Alien Truth

by pyb • 4 years ago

188 367 4 years ago

mberning• 4 years ago

I didn’t realize that the concept of absolute or universal truths was so boring that it needed an “ancient aliens” style rebrand.

znpy• 4 years ago

What did you expect from the idol of the startup scene?

felipeccastro• 4 years ago

Perhaps it’s not that they are boring, but fearful. I can’t recall a single time I mentioned these words in a conversation that weren’t abruptly interrupted with “there is no absolute truth!”. If the rebranding helps us calm down and think about it without fear, it might be worth it.

bkishan• 4 years ago

Looks like PG was inspired by reading Project Hail Mary, and decided to be philosophical about it :)

blueprint2• 4 years ago

that's the definition of truth. all truths are fixed.

nh23423fefe• 4 years ago

lol tarski

blueprint2• 4 years ago

"[when] the inferior scholar hears of Dao, he greatly ridicules it" -laotzu

mark_l_watson• 4 years ago

Perhaps a little off topic, but I have thought about this a bit: the type of consciousness and ways of acting in physical reality would probably be very different for digital vs. biology-based life. As strangely different alien biological life might be, true AI will be stranger, unless it is designed and evolves to emulate us in some sense.

I am reading the sci-fi book The Sea of Rust right now, that takes place on earth after AI’s have finally killed the last humans. In this fictional work, AIs take on human traits and I don’t find that “believable” even for sci-fi.

gpvos• 4 years ago

Indeed. Intelligent alien life is likely to have evolved out of other forms of life, so concepts as competition, survival, cooperation, are likely to be innate somehow (not necessarily in a conscious way). AI does not need to share that basis at all.

songeater3• 4 years ago

I disagree. "AI" even if it were to exist independently of humans or other pre-existing life still needs to process and dissipate energy in order to perpetuate itself... ie it needs to be "life" first. Intelligence requires the processing of information, and the processing of information requires energy.

For example, even if silicon-based AI replaced humans on earth, it would eventually [0] need to find a way to power itself / continue itself. Ultimately, it would have to revert to solving the same "problem of life"... how do we transform energy/entropy available in the environment into something that "perpetuates the system." When that happens, this AI will itself become subject to the forces of natural-selection, and - over a long enough period of time - naturally-selected traits will be re-aquired (even if such traits were "lost" during a human-to-AI hand-over).

[0] Yes, of course, there could be a very large period of time during which currently constructed energy infrastructure continues on... and this period could be measured in hundreds/thousands of years... very long in terms of human lifespans, but not in geological terms.

rrwo3• 4 years ago

That's a rather naive view of truth. For intuitionistic mathematics (which is very important for theoretical computer science), truth is a mental construct of a proof in a language, and only shared by communicating that construct to other minds.

The question is whether we can communicate our mathematics to non-humans, whose senses may be radically different from our own.

And likewise, would we be able to understand a non-human proof?

jondeval8• 4 years ago

That's a rather naive view of truth.

I'm a puzzled by the confidence here. I would assume pg is at least minimally familiar with some of the key philosophical themes and schools of thought around this topic.

For intuitionistic mathematics ... truth is a mental construct of a proof in a language, and only shared by communicating that construct to other minds.

Even assuming you are fully and accurately representing the intuitionist view, you must be aware that there are competing schools of thought with strong pedigrees, like mathematical platonism, that are grounded in a more realist view of mathematical objects.

PG didn't go so far as to stake out that position here in the essay, but his thought experiment leverages a view of mathematical truth that hues closer to this (platonist) camp.

The question is whether we can communicate our mathematics to non-humans ...

That is an interesting question, but pg did not ask that question in the essay, and its answer doesn't seem relevant to the point he was trying to make.

n4r92• 4 years ago

It's Graham's confidence that I (and I think OP) find puzzling. He doesn't say "According to Platonist ideas...", or "In my opinion...". Just "mathematical truths are true by definition". There's a brashness and lack of nuance there that makes me want to stop reading.

svnt2• 4 years ago

I would assume pg is at least minimally familiar with some of the key philosophical themes and schools of thought around this topic.

But even a brief foray into discussions by actual philosophers will show that to not be true. What Paul Graham is doing is providing small subcultural insights tailored to an audience with a passing interest in philosophy.

kybernetikos• 4 years ago

his thought experiment leverages a view of mathematical truth that hues closer to this (platonist) camp

I think the word in that idiom is 'hews', which means to adhere strictly to a standard, probably from the sense of the word meaning to strike or cut or beat - often used to talk about cutting a tree into shape.

naasking18• 4 years ago

The question is whether we can communicate our mathematics to non-humans, whose senses may be radically different from our own.

I'm not sure why people find this so relevant. Regardless of the sense, there must be enough discernible structure to detect whether 0 of something is there, whether 1 of something is there, or whether there are many more than 1.

Human sense of smell might top out at differentiating maybe 4 or 5 different things, dogs can probably sense a lot more, but either way it lets us set up basic counting, and that's generally all you need for most of our math.

rrwo3• 4 years ago

How can you communicate the axioms of Peano arithmetic to intelligent extra-terrestrials, in a way that they would recognize it?

boh• 4 years ago

My dog is an intelligent being and he doesn't share our affinity for math. We have to acknowledge that our concept of intelligence is human-centric. What we interpret as knowledge is based on our specific limitations and perceptions. We don't know what intelligence is and won't necessarily know it when we see it.

yetihehe• 4 years ago

My dog is pretty dissatisfied when I show him 3 treats and then give him 2, so he has uses for maths, but he can no longer multiply.

swalsh• 4 years ago

Your dog is unlikely to visit other planets searching for other intelligent life

myshpa• 4 years ago

Let's hope then that aliens coming here will be vegan.

We're not intelligent enough yet not to harm others, or to go to other star systems, or even other galaxies. Would we be considered intelligent, or a source of protein?

swader999• 4 years ago

Why does my dog growl at my other dog when it tries to eat it's food? It seems to understand subtraction at a basic level.

dandanua• 4 years ago

Many "successful" humans don't know a lot of math or physics either. It seems you only need to know how to subtract and divide.

carapace3• 4 years ago

Has your dog ever jumped somewhere and landed where he intended to? Has he ever caught a ball or frisbee that you've thrown?

If so, then he understands basic calculus.

He can't write the equations, but he can solve them.

mikkergp2• 4 years ago

I appreciate what he is saying, but this also feels like the speech given at the beginning of a sci-fi/horror movie where you realize you’re completely wrong.

motohagiography• 4 years ago

The beauty of thinking about other civilizations is it provides a due balance for materialist views, where instead of a universal truth, the question becomes what values and principles would be sufficient for us to co-exist with more (and less) advanced beings without respective reduction to foodstuffs, pets, or slavery.

To a more advanced civilization, we are chimpanzees who are both outwardly intelligent, but also tremendously dangerous, and so on what basis could they establish trust with us, or could we establish trust with a civilization of others? As Graham notes, math is one indicator that we are capable of apprehending the universe around us, but given the infinity of life and its necessary physical conditions of beginning and ending, and evolving in aggregate using tools and principles, it's not sufficient. Maybe one way to ensure trust is to share DNA, so that we become each other and we are all "us" - or, perhaps the Girardian mimetic concept generalizes such that it is better to preserve our differences so that we are not competitors for the same resources, and so that we can co-exist with an obvious other but without an existential threat or intrinsic power struggles.

Are there existing moral or philosophical systems that are suited to this problem? Probably, I'm not a religious scholar, but the golden thread that links them seems pretty consistent in attempting to derive alignment to an external truth. The proto-Christian tribe of Essenes, from whom John the Baptist originates and who was the one who baptized Jesus into what became Christianity (solving a weird bootstrapping problem, imo) espoused the values that became the first Church, so there is a historiographical way of looking at moral systems instead of as dogma. Outside religion, in the search for these values that would be suitable for a community of inhabitants, I've come to suspect this is what freemasonry is about, and while not about aliens, I was impressed by their allegorical emphasis on tools instead of doctrine as the landmarks for discovery.

The essential question to me is, once you have accepted there is an other that is greater, or a place that is elsewhere, does it matter whether it's a dude with a beard, multi-armed flying blue people, or an ineffable oneness? That there is a concievable elsewhere beyond your current limits, there must therefore be some point or idea to align and orient yourself to so as to be able to relate to the other beings who have discovered the same point outside our current perspective.

It's all very meta, but it implies a logical and even rational case for some guidance or alignment to this otherness to navigate our present, and that isn't material. The value of the idea of an "alien" truth is it is a means to reconcile secular rational thinking and moralism with universal, essential, or spiritual values, and that could be a very useful tool.

incomingpain3• 4 years ago

I wrote a scifi book in which I wrote 'heaven' as being an alien construct. Somewhere in the universe a tremendously technologically advanced civilization constructed a device which simulates 'heaven' for all people in the universe. Through 'enlightenment' the discoverer is able to bring knowledge of 'heaven' back to their people but in our history how could a figure like Buddha or Jesus post-enlightenment explain aliens and advanced technology. So you end up producing a story at a level of your current day scientific understanding.

Fundamentally your message to humanity post-enlightenment would be the rules on how to get to heaven. Which many world-religions classes go into depth. There are fundamental rules that benefit everyone to follow that wouldn't really be inherently human to follow.

We'd probably share Occam's razor. There doesn't seem anything specifically human about any of these ideas.

Aliens will also have developed the piano and chess. They are inherent things to discover eventually.

Fundmantally a great way to analyze what the rules are would be impossible to list. Just look at the list of crimes in countries which are so large lawyers dont even know them all. So you need a system that's much more simply. Isn't that system 'karma'.

bmitc12• 4 years ago

Aliens will also have developed the piano and chess. They are inherent things to discover eventually.

How could that claim be true? We have highly intelligent beings (i.e., “aliens”) right here on Earth that have not developed these things.

These discussions on aliens are often off the rails from the start because they implicitly begin with the assumption that humans are the only intelligent beings on Earth.

incomingpain3• 4 years ago

How could that claim be true? We have highly intelligent beings (i.e., “aliens”) right here on Earth that have not developed these things.

Are you using the 'illegal immigration' definition of alien?

These discussions on aliens are often off the rails from the start because they implicitly begin with the assumption that humans are the only intelligent beings on Earth.

Do please elaborate because I don't share this opinion. Do you believe aliens live amongst us?

zelienople• 4 years ago

That is a work of stunning arrogance and foolishness.

Math is a game we play in our heads that represents a fictionalized ideal version of reality.

An alien intelligence might have realized that two plus two never equals four not because the underlying logic is wrong, but because two does not exist in reality.

The idea that the little game of math we play represents an immutable and universal truth is typical of the overwhelming anthropocentrism of our kind.

dan_mctree• 4 years ago

This is a comment of stunning ignorance.

Just because some alien societies will not mimic our rules of addition, we do know for certain it is possible that other societies can build abstract concepts that are isomorphic to those we have. And many of these concepts, such as addition, are very useful.

