An Alien Gift

[Gil Hamilton]

A couple days ago, one of my fellows mentioned that some group has managed to provide an exact solution to the Three Body problem in physics. I expressed disbelief to this, because if that was true, about five minutes after the solution was published, it would be front page news for a great amount of journals and the Nobel prize for next yeat would automatically be determined.

But it did make me think of a scenario. Suppose an alien ship entered orbit around the Earth. They are researchers passing through, picked up some of our broadcasts, and made a detour to investigate. After learning a number of human languages via sophisticated Natural Language AIs, they explain that they really are just passing through. However, people come to note that even though it is foolish to anthropomorphize aliens and apply human psychology to them, they come across largely as a good natured research professor and his group of geeky graduate students. They continue on to explain that they've always wanted to meet aliens and are willing to prepare a gift. Human beings may request a solution to any problem in mathematics, physics, chemistry, et cetera that people can think of. We can't request devices of any sort or blueprints, but they want to advance human knowledge in some way. They care nothing of human politics, so they will ensure once the request is made, everyone on the planet has access to it.

An example to this would be an exact solution to the N-Body Problem for any value of N (this, incidentally, would be my request).

What sort of solution would you request?

[phongn]

Theory of Everything. Given that, we should be busy for quite awhile.

EDIT: Failing that, the N-body problem is as good as any. Perhaps a solution to modeling turbulent flow.

[Surlethe]

Riemann hypothesis? Existence of solutions to n-dimensional Navier-Stokes equation? It might be interesting to ask them to pose their deepest unsolved problem and teach us the material necessary to understand it; that would probably advance human knowledge far more than the solution of a single existing human unsolved problem.

[tezunegari]

If memory serves right there has been a mathematical prove that FTL is impossible because it would cause time travel.
So if the aliens are 'just passing by' in their nifty FTL-capable ship...

The mathematical prove that FTL is possible.

[Coyote]

I was thinking "FTL" too. Unlocking that secret will probabyl be applicable to a lot of other things, and even if it isn't, we'd have the ability to go out and find the other answers "out there".

[Serafina]

Tell us what your FTL does".

Really, we do not need to know HOW he does it - merely knowing WHAT it does would be a huge leap.

If the answer is "Einstein was wrong" - then we have a whole new field of study.
If the answer is "subspace of some sort" then we know what to look for.
If the answer is "Tachyon-Transformation" then we know that we have to look for that process.
And so on.

This answer could also be given by a relatively undeducated person.
I can tell you the basic principle of a lot of technology (say, microchips), but i have no clue of any details.
Similary, most of these aliens propably know the basic principle of their FTL - but perhaps not how exactly it is achieved.

It's really interesting to think about it - a single layperson from such a civilisation could have a huge impact on our civilisation.
Of course, any alien scientists would cut research by a few decades or so and would be way better, too.

[phongn]

How do we know that the aliens arrived via FTL travel?

[Solauren]

I'd ask for a list of what they could give us first, and then decide from their.

However, if they have FTL, I'd want the formulas behind that.

Otherwise, depends what they have.

[Patrick Degan]

How do we know that the aliens arrived via FTL travel?

It would be a reasonable surmise, given the implicitly small size of the expedition and the fact that they were apparently just "looking around". Without some form of travel enabling the crossing of galactic distances in very reasonable timeframes, it would hardly be feasible for any culture to mount a manned slower-than-light mission to another star system simply for the purpose of research.

[Kodiak]

Blueprints for perpetual motion would be nice.

[Coyote]

Blueprints for perpetual motion would be nice.

An X-ray of Glenn Beck's jaw?

Seriously, perpetual motion would be useful only if we could harness power from it. The act of slaving a PM machine to a generator may cause enough "drag/friction" that it is no longer PM. I think that if the "Perpetual Motion" machine truly exists out there, it would be something that can only serve as a form of art.

[Gil Hamilton]

The aliens can't give you a solution for something that fundamentally violates the laws of physics, which covers perpetual motion.

Also, I said nothing about them arriving by FTL. They could be travelling sublight and have an entirely different view on what constitutes a reasonable amount of time to do things (such as them being medically immortal or that they spend most of their time in stasis). Also, their drive system could operate at very close to the speed of light, such that they experience very little of the trip due to relativity. The aliens and their technology themselves, of course, are not the point of the exercise, but rather discussing the relative importance of human unsolved problems.

[Glass Pearl Player]

Some more candidate questions:

• For which formal languages does N==NP hold?
• Is the standard set theory consistent?
• What is the proper way to mathematically describe spacetime?
• Can we have a primer in quantum gravity please?
• What's the show stopper for the Alcubierre/van-den-Broeck warp drive?
• What is the best algorithm to compute Groebner bases, and can we have a sharp bound on its runtime?
• Do we really need the axiom of choice?

