 0.905797    70: 1341/1546 = 0.867400
7: 144/160 = 0.900000    80: 1531/1766 = 0.866931
8: 163/182 = 0.895604    90: 1721/1986 = 0.866566
9: 182/204 = 0.892157   100: 1911/2206 = 0.866274
``````

H. V. McIntosh
Posts: 49
Joined: June 20th, 2009, 5:26 pm
Location: Mexico

Re: Spaceship speed limits

Still, although the velocity of light has not been exceeded, the space ships still seem to be moving along faster that c/2, namely 19/22 nds of c; probably explicable by the bulk of the stargate mechanism. Although a single jump is plausibly an illusion, the criterion of "how long does it take for the consequences of an event in one place to reach another?" still stands in contradiction to the properties of space ships, even though it does fall within the limits of causality. Probably the illusion results from our tendency to see whole patterns where they don't really exist; tracing the movement of individual bits probably doesn't move them as fast as the apparent single step jump calls for.

Actually, examining the fast forward construction, it seems that we basically have a three glider near synthesis of a light weight space ship. Interestingly, if it takes place just in front of an oncoming space ship, the cloud of trailing debris dissipates; approximately thirty generations are required. Otherwise the construction fails although, the space ship almost escapes. It would be interesting to know more about the search strategy via which it was discovered; also whether it could be applied to longer space ships. It would also be interesting to have more details of the glider syntheses at hand, since promoting such a reaction to a stargate evidently involves knowing the size of the debris cloud, whether more gliders are needed to kill it, and the required packing of all the glider sources involved.

As for the teleportation itself, there is an eating mechanism and a production mechanism at work. To obtain a causal coupling between them, we need to cover the distance between the head of the deceased and the tail of the newborn; the gap between head and tail then measures the jump which can be attributed to teleportation. Waiting for debris to settle affects the overall velocity, depending on how far the space ship has to move at its regular velocity before being hurled forward again.

That Wiki page is still a molestation - not only for the scale, but for locating the spaceships. For example, the gliders come in from both directions, so the space ships at the bottom of the figure must be for comparison, since they cannot be teleported. Also, I'm sorry if I don't think Java programs should be incorporated into text pages.
-hvm

H. V. McIntosh
Posts: 49
Joined: June 20th, 2009, 5:26 pm
Location: Mexico

Re: Spaceship speed limits

The illusion part of the fast forward force field sems to be settled, the teleportation's jump being related to the distance between the bow and the stern of the teleportee. Except for the stargate, which employs serial fields, there don't seem to be other instances of teleportation among the Life patterns, raising the question of whether there really are any other instances and if so, how many of them have been found? In other words:
1) can longer space ships or even flotillas be teleported?
2) can the teleportee be offset, rather than just skipping forward in the same trajectory?
3) can it be turned into an orthogonal course?
4) can it be reflected back by some distance?
5) are there other force fields?
-hvm

H. V. McIntosh
Posts: 49
Joined: June 20th, 2009, 5:26 pm
Location: Mexico

Re: Spaceship speed limits

I wrote: ..... 5) are there other force fields?
In a manner of speaking, conduits are also force fields; their action is probably not regarded as teleportation because the effects are not instantaneous. But then, neither is what we have been calling teleportation. Quoting from the LifeWiki,
A conduit is an arrangement of still lifes and/or oscillators that moves an active object to another location without themselves being permanently damaged. .....
We are only missing the gliders, but we are accepting the possibility of rotation, flipping, displacement, and transmutation; all of which were possibilities in the above query.

The conduit page in the Wiki could probably use some elaboration; it only asserts that there are sixteen elementary Herschel conduits. But
[*] Buckingham's list only contains eight, although
[*]images for them are provided. Presumably there is a
[*]calculus, or grammar for combining them

The complexity of this latter is probably why there are search programs, and that the results reported are only loosely assorted into families.
-hvm

doccolinni
Posts: 25
Joined: May 18th, 2010, 11:36 pm

Re: Spaceship speed limits

I'm sort of a new guy here, but I hope you won't mind me sharing my take on what the so-called Stargate actually does.