Does this guarantee that aliens come up with the same stuff? No. Does it guarantee that if they did, they would these concepts to the same esteem? No. Is there an element of 'truth' here that can be replicated by others? Absolutely

deugtniet• 4 years ago

I guess I disagree that math and physics are universal truths.

For maths, I would say 1+1=2 is a pretty universal truth (although it takes a while to get there in the principa mathematica), but didn't we just invent complex numbers because they are useful?

Same goes for physics, the speed of light is the same everywhere, but how quantum mechanics work is still subject to many discussions.

Love to hear some thoughts on this, as claiming a whole field as universal truth is something I'm a little uncomfortable with.

Koshkin15• 4 years ago

because they are useful?

But the usefulness is objective, that is, it is not an arbitrary product of the mind but rather it is dictated by the logic of things once the goal is set, so invention (or discovery) of useful things is more or less unavoidable.

As to quantum mechanics, you are talking about the variety of interpretations which from the practical standpoint are simply different ways of looking at quantum behavior, which, in turn, sometimes leads to different methods of calculation.

mistermann3• 4 years ago

But the usefulness is objective, that is, it is not an arbitrary product of the mind but rather it is dictated by the logic of things once the goal is set, so invention (or discovery) of useful things is more or less unavoidable.

It certainly seems like it is objective, and often it probably is, but in a more general sense, any instance of "x 'is' y" very often turns out to be subjective very quickly. Even with "is useful", things get complicated if one explicitly injects the dimension of Time into the question (it is there in the first place implicitly, but is easily overlooked).

m-watson• 4 years ago

I think the argument is mostly that there are universal truths than math and physics describe not that our current level of math and physics are universal truths. So finding an example that we do not understand fully doesn't mean that there aren't truths in other aspects of math and physics. As for things like complex numbers there is an underlying debate that has been around in philosophy of science and math that distinguishes between discovery and invention. Our representation may have been invented but we discovered some thing that works historically and has predictive power.

simiones4• 4 years ago

but didn't we just invent complex numbers because they are useful?

Not any more than we invented natural numbers because they are useful.

There are several ways to naturally derive complex numbers, either from mathematics or from physics.

For one, complex numbers are probably the simplest possible extension of the real numbers in which all real-valued polynomials have roots (for example, x^2 + 1 doesn't have a root if x has to be real). This is the same reason why the non-transcendental irrational numbers were invented (such as sqrt(2) ).

(Incidentally, the transcendental numbers (pi, e) are less justified than the complex numbers from this point of view - any polynomial of any rank whose coefficients are non-transcendental real numbers has roots that are either real non-transcendental numbers, or a complex number whose real and imaginary parts are real non-transcendental numbers )

For a physical explanation, complex numbers are the best way we know of describing wave mechanics (either classical or quantum), and in general periodic phenomena and how they compose.

koyanisqatsi6• 4 years ago

I think you have the right idea. Most human truths are contingencies of our evolution and the evolution of life on earth. It's very hard to extrapolate from this to universal and alien truth.

deltasevennine16• 4 years ago

For example, I think we'd share the principle that a controlled experiment testing some hypothesis entitles us to have proportionally increased belief in it.

This isn't even a shared principle among humans. How many experiments does it take for you to have 50% belief in a hypothesis?. What is the number of experiments? It's literally impossible to answer. It's not even clear what "belief" is or what 50% means.

This ambiguity of the word isn't even the main problem. If I run the same experiment with perfect observational tools 10 billion times and it verifies my hypothesis. Does that raise my belief further? What if on the 10 billionth and first time the test shows a negative result? That literally invalidates the hypothesis. Keep in mind we are assuming my observational tools are perfect. Does this make my belief shoot down to zero?

If this possibility of a negative result remains true after any number of tests then what does it say about belief? Why should I believe anything if a single negative experiment can invalidate 10 billion positive experiments (assuming perfect observational tools of course)?

Let me bring a more concrete example. I hypothesize all zebras have stripes. I observe zebras 10 billion times. They all confirm my hypothesis. Then on the 10 billionth and first time I see a zebra with spots. My hypothesis is wrong. This can happen any time.

Anyway to bring it back to his point. Don't assume shared axiomatic truths. PG already assumed that it's shared among humans. He's wrong. The nature of science and the scientific method is not universally shared or even fully understood among humans. He's likely also wrong about aliens as he is about humans.

naasking18• 4 years ago

This isn't even a shared principle among humans. How many experiments does it take for you to have 50% belief in a hypothesis?. What is the number of experiments? It's literally impossible to answer. It's not even clear what "belief" is or what 50% means.

https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_induc...

deltasevennine16• 4 years ago

A bit of a complicated read. Not sure what you're trying to say here and I don't even completely understand it. But anything that gets into bayesians and frequentists ends in a fundamental divide in humanity. Humans don't agree on which interpretation is correct. Which is the point of everything I wrote.

So why would aliens hold this "principle" the same if humans don't even agree on it? PG is wrong. His own principles upended not even by aliens, but by humanity, thus how accurate can his assumptions about universal principles even be? No that accurate imho.

simiones4• 4 years ago

I hypothesize all zebras have stripes. I observe zebras 10 billion times. They all confirm my hypothesis. Then on the 10 billionth and first time I see a zebra with spots. My hypothesis is wrong. This can happen any time.

Even if the original belief turns out to be wrong, you only have to slightly weaken it and it will remain true: "the vast majority of zebras have stripes". Even if you discover a new continent full of hordes of uniformly-colored zebras, the true hypothesis becomes "the vast majority of zebras in my original continent are striped".

Essentially every observation brings proof for a whole family of hypotheses. We normally only talk about the strongest of these hypotheses, but that doesn't meant that a negative example rules out the entire family.

For example, even if we didn't find a deductive proof the Fermat's last theorem was wrong even after all of the empirical proof that it probably wasn't, a weaker version would have still remained true - the one validated by that empirical proof.

deltasevennine16• 4 years ago

Even if the original belief turns out to be wrong, you only have to slightly weaken it and it will remain true: "the vast majority of zebras have stripes". Even if you discover a new continent full of hordes of uniformly-colored zebras, the true hypothesis becomes "the vast majority of zebras in my original continent are striped".

The hypothesis does not remain true. It was never proven to be true and the new hypothesis is still not proven to be true. Science cannot prove anything to be true. I can find a cave full of of spotted zebras, and you have to further weaken your hypothesis of continents, I can then find that the stripes were actually microscopic spots and my perfect observation tool, though never wrong has limited resolution. Ad infinitum. Nobody ever considers your made up philosophy because it's changing the rules of the game. It's making a statement then adjusting your statement once it's proven wrong... people look down on that kind of thing.

What I'm writing here isn't something I pulled out of my ass. It's well known that in science, the scientific method, and reality itself, nothing can be proven. Proof is the domain of math and logic, not science. In science, things can only be falsified. To quote Einstein:

“No amount of experimentation can ever prove me right; a single experiment can prove me wrong.”

Einstein obviously isn't saying stuff like a single experiment causes me to adjust my hypothesis and divide split it into two different ones because it's kind of inconsistent.

There are people who truly understand science, but most of the population doesn't (including PG). I think what's going on with you is you're in the later camp, you've long held the incorrect belief that science can prove things and this long held ideology is coming into contact with the actual logic of the situation and your adjusting your belief to maintain a biased ideology.

Do you look up to PG? Bias can be corrected when an authority confirms the opposite. I quoted Einstein here. One of the ultimate authorities on science, a person who overturned the hypothesis about Newtonian physics being a model for motion. A single experiment proved it wrong and now Newtonian physics is simply an approximation that is ultimately wrong. Hopefully that will clear things up, if not... then you must be an Alien far more strange then what PG is describing.

jefftk• 4 years ago

In addition to alien truth there are probably also alien games: ones so simple for their level of depth and enjoyment that you would expect them to be independently discovered. For example, Hex [1] is reasonably deep and has been invented at least twice. Go, with something like the Tromp-Taylor rules [2] might be as well? Probably not Chess, though!

[1] https://en.wikipedia.org/wiki/Hex_(board_game)

[2] https://senseis.xmp.net/?TrompTaylorRules

bmitc12• 4 years ago

The truths of mathematics would be the same, because they're true by definition. Ditto for the truths of physics

These are pretty strong statements for which there’s no arguments provided for but serve as assumptions for the rest of the article. I don’t think there’s consensus among mathematicians, philosophers, cognitive scientist, or biologists on this.

Mathematics is most definitely a human endeavor, and so we can’t really make claims about its existence in the universe independent of humans. I think alien analogs to mathematics are unlikely to match ours. If we are lucky, I think it could be the case that the various structures could be similar, but the likelihood the implementations resemble each other are slim. It’s even a stretch to assume the structures would relate. Even humans do not fully agree on mathematics. There is no “one” mathematics because mathematics is the human exploration of idealized objects using a variety of human logical systems.

And then there’s the possibility that our mathematics and overall perception of reality is shaped by our biology in far deeper ways than we imagine and currently understand.

cloogshicer• 4 years ago

Fully agreed.

These beliefs you quoted from the article, which unfortunately most people don't even recognize as beliefs, form the basis of the dominant religion of the western world (scientism).

The worrying thing is that the majority of people who believe in this religion don't even realize they are believers.

bmitc12• 4 years ago

If I am not mistaken, this is similar to what Feyerabend seemed to be on about.

https://blogs.scientificamerican.com/cross-check/was-philoso...

gregmac• 4 years ago

Science doesn't have "facts" or "truths". It is based on falsifiability: for a theory or hypothesis to be considered scientific it must be able to be tested and conceivably proven false.

This is the key difference from religion, which has no such "falsifiability" equivalent.

The closest thing to "beliefs" is probably an individual following which of several competing theories is most likely correct -- but there's always the underlying basis that any of them might have evidence showing they're incorrect at any time, and one's view should adjust as a result.

Often this comes in the form of deferring to other people or a consensus view, which could be construed as "faith" but is different: If you asked me how the universe exists, I'd say the big bang theory is the best answer we have, but I don't understand enough about the underlying science to explain why nor can my brain comprehend the reality of it. I have no loyalty or allegiance to this view, though; I could be swayed to another theory if the big bang is ever proven false or if a better theory arises.

Further reading: https://www.theatlantic.com/science/archive/2015/11/why-scie...

simonh10• 4 years ago

The thing that differentiates science from religion is repeatability. With religion everyone has their own opinion, people out of contact with each other come up with radically different religious beliefs and there is no way to bridge between those beliefs. If we forgot everything we know about religion, in a thousand years we might rediscover religion again but they'd be entirely different religions from what we have now.

