SETI

[Layra-chan]

Mecill

Hmm... I read this thread since it was bumped up. smile It's been a while since I've seen the movie Contact... but it was kind of a fun scifi.

So... I think math is our language for describing numerical/quantitative relations, and physics is applying that to the natural world. So if you have math that is specific enough you can infer what you are talking about physically from the context (like they did in Contact).

But there is no way to determine context. Mathematical statements, like all languages, are expressed in strings of arbitrary symbols, and truth or relevance or even meaning is only inserted from outside. Mathematics is built so that by following certain rules, strings can be manipulated to form other strings in a way that preserves truth value, but the meaning of a given string must be inserted from outside. For any advanced mathematics textbook, a good quarter of it is usually setting out notation and terminology, often in a way that is totally incompatible with all other textbooks, even in the same branch of mathematics.
This is in fact perhaps the goal of mathematics; to remove semantics so as to be able to apply patterns in as general a setting as possible. The more that it becomes a game of pushing around symbols, the better.  

[Mecill]

Layra-chan

Mecill

Hmm... I read this thread since it was bumped up. smile It's been a while since I've seen the movie Contact... but it was kind of a fun scifi.

So... I think math is our language for describing numerical/quantitative relations, and physics is applying that to the natural world. So if you have math that is specific enough you can infer what you are talking about physically from the context (like they did in Contact).

But there is no way to determine context. Mathematical statements, like all languages, are expressed in strings of arbitrary symbols, and truth or relevance or even meaning is only inserted from outside. Mathematics is built so that by following certain rules, strings can be manipulated to form other strings in a way that preserves truth value, but the meaning of a given string must be inserted from outside. For any advanced mathematics textbook, a good quarter of it is usually setting out notation and terminology, often in a way that is totally incompatible with all other textbooks, even in the same branch of mathematics.
This is in fact perhaps the goal of mathematics; to remove semantics so as to be able to apply patterns in as general a setting as possible. The more that it becomes a game of pushing around symbols, the better.

Yeah, I see what you're saying now... That makes sense. So I was thinking along the lines of... say we received some mathematical statements sent by aliens... Do you think we'd be able to match it to equivalent mathematical statements developed by humans? I mean, assuming in physics that mathematics gives accurate predictions, should the only difference be the notation?

Actually, I think it would be easier to send pictures if we were trying to talk to aliens, but that's just me. And then if they were digital you have to worry if they're going to be able to receive them properly and all that...

According to the news recently Steven Hawking thinks we might want to avoid alien contact if possible, since they could be dangerous... rolleyes  

[Vannak]

Mecill

Layra-chan

Mecill

Hmm... I read this thread since it was bumped up. smile It's been a while since I've seen the movie Contact... but it was kind of a fun scifi.

So... I think math is our language for describing numerical/quantitative relations, and physics is applying that to the natural world. So if you have math that is specific enough you can infer what you are talking about physically from the context (like they did in Contact).

But there is no way to determine context. Mathematical statements, like all languages, are expressed in strings of arbitrary symbols, and truth or relevance or even meaning is only inserted from outside. Mathematics is built so that by following certain rules, strings can be manipulated to form other strings in a way that preserves truth value, but the meaning of a given string must be inserted from outside. For any advanced mathematics textbook, a good quarter of it is usually setting out notation and terminology, often in a way that is totally incompatible with all other textbooks, even in the same branch of mathematics.
This is in fact perhaps the goal of mathematics; to remove semantics so as to be able to apply patterns in as general a setting as possible. The more that it becomes a game of pushing around symbols, the better.

Yeah, I see what you're saying now... That makes sense. So I was thinking along the lines of... say we received some mathematical statements sent by aliens... Do you think we'd be able to match it to equivalent mathematical statements developed by humans? I mean, assuming in physics that mathematics gives accurate predictions, should the only difference be the notation?

Actually, I think it would be easier to send pictures if we were trying to talk to aliens, but that's just me. And then if they were digital you have to worry if they're going to be able to receive them properly and all that...

According to the news recently Steven Hawking thinks we might want to avoid alien contact if possible, since they could be dangerous... rolleyes

That is probably not at all the case. Mathematics gets developed all the time. For instance, calculus is only 300 years old. Think about that for a second. If we're communicating with aliens, and we're at far as 300 years apart in terms of progress, our ideas about what's possible with mathematics is going to be fundamentally different. Mathematics isn't a stable thing, and sure, they might have common roots, but what if they have a mathematical system that isn't based on operators like adding, subtracting, and the like. There's plenty of human baggage in mathematics, despite popular belief.

As for Hawkins, He's probably right. We wouldn't want to meet any aliens far enough ahead of our tech to actually be able to meet us.  

