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.
First, the answer to whether or not an alien would understand the lambda calculus is no different than whether a dog or a dolphin can understand the lambda calculus. It depends on the wiring of their brain. The lambda calculus is recursive; perhaps then self-awareness/self-reference is a prerequisite to understanding.
Second, the claim that the lambda calculus was discovered but all programming languages are invented does not take into account LISP, which was both discovered and invented (cf. Paul Graham's "Roots of Lisp" (https://sep.yimg.com/ty/cdn/paulgraham/jmc.ps?t=1564708198&).
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.
What about a civilisation who never invented silicon diodes but kept using vacuum tubes? Or what about a civ. who invented logic programming first and never then invented lambda calculus. Or what if they come from a much lower gravity planet, their spaceships might look completely different. Or what if they're not a carbon based species; why do we then assume they'd have to travel a similar tech path as us?
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.
You are relying on implicit assumption that quantum mechanics is the only possible theory that could lead to an invention of MOSFET transistors. Maybe this assumption is true, but I do not know it to be proved. Of course QM is the only known to us theory that had led to MOSFETs, but it doesn't mean that one couldn't invent some completely different way to describe reality which would enable him to invent MOSFETs.
In order to build a MOSFET, you need to know how do electrons react in the presence of thin barriers, and how thick should the gate oxide be to prevent breakdown while still keeping the field strong.
Does a civilization know this? If no, they cannot make MOSFETs. If yes, than whatever branch of physics and math describes this is called “quantum mechanics”
Can it be different, can you do QM without Schrödinger Equation? Sure, but it will still be QM. One can rearrange terms on formulas, use different units, work with voltage instead of energy, introduce various metrics and so on. Physicists do it all the time, it is simply theory reformulation.
>In order to build a MOSFET, you need to know how do electrons react in the presence of thin barriers, and how thick should the gate oxide be to prevent breakdown while still keeping the field strong.
And yet I somehow managed to produce a pretty complex quantum computer before I was even born: my brain. Or maybe my mom did, but she is nearly as ignorant of quantum physics and biology as I was as a fetus, so the point stands.
The person above was wrong about your implicit assumption about QM and dependency chains. Your real assumption is that interstellar societies will develop technologies intentionally using explicit knowledge that charts such a dependency chain, rather than evolving capabilities via or alongside implicit knowledge, such as the implicit knowledge we all share in which allows us to produce human brains with no intellectual effort whatsoever. We don't and can't know what chunks of those dependency chains are innate for other species, which in turn means we don't know how they will traverse such a chain, even assuming ad arguendo your hypothesis that the dependency graph is essentially linear.
This is a popular theory. But so far the best we've got is that quantum mechanics are maybe necessary to explain neuron interactions. Which is basically equivalent to calling a computer "quantum" because it's made of MOSFETs.
While I agree in doubting that the Sapir-Whorf hypothesis can be used in the way the author does (for one thing, I do not think the strong version is supported by the evidence, and I think the strong version is required here), I think it is worth noting that De Forest, inventor of the audion (precursor of the triode), had a very mistaken idea of how it worked. Today, we have devices that use high-temperature superconductors without having a complete theory of how they work. The inventors of smelting and gunpowder did not understand the chemistry of their inventions...
> In order to build a MOSFET, you need to know how do electrons react in the presence of thin barriers, and how thick should the gate oxide be to prevent breakdown while still keeping the field strong.
Here you are speaking using words like "electron", "thin barrier", "oxide" and so on. So you are thinking in a framework of our culture and our variant of STEM. Doing so you are trying to prove that there is no way to invent another variant of STEM. I believe, that such an approach could achieve nothing.
I mean, to speak "electron" you need to rely implicitly on a whole mountain of theories about reality. So even if you proved that one cannot build MOSFET without QM, it would mean that he cannot do it while relying on this mountain of theories. It wouldn't prove that there are no other mountains allowing to invent MOSFET.
> Can it be different, can you do QM without Schrödinger Equation? Sure, but it will still be QM.
It is a trivial proposition. "QM without Schrödinger Equation" is QM by definition. The question is if it possible to build some other models of reality that allow to invent MOSFET. As I see it you are trying to remove QM from the mountain of theories and to think what could replace QM. It is completely possible that nothing but QM could replace QM in such a setup. But what would happen if you remove all of the mountain of theories and start from scratch?