My Pick: I'd ask for an optimal algorithm for groebner bases, and sharp runtime bounds.

[Simon_Jester]

I would advise against asking about Alcubierre drives, because the most likely show-stopper is the trivially simple "We can't find any piece of matter with less than zero mass." Which would tell us very little that we don't already know (or can't reasonably infer).

I wish I knew what Groebner bases were.

[Surlethe]

I would advise against asking about Alcubierre drives, because the most likely show-stopper is the trivially simple "We can't find any piece of matter with less than zero mass." Which would tell us very little that we don't already know (or can't reasonably infer).

Good point - we want to avoid questions with potentially trivial answers. Do you have any questions that you'd like to put forward?

I wish I knew what Groebner bases were.

If I'm recalling this at all correctly, a Groebner basis is a basis for an ideal I in a polynomial ring over a finite field that, roughly, allows one to perform division with unique remainders - i.e., a member of the ideal will always have a zero remainder when you mod out by the elements of the Groebner basis. (In general, that doesn't hold; if a polynomial is zero mod your given basis, it's definitely in the ideal, but members of the ideal can be nonzero mod your basis.) Calculating them is important for cracking multivariate public key ciphers; the most prominent, and best, GB calculation algorithm is F4 (although I prefer XL and its variants, especially MXL, for cracking the ciphers, because I happened to work on them).

[RedImperator]

How do we know that the aliens arrived via FTL travel?

It would be a reasonable surmise, given the implicitly small size of the expedition and the fact that they were apparently just "looking around". Without some form of travel enabling the crossing of galactic distances in very reasonable timeframes, it would hardly be feasible for any culture to mount a manned slower-than-light mission to another star system simply for the purpose of research.

The "crew" could be a group of uploaded brain-states stored on a computer, on a ship the size of a sunflower seed, built by a culture that has enshrouded its home star in a Dyson cloud of solar panels for making antimatter. It would be trivial for that kind of civilization to shotgun ships and crews at relativistic speeds all over the galaxy.

[Grog]

A groebner base is a generating set for an ideal in a polynomial ring where there is a special type of order on the monomials. The groebner base has the property that any leading term in a polynomial in the ideal is divisible by a leading term of one of the polynomials in the groebner base.

The polynomials don't have to be over a finite field. I'm a bit tired but I do not understand what it means that something in the ideal is nonzero mod the basis?

I'm not sure what I would ask. What is the best way to colonize the solar system?

[Simon_Jester]

I would advise against asking about Alcubierre drives, because the most likely show-stopper is the trivially simple "We can't find any piece of matter with less than zero mass." Which would tell us very little that we don't already know (or can't reasonably infer).

Good point - we want to avoid questions with potentially trivial answers. Do you have any questions that you'd like to put forward?

The only ones I can think of are broadly similar the ones that virtually everyone here is already suggesting.

For choice I'd ask physics-related questions:
"Is string theory valid, and if so, which one?"
[I do not understand string theory, and am not qualified to formulate this question precisely]
"How do you fit dark matter and/or dark energy into your models of particle physics and forces?"
Those are the only ones that come to mind.

I doubt we could or should ask questions about our own biology, because they almost certainly won't know enough details to tell us much we don't already know, unless we are luckier than we deserve. Asking questions about their biology would be interesting, but might not tell us anything we could actually use.

Likewise, it is probably not a good idea to ask a pure engineering question, such as "what is the best way to colonize our solar system?" unless we can confidently expect to get complete blueprints for all the devices we'd need, including instructions on how to build the tools to make the devices. And that might be too much to ask for. We do not have a critical shortage of capable engineers, and most pure engineering problems can be solved (in the sense of "we know how to do this," not in the sense of "we have done this") by throwing talent at the problem. Plus, engineering talent is relatively fungible, because there are usually many engineers capable of doing front line work on a given problem. Scientific problems are trickier, because they often depend on serendipity, nonfungible talent that only a very few people have, and a healthy dose of blind luck.

If we want answers we can use to questions we probably couldn't have answered on our own in a reasonable time frame, I think physics, math, and computation are the best subjects.

This gets a lot easier if we are allowed to engage in at least a modest dialogue, such that "I don't know" as the answer to our first question doesn't mean we've blown an irrecoverable opportunity.

The "crew" could be a group of uploaded brain-states stored on a computer, on a ship the size of a sunflower seed, built by a culture that has enshrouded its home star in a Dyson cloud of solar panels for making antimatter. It would be trivial for that kind of civilization to shotgun ships and crews at relativistic speeds all over the galaxy.

If the ship is that small we'll never find it, let alone work out a useful way to communicate it. And I'm not sure it will be able to stop long enough for us to ask it a question.

But I do take your meaning; uploads are a very plausible form of "crew" for such a ship, and they greatly reduce the potential costs of STL travel.