Whether the Stargate actually makes the LWSSes move faster than light or just creates an illusion of it is an irrelevant and in fact purely philosophical matter - the LWSS that hits the gliders from the left gets destroyed so although a new LWSS is created on the right one might say that that's a new LWSS and previous one is not there any more at all, but then again if an LWSS didn't hit the gliders from the left side the new LWSS wouldn't have been created on the right side at all so one might say that as the direct consequence of the "old" LWSS the "new" LWSS basically makes the old one live on... See, it's all just philosophical nonsense.

What's really important here are the information throughputs of a stream of LWSSes travelling regularly and with the aid of the Stargate. Let me explain what I'm talking about...

First of all, what's actually sneaky in that Stargate pattern lies down below - it's the regularly-travelling LWSSes that serve the purpose of comparing the regular travel of LWSSes to the one aided by the Stargate. A more fair comparison is actually provided by this pattern:

Code: Select all

``````x = 155, y = 133, rule = B3/S23
25b2o85b2o\$24bobo44bobo37bobo\$10bo12b3o4b2o34bo4bo2bo35bo13bobo\$5bo4b
4o8b3o4bo2b4o31b2o5b2o8bo16b2o7bo2bo6b2o2bo2bo\$5bo5b4o8b3o4b2ob3o26b2o
8bo3b2o5bobo15b2o7bo8bobo5b2o\$2o9bo2bo9bobo35b2o10b2o6bob2o25bobo3bo3b
o3bo3b2o4b2o\$2o9b4o10b2o44bo2bo6b2ob2o10b2o14b2o2b2ob3o5b2o6b2o\$10b4o
8bo48bobo8bob2o10b2o21b2o3bo2bo\$10bo12bo59bobo20b2o16bobo\$21b3o50bo9bo
21bo\$34b2o19b2o16bo21b2o7bobo\$5b2o28bo19bo17b3o19b3o6b2o4bo\$5b2o28bobo
6b2o7bobo25bo15b2obo9bobo\$36b3o5bobo6b2o24bobo4b3o8bo2bo9b2o\$38b3o6bo
30bobo16b2obo\$5bo32bo2bo2bo2bo29bo2bo7bo2b2o2b3o\$4bobo32b2o6bo8bo21bob
o7bo3bo2b2o\$3bo3bo8b3o25bobo9b3o7bo7b2o3bobo6bo2bo29b2o23b2o\$3b5o10bo
25b2o13bo6bobo4bobo5bo8b2o11bo17bobo22bo\$2b2o3b2o8bo40b2o6b2o5bo28bo
13b2o6bo11bobo5bobo\$3b5o13bo30b2o18b2o28b3o7b2obo2bo2bo2bo10bo2bo5b2o\$
4b3o12b3o31bo58b2o2b2o6bo9b2o12b2o\$5bo12bo18bo6bo8bobo65bobo8b2o3bo10b
2o\$18b2o18bo6b2o7b2o21b2o42b2o11b2o12b2o\$9b2o25b3o5b2o15b2o13b4o11b2o
33bo8bo2bo10bo\$8bobo4bo12b2o30b2ob2o10b2ob2o10b2ob2o29b2o10bobo9bobo\$
10bo4bo11bobo31b4o11b2o13b4o21b2o7b2o21bobo\$29bo32b2o28b2o22bo32bo\$
106bo7bobo\$13b2o3b2o79b2obo3b4o4b2o\$14b5o4b2o68b2o2b2obobo4b4o35b2o3b
2o\$15b3o4bo2bo66bobo2b2obob2o3bo2bo35bobobobo\$16bo49bo24b3o8b2o3b4o6bo
bo27b5o\$6b3o11bo43bobo15b2o6b3o8b2o3b4o7b2o29b3o\$5bo3bo12bo42b2o15b2o
7b3o12bo11bo30bo\$21bo70bobo\$4bo5bo82b2o\$4b2o3b2o41bo6bo83b2o\$30b3o20bo
6b2o81bo\$30bo20b3o5b2o50bo21bobo5bobo\$7bo23bo77b2o22bo3bo3b2o\$6bobo8b
3o90b2o5bo19bo8bobo\$6bobo106b4o14bo4bo7b2o\$6bo10bobo26bobo65bobob2o4bo
12bo9bo\$6bo9b5o17b3o5bo3bo62bo2bob3o5b2obo3bo3bo\$6bo2bo5b2o3b2o11b2o2b
