Scott Aaronson: The Greatest Unsolved Problem in Math
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- Опубліковано 20 чер 2024
- Scott Aaronson joins us to explore quantum computing, complexity theory, Ai, superdeterminism, consciousness, and free will.
TIMESTAMPS:
- 00:00:00 Introduction
- 00:02:27 Turing universality & computational efficiency
- 00:12:35 Does prediction undermine free will?
- 00:15:16 Newcomb's paradox
- 00:23:05 Quantum information & no-cloning
- 00:33:42 Chaos & computational irreducibility
- 00:38:33 Brain duplication, Ai, & identity
- 00:46:43 Many-worlds, Copenhagen, & Bohm's interpretation
- 01:03:14 Penrose's view on quantum gravity and consciousness
- 01:14:46 Superposition explained: misconceptions of quantum computing
- 01:21:33 Wolfram's physics project critique
- 01:31:37 P vs NP explained (complexity classes demystified)
- 01:53:40 Classical vs quantum computation
- 02:03:25 The "pretty hard" problem of consciousness (critiques of IIT)
NOTE: The perspectives expressed by guests don't necessarily mirror my own. There's a versicolored arrangement of people on TOE, each harboring distinct viewpoints, as part of my endeavor to understand the perspectives that exist.
THANK YOU: To Mike Duffy, of dailymystic.org for your insight, help, and recommendations on this channel.
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LINKS MENTIONED:
- Scott's Blog: scottaaronson.blog/
- Newcomb's Paradox (Scott's Blog Post): scottaaronson.blog/?p=30
- A New Kind of Science (Stephen Wolfram): amzn.to/47BTiaf
- Jonathan Gorard's Papers: arxiv.org/search/gr-qc?search...
- Boson Sampling (Alex Arkhipov and Scott Aaronson): arxiv.org/abs/1011.3245
- Podcast w/ Tim Maudlin on TOE (Solo): • Tim Maudlin: Debunking...
- Podcast w/ Tim Palmer on TOE: • Tim Maudlin Λ Palmer: ... - Наука та технологія
TIMESTAMPS:
- 00:00:00 Introduction
- 00:02:27 Turing universality & computational efficiency
- 00:12:35 Does prediction undermine free will?
- 00:15:16 Newcomb's paradox
- 00:23:05 Quantum information & no-cloning
- 00:33:42 Chaos & computational irreducibility
- 00:38:33 Brain duplication, Ai, & identity
- 00:46:43 Many-worlds, Copenhagen, & Bohm's interpretation
- 01:03:14 Penrose's view on quantum gravity and consciousness
- 01:14:46 Superposition explained: misconceptions of quantum computing
- 01:21:33 Wolfram's physics project critique
- 01:31:37 P vs NP explained (complexity classes demystified)
- 01:53:40 Classical vs quantum computation
- 02:03:25 The "pretty hard" problem of consciousness (critiques of IIT)
The selected branch would likely be the one that requires the least energy.
Scott is one of the great public intellectuals of our time and a great thinker that has contributed a lot to his field. What a pleasure to hear him! I highly recommend his book “Quantum computing since Democritus.”
How complicated is it? Is it going to be a struggle for someone without a degree in computer science? Thanks in advance for any info.
He's got YOU fooled. Great intellectuals of our time are people like Chris Langan and Roger Schafly. This guy is just a shyster. Quantum computing is a scam to tap into the public trough.
@@nomadchad5733No it’s similar to a book like “Gödel Escher Bach.” It’s challenging but doesn’t require any specialized knowledge.
@@nomadchad5733 It's on the advanced end of "popular" science writing. Some parts you won't fully understand but you'll learn a lot.
@@nomadchad5733 check out the free preview in google books; www.google.com/books/edition/Quantum_Computing_Since_Democritus/jRGfhSoFx0oC?hl=en&gbpv=1
Started by listening to the Chris Lang podcast thinking this is pure madness, then listened to Chris + CERN Scientist, and now im staying because youre awesome Curt
A Michu and Tyson diss in the first five minutes …
Subcribed
I can't watch anything with those two.
@@y5mgisi be careful 🥺
You might be seen as a humanphobe
Scott is one of the best minds alive. He is both deep and clear at the same time. He is devoid of woo but he still does not mind touching difficult topics.
I love long form content. Thanks Curt! Commenting for algo.
nice to see you here,
Reminded me of Dr. McCoy never trusting the teleporter 41:27, thank you both for sharing your time and work Scott and Curt, Scott's enthusiasm is great to see, love his honesty regarding looking at others theories, peace
this man is truly scary smart. Gonna need a good few passes to fully go thru all the material Scott is casually splurting out. Really nice drop!
Excellent conversation ✌️🤘🏿❤️
Excellent Guest…. You ask very good questions …! Excellent interview!
❤ I always enjoy hearing Scott Aaronson speak
thank you Scott Aaronson for correctly and succinctly definining superposition! As my Quantum Physics I professor said "it (electron, photon, etc.) is not either, nor neither, nor both, but in a superposition, which we don't have the language to describe."
Looks like language to me..
Curt, again and again people misunderstand what computational irreducibility is, and I am extremely disappointed in Scott making the exact same mistakes. Yes it is in fact a new concept. And no, it is not just chaos.