I do not know. To see what would happen I need to design an empirical research that would involve some millions of people and a few millennia. To be sure I would need to repeat this at least 50 times.
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 that show specific operations they must also be able to express those operations.
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 surprised, but that’s besides the point, and even if someone is currently rolling their eyes and preparing to explain why I am wrong and electrons can’t possibly be “like phlogiston” (not a position I actually hold so don’t waste your time), an alien civilisation could make an analogous mistake and fill the electron-shaped gap in their physics model with something completely different analogous to the way phlogiston filled the oxygen-shaped gap in chemistry.
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.
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.
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.
> 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 it necessary to study atoms to build a MOSFET transistor? Or maybe it is possible to discover, for example, some macro-theory which would give enough precision of predictions to build a MOSFET?
> the result of our experiments will have to be the same and since we can develop experiments that show specific operations they must also be able to express those operations.
To stage experiment you need a theory, you need to watch reality first and to perceive it in a specific way. The way you perceive reality based on how you interact with reality. For example to see person and his hat as a different objects there must be a reason to see them as a separate objects. If hat changed nothing, than you wouldn't be able to see a difference between person in a hat and person without a hat. As an anecdot: I mostly cannot describe people I met. Do they wear glasses? Skirt or pants? I do not know, because I'm not paying attention for such unimportant details. To see difference between apple on tree and apple falling on your head, it must be important in some ways to you. For example, falling apple could inflict pain and may be eaten, while apple on a tree is hard to reach. It is enough difference to notice it and to start searching for correlates: like pain on the head correlates with the apple fall, probably there is a causation. (Though correlation/causation are also concepts from our culture, they may be unnecessary to build a MOSFET.)
If you perceive reality some other way and rely on other theories your experimental setups would be completely alien. Moreover, experimental method is the best known to us, but didn't you think that there are possibly other superior methods to explore reality?
People invented experiment after tenth of thousands years of their history. So it is not a trivial and obvious discovery. It is a complex find, which based on tenth of thousands years of culture evolution. We need to assume that this evolution could go in convergent ways, if we want to state that experimental method is necessity for any advanced civilization.
I do not state that process is not convergent, but I do not state that it is convergent either. I do not know and I wish to share my ignorance. Perceived ignorance is the most valuable kind of knowledge. ;)
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)
You seem to think that knowledge of electrons (regardless of what we call them or how we arrive at that knowledge) has some cultural significance or requisite, which it does not.
Oxidation is a chemical process - any entity on any planet with a laboratory will be able to mimic and study that same chemical process (regardless of the chemical makeup of them or their world).
AFAIK triodes (vacuum tubes) were discovered by accident. Could you not say that a MOSFET works on a principle very similar to a triode, but on a much smaller scale (small enough to exploit quantum phenomena)? I think it's possible that someone could discover MOSFETs by accident, maybe after theorizing that you could build triodes on a microscopic scale.
Sure, they can build a MOSFET. But it will be pretty bad, you need to have a theory of operations before you can make reliable, powerful and small device we have today.
In fact, a field effect transistor (the FET part of MOSFET) was discovered in 1925 and 1934, but nothing happened with it until the theory was there, and someone (Shockley) spent years refining the theory with experiments.
>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.
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.)
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.
> 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.
Indeed - if/when we meet aliens that we can communicate with, I suspect that they will have their own theory that we can all agree is also part of the isomorphism.
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.
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)
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?
I'm not sure I follow the argument at the end. The author has given a good explanation for why our current metaphors describing the lambda calculus might not be applicable to aliens (requiring the concepts of direction and containment), but I don't see why, for example, the gas-planet aliens might not have their own metaphors relating to wind patterns or aerial acrobatics or something we wouldn't understand at all. There can be multiple metaphors for the same math.
Any article that congratulates hyoo-mons on their uniquely superior capacities instantly disqualifies itself from representing anything fundamentally correct.
Either (1) fundamental mathematical principles are universal, and every society that incrementally improves will converge on them, or (2) our mathematical principles are socially constructed, and other societies will evolve their own structures that may be closed to us. There is no middle ground.
There is, however, a third possibility: some of the universal fundamentals may be inaccessible to humans because of innate limitations in our savanna-evolved monkey brains, where aliens need not be so restricted. In other words, we (and everybody else) have access to the basics, but not everybody gets beyond the basics.
