“Why does the universe exist?” … finally answered (or dissolved) in this blog post!
In my previous post, I linked to seven Closer to Truth videos of me spouting about free will, Gödel’s Theorem, black holes, etc. etc. I also mentioned that there was a segment of me talking about why the universe exists that for some reason they didn’t put up. Commenter mjgeddes wrote, “Would have liked to hear your views on the existence of the universe question,” so I answered in another comment.
But then I thought about it some more, and it seemed inappropriate to me that my considered statement about why the universe exists should only be available as part of a comment thread on my blog. At the very least, I thought, such a thing ought to be a top-level post.
So, without further ado:
My view is that, if we want to make mental peace with the “Why does the universe exist?” question, the key thing we need to do is forget about the universe for a while, and just focus on the meaning of the word “why.” I.e., when we ask a why-question, what kind of answer are we looking for, what kind of answer would make us happy?
Notice, in particular, that there are hundreds of other why-questions, not nearly as prestigious as the universe one, yet that seem just as vertiginously unanswerable. E.g., why is 5 a prime number? Why does “cat” have 3 letters?
Now, the best account of “why”—and of explanation and causality—that I know about is the interventionist account, as developed for example in Judea Pearl’s work. In that account, to ask “Why is X true?” is simply to ask: “What could we have changed in order to make X false?” I.e., in the causal network of reality, what are the levers that turn X on or off?
This question can sometimes make sense even in pure math. For example: “Why is this theorem true?” “It’s true only because we’re working over the complex numbers. The analogous statement about real numbers is false.” A perfectly good interventionist answer.
On the other hand, in the case of “Why is 5 prime?,” all the levers you could pull to make 5 composite involve significantly more advanced machinery than is needed to pose the question in the first place. E.g., “5 is prime because we’re working over the ring of integers. Over other rings, like Z[√5], it admits nontrivial factorizations.” Not really an explanation that would satisfy a four-year-old (or me, for that matter).
And then we come to the question of why anything exists. For an interventionist, this translates into: what causal lever could have been pulled in order to make nothing exist? Well, whatever lever it was, presumably the lever itself was something—and so you see the problem right there.
Admittedly, suppose there were a giant red button, somewhere within the universe, that when pushed would cause the entire universe (including the button itself) to blink out of existence. In that case, we could say: the reason why the universe continues to exist is that no one has pushed the button yet. But even then, that still wouldn’t explain why the universe had existed.
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Comment #1 February 6th, 2016 at 11:44 am
The universe exists for the same reason and in the same sense that math exists.
Comment #2 February 6th, 2016 at 11:44 am
>> what causal lever could have been pulled in order to make nothing exist? Well, whatever lever it was, presumably the lever itself was something
So are you saying that the universe necessarily exists?
Comment #3 February 6th, 2016 at 12:48 pm
Your answer (up to isomorphism) is equivalent to “I don’t know”.
I think, questions like “why 5 is prime in Z+” are questions about necessary being, and questions like “Why do planet Earth happened to be 8 light minutes 20 seconds distant from the star Sun” are questions about contingent being. These are totally different questions. Following st. Thomas Aquinas, I prefer to look for reasons of contingent being in necessary being.
Comment #4 February 6th, 2016 at 1:21 pm
Well, I’ll grant that Scott’s answer does *partially* dissolve the question, but I’m still not fully satisfied.
True, point granted: there always has to be some sort of ‘ground-state’ of existence that must neccesserily be assumed every time an attempt at an answer is made. Scott’s point is well taken:
“what causal lever could have been pulled in order to make nothing exist? Well, whatever lever it was, presumably the lever itself was something”
Yes, but that ‘something’ could be very minimal indeed. So there could in fact be some causal lever that when pulled does in fact reduce reality to (if not quite ‘nothing’) then something very close to it. So what is that ‘something’?
The rest of the answer could lie in Scott’s comments about mathematics and Godel (see video).
My solution to the ground-state of existence was to postulate a small ‘kernel’ of pure mathematics, enough to form a thing called COHERENCE. As I concluded in the other thread:
“If we imagine ‘pulling out’ coherence, then ‘existence’ is lost for (all aspects of reality)! So perhaps we can say that COHERENCE is the reason why the universe exists.”
Comment #5 February 6th, 2016 at 1:26 pm
>> On the other hand, in the case of “Why is 5 prime?,” all the levers you could pull to make 5 composite involve significantly more advanced machinery than is needed to pose the question in the first place.
In this case, the more natural lever to change is the definition of Prime Number, which is why the more satisfactory answer is just a reiteration of the definition. There’s a centrality component to satisfactorily answering “why” – for example, answering “why are you hungry” with “because I’m not an asteroid” is technically true but unsatisfactory, since the lever that would turn you into an asteroid is somewhat obscure.
Comment #6 February 6th, 2016 at 2:30 pm
“exist” is a dangerous word. It’s models all the way down.
Comment #7 February 6th, 2016 at 2:33 pm
Infinitely many ways for there to be something; only one to be nothing. So it’s incredibly unlikely.
Comment #8 February 6th, 2016 at 2:35 pm
wolfgang #2:
So are you saying that the universe necessarily exists?
No, that wasn’t the point at all! The point is that, in an interventionist account of causality, there can’t be a reason for the universe to exist, because that would imply a possible intervention that (if you applied it) would cause nothing to exist or have ever existed, but there can’t be such an intervention, because if the intervention exists then something does.
Comment #9 February 6th, 2016 at 3:11 pm
@Prof. Aaronson – couldn’t that line of reasoning instead be a reductio ad absurdum of interventionism? Between the premises (1) interventionism is the correct account of how to go about ansering this class of ‘why’ questions, and (2) there’s a reason that the universe exists, why do you (seem to?) reject the latter rather than the former?
Comment #10 February 6th, 2016 at 3:22 pm
Matt #9: Excellent question! I would say: because I feel like I have lots of independent evidence telling me that interventionism is the “right” account of causation. Namely, there are dozens of other examples of “why-questions” that I’ve pondered over the years, and in every case where I’m now satisfied, it’s because I now know either an interventionist answer or at least an interventionist interpretation of the question. Also, interventionism seems like the best way that AI and machine learning and statistics researchers have been able to make progress on explanation and causation.
By contrast, I have no independent evidence that there should be a reason why the universe exists, if the best account I know of “reasons why” tells me the notion of such a reason is incoherent.
Comment #11 February 6th, 2016 at 4:03 pm
@Prof. Aaronson – thank you very much for your thoughtful reply! Some follow-ups: are there any “why-questions” for which the interventionist framework is inapposite? If interventionism relates to issues of causation, then this question might boil down to “are there any non-causal ‘why-questions’?”. And, if the answer is yes, could the contradiction that arises with respect to the question “why does anything exist?” result from the background assumption that the question is to be answered in terms of cause and effect? In other words, might a category error be lurking in the wings?
Comment #12 February 6th, 2016 at 4:09 pm
I think that I have had this exact same thought. It is what motivated me to transcribe Richard Feynman answering a why question by refusing to answer it and instead talking about why questions: http://lesswrong.com/r/discussion/lw/99c/transcript_richard_feynman_on_why_questions/
And I don’t know how to communicate it.
One way to break down “why” is causal origins versus justifications. If someone you love dies, you can know perfectly well the causes for it, and know that you know them, and find yourself unable to stop asking “why, why is the world like this” because it feels so arbitrary.
But these two types of “why” aren’t a factual question versus an emotional one. Things can have purposes. I think that’s why Aristotle included a fourth “cause”, the telos. When people wonder whence cometh something, sometimes they are satisfied when they know the thing’s purpose. And sometimes they can’t be satisfied, if the thing never had any purpose.