In chaotic systems, you can always "look ahead" and predict the future state at a time t, provided you have extremely accurate information about the initial conditions.
In computationally irreducible systems, you can do no "looking ahead". It's impossible regardless of the accuracy of your initial knowledge.
Chaotic -> tiny change big consequence
Irreducible -> no shortcut calcuation
I don't think Scott is really conflating chaos and irrediucibility. First he correctly states what Wolfram means with computational irreducibility. Then he explain chaotic systems and mentions that computational irreducibility is the analogue of chaos for discrete systems. (I agree that the way he jumps between these concepts is less than ideal from a pedagogical point of view, but the video is not a lecture.)
I somewhat agree with Scott's analogy but only in the sense that both principles express that magic does not exist.
If a continuous system is "too complex", our ability to make accurate predictions about its future behaviour is necessarily limited.
If a discrete system is "too complex", our ability to efficiently predict its behaviour by means of a clever shortcut is necessarily limited.
But in practical terms the two situations indeed can hardly be more different. The "computational irreducible" discrete system is a system that can be perfectly modelled by a digital computer or even only exists within a computer. The rules of the system just happen to lack a structure that allows us to bypass the need to brute force it.
One of the best conversations you’ve had!
35:23 Computational irreducibility isn't necessarily chaos. It means that there's no algorithm which shortcuts the result of a simulation over a period of time without actually simulating the system itself. Imagine every step you apply sine to a number. At step 4 you'd have sin(sin(sin(x))). You have to apply all those sines to get the result at the nth step. You can't shortcut it despite the fact that the system isn't chaotic. It's computationally irreducible. If you instead multiplied by -1 each step, then the result at step n is -x (-1)^n.
How the heck do you think it's possible that Scott doesn't understand this? Like I am baffled that he had this misconception in the interview.
@@luken476 I have absolutely no clue. I knew Wolfram didn't like Aaronson for some comments he made regarding NKS, but I didn't know what. Now I understand. Also, the quantum thread idea Aaronson critiques at 1:26:48 is basically ER=EPR where the threads are actually wormholes. This creates a non-local connection between entangled particles which is sufficient to violate Bell's inequality. Sure, it's currently mathematically underdeveloped, but Aaronson _should_ realize this could be used to create a deterministic interpretation of QM. I feel like Aaronson is being unreasonably dismissive about some of Wolfram's ideas.
@@luken476 i usto like Aaronson a while back, but it's clear he's not in this for the science.
How nice of you to put a link on screen to the episode with Chris Langan, at the exact point where Newcombs paradox is being discussed. I think Langans solution to the problem was published in 1989, so quite a bit earlier.
One of the few honest people in modern science.
What do you mean, like >95% of modern scientists are liars? WTF BS is this comment.
Damn, Curt. This one was a banger! Thanks.
@14:00 I actually think we do know a perfect brain prediction machine isn't possible, because similar to the halting problem and the variants, you can pose that you could have an interaction with the machine itself, and just as the halting problem cannot know itself, the perfect brain prediction machine cannot predict itself and therefore cannot perfectly predict a brain interacting with it
Nice Curt...great upload. I think it has to be P doesn't equal NP. Our universe doesn't work the other way around. I think the problem is somehow deeply tied to entropy. Like literally checking the steps of a problem never takes as much work/time/energy as coming up with a solution in just about every aspect of life....things would be easier if they did!
Love this channel its one of greats l found on UA-cam ❤
Thanks, I finally got a lucid explanation of P=NP (although he should have been aware he was saying "in P" and also "NP"!)
52:00 The same issue appears in Many Worlds with the "self -identity uncertainty":
If I am an experimenter, there's no way to know ( in principle, not just in practice) beforehand "in which branch I'll find myself afterwards" ( in MWI terminology ...).
The problem is that:
- My perception of the world ( the branch I'll find myself in) is an emergent physical property that has to be described in principle, by the same fundamental laws as everything else.
- This randomness ( the self location / identity uncertainty) that appears only at the macroscopic level is irreducible ( it cannot be deduced from the fundamental deterministically evolving Wavefunction).
- There's no clear dividing line that specifies how this irreducible stochasticity appears macroscopically.
It is both strongly emergent and also unavoidable, so it is equally fundamental in that sense!
So after all, Everettian QM is a deterministic/ Probabilistic hybrid ( probability is fundamental, as this irreducible randomness clearly suggests that the Born Rule has to be imposed as an extra postulate, just like in Copenhagen ). So , contrary to the claims, MW is not simpler than textbook QM and moreover it has extra baggage!
Honestly, I don't really see how "many worlds" is even remotely practical aside from the philosophical or sci-fi appeal.
About the best I can come up with is the notion of the quantum bomb detector - a single photon can tell us something about the path it didn't take - something that didn't happen.
One could interpret this to be a "all things happen" evidence and we just got information from a parallel world....
But this also relies on a view of the photon and reality which create it. The wave function, a fundamentally nonlocal concept, describes what each local frame will experience.
The implication would be that our normal experience of locality, time, and space is not accurate as opposed to there being many worlds where everything happens.
