Well, what exactly an “idea” is might be a little unclear, but I don’t think it clear that the complexity of ideas that result from combining previously obtained ideas would be bounded by the complexity of the ideas they are combinations of.
Any countable group is a quotient of a subgroup of the free group on two elements, iirc.
There’s also the concept of “semantic primes”. Here is a not-quite correct oversimplification of the idea: Suppose you go through the dictionary and one word at a time pick a word whose definition includes only other words that are still in the dictionary, and removing them. You can also rephrase definitions before doing this, as long as it keeps the same meaning. Suppose you do this with the goal of leaving as few words in it as you can. In the end, you should have a small cluster of a bit over 100 words, in terms of which all the other words you removed can be indirectly defined.
(The idea of semantic primes also says that there is such a minimal set which translates essentially directly* between different natural languages.)
I don’t think that says that words for complicated ideas aren’t like, more complicated?
Asking what it “is made of” seems like a somewhat ambiguous question to me. Still, the answer would not be “mathematical abstractions that fit the data”, but “these mathematical abstractions”. (And, there is a lot of meaning behind these “abstractions”. For example, there is a close correspondence between the Higgs mechanism for mass and superconductivity.)
Really, what possible answer could you ask for that wouldn’t be of this form?
When you describe an idea sufficiently precisely, you do mathematics; that’s almost what mathematics is.
It feels to me like complaints like yours tend to derive from an unwillingness to believe that things aren’t at their core made of solid objects or fluids or other stuff which behaves like macroscopic objects we have everyday experience with.
Can you describe an explanation that wouldn’t be like that but which (if it were true) you would find satisfying?
If you can’t describe how an explanation could (if it were true) satisfy you without being like that, then, if the universe isn’t like that, you have to be disappointed. And, in that case, again, I have to say, take it up with God.
On the other hand, if you can describe how an explanation (if it were true) could possibly satisfy you without saying “at its core, the universe works based on [behavior that you have plenty of physical intuition for based on your everyday interactions with macroscopic stuff]”, I would very much like to hear it.
I think probably in the past what one might have expected to find is akin to something like a magical material that couldn't be further probed. That would have been satisfying in a sense because it brings a wonder back into it while connecting you to the fundamental "thing".
What we have now is not that, it's still very much a mechanistic explanation where the "magic" is hidden within abstractions that make no sense to anyone, i.e abstract fields with properties but no material realty, instantaneous wave function "collapse", wave-particle duality, virtual particles etc. The reality of these things is glossed over.
But my point is that if that's what we've been driven to, why are we still engaged in this enterprise? We're just receding further into these abstractions. What are we going to find next year or next decade? A better mathematical model to fit the data? The mission has gone from finding out what the universe is made of to finding a better abstract model. Particles aren't real, they're excitations in a field, etc. It's an engineering enterprise now. So we're not going get a satisfying answer, were just going to get better lasers or whatever the next tech is.
That makes little sense to me. “Can’t be further probed”?
A thing behaves in some way. If you do things, things happen.
One can do certain measurements about how things behave, and then record these measurements.
What would it even mean for a material everything is based in to be magical? If there was some exceptional material that is unlike other things, following different rules, I can understand calling that “magical”. But, the only meaning I can think of for a material underlying everything to be “magical” is that either everyone just, declines to study it, or its behaviors like, depend on the intent of those studying it or something like that.
I also don’t get your statement that “brings a wonder back into it”. Like, do you not experience wonder when contemplating the nature of fundamental fields?
Like, if we set aside the “magical” part, it kinda sounds like your objection is that fields aren’t a substance/material. But, if you just generalize your notion of “material” a bit, why don’t quantum fields satisfy all your requirements?
And, if they do, don’t you want to understand how this “magical material” behaves??
You decry these things as “abstractions”, and say that they “make no sense to anyone”. They can certainly be confusing, but they aren’t beyond comprehension, and I don’t see them as any less “material reality”? Macroscopic things just behave differently.
I don’t think I agree with “particles aren’t real” either. Electrons being excitations in the electron field, doesn’t make them “not real” any more than an apple being made of atoms makes it not real, or sound being vibrations in a medium makes sound not real.
