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Would aliens understand lambda calculus? (2018)

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Re: Would aliens understand lambda calculus? (2018)

#51

Post by lkbm »

ducaale wrote: post #45
lkbm wrote: post #41

Earlier quoted context omitted.

Not if they're both building on top of a shared body of mathematics (or even shared sensory organ evolution and brain structure). Aliens may be working from an entirely different foundation, resulting in entirely different mathematics.

So you are saying that there could be aliens that would percieve 1+1 as 3, how would that even make sense? If our society is built by mathmatics that can be seen as wrong by aliens, how would they percieve our reality and how would they explain the complicated structures we have built using our mathmatics?

> So you are saying that there could be aliens that would percieve 1+1 as 3

Nope. More likely they'd skip the concept of "1" and "+" and "3", but that's also more specific than what I'm saying.

What I said was that your stated evidence doesn't support the claim you made. Multiple people didn't come up with the same branch of mathematics completely independently. They did so from the same foundations.

[EDIT: Oh yeah, also said that aliens may be using compeltely different math. See below for explanation of that.]

> how would that even make sense?

I've no idea. That's the point.

> If our society is built by mathmatics that can be seen as wrong by aliens,

There's a difference between wrong and incomprehensible.

Think about some of our foundations:

- We think of numbers as deterministic. We've come to understand that the universe is probabilistic.

- We think of numbers as continuous. We've come to understand that the universe is discrete.

- We think of a table as a distinct thing. It's actually a bunch of atoms bonded together that are constantly shedding and gaining atoms. Oh, and that table over there is welded to the floor, so it's actually bonded to the floor in the same way, yet we think of the floor (and entire building) as a different distinct object.

These new ideas are comprehensible to us, but kinda weird and foreign. Suppose instead of starting with the naive view of determinism, continuous space, and distinct "platonic" objects, you start with the weird reality where those aren't true. What will your mathematics look like if your foundational mathematics is based on that?

Do you think in terms of "1" and "1" and "2", when you don't think of two tables as two items? Do you think of deterministic addition when your perception of the universe is non-deterministic?

And these are just variations I thought up using my human brain based on things that human brains have managed to understand. I'm saying "hey, completely differently structured brains could think in a way our human brains don't understand". "But that makes no sense to my human brain" is pretty clearly not a refutation, and asking for an explanation of it also misses the point.

Re: Would aliens understand lambda calculus? (2018)

#52

Post by theamk »

ordu wrote: post #36
afiori wrote: post #28

Earlier quoted context omitted.

The fact that the electron exist is not culturally dependent. As much as the fact that stars exists. Any alien civilization capable of studying the behavior of atoms must also be able to express concept that are compatible with ours. Maybe the do not use numbers, calculus, or maybe they do not even use unit of measures. Yet the result of our experiments will have to be the same and since we can develop experiments th…

> The fact that the electron exist is not culturally dependent. As much as the fact that stars exists. I'm not so sure about it. All I know is I'm unable to imagine how to think about Universe without splitting it into stars and electrons. But my inability doesn't prove anything. > Any alien civilization capable of studying the behavior of atoms must also be able to express concept that are compatible with ours. Is i…

Some things are common no matter where you are and how you perceive the reality.

You have objects which interact. Find a type of interaction which works at macroscopic distances and does not depend on inertial mass. You can call it "electromagnetic interaction". Note that some objects interact stronger, and some weaker. Call this property "charge". Find the smallest unit of "charge" and try to split it further, until you cannot split it anymore. Choose the smallest particle of this kind. Congratulations, you found "electron"!

Note nowhere in the previous paragraph I have specified how you perceive the reality. Maybe you were looking at the charged oil film on the water surface with human eyes, or maybe you were using your telekinetic senses to feel zorks on the bazzer, or maybe you were sentient gas cloud observing startdust falling in the black hole. It does not matter, once your culture starts exploring interaction of atoms, they will the same physical law, that there is a minimum charge unit, and arrive to the same physics.

(or they might not discover that branch of physics at all -- but then they are unlikely to be an interstellar civilization)

Re: Would aliens understand lambda calculus? (2018)

#53

Post by Aperocky »

grawprog wrote: post #44
VLM wrote: post #4

The problem with the Sapir-Whorf hypothesis as an argument against academic knowledge is it may be true for the general population, however, the entire purpose of STEM academia is to subvert the Sapir-Whorf hypothesis. Teaching a kid quantum mechanics or calculus inherently has little to do with the general population's belief in religion or astrology or virtue signalling, for example. The average Joe_6_Pack Arrival…

>You can play games with early steam engines burning lignite or peat and it won't matter terribly much at the time or in the long run, but it seems there's only one way, using metal catalysts, to "invent" your first organic chemistry hydrogenation process, for example. You can make steel in a low tech medieval blacksmiths shop, but transistors have tighter constraints. But, what if these aliens are say chromium or si…

I don’t believe there would be silicon based life not because they are impossible, but because of Occam’s razor.

If something is easier (carbon), it would happen faster and out compete harder things. It’s the nature of entropy.

Re: Would aliens understand lambda calculus? (2018)

#54

Post by jammygit »

whatshisface wrote: post #8

I think the answer is kind of obvious if you understand the foundations of mathematics. Any alien that was smart enough to manipulate written symbols according to rules would agree that our induction rules applied to our axioms would lead to our theorems, because proofs are a purely symbolic game that even a computer can do. Aliens might not agree on the axioms or induction rules except by pure coincidence, because e…

I personally hold that math is a science of sorts that is grounded in physical reality. What then if their maths were experimental in nature with less logical abstraction?