o2bobo7bo42bo19b2obob2o5b4obo2bobo\$7b2o6b2o3b2o9bo2bo2b2o7bo4bo41b3o
15b3ob4o6b2o2b2o19b3o\$30bo19bo30bo14bo5bobo5bobo4bo31bo3bo\$30bo10b3o2b
o3bo3b2o23bobo13b2o5b2o6bo29bo7bo5bo\$18bo11bo15bobo5bobo23b2o7b2o12bo
5b2o27b2o9bo3bo\$16b2o6b2o5bo2bo21bo33bo48b2o9b3o\$23bobo7b2o21b2o32bobo
57b3o\$15bo7bo43bo6bo16b2o4bo2bo26bo2bo\$22b2o44bo6b2o19bo14b4o11bo\$16bo
2bo46b3o5b2o20bo3bo10bo3bo10bo3bo\$18b2o76b4o11bo14b4o20b2o\$112bo2bo34b
2o\$135b2o8bo\$135bo2bo6bobo\$130b2o2bo3bo7bobo4b2o\$129b3o2b2o2bo7bo2bo3b
2o\$119b2o5bob2o16bobo\$96bo5bobo14b2o5bo2bo8b3o4bobo\$94bobo6b2o21bob2o
15bo\$95b2o6bo25b3o\$130b2o2\$82bo6bo\$83bo6b2o\$17b2o28b2o28b2o2b3o5b2o\$
15b2ob2o25b2ob2o25b2ob2o\$15b4o26b4o26b4o9bo\$16b2o28b2o28b2o9b2o\$87bobo
2\$128b2o\$128b2o\$112b2o26b2o\$111b2o27b2o\$88bo24bo\$88b3o\$91bo51bo\$90b2o
36b3o11bo\$142bo\$128bobo\$127b5o\$103bo22b2o3b2o5b2o3b2o\$93bo8b2o22b2o3b
2o8bo\$92b3o7bobo33bo5bo\$91b5o43b2ob2o\$90bobobobo43bobo\$90b2o3b2o44bo\$
127b2o12bo\$126b2o\$93bo31bo2bo2b2o\$92bobo32bo3bo\$91b2obo37b3o\$91b3o40bo
\$90bo2bo43bobo\$90b3o44b2o\$89bo3bo44bo3b3o\$88bo5bo23bo22bo3bo\$89bo3bo5b
o17b2o21bo5bo\$90b3o7bo16bobo20b2obob2o\$98b3o\$131bo\$129b2o\$130b2o\$111b
2o\$110bobo32b2o\$107bo4bo12b2o18bo\$88b2o15bobo17b2o19b3o\$89bo16b2o40bo\$
86b3o26b2o21b2o\$86bo29bo21bo2bo\$92b2o22bobo9bo3b3o7bo\$90bo3bo5bo2b3o
11b2o8b5o3bo6bo\$89bo5bo9bo3bo16b2ob2o3bo7bo\$88bo2bo3bo8bo4bobo13b3ob2o
3bo3bo2bo5b2o\$95bo16b2o12b2ob4o5b2o7bobo\$86bo3bo3bo17b2o13b4o18bo\$85bo
b2o3b2o18b2o14bo20b2o\$85bo23bobo4b2o\$84b2o23bo6bobo\$118bo\$118b2o4\$14b
2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o\$12b2ob2o2b2ob2o2b2ob2o2b2ob2o2b
2ob2o2b2ob2o2b2ob2o2b2ob2o2b2ob2o2b2ob2o\$12b4o3b4o3b4o3b4o3b4o3b4o3b4o
3b4o3b4o3b4o\$13b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o!
``````
Notice that in the regular stream of LWSSes (the one in the bottom of this pattern) each LWSS takes up 7 cells (if we tried to squeeze them any more they'd destroy each other). We can now imagine using an LWSS stream to transfer information by making each 7 cells in the stream represent either a 1 or a 0 depending on whether those 7 cells contain an LWSS or not. Therefore in the regular LWSS stream the amount of bits per cell of the stream is 1b/7c ("1 bit per 7 cells").

Notice now, though, that for a stream of LWSSes to successfully pass through the Stargate the distance between consecutive LWSSes in the stream has to be increased, so in an LWSS stream which is to pass through the Stargate each LWSS doesn't take up 7 cells any more, but instead it takes up 30 cells. If we were to use this stream to transfer information analogously to the way we used a regular stream of LWSSes, the amount of bits per cell of this stream would therefore be reduced to 1b/30c.