Comment #13 February 6th, 2016 at 4:15 pm
It seems to me that either (1) the all-encompassing causal network that produces the things we experience is acyclic, i.e. the concept of causality breaks down if we just go far enough up the tree of causalities, or (2) the network is cyclic (then the reason why the universe exists is because it causes itself), or (3) the network is infinite, i.e. the first cause is undetermined (which is similar to, if not the same as 2).
Comment #14 February 6th, 2016 at 4:18 pm
Matt #11: To my current way of thinking, asking whether there are any “why” questions with non-interventionist answers, is like asking whether there are “when” questions with non-temporal answers, or “where” questions with non-location answers!
I.e., sure, you can always decline to answer a question, or deflect it with humor, or try to convince the questioner that it’s meaningless, or do like a US presidential candidate and say “let me round your question to one for which I have a rehearsed answer,” or countless other responses.
But still, it seems to me, a why-question is asking for a causal lever in exactly the same sense that a when-question is asking for a time.
If you disagree, do you have a proposed counterexample—hopefully more down-to-earth than why the universe exists?
Comment #15 February 6th, 2016 at 5:30 pm
Would it be improper to answer a why question retrocausally/telically? Why do we have to assume that causes are moving only one way temporally? Sometimes retrocausal answers to why questions can be more satisfying than alternatives for some psychologies: Why did loving wonderful x have to die? To enable for some even more loving wonderful x’ to be born somewhere else.
Comment #16 February 6th, 2016 at 5:39 pm
@Prof. Aaronson – I don’t necessarily disagree, but for Socratic purposes I’m going to act as if I do :).
As for a counterexample (though not a particularly down-to-earth one), how about “why is interventionism true?”? I suspect that this can’t be satisfyingly answered in terms of interventionism, since such a response would presuppose the very thing it’s supposed to be accounting for.
Of course, any theory of justification is probably vulnerable on just these groungs, if indeed this really amounts to a vulnerability and not just an unsound commingling of object-level and meta-level discourse. Nonetheless, this looks like a counterexample – a “why-question” that can’t be answered by recourse to interventionism (although perhaps because it simply can’t be answered, full stop).
Relatedly, I took a course on Kant’s Critique of Pure Reason as an undergraduate in which the professor argued, essentially, that Kant thought that the question of existence is more like the question “why is interventionism true?” than, say, “why is the sky blue?”. On the professor’s interpretation, Kant was arguing that existence, rather than something that can be judged according to the epistemic rules we might use to judge questions like “why does water turn solid below a certain temperature?”, instead forms the ground that makes such judgments possible in the first instance. Attempting to answer the question of existence is therefore self-defeating for basically the same reason as attemping to answer the question “why is interventionism true?”: any answer must presuppose exactly the thing it’s supposed to be justifying.
Comment #17 February 6th, 2016 at 6:01 pm
In your view of the interventionist interpretation of causality, is causality in the map or the territory?
Comment #18 February 6th, 2016 at 6:30 pm
Matt #16: For me, “Why is interventionism true?” is not a question about the world, but more like a practical or moral question—it’s equivalent to “Why should we interpret why-questions in interventionist terms?” And I can give what I think are perfectly good interventionist answers to the latter question! E.g., by talking about all the nonsense we’re liable to fall into if we interpret why-questions some other way. 😉
Comment #19 February 6th, 2016 at 6:37 pm
Douglas #17: I don’t really understand what that question means. I.e., when I try to imagine a world where “causality is part of the objective structure of reality,” and a second world where “causality is just something we use to understand the objective structure of reality,” I can’t figure out how the worlds differ. Same thing with the century-old debate about whether quantum states are “part of the map or part of the territory.”
Or, to put it in a more Zen way for you to chew on:
For me, the distinction between “map” and “territory” is part of the map, not the territory.
[gong sound]
Comment #20 February 6th, 2016 at 6:42 pm
So what about the idea that He is so powerful that He can create the universe even if He does not exist?
Comment #21 February 6th, 2016 at 8:16 pm
wolfgang #20: LOL, that’s a new (to me) twist on the Ontological Argument. Instead of God being so perfect that He has to exist, call Him so perfect that He can do whatever a God needs to do without even existing!
Comment #22 February 6th, 2016 at 8:21 pm
If you can only imagine one possibility, it might be because the two hypotheses are the same, but it might be because one of them is false.
Comment #23 February 6th, 2016 at 8:31 pm
Relevant xkcd:
https://xkcd.com/1505/
Comment #24 February 6th, 2016 at 9:21 pm
This raises a related issue: does focusing on interventionist notions of “why” help us understand the thorny questions of when to accept anthropic explanations?
Comment #25 February 6th, 2016 at 9:44 pm
Joshua #24: I would say, emphatically yes! Either an anthropic explanation gives me new insight about the causal levers underneath my “why” question (e.g., the mechanics of the eternal inflation process that causes the apparent laws of physics to vary from one Big Bang to another, or what-have-you), or else I can’t see that it’s doing the kind of explanatory work we want in science. At best, such an “explanation” is telling me about simple mathematical levers that I could pull: e.g., whether to multiply my naïve prior by (what I take to be) the number of conscious beings in existence when I try to apply Bayes’ Theorem. Or more likely, the explanation is simply telling me (rightly or wrongly) that I shouldn’t bother to look for causal levers—because the only levers I could pull to make explanandum false, would also cause me never to have existed to ask the question in the first place. It’s like the 404 Not Found of explanations.
Comment #26 February 6th, 2016 at 10:54 pm
Scott, your ‘For me, the distinction between “map” and “territory” is part of the map, not the territory’ is awfully close to Shminux’s ‘It’s models all the way down,’ but I get the sense that for you it is a flip cop-out and you aren’t seriously endorsing the position the way Shminux seems to be.
Comment #27 February 7th, 2016 at 1:34 am
I always liked the answer provided in the Hitchhiker’s Guide to the Galaxy:
Comment #28 February 7th, 2016 at 1:42 am
I’d think it hinges on the definition of the word “universe”. If our universe is a sim running on some extrauniversal computer, then the causal level that causes our universe to exist is the execution of the program.
Seems to me vaguely anthropocentric to think our universe is the only one that exists, or that there is any causal connection between them.
Comment #29 February 7th, 2016 at 2:03 am
I bet that, if we were to discover why the Universe exists, we’d find it has nothing to do with us.
And we might find it to be very uninteresting. Or absurd.
I already know how i would react to that knowledge, so it’s pointless information.
I wouldn’t want to know anyway.
Comment #30 February 7th, 2016 at 2:55 am
Darrell #28: For this question, I’m interpreting the word “universe” to mean the totality of what exists, including anything before or outside our Big Bang, any computer simulating our Big Bang, etc. And the question I’m trying to dissolve is why that exists.
Comment #31 February 7th, 2016 at 6:16 am
The best answer is that of Spinoza, in his “Ethica more geometrico…”, and in the concept of “causa sui”. Universe and God are the same and It is caused by itself. We can’t go farther with our logic or mind or whatever. On the contrary there is only an infinite chain of causes (or whys) we can think of. And like in physics infinite is a bad answer.
My 2 cents.
Comment #32 February 7th, 2016 at 7:30 am
Here’s a question that always gives me headaches: let’s say we computer scientists hold the key to the answer, and the universe turns out to be a fully computational, deterministic process. For instance, we discover that if you take the Mandelbrot set and transform it in a certain you get a perfect 4D image of our own universe (with uncomputability taking care of quantum mechanics and paradoxes of predicting the future by studying the set).