We can reasonably conclude that we have thus far only touched on the basics, because we have only just started looking. Whether we will progress beyond those basics has yet to be demonstrated. If civilization collapses as the natural world breaks under the strain put on it by industrial society, we might stop at this level. Or, if the number of people with mental capacity to comprehend increasing levels of sophistication declines, eventually it will reach one, and then zero.
Our only hope might be inventing machines that can progress beyond us, but they would then supplant us. The aliens might see no value in talking with us, but only with our machines, and we would never understand what they were saying to one another.
All of the above is the natural progression of the Copernican revolution: any assumption of specialness is flawed in exactly the degree by which it flatters us.
All the things we are discovering and inventing are only result of how we fundamentally see the Universe (which is strongly connected to how our perception organs work), not other way around.
I would say they might understand anything we understand on a basis that we do so it is possible and it is equally possible that they might not understand us at all :)
This philosophical approach to mathematics is still rooted in conceptions of mathematics from the beginning of the previous century, perhaps even earlier. This may very well be because professional philosophers have not really engaged with mathematics since then and so don't have the experience required to ascertain its current philosophical undercurrents. Even more, most mathematicians also understand the philosophy of mathematics from this outdated point of view, perhaps because most professional mathematicians have not engaged with philosophy since then.
For a philosophical exposition of recent mathematical activity, I don't think there's any book other than Synthetic Philosophy of Contemporary Mathematics by the mathematician Fernando Zalamea. The translation reads a little clumsy to me, but the ideas are very much worth it.
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?
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.
"""
> 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.
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.
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.
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[ 3.9 ms ] story [ 131 ms ] threadI 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.
Second, the claim that the lambda calculus was discovered but all programming languages are invented does not take into account LISP, which was both discovered and invented (cf. Paul Graham's "Roots of Lisp" (https://sep.yimg.com/ty/cdn/paulgraham/jmc.ps?t=1564708198&).
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.
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.
Does a civilization know this? If no, they cannot make MOSFETs. If yes, than whatever branch of physics and math describes this is called “quantum mechanics”
Can it be different, can you do QM without Schrödinger Equation? Sure, but it will still be QM. One can rearrange terms on formulas, use different units, work with voltage instead of energy, introduce various metrics and so on. Physicists do it all the time, it is simply theory reformulation.
And yet I somehow managed to produce a pretty complex quantum computer before I was even born: my brain. Or maybe my mom did, but she is nearly as ignorant of quantum physics and biology as I was as a fetus, so the point stands.
The person above was wrong about your implicit assumption about QM and dependency chains. Your real assumption is that interstellar societies will develop technologies intentionally using explicit knowledge that charts such a dependency chain, rather than evolving capabilities via or alongside implicit knowledge, such as the implicit knowledge we all share in which allows us to produce human brains with no intellectual effort whatsoever. We don't and can't know what chunks of those dependency chains are innate for other species, which in turn means we don't know how they will traverse such a chain, even assuming ad arguendo your hypothesis that the dependency graph is essentially linear.
Here you are speaking using words like "electron", "thin barrier", "oxide" and so on. So you are thinking in a framework of our culture and our variant of STEM. Doing so you are trying to prove that there is no way to invent another variant of STEM. I believe, that such an approach could achieve nothing.
I mean, to speak "electron" you need to rely implicitly on a whole mountain of theories about reality. So even if you proved that one cannot build MOSFET without QM, it would mean that he cannot do it while relying on this mountain of theories. It wouldn't prove that there are no other mountains allowing to invent MOSFET.
> Can it be different, can you do QM without Schrödinger Equation? Sure, but it will still be QM.
It is a trivial proposition. "QM without Schrödinger Equation" is QM by definition. The question is if it possible to build some other models of reality that allow to invent MOSFET. As I see it you are trying to remove QM from the mountain of theories and to think what could replace QM. It is completely possible that nothing but QM could replace QM in such a setup. But what would happen if you remove all of the mountain of theories and start from scratch?
I do not know. To see what would happen I need to design an empirical research that would involve some millions of people and a few millennia. To be sure I would need to repeat this at least 50 times.
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 that show specific operations they must also be able to express those operations.
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 surprised, but that’s besides the point, and even if someone is currently rolling their eyes and preparing to explain why I am wrong and electrons can’t possibly be “like phlogiston” (not a position I actually hold so don’t waste your time), an alien civilisation could make an analogous mistake and fill the electron-shaped gap in their physics model with something completely different analogous to the way phlogiston filled the oxygen-shaped gap in chemistry.