Of course, it's not all about how spread out the bits in a stream are, it's also how fast they travel that's important, so now comes the calculation part. Instead of writing the speed of a spaceship the common way as, for example, "c/2", I'll write "1c/2g" instead, which stands for "1 cell per 2 generations", so it's the same thing, but this format better suits the calculations I want to do or, to be more precise, the value I want to get from those calculations.

Since the regular LWSS stream travels at 1c/2g and has information density of 1b/7c, the amount of bits per generation that a regular LWSS stream delivers is (1c/2g)*(1b/7c) = 1b/14g (1 bit per 14 generations).

Whether LWSS stream itself passes through the Stargate or not is, like I said, a philosophical question, but it is indisputable that the information which that stream carries does pass through the Stargate - if we interpret the LWSS stream that comes out of the Stargate the same way we would have interpreted the one that went in it we'll get the same stream of bits, so information does pass through the Stargate at the speed of 15c/14g, therefore the amount of bits per generation that an LWSS stream travelling through the Stargate delivers is (15c/14g)*(1b/30c) = 1b/28g.

Would you ever have guessed it - the amount of bits per generation that a regular LWSS stream can deliver is precisely two times greater than the amount of bits per generation that an LWSS stream travelling through a Stargate can deliver.

Of course, the immediately obvious remark to my calculation is that for the compact stream of LWSSes which transfers 1 bit of information per 14 generations to work one would need a device which is capable of reading the input LWSS stream at c/14. As a noob I'm not really familiar with which kinds of LWSS-stream-reading devices there are in Life, but checking out the Turing Machine (http://www.conwaylife.com/wiki/index.ph ... ng_machine) it seems that what we have at the moment is this (the thing on the left in the pattern):

Code: Select all

``````x = 150, y = 45, rule = B3/S23
114b2o\$115bo\$115bobo6bobo21b2o\$116b2o5bo2bo21bo\$122b2o10bo6bo4bobo\$
120b2o3bo8bo5bobo3b2o\$122b2o9bo6b2obo\$123bo2bo2b2o9b2ob2o\$124bobo2bo2b
3o5b2obo\$129b4o7bobo6bo\$130b2o9bo5b3o\$32b2o28b2o28b2o28b2o22bo\$31b4o
11b2o13b4o11b2o13b4o11b2o13b4o21b2o\$30b2ob2o10b2ob2o10b2ob2o10b2ob2o
10b2ob2o10b2ob2o10b2ob2o\$31b2o13b4o11b2o13b4o11b2o13b4o11b2o\$47b2o28b
2o28b2o\$143b3o\$133b3o\$22b2o109bo9bobo\$20bo3bo109bo7b5o\$11bo7bo5bo115b
2o3b2o\$11bobo4b2obo3bo97b3o15b2o3b2o\$14b2o3bo5bo99bo\$14b2o4bo3bo7b2o
80bo9bo\$14b2o6b2o8bobo78bobo25b2o\$2b2o7bobo20bo78b2obo8bobo11b2obo\$bob
o7bo22b2o77b2ob2o6bo2bo11bo\$bo111b2obo6b2o\$2o101b2o8bobo5b2o3bo13b3obo
\$102bobo9bo8b2o19bo\$102bo21bo2bo5b2o9bo\$101b2o22bobo5bobo\$135bo\$135b2o
2\$139b2o3b2o\$141b3o\$140bo3bo\$141bobo\$142bo2\$139b2o\$140bo\$137b3o\$137bo!
``````
which is if I recognise it correctly a slight variation of Gosper glider gun, which can therefore obviously only read the input LWSS stream at c/30, meaning that each LWSS in the stream must take up 30 cells (which they indeed do there), which in turn means that the amount of bits per generation which can be received is (1c/2g)*(1b/30c) = 1b/60g. Yes, that's more than two times worse than what an LWSS stream travelling through the Stargate can do, but if we ever found a way to read the input LWSS stream sufficiently fast, the Stargate would obviously become completely useless.

Incidentally, the frequencies at which a regular LWSS stream is more than or equally efficient as a "Stargate LWSS stream" are pretty easy to calculate (I hope everyone can read Unicode, if not those weird symbols are the symbols for "greater or equal" in the first two lines and "less or equal" in the third line):

(1c/2g)*(1b/xc) ≥ (15c/14g)*(1b/30c)
(1/2)*(1/x) ≥ (15/14)*(1/30)
x ≤ 14

So if we ever found a device which is capable of reading the input stream of LWSSes at c/14 or faster, Stargate would become completely useless. But then again, I'm not entirely sure that we've got a device which can read it at c/30 (the frequency of Stargate-aided LWSS stream) in the first place...