With science it doesn't matter who does a given experiment, anyone else doing the same experiment will get the same results. There's no scope for disagreement about verifiable scientific facts. Just do the experiment and find out. If we forgot everything we know about science, in a thousand years if we rediscovered science, very quickly we'd rediscover all the exact same facts about the world again.

tambourine_man• 4 years ago

Yeah, lots of strong baseless assumptions in the first paragraph made me stop reading.

adrianN• 4 years ago

I'm pretty sure that any sufficiently advanced species that does any kind of mechanical engineering will have maths that is homomorphic to analysis.

exitb• 4 years ago

Isn't the basic math largely driven by attempts to understand and quantify the world around us? In such case, it depends on more universal concepts like distance, time, speed, acceleration etc. Concepts which I would imagine to be familiar to any intelligent being that takes a physical form. I can't imagine an alien wondering about a period of a pendulum and arriving at an answer that's really different from ours.

p0pcult2• 4 years ago

Funny that you chose pendulums:

https://cosmosmagazine.com/technology/artificial-intelligenc...

naasking18• 4 years ago

I think alien analogs to mathematics are unlikely to match ours.

So aliens won't be able to count? They won't have a concept of zero? They won't have a concept of 1=successor(0)? I find this very, very hard to believe, and a lot of mathematics follows from the structure of the natural numbers.

If you accept evolution by natural selection is a universal law, then I think it naturally follows that ability to count must evolve. After all, it's pretty important to know whether there are 0, 1, or many predators/food/prey/enemies.

bmitc12• 4 years ago

I think this is one argument that leads to the idea that the structures could be relatable, if a being could count. But who knows? Our mathematics relies strongly on the logical and axiomatic systems used. Things can get weird real quick with small tweaks to these systems, so it doesn’t seem like a stretch that whatever mathematical analogs aliens may possess may be wildly different. And there’s a lot of developments that our perception of reality is shaped by our biology in ways we barely understand.

There are intelligent beings on Earth that don’t seem to even have analogs to human mathematics, at least that are apparent to us. We can barely communicate with a small subset of animals and plants on Earth. So I am just inherently skeptical of claims that alien thinking will bear any resemblance to human thinking.

Koshkin15• 4 years ago

Counting implies the ability to perceive the discrete, but such discreteness may not be obvious to a shapeless creature living in a liquid or a gaseous substance.

RxVd2• 4 years ago

They won't have a concept of zero? They won't have a concept of 1=successor(0)? I find this very, very hard to believe

Most of the world did mathematics for a long time without zero (I hope you know that most number systems like Roman didn't have zero till that eventually came from India, and we evolved to have the current number system). Who knows what direction different number systems might have taken if they didn't come in contact with zero.

bena2• 4 years ago

Hacker News, the place where you will get told that we are definitely going to invent spacecraft that will be able to traverse the galaxy by solving the light speed issue, the gravity issue, and the radiation issue (among others) but that when we meet extraterrestrial lifeforms, they won't know how to fucking count.

Sorry. That's the one. That's the one that broke me. Jeremy Bearimy

zhynn• 4 years ago

What if aliens have no notion of discrete numbers, what if everything is probabilistic analog math? What about an organism that can see/focus/sense multiple things simultaneously, and a single "thing" is a set. What about a creature whose primary sensing organ is diffuse molecules (smell/taste) instead of sight and use light (instead of meat tentacles) to interact with matter. How might an organism that touches matter with laser fingers and smells the consequences count differently? I wouldn't have the first idea, honestly.

There could be an entirely different paradigm to "counting" and consequently to the fundamentals of maths.

The math that we invented is influenced by our biology and capacity to sense our environment. Our brains and how those brains work with our sense organs. This pattern is likely universal (all life will have methods of sensing their environment and interacting with it), but the methods might be very different.

geomark• 4 years ago

What if aliens did not perceive distinct objects, but rather that everything observable is part of a greater whole? Would they need counting numbers?

LocalH• 4 years ago

Mathematics is most definitely a human endeavor, and so we can’t really make claims about its existence in the universe independent of humans.

I think the idea is that math is not created by humans, but documented by humans. Sure, the specific terminology may be our invention, but there are basic mathematical properties that seem (from our perspective) like they should be universal. For example, whatever names a being has for the numbers 1 and 2, if you take that 1 and add 1 more, you must get 2 (or the "local equivalent") as the result.

My guess is that, if what we call math isn't truly universal, it's probably at least universally true within the realm of physical life, and there's likely some massive causal chain from the root properties of physics itself to the mathematical properties that we call "math". When it comes to raw, untethered "consciousness" (or whatever one would prefer to call it), this may not hold true even in the slightest.

Yes, this comment steps slightly outside what could ever be determined purely by the scientific method at the end. I feel it is useful to do so in discussion, even when that cannot directly enter into research. There are some truths to the larger universe that I don't think the scientific method will ever truly be able to uncover, just due to it's rigor. Some aspects of the universe are just simply not falsifiable, but they're still worthy of discussion with an open mind.

dTal• 4 years ago

There is most certainly a massive causal chain between physics and what humans call "math", because everything humans do is determined by the laws of physics. The causal chain leads through millions of years of evolution and tens of thousands of years of culture. "The numbers 1 and 2" are a complex web of analogies that have not actually been demonstrated to "exist" outside of our minds, so evidence that alien mathematicians would have words for them is much weaker than our intuition would suggest. The question that must be answered is "Given the constraint of precisely modelling the world in a useful way, to what extent are all rule-based systems isomorphic?"

Responding to your second point, I'm afraid I can't agree with you that unfalsifiable propositions are "useful" discussion contributions - especially not with an "open mind". The only criterion on which such propositions can be judged is whether they are fun to believe, and that is a very dangerous muscle to flex.

dagw8• 4 years ago

I think alien analogs to mathematics are unlikely to match ours.

Almost certainly not, but they're probably isomorphic. And either way if we show them our axioms they will be able to validate our mathematics and vice versa.

The truths of mathematics are of the form 'if A then B'. Even if they don't start at A or even accept A as true, but will should still get B if they assume A.

Koshkin15• 4 years ago

they're probably isomorphic

That's a strong statement. I'd probably talk about homomorphism.

mr_mitm• 4 years ago

Even humans do not fully agree on mathematics. There is no “one” mathematics because mathematics is the human exploration of idealized objects using a variety of human logical systems.

Maybe not in its entirety, but I find it hard to imagine that any civilization as advanced as ours (let's say a civilization that manages to harness nuclear fission, just to set a baseline) will not come up with concepts such as prime numbers, real number, complex numbers, calculus, etc. If they do that, they will inevitably find the same structures we found using function theory. They will know about differential equations and prove similar theorems about them as we did. And the Pythagorean theorem is a universal truth that holds everywhere.

lostmsu• 4 years ago

In that list prime numbers might not be a thing.

lmkg2• 4 years ago

real number, complex numbers, calculus, etc

Some humans believe that the prominence of real numbers is a historical accident. It seems quite plausible to me that a human society, much less an alien one, would go down a mathematical evolutionary path based on the constructable numbers and the computable numbers.

Regardless of whether we eventually find the same structures, there are things that we might consider basic which they find esoteric and vice-versa.

Heaven forbid we encounter an alien civilization that discovered an O(log n) algorithm for integer factorization before they invented steam power.

illogical_spock3• 4 years ago

And the Pythagorean theorem is a universal truth that holds everywhere.

Or at least in every world where there exist straight lines, yes? For instance:

The Pythagorean theorem is derived from the axioms of Euclidean geometry, and in fact, were the Pythagorean theorem to fail for some right triangle, then the plane in which this triangle is contained cannot be Euclidean. More precisely, the Pythagorean theorem implies, and is implied by, Euclid's Parallel (Fifth) Postulate.[59][60] Thus, right triangles in a non-Euclidean geometry[61] do not satisfy the Pythagorean theorem. For example, in spherical geometry, all three sides of the right triangle (say a, b, and c) bounding an octant of the unit sphere have length equal to π/2, and all its angles are right angles, which violates the Pythagorean theorem because {\displaystyle a^{2}+b^{2}=2c^{2}>c^{2}}.

https://en.wikipedia.org/wiki/Pythagorean_theorem#Non-Euclid...

agent008t• 4 years ago

The statement that "the truths of mathematics would be the same, because they are true by definition" is correct. Mathematics exist independently of biology or perception of reality. It is just a collection of arbitrary abstract definitions and what follows from them. The alien species may come up with different base definitions that they find more useful or interesting. But they would derive the same conclusions as we would if they were starting from the same definitions and applying the same abstract rules.

bmitc12• 4 years ago

Mathematics exist independently of biology or perception of reality.

Is there a “proof” of that? How could a proof exist? You’d probably win several awards if you had one.

It is just a collection of arbitrary abstract definitions and what follows from them.

… created by humans.

rendall9• 4 years ago

Mathematics exist independently of biology or perception of reality.

Even the concept of "number" itself is almost certainly an artifact of perception that enabled our ancestors to survive our niche, planetary environment, and not an inherent feature of objective reality.

Aliens, evolved to survive in another environment entirely with a different set of initial conditions, almost certainly would not have the same, nor even any, understanding of "number".

Would we consider such aliens a civilization or some kind of insensate "process"?

dbsmith833• 4 years ago

Mathematics is most definitely a human endeavor, and so we can’t really make claims about its existence in the universe independent of humans.

Can you give an example of a mathematical concept which could be different?

I believe that math is universal. We may use models to understand it (infinity, perfect circles, etc.), but the underlying mathematical truth is independent of humans. The same is true for science. There are physical laws which we look to discover. We use models in science to understand them, but the models are not the same as the underlying truth

rendall9• 4 years ago

I believe that math is universal. We may use models to understand it (infinity, perfect circles, etc.), but the underlying mathematical truth is independent of humans.

Humans (probably) perceive and understand a slim subset of reality. We have an illusion of universalism of our perceptions because we perceive nothing outside of them. Also, we are the dominant species of the planet, which gives us a reason to believe that our perceptions are "more accurate" than, say, a bat's.

Personally, I don't think an alien's perceptions and understanding would contradict our own, but if it's given that our perceptions are a subset of reality, then an alien's understanding might include elements of reality that we literally cannot perceive or even understand.

Can you give an example of a mathematical concept which could be different?

By definition, no. But, hmm. What would number and a mathematical system look like from creatures who thought in logarithms? Or in primes? Or that had no concept of "number"? What if even "greater than" and "less than" had no relevance to an alien civilization?

Koshkin15• 4 years ago

I believe that math is universal

The only thing that is "universal" is Nature itself. Mathematics, on the other hand, is a reflection of Nature in the human mind; or, put differently, it's Nature's language we humans are capable of understanding. It is therefore conceivable that other creatures, far removed from us, could "hear" a language that is just as far removed from ours.

pattt• 4 years ago

Fully agreed, the way I'd approach this would be that the said mathematical proofs about certain truths "by definition" rely on human logic as the main building block and substrate. Logic is a human basis of agreeing which seems necessary evolutionary. Counting and separating observable objects turned out to be quite necessary for survival as well. Hence this statement seems to imply that aliens would need to have a corresponding logic reasoning system and observational abilities. If that was the case perhaps there would be a strong inclination to believe that the isomorphic reasoning would be deduced.

rendall9• 4 years ago

there’s the possibility that our mathematics and overall perception of reality is shaped by our biology in far deeper ways than we imagine and currently understand.