Like, buckyballs are clearly “real” (they can act like little cages with something else contained inside), but they also clearly are “particles” like protons are (you can do a double slit experiment with them and get an interference pattern).
Also, I don’t think I’d say the enterprise was ever “What is the universe made of?” so much as “How does the universe work?” ? It is a drive to understand! It is asking “How do initial conditions relate to final conditions?”. The tech is ancillary to this!
I'm not interested really in how something behaves, that's an accounting or record keeping task. I am interested in why it behaves a certain way, or what it is. Why does the earth go around the sun? We're told it's because of space time curvature. Curvature of what? Where is space time and what it is made of that it has a shape or geometry? There is no ether, space is not made of anything. Yet it has a shape, or at least there is some accounting going on somewhere that keeps everything moving like it's supposed to. Where is that, what's the mechanism? What we have is a mathematical model that fits the data, but doesn't explain anything. Yes, A behaves in a certain way when B is in a certain position relative to A, we can model that and we call that relativity or whatever, but what is the mechanism? That's where the abstraction is. Are we satisfied with modelling an alien system that we can't understand in any other way? To me that's not that interesting, it just leads to getting lost in abstractions. Maybe relativity will be replaced by a more complicated model that covers more edge cases, but that doesn't tell you what it is. It just tells you how it behaves, as you said. It's like if what you thought was your dog meowed and liked to climb trees instead of barking and chasing squirrels. You don't know what it is anymore, it's not a cat it's not a dog, you don't know what it is but you can model it's behavior. That's what you're forced into. The familiarity is gone. Acting like that's some big accomplishment or achievement is a cop out. We found out the universe is not amenable to our knowing it with any familiarity. Is that something to celebrate? No, it's like finding out your parents were androids. So what are we left with, just accounting rules and accounting models. All they'll give us are ways to make better tools.
Your concept of “explains” seems like nonsense to me.
“what’s the mechanism?”? “[…] but that doesn't tell you what it is. It just tells you how it behaves […]”? A thing is what it does. C.f. the Yoneda lemma.
Again, your complaints sound like dissatisfaction with the fact that the world doesn’t run on stuff that fundamentally resembles substances we have everyday familiarity with.
You speak of “fitting the data”. I say “is compatible with the evidence”.
Also, asking where spacetime is, is a goofy question.
Oh, I see, you are expecting intrinsic curvature to derive from extrinsic curvature? There is no need for that. You could posit a larger (flat) space to allow that, but there is no reason to, as it would be indistinguishable from the simpler alternative.
“ We found out the universe is not amenable to our knowing it with any familiarity.” : You have to remember: it all adds up to normality. Any part of how the world works that seems “weird”, was already like that before you learned of it, and is, in fact, normal.
When I said “take it up with God”, that wasn’t just a figure of speech. Isiah 55:8-9 : “ “For my thoughts are not your thoughts,
neither are your ways my ways,”
declares the Lord.
“As the heavens are higher than the earth,
so are my ways higher than your ways
and my thoughts than your thoughts.”
God’s thoughts, God’s designs, are greater than our own. If how the universe functions offends our sensibilities, it is our sensibilities that need to change.
At the same time, Philippians 4:8 : “ Finally, brothers and sisters, whatever is true, whatever is noble, whatever is right, whatever is pure, whatever is lovely, whatever is admirable—if anything is excellent or praiseworthy—think about such things.”
You say “ All they'll give us are ways to make better tools.” , but, better tools? This is certainly not my motivation! My motivation is to know truth! And, there is much that is both lovely and true in what you dismiss as “models that fit the data”.
> Again, your complaints sound like dissatisfaction with the fact that the world doesn’t run on stuff that fundamentally resembles substances we have everyday familiarity with.
Ok, so you tell me, what does it run on? Intrinsic curvature and virtual particles, or what?
I wouldn’t say it “runs on” virtual particles per se. I think the virtual particle terms are more tracking the interactions between different fields. I would say it runs on quantum fields on a curved spacetime, yeah. And, as for what precisely a quantum field is, this is somewhat mysterious, but generally it is a quantum version of a classical field, where there is a value (e.g. “value of the electromagnetic field”) at each point in spacetime. For quantum fields, instead of each point having a definite value, for any region there is an observable for the total value in that region.