It just defers most of the problems to "which branch", as you say, and doesn't really provide much of a falsifiable premise to examine. It's fun to play with, but it's almost kind of a counter-nihilistic response to "shut up and calculate." "None of this matters, anyway, so why not - maybe it all just happens anyway."
In discussion of a prediction machine, I think it is overlooked that some choices will be easily predicted by anyone familiar with you while others will be difficult to predict. And also if your brain has a chaotic evolution, the amount of time between the prediction and you choice will be important.
Great informative interview!
Two typos in subtitles that unfortunately result in factual mistakes:
1:38:52 - "Yeah, yeah, yeah. I agree. If yo ujust want to know if the number is divisible by three, that is NP." -> should be "that is in P."
and then the next one:
1:39:04 - "Yeah. In fact, in fact, if you want to know if it's divisible by any fixed number, that's NP, right?" -> should be "that's in P, right?"
Good job, Curt.
The prediction machine Scott describes is exactly the concept at play in the show Devs with Nick Offerman, Ron Swanson from parks and rec :] it's very good.
AMAZING!!!
Yes..so..ah…hmm..ah…Consciousness … his brain must hold so many ideas and models. Brilliant!
100% agree with his view of free will. I created exactly the same argument about free will in something like 2012, and I'm glad that Curt asked about the sealed envelope, because if freewill being an illusion depends on the fact that I can't look in the envelope, then your argument against free will is tautological by design.
In fact the argument for free will is simultaneously an argument against the core and universal determinism of the universe.
Already commented this but in terms of perfect mind predictions, you can just use a similar model to the halting problem, if the mind interacts with the predicting machine then it cannot predict itself so therefore it's again a contradiction
FREEWILL is a myth. Sam Harris has already destroyed that concept.
Next...
@@happywednesday6741 Absolutely. It's Gödel all the way down.
@@vfwh Wish I was smart enough to know what you mean by that haha
@@happywednesday6741 You can look up Gödel's incompleteness theorems. It's a pair of fundamental theorems of logic/math that show that any logical algorithmic system that is sufficiently sophisticated can say things about itself that cannot be proven true or false within itself.
When you put it like that, it doesn't seem related, except when you understand that the way it does that is basically by showing that any such sophisticated system can be made to "predict" things about itself, and then to predict consequences of whether that prediction is true, in such a way that, if the second prediction is true, then you can't tell if the first prediction is true (which therefore makes the first prediction undecided).
If you consider (that's the leap that I'm making) that the universe itself is an extremely sophisticated logical algorithmic system (like maths are), then this means that it is able to make predictions that are undecidable, which you can interpret (like I do) to mean undetermined (until they actually happen).
What you call "contradiction" above.
18:00 The most plausible answer to Newcomb 's paradox is that it's a kind of reductio ad absurdum for strict determinism and full predictability.
Okay, this annoyed me so i'll just explain it for Aaronson and others because i feel like at this point his point of view is just misinformation:
Computational Irreducibility and Chaos are similiar but not the same. This difference is explained in NKS, but I'll explain it more deeply. Computational Irreducibility is formally, the notion that all systems are equivalent to a Turing machine (under principle of computational equivalence) and therefor is subject to the halting problem : That if you were to predict the future outcome of that system...it is arbitrarily complex, and therefor you can not predict whether that system will halt, or not halt.
In more practical terms it's obvious to see why : Subsystems in the universe, can not be isolated from other systems, and so there is an arbitrarily large number of subsystems that act as inputs, for the system you are trying to produce output for. This is why the rules in Wolfram's CA experiments emulating other rules under different initial conditions is so important in the book: It proves the deep connection that systems emulate one another because of this phenomenon of reaching out in the rule space of other rules.
This is STRICTLY a stronger statement than chaos...which is only a statement about initial conditions and not knowing them to precision...where as computational irreducibility is saying much more then that : That you can not in principle predict systems because the problem of doing that is arbitrarily complicated.
That means its not just a problem of finding out what the initial condition is for your system...it's the fact that you CAN NOT find out the systems initial conditions cause the system can not be isolated: you need information of the system, and all of the subsystems in the universe, which is both the full set of information of the past AND future (the full state-space of a true Turing machine)
amazing!!
Enjoyable!
Bell tests and ghz and so on is easy to explain, but what is interesting is that once you hit upon the right idea you get quantized spin in magnetic fields for free, there is a clear and easy way to get the behaviour of electrons or magnetic atoms in magnetic fields in a classical way, but if you think about it, that sort of has to be true if it works or it would be very strange.
Haven’t gone to school yet but I’m going to school for philosophy of physics. Thank you Kurt for all you do in getting people like me into school. Look out for a new quantum theory in the future.
Great to know that you are familiar with this channel!)
Go for actual physics, not the philosophy of it
Appreciate your efforts Curt
that hair line comeback is legendary
Thanks!
Very thought provoking stuff guys...nice to see I am not the only that is fascinated by these things.
Thanks so much!