In other words, there exists some tiny, elegant Turing machine, with an empty tape, which, when run, simulates the entire universe.
The question is: do we still need to assume that somebody (God) is running this program? Since all that is and will be is defined by this one program, including our thoughts and feelings from moment to moment, do we really need someone to actually crank the TM in some higher meta-universe, or is the existence of such a description enough to cause us to exist?
Comment #33 February 7th, 2016 at 7:38 am
I’ve given this some that and come to belief that there are some higher level logical or mathematical truths which put constraints on what can exist. For example internal self-consistency and pi being always about 3, assuming the appropriate axioms. Those ideas exist even outside the universe – they are elements of truth.
Perhaps the physical universe is the only self-consistent expression of those truths. Non-Existence cannot exist since that would be inconsistent. We can have a vague idea of that it is, but that idea can never be manifested physically like true ideas.
A little bit of evidence for this belief comes from recent paper which claims that if we assume (1) our division of the universe into subsystems is arbitrary and (2) information must be recorded by a change, QM is the only way to model that universe. (http://www.ijqf.org/wps/wp-content/uploads/2015/10/IJQF-3093.pdf)
Comment #34 February 7th, 2016 at 8:44 am
I like Sidney Morgenbesser’s supposed answer to (basically) this question:
If there were nothing, you’d still be complaining!
Comment #35 February 7th, 2016 at 8:53 am
Devin #33: There are clearly other possible universes, dramatically different from ours, that are also mathematically self-consistent. For example, what about Conway’s Game of Life? Why shouldn’t our world have followed those laws?
There have been several arguments over the past ~15 years that you can “derive” quantum mechanics from simple postulates, with perhaps the most famous being those of Lucien Hardy and Chiribella et al. I’m not familiar with the particular argument you cite, but I’d strongly advise you to “read the fine print” on any of them. The danger is that such an argument relies on verbal postulates sound good to the reader, but that actually, as the author deploys them, have very non-obvious mathematical content that was designed with the specific goal of getting QM out the other end.
Comment #36 February 7th, 2016 at 9:08 am
I don’t find the interventionist answer to “Why is this theorem true?” at all satisfying. If the theorem is of the form [If hypotheses then conclusion], saying that the result may fail if we change the hypotheses strikes me as missing the point. It seems to amount to “Because we could have mis-stated the theorem but we didn’t.”
Surely the usual answer to “Why is this theorem true?” is “Because [proof]”.
Comment #37 February 7th, 2016 at 9:32 am
Richard #36: No, “[proof]” is the answer to “What is the proof of this theorem?”
For me, anyway, a useful answer to “Why is this theorem true?” is a much more conceptual discussion around the proof—and any such discussion had better include a detailed examination of the hypotheses, and why the proof depends on them, and what happens if you drop them.
There are a few math textbooks and lecturers who understand this, but I really wish more did! If they had, maybe I would’ve been a math major rather than a CS major.
(Hark! Have I just given an interventionist explanation for why I ended up majoring in CS? 🙂 )
Comment #38 February 7th, 2016 at 10:15 am
I wouldn’t be very surprised if future historians will look back at our time and find the popularity of one directional narratives as basis for answering why questions posed to what may be event clouds somewhat notable.
Is it rational to assume the necessity of one directional descriptions of cloud evolutions to resolve why questions? Is it enough? Cannot clouds be ascribed any description that is either causal (forward in time), retrocausal (backward in time), coherent (bidirectional)?
I see some utility in relating to us as in the subconscious habitual role of the narrator selecting preferred description algorithms thus instantiating coherent networks within clouds and so attributing a narrative as if it would be a property of the general cloud since that is the best we can do unless we consider ourselves the cloud.
All my experiences (as I remember them) only tells me that prior events (as I remember them) are clearly coherent with current events (as I remember them) and current event (as I remember them) are clearly coherent with prior events (as I remember them) as well as current events (as I remember them) are expected to be coherent with future events (as I imagine them to be) and future events (as I imagine them to be) are expected to be coherent with current events (as I remember them).
This exercise tells me that everything my sensors, database, and eco-/algorithms produces seems to be coherent for me (which is clearly a necessity for me to consider myself sane and probably fit for life). But is this individual coherence a general property of the greater Universe or just a useful attribute I assign to it by means of my very personal dynamically coherent map of it that I embody and live? Might we not be like dynamically self-propagating filters in clouds that seek sustain networks of coherent meaning, somewhat like one half of the final message in some visual cryptography schemes, where the other half is purely random but the other is seeking to be simply approximately inversely random?
See http://www.datagenetics.com/blog/november32013/
The Universe might as far as I care be completely random globally, but our local universes need not be. It would not surprise me if we would be considered instantiating perceptually the very meaning in our universes we might seek attain from the Universe.
When we seemingly learn (read: let program ourselves) something about the Universe that seems to enable us to develop capabilities to interact with our universe more efficiently and query the Universe ever more profoundly interesting questions (building on previous query links in our memories) to develop ever more capabilities to extracting and decoding meaning from it.
It seems it is us who change with the programming we approve of and so with it our universe. The Universe might still be a random event cloud, but that needn’t be so bad as we seem to become ever capable of tuning and transforming our filters ever faster into a larger and more instrumental, meaningful and coherent universe by attaining increased efficiency and complexity in our descriptions of it with more intelligent use of fixed resources so that we are capable of more with less. (A type of evolutionary coherence compression algorithm).
Also, who says that the Universe of events must conform even approximately to a relational structure such as our nervous system? Are there any known data structures that cannot be coded by any relational/graph structure in arbitrary dimensions efficiently?
Might it not be so that the Universe answers as we ask it? If we provide the Universe a query assuming a relational structure that the Universe simply complies to provide a relational response, not because its nature is even approximately relational but because the query was relational and it inversely provided a relational counter pattern as that is the nature of the interaction? But if we could query the Universe some (more “powerful”?) non-relational query, then might the Universe might provide a non-relational counter pattern response? I have no idea what that would mean operationally in a measurable sense, but I hope someone more competent than I would someday either prove or try prove this query complete nonsense or at least give me some more insight in what it would mean practically.
So why seem neither retrocausal or coherent descriptions equally popular in some how come/why questions? Is it because we feel we cannot confidently justify them by means of simply pointing to our databases or by applying any algorithm to extrapolate from such since our certainty of future events is by definition <100%?
Would this apprehension still exist if we all lived in a world where coherent or retrocausal narratives were the norm and everyone simply assumed that ever more complete resolutions of some why queries would continuously follow later as more data and analysis becomes available although we have capacity to provide partial answer here and now? Isn't that somewhat the more scientific way of relating to the world of knowledge?
It seems the biggest and deepest fundamental questions require the largest descriptive coherence to be meaningful and produce ultimate satisfaction. Not just causal descriptions, but symmetrically retrocausal and coherent such.
Finally, I have noticed that it has been very fruitful to approach the Universe as it would be a crypto game, where this Universe is feeding constant multichannel bitstreams of inspiring encrypted messages of ultimate possibilities but our current filters and the following universe is simply the one we are capable coherently decoding, instantiating and meaningfully realizing due to our current mastery of interacting with the random patterns it provides.
I see no reason to believe there aren't much more to be decoded. Retrocausal and coherent descriptions will probably play some part in it.
Comment #39 February 7th, 2016 at 12:13 pm
A quibble: 5 does not admit nontrivial factorisations over $latex Z[\sqrt{2}]$. That ring is a Eclidean domain and hence a unique factorisation domain. The factorisations are trivial in that one of the factors has to be a unit. In the same way that $latex 5 = -1 \times -5$ is a trivial factorisation, so is $latex 5 = (5+ 5\sqrt{2}) \times (-1 + \sqrt{2})$.
