Would aliens understand lambda calculus? (2018) • Hacker News Board

Re: Would aliens understand lambda calculus? (2018)

#41

Post by lkbm » Fri, Oct 25, 2019, 4:22 PM UTC

ducaale wrote: post #39

What would happen if this question was reformalated as "If there was another civilization, would they have invented lambda calculus?" As for the question of "is mathmatics discovered or invented", if two or more people can discover the same branch of mathmatics, wouldn't that mean that it is a universal truth that could even be discovered by aliens?

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.

Re: Would aliens understand lambda calculus? (2018)

#42

Post by theamk » Fri, Oct 25, 2019, 4:28 PM UTC

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…

The good thing is, it does not matter. It is entirely possible the electrons are not "real" -- so what? The electric field is not "real" either (in the sense that there is no corresponding physical object), and the magnetic field is even less "real", it is just a change in electric field.

As long as there is predictive power, we can use a theory. And once we discover there are unpredicted cases, we can update the theory.

In particular, the reason phlogiston theory was discarded was not some philosophical reasons -- it was because it made bad predictions (specifically, that things always lose mass when burned).

There is a beautiful exercise in where you take two very basic physics rules (electrostatic force between two individual charged particles and speed of light equation), and derive basically entire electromagnetic theory from it. Really drives the point that underlying physics is simple, and most of the formulas, especially introductory ones, are just shortcuts to make reasoning and computation easier.

Re: Would aliens understand lambda calculus? (2018)

#43

Post by cgiles » Fri, Oct 25, 2019, 4:33 PM UTC

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…

In my vague understanding, you can consider objects like electrons as either particles or as amplitudes in a field. Although these two (currently known) ways of viewing it lead for the most part to similar intuitions, these paradigms can be somewhat misleading.

For example, the fact that we viewed elementary particles as particles, analogous to macro physical objects, for so long meant it was hard to get a grip on wave-particle duality of light and quantum teleportation. In normal life, small particle-like objects don't tend to pop in and out of existence or move around spontaneously. But in many ways, electrons do in fact behave as discrete particles.

Physical realists, like most of us on the board probably, don't dispute there is a single physical reality (possible multiverses aside). However there are multiple theories and models that can describe the same reality. These models tend to have different strengths and weaknesses. So we do not know how many possible ways of looking at these things there are, and to what extent aliens might see them similarly or differently.

Re: Would aliens understand lambda calculus? (2018)

#44

Post by grawprog » Fri, Oct 25, 2019, 4:39 PM UTC

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 silicone based life from a planet with a chlorine or fluorine based atmosphere. I imagine the dependency chain would look totally different for a species like that. The chemical reactions we rely on for many of our sciences on earth would not work at all in an evironment like that. Combustion based technology would likely not be at the forefront of such a species.

I think a lot of anthropomorphization goes on when it comes to aliens. Just on earth we've got billions of different forms of life, all of which is specifically adapted for earth's conditions. Change any of those conditions even a little and life on earth would look totally different, as it has for most of earth's history.

I see no reason why any kind of aliens, interstellar travellers or not, would need to resemble us or any of the technological dependency chains we've created. It assumes everywhere else works mostly the same as it has here for the short window as humans have existed and that the chains of technological dependencies humans have created based on the resources available on earth are a universal technological progression all intelligent life must goes through, which just seems arrogant and all knowing to me.

Re: Would aliens understand lambda calculus? (2018)

#45

Post by ducaale » Fri, Oct 25, 2019, 4:49 PM UTC

lkbm wrote: post #41

ducaale wrote: post #39

What would happen if this question was reformalated as "If there was another civilization, would they have invented lambda calculus?" As for the question of "is mathmatics discovered or invented", if two or more people can discover the same branch of mathmatics, wouldn't that mean that it is a universal truth that could even be discovered by aliens?

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?

Re: Would aliens understand lambda calculus? (2018)

#46

Post by BadThink6655321 » Fri, Oct 25, 2019, 5:06 PM UTC

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…

A lambda calculus of two variables requires the law of the excluded middle, or it won’t work. The alphabet of the calculus has to be distinguishable and unambiguous.

Re: Would aliens understand lambda calculus? (2018)

#47

Post by AnimalMuppet » Fri, Oct 25, 2019, 5:26 PM UTC

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 are assuming that lambda calculus is a necessary part of that path. So far as I can see, you did nothing to substantiate that assumption.

Can you reach the stars without computer programming? Probably not. Can you do computer programming without lambda calculus? Absolutely. You can do it based on Turing Machines, for example. (Are they equivalent? Yes, but also no. The Church-Turing Thesis says that they are formally equivalent. Yet nobody, when they say "lambda calculus", is thinking of Turing Machines and calling that lambda calculus.)

Re: Would aliens understand lambda calculus? (2018)

#48

Post by voxl » Fri, Oct 25, 2019, 5:29 PM UTC

BadThink6655321 wrote: post #46

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…

A lambda calculus of two variables requires the law of the excluded middle, or it won’t work. The alphabet of the calculus has to be distinguishable and unambiguous.

The law of the excluded middle is about the truth status of any proposition. The fact that the alphabet of the language has to have a decidable equality does not mean the law of the excluded middle is true for any theory built from the lambda calculus. (Or true in general)

Re: Would aliens understand lambda calculus? (2018)

#49

Post by ghgfhgfhn » Fri, Oct 25, 2019, 5:34 PM UTC

I don't get these arguments. Surely it's simply about picking out pattern in the world that surrounds you. Finding a mathematical system that is useful us akin to spotting a recurring pattern in a picture. Do we say the pattern in this or that picture is universal? Maybe. Maybe not. But to imagine that aliens will have trouble spotting the same patterns as us is not a question about the ultimate meaning of the patterns, it's only a question about the distribution of those patterns wrt their usefulness.

Re: Would aliens understand lambda calculus? (2018)

#50

Post by dylanfw » Fri, Oct 25, 2019, 7:03 PM UTC

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?

This reminds me of a passage in "Godel, Escher, Bach" by Douglas Hofstadter discussing the Golden Record[1].

""" [C]onsider a meteorite which, instead of deciphering the outer-space Bach record, punctures it with colossal indifference, and continues in its merry orbit. It has interacted with the record in a way which we feel disregards the record's meaning. Therefore, we might well feel tempted to call the meteorite "stupid". But perhaps we would thereby do the meteorite a disservice. Perhaps it has a "higher intelligence" which we in our Earth chauvinism cannot perceive, and its interaction with the record was a manifestation of that higher intelligence. Perhaps, then, the record has a "higher meaning"-totally different from that which we attribute to it; perhaps its meaning depends on the type of intelligence perceiving it. Perhaps. """

1: https://en.wikipedia.org/wiki/Voyager_Golden_Record