Free will seems to be a confusion. Take the concept of 'will'---the desire, motivation, plan, intent etc to do something or have someone do something. Where does that come from? Every experience we have arose in the background of our environment. The self-organisation of the brain as a child develops is impacted both by their existing Neural architecture and by the inputs from external sources. Will therefore must have a bottom up component but certainly can't be said to have arisen independently of external information. Yet due to self-organisation of Neural networks, the growing Neural architecture of a person becomes nearly informationally closed in the sense that the Neural structures process new information according to their own internal organisation and not by any external direction. So will becomes less external and more internal in source as consciousness develops, thus becoming more resistant to influence. Yet, we can admit still that the prior structures of the Neural networks give rise to will, so it still counts as bottom up. But then, the internal structures may give birth to insight on a problem that might arise from internal unexpected connections that are emergent and not just ordinary in the sense of being linearly deterministic. These emergent structures might change the perception of underlying beliefs or values, thus the understanding giving rise to will maybe operated upon by emergent insights thus altering will via downward causation. This bi-operational system where upward and downward causation both occur as consciousness operates cam still be said to have arisen due to the initial conditions, as the downward causation emerged out of the structures arising from normal bottom up development.
So what's free about it? Well that depends on whether you use the etymological root of free or use the word in the sense of unfettered/no bias etc. Etymological, free comes from Old English Freo, and that from Goth Frio. Frio is cognate with Latin Prio meaning the first one or the self ie, one's own. This is why freo was used also in Old English for wife, as back in the 6th century, wives were one's own property ie private property. In this sense of one's own, will is the product of internal processing only ie, not impinged upon, directed or coerced by external top-diwn control. Free will then is only impinges upon when the mind makes a calculation that following someone else's will leads to a better overall outcome for the self than does following one's own will. In that sense, the individual mind joins a group mind where consideration exceeds the individual want and considers the group dynamic (whether that be a democratic or autocratic process).
The other sense of free is liberated, unhinged from. If will is said to be made up of a network of interdependent variables and the expression of will could then be the output of a system that processes input variables, then the resulting will depends upon inputs plus system processing. If the inputs are altered or the system process is influenced,,then the output will is likely to alter. For instance, choosing an ice-cream from myriad options. Normal will might be influenced by the memory of past experiences tasting various flavours. Thus, following that experience, you might easily choose mint-choc chip because your experience tells you that flavour is most tasty to you. Despite there being some new flavours, your will is focused on maximising your enjoyment, so better the devil you know. In order to have the freedom to try some new flavour, there must be a willingness to not maximise enjoyment---the goals have to be revaluated. Thus, from that perspective, free will arises from rearrangement of internal goals and objectives. This could be thought if as a result of introspection.
Another possible interpretation of free will is one in which random variables interfere will the mind system and it's inputs/outputs. If at the very smallest scales, quantum foam influences interactions at the subatomic level, could such random interactions generate a butterfly effect which would then propagate through the mind influencing the deliberation process? Random variables would be impacting upon an orherwise informationally closed system (informed upon/shaped by the past experience), thus abrogating the balance of such a system, perhaps tipping it over some threshold thus generating a different decision. If random variables feed through (from bottom up) eventually to mess with the input or process of a Neural algorithm, then the outcome could be said to be will free from the self yet still undirected by an external agent such as another human.
Finally the last consideration: is there a self free of everything else at all? In a universe where everything is connected to everything else non-locally (eg like information information on a holographic film), then if the projection is our universe, and the projection can somehow affect the holographic matrix (downward causation) then all action occurring anywhere else in the projection could alter everything else. This would especially be relevant if the projection generated local emergence which impacts the projection matrix thus feeding back upon the projection non-locally. In such a non-linear system, no computer could accurately predict your future beyond a certain time period (just as the weather cannot be accurately modelled.
Where were algebraic closures and quaternions discussed? I wanted to look into that further. I was doing house work while listening and I don't know the exact context.
Found it is is around 1:12:00.
At the end Scott was like "K bye" lmao
God he’s smart. Wow this is really interesting stuff though
I love the Leonard Suskind shout out
What does Scott thinks of DeepMind's GraphCast weather predicting model?
I was surprised in the section on various interpretations and/or theories of quantum mechanics 00:46:43 , there was no mention of J.A. Wheeler's "It from Bit" theory, i.e. that all quantum phenomena (and indeed "all there is") are information-theoretic in origin. If you're interested, a good starting point is Wheeler's 1989 paper "Information, Physics, Quantum: The Search for Links", which if nothing else contains a lot of valuable cited references.
There is a modern funding initiative called "It from qubit", and Scott was one of their investigators. So Wheeler's idea is alive and well in the quantum information community, and collaborations between high energy physicists and theoretical computer scientists have been happening. We don't call it a theory or interpretation of QM though, 'it from bit" is more like a pointer towards finding new things.
@@iyziejane this is great to hear! And thank you for your succinct and clear explanation.
@1:13:00 I have a different take, but the same conclusion. It is *_not_* the case that you "need complex number amplitudes for QM." It *_is_* the case that a bivector structure is "needed". But all bivectors in the STA are themselves equipping you with complex analytic structures (every planar subspace with a scalar + bivector is isomorphic to ℂ) . The "complex value functionality" in QM is really derived from the bivector algebras. This moves the question to _why bivectors?_ The answer I would give is because of the symmetries of spacetime and QM, which are all smooth continuous Lie group/algebras. All the generators are bivectors (all Lie groups are Spin groups, is the way a math-phys geek might put it.)