As for how the curvature of spacetime fits with all that, that is an open question that has yet to be resolved. Well, constructing a quantum field theory within a given curved spacetime is fine, but we don’t know how exactly GR and QFT fit together.
I expect that your response is going to be to call these “abstractions” or something, as if this does anything more to discredit them than complaining that any idea is “just an idea”. But these are measurable things. That which can be measured is a real thing.
You seem to be asking about “divine hiddenness”. I don’t know why God doesn’t make His existence more obvious to those that don’t seek Him. Like I quoted above, his ways are above our ways. That’s not to say that the reason is definitely beyond what I can comprehend, just that it is beyond what I do comprehend.
(On the off chance that you were being sincere in your question about mana: no.)
The point I was trying to make by quoting that passage was the necessity of humility. The way the world works doesn’t need our approval. It is above us.
science still cannot predict the path of a particle through a double slit. they cannot explain why this is the case. its claimed that the particle bounces of vacuum fluctuations, yet the energy predicted by these fluctuations is way bigger than what we measure.... how is that satisfactory to you?
I don’t expect the particle has a one single path it takes. This is just an example of reality telling us our assumptions (“each particle has a single well-defined path it takes”) were mistaken.
“It’s claimed that the particle bounces off of vacuum fluctuations” : hm? Like some kind of classical particle bouncing off of something?
“ yet the energy predicted by these fluctuations is way bigger than what we measure” : This is indeed a mystery, one which people are working to resolve. You spoke earlier of wonder. Is this not something to wonder about?
no, i dont wonder about it, i worry about it. it means the theory is wrong - works most of the time like newtons, but cant explain these weird edge cases... highly likely to not be the full story. odds are on my side for that statement.
> This is just an example of reality telling us our assumptions (“each particle has a single well-defined path it takes”) were mistaken.
this is just a copout to explain the path integral. it acts AS IF it takes every path, but it cannot possibly take every path in an instant. mass creates gravity, so where were these gravitational effects? cannot be found. so this particle taking every path did it without mass somehow. little details like this conveniently without explanation in your theory.
Hm, I think you are taking the language “takes every path” too literally. Like, set aside the “infinitely many paths” issue for a moment, and consider just two paths. A quantum superposition of two paths doesn’t mean “it took this path and also it took that path”. A quantum superposition is a different kind of thing from that. A quantum superposition is a linear combination.
A path integral involves an integral of e^{i S/hbar} where S is the action for a given path, with the integral being over the path, and evaluates to the amplitude from the starting state to the ending state.
(Of course, there are some difficulties defining integration over paths, especially if you want to get into QFT. Still.)
If you want to incorporate gravity into this, you probably need to do so within the path integral, with it being incorporated into the action.
But, of course, quantum gravity hasn’t been resolved, so to see why the issue you point to isn’t actually an issue, let me point out that the point you propose applies equally to electromagnetism: say we have an electron, and it goes from one point to another, and nearby we have a positively charged balloon. Replace “mass” with “electric charge” and “gravity” with “electromagnetic force” in your point, and we obtain an argument of the same form. But, QED works extremely well, and doesn’t predict an infinite electric charge in a region when an electron travels from one point to another (for the reason I said: the electromagnetic interaction between the electron and the balloon will appear within the action).
The universe is not obligated to appeal to your aesthetic tastes in its innermost functioning.
Maybe you aren’t going to be satisfied with the sort of complicated mathematics which appears to be correct (or, on the right track).
If you have complaints about the aesthetics of how the universe works, take it up with God.
Personally, I think there is a lot of beauty to be found in it.
I’ll admit that there are a few parts that go against my tastes (I don’t like needing to resort to distributions instead of proper functions), but that’s probably just intellectual laziness on my part.
> The universe is not obligated to appeal to your aesthetic tastes in its innermost functioning.
This is truly a copout. When science faulters in explaining the world we get answers like this. His argument isnt with the universe, but with out own scientific theories. If you dont want your theories about the physical world to explain physical world, then be an engineer. Science explains the world, engineers use those theories. QM has large gaps and doesnt actually explain much, but I guess the universe doesnt care whether our theories are wildly off the mark or not.
