## Spaceship speed limits

For general discussion about Conway's Game of Life.

### 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.

Macbi

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Joined: March 29th, 2009, 4:58 am

### Re: Game of Life Links

> 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.

`        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:

`               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---

dvgrn
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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.

Elithrion
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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.

Nathaniel

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Joined: December 10th, 2008, 3:48 pm

### 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.

dvgrn
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### 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
H. V. McIntosh

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### 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!

calcyman

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Joined: June 1st, 2009, 4:32 pm

### 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

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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
H. V. McIntosh

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Location: Mexico

### 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!

PM 2Ring

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Joined: March 26th, 2009, 11:18 am

### 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
H. V. McIntosh

Posts: 49
Joined: June 20th, 2009, 5:26 pm
Location: Mexico

### 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!

calcyman

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Joined: June 1st, 2009, 4:32 pm

### 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.
`x = 39, y = 18, rule = B3/S2321bo5bobo\$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.

PM 2Ring

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Joined: March 26th, 2009, 11:18 am

### 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:

`x = 430, y = 176, rule = B3/S23bob4o4boobboo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo\$obboboo4boobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbo\$bob4o4boobboo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3\$12bo\$\$12bo\$\$12bo\$\$12bo\$\$12bo\$\$12bo255bo6bo\$269bo6boo\$12bo254b3o5boo\$\$12bo244bo5bobo\$255bobo6boo\$12bo243boo6bo\$245bo6bo\$12bo233bo6boo\$244b3o5boo\$12bo\$234bo5bobo\$12bo219bobo6boo\$233boo6bo\$12bo209bo6bo\$223bo6boo\$12bo208b3o5boo\$\$12bo198bo5bobo\$209bobo6boo\$12bo197boo6bo\$199bo6bo\$12bo187bo6boo\$198b3o5boo\$12bo\$188bo5bobo\$12bo173bobo6boo\$187boo6bo\$12bo163bo6bo\$177bo6boo\$12bo162b3o5boo\$\$12bo152bo5bobo\$163bobo6boo\$12bo151boo6bo\$153bo6bo\$12bo141bo6boo\$152b3o5boo\$12bo\$142bo5bobo\$12bo127bobo6boo\$141boo6bo\$12bo117bo6bo\$131bo6boo\$12bo116b3o5boo\$\$12bo106bo5bobo\$117bobo6boo\$12bo105boo6bo\$107bo6bo\$12bo95bo6boo\$106b3o5boo\$12bo\$96bo5bobo\$12bo81bobo6boo\$95boo6bo\$12bo71bo6bo\$85bo6boo\$12bo70b3o5boo\$\$12bo60bo5bobo\$71bobo6boo\$12bo59boo6bo\$61bo6bo\$12bo49bo6boo\$60b3o5boo\$12bo\$50bo5bobo\$12bo35bobo6boo\$49boo6bo\$12bo25bo6bo\$39bo6boo\$12bo24b3o5boo\$\$12bo14bo5bobo\$25bobo6boo\$12bo13boo6bo\$15bo6bo\$16bo6boo\$10boobb3o5boo\$8booboo\$8b4o9bo\$9boo9boo\$20bobo\$\$39boo\$38boo\$40bo\$58bo\$57boo\$57bobo\$\$76boo\$75boo\$77bo\$95bo\$94boo\$94bobo\$\$113boo\$112boo\$114bo\$132bo\$131boo\$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\$371boo\$373bo\$391bo\$390boo\$390bobo\$\$409boo\$408boo\$410bo\$428bo\$427boo\$427bobo!`

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:

`x = 430, y = 176, rule = B3/S23bob4o4boobboo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo\$obboboo4boobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbobobbo\$bob4o4boobboo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3boo3\$12bo\$\$12bo\$\$12bo\$\$12bo\$\$12bo\$\$12bo255bo6bo\$269bo6boo\$12bo254b3o5boo\$\$12bo244bo5bobo\$255bobo6boo\$12bo243boo6bo\$245bo6bo\$12bo233bo6boo\$244b3o5boo\$12bo\$234bo5bobo\$12bo219bobo6boo\$233boo6bo\$12bo209bo6bo\$223bo6boo\$12bo208b3o5boo\$\$12bo198bo5bobo\$209bobo6boo\$12bo197boo6bo\$199bo6bo\$12bo187bo6boo\$198b3o5boo\$12bo\$188bo5bobo\$12bo173bobo6boo\$187boo6bo\$12bo163bo6bo\$177bo6boo\$12bo162b3o5boo\$\$12bo152bo5bobo\$163bobo6boo\$12bo151boo6bo\$153bo6bo\$12bo141bo6boo\$152b3o5boo\$12bo\$142bo5bobo\$12bo127bobo6boo\$141boo6bo\$12bo117bo6bo\$131bo6boo\$12bo116b3o5boo\$\$12bo106bo5bobo\$117bobo6boo\$12bo105boo6bo\$107bo6bo\$12bo95bo6boo\$106b3o5boo\$12bo\$96bo5bobo\$12bo81bobo6boo\$95boo6bo\$12bo71bo6bo\$85bo6boo\$12bo70b3o5boo\$\$12bo60bo5bobo\$71bobo6boo\$12bo59boo6bo\$61bo6bo\$12bo49bo6boo\$60b3o5boo\$12bo\$50bo5bobo\$12bo35bobo6boo\$49boo6bo\$12bo25bo6bo\$39bo6boo\$12bo24b3o5boo\$\$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\$\$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\$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!

calcyman

Posts: 2072
Joined: June 1st, 2009, 4:32 pm

### 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:
`0:  11/  6 = 1.833333    10:  201/ 226 = 0.889381   1:  30/ 28 = 1.071429    20:  391/ 446 = 0.8766822:  49/ 50 = 0.980000    30:  581/ 666 = 0.8723723:  68/ 72 = 0.944444    40:  771/ 886 = 0.8702034:  87/ 94 = 0.925532    50:  961/1106 = 0.8688975: 106/116 = 0.913793    60: 1151/1326 = 0.8680246: 125/138 = 0.905797    70: 1341/1546 = 0.8674007: 144/160 = 0.900000    80: 1531/1766 = 0.8669318: 163/182 = 0.895604    90: 1721/1986 = 0.8665669: 182/204 = 0.892157   100: 1911/2206 = 0.866274`