For the hard-core geeks, the Born Rule is a statistical rule. It is based on the formalism adopted by QM. Since the spinors viewed as multivector transforms act double-sided in the spacetime algebra (they are STA rotors, or scaled rotors) the natural _bilinear invariants_ of the theory (the particle currents and associated conserved quantities) are going to be squared rotors. That's Born's Rule if I handed you a spinor.
The point being a spinor is a field since it has values at all spacetime locations, even if asymptoting to zero scalar part. _How come it has to be a field?_ is the near to last question you'd want to ask. The trite answer is because empirical evidence says so, in the form of empirical superpositions being observed. This affords a one layer deeper question at the heart of QM, which is why tf superpositions? Answer that and check with my take, I do not want to bias you with my views, but you may inquire into my highly off-neat non-standard crackpot views here, t4gu.gitlab.io/t4gu/philosophy/ for some serious related fun musings.
A few years ago I exchanged a couple of e-mails with Scott where I proposed to him (and he agreed) that ITT seems to describe the wrong thing because one thing we correlate with our conscious experience is that we are able to report that we have it. Even if thermostats are more conscious than me and exhibit qualia that they cannot report as having, what is the mechanism that somehow makes me report that I have a non-zero value of phi? Because it is this very mechanism that raises our question about consciousness to begin with, it is the only reason we're acknowledging this phenomenon. Whatever explanation we end up with should have some bearing on the behavior of conscious systems that report that it feels like something to be such systems.
Interesting, quote strong positions on subjects. IIT is such a child compared to many other theories. I think it is too early to say anything complete about it. Many proposition tend to branch and some of the branches can still deliver better than original.
But Curt, I heard you again mentioning Kähler geometry. Can you provide a source where you learned to make that connection between it and QM/GR? Wiki pages had no URLs so it is hard to find what you showed. The pages I found mostly connect Kähler with string models and supergravity. Not standard physics.
1:48 - Man after my own heart! ^.^
All right, Scott Aaronson is genius.
I will watch this again.
I'm glad! - Curt
Numbers in a nice ring structure fall into four categories: primes, composits, units, and zero. The integers have two units: 1 and -1. Some rimgs have more. It is becaise units, in general, have interesting properties, that we distinguish it from primes. Primes have different interesting properties.
Genuinely surprised to hear serious consideration of Newcomb's paradox, because in a universe with working QM, no Predictor can have over 50% accuracy on Boolean queries. Proof: flip a quantum coin ("Conway's coin") with a BBO crystal, precommitting to the result of the coin; Conway's Free Will does the rest. I blame Yudkowsky for misunderstanding QM and taking this to be a serious problem.
If possible have a podcast with Dr Elizabeth Bik , the science integrity specialist
It's so obvious, N = 1
I can't believe how they haven't figured this out yet...
Newcombs paradox is just another time travel paradox, like the grandfather paradox but looking forward. The predictor has to see the future to know what you will predict, because you haven’t done it yet.
Good conversation. Better than Neil DT. Now to nitpick:
@28:58 - Scott claims that the strange part about light interference is that blocking a path increases the chance of being found where is was not when the path was clear. But that is normally what waves do classically. Like a wave hitting a wall with one opening vs two. There will be peaks and troughs after passing through the slits, but not with only one slit open. That is not special.
I think the strange part is when only single photons pass through one of two slits randomly and the photon hits a further wall in a way that shows interference even when there was no other photon going through the other slit. my opinion.
Btw the mistake is that there doesn't need to be genuine new randomness, the inference is not precise. Lets just take a bell test, we choose to measure one out of 3 directions. Given that the conclusions of bells theorem are correct, there are two ways you can habe the outcome of experiements be determined at the outset, either the particles where imbued with an outcome and the measurement settings that will be chosen for them, then you can explain it as predetermined. All you need to do is envoke conspiracy and you can do it even without an interactions. Or you can have an interaction that makes it so that one particle retains an interaction with its partner such that when it is measured, the other particle adopts the opposite orientation, or if you will the interaction has the effect on the second particle of undergoing a measurment in the same chosen direction as the first, this isnt known to us but it is prepared for any other choice of axis as if it had been measured and so after the first of measured the second has a known outcome for the same axis and a simple cos squared for the other orientations, so the problem with an interaction that does exactly this will turn into a problem you can very easily describe classically. It doesn't need fresh probability in any sense, and the cos^2 of the angle that gives you the probability for the second particle depending on the first is as simple to explain as a prepared state of the same kind with no entanglement where the outcome is known for some axis in particular. This works for bell tests and makes it viable to explain classically because there simply is no need for a non contextual map of the two outcomes to exist prior without reference to the chosen settings, the first particle being measured plus the interaction imbues the second particle with a well defined normal probability distribution and so we just consider the first measurement as kind of random with some unknown preparation and the second is well defined by means of the interaction. The point about not being able to define a non contextual map, the argument about why you need fresh probabilities in the first place only applies of you don't have such an interaction. You can very well define additional variables with this exact behaviour, but then the outcome for the first needs to "prepare" the second particle by means of an interaction. But when that is the case the argument about it not being predeterminable falls away, it only applies to cases when there is no interaction.