Comment #40 February 7th, 2016 at 12:14 pm
Peter #32,
If that was found for the Mandelbrot set, what aspect of this finding would you consider different from what we can already demonstrate for Champernowne’s number?
Comment #41 February 7th, 2016 at 12:24 pm
@Scott#37 >For me, anyway, a useful answer to “Why is this theorem true?” is a much more conceptual discussion around the proof
Sure – and that had occurred to me too – but I think there’s a distinction answer between a _useful_ answer and the _correct_ answer. If I’m struggling to understand a new topic and ask an expert “why is this theorem true?”, what I’m really asking is “can you help me understand the proof?”, i.e. please show me an overview, point me to the key steps and ideas, and explain why certain hypotheses are made, etc.. Once I’ve become an expert myself, all of that gets incorporated into the proof as I understand it.
Having said all of which, there here is some merit to the idea that “why” demands an account of a theorem’s hypotheses. Suppose I prove a theorem under the assumption of the Axiom of Choice. My answer to “why” would include “because choice”. But that might be wrong – maybe tomorrow some bright spark shows that choice can be dropped. In that case my proof was right but my “why” was wrong.
I suppose if you take this view then the question of why mathematical theorems hold receives its ultimate answer in the subject of Reverse Maths.
Comment #42 February 7th, 2016 at 12:43 pm
Tom #39: Thanks for the correction! So then, can someone give me a ring in which 5 does admit a factorization into two non-units (if such exists)? If so I’ll gladly update the post.
(Broader question: is there a characterization of which integers are composite in some algebraic extension ring?)
Comment #43 February 7th, 2016 at 1:03 pm
Richard #41: What I should’ve said—and what might synthesize what you’re saying with what I’m saying—is that understanding why a theorem is true means building up a mental model in your head of the gears and levers of a machine that inputs the hypotheses and outputs the theorem statement. Which is precisely what the interventionist account says that understanding anything means! I.e., “pull back the curtain for me; show me some of the causal gears and levers that produce the phenomenon I asked about. I’ll know that those are the right gears and levers if, by mucking with them, I could change the phenomenon or prevent it.”
Of course, if removing a hypothesis would make a theorem false or plausibly false, then understanding that is a central part of understanding “why” the theorem is true. But even if the theorem would still hold without the hypothesis, if the only known proof makes essential use of the hypothesis, then the hypothesis is still a lever in the machine that we need to understand.
Here’s an analogy: it might be perfectly accurate to say that you got sick because you caught it from your friend, even if something more general happens to be true, and the disease is so prevalent that you still would’ve caught it even had your friend been nowhere in the vicinity. Likewise, in your example, if you understand why a theorem holds under AC, then at least you understand why shutting off the AC lever is a prerequisite to making the theorem false. There might turn out to be additional levers that you also need to flip, but you can start with that one.
(Incidentally, is this the first time “shutting off the AC” has referred to the Axiom of Choice? 🙂 )
Comment #44 February 7th, 2016 at 1:45 pm
Well, in $latex \mathbb{Z}[i]$, $latex 5$ breaks as $latex 2-i$ and $latex 2+i$, both primes.
Add me to the list of people who do not think the interventionist idea works for answering why-questions about theorems.
I think whenever a mathematician really understands why a theorem is true and he opens his mouth to say it, to his surprise, it is a ‘proof’ that comes out. And I can’t think to do any better he has to be able to vocalize certain sensorimotor facts, which are simply not available to him (our evolutionary history didn’t think it important to give human languages this capacity).
Comment #45 February 7th, 2016 at 2:01 pm
Thanks for the correction! So then, can someone give me a ring in which 5 does admit a factorization into two non-units (if such exists)? If so I’ll gladly update the post.
(Broader question: is there a characterization of which integers are composite in some algebraic extension ring?)
For the first, take Z[\theta] with theta= (1+5^(1/2))/2 For the second, every rational integer n other than 0,1 and -1 will be composite in the ring of integers of Q(n^(1/2) ).
Comment #46 February 7th, 2016 at 2:33 pm
Joshua #45: Thanks (bangs forehead on desk). And if we want n to be composite but not a perfect square?
Comment #47 February 7th, 2016 at 2:38 pm
Is it just me or does Tom’s comment not really make sense? All the statements in it are true, but it seems to be suggesting a statement that is not true. It’s correct that Z[√2] is a Euclidean domain and hence a UFD; that 5 does stay prime in Z[√2]; and that the listed “factorization” of 5 in it is actually trivial because you’re just multiplying by a unit — but the comment reads to me as suggesting that Z[√2] being a UFD somehow entails that 5 stays prime in it, which is of course not corect. For instance, to reuse sntx’s example, Z[i] is a Euclidean domain (and hence UFD), but 5 doesn’t stay prime in Z[i]; it factors as (1+2i)(1-2i).
Comment #48 February 7th, 2016 at 2:39 pm
Scott @46,
I suspect that doing the same thing with taking a cube root of n would work but I haven’t checked. Extensions created by taking a cube root can be weird (partially because the corresponding field isn’t well behaved).
You should also be able to do so with appropriate other quadratic extensions but you may need to think a small amount to make sure you didn’t end up with a trivial factorization.
Comment #49 February 7th, 2016 at 2:55 pm
Scott #42. No problem. In fact my correction is sort of wrong: 5 happens to be irreducible in the ring Z[2^(1/2)], so it doesn’t have a non-trivial factorisation. The fact that Z[2^(1/2)] is a unique factorisation domain is irrelevant, except in showing that even if 5 wasn’t irreducible in this ring, any factorisation would be unique (up to units).
Comment #50 February 7th, 2016 at 3:05 pm
Scott #46: For n other than ±2 (and of course other than 0 and ±1, for which there’s nothing you can do), you can take R=Z[√(n+1)], and factor n as (√(n+1)+1)(√(n+1)-1). Now, n+1 might not be squarefree; it might even be a square, so that R=Z. But (so long as n is not 0 or ±1) this will be a nontrivial factorization, and, so long as n≠±2, the two factors won’t be related by a unit.
That leaves the case of n=±2, but I’m hoping it shouldn’t be hard to find examples to cover that case…
Comment #51 February 7th, 2016 at 3:34 pm
Jay #40: That’s a good point. There are many small Turing machines whose output _contains_ the universe (infinitely often, at all levels of accuracy. I suppose I was trying to sketch a situation, where we find a super-elegant description of the universe. Something that shows that it has low Kolmogorov complexity, if you will. A single program that is so small, and describes only the universe and nothing else, that we can only conclude, that this is what we are: some entity is running this program which is causing us to “be”.
The next step is the realization that we don’t actually need an entity to run the program, our existence is determined by the program.
Basically, the whole thing shows us how pointless it is to try to reason about things outside the universe. If god has the program for the universe, it doesn’t matter if he runs it or not, our existence is determined by the program existing. And then, maybe God didn’t come up with the program, but he still might’ve. It still exists in the mathematical sense.
And then, even if the universe isn’t compressible at all, or very elegantly. There’s still some Turing machine that produces it. And that’s what questions like “why do we exist” try to do: they ask about things in this domain: outside our universe. Why did someone pull the lever that caused our universe to exist? But then if he hadn’t, our existence would still have been “encoded” in the action of pulling the lever, and we wouldn’t feel the difference.
Comment #52 February 7th, 2016 at 3:55 pm
@Sniffjoy
I think the thing is whereas \mathbb{Z}[\sqrt{2}] has class number 1 just like the Gaussian integers, it also has, like any other ring of integers inside a real quadratic number field, an infinite number of units.
