Gauss's Pythagorean right triangle proposal

https://en.wikipedia.org/wiki/Gauss%27s_Pythagorean_right_triangle_proposal

by benbreen • 4 years ago

44 27 4 years ago

en.wikipedia.org

yoyopa• 4 years ago

hmmm.. what about a giant dickbutt, that way it would be much easier to draw.

turing_complete• 4 years ago

Every civilization will discover the Pythagorean theorem; only a select few will discover dickbutt.

amelius• 4 years ago

And the dickbutts of some civilizations will look like the Pythagorean theorem.

lstodd• 4 years ago

Aha, that's what Tunguska was: aliens telling us to not bother with this.

thanatos519• 4 years ago

But seriously, what could we do to make ourselves evident in every direction to distant beings with telescopes at least as good as ours? Something that would never ever happen naturally.

I'm thinking something passive (i.e. reflective) and orbiting a Lagrange point... maybe one we don't need much, like Mars L4 or L5. Make a dozen reflective spheres, of mirror mylar inflated with a little bit of some big-molecule gas that won't leak out. Arrange them in a static icosahedral form at the Lagrange point.

From any angle except perhaps very normal to the ecliptic, there would be a distinctive changing pattern of reflected light. Maybe each sphere could have a different notch filter coating on it so there would be some signal on the spectrograph too.

downboots2• 4 years ago

consider the situation at home of already being evident to other species and its results

ehecatl42• 4 years ago

Aye. Our sensory apparatus, let alone our ability to process the totality of inputs from it, is pretty limited. WTF can comprehend even what fungi "feel"? And we're of the same origin.

Maybe in 100 million years? Chump change, of course, even in biological time; but then "we" won't be worrying about triangles.

leashless• 4 years ago

Yeah that's not bad. Any way to work prime numbers into it? I'm thinking bright objects worked into an orbit, with the gap between each reflector in orbit being say 5, 7, 11, 13, 17 so you'd see these periodic increases in brightness in an unmistakable pattern?

Jabbles• 4 years ago

It would be much easier to pick the nearest N stars and point lasers at them with a peculiar frequency that would stand out on any spectra.

This random quora answer[1] suggests lasers could potentially have a spread of ~0.1 arcseconds so that would be (10 * 60 * 60)^2 * 40k ~ 1e13 times less power required (per target) than an omnidirectional source.

[1] https://qr.ae/pvZZjd

Someone• 4 years ago

It would have to be huge to be seen with telescopes as good as ours.

Looking at https://en.wikipedia.org/wiki/List_of_smallest_exoplanets:

- https://en.wikipedia.org/wiki/SDSS_J1228%2B1040_b has about 1/1000 the radius of Jupiter, but only could be detected because it’s heavy at 70% of the mass of the sun.

- https://en.wikipedia.org/wiki/Kepler-37b is larger than the moon.

So, it seems we can’t (¿yet?) build such a structure in a way that makes it visible enough.

If we let go of the idea that a proposal must be feasible with current tech, here’s an idea: split the sun in two halves, creating a binary star system. Then, merge the two again. Repeat. That should draw attention.

noobermin• 4 years ago

In order to have something visible in every direction is just impossible I think. It's best to just do something like flash lights or radio waves in such a way to spell out the first few prime numbers. EM waves spread out naturally from a small source, that seems much easier to me.

ndsipa_pomu• 4 years ago

I'm not convinced that drawing a huge 2-dimensional representation on a non-flat surface (i.e. a globe) really demonstrates intelligence

laszlokorte• 4 years ago

But it might trigger some aliensplaining: they will come here to tell us about non-euclidean geometry and how to do it properly

gxt• 4 years ago

Aliensplaining like the conquistadors? No thank you.

drooby• 4 years ago

Much better is the idea to redirect asteroids into the sun’s orbit that encodes flashes of light in some unique pattern (pi?). The light sends the signal in potentially all directions and the signal would last for a lonnng time.

The ability to achieve that feat is in itself evidence of the beings intelligence and accomplishments.