As a mathematician I can confidently say that if you ask 100 mathematicians what is the greatest unsolved problem in mathematics only tiny few would pick P=NP. Most analysts would say it is the question whether solutions of the Navier-Stokes equation exist and remain smooth for all time (this also relates to the question on how turbolence develops). If you ask number theoretist they would probably rank no.1 the Riemann hypothesis, an algebraist would say it's the Langlands programme. Hence, I object the title as it gives non-mathematicians a very one-sided view of what mathematics is.
The title is fine. At worst, it gives non mathemeticians a very one-sided view of Scott Aaronson's opinions on what mathematics is
He is the genuine deal when discussion centers on computation NOT wolfram although latter has been a very successful businessman and definitely is quite intelligent.
Scott and Curt, one of The Greatest Unsolved Problems in Math, amongst others, is THE MATHEMATICS OF QUANTUM GRAVITATION.
We now have an empirical theory of Quantum Gravity- The unitary Trinity God Theory and Equations that are deeply hidden in plain sight and manifested by Quantum Gravitation, Quantum Gravitational Entanglement and Gravitational Quantum Computation.
Also, Quantum Gravity is the key to unification of Gravity ang Quantum Mechanics. Quantum Gravity and the theory, mathematics, laws, reproducible experiments and observations that underpinned it, is crucial for an empirical real true Quantum Theory of Gravity that would finish Einstein's Revolution in physics. Problem is that, since the 17th century up to the present, the Mathematics that we have so far cannot solve the problem of quantum gravitation.
Mathematics is invented and discovered. That's my personal experience. I've invented/discovered a completely new mathematics in the course of my 30-year-long basic research on Quantum Gravity in Singapore. I called it Majulah Matematika in honour of my home country Singapore. I use it to solve one of the most difficult conundrums in physics- the True Nature of Gravity. In addition, I also have invented/discovered the elusive Magnetic Monopole and the Gravitational Computation Language and Codes that program and run the Quantum Gravitation and the Universe itself as the Ultimate Massive Cosmic Computer System covering the entire observable Universe.
Here is one of the many solutions that we can derive from my new mathematics: A Computer Universe that is real. It is run by Quantum Gravitational Computation, Quantum Gravitational Entanglement and Quantum Gravitation covering the entire Universe. An empirical Theory of Quantum Gravity is the key. And it will led us to understanding of how and why Gravity works. It will also at the same time, debunk and invalidate String Theory, Loop Quantum Gravity, M Theory, Theory of General Relativity and all failed and wrong theories of gravity. But it will proved and validate Einstein's Hidden Variables and EPR's authors Einstein, Podolsky and Rosen correct. The Hidden variables are: Quantum Gravity, Quantum Anti-Gravity, Quantum Neutral Gravity, the macroscopic cosmic scale Gravitational Quantum Entanglement and Gravitational Quantum Computation. All these would complete the Quantum Foundation, Unification of Gravity with Quantum Mechanics and the realization of Theory of Everything in Physics.
I have discovered and cracked the code of the true nature of Gravity in my over 30 years of basic research works in Singapore. This discovery/invention/theory of mine include THE GOD EQUATION - THE TRINITY Equations, Laws and Codes For QUANTUM GRAVITATION , QUANTUM GRAVITATIONAL ENTANGLE MENT and GRAVITATIONAL QUANTUM COMPUTATION that pave the way for Theory of Everything in Physics: - THE 3-in-1 HOLY GRAILS of Physics:
1. Quantum Anti-Gravity/Spin Up Quantum Gravitational Entanglement/0 Rhu Bit or R Bit:
QAG = ∆QGOρ < ∆QGFρ = ↑α
2. Quantum Gravity/Spin Down Quantum Gravitational Entanglement/1 Rhu Bit or R Bit:
QG = ∆QGOρ > ∆QGFρ = ↓α
3. Quantum Neutral Gravity/Superposition Quantum Gravitational Entanglement/01 and/or 10 Rhu Bit or R Bit:
QNG = ∆QGOρ = ∆QGFρ = ↑↓α
We now have a working Quantum Theory of Gravity that is testable and complete with reproducible empirical experiments with the same results if repeated over and over again and again, confirmed by empirical observations in nature with 7-Sigma level results, guided by empirical Laws, Cosmic/Universal Computation and physical/mathematical Trinity God Equations that are predictive, precise and does no collapse even in high energies of Big Bang and singularity of Black Hole.
Quantum Gravity or Quantum Gravitation have three types that are equivalent to and manifested by Quantum Computational Gravitation- the biggest and most powerful Computer Software Program and Hardware in the Universe and Quantum Gravitational Entanglement - a Quantum Entanglement at Macroscopic Cosmic Scale namely:
1. Quantum Anti-Gravity = Spin Up Quantum Entanglement State;
2. Quantum Neutral Gravity = Superposition Quantum Entanglement State;
3. Quantum Gravity = Spin Down Quantum Entanglement State.
Quantum Gravitation is governed by and follow the unitary Trinity Laws, Mathematics and Physics of Quantum Gravitation, Gravitational Quantum Computation and Quantum Gravitational Entanglement. We now have a new Laws of Physics and two newly discovered Fundamental Forces of Nature - The Quantum Neutral Gravity and Quantum Anti-Gravity which completed the heart of the Quantum Theory of Gravity published in London. Paris and Zurich last December 2022 as follows:
1. First Law of Quantum Gravitation: Rovira’s Universal Law of Quantum Gravitation:
“The greater mass density of gravitating Quantum Objects than the Quantum
Gravitational Field causes a downward acceleration of the Quantum Objects in a
Quantum Gravitational Field instantaneously mediated by Graviton.”