It's not a matter of taste. This is like going to a restaurant, expecting a delicious meal, and being brought a dish with a fancy name made out of the actual menu itself. Would anyone go back there to eat?
Systems can hypothesize about themselves but they cannot determine why the rules they can learn exist in the first place. Prior states are no longer observable so there is always incomplete history.
Conway's Game of Life can't explain its own origins just itself. Because the origins are no longer observable after they occur.
What are the origins of our universe? We can only guess without the specificity of direct observation. Understanding is incomplete with only simulation and theory.
So the comment is right. We would expect to be able to define what is now but not completely know what came before.
like, the part where they get a_i log p_i ,
well, the sum of this over i is gives the number,
but it seemed like they were treating this as… a_i being a random variable associated to p_i , or something? I wasn’t really clear on what they were doing with that.
Take an $n$, chosen from $[N,2N]$. Take it's prime factorization $n = \prod_{j=1}^{k} q_j^{a_j}$. Take the logarithm $\log(n) = \sum_{j=1}^{k} a_j \log(q_j)$.
Divide by $\log(n)$ to get the sum equal to $1$ and then define a weight term $w _ j = a_j \log(q_j)/\log(n)$.
Think of $w_j$ as "probabilities". We can define an entropy of sorts as $H_{factor}(n) = - \sum_j w_j \log(w_j)$.
Heuristics (such as Poisson-Dirichlet) suggest this converges to 1 as $N \to \infty$.
OpenAI tells me that the reason this might be interesting is that it's giving information on whether a typical integer is built from one, or a few, dominant prime(s) or many smaller ones. A mean entropy of 1 is saying (apparently) that there is a dominant prime factor but not an overwhelming one. (I guess) a mean to 0 means dominant prime, mean to infinity means many small factors (?) and oscillations mean no stable structure.
Ok, how about "a pile of linear algebra [that is vastly simpler and more limited than systems we know about in nature which do experience or appear to experience subjective reality]"?
> If that were the case, we would only really love the games we grew up with.
I’m not sure that’s true? Like, perhaps the preference might generalize from the several games one did play as a child to other games which are similar to the ones one played as a child, with the preference still being a result of which games one played as a child.
Utilitarianism, for example, is not (necessarily) relativistic, and would (for pretty much all utility functions that people propose) endorse lying in some situations.
Moral realism doesn’t mean that there are no general principles that are usually right about what is right and wrong but have some exceptions. It means that for at least some cases, there is a fact of the matter as to whether a given act is right or wrong.
It is entirely compatible with moral realism to say that lying is typically immoral, but that there are situations in which it may be morally obligatory.
I think you are interpreting “absolute” in a different way?
I’m not the top level commenter, but my claim is that there are moral facts, not that in every situation, the morally correct behavior is determined by simple rules such as “Never lie.”.
(Also, even in the case of Kant’s argument about that case, his argument isn’t that you must let him in, or even that you must tell him the truth, only that you mustn’t lie to the axe murderer. Don’t make a straw man. He does say it is permissible for you to kill the axe murderer in order to save the life of your friend.
I think Kant was probably incorrect in saying that lying to the axe murderer is wrong, and in such a situation it is probably permissible to lie to the axe murderer. Unlike most forms of moral anti-realism, moral realism allows one to have uncertainty about what things are morally right.
)
I would say that if a person believes that in the situation they find themselves in, that a particular act is objectively wrong for them to take, independent of whether they believe it to be, and if that action is not in fact morally obligatory or supererogatory, and the person is capable (in some sense) of not taking that action, then it is wrong for that person to take that action in that circumstance.
Any countable group is a quotient of a subgroup of the free group on two elements, iirc.
There’s also the concept of “semantic primes”. Here is a not-quite correct oversimplification of the idea: Suppose you go through the dictionary and one word at a time pick a word whose definition includes only other words that are still in the dictionary, and removing them. You can also rephrase definitions before doing this, as long as it keeps the same meaning. Suppose you do this with the goal of leaving as few words in it as you can. In the end, you should have a small cluster of a bit over 100 words, in terms of which all the other words you removed can be indirectly defined. (The idea of semantic primes also says that there is such a minimal set which translates essentially directly* between different natural languages.)
I don’t think that says that words for complicated ideas aren’t like, more complicated?
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