“Intelligence was here”

BiteCode_dev• 4 years ago

Liu cixin would be proud. And horrified.

motohagiography4• 4 years ago

Something I've been hacking on that I don't think anyone has discovered yet is that around the time of the decision of what images and artifacts place on the Voyager spacecraft as evidence of human civilization, there were a number of candidates. Among one of the successful candidates was Laurie Spiegel[1], an early electronic musician (1970s) and programmer from Bell Labs, and her work "Music of the Spheres" introduces the section "Sounds of the Earth," instead of being included in the "Music of Earth" section on the golden record we sent in the hopes of it being discovered by some other spacefaring civilization.

There is a coincidence I'm running down to see if there is any substance to it, as there was another more prominent piece of music written at the same time by a more prominent composer that was not included in the space program, and it too used a procedural method, which could also be used to encode information to an advanced civilization in an unambiguous way, independent of what those aliens might look like, so long as they understood the same physics.

Obviously, it would make more sense to transmit a message via radio or laser or some other means that travelled at the speed of light, but the big question is, what message would you use, and how would you encode it so that it would be an unambiguous signal of our place in the universe?

Arvo Pärt is an Estonian, former Soviet subject and orthodox Christian, whose early work was largely inspired by gregorian chants, and early, religious music, and he's reputed to be a bit of a mystical hermit. Some writers have written about symmetries and "shapes" in the structure of his pieces, and what people examinging Arvo Pärt's music to interpret his "Tintinabuli" and geometric procedural composition style have overlooked is the time and context in which this specific piece was written. The piece was famous then as it is now, and it is called "Spiegel im Spiegel" or Mirror in Mirror by Arvo Pärt.[2]

Not only do I think that Pärt was inspired by Gauss's proposal, but what I think I have found that is new is that the violin melody from Spiegel im Spiegel isn't just made of triangles, as some academics have suggested, but rather a sequence of negative and positive integers, and specifically the integer sequence that is the result of iterating Euler's Identity e^ipi = -1. When you scratch the surface of what function could produce this undulating wave of -1, 1, -2, 2, -3, 3... it is a succinct demonstration that we have found e, pi, i, 0, 1.

This is what we should encode as a message in sound, or in light, to send out as evidence of the state of our civilization. That this encoding of Euler's identity in procedural quasi-religious music was written at the same time as our societies around the world were reflecting on who they were and what artifacts they would choose to represent themselves to a distant civilization - and it happened to be coincidentally named for one of the artists whose work was sent out - is perhaps a just-so story, but it has been quite a fun journey into who these people were and what they may have intended.

TL;DR, I think I discovered that Arvo Pärt's Spiegel im Spiegel is an encoded expression of Euler's identity e^ipi = -1, and since it can be looped infinitely at any scale, over any analog transission medium, just like two mirrors reflecting each other, it is a better candidate for Gauss's proposal than using Pythagoras. I've been trying to figure out what the piano accompanyment was produced by, but it's pretty likely that there is something similar encoded in it.

[1] https://en.wikipedia.org/wiki/Laurie_Spiegel [2] https://www.youtube.com/watch?v=kVaEUBvppMI

drdeca4• 4 years ago

I don’t see how the sequence (-1, 1, -2, 2, -3, 3...) demonstrates having found Euler’s identity.

motohagiography4• 4 years ago

I looked for functions that generated the sequence in the music. The closest function that generated that sequence (which describes the scale notes in the violin piece) is:

y = (cosx(x)/2pi

...an increasing wave, which can be expressed alternatively as:

1/4 π e^(-i x) + 1/4 π e^(i x)

...which I have interpreted as requiring knowledge of the relationship between e, i, pi, 0, and 1.

...implying knowledge of Euler's identity.

It isn't a proof, but given it was procedural music, these kind of harmonious coincidences seemed consistent with expressing intelligent intent.

Arvo Pärt is still alive, I just wish there were a way to reach out an ask him if this interpretation is correct.

alpple• 4 years ago

We might want to be quiet until we have a better idea of our surroundings.

Gauss's Pythagorean right triangle proposal

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