- Roel Real Rovira
Equation for Quantum Gravity, and Spin Down Quantum Gravitational Entanglement:
QG = ∆QGOρ > ∆QGFρ = ↓α
Where:
QG is Quantum Gravity in Rovira (value of downward acceleration force due to quantum gravity) in kg.
∆QGOρ is Differential Change in greater mass density of Quantum Gravitating Objects than the mass density of Quantum Gravitational Field in kg/m2 or g/cm3.
∆QGFρ is Differential Change in mass density of Quantum Gravitational Field in kg/m2 or g/cm3.
↓α is the Resultant Downward Acceleration of Gravitating Quantum Objects in mtr/sec.
2. Second Law of Quantum Gravitation: Rovira’s Universal Law of Quantum Anti-Gravity.
“The lesser mass density of gravitating Quantum Objects than the Quantum Gravitational
Field causes an upward acceleration of the Quantum Objects in a Quantum Gravitational
Field instantaneously mediated by Graviton.”
-Roel Real Rovira
Equation for Quantum Anti-Gravity/Spin Up Quantum Gravitational Entanglement:
QAG = ∆QGOρ < ∆QGFρ = ↑α
Where:
QAG is Quantum Anti-Gravity in Rovira (value of upward acceleration force due to quantum anti-gravity) in kg.
∆QGOρ is Differential Change in lesser mass density of Quantum Anti-Gravitating Objects than the mass density of Quantum Gravitational Field in kg/m2 or g/cm3.
∆QGFρ is Differential Change in mass density of Quantum Gravitational Field in kg/m2 or g/cm3.
↑α is the Resultant Upward Acceleration of Anti-Gravitating Quantum Objects in mtr/sec.
3. Third Law of Quantum Gravitation: Rovira’s Law of Quantum Neutral Gravitation.
“The equal mass density of gravitating Quantum Objects and the Quantum Gravitational
Field causes a zero acceleration or floating or hoovering of the gravitating Quantum Objects
in a Quantum Gravitational Field, instantaneously mediated by Graviton.”
- Roel real Rovira
Equation for Quantum Neutral Gravity and Superposition Quantum Gravitational Entanglement:
QNG = ∆QGOρ = ∆QGFρ = ↑↓α
Where:
QNG is Quantum Neutral Gravity in Rovira (value of zero acceleration force due to quantum neutral gravity) in kg.
∆QGOρ is Differential Change in equal mass density of Quantum Neutral Gravitating Objects to the mass density of Quantum Gravitational Field in kg/m2 or g/cm3.
∆QGFρ is Differential Change in mass density of Quantum Gravitational Field in kg/m2 or g/cm3.
↑↓0α is the Resultant zero acceleration or non-acceleration of Neutral Gravitating Quantum Objects in mtr/sec.
More detailed information could be found on the published papers 2 years ago in London, Paris, and Zurich, online and at the two scientific Journals ACADEMIA and REAL TRUE NATURE. Alternatively, you can google the name of the author ROEL REAL ROVIRA to arrive at the published paper on Quantum Gravity.
Most recently, additional two well respected scientific journals namely NATURE and the AMERICAN PHYSICAL SOCIETY APS Physical Review Journals have officially invited this author to submit manuscripts on his Research on Quantum Gravity for publication for PRX QUANTUM in preparation for a celebration for International Year of Quantum IYQ 2025 to showcase the best papers of the year.
Copyright 2022 ROEL REAL ROVIRA. All Rights Reserved.
Query: (to any cosmologist) Are there conventional models that extrapolate our observable patch of space time in a way that our perceived accelerated expansion was just a local thing? This would make dark energy less fundamental since its value could be just a local fluke.
Also: Are multiple big bang singularities conceivable in one solution to Einsteins field equation, maybe having observers experiencing different timelike directions away from those low entropy big bang patches? There is this Janus model around our Big Bang, but maybe you can have even multiple bangs in one universe/metric (not multiverse!)
I wouldn't call the question of P-vs-NP unsolved. I'd call it a *wrong question* ... or, at the very least, an *incomplete question* . The real question is actually this: Which NP problems can be solved in P(olynomial) time *in the given space* (or, rather, with the given *memory* boundaries). Let's back up a little, first...
Axiom (in fact, one of the basic rules of this universe) #1: *Time and space are interchangeable.*
Hypothesis #1: Any time-intensive problem can be converted into an *equivalent* space-intensive problem, and vice versa.
Theorem #1: Every time-NP problem can be converted into equivalent space-P problem.
Theorem #2: Every space-NP problem can be converted into equivalent time-P problem.