Almost certainly true. We as evolved creatures do not perceive objective reality, but only enough reality as to enable our ancestors to survive our very niche environment (niche relative to the entirety of the universe). Our science and mathematics model only our perceptions of reality, and not reality itself.

It is folly to assume that an alien, evolved along an entirely different set of initial conditions, would share our perceptions of reality. Our mathematics, modeling as it does our perceptions, serves human needs and perceptions only.

slibhb• 4 years ago

While it's true that there's no consensus on this topic, that doesn't imply that people can't make claims one way or the other. In fact, the claims that the essay makes (Platonism) are very commonly made.

pfortuny• 4 years ago

I guess he was thinking of arithmetic.

In any case, any model which includes infinity (and Peano arithmetic already does) is pure convention and unconsciously assumes a lot of things.

Finitary induction may make sense as something "universal". Further than that, we are making things up as we go (and I am a professional mathematician). The fact that they work to solve real problems does not make them more real.

illogical_spock3• 4 years ago

More to the point, our mathematics work to solve real problems up to a certain point. For instance our mathematics have not yet been able to identify polynomial-time solutions to problems in the class NP and it's possible that this is exactly because our mathematics are inadequate to express such solutions, if such solutions do exist (and Donald Knuth, for example, believes they do). In which case we'll never know whether P = NP (or we will, but it won't be any use, similar to what Knuth, again, suggests).

It is a tautology that the famous incompleteness results in mathematics and computer science are the result of the axioms of arithmetic used to derive them. Would Gödel be able to derive his incompleteness result without Peano's axiomatisation of arithmetic? Not really. Arithmetic is axiomatic and our axioms of it are arbitrary and ad hoc. Because they're axioms. Who says aliens would come up with the same ones?

There are huge assumptions made in this thread that only indicate the brief time that the contributors have given to thinking about all this stuff. If you think about it for a couple of minutes, sure, it all feels very natural. Zero, infinity, division, mathematical logic, set theory, etc. But if you think about it a bit more, and then do a bit more than think, and go read about it, it's obvious that those are just the ideas that we chose to go with, not the only ones that exist, and certainly not the only ones proposed by mathematicians, logicians, computer scientists and philosophers over the years. For instance, Hilbert was a finitarian, division doesn't work with zero, zero doesn't work with division, dividing an infinity multiplies it, material implication leads to counter-intuitiveness paradoxes, set theory with only the membership relation leads to paradoxes, etc etc etc. Mathematics is full of unnatural holes that need constant patching up, and there is nothing to say that it is in any way, shape or form "real", let alone universal as so many people in this thread seem to be saying.

p0pcult2• 4 years ago

I also take issue with the author's assumptions. Consider the case of AIs trained to identify new variables in a system of pendulums:

https://cosmosmagazine.com/technology/artificial-intelligenc...

Different truths that describe the same system.

sovande• 4 years ago

Somethings in mathematics are constant, both here and on alpha centauri, like the circumference of a circle divide by its diameter is Π or the hypotenuse squared is the sum of each leg squared in a right triangle etc.

lmkg2• 4 years ago

But neither of those facts are true in non-Euclidean geometries like Spherical Geometry or Hyperbolic Geometry. The jury is still out on whether the universe is flat or has some sort of curvature. Meanwhile spherical geometry is fundamentally useful because we live on a sphere, not on a plane, and it is more accurate at modeling the 2-D space that we navigate in.

My point being, assumptions get baked-in to systems in surprising ways. Even something seemingly-objective like math. Especially when you're using it as the basis for communication, then what counts as "basic" or "fundamental" or "standard" reflects a perspective, not a fundamental truth.

It's likely their mathematical systems would eventually reach the same conclusions as ours, but the prominence or significance of fields or results (like circles and triangles) might be radically different. Even though we view those components as absolutely fundamental, it's possible an equivalent system could be built from different primitives.

carapace3• 4 years ago

I think mathematics could be defined as that part of philosophy which is self-evident and universal. The value of Pi isn't contingent?

Aliens may have different biochemistry, but it would be made from the same chemical elements as ours. Likewise their formal systems may be wildly different from ours, but they will still be based on form (even implication is ultimately a very simple formal structure. Math doesn't even require causality as a prerequisite!)

Last but not least. many people (Kurt Gödel among them) believe that mathematical thought is actually perception of real phenomenon in a "higher" plane of reality, which, if true, seems to me to imply that alien mathematicians would be perceiving the same phenomenon as humans, literally. In this view, the "truths of mathematics" are literally the same "objects" for them and for us.

rewgs• 4 years ago

There is no “one” mathematics because mathematics is the human exploration of idealized objects using a variety of human logical systems.

But isn't the whole point to to do our best to bypass human-centric systems of understanding, and arrive at the "core truth" of the matter? Whether that's possible is another matter, but even if it's not possible, surely it's something that can be theoretically approached, and I would wager is precisely what PG means by "one mathematics."

And then there’s the possibility that our mathematics and overall perception of reality is shaped by our biology in far deeper ways than we imagine and currently understand.

Yes, but also no. Consider some first principles:

-We have every reason to believe that any and all life would not live forever, or if the life in question is "intelligent" (a nebulous/human-centric term, for sure) would at the very least conceive of other things not lasting forever (such as stars, or even the universe itself [or, if you want to be really generous, "this current iteration of the universe"]). -Therefore we can reasonably assume that all "intelligent" life in the universe would understand the concept of scarcity (either via finite lifespans/time, food/energy sources, both, or something else), non-infinity. I'd go so far as to say that any life form that doesn't understand its own mortality or other such limits should be not be considered "intelligent," at least for the reasons of this discussion. -Therefore we can reasonably assume that said intelligent life would somehow conceptualize a binary state (you're either alive or you're not, you either have access to an energy source or you don't, etc), and consequently would somehow or another understand the concept of "zero," "nothing," etc, as well as its opposite, "something." And from there, would necessarily discern the differences between two states of "somethings" (the state of "something" that is "one" is different than the state of "something" that is "two").

I know I'm using a lot of loaded terms here -- "reasonably," "assume," "discerning" -- but just like we look for life by looking for the markers of life that we know were necessary for Earth (carbon, water, etc), we can look for intelligence that exhibits the properties that we understand it to have. We need some sort of frame of reference, after all, if we are to do anything other than simply flail. If that frame of reference is to be proven wrong, that's wonderful, but until that's the case, I don't think it's unreasonable to assume that the universe's "primitives" would be perceived in any truly, truly different way such that the species' interpretation would cause humans to rethink our own understanding of the universe's "primitives" from the ground up.

After all, conceiving a difference between hydrogen and helium requires being able to tell the difference between one and two (electrons, as well as separate elements themselves). And considering we have every reason to believe that those make up the majority of the mass in the universe, any "intelligent" life (there's that human-centric term again) can be expected to somehow conceptualize that difference, and thus, do something like counting, and thus, approach the same primitives of mathematics that we do. The approach might be different, but what they're approaching -- the very fabric of reality, hopefully as objectively as possible -- must be assumed to be the same (again, that is, until we're given compelling evidence to believe otherwise).

That said, I've never studied the philosophy of mathematics, so I could be talking out of my ass here, this is just the reasoning of a layman after all. If anyone reads this and goes "no you're way off base," I'd love to hear it!

kardianos• 4 years ago

I call Alien Truth "What Is". It must form a common reality that each individual can point to and share.

More at: https://corinth.kardianos.com/

randallsquared2• 4 years ago

I wouldn't want to bet that all intelligent beings would understand the concept of justice, but I wouldn't want to bet against it either.

Given that even people (loosely) in the same culture often disagree about what constitutes "justice" and use the term in mutually exclusive ways, we should definitely bet against the proposition that "all intelligent beings" understand it.

garbagetime3• 4 years ago

For a person to have an opinion about what constitutes justice is for them to demonstrate an understanding of the concept of justice (assuming their opinion is cogent). So, if people are disagreeing about what precisely justice is, it actually means that they do understand the concept of justice.

koliber• 4 years ago

Maybe for some highly abstract definition of justice. But for more everyday use, it's not hard to come up with examples that one society considers just while the other unjust.

Justice does not have to be cogent, which is defined as "(of an argument or case) clear, logical, and convincing.". There were and are justice systems that leave out one or more of these ingredients to some extent. Some leave out some logic by presuming the existence of a supernatural being. Some are more authoritarian and not very convincing.

Koshkin15• 4 years ago

But “the concept of justice” is not universal, because it really cannot be understood outside the context of law.

jondeval8• 4 years ago

This is spot on. For concreteness, let me give a candidate definition for the virtue of justice:

Justice - rendering to each person what is owed to them.

It's obvious that we will very often disagree about 'what is owed', but doesn't our passionate disagreement in this case show that (1) we agree that practicing justice is good and (2) we are closely aligned on the existence of this thing called 'justice'?

mikkergp2• 4 years ago

I agree with you so I was trying to think of some counter examples and the one that comes to mind would be species that have hive minds? Is justice as important if the many are considered part of the whole? If I drop a stone on my foot and lose my foot, justice is not involved

hbrn• 4 years ago

we should definitely bet against the proposition that "all intelligent beings" understand it

Hey, we can always claim that those who disagree with us are not intelligent.

I'm only partially joking. Lots of today's "justices" have so many internal contradictions that I feel like we should separate them into their own category.

songeater3• 4 years ago

Tit-for-tat is a highly effective strategy when playing an iterated-prisoner's dilemma[0]... ie the "concept of justice" can emerge through natural selection if "intelligent beings" were forced to play such games on which their survival depends (a plausible model of "society").

[0] https://en.wikipedia.org/wiki/Prisoner%27s_dilemma#The_itera...

benjaminjosephw• 4 years ago

Would injustice exist in an alien society if that society didn't recognise it as such?

jondeval8• 4 years ago

I really liked this essay. It poses some interesting questions, but it's short and it doesn't try to do too much.

There is overlap between pg's ideas and what in the classical tradition is called Natural Law Theory. PG may or may not be interested in drawing out the connection, but since he references Aristotle I have to believe he is at least aware of a touch point.

To give a distilled definition, Natural Law Theory is the application of the laws of nature to rational creatures.

In the context in which NLT developed, the only free rational creature was the human being. But both AI development, and concepts from evolution through natural selection, potentially allow us to apply aspects of the theory to different rational agents.

rbanffy• 4 years ago

that it would be true for aliens that one can get better at something by practicing

I think that one depends a lot on how they learn or can transfer knowledge. We rely on language for it, and language is severely limited - We can't learn olympic gymnastics from watching TV, but a species that could directly transfer memories and behaviors would have a huge leg on us in that regard - I'd assume we'd quickly notice their fast-paced technological advance.

Or completely miss it, because they'd anyhilate themselves a couple hours after discovering the military use of nuclear fusion ;-)

cies• 4 years ago

If Occam's razor is presented as a truth (which is pretty subjective, as it depends on what we/someone considers "simple"). Then finding one case where what most people thought was the simple reason, was not actually the reason after evidence came to light, then Occam's razor can be rejected as a theory right?

