Would aliens understand lambda calculus? (2018)

I bet even the majority of relevant STEM graduates (CS, math, Philosophy (?), etc.) do not understand lambda calculus beyond the bits and pieces they remember from "that dreadful class about formal logic or something like that" they had in their first college semesters.

I learned to calculate/reduce (are those the right words?) lambda calculus expressions where one line would span multiple lines on wide paper for college. I don't think I ever understood much of it. Thinking back on this makes me so, so glad I will never have to study this ever again.

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 movie heptapod might culturally have an easier or harder time learning lambda calculus; its certain that the only people (well, heptapods) who would matter, the CS academics, would be quite familiar with lambda calculus.

STEM has a dependency chain such that its hard to do quantum mechanics without something like statistical thermodynamics and basic probability theory. Thus, cultures without statistical thermodynamics, like Ancient Rome or non-European cultures in general never developed quantum mechanics, therefore no nifty MOSFET transistors therefore no electric cars or industrial VFDs therefore no solar non-petrochemical energy industry therefore they die out or are replaced with more advanced cultures before interstellar travel is reached.

We don't know the dependency chain for interstellar travel but the more complicated things are, the more fragile they are, always, so its HIGHLY likely any two interstellar cultures would have identical dependency chains to pass various gates along the path. 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. Most of advanced civilization is a mask over fragile, complicated, and delicate dependency chains.

We'd like to think we're on the path to interstellar travel rather than self destruction, so obviously all interstellar aliens would have lambda calculus much like ourselves, because the gates we have to pass thru only pyramid and narrow as the task gets more complicated. And interstellar travel seems likely to be complicated.

> The naive argument that computer scientists often make is that lambda calculus is at the heart of the isomorphism between logic, computation and category theory and this suggests that it refers to some eternal truth. This is a Platonist view of mathematics which is just one of several positions. The main problem with it is that it cannot be tested and so it is more a religious belief than a scientific claim. However, it also ignores the social, cognitive and cultural aspects of mathematical knowledge.

I still feel like this Platonist idea somewhat holds. Eventually you'd land on some isomorphic variant of logic, computation or category theory.

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 even within our own species there is disagreement over which axioms (choice for example) or induction rules (the excluded middle in intuitive mathematics for example) are self-evident.

The law of the excluded middle might seem obvious to you, but not to these guys: https://plus.maths.org/content/intuitionism

Vacuum tubes are inherently limited by physics, they cannot be used to create an efficient and small power converters. So if civilization is stuck with vacuum tubes, it is highly unlikely they’ll get to renewable power sources, and therefore they’ll likely to die off once they run off of their oil-equivalent.

If the civilization comes to us, it is likely they are at least as technological advanced as we are. Which means they likely has invented all the same math we did, and more. There is no guarantee that their version of lambda calculus is popular in their world, it could be it is an obscure and boring topic that no alien cares about, but they’ll still understand it if they need to.

People did design and even flew spaceships from lower gravity planet - this was Appolo lunar module. The lunar module did look different that earth based rockets, but it was still pretty similar.

Carbon life or not, there are only so much shapes a spaceship can take, physics forces your hand. There are only so many stable elements in the periodic table, and they combine in identical way everywhere. Lack of water and oxygen in the atmosphere may allow aliens to use a different metal, but a reaction rocket spacecraft will still look like a enclosure with rocket-shaped nozzles at the rear end.