Re: Would aliens understand lambda calculus? (2018)

#56

Post by nemosaltat »

Aperocky wrote: post #53
grawprog wrote: post #44

Earlier quoted context omitted.

>You can play games with early steam engines burning lignite or peat and it won't matter terribly much at the time or in the long run, but it seems there's only one way, using metal catalysts, to "invent" your first organic chemistry hydrogenation process, for example. You can make steel in a low tech medieval blacksmiths shop, but transistors have tighter constraints. But, what if these aliens are say chromium or si…

I don’t believe there would be silicon based life not because they are impossible, but because of Occam’s razor. If something is easier (carbon), it would happen faster and out compete harder things. It’s the nature of entropy.

There’s a good explanation/discussion on this in “The Disappearing Spoon.” It’s a fun read, on the history of the elements in the periodic table.

Re: Would aliens understand lambda calculus? (2018)

#57

Post by tetron »

VLM wrote: post #4

The problem with the Sapir-Whorf hypothesis as an argument against academic knowledge is it may be true for the general population, however, the entire purpose of STEM academia is to subvert the Sapir-Whorf hypothesis. Teaching a kid quantum mechanics or calculus inherently has little to do with the general population's belief in religion or astrology or virtue signalling, for example. The average Joe_6_Pack Arrival…

This is my take as well. The unreasonable effectiveness of mathematics to describe physics suggests it is more fundamental than something our monkey brains came up with. If aliens are operating with the same physics, they are going to create a mathematics that is isomorphic to our own.

Re: Would aliens understand lambda calculus? (2018)

#58

Post by afiori »

ben_w wrote: post #31
afiori wrote: post #28

Earlier quoted context omitted.

The fact that the electron exist is not culturally dependent. As much as the fact that stars exists. Any alien civilization capable of studying the behavior of atoms must also be able to express concept that are compatible with ours. Maybe the do not use numbers, calculus, or maybe they do not even use unit of measures. Yet the result of our experiments will have to be the same and since we can develop experiments th…

Electrons are a perfectly adequate model for reality. I do not read the previous poster as disputing this point. Instead, they appear to be asking, “is there another model for reality which would also work well enough to build a MOSFET?” I do not know either. That said, people keep telling me that both QM and GR are known to be incomplete, so perhaps electrons are no more real than phlogiston? I would certainly be su…

I completely agree, but if they are able to properly (as in with predictive power for variations) build a MOSFET or anything of similar complexity they would likely be able to understand our concept of an electron.

I believe that is very unlikely as it is very unlikely to miss atoms and then it is very likely to miss electrons. Of course I also do not think that it is provably impossible.

Re: Would aliens understand lambda calculus? (2018)

#59

Post by Sysreq1 »

So I think the fundamental problem with a lot of the arguments I am seeing presented here is this fascination with logic and thought as being a universal truth. We are, in fact, no different than Flatlanders.

If we walk through the evolutionary history, we can see a clear pattern of each advancing step slowly creeping into further and further dimensions. First it was single cell protobacteria being able to detect light or dark above them, and gradually growing more and more complex. A dog, while a 3 dimensional construct, is really little more than a 2 1/2 dimensional being. Humans, by extension, are really the first fully realized 3 dimensional being. And also one of the first to take steps into the perception of the 4th dimension. And as evolution continues to advance, there is no reason to suspect our ability to perceive the 4th, or even 5th dimensions won’t continue to advance. Soon our ability to manipulate those dimensions will follow suite, and with it, will come a fundamental shift in how that creature conceptualizes the physical world.

To say that a 4th or 5th dimensional creation would still use a binary logic system equal to true or false, on or off, is nonsense. And as such, any mappings of our current logic systems would fall relatively flat.

Our world is still flat, confined by the limits of our own physical hardware. In a billion years what ever comes after us will be completely different. Confined by its own limited hardware.

Re: Would aliens understand lambda calculus? (2018)

#60

Post by magusdei »

tetron wrote: post #57
VLM wrote: post #4

The problem with the Sapir-Whorf hypothesis as an argument against academic knowledge is it may be true for the general population, however, the entire purpose of STEM academia is to subvert the Sapir-Whorf hypothesis. Teaching a kid quantum mechanics or calculus inherently has little to do with the general population's belief in religion or astrology or virtue signalling, for example. The average Joe_6_Pack Arrival…

This is my take as well. The unreasonable effectiveness of mathematics to describe physics suggests it is more fundamental than something our monkey brains came up with. If aliens are operating with the same physics, they are going to create a mathematics that is isomorphic to our own.

Isomorphism != equality. Formulas in greek numerals are trivially isomorphic to ones using arabic numerals, because they are different representations of the "same" concepts, but nobody would argue that arabic numerals aren't more practical (at least for us).[1] So even though the concepts the aliens come up with might be technically isomorphic to (a version of) lambda calculus on some extremely abstract level, there is no guarantee that either we or they would be able to recognize this, owing to a vast difference in representation.

[1] Similarly, a basic theorem in algorithmic information theory states that all programming languages are about equally efficient in terms of program size,[2] but that doesn't mean that all programming languages are actually equally good for every problem in practice, as the constant debates about "the best language" among programmers clearly show.

[2] The basic argument is that, if programs written in language A are vastly shorter than those written in language B, it is possible to write an interpreter for language A in language B of constant length c. So all programs written in language B are at most c chars longer than those written in language A.

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