I think this has long happened, and do not understand why this is still presented as "truth".

I prefer the standard of truth used by natural-sciences. The rest I find pretty bendable (virology included).

naasking18• 4 years ago

If Occam's razor is presented as a truth (which is pretty subjective, as it depends on what we/someone considers "simple").

It doesn't though. Firstly, Occam's razor is not about simplicity but about "parsimony". Parsimony is calculated in information theory via Kolmogorov complexity:

https://en.wikipedia.org/wiki/Kolmogorov_complexity

This then lets us describe how to do induction so it provably converges in the fastest way possible, Solomonoff Induction:

https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_induc...

Arguably, this can be seen as a formalization of the scientific process.

mistermann3• 4 years ago

It doesn't though. Firstly, Occam's razor is not about simplicity but about "parsimony". Parsimony is calculated in information theory via Kolmogorov complexity

In theory perhaps, but in practice it is firstly calculated by the mind of the person who plays the Occam's Razor card, and then subsequently by people who ingest the claim, and typically all participants are performing their calculations using biased heuristics and flawed logic, and have negative interest in what is actually true, or if truth is even reachable.

amelius• 4 years ago

Hopefully they don't share the belief with us that there must be one species conquering them all.

bo1024• 4 years ago

(1) The examples he gives of "non-mathematical" concepts are pretty mathematizable. Randomized controlled testing -- mathematics can prove why this is a good idea. Occam's razor - usefulness can be formalized in the machine learning context. Different conceptions of justice, fairness, etc. can be modeled mathematically (at least certain aspects of them can), which helps one understand and distinguish them. (Examples: utilitarianism, equality of outcome versus equality of opportunity.)

(2) The question of "functionally equivalent" is interesting here. If an alien species accurately predicts the trajectory of a complex rocket, many of us would say they must be using math, because we know that our mathematics governs how rockets move. Even if they cannot communicate their method in a way we can understand. Economists sometimes use the phrase "as if", e.g. the alien acts "as if" they have a utility function, regardless of whether that's how they conceptualize their own action. Similarly. they would certainly act "as if" they had math and physics. But the question of whether that would imply they "do", I'm less sure of.

radford-neal• 4 years ago

This essay would benefit from some examples of common beliefs that he thinks are not "Alien Truths", and what he thinks the implications of that are. As it is, I don't really see what he's trying to get at...

GistNoesis• 4 years ago

There is only one truth : There is no single truth !

Is a forest intelligent ? Is a cat intelligent ? Is a human intelligent ? Is a chess program intelligent ? Is a proof-assistant intelligent ? Is a numerical solver intelligent ? Is the universe intelligent ?

Depending on your choice of definitions, you can get the answers you like.

Some intelligences will be able to comprehend other types of intelligence. Depending on their resources. There is usually a price to be paid, whether in raw computation, memory, or speed. And this price may often induce a hierarchy where the relation is only one way : where the greater intelligence can predict how the states of the lesser one will evolve, but the lesser one can't.

Because these resources are of various nature, they generate a Pareto frontier. Only while the resources constraint stay relevant. For example, once you reach enough intelligence, given the rules of tic-tac-toe, you can play the optimal game. Similarly there are end-game tables for chess, that allow computers to play perfectly, but humans must use heuristics because they don't have enough memory.

But you can always create a bigger game, or constrain your resources. You can always be a collector of mathematical curiosities, that are in some sense some extrema in the space you chose to restrict yourself to.

AI will probably choose to live in constructs, where this dynamic game of collecting resources until they are no longer a constraint is perpetually maintained to keep it interesting, because the alternative omnipotence is no fun.

Those constructs will be so disconnected from reality, that we won't be able to acknowledge their existence.

BiteCode_dev• 4 years ago

Just because we use a model of physics to describe our universe doesn't mean aliens would use the same model.

miki123211• 4 years ago

It's also worth thinking about the exact opposite of this, what truths are we least likely to share with aliens?

The beauty and importance of art and culture comes to mind, and so does humor and jokes. Try explaining, in scientific terms, what makes a joke funny, and the task turns out to be far harder than expected.

MichaelZuo2• 4 years ago

Every pg essay seems to bring out a cohort of nay-sayers and weirdos.

Maybe there is also a revealed alien truth somewhere in there about the psychological effects of differences in expertise, knowledge, social status, writing skill, etc...

koyanisqatsi6• 4 years ago

That wouldn't be an alien truth, that would be a mundane fact of human psychology.

MichaelZuo2• 4 years ago

How would you know aliens don't share the same 'mundane facts'?

It seems entirely possible.

0898• 4 years ago

If there were intelligent beings elsewhere in the universe, they'd share certain truths in common with us. For example, I think we'd share the principle that a controlled experiment testing some hypothesis entitles us to have proportionally increased belief in it.

I was thinking more "triangular sandwiches taste better than square ones", but you do you!

rfreytag• 4 years ago

PBS SpaceTime notes the fine structure constant (~1/137) is dimensionless and ubiquitous in physics. As a result, transmitting that ratio would be a good and clear indication we are intelligent enough to have at least that much physics: https://www.youtube.com/watch?v=RCSSgxV9qNw&t=564s

This might be better than mathematical constructs which conceivably do not require technology, "just" thought to discover.

koyanisqatsi6• 4 years ago

But this constant is an artifact of our symbolic encoding of universal properties. What reason is there to believe that alien civilizations would encode physics exactly as we do and would recover the same constant?

jondeval8• 4 years ago

What reason is there to believe that alien civilizations would encode physics exactly as we do and would recover the same constant?

There is no reason to believe the symbolic encoding would be the same. For example, if they evolved with 8 fingers instead of 10 they could be driven to encode their symbols in a base 8 system.

I think the point of the OP sharing the PBS spacetime video in this context is that we have reason to believe that the fine structure constant is truly constant throughout the universe. So if the aliens have the capability of measuring and reasoning about electron orbitals and their binding properties with nucleus, then there will likely be significant overlap between our mutual concepts of 'fine-structured-constantness'. Just made that word up. :-)

This would be independent of encoding scheme and independent of practical communication issues.

nine_k3• 4 years ago

Another good signal could be transmission at the frequently of free hydrogen times pi, or times e, or both.

The problem here is not even in the need to spend colossal amounts of energy to signal one's presence. The question is whether such advertising is a good idea if the civilization strives to survive; very likely it is not.

HardlyCurious• 4 years ago

Well, this was held up as a universal truth because it doesn't depend on units, and so those don't need to be defined... But we still can't just show them the image '1/137' and have them understand the characters and operations. Our presentation isn't universal.

And I would argue that showing the length of distance we use isn't fundamentally different than explaining which syntax we use for division.

Dylan168072• 4 years ago

But we still can't just show them the image '1/137'

You can dump energy into two frequencies. You're overcomplicating it.

The video suggests binary which is also pretty simple.

authpor2• 4 years ago

Why doesn't reader mode work in that webpage?

Whatever happened to the (failing) promises of HTML + CSS ? where I was gonna be able to swap out this CSS for whatever I wanted?

m3kw92• 4 years ago

An alien truth that we can derive a lot of alien truth from is that life forms all prefer order rather than chaos. Having life is by itself is a very orderly process in relation to chaos, which implicitly opposes it.

m3kw92• 4 years ago

one derivative would be discipline vs procrastinating, aliens won’t get far if they didn’t have any discipline. Heck even single cell organisms are highly single track disciplined.

bobabob• 4 years ago

We'd probably share Occam's razor. There doesn't seem anything specifically human about any of these ideas.

Except the fact that humans are the only species that we know so far to have thought about them?

hlwaters• 4 years ago

Timely article to prop up OpenAI.

dr_dshiv• 4 years ago

In the late 1600s, Christian Huygens proposed that aliens would share our geometry (circles, spheres, etc) and even our rough musical ratios (like an octave is a doubling of frequency and a fifth is 3:2)

elihu6• 4 years ago

Music is an interesting one. There's a lot of subjectivity in the understanding of music, but there are some very basic principles that seem near-universal in human cultures at least. Octave equivalence, the consonance of small-number frequency ratios.

Presumably aliens wouldn't experience music the same way we do, especially if they don't have ears or physical bodies. But music itself might be interesting to them even if they don't really "get" it, due to the mathematical relationships involved. And they might have something analogous that we can't fully understand.

On the other hand it's also at least possible that aliens would understand our music perfectly well, and find it boring or atrociously bad due to our obliviousness to phase relationships, or the inherent out-of-tuneness of modern music, or how the tempo of the music is untethered from its pitch, or because our range of human hearing misses out on all the good stuff that happens above 15-20khz.

kmod5• 4 years ago

As much as I like PG's writing in general, this is him dipping his toes in waters that are already well studied and coming off as ignorant and/or presumptuous.

His very first premise "The truths of mathematics would be the same, because they're true by definition" shows an ignorance of an entire field of discourse called the philosophy of mathematics. Whether aliens would have the same math as us is one of the fundamental questions, and to presume the answer shows a disdain of the existing body of thought on this topic.

In particular, we humans still hotly debate which math is the "right" math. Is the axiom of choice "true"? Does it make sense to say that it has a truth value? Is such a truth value amenable to human discovery? Does PG know the answers to all of these questions?

PG is either unaware of the human-choice nature of the fundaments of math or he thinks he has special knowledge of it. Either way makes this essay one of my least favorites.

danielvaughn5• 4 years ago

No shade to you personally, but I really dislike this frame of thought.

There are mountains and mountains of literature about a great deal of things, no one human can be expected to be aware of them all.

Since that is obviously true, the lack of awareness about a single topic isn’t “ignorance” - it’s not like PG studiously ignored all of that literature. More likely he just never came across it, so the more apt word is “unaware” rather than “ignorant”.

To criticize someone merely for pondering about a subject they aren’t well-versed in is hostile gatekeeping. I think those who are educated in the relevant subject would do well to be more welcoming and informative to newcomers.

apeace• 4 years ago

That's true, but this essay is written with an authoritative voice, not a pondering one. PG tends to write as if he is teaching his audience something profound. So I think it's fair to call out when he is wrong or misguided.

deltasevennine16• 4 years ago

True. But PG's authoritative status is weakened due to his lack of awareness no matter how you change the wording. This entire essay is weaker because of it as my opinion about his knowledge.

To criticize someone merely for pondering about a subject they aren’t well-versed in is hostile gatekeeping.

The words "hostile gatekeeping" makes me classify your statement as accusatory and an actual attack. The Op's statements are just criticism. Harsh but valid, it certainly isn't hostile gatekeeping. In fact, PG is the gatekeeper here. He owns the site.