Comment #53 February 7th, 2016 at 3:58 pm
Sniffnoy #47 Yes, I mixed up unique factorisation with 5 having a non-trivial factorisation at all. Of course since 5 is irreducible in the ring, and the ring is a UFD, the trivial factorisation of 5 is the only one. But 5 is irreducible so no non-trivial factorisation is a given!
Luckily for me, 5 was still irreducible in the ring so nothing I said was false. If Scott had chosen Z[i] I’d have been wrong, as you say.
Comment #54 February 7th, 2016 at 5:08 pm
Josh: Actually I don’t think it’s too hard to show that Z[³√n] works in general (assuming of course we count this as Z when n is a cube). Just look at the norm.
So that settles that question… but if you want n to factor in a manner that isn’t a perfect power, that still leaves the case of ±2, like above.
Note: Since we might not be looking at UFDs, it’s not immediately obvious to me whether “n factors in a manner that isn’t a perfect power” is the same thing as “n factors, and is not a perfect power” or whether it’s weaker. I actually only just realized I made that mistake when I talked about Z[√(n+1)] above — I only checked that the given factorization of n isn’t writing it as a square, not that there’s no way to do so. But — correct me if I’m wrong — I’m pretty sure that (unless n is ±2) (possibly passing to the ring of integers rather than sticking to Z[√(n+1)]) the discriminant rules that out, so yay.
Comment #55 February 7th, 2016 at 7:39 pm
OK — I’ve managed to do it for 2 and -2 as well now. Each can be done by passing to Z[(1+√17)/2]. There, 2 factors as
(14+½+(3+½)√17)(14+½-(3+½)√17),
while -2 factors as
(18+½+(4+½)√17)(18+½-(4+½)√17).
So for n other than ±2, you can do it by passing to Z[√(n+1)], while for n=±2, you can do it by passing to Z[√17]. (Excluding n=0 or ±1, of course.)
Comment #56 February 7th, 2016 at 9:22 pm
Has anyone here ever read the essay “Why Anything? Why This?” by Derek Parfit? It’s the best explanation/hypothesis of why this particular reality exists that I’ve ever come across, and I’m surprised that no one has mentioned it. Here’s the link to the essay: http://www.sfu.ca/~rpyke/cafe/parfit.pdf
Comment #57 February 7th, 2016 at 9:55 pm
Existential questions like these seem to be meaningful only for subsystems of the universe (under a suitable definition of “universe”), since your definition of “universe” provides you with the raw materials/ingredients with which you can probe the existence (or question the existence!) of a subsystem.
So, e.g., what if I put a gun to your head and asked you to answer the question “Why is a theorem true?”, but told you that the concept of complex numbers is not available to you? You will probably shout back at me saying how I could possibly even make sense of that question after taking away the ingredients of what makes that theorem falsifiable!
I am not sure asking the same question of the entire universe makes sense, unless you can suitably, consistently define the universe to be a subsystem of a suitably defined “superverse” (whatever that means).
Comment #58 February 8th, 2016 at 12:22 am
“But then I thought about it some more, and it seemed inappropriate to me that my considered statement about why the universe exists should only be available as part of a comment thread on my blog.”
This reminds me a little of why I always found Hilbert’s sixth problem somewhat amusing. Who else would put the task of axiomatizing physics as the sixth item in their 23 point to-do list?
Comment #59 February 8th, 2016 at 12:31 am
Nooo Scott!! What did you do to the blog’s website?? The beautiful Shtetl picture and the complexity classes are gone! This was part of history and you wiped it away! Please: reconsider!! 😉 K.
Comment #60 February 8th, 2016 at 1:04 am
Peter 3:34,
If you haven’t read it already, you’ll most likely enjoy this:
http://gregegan.customer.netspace.net.au/PERMUTATION/FAQ/FAQ.html
Comment #61 February 8th, 2016 at 1:44 am
I couldn’t help but notice you managed to skip over the question of whether the universe exists at all (is reality really real?) to asking why that is. progress!
Comment #62 February 8th, 2016 at 8:05 am
anon #59: It wasn’t me, I swear! Every time WordPress automatically updates to a new version, the theme reverts to the default one. But I saved a backup copy of the theme you know and love so that I can easily switch back.
Comment #63 February 8th, 2016 at 9:47 am
Jay #60: Cool concept… I’ll definitely read it.
Comment #64 February 8th, 2016 at 11:11 am
Great, thanks Scott (#62)! I think your blog headline is really iconic.
Comment #65 February 8th, 2016 at 12:09 pm
Is there really a fundamental qualitative difference between what we call a dream and what we call reality?
I.e. could reality be a “super” dream?
The quantitative differences are:
– the degree of logical/self-consistency in dreams.
– the degree of hidden(unconscious) resources necessary to generate the “scenarios” of the dream world (e.g. instantiate the illusion of other sentient beings). If you can dream a complex physics experiment (or a computer solving a tough NP-hard problem), your “brain” has to come up with the necessary resources, but so does the real universe.
I guess it all boils down to saying that if you have enough computing resources to fully simulate a closed physical system (from the outside), the simulation and the “real” system are by definition equivalent for a consciousness that’s “inside” them (part of the simulation)?
Comment #66 February 8th, 2016 at 5:26 pm
Fred #65
Two favorite quotes:
“…there is nothing more real than dream. This statement only makes sense once it is understood that normal waking life is as unreal as dream, and in exactly the same way.” – Tenzin Wangyal Rinpoche in The Tibetan Yogas of Dream and Sleep
“… do not alter the reality of the dream; do not divorce the magic of the story or the vitality of the myth. Do not forget that rivers can exist without water but not without shores. Believe me reality means nothing unless we can verify it in dreams.”- Don Manuel Cordova (Ino Moxo) speaking in Cesar Calvo’s The Three Halves of Ino Moxo.
Comment #67 February 8th, 2016 at 5:46 pm
fred:
In recent years, in dreams, I am often aware that I am dreaming, which sometimes wakes me up, so I remember it.
Related observation. I am kind of addicted to reading, and anything with writing on it grabs my attention and I try to read it, even if upside down, etc. When dreaming, I sometimes see a book or newspaper, and try harder and harder to read it. But there is never anything that I can make out, and I wake up from the frustration of not being able to read it. This makes me wonder if there is some incompatibility between reading and dreaming.
This happen to anyone else?
Comment #68 February 8th, 2016 at 6:18 pm
If you want k to have lots of factors, it is enough to make a prime factor have lots of factors. So we might as well assume k is prime.
In the ring Z[ζ_pⁿ], p factors into many factors, growing with n. But it’s almost all repetition. If q is a different prime, then in Z[ζ_qⁿ] p factors into lots of factors with little repetition (each factor is repeated < q times, but the number of factors grows with n). Following Sniffnoy, I think that if you take any square-free number n congruent to 1 mod p (p not 2), then p factors into two distinct factors in Z[√m]; and if m₁, m₂… are a bunch of such numbers, then p factors into many factors in Z[√m₁,√m₂,…]. I think that gives the maximum number of factors, 2ⁿ. (You probably want the m's to be coprime, which might take some work. Ideally prime, but that's a lot of work.)
I think that's all true without concern about the ideal class group, but such problems can be solved by adding 1/N to the ring.
Comment #69 February 8th, 2016 at 7:33 pm
Cough…
This answer can be quoted pretty much verbatim when answering the question: “Why does the Omnipotent Being, a.k.a. God Almighty, exists?”
… And then we come to the question of why anything exists. For an interventionist, this translates into: what causal lever could have been pulled in order to make [omnipotent being not exist]? Well, whatever lever it was, presumably the lever itself was [an omnipotent being] — and so you see the problem right there.