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.
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.
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.
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 it necessary to study atoms to build a MOSFET transistor? Or maybe it is possible to discover, for example, some macro-theory which would give enough precision of predictions to build a MOSFET?
> the result of our experiments will have to be the same and since we can develop experiments that show specific operations they must also be able to express those operations.
To stage experiment you need a theory, you need to watch reality first and to perceive it in a specific way. The way you perceive reality based on how you interact with reality. For example to see person and his hat as a different objects there must be a reason to see them as a separate objects. If hat changed nothing, than you wouldn't be able to see a difference between person in a hat and person without a hat. As an anecdot: I mostly cannot describe people I met. Do they wear glasses? Skirt or pants? I do not know, because I'm not paying attention for such unimportant details. To see difference between apple on tree and apple falling on your head, it must be important in some ways to you. For example, falling apple could inflict pain and may be eaten, while apple on a tree is hard to reach. It is enough difference to notice it and to start searching for correlates: like pain on the head correlates with the apple fall, probably there is a causation. (Though correlation/causation are also concepts from our culture, they may be unnecessary to build a MOSFET.)
If you perceive reality some other way and rely on other theories your experimental setups would be completely alien. Moreover, experimental method is the best known to us, but didn't you think that there are possibly other superior methods to explore reality?
People invented experiment after tenth of thousands years of their history. So it is not a trivial and obvious discovery. It is a complex find, which based on tenth of thousands years of culture evolution. We need to assume that this evolution could go in convergent ways, if we want to state that experimental method is necessity for any advanced civilization.
I do not state that process is not convergent, but I do not state that it is convergent either. I do not know and I wish to share my ignorance. Perceived ignorance is the most valuable kind of knowledge. ;)
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)
Oxidation is a chemical process - any entity on any planet with a laboratory will be able to mimic and study that same chemical process (regardless of the chemical makeup of them or their world).
Culture is irrelevant in both of these.
In fact, a field effect transistor (the FET part of MOSFET) was discovered in 1925 and 1934, but nothing happened with it until the theory was there, and someone (Shockley) spent years refining the theory with experiments.
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.
If something is easier (carbon), it would happen faster and out compete harder things. It’s the nature of entropy.
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.)
[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.
I still feel like this Platonist idea somewhat holds. Eventually you'd land on some isomorphic variant of logic, computation or category theory.
The law of the excluded middle might seem obvious to you, but not to these guys: https://plus.maths.org/content/intuitionism
The Mackenzie book chapter discusses both the Fetzer and DeMillo Lipton Perlis controversies.
It's really interesting that the debate got into the questions like, can one formally verify a bridge?
Either (1) fundamental mathematical principles are universal, and every society that incrementally improves will converge on them, or (2) our mathematical principles are socially constructed, and other societies will evolve their own structures that may be closed to us. There is no middle ground.
There is, however, a third possibility: some of the universal fundamentals may be inaccessible to humans because of innate limitations in our savanna-evolved monkey brains, where aliens need not be so restricted. In other words, we (and everybody else) have access to the basics, but not everybody gets beyond the basics.
We can reasonably conclude that we have thus far only touched on the basics, because we have only just started looking. Whether we will progress beyond those basics has yet to be demonstrated. If civilization collapses as the natural world breaks under the strain put on it by industrial society, we might stop at this level. Or, if the number of people with mental capacity to comprehend increasing levels of sophistication declines, eventually it will reach one, and then zero.
Our only hope might be inventing machines that can progress beyond us, but they would then supplant us. The aliens might see no value in talking with us, but only with our machines, and we would never understand what they were saying to one another.
All of the above is the natural progression of the Copernican revolution: any assumption of specialness is flawed in exactly the degree by which it flatters us.
I would say they might understand anything we understand on a basis that we do so it is possible and it is equally possible that they might not understand us at all :)
For a philosophical exposition of recent mathematical activity, I don't think there's any book other than Synthetic Philosophy of Contemporary Mathematics by the mathematician Fernando Zalamea. The translation reads a little clumsy to me, but the ideas are very much worth it.
https://www.urbanomic.com/book/synthetic-philosophy-of-conte...
[1] http://tromp.github.io/cl/diagrams.html
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?
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?
""" [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
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.
who cares
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.