ASalazarMX• 4 years ago

the lack of awareness about a single topic isn’t “ignorance”

Since everybody is nitpicking here, I'll add that this is indeed ignorance. We're know what we know, and are ignorant of what we don't. Being ignorant by itself shouldn't be viewed as a flaw, but an inevitable state of our limited capacity to learn. The real flaw is being proud of staying willfully ignorant.

mechanical_bear2• 4 years ago

Ignorant is unaware. I’m sure there are loads of things that you have ignorance of, such as the meaning of Ignorance:

lacking knowledge, information, or awareness about a particular thing: "they were ignorant of astronomy"

malux852• 4 years ago

I agree with what you’re saying, at the thresholds of math (and even quite a bit before) it gets very murky very quickly,

But I think in this context he may have been better to say “arithmetic” or maybe root logical operations, because he was trying to convey small axiomatic units of universal truth rather than pull an entire field “into purity”

I could say the same about his comment about Carbon, the exact mass of carbon we use is influenced by isotopes and is not exactly standardised in all human chemistry - so it’s likely the aliens idea of “the mass of carbon” would also be slightly different. A better example would be “the atomic number of carbon” which is always the same because it’s definitional and integer, but the same point is there - he’s conveying the existence of the tiny axioms (alien truths), not trying to define them

TuringTest7• 4 years ago

But I think in this context he may have been better to say “arithmetic” or maybe root logical operations, because he was trying to convey small axiomatic units of universal truth rather than pull an entire field “into purity”

What makes you think that arithmetic and logic are universal? A culture with a completely different way of thinking may not arrive to a system similar to our mathematics based on logical reasoning and search of consistency. Heck, we can see it in a lot of human beings who are not capable of consistent logical reasoning, and they're not even alien.

nine_k3• 4 years ago

Math is a formal game. You can define vastly varied algebraic structures, and, as long as they are internally consistent, we could consider them "mathematical".

But the physical reality makes some structures more important in practice. Hence natural numbers, or real numbers, or complex numbers stand out among the sea of possible group structures.

Chances are very high that aliens live in the universe with the same laws of physics, which make the same, or isomorphic, structures important for them, and thus informing the development of their mathematics.

But this is not a given, of course; there can potentially be different ways to describe physical reality which are comparably successful, but which grow from entirely different foundations, are internally consistent, and otherwise work like our mathematics, but are not connected to it (yet).

Even more funny is that Gödel's incompleteness theorem guarantees that "our" (currently developed) mathematics contain true statements which cannot be proven either true or false within the set of axioms which produce our mathematics. One can imagine that these true statements can be used to successfully describe important aspects of physical reality and were discovered by aliens for this purpose, while remaining incomprehensible for us. (But this is softer sci-fi stuff, of course.)

pluijzer2• 4 years ago

But this is not a given, of course; there can potentially be different ways to describe physical reality which are comparably successful, but which grow from entirely different foundations, are internally consistent, and otherwise work like our mathematics, but are not connected to it (yet).

Are you or anybody else aware of any other way to describe physical reality? Maybe some culture took a different path. That would be very interesting. It seems almost impossible to imagine one for me though.

theonemind• 4 years ago

Math is a formal game
Even more funny is that Gödel's incompleteness theorem guarantees that "our" (currently developed) mathematics contain true statements which cannot be proven either true or false within the set of axioms which produce our mathematics

These two statements together suggest that math isn't actually a formal game, but that formal methods offer an useful method for dealing with it.

patientplatypus• 4 years ago

I agree. Consider the octopus - each of it's limbs contains it's own cortex and so it has in essence 8 separable brains. Or ants and bees which contain a hive intelligence. An ant has almost no neurons, but the collective number of neurons of an ant hive approaches that of a human brain. These are only creatures that are on our earth that have radically alternative ways of experiencing intelligence. Why would we expect aliens to have an intelligence that's at all comparable to humanity when even somewhat intelligent animals on our planet don't exhibit the same characteristics?

spookthesunset3• 4 years ago

There is also bats who basically navigate the world by pinging sound off things.

Don’t forget microscopic creatures like Tardigrades. Their world is so small that the air around us acts like water.

poulpy123• 4 years ago

I don't know for the axiom of choice but I would be surprised if 1+1=2 is not universal, whatever way is used to express it

colordrops2• 4 years ago

Is that "math" though, or just a particular construct in the system of math? I could imagine an alien mind that does not break things down across integer boundaries, when you consider that any labelings and groupings are arbitrary. That 1 "hat" you are wearing plus that 1 "hat" your buddy is wearing are actually not 1 and 1 but a conglomeration of fields/particles in an arbitrary configuration that can be torn or shredded or turned into plasma.

dooglius• 4 years ago

This seems like an uncharitable take, the set of axioms and definitions used doesn't really fall under "mathematical truths", it's about agreement on what is implied by a given set of axioms. Even on Earth many people work in alternatives to ZFC and generally don't really disagree about what is "true".

TuringTest7• 4 years ago

Yet "what is implied by a given set of axioms" is the most common definition of "what's true" in mathematics. Therefore, an alien culture using completely different axioms and rules could arrive to an extremely alien math.

There might be some parts of it that are translatable to our own systems, but there's no guarantee that both systems will be ultimately compatible.

jsbg• 4 years ago

"The truths of mathematics would be the same, because they're true by definition" means that "(x => y) AND x" means y is true based on the definition of => and AND. There's no "philosophy" behind this.

lupire3• 4 years ago

Why would aliens have the same definitions? Your AND maybe wouldn't exist to them. They could have a more statistical/global non-binary/discrete mathematics.

simonh10• 4 years ago

I think, like many commentators here, you're taking a very narrow technical view of what PG is talking about in what is actually a very broad a high level discussion.

Whether or not it's possible to prove a specific postulate in set theory is formally true (the axiom of choice, which was only formulated in 1904) isn't going to stop aliens counting objects and calculating the area of squares. They may not agree with us about formalism vs intuitionism, but it seems likely they would agree with us about a huge array of practical mathematical operations and results. PG is just asking what are the areas we would be extremely likely to agree on. Pointing out that there might be specific, advanced, highly obscure controversies we might disagree on isn't even in contention. Of course there are.

kmod5• 4 years ago

It's turtles all the way down -- we don't know what "truth" is, or how one can come to "know" truth (as opposed to just believe it). I'm less informed on these topics so I avoided them, but I've heard that our notion of truth is intimately tied to our experience of physical reality, and it seems easy to imagine aliens that have different experiences of reality.

For example, what if aliens are so large that the non-euclidian nature of space becomes obvious to them? Perhaps they would never come up with euclidian geometry. Maybe they would never create the notion of pi. Yes it shows up in other areas but you can certainly imagine an alien civilization that has a different circumference-to-radius ratio or disavows the entire idea of having a constant circumference-to-radius ratio.

waffletower• 4 years ago

Squares do not exist outside of abstract axioms. Solids projected from them share the same status. A mason making a tile forces reality to approximate the concept. Even crystalline structures which suggest them are too approximate. Why is a square implicit to an alien?

spookthesunset3• 4 years ago

In particular, we humans still hotly debate which math is the "right" math. Is the axiom of choice "true"? Does it make sense to say that it has a truth value?

I would love examples of this. Seems pretty cool to think about. I always assumed that “math” would be one of the constructs we could always reliably communicate with.

kmod5• 4 years ago

I really like the Stanford encyclopedia of philosophy. In this case: https://plato.stanford.edu/entries/philosophy-mathematics/

witherk• 4 years ago

Math isn't choosing which axioms to use, is finding the consequences of a given set.

golemotron• 4 years ago

To be fair, someone writes this type of comment every time he posts. It's not a unique take. It falls into the "well studied" category you mention.

AnimalMuppet• 4 years ago

Take some number of things. Lay them out more or less in a straight line. Somewhere in that line, put a little gap. Count them from left to right. Then count them from right to left. You get the same number.

That experiment is saying that addition commutes. If an alien ran that experiment, they would get the same answer.

Lay out some things in regular rows in a rectangle. Count the things row by row. Then count the things column by column. You'll get the same answer. So will an alien. That is, multiplication commutes both for us and for the aliens.

Now, as you go further into mathematics, things are true because they follow from the definitions, but the aliens may use different definitions. They may have a different definitions for, say, a commutative ring, and so abstract algebra may be different for them. But with the same definitions, we would arrive at the same conclusions.

Koshkin15• 4 years ago

If an alien ran that experiment, they would get the same answer.

This depends on the world they live in. If, for example, things were hard to control, tended to move, to disappear (and reappear in a different place), to look the same, etc., they would probably discover quantum field theory before arithmetic!

wizofaus4• 4 years ago

Good analogy but is it so crazy to think the concept of counting in a particular direction wouldn't make sense to an alien intelligence? That the way their brain processes inputs means that the knowledge of the total number occurs to them either subconsciously or as the result of parallel processing that is beyond what human brains can even imagine being aware of? Even if the input signals being counted are separated by time (e.g. pulses of light or sound), such that their brains must logically store the previous count and increment it as new signals are detected, the concept of ordered addition (i.e. where we can conceive of "x plus y" and "y plus x" as separate concepts, even if they yield the same result) might simply not be necessary or possible in an alien brain.

What even qualifies as "addition" at all is somewhat murky - e.g. "addition" of relativistic velocities is non-commutative (*), but is it meaningfully even addition in the same way adding integer counts is?

* https://en.wikipedia.org/wiki/Velocity-addition_formula#Prop...

mcqueenjordan• 4 years ago

https://en.wikipedia.org/wiki/Principle_of_charity

Or, infinitely caveating all of your writing is tedious and makes it less interesting to read. It's more respectful to your readers to assume they understand this and will apply the principle of charity.

VyseofArcadia• 4 years ago

In particular, we humans still hotly debate which math is the "right" math. Is the axiom of choice "true"? Does it make sense to say that it has a truth value? Is such a truth value amenable to human discovery? Does PG know the answers to all of these questions?

If we did encounter intelligent (and peaceful!) beings out in the universe, there would be a set theory gold rush as people race to put out papers that such-and-such alien axiom implies choice, diamond principle, etc., or the other way around.

Every field of math would have such a gold rush really, on both sides, as we discover similarities and differences in techniques and formulations. And I bet famous unsolved problems on both sides would get solutions if not outright provided by the other species, then at least using novel tools from the other species.

I can't imagine a more exciting time for math as a whole than first contact.

benlivengood• 4 years ago

I'd expect aliens to have discovered their equivalent of the Church-Turing thesis, Tarski's externality of truth, Godel's incompleteness theorems, etc. That would give them a strong ability to model our mathematics within their own and see its computational structure and begin finding correspondences to theirs. Similarly, we could begin modeling their conception of mathematics in a similar way and as soon as we both have arrived at a morphism between our representation and theirs of some particular theorem we could grow our knowledge and understanding of the other.

The key is that mathematics flows from logic and logic flows from computation and computation is universal.

solveit• 4 years ago

Is the axiom of choice "true"? Does it make sense to say that it has a truth value? Is such a truth value amenable to human discovery?

I imagine PG would say that these are not purely mathematical questions, but rather metamathematical questions. Theorems remain theorems regardless of whether the axiom of choice is "true", although one may contend that theorems assuming that the AOC is false (or true) are vacuous. Aliens would surely agree with us on statements of the form "working in first-order logic (or whatever) formalized in XXX way, assuming axioms YYY and ZZZ, we may prove that...".