Comment #70 February 8th, 2016 at 7:49 pm
Dreams don’t have the bandwidth of reality because all sensory input has to to simulated by the sleeping brain and it doesn’t have the capacity. That’s why you can’t read books (except for a few words) and can’t touch or taste anything. The brain devotes a lot of its capacity to visual input so that’s what we get in dreams. To dream a complete reality your brain would have to have the local computing capacity of reality, and it doesn’t. Or so I think.
Comment #71 February 8th, 2016 at 8:24 pm
To appreciate the vast STEAM-power that Scott’s suggestion generates, it is helpful to consider a concrete proposition, namely X = “The quantum metrology triangles of the Systeme Internationale can be physically realized with exponentially small error, and can be computationally simulated to any physically realizable error with PTIME resources.”
Or to strengthen the proposition, X = “For any finite laboratory temperature, in the limit of vanishing measurement error, the entropic cost of computationally simulating an SI measurement process is equal to the entropic cost of conducting the measurement.”
It’s fun to see how naturally this “X-postulate” generates the great themes of quantum mechanics and geometric mechanics. Grothendieck’s celebrated question “What is a metre?” inspires us to conceive interferometers; the quest for stable wavelengths inspires us to conceive lasers; stable lasers (and masers) answer the question “What is a second?”; with metres and seconds in-hand we observe the trajectories of (conserved) masses and (conserved) charges, so that the questions “What is a kilogram?” and “What is a coulomb?” receive answers, the coupling of magnetic fields yields answers to “What is a tesla?”; with Josephson junctions and the integer quantum Hall effect we close metrology triangles by answering questions like “What is a volt?” and “What is an ohm?”.
Finally (and most mysteriously) the practical need to conduct experiments deep in a gravity well in an accelerated frame-of-reference forces us to scrupulously account for general relativistic effects (at the classical level).
The ability to efficiently simulate these experiments is (at it seems to me) equally miraculous to the ability to accurately conduct, and here Scott’s question ‘What could we have changed in order to make X false?’ receives a natural answer, namely: “The (strictly restricted) set of Hamiltonian functions that nature provides is naturally matched to the (strictly algebraic) state-spaces that geometric mechanics requires for efficient simulation, such that neither can be altered without falsifying ‘Postulate X’.”
Conclusion The rising tide of textbooks on this topic — e.g. Doran and Lasenby’s Geometric Algebra for Physicists (2003), and Holm, Schmah and Stoica’s Geometric Mechanics and Symmetry: from Finite to Infinite Dimensions (2009) … and there are many more — helps us to perceive an abundance of practical 21st century STEAM-implications that flower naturally from Grothendieck’s quasi-philosophical question “What is a metre?”
Open questions Is Nature mindful of the Postulate X’s link of privileged Hamiltonian functions to privileged algebraic geometries? Or are these computational/experimental associations mere fortuitous accidents, of interest mainly to experimental physicists and engineers?
These are the sorts of questions regarding which, in Mark Twain’s phrase, “It were not best that we should all think alike.”
Comment #72 February 8th, 2016 at 9:29 pm
Raoul #67, what you report happens also with me, with the exception that sometimes I actually can read a word or two, but then if I try to re- read it, it has changed, and this always wakes me up.
Comment #73 February 9th, 2016 at 6:58 am
JimV #70
So where does that leave experiences with hallucinogens like DMT and ayahuasca?
The brain is capable of generating a complete reality that actually seems more real than normal reality. Researchers have actually found the same neural circuits activated that are used in normal vision.
https://www.newscientist.com/article/dn20978-drug-hallucinations-look-real-in-the-brain
Similar experiences in sensory deprivation and near death experiences.
Comment #74 February 9th, 2016 at 8:26 am
“Listen to the noise …” is a practical maxim of high-precision engineering. To measure a resistance, observe its Johnson noise. To calibrate a micro-cantilever, observe its Brownian motion.
Fancy instruments aren’t needed. When we are sleeping uneasily with the flu, and we cough at night, then if there is a piano in the room, we hear each string excited in sympathy with our coughs; the presence of the piano has altered the acoustic vacuum of the room, and hence our noisy coughs elicit hear all the chords that the piano can play.
Similarly in advLIGO (which has a major announcement coming this Thursday!) the outgoing photons carry in their spectral fluctuations a complete picture of the dynamics of the suspended test-masses. “Onsager’s Regression Hypothesis” is the fancy name that quantum physicists give to this exceedingly useful dynamical principle.
So fundamental a principle finds reflections too in psychology and sociology. In sleep our sympathetic neurons fire like piano strings, each excited by the noise of all the others; we experience the emergent chords as dreams. Similarly in the silence of unprogrammed worship, Friends are deliberately mindful of random settling thoughts, which provide a LIGO-style portrait of the sympathetic connectome of the spirit.
Conclusion One reason to study quantum dynamics (not the only reason, to be sure) is to discern in Lars Onsager’s mathematical physics a beautifully natural grounding for Pessoa’s principle, which is Freud’s principle too, that in unprogrammed dreams and mindful silence, “our hidden orchestras reveal themselves.”
An open question Perhaps the “Big Bang” might aptly be renamed the “Big Cough”?
Comment #75 February 9th, 2016 at 9:44 am
Raoul #67
Definitely happens to me.
It’s often related/triggered by some programming problem I’m dealing with at work.
But, within the dream, the problem appears “mutated” or “dumbed down”, as some sort of puzzle using symbols.
Within the dream it’s as if I have no medium term memory – I can only hold on to the last 20-ish seconds (or a couple of minutes at the most), so it’s very hard to deal with anything that requires time coherence (like reading or puzzle solving).
It doesn’t usually wake me up but makes me very frustrated within the dream, and then I eventually wake up feeling exhausted.
Once I actually experienced something similar in real life.
I was in the office, working on some very familiar code base I had written over the last few months.
Suddenly I felt like waves of “deja vu” feelings washing over me, the feeling you get from suddenly remembering some dream you had forgotten, but as a constant stream rather than some fleeting sensation.
And at the same time the code I was working on suddenly felt totally unfamiliar – no matter how much I stared at it, I couldn’t recognize the file names, I couldn’t remember how it all fit together… It felt like I was in a dream!
I joked with colleagues that I was probably experiencing some sort of seizure and I headed home, but those strange sensations kept coming on and off. In the subway it felt so overwhelming that I nearly lost consciousness. Later, in the street, I opened my laptop to even check my code, hoping I would now recognize it, but I didn’t. Once I got home I went to bed and after a few hours the symptoms finally had disappeared.
I saw a specialist (and had an MRI done) but he wasn’t sure what happened. He claimed it was a seizure, but I think it must have been more like a brain aneurysm.
For a few months concentrating was very difficult (my head often felt like in cotton, with headaches), but eventually things got back to normal.
Up to that point I’ve always taken for granted my capacity to solve problems and keep complex models in my head to make a living… that ordeal was quite terrifying.
Comment #76 February 9th, 2016 at 11:01 am
JC @ $73: I have never had a drug-induced hallucination so I don’t know, but expect they also do not completely simulate reality and lack some bandwidth, such as a sense of touch.
My only data point is a documentary I saw about a serial killer whose defense was that he was subject to hallucinations. He agreed to relive one of the hallucinations under hypnosis to prove his case and a psychologist who analysed the video tape said the killer was faking because he mimed shaking hands with an illusionary person and in real hallucinations the brain avoids situations which require a sense of touch.
“Researchers have actually found the same neural circuits activated that are used in normal vision.” Of course, this was my conclusion as well in my original post. What other neural circuits would the brain use to simulate sight?
