Is every spaceship edible?

[Dannyu NDos]

If every spaceship is edible, that means every gun implies corresponding oscillator.

[Macbi]

This is the kind of thing which we suspect is true, but which no one has ever thought of a way to prove.

[dvgrn]

This is the kind of thing which we suspect is true, but which no one has ever thought of a way to prove.

In this case we can come unusually close to a proof, though:

1) No spaceship is unstoppable. (Proof by contradiction: aim the outputs of two "unstoppable" spaceship guns directly at each other. Most likely both spaceships, but certainly at least one of them, will be stopped.)

2) Every spaceship that we know of, or that we can design, can be stopped by colliding with a large enough field of (random or designed) simple ash objects, and the product of the collisions can be arranged to be just more simple ash objects.

3) We know how to construct or destroy arbitrarily large fields of simple ash objects by colliding gliders.

So as long as a spaceship gun has a high enough period, we can be very confident that an engineered eater exists for that gun. Maybe the biggest weakness in the "every gun implies an oscillator" statement is that there might exist spaceship guns with such a low period that no engineered eater recovers quickly enough to eat the spaceship stream successfully.

[apg]

How do we know that there's not a soliton-like spaceship such that any collision between solitons has the same effect as if they passed straight through each other?

[dvgrn]

How do we know that there's not a soliton-like spaceship such that any collision between solitons has the same effect as if they passed straight through each other?

That can be one of the reasons why we're only "unusually close to a proof" instead of actually having a proof.

Meanwhile, go ahead and post your soliton spaceship candidates here, and if I can't immediately respond with an example configuration where two of them abjectly fail to pass harmlessly through each other... then I'll send you a nickel instead, with a profile of John Conway on it instead of the usual Jefferson.

[testitemqlstudop]

But the universal constructor argument

[dvgrn]

But the universal constructor argument

That's a bit too vague. Do you mean the universal constructor argument already addressed above ("We know how to construct or destroy arbitrarily large fields of simple ash objects by colliding gliders."), or some kind of universal-constructor argument for the existence of Conway's Life solitons?

I can't immediately rule out a self-constructing mega-spaceship that is able to mutually communicate with any other instance of itself, in any orientation and relative position and phase, in such a way that each mega-spaceship builds a special construction arm that reaches around the other spaceship, resulting eventually in two spaceships in the same phase and position as if they had passed directly through each other. It's certainly possible for specifically chosen positions and phases.

However, that only shoots a hole in the oversimplified "there are no unstoppable spaceships" non-proof that I gave above -- it doesn't do anything to show that there are unstoppable spaceships. You could probably stop one of these mega-soliton things by putting a single blinker in its path, or anything it wasn't programmed to test for.

[testitemqlstudop]

Ok, my blueprint is something like this:

First choose some arbitrarily large integer n.

Then, assemble in front of the spaceship some shield indestroyable to a glider stream in any orientation, given that in 2n ticks there is at most one glider. Furthemore, when hit by a glider, it self-recovers and then duplicates the glider back.

Every time the universal constructor tries to duplicate itself, it first fires a glider and waits 4n ticks. If it receives in its shield a glider, it does not duplicate in its normal place but "stretches" its normal arm across the span of the spaceship and duplicates. Otherwise it duplicates normally.

There are several holes, like how to make a universal clock that won't blow up, but it's a blueprint.

[dvgrn]

There are several holes, like how to make a universal clock that won't blow up, but it's a blueprint.

... Yeah, it seems like you'd need to establish some more detailed communication between two approaching mega-spaceships somehow, so that each one knows the other's precise phase and position. Otherwise what's to prevent two mirror-image spaceships from approaching each other at 180 degrees, and both attempting a sideways offset in the same direction?

The rest of the blueprint is all pretty much just hand-waving anyway until the actual mechanisms are developed. I think with current technology it's not impossible to make a self-recovering glider-reflecting shield, for any given number of incoming glider lanes, but the mechanism ends up being ridiculously deep compared to its width. It's very hard to come up with an effective shield that would cover all lanes that would impinge on a self-constructing mechanism.