WalterBright• 4 years ago

Math has proven its predictive powers in the real world over and over. It's quite a stretch for it to be fundamentally wrong.

pazimzadeh• 4 years ago

Not that I agree with the argument, but this is relevant:

https://www.quantamagazine.org/the-evolutionary-argument-aga...

kubanczyk2• 4 years ago

A very interesting take. Your link is a worthy prize for enduring most of the other comments around this thread.

li4ick• 4 years ago

Yeah, that first paragraph is completely wrong if you think about the universe in terms of computation...

adamc• 4 years ago

"The Zoologist's Guide to the Galaxy" covers this, and a lot more: https://www.audible.com/pd/The-Zoologists-Guide-to-the-Galax...

theboywho• 4 years ago

it would be true for aliens that one can get better at something by practicing

We get better by practicing only because of our brain's neuroplasticity, which one might argue, is a mechanism of adaptation, and thus a result of evolution. An intelligent life might have developed other ways of coping with change, and not necessarily through a neuroplastic brain, but for example, through an instant rewiring of the brain that doesn't require any practice.

The same can be said for justice, even though it might seem as a social construct, it's still rooted in our biology (emotions are still "physical" reactions in our body) and so an intelligent life might have developed a different biological system different than that of emotions.

notshift3• 4 years ago

for example, through an instant rewiring of the brain that doesn't require any practice.

You might have an alien species that can copy the brain state of someone who already knows a task, or one that can gain skills extremely quickly through practice, but I don't think practice is going away. The fact that neural networks have been the only way we've been able to solve a lot of problems, which approximate the way that the human brain learns, is pretty strong evidence of this. You start out with some weights, you measure loss, you adjust weights, and then you try again.

Justice as an emotion might go away or exist in a different form, but the underlying reason why humans have a sense of justice is evolutionary psychology / game theory. Probably any life form which is shaped by evolutionary forces would have some similar instinct. (Certainly not all possible intelligent life forms though, I'd agree.)

asdff5• 4 years ago

The fact that neural networks have been the only way we've been able to solve a lot of problems, which approximate the way that the human brain learns, is pretty strong evidence of this.

Chances are a lot of machine learning implementations can be replaced with just "boring" statistical models and achieve more power.

OTOH plenty of creatures don't need to learn. Does a mosquito need to learn? No, it spawns thousands of offspring and doesn't live very long. The high spawn rate means you have a wide variety of natural mutations in your offspring, meaning one or a few of them are likely to have higher fitness in a given niche. It doesn't matter if most die if a few go on to survive. This is the strategy many organisms use to dominate the world in far greater numbers than our own species.

ketralnis• 4 years ago

The fact that neural networks have been the only way we've been able to solve a lot of problems, which approximate the way that the human brain learns, is pretty strong evidence of this

These are all difficult assertions to make because we're trying to prove a negative. Your claim is evidence that neural networks are one way to do it, and nobody's arging that. But it's not evidence that there doesn't exist a better way, or that alien life might evolve a different and even less optimal way.

Legs are pretty ubiquitous, even flying insects have them. If we'd never seen a fish or snake we might conclude that they're inevitable. Somebody that evolved to be rad-hard on a planet without a magnetosphere might conclude that life can't exist without the thick carapace that they're made of and only look for planets rich in silicon and calcium.

vmoore• 4 years ago

an intelligent life might have developed a different biological system

One theory is that some intelligences evolved the opposite to us. They started in pure silicon form and developed super-intelligence in the early stages and didn't evolve from carbon. They were /born/ computers and evolved from there into hyper-intelligence capable of exploring galaxies with Von Neumann probes[0]

[0] https://futurism.com/von-neumann-probe

breuleux• 4 years ago

Computers are a specifically engineered thing, they are not the sort of object that evolves naturally, at least not as an initial step (the first step is autonomous nourishment and, you know, motion). Silicon-based life forms would likely not be computer-like at all. They would probably still extract energy from oxygen and various other chemicals, they would have their own bacteria and fungi that eat and decompose silicon compounds, and they would probably still not survive in space.

Also, even though silicon has interesting properties on its own, carbon is kind of just better at everything else. It can make bigger and more stable structures, for example. Its oxide is also not, you know, a stable and unreactive solid. So it would be surprising for life forms not to use carbon extensively, unless it was much too rare, and in that case I honestly doubt it would get very far. As a building block, carbon is just outstanding, there is a reason life on Earth is based on it even though there is a thousand times more silicon than carbon on the planet.

simonh10• 4 years ago

through an instant rewiring of the brain that doesn't require any practice

How does the rewiring system know what the ideal end state is in advance, and how does the alien evaluate if the new state is fit for purpose?

I'm with you on justice though. A parasitic species might have a completely different view of rights and obligations than we do.

apriljest• 4 years ago

What happens upon contact with aliens? I believe that to be an important question, and one look at the warfaring, fearful history of humankind makes it clear, as best said from the most reprehensible book on philosophy I have ever read:

"477. "If intelligent entities from other parts of the universe exist at similar or superior technological levels to ours, would they draw the same or at least similar philosophical conclusions to us?" That is a very good question. And my answer is this. They better f#%*ing do if they want to have any hope of withstanding our relentless, merciless onslaught."

jtwebman• 4 years ago

So very human of us to think our truths are some other beings truths. Maybe they proved math isn't true? Maybe they don't think in any way like we do.

koyanisqatsi6• 4 years ago

Michael Levin has an interesting perspective on this. The idea is that biology and evolution are processes that reveal some inherent and latent universal structures and so they would be the same across all life in the universe even if such life was not carbon based. But at this level of generality it gets pretty abstract and the definition of truth essentially becomes some kind of structural similarity in form and function.

OscarCunningham• 4 years ago

This is a side topic, but does anyone else have problems with the RSS feed for pg's essays? http://paulgraham.com/rss.html I regularly find every essay appearing together in my reader, as though they were all new again.

Apparently the feed was created by Aaron Swartz himself, so I wouldn't think there would be any errors there. But it looks like it's hosted via Aaron's own site, so perhaps there's some problem caused by it not being maintained?

gnramires• 4 years ago

I personally believe we should also approach ethics from an Alien Truth perspective -- there's a lot of ethics and how we live our lives that's specific to our human being species, but we should expect the principles of human life to be compatible with more general principles, of which ours would be a special case. This really allows having a clearer global picture of ethics, and striving towards progress in ethics and human existence.

chatterhead• 4 years ago

1 + 1 = 3 (Because some aliens understand what state changes occur in the future and the equation is specific to the singularity of something not the progressive time.)

breckinloggins• 4 years ago

We might find, for example, that it's impossible to create something we'd consider intelligent that doesn't use Occam's razor. We might one day even be able to prove that.

I have no idea how one would go about proving this but personally I would start with something like the "Principle of Least Action" applied to thought.

carapace3• 4 years ago

Speaking in broad generalities (heh) Category Theory is what you would use for that (AFAIK.)

TuringTest7• 4 years ago

Because using Category Theory for explaining things is the opposite of applying Occam's Razor? :-P

deltasevennine16• 4 years ago

Justice, for example. I wouldn't want to bet that all intelligent beings would understand the concept of justice, but I wouldn't want to bet against it either.

Justice is a biased concept. It's a biological phenomenon. Most of us are born with justice modules in our brain. Certain people aren't, they're called psychopaths and these people are basically proof about the genetic component of justice.

Justice is simply a set of behaviors that helps you and your tribe survive from an evolutionary perspective. If you robbed and killed people all the time, well that doesn't help with survival does it? So brains evolve justice modules. There are alternative survival strategies that involve behaviors that are unjustified... and your emotions reflect this possible alternative path. One can be emotionally tempted by unjustified behavior and move in that direction when the situation allows for it. It's all preprogrammed...

For PG to talk about justice as possibly universal is like talking about English as possibly universal. Clearly these are biased concepts unique to humanities biological situation. It's unlikely that a frog feels justice simply because the evolutionary pressures to make him feel that way don't exist. Hardly a candidate for even consideration of being universal.

There can be aliens that are highly intelligent but anti-social. Such creatures have little need to develop a biological justice module as part of their intelligence. I would imagine communities of these creatures are only held at equilibrium because of mutually assured destruction. This has certainly been the case for humanity as humanity has multiple modes of operation, justice is just one component, fear of death is another.

alfor2• 4 years ago

All of our truths are based on biology.

Without our body we cannot see, feel and experience. Something is true when it is useful, predictive to us, to our body, when it allow us to move away from pain and toward pleasure.

If there is no observer and no sensations(feedback) I don’t think we can ever come to any truth.

deltasevennine16• 4 years ago

Some truths seem to be universal meaning they exist separate from our biology, for example: logic.

Other truths seem inextricably tied to our biology, for example: happiness.

One that is ambiguous is, Justice. To which I say the ambiguity is an illusion. Justice is like happiness. Completely unique to the human experience.

verrp• 4 years ago

I have long suspected that the aliens will recognize Go (the game), but (obviously) not Chess (the other game).

I suspect they will even recognize Go's 19x19 board (b/c it has properties other board sizes would not have).

But would they recognize 12 tones scales?

themodelplumber• 4 years ago

But would they recognize 12 tones scales?

Relatively? More likely. "Oh yeah, we get that. At a number of levels which we call honktaves, incidentally."

Absolutely? As in, we have that set of frequencies bolted on to our culture too? Seems less likely.

mostlylurks• 4 years ago

But would they recognize 12 tones scales?

Assuming they have musical instruments and don't have far more digits (fingers or other dextrous appendages) than us, they probably would, and even if they did have more digits, it'd seem like a fairly obvious choice for a species with our anatomy. Especially for equal temperament, but also for just intonation, a 12-tone scale provides exceptionally good approximations or numerous instances of the simplest possible frequency ratios, so any creature that has to limit the number of tones on their instruments for practical considerations will have a high likelihood of stumbling on a 12-tone scale even before developing an understanding of why it actually works so well and/or find it a very compelling option given a more in-depth analysis.

elihu6• 4 years ago

But would they recognize 12 tones scales?

It's possible that they might, but if they have any kind of musical discernment they might find it objectionable unless they're as lazy as we are.

12-tone equal temperament works more-or-less because it gives good-enough approximations of almost all the small-number ratios that a musician making relatively straightforward music would care about. However, thirds and sixths are pretty out-of-tune and frequency ratios with sevens in them like 7:6 and 7:4 don't have any reasonable approximation.

On the other hand, 41-tone equal temperament is a much better system in just about any way you might care about, except that it makes building physical instruments more complicated because there's more notes to worry about. 53 is also really good, but that's even more notes.

And then there's pure just intonation, which is a great option if you don't really care about being able to transpose freely to/from any key, but you want each note pitch to be dead-on exact.