Comment #77 February 9th, 2016 at 5:02 pm
Whenever I encounter a metaphysical question of this sort, I find it more manageable to imagine humanity creating a simulated universe, and then thinking about how residents of that universe might think about this question.
In that case, the answer to their question would be that their universe exists because we decided to simulate it. But I think it would be very difficult for them to work this out unless we told them.
Of course, you can always kick the question up a level and ask why our universe exists, which is the ultimate reason why their universe exists. But that sort of ducks the point of the exercise. The point is that their question ends up being well-defined in the sense that there’s more to the story. So while the question may not have an “ultimate” answer that is completely satisfying, it *does* have an answer that conveys information about their universe. And in fact, it’s a very reasonable question to ask at our level, e.g. “Why did you guys create a universe?”
One possibility is that, if you went up to higher levels above our universe (if such exist), you would reach a level at which the universe is clearly self-existing in some way. I guess this is the classic theist view.
Comment #78 February 9th, 2016 at 6:45 pm
Fred #75, you might be interested in (Fields Medalist) Vladimir Voevodsky’s personal experience of involuntary altered cognition (here Google Translate is a big help).
Needless to say, when it comes to understanding and healing in these matters, humanity is presently in the dark ages. 🙁
Comment #79 February 9th, 2016 at 11:42 pm
I think there’s a reasonable non-interventionist interpretation of “why is 5 prime?”: 5 is prime because “n is prime” means “n has exactly two positive integer factors,” and this can easily be checked case by case. This (and the related “why-questions are answered with proofs” arguments above) is clearly quite different in spirit than the more demanding interventionist standard for answers to why questions.
But my point is that even with the easier standard of “proofs as explanations,” it’s quite hard to explain why the universe exists. It seems metaphysically possible that nothing would exist and the universe would just be the empty universe. Your experience of such a universe would be very similar to your experience of the first 13.82 billion years of our own universe, just without the interesting bits at the end. Any sort of proof that the empty universe is logically or metaphysically impossible would seem very interesting to me, even if it falls short of an interventionist account.
Comment #80 February 10th, 2016 at 9:13 am
In the case of “why is 5 a prime”, the “lever” seems to me to be an abstract concept, so in the case of the universe’s existence must we not also allow levers which are abstract concepts – at least until you prove otherwise? Until then, the question becomes are abstract concepts “something” (as Plato might have argued), or are they not physically real and therefore capable of existing even in a universe of nothingness? I.e., my small brain is stuck on some steps that you may have jumped over as obvious to the student.
(Possible abstract concept candidate: 0 = -1 + 1.)
Comment #81 February 10th, 2016 at 9:44 am
jonathan #77
the problem with “closed” software simulations and digital universes like the game of life is that a computation isn’t really something “physical” when you think about it.
We tend to associate computation with a computer, i.e. a physical closed black box made of “stuff”, the digital equivalent of an organic brain (the Chinese ideograms for “computer” is “electric brain”).
But a computation can just as well be carried by hand, with a big piece of paper and a pencil (emulating the rules of the ALU and memory), or you could use stones on a beach.
The simulation state is really just a big number, and the whole simulation is just characterized by a long sequence of integers (And the sequence of integers can also be transformed arbitrarily by any encoding).
Any scheme is good to “record” the states – you could just use a really long ruler and mark each state with a notch, by counting the number of atoms along the length.
But you don’t even need to record the whole sequence, you just need to acknowledge the current state to derive the next one.
All those schemes are all perfectly equivalent for carrying out a world simulation.
At that point, one wonders, when would the consciousness of the inhabitants of the simulated world be actually realized?
When a sequence of 0s and 1s on the paper? When we carve a notch in a ruler? When we carry out the individual intermediate state updates (all using very simple dumb logical operations of an ALU)?
It seems that the mere existence of the concept of integer is enough to realize any possible simulated universe, passively.
But it’s also the case that an external consciousness (ours) is always needed to kick-start any simulation, regardless of how the simulation is carried out (it could be delegated to non-conscious automatons, like an actual PC).
And maybe this is enough to entangle/link forever the simulation with the consciousness that started it (in the sense of Scott’s theory of how consciousness are unique objects that can be traced back to the initial conditions of our universe). So, the realized consciousness within the simulation would just be indirect “extensions” of the consciousness that started them (through causality)?
Comment #82 February 10th, 2016 at 3:18 pm
Fred:
Good points! Yes, if we take this idea seriously we quickly get into deep metaphysical waters.
But that was sort of the point of my exercise — to step back from the general question and instead envision a particular case within the physics we experience every day.
So suppose we created a physical computer here on earth that simulated a universe, in which conscious beings evolved (or maybe we knew how to program them directly).
Now let’s tackle your comment. As I see it, you’ve posed three questions: (1) does it matter how the computation is implemented? (2) does it matter if the computation is run at all? (3) Isn’t the simulated consciousness just an extension of our own consciousness?
First, does it matter exactly how we implement this simulation? (i.e. silicon, paper and pencil, stones on a beach…). Clearly it doesn’t matter for the actual computation — assuming perfect accuracy, these methods would all calculate the same things, and any intelligent beings would think exactly the same thoughts, at the same (relative) points in time.
Would the beings have the same subjective experience? I have no idea. Certainly if someone (in the simulation) asked them to describe their subjective experience, they would give the same response. That’s just a consequence of the computation. I’m not sure how to answer the question beyond this. Certainly I don’t see how it would make any observable difference in my scenario.
[other two questions answered in next comment]
Comment #83 February 10th, 2016 at 3:20 pm
fred (cont):
Now for your second question — does it matter if we actually carry out the calculation, or is it enough that we *could* carry it out? If this simulated world is just an integer (bit string encoding the world state) on which we are repeatedly performing a mathematical operation, then do we need to actually perform this calculation, or is it enough that this universe exists among possible universes?
My intuition is that we have to actually calculate it. I’m not a Platonist: I don’t think that all possible mathematical calculations actually exist somewhere without something performing them. The beings in the simulation exist when their behavior is actually calculated by some calculator.
But in a sense, existence is relative to the substrate (warning: I’m running into limits of language to express these ideas). What I mean is that a being truly exists within a simulation, since (for instance) that being would exist as an entity in the thought processes of another being within the simulation. Would that being have a separate existence outside the simulation? In a sense — you could make true statements about the world in which you discussed that being. But I’m not sure what it means to say that the being exists at that higher level. Certainly if time passes in the wider world, while the simulation is paused, then that being has no subjective experience during that time.
Going back to my example: if we didn’t actually perform the computation in some sort of computer here on Earth, it’s not clear just where these beings would be, or what form their existence would be. But if we did perform the computation, then we could point to physical things in reality corresponding to every observable fact of their existence. So it seems that performing the computation is necessary.
To your third point: I definitely don’t think that any simulated consciousness would be an extension of our own consciousness. For starters, simulating a universe does not require a conscious or intelligent being. You could just have a non-conscious process that simulates lots of universes until it (by chance) comes upon one that produces conscious beings. But even if the simulation were designed by conscious beings for the express purpose of producing other conscious beings, the simulation would be independent of our own brains. The only case in which I would be comfortable saying that a conscious being was merely an extension of another’s consciousness would be if the simulation took place fully within another conscious being’s brain. (i.e. Scott’s example of the Newcomb’s problem possibly being within Omega’s simulation of him.)
Comment #84 February 11th, 2016 at 1:22 pm
Why is there something rather than nothing?
Because if there were nothing rather than something, there would be, in particular, no reason for anything, and in particular, no reason why there were nothing rather than something, and the question “Why?” would not make sense.