PM 2Ring

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

### 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
H. V. McIntosh

Posts: 49
Joined: June 20th, 2009, 5:26 pm
Location: Mexico

### 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:

`x = 155, y = 133, rule = B3/S2325b2o85b2o\$24bobo44bobo37bobo\$10bo12b3o4b2o34bo4bo2bo35bo13bobo\$5bo4b4o8b3o4bo2b4o31b2o5b2o8bo16b2o7bo2bo6b2o2bo2bo\$5bo5b4o8b3o4b2ob3o26b2o8bo3b2o5bobo15b2o7bo8bobo5b2o\$2o9bo2bo9bobo35b2o10b2o6bob2o25bobo3bo3bo3bo3b2o4b2o\$2o9b4o10b2o44bo2bo6b2ob2o10b2o14b2o2b2ob3o5b2o6b2o\$10b4o8bo48bobo8bob2o10b2o21b2o3bo2bo\$10bo12bo59bobo20b2o16bobo\$21b3o50bo9bo21bo\$34b2o19b2o16bo21b2o7bobo\$5b2o28bo19bo17b3o19b3o6b2o4bo\$5b2o28bobo6b2o7bobo25bo15b2obo9bobo\$36b3o5bobo6b2o24bobo4b3o8bo2bo9b2o\$38b3o6bo30bobo16b2obo\$5bo32bo2bo2bo2bo29bo2bo7bo2b2o2b3o\$4bobo32b2o6bo8bo21bobo7bo3bo2b2o\$3bo3bo8b3o25bobo9b3o7bo7b2o3bobo6bo2bo29b2o23b2o\$3b5o10bo25b2o13bo6bobo4bobo5bo8b2o11bo17bobo22bo\$2b2o3b2o8bo40b2o6b2o5bo28bo13b2o6bo11bobo5bobo\$3b5o13bo30b2o18b2o28b3o7b2obo2bo2bo2bo10bo2bo5b2o\$4b3o12b3o31bo58b2o2b2o6bo9b2o12b2o\$5bo12bo18bo6bo8bobo65bobo8b2o3bo10b2o\$18b2o18bo6b2o7b2o21b2o42b2o11b2o12b2o\$9b2o25b3o5b2o15b2o13b4o11b2o33bo8bo2bo10bo\$8bobo4bo12b2o30b2ob2o10b2ob2o10b2ob2o29b2o10bobo9bobo\$10bo4bo11bobo31b4o11b2o13b4o21b2o7b2o21bobo\$29bo32b2o28b2o22bo32bo\$106bo7bobo\$13b2o3b2o79b2obo3b4o4b2o\$14b5o4b2o68b2o2b2obobo4b4o35b2o3b2o\$15b3o4bo2bo66bobo2b2obob2o3bo2bo35bobobobo\$16bo49bo24b3o8b2o3b4o6bobo27b5o\$6b3o11bo43bobo15b2o6b3o8b2o3b4o7b2o29b3o\$5bo3bo12bo42b2o15b2o7b3o12bo11bo30bo\$21bo70bobo\$4bo5bo82b2o\$4b2o3b2o41bo6bo83b2o\$30b3o20bo6b2o81bo\$30bo20b3o5b2o50bo21bobo5bobo\$7bo23bo77b2o22bo3bo3b2o\$6bobo8b3o90b2o5bo19bo8bobo\$6bobo106b4o14bo4bo7b2o\$6bo10bobo26bobo65bobob2o4bo12bo9bo\$6bo9b5o17b3o5bo3bo62bo2bob3o5b2obo3bo3bo\$6bo2bo5b2o3b2o11b2o2bo2bobo7bo42bo19b2obob2o5b4obo2bobo\$7b2o6b2o3b2o9bo2bo2b2o7bo4bo41b3o15b3ob4o6b2o2b2o19b3o\$30bo19bo30bo14bo5bobo5bobo4bo31bo3bo\$30bo10b3o2bo3bo3b2o23bobo13b2o5b2o6bo29bo7bo5bo\$18bo11bo15bobo5bobo23b2o7b2o12bo5b2o27b2o9bo3bo\$16b2o6b2o5bo2bo21bo33bo48b2o9b3o\$23bobo7b2o21b2o32bobo57b3o\$15bo7bo43bo6bo16b2o4bo2bo26bo2bo\$22b2o44bo6b2o19bo14b4o11bo\$16bo2bo46b3o5b2o20bo3bo10bo3bo10bo3bo\$18b2o76b4o11bo14b4o20b2o\$112bo2bo34b2o\$135b2o8bo\$135bo2bo6bobo\$130b2o2bo3bo7bobo4b2o\$129b3o2b2o2bo7bo2bo3b2o\$119b2o5bob2o16bobo\$96bo5bobo14b2o5bo2bo8b3o4bobo\$94bobo6b2o21bob2o15bo\$95b2o6bo25b3o\$130b2o2\$82bo6bo\$83bo6b2o\$17b2o28b2o28b2o2b3o5b2o\$15b2ob2o25b2ob2o25b2ob2o\$15b4o26b4o26b4o9bo\$16b2o28b2o28b2o9b2o\$87bobo2\$128b2o\$128b2o\$112b2o26b2o\$111b2o27b2o\$88bo24bo\$88b3o\$91bo51bo\$90b2o36b3o11bo\$142bo\$128bobo\$127b5o\$103bo22b2o3b2o5b2o3b2o\$93bo8b2o22b2o3b2o8bo\$92b3o7bobo33bo5bo\$91b5o43b2ob2o\$90bobobobo43bobo\$90b2o3b2o44bo\$127b2o12bo\$126b2o\$93bo31bo2bo2b2o\$92bobo32bo3bo\$91b2obo37b3o\$91b3o40bo\$90bo2bo43bobo\$90b3o44b2o\$89bo3bo44bo3b3o\$88bo5bo23bo22bo3bo\$89bo3bo5bo17b2o21bo5bo\$90b3o7bo16bobo20b2obob2o\$98b3o\$131bo\$129b2o\$130b2o\$111b2o\$110bobo32b2o\$107bo4bo12b2o18bo\$88b2o15bobo17b2o19b3o\$89bo16b2o40bo\$86b3o26b2o21b2o\$86bo29bo21bo2bo\$92b2o22bobo9bo3b3o7bo\$90bo3bo5bo2b3o11b2o8b5o3bo6bo\$89bo5bo9bo3bo16b2ob2o3bo7bo\$88bo2bo3bo8bo4bobo13b3ob2o3bo3bo2bo5b2o\$95bo16b2o12b2ob4o5b2o7bobo\$86bo3bo3bo17b2o13b4o18bo\$85bob2o3b2o18b2o14bo20b2o\$85bo23bobo4b2o\$84b2o23bo6bobo\$118bo\$118b2o4\$14b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o5b2o\$12b2ob2o2b2ob2o2b2ob2o2b2ob2o2b2ob2o2b2ob2o2b2ob2o2b2ob2o2b2ob2o2b2ob2o\$12b4o3b4o3b4o3b4o3b4o3b4o3b4o3b4o3b4o3b4o\$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.php?title=Turing_machine) it seems that what we have at the moment is this (the thing on the left in the pattern):