In other words, 12-TET is a kind of local optimum that we're stuck in for historical reasons and because the barriers to change are high. You might as well ask if an alien civilization would recognize the concept of daylight-savings-time, or the QWERTY keyboard, or the electoral college.

tiffanyh• 4 years ago

PG use of image maps for site navigation always bring back 1990s Web "1.0" nostalgia to me.

lowbloodsugar• 4 years ago

For example, I think we'd share the principle that a controlled experiment testing some hypothesis entitles us to have proportionally increased belief in it.

I wouldn't want to bet that all intelligent beings would understand the concept of justice

It would be unjust if a technologically advanced society murdered all its scientists for heresy during a religious coup, but Paul is unwilling to bet that all alien societies understand justice. Why the belief in science then? Our own planet has theocracies and a President of the supposed #1 country has updated scientific hurricane reports with a sharpie.

Plenty of science fiction authors have speculated meeting theocratic aliens. Peter Hamilton's Salvation comes to mind (you get where that series is going from the title).

at_a_remove• 4 years ago

If I had to lay money on it, I'd be willing to favor the position that aliens we're talking to via radio have the concept of electrons, and metals, and the number forty-seven.

The really esoteric branches of mathematics, I could see huge variances. Materials sciences would vary widely. But the basic high school stuff? I'd lay odds on it.

srvmshr• 4 years ago

It makes me slightly sad that a well-read tech icon like PG dabble in writing things which are not only beyond his creative expertise, but also speculative, imaginative & open to wide variety of interpretation, spirituality including.

Aliens may exist as very intelligent species or maybe dumb bacteria. We are discovering the laws of nature ourselves. We don't know enough of the laws of nature, despite the vast strides we have made in the last century. Maybe there are universal truths & representations, like the GUT which all life forms may eventually discover in their notation/formalism. Or maybe the laws of physics will have different implications in different corners of universe or multiverses, and we don't know those too with any degree of certainty.

Sufficiently long timelines of existence doesn't guarantee intelligence of species. Dinosaurs existed for about 140 million year & more, whereas we have stepped on moon in less than 25000 years of evolution. These things are entirely uncharted territory, left best to astronomers who discover life form or make any contact one day

akomtu• 4 years ago

In the ancient Greece there was a tradition of studying math. To the outsiders it appeared as if a bunch of dudes in white robes studied triangles, but the inner circle studied the absolute truths that happened to be represented well by geometry. The Pythagora's triangle wasn't just a shallow numeric relationship to them, they saw the inner truth behind it.

bglazer• 4 years ago

One of the bitter lessons I've learned is that when I think of something, I should always (always!) do a couple searches to see if anyone else has thought of it, before I commit to writing down my thoughts as novel or authoritative.

Someone (typically at Bell Labs in like 1973) has nearly always already had my thought, but then explored it in much richer, finer detail than I have. It's disappointing to learn I'm not an unmatched genius, but much more illuminating to read and think about how others have considered similar issues.

I don't fault Paul for not doing this, it happens to everyone, and I imagine he's quite busy. I do fault all the people who read this draft and didn't do this very easy exercise for him. I think it reflects a undue deference towards frankly uninformed and pretty basic observations.

ifyoubuildit• 4 years ago

These threads seem to invite lots of comments of the form "[I|someone I know of|both] [am|is|are] smarter than PG for xyz reasons". These can be interesting to read if you want to get into the nitty gritty.

But they don't often seem to engage with the overall point. In this case, I think that point is that there are probably local truths and universal truths, and wouldn't it be neat to focus on the universal ones, or figure out which ones are only locally true, and why? But who knows, that's just my interpretation.

sillysaurusx• 4 years ago

Agreed. One of pg’s examples was “If there are aliens, they’d probably discover that a stool with three legs is the most stable.” I’m surprised he didn’t include it in this essay.

asdff5• 4 years ago

What was the reason a three legged stool is the best? Doesn't that depend on your environment? E.g. the amount of gravity, perhaps wind, or the quality of materials available to construct a stool?

robocat• 4 years ago

a stool with three legs is the most stable

I don’t think stable is the right word. A stool with three legs is less wobbly on an uneven surface.

A high stool with three legs is less stable to horizontal forces (forces towards the gap between legs).

I would say a tall stool with four legs is more stable (assuming the outer diameter of the footprint of the feet remains the same.)

It is the same reason three-wheeled cars are less stable than four wheeled cars.

If you want a stable seat on an uneven surface, you use a one legged stool (your legs make the other two adjustable legs).

Finally, the concept of a stool depends on two-legs and various other human specific environmental details. Aliens might not understand our stool analysis at all.

dav• 4 years ago

Paul Graham needs to read this and get back to us.

Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being by George Lakoff

https://www.goodreads.com/book/show/53337

dropit_sphere• 4 years ago

lol holy shit you guys are a rough crowd

lakomen• 4 years ago

SCNR has this guy never heard of https?

galaxyLogic• 4 years ago

This seems like lots of camp-fire speculation in awe of the night sky.

Before discussing what might be different with our "truth" and alien "truth" we should first define what we mean by "truth".

What if there is a War of Worlds? And we win. But according to the "alien truth" they win. This kind of thing seems to be going on some TV-channels already, The notion of "facts" is diluted by claiming that "We have alternate facts". "We have alternate electors". That just means it is unclear to many people what facts and truth mean and it is easy to misguide them.

skybrian• 4 years ago

An assumption that this essay buys into is that "universal" truths are somehow higher-status and more worthy of study. How people come up with reasonable fixes to local messes doesn't get enough attention.

asdff5• 4 years ago

Why do people assume alien life would be intelligent? Intelligent life is extremely rare on earth and has only occured for a brief moment in its history due to highly specific environmental scenarios at the time as well has historical events. If we didn't get that meteor that wiped out the dinosaurs, mammals would probably still be shrew like creatures as they were for millions of years until mass extinction exposed new ecological niches. The great oxygenation event could have easily killed off all life on earth too. Most of the biomass on earth today comes from plants, famously unintelligent and sessile, commonly using strategies that favor spawning thousands of offspring that have random mutations, with a few who go on to survive in an ecological niche.

If we use our own earth as a model, alien life is far more likely to be unintelligent. Its a big human bias to assume that if there were intelligent life out there, it would even think like human life, so our abstractions such as mathmatics and physics will probably look entirely different when a completely different mind formed from a different evolutionary trajectory encounters natural phenomenon and attempts to make truths. Even with our own species it took us millions of years to establish our current truths about what we consider true. This begs the question, if in millions of years we will consider our current abstractions that interpret physical laws of the universe to be just as worthless as past interpretations for these same physical laws that we used as truths in centuries previous.

dadboddilf2• 4 years ago

I'm very confused, I see the page with that guy's article (or any of his articles for that matter), but I don't see any instructions on how you can get paid to read it.

benevol• 4 years ago

If there were intelligent beings elsewhere in the universe

Wow some people still think we're alone. Wow. Just, wow.

songeater3• 4 years ago

I think this discussion of convergent evolution is pretty interesting in context [0]. Namely, "intelligence" arises from natural-selection (ie from some non-intelligent predecessor that developed incrementally to better fit its environment)... and the process of natural-selection would necessarily lead to various commonalities between intelligent creatures that came to be independently.

PG's essay seems to (implicitly, not explicitly) compare between technologically-sophisticated intelligence - ie not between octopuses and humans, but between species that could at least communicate through inter-stellar distances, if not traverse them directly. If so, convergent evolution would have imposed even more onerous similarities between such species: to develop a radio-transmitter, intelligent creatures would also likely to have been very socially developed, or how else would they have been able to transform the resources around them to build a transmitter?

Therefore it is the physical world in which we live that most likely leads us to conceive "math" similarly... and even "justice." [1]

[0] https://www.quantamagazine.org/arik-kershenbaum-on-why-alien...

[1] tit-for-tat being one of the best strategies to solve an infinitely-recurring prisoner's dilemma

hangaard• 4 years ago

We'd also share algorithms. Including evolution.

kubanczyk2• 4 years ago

Maybe, knowing what we know today (i.e. almost nothing), a less boring approach would be from the opposite direction: assume there is a life which is not a result of evolution, offer educated guesses how would that work.

lloeki• 4 years ago

was more discovered than invented

I chuckled at this one because one of the first things I was taught early in science class was that the root of "to invent" is latin "invenire", which translates to "to find", "to discover".

Kind of a humbling moment to realise we're not creating anything, merely too blind to see, groping in the dark for truths that lay out there for us to trip upon.

politician• 4 years ago

Would aliens use Zermelo–Fraenkel set theory as the foundation of their mathematics?

machina_ex_deus• 4 years ago

We'd probably share Occam's razor.

I already disagree here. Simplicity is a heuristic in the brain. Like all heuristics it helps you solve some problems easier, but behind the word stands the entire life experience of someone, and whatever is "simpler" depends on way too many human things in his life. "Simple" is something human. So is Occam's razor.

Tao3300• 4 years ago

It's not we exactly "simplicity". If you have two explanations arriving at identical results, take the one with less assumptions.

It's helpful to look at it the other way around. Thomas Aquinas worded his version of it:

it is superfluous to suppose that what can be accounted for by a few principles has been produced by many.

There's a subtle difference, and that's probably why we see it called the parsimony principle instead of the simplicity principle. The point being not to have nonessential crap hanging off your theory -- provided you've established that it's genuinely nonessential.

SkyMarshal2• 4 years ago

What should we call the search for alien truth? The obvious choice is "philosophy."

Minor nitpick, but the subfield of Epistemology (or Alien Epistemology) might be a better term. Literally the study of knowledge, or how we know what we know and what is true.

https://plato.stanford.edu/entries/epistemology/

But trying to look at it from an alien (or AI) point of view is a really interesting thought experiment. What are universal truths in the literal sense of the word "universal"? And what are merely helio-centric cultural trends masquerading as universal truths.

I wonder if that's ever been done before. There's a little bit of discussion of it online, but not much it seems:

https://www.google.com/search?q=%22alien%20epistemology

elihu6• 4 years ago

I think alien truth about alien truth would be epistemology. The number of protons in helium might be an alien truth but it isn't really epistemology, it's just a fact. Whereas the scientific method itself would be a system of epistemology.

SkyMarshal2• 4 years ago

It also occurs to me to wonder if AGI will ever invent its own version of epistemology, wondering how it knows what it knows. Or will minds based fundamentally on binary logic, rather than the human mind's fuzzy logic, even need such a field?

anonym29• 4 years ago

Anyone else getting a TLS cert for this link with a CN of *.store.yahoo.com?

hoseja• 4 years ago

Math might be universal but I think you're really underestimating the potential for wildly differing perspectives on it.

simonswords82• 4 years ago

Paul is well out of his depth here. We can all sit around pondering the universe - that's easy.

Answering these questions is significantly harder - impossible given today's science.

This essay reads like the ramblings of a man who's smoked too much weed.

Paul should stick to tech start ups - if you want serious insight around science, space and the universe hit up people like Richard Feynman...

https://www.youtube.com/watch?v=36GT2zI8lVA

Alien Truth

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