For the question “Why?” to make sense, it is therefore necessary that there be something rather than nothing.
One might go on to ask “Why should the “Why?” question make sense”, implicitly suggesting that it might not make sense, but to ask this latter question presupposes that _it_ (the latter question) makes sense, so that even if the original “Why?” question does not make sense, this new one must do so.
The next (diagonalized) step might be to ask “Why does this question make sense?”, where ‘this question’ is “Why does this question make sense?”, and so on. But even here the asking of the question is tantamount to the presumption of there being something (that is, a reason) rather than nothing.
In short, the reason there is something rather than nothing is that the question is asked. Were there no question, or had it no sense, there might very well be (would be; could be…) no answer and no reason. But, assuming the question does make sense, the necessity of an answer issues forth from the question itself.
Comment #85 February 11th, 2016 at 2:27 pm
Per my seminal work (I kid), I operationalize “why” a bit differently. I take a “why” question as “Integrate this into the rest of my worldmodel so it falls out as an implication rather than being an isolated factoid.” You should (in theory) be able to trace everything back to your primary sense data (though that would be overkill for most purposes).
It’s equivalent to Scott’s, in a sense, because “asking what lever you’d have to change” is striking at the core of your understanding of why things are this way.
There’s a corollary to my definition (also a useful heuristic): you should never change your mind on one thing in isolation — every change should correspond with a more general improvement in your worldmodel. So I tell people: don’t try to convince me of anything! Just improve my worldmodel and that should fall out! If there is no such improvement, the problem might be on your end…
Comment #86 February 12th, 2016 at 10:29 am
Maybe a satisfactory way to answer any “Why?” is to be able to come up with a digital simulation that generates an output “qualitatively” indistinguishable from the simulated system.
I say qualitatively because it’s clear that one can’t simulate fully a system from within itself.
So, you can always answer a “why?” as long as you have some way to carry out a computation.
The question “why is there something instead of nothing?” is reduced to “why can we ask why?”, i.e. “why can we even compute anything at all?” (the actual particulars of reality beyond that isn’t relevant).
“Nothingness” would be any universe where no computation can be carried out?
Comment #87 February 12th, 2016 at 1:14 pm
Out of topic, but I was reading up about that LIGO gravity wave announcement.
What’s mindblowing to me is that they detected distance variations of 10^-18 m over a 4km length.
That’s a 1/10^21 precision.
It’s the equivalent to:
– a hair width over the distance between our sun and Alpha Centauri.
– the Planck length over the size of an electron.
Comment #88 February 16th, 2016 at 9:15 pm
Questions like these tell something important about us, and the underlying mechanism of curiosity, intellect and our fundamental need to know.
These questions are grammatically and semantically correct, tickle our intellect and seem like fundamental, but yield no answer that can satisfy us. If the question fits the pattern of correctly formed fundamental question, we feel the question in our guts and there is feeling that this question is important and needs an answer.
When we look at the whole question, the details fade; When we look for the the details, we find nothing. But there is an itch.
Fortunately people have been thinking these same things for thousands of years. Correctness aside, some answers have aesthetic beauty in them that smooths the mental rash caused by deep question without an answer. For someone it’s prime mover, to me the best lotion is Indra’s Net and the theory of dependent origination. University exists because someone asked the damn question.
Comment #89 February 19th, 2016 at 4:23 am
“Why does the universe exist?”
I need more explanation to be convinced that a “why” question
requires an interventionist interpretation. Still, …
As stated above in different ways, the universe exists because we
are here. I think this is called the anthropic principle. Perhaps that
statement is equivalent to “we are here” becoming the interventionist
“lever”. In other words for the universe to not exist we must not be
here to ask the question.
Really though, why ask “why”?
I wonder why. I wonder why.
I wonder why I wonder.
I wonder why I wonder why I wonder why I wonder!
– Richard Feynman
Comment #90 February 21st, 2016 at 2:50 pm
You should teach a class on anthropic reasoning sometime, maybe write another book eventually.
Comment #91 March 7th, 2016 at 12:22 am
I used to think a lot about this question when I was younger. The answer I finally came up with was so simple it surprised me:
Because we are part of the universe we can only observe that it exists. We would not be able to observe the non-existence of the universe. When the only possible observation is that the universe exists, it must exist.
But why? Simply because we can observe it. Without observing the universe the question of if or why the universe exists would not make sense. Not even the question would exist.
Comment #92 April 1st, 2016 at 6:43 am
Scott’s discussion has become rather abstruse, with the intrusion of advanced maths. I think Comment # 91 probably sums up the most relevant answer to the question as to why the Universe exists. Scott’s oveer-insistence on seeking answers to his “why” questions seems to have considerably reduced the validity of his proposed “interventionist” solutions.
Comment #93 April 26th, 2016 at 4:04 pm
“in an interventionist account of causality, there can’t be a reason for the universe to exist, because that would imply a possible intervention that (if you applied it) would cause nothing to exist or have ever existed,”
The error here is to conflate Subsistent (self-existing) Being, aka God, with contingent being, i.e. the universe. There is a possible intervention that would cause the latter never to have existed: God’s decision not to create it. Conversely, there is a reason for the universe to exist: God’s decision to create it.
Comment #94 April 26th, 2016 at 4:35 pm
Johannes #93: OK, but I don’t acknowledge that there can be a thing that “necessarily exists,” except as a consequence of other things that exist. Mathematical objects have necessary properties, but need not have anything corresponding to them with causal power in or over the physical world.
But even if I granted that God was a “necessary being,” I’d still be unsatisfied with “because God chose to make it” as an explanation for why the universe exists. Like, how did it come about that a necessary being was able to make this contingent choice? Isn’t that kind of like the unique factorization of the integers deciding to create an anteater?
Comment #95 April 26th, 2016 at 11:24 pm
“I don’t acknowledge that there can be a thing that “necessarily exists,” except as a consequence of other things that exist.”
That’s true in the order of knowing but not in the order of being. In the order of (our) knowing, the notion of Subsistent Being comes as a consequence of our consideration of contingent beings (Rom 1:19-20). In the order of being, the existence of contingent beings comes as a consequence of the creative action of Subsistent Being.
Now, Subsistent Being is not “a” being, just more powerful/wise/etc., but the absolute fullness of being, with several consequent attributes: absolute simplicity, infinity, eternity, immutability, etc. Thus, the decision to create does not change anything in God, it only results in the fact that the universe exists. On the other hand, if God did not create with absolute libertarian free will, He would not be absolutely perfect.
In contrast, in Christian trinitarian doctrine the eternal generation of the consubstantial Son is not by free will, but by nature.
Comment #96 April 27th, 2016 at 7:35 am
Johannes #95: OK, but now you’re using arguments that you can’t possibly expect to be persuasive to someone from outside the specific religious tradition that you invoke.
Comment #97 April 28th, 2016 at 5:18 pm
Scott, I assume you are referring to St. Paul’s quote in the 2nd paragraph, because the mention of Christian trinitarian doctrine in the last paragraph was clearly not for the sake of argumentation, but just a comparison.
Now, the statement in the two NT verses referred on the 2nd paragraph, namely that the invisible attributes of God, his eternal power and divinity, can be known through rational consideration of created, contingent beings (including us), is hardly exclusive to Christianism. You can find similar views in Jewish and Islamic philosophy (e.g. Maimonides, Ibn Sina or Avicenna, etc.)
And I certainly did not quote the two verses as an argument of authority, but just to show that I was not being original.
The third paragraph, in turn, is standard classical theism, again not exclusive to Christian philosophy, but also found in Jewish and Islamic philosophy.