Phantom Hoover
Posts: 20
Joined: May 16th, 2010, 3:54 pm

Re: Spaceship speed limits

Allow me to clarify this to you. Information cannot travel more than 1cell/generation in Life. It is incredibly obvious; it derives from the axioms of Life. This is not a "philosophical" matter; it is hard mathematical reality. The Stargate does not send information at 15c/14; this is an illusion that derives from your godlike, three-dimensional observer status, able to instantly see the state of every cell in the universe.

calcyman
Posts: 2199
Joined: June 1st, 2009, 4:32 pm

Re: Spaceship speed limits

Doccolinni:

I believe that you have confused your 'p's and 'c's. 'c' is the fundamental unit for speed in Life; p is an abbreviation for period. For example, the Gosper glider gun is period-30, or p30. The period of a pattern is measured in generations per cycle, and is inversely proportional to frequency.
... 1b/14g (1 bit per 14 generations).
Your compound unit "b/g" is inversely proportional to the commonly accepted "p". So, "1b/14g" is equivalent to p14.

one would need a device which is capable of reading the input LWSS stream at c/14.
You mean period-14 -- c/14 is a measure of speed, not transmission rate. And yes, it is possible to read a LWSS stream at period-14:

Code: Select all

``````x = 404, y = 460, rule = B3/S23
oo\$bo\$bobo\$bboo4bobbo24bobbo10bobbo24bobbo10bobbo24bobbo\$7bo6b4o10b4o
3bo6b4o3bo20b4o3bo6b4o3bo6b4o10b4o3bo\$7bo3bobbo3bo9bo3bobbo3bobbo3bobb
o3bo16bo3bobbo3bobbo3bobbo3bobbo3bo9bo3bobbo3bo\$7b4o3bo13bo6b4o3bo6b4o
17bo6b4o3bo6b4o3bo13bo6b4o\$15bobbo10bobbo10bobbo24bobbo10bobbo10bobbo
10bobbo3\$5bo\$4boo\$4bobo\$\$8boo\$7boo\$9bo\$12bo\$11boo\$11bobo\$\$15boo\$14boo\$
16bo\$19bo\$18boo\$18bobo\$\$22boo\$21boo\$23bo\$26bo\$25boo\$25bobo\$\$29boo\$28b
oo\$30bo\$33bo\$32boo\$32bobo\$\$36boo\$35boo\$37bo\$40bo\$39boo\$39bobo\$\$43boo\$
42boo\$44bo\$47bo\$46boo\$46bobo\$\$50boo\$49boo\$51bo\$54bo\$53boo\$53bobo\$\$57b
oo\$56boo\$58bo\$61bo\$60boo\$60bobo\$\$64boo\$63boo\$65bo\$68bo\$67boo\$67bobo
184boo3booboo74boo3booboo\$239bo14bobo3bobobo58bo14bobo3bobobo\$71boo
166b3o10boobb4obbobo3bo54b3o10boobb4obbobo3bo\$70boo170bo8bobboo3bobobo
3bobo56bo8bobboo3bobobo3bobo\$72bo168boo8bobobbo4bo5bobo55boo8bobobbo4b
o5bobo\$75bo174boob4o3boo4boobobo62boob4o3boo4boobobo\$74boo168bo7bo3bob
oobobbo4boobo55bo7bo3boboobobbo4boobo\$74bobo166bobo5boo3bobboo3bob3o3b
o54bobo5boo3bobboo3bob3o3bo\$239boobboo7bo3boboobobbo5b3obo48boobboo7bo
3boboobobbo5b3obo\$78boo159boo9boob4o3boo4boobo3bobo47boo9boob4o3boo4b
oobo3bobo\$77boo172bobobbo4bo5boboboobbo59bobobbo4bo5boboboobbo\$79bo
171bobboo3boboboboboboobobo60bobboo3boboboboboboobobo\$82bo169boobb4obb
oboobboboboboo17booboo38boobb4obboboobboboboboo\$81boo171bobo3bobo3bobo