[Mecill]

Vannak

Mecill

Layra-chan

Mecill

Hmm... I read this thread since it was bumped up. smile It's been a while since I've seen the movie Contact... but it was kind of a fun scifi.

So... I think math is our language for describing numerical/quantitative relations, and physics is applying that to the natural world. So if you have math that is specific enough you can infer what you are talking about physically from the context (like they did in Contact).

But there is no way to determine context. Mathematical statements, like all languages, are expressed in strings of arbitrary symbols, and truth or relevance or even meaning is only inserted from outside. Mathematics is built so that by following certain rules, strings can be manipulated to form other strings in a way that preserves truth value, but the meaning of a given string must be inserted from outside. For any advanced mathematics textbook, a good quarter of it is usually setting out notation and terminology, often in a way that is totally incompatible with all other textbooks, even in the same branch of mathematics.
This is in fact perhaps the goal of mathematics; to remove semantics so as to be able to apply patterns in as general a setting as possible. The more that it becomes a game of pushing around symbols, the better.

Yeah, I see what you're saying now... That makes sense. So I was thinking along the lines of... say we received some mathematical statements sent by aliens... Do you think we'd be able to match it to equivalent mathematical statements developed by humans? I mean, assuming in physics that mathematics gives accurate predictions, should the only difference be the notation?

Actually, I think it would be easier to send pictures if we were trying to talk to aliens, but that's just me. And then if they were digital you have to worry if they're going to be able to receive them properly and all that...

According to the news recently Steven Hawking thinks we might want to avoid alien contact if possible, since they could be dangerous... rolleyes

That is probably not at all the case. Mathematics gets developed all the time. For instance, calculus is only 300 years old. Think about that for a second. If we're communicating with aliens, and we're at far as 300 years apart in terms of progress, our ideas about what's possible with mathematics is going to be fundamentally different. Mathematics isn't a stable thing, and sure, they might have common roots, but what if they have a mathematical system that isn't based on operators like adding, subtracting, and the like. There's plenty of human baggage in mathematics, despite popular belief.

I'm not sure though, because do you think a person would have been capable of learning calculus from an alien over 300 years ago? Have we changed that much as a species since then? Since most of what we learn isn't what we ourselves developed anyway would it have to be a significant barrier? Also, aren't the concepts behind calculus older, though it wasn't put into a system that could be used until Newton and Leibniz?

Quote:

As for Hawkins, He's probably right. We wouldn't want to meet any aliens far enough ahead of our tech to actually be able to meet us.

Yeah, I think he had a good point about how it might like be when European explorers discovered the Americas and the native population got hurt. Even then, though, we're all still the same species and people crossed over on the land bridge from Russia through Canada. It might be different if it's aliens coming from a place completely isolated from Earth.

I mean, if they're far ahead of our tech, and visiting for the purpose of exploration rather than conquering and getting resources, (cause it seems like there are a lot of places to get resources in space besides Earth), I think it might be okay. Well, unless they wanted to use us for something like slave labor. Hope not. sweatdrop  

[Mecill]

Another thing... if it's not an operator based system, what alternatives are there?  

[Layra-chan]

I think what Vannak meant is that what if they had a different set of basic operators? What if for some reason they defaulted to a non-commutative multiplication rather than a commutative one like we do? What if their basic operators took three operands instead of two (making them trinary operators instead of binary)? What if they worked directly with sets or groups or categories?
Addition and multiplication make sense when dealing with what we call the 'natural numbers', and can be extended in some fashion to other systems, but aren't necessarily the only such operators with such expressive power.  

[Basilia Ann E]

Sioga

Would it be possible for other species to have lived on Mars? Because the evidence is pretty convincing that at one time there was water. And doesn't water mean there should be life?

The idealism related to Mars & SETI is a bit unrealistic.

Consider this; we (on Earth) did not just pop-up with our knowledge & understanding - or with our technology. Now consider, the impact we have had on our planet - thus far.

Do we see any of this on Mars? - no. The canals, that were once thought to be there - weren't.

We know of other before us, because of their impact on the surrounding environment (this is the basis of archeology).

We, also, know of other life before us, because of their impact on the surrounding environment (this is the basis of paleontology).

Neither paleontology or archeology has shown up on Mars.

 

[Vannak]

As far as learning new mathematics, sure we could, but you need to go back to basics. It could take a well motivated person probably take 5 years to go from arithmetic to differential calculus, and that's already with a common base of language and physical picture aids.

As far as something that would be completely foreign, image a system base in an irrational number like e. Once you get there, you could see change of bases from one irrational number to another, you can see form for coming up with integers from irrational numbers and other things.