`x = 150, y = 45, rule = B3/S23114b2o\$115bo\$115bobo6bobo21b2o\$116b2o5bo2bo21bo\$122b2o10bo6bo4bobo\$120b2o3bo8bo5bobo3b2o\$122b2o9bo6b2obo\$123bo2bo2b2o9b2ob2o\$124bobo2bo2b3o5b2obo\$129b4o7bobo6bo\$130b2o9bo5b3o\$32b2o28b2o28b2o28b2o22bo\$31b4o11b2o13b4o11b2o13b4o11b2o13b4o21b2o\$30b2ob2o10b2ob2o10b2ob2o10b2ob2o10b2ob2o10b2ob2o10b2ob2o\$31b2o13b4o11b2o13b4o11b2o13b4o11b2o\$47b2o28b2o28b2o\$143b3o\$133b3o\$22b2o109bo9bobo\$20bo3bo109bo7b5o\$11bo7bo5bo115b2o3b2o\$11bobo4b2obo3bo97b3o15b2o3b2o\$14b2o3bo5bo99bo\$14b2o4bo3bo7b2o80bo9bo\$14b2o6b2o8bobo78bobo25b2o\$2b2o7bobo20bo78b2obo8bobo11b2obo\$bobo7bo22b2o77b2ob2o6bo2bo11bo\$bo111b2obo6b2o\$2o101b2o8bobo5b2o3bo13b3obo\$102bobo9bo8b2o19bo\$102bo21bo2bo5b2o9bo\$101b2o22bobo5bobo\$135bo\$135b2o2\$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...
doccolinni

Posts: 25
Joined: May 18th, 2010, 11:36 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.
Phantom Hoover

Posts: 20
Joined: May 16th, 2010, 3:54 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:

`x = 404, y = 460, rule = 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What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

Posts: 2072
Joined: June 1st, 2009, 4:32 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:

`x = 404, y = 460, rule = 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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.
doccolinni

Posts: 25
Joined: May 18th, 2010, 11:36 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.
Phantom Hoover

Posts: 20
Joined: May 16th, 2010, 3:54 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.
doccolinni

Posts: 25
Joined: May 18th, 2010, 11:36 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!

calcyman

Posts: 2072
Joined: June 1st, 2009, 4:32 pm

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