Theorem #3: Every problem (either time-NP or time-P one) can -- in theory, and with enough available space -- be converted into equivalent (let's call it time-1) problem that can be solved in just one (again, just one!) (time) step.
Theorem #4: Analogous to #3 as #2 is analogous to #1, or... Every problem (either space-NP or space-P one) can -- in theory, and with enough available time -- be converted into equivalent (let's call it space-1) problem that can be solved with just one (again, just one!) bit (of available space/memory).
Some examples from the real world (Computer Sciences): Lookup tables, function unrolling, recursive functions...
I wish this this guy would smile more
I would recommend Scott to read the IIT 3.0 paper at least to the half. Then think about cause-effect repertoire and informational existence of a system for itself. And just after that start with criticising. His arguments, however mathematically precise are not really ad rem.
@1:17:00 the Quaternion and some Octonion people are misguided. They have the wrong impression about what QM is in essence. It is *_not_* a theory about generalized probabilities and whatnot (although it is in a unique class of GPTs). QM _is_ a theory of measurement processes, but with entanglement. The employment of octonions is related to how to best represent the particle states and how they "internally" (which just means locally in spacetime) transform (mix or interact). The amplitudes squared is still the same as for any spinor though. The octonion or quaternion is (or _should be_ ) treated as an _instruction_ for measurement processes, not as the statistical amplitude. So, for example, in the STA approach, one is still "doing QM" over the reals (not "over" the quaternions). The bivector structure provides the complex geometric analytic structure - not the quaternion or octonion, they have a different role (group irreps.) - (I should also include the spacetime pseudoscalar as the additional complex structure, also important for certain conventions on how one chooses to "square root" the Klein-Gordan eqn.)
QM says effect can come before cause and this has been experimentally verified in 2017. Furthermore, for a quantum system the way around cause and effect is, can be a supposition of the two states of C-> E + E-> C.
I got into computers in the 80's, selling commodore 64 computers. I programmed basics into my commodore, what a nightmare, however it gave me an entry into govt employment. In those days if you said you used computers in your work, silence, most people had no idea of what you could be doing. Then in 1994, came Windows 396, or something like that, I've forgotten. at that time I'd freed myself from employment. In 1995, I was living in Alexandria, Egypt, when a orb appeared over my balcony at a party I held, then back in Australia I saw a doco in 1996, about fractals by Arthur c Clark. Straight away I knew fractals were mine. Then came the game of life and Wolfram. Now I've published 292 videos of a new kind of physics. Any question?
My man bopping to a beat
On Aaronson's approach to Newcomb's paradox: Is the idea that the *only* way to account for the predictor's record of success is to assume it has access to perfect simulations of the subjects? Set aside that this isn't *entailed* by the predictor's success; this approach seems to assume that *causal* decision theory is the right account of rationality. And the upshot would then be that even the causal decision theorist should be a one-boxer rather than a two-boxer. That would mean that the paradox doesn't really track the difference between causal and evidential decision theory. Anyway, this is all moot insofar as his argument that the causalist should be a one-boxer is invalid.
I am skeptical...I am sure that it is possible that p=np...but it probably depends on another factor, data storage and search efficiency relative the size of data.
Someone has recently proven that P=NP, but the news won't be public right away because of setbacks. Scientists are so sure that it cannot be proven that the person cannot get scientists to take him seriously, because they refuse to believe that a person without a degree could do what the experts could not. So he gave up on them and has gone to big investors and corporations instead. It will be announced within the next few months.
I don't understand, given infinite compute wouldn't P=NP. Small analogy, I can add using an abacus but a calculator does it near instantly. Time isn't a factor imo, given enough compute.
Newton's Math and Physics say that 0 is not-necessary and 1 is necessary.
Leibniz's Math and Physics says that 0 is necessary and 1 is not-necessary.
Which one matches quantum physics more?
Were using Newton's Math and Physics currently. Maybe try Leibniz's Math and Physics?
And btw what i am claiming is that in some regimes quantum mechanics is just wrong, and its wrong in a way that breaks lorentz symmetry. But that doesn't mean quantum computers can't work, because it means entanglement is this interaction between bits essentially with a very complicated network of interaction that essentially gives you all possible configurations and operations anyway, so ultimately it just means that you can't male it arbitrarily large or arbitrarily fast, or without error if for example two entangled bits are measured at the the same moment and so on, but for stuff that fits in a room it would be tiny anyway in terms of restrictions, i think rather that you could say something like for example a teleportantion protocol or something lile that cannot happen at the certain range or witha certain timing, but then again given that you have to transfer classical info slower than light it kind of doesn't matter anyway. But i think the constraints for almost anything anyone wants to do with quantum computers would be fine, i would worry about trying very fast operations maybe, or if you have very øarge networks of entangled states you might very well need a lot of error correction. But not much in excess given what i think is true is true.
Bell said it could be explained via superdetermanism. Evreryone always leaves out what Bell himself said.
His "strongest argument" is based on a very easy to correct error.
How many boosters does Scott have?
Amplitudes are just a displacement of a wave function. Why would the displacement exist, but not the wavefunction?
Scott is so true about the commutative law. You don't really understand it until