bobobbo16bobboo5boo34bobo3bobo3bobobobobbo\$81bobo170boo3boobobooboboo
bbo19bo4bobbobbo33boo3boobobooboboobbo\$263bo3boboboo17b3ob4obobbobo42b
o3boboboo\$85boo177bobobbobo17bobbobo4booboboo15bo26bobobbobo\$84boo165b
o11booboobobobo16bobo3boo6bobbo13boo24booboobobobo\$86bo165bo10bo5boobo
bo12b4obobo3boboobboboo12bobo24bo5boobobo\$89bo160b3o12boobo5bo11bo4bo
4boo3boboobo42boobo5bo\$88boo143boo31bob6o13b3o3b3obboobo4bo43bob6o\$88b
obo143boo30bo4bo17bobobo3bobboob3o33bo10bo4bo\$233bo33b3o20b3obboobo4bo
33bobo11b3o\$92boo175boo14boo9boboboo36boo13boo\$91boo191bobbo7bo3boboo\$
93bo62boo126b3o9b3o\$96bo58bobbo128b3o3b3o\$95boo55bo3bobo125boo3bo3bo3b
oo\$95bobo52b6obo126boboobb3obboobo\$149bo5bo130bo4bo4bo\$99boo48boboobo
bbo128bobbobobobbo\$98boo50bo3boboo127boobo5boboo\$100bo51bobo129bobbob
5obobbo41boo\$103bo47boo3boo126booboboboboboboo34boo5boo\$102boo46bobboo
bo129bobo5bobo6boo28boo\$102bobo43bobbo3bobbo110bo16bo3b3o3bo7boo63boo\$
148boobo3boboo9bo98bobo17b3obob3o7bo65bo\$106boo41boboboobo9b3o47bo51b
oo19bobobo41boo33bo\$105boo41bobb3obbo8bo50boo117boo19bo12boo\$107bo40bo
bo3boboo7boo22boo24bobo60boo5boo3b3o36boo26bo\$110bo38bob4obbo32bo87boo
5bo43boo24b3o\$109boo40bo3bo7bo26bobo90bobo104booboo\$109bobo39boboobbo
bboboboo25boobboo37bo48boo6bo92boo5boobbo\$152boboboo9boo26boo35b3o44b
oo9bobo44boo14bo29bobbobbo4bo\$113boo39bobo3bo7bo43boobbobo12bo47bobo9b
oo58boo14bo15bobobbob4ob3o\$112boo39bobbo9boo43b3obo3bo11boo14boo31bo6b
oo61boo14boo14boobb3o4bobobbo\$114bo39boo5bobboo44boo6bo28boo37bobo60bo
30bobbobo3b4obbobo\$117bo44b3o46bob5o68bo5boo56b5o25boobob5obb3obb4o\$
116boo29boo5boo56b4o37bo31boo5boo57bo29boboo5boo4bo4bo\$116bobo29bo5boo
58bo35bo3bo126bo4boboobb3obob3o\$148bobo95bo7bo23b5o99b3oboobbo3bobobo\$
120boo27boo84bo9bobo3bobo22b3obob3o18boo39booboo35bo4boboo\$119boo32boo
78b3o10b5o16bo7bo4bo4bo17bobo37bobobobo22boo12boobobo3b3o3boo\$121bo30b
obo78b3o11b3o15boo8bobooboboobo17bo22boo16bobbobo21boo12boobo3bo7bobbo
\$124bo28bo35boo41bo3bo6boo3b3o15boo5boobobo3boboboo39bo8b3o8boboo8bo
13bo15b3o9b3o\$123boo63bobo16boo24b4o6boo5boo21bobbo7bobbo39bobo8bo7boo
3bo8boo30b4ob4o\$123bobo62bo6b3o9bobo10bo12boobo13boobboo18boob7oboo41b
oo7b3o3bobobbobo8boo28boo3bobobo3boo\$187boo6boobo10bo9bobo32boo19bo9bo
57boobbooboo37boboobb3obboobo\$127boo9boo7boo44boobobo4boo4boo10boo52bo
9bo105bo3bobo3bo\$126boo9bobboboobobbobbooboo47bobo24boo3bo37boboo7boob
o103bo9bo\$128bo8bobo3boboobb3obob3o38boo7bo24bo3bobo36boo5bo5boo102boo
b7oboo\$131bo6boboo5boo4bo4bo46boo10boo12bo3boo39b9o104bobbobo3bobobbo\$
130boo8bobooboobboboob4o22boo34bobo13bo40b3obbo3bobb3o101boobobo3bobob
oo\$130bobo7bobo3bobbobbobo12bobo9boo35bo13bob5o32boobo3bobbobobbobbo
103boboo3boobo\$139boobb3obo4bobbo12boo11bo33boo13boo4bo33boobobo9boo
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11bo45bo\$149boo5boo102boo30bo5bo15bobo9boo42b3o\$149boo5bo56bo46bobo27b
obb4obo15boo63boo5boo\$154bobo54b3o47bo28boobobobo81boo5bo\$154boo54bo
82bobo88bobo\$150boo42boo14boo62boo14booboboo87boo\$150bobo41boo65bo11bo
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67boo8bobobobbobbob3o5b3o7booboboboboo31b3o47bo\$181bobo66boo5b3o3b3obb
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15b3obob3obboobo3bobo60bo29bobbobo4b3obboo7boboboobboo3bo20booboo57boo
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4boobboo8boobo24bo31boo22b3obob3obboobo3bobo\$128boboboo9boo3b4ob4obboo
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o\$127boboo8boobboo6boboboboo4bobo31boo52bobboo5boobb3o4boo17bobo25bo
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128bo3bobo20bobo52b3ob3o9bo16boboobb3obboobo40boo36bo16b3o\$131bobbo21b
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bo5boboo95boboo\$194boo47bobbobobobobobbo21bo45b3o25b3o\$141boo7boo48boo
32boo7booboboboboboboo21bobo42bobobobo23bo\$140bobboboobobbobb5o41boo
33bo9boboo3boobo6b3o14boo43bo3boboo\$140bobo3boboobb3obob3o73bo10bo3b3o
3bo8bo59boobbobo\$141boboobo3boo4bo4bo72boo10b3o3b3o8bo50boo10bo5bo\$
143bobooboobb4ob4o37boo48bo3bo61boo10bobboboo\$143bobo4boobobobo40boo5b
oo113boo5boboo23boo\$142boob4obobbobobbo46boo43bo69boo33bo\$143bobobbob
4ob3o14bobo75bo103bo\$143bobbobbo4bo18boo179boo\$144boo5boobbo17bo76bo
67boo29boo\$150booboo94bobo66boo5boo20b3o\$207b3o40boo73boo5boo12bo4bo\$
209bo36boo66bobo14bobo12bob6o\$208bo36bobo67boo16bo11boobo5bo\$245bo5boo
62bo27bo5bobbobo\$218boo24boo5boo90boob4obobo\$216b3o43bo81bobobbobo\$
215bo4bo40bo81bo3bo3boo\$215bob6o30bo7b3o70boo3boobobooboboobbo\$214boob
o5bo28bobo79bobo3bobo3bobobobobbo\$212bo5b4obo28bobo10boo65boobb4obbob
oobbo3boboo\$212boob4obobo27boboboo5boobboo64bobboo3boboboboboboobobo\$
213bobo4bo28boboobbo4bobo68bobobbo4bo5bo3boobbo\$212bo3boboboo27bo3b3o
5bo57boo9boob3o4boo4boobo3bobo\$190bo12boo3booboboobobo3bo24bob4obbo63b
oobboo7bo4bobo5bobb5obo\$191boo10bobo3bobo3bobob3obbo21bobo3boboo7boo
58boboboo3boboo3boo3b3obo3bo\$190boo9boobb4obboboobboboboboo21bobb4obo
8bo60bo7bo4bobo5bo3boobo\$200bobboo3bobobobobobobbobo23bobobbobo9b3o63b
oob3o4boo4boobobo\$200bobobboo3bo5bob4obbo21booboboboboo9bo54boo8bobobb
o4bo5bobo\$188boo9booboo5boo4boobo3bobo21bobb3obobbo65bo8bobboo3bobobo
3bobo\$188boobboo4bobbobo3bo7bobb4obo24bo3bobo64b3o10boobb4obbobo3bo\$
192bobobb3obboo3bo7b3o3bo27booboboo63bo14bobo3bobobo\$193bo4bobbobo3bo
7bobboobo28bo4bo78boo3booboo\$199booboo5boo4boobobo27bobob3o\$190boo8bob
obboo3bo5bobo28bob4obb3o\$191bo8bobboo3bobobo3bobo28bo5bobobbo\$188b3o
10boobb4obbobo3bo30b6o3boo\$188bo14bobo3bobobo36bo3bo\$203boo3booboo40b
oo!``````
What do you do with ill crystallographers? Take them to the mono-clinic!

doccolinni
Posts: 25
Joined: May 18th, 2010, 11:36 pm

Re: Spaceship speed limits

calcyman wrote:Doccolinni:

I believe that you have confused your 'p's and 'c's. 'c' is the fundamental unit for speed in Life; p is an abbreviation for period. For example, the Gosper glider gun is period-30, or p30. The period of a pattern is measured in generations per cycle, and is inversely proportional to frequency.
... 1b/14g (1 bit per 14 generations).
Your compound unit "b/g" is inversely proportional to the commonly accepted "p". So, "1b/14g" is equivalent to p14.

one would need a device which is capable of reading the input LWSS stream at c/14.
You mean period-14 -- c/14 is a measure of speed, not transmission rate. And yes, it is possible to read a LWSS stream at period-14:

Code: Select all

``````x = 404, y = 460, rule = B3/S23
oo\$bo\$bobo\$bboo4bobbo24bobbo10bobbo24bobbo10bobbo24bobbo\$7bo6b4o10b4o
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17bo6b4o3bo6b4o3bo13bo6b4o\$15bobbo10bobbo10bobbo24bobbo10bobbo10bobbo
10bobbo3\$5bo\$4boo\$4bobo\$\$8boo\$7boo\$9bo\$12bo\$11boo\$11bobo\$\$15boo\$14boo\$
16bo\$19bo\$18boo\$18bobo\$\$22boo\$21boo\$23bo\$26bo\$25boo\$25bobo\$\$29boo\$28b
oo\$30bo\$33bo\$32boo\$32bobo\$\$36boo\$35boo\$37bo\$40bo\$39boo\$39bobo\$\$43boo\$
42boo\$44bo\$47bo\$46boo\$46bobo\$\$50boo\$49boo\$51bo\$54bo\$53boo\$53bobo\$\$57b
oo\$56boo\$58bo\$61bo\$60boo\$60bobo\$\$64boo\$63boo\$65bo\$68bo\$67boo\$67bobo
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oo!``````
Yeah to all you said, sorry - like I said, I'm a noob with this stuff so I'm not yet quite familiarised with terminology, but I hope what I said was nevertheless understandable. I feel especially dumb for using the c for transmission rate. >.<

Oh well, I'll learn.

edit: Ah, by the way, it's nice to see that reading an LWSS stream at period-14 is possible.

Phantom Hoover
Posts: 20
Joined: May 16th, 2010, 3:54 pm

Re: Spaceship speed limits

However, most technology runs at either p30 or p46 or is stable, so you wouldn't be able to process the data fast enough.

doccolinni
Posts: 25
Joined: May 18th, 2010, 11:36 pm

Re: Spaceship speed limits

Phantom Hoover wrote:Allow me to clarify this to you. Information cannot travel more than 1cell/generation in Life. It is incredibly obvious; it derives from the axioms of Life. This is not a "philosophical" matter; it is hard mathematical reality. The Stargate does not send information at 15c/14; this is an illusion that derives from your godlike, three-dimensional observer status, able to instantly see the state of every cell in the universe.
Okay, maybe not at over the "speed of light" in the Life space, but the Stargate definitely transmits information faster than an LWSS stream at period-30 does on its own. It doesn't do it at 15/14, but it definitely is over 1/2. That is yet even more proof of the fact that the Stargate is completely useless, because LWSS stream at period-14 now definitely transmits more data per generation than an LWSS stream at period-30 "assisted" by the Stargate, despite the speed-up.

Yes, from your explanation now it's obvious that nothing in Life space can travel faster than 1cell/generation, I can't believe I actually presumed Stargate did transfer data at 15/14...

Sleep deprivation, I tell ya.

calcyman
Posts: 2199
Joined: June 1st, 2009, 4:32 pm

Re: Spaceship speed limits

... the Stargate is completely useless ...
It's not completely useless at all: it's fun to see how many people fall for the trap of thinking that it performs the impossible.

Anyway, Jason Summers has constructed a device to transmit information at lightspeed orthogonally, and I have produced a stable version. So, the Stargate is not ideal for practical signal acceleration, as there are much more effective ways of transmitting information at high speeds. Dave Greene and Noam Elkies' 2c/3 transceiver is another pattern that transmits information at a supervacual rate.
What do you do with ill crystallographers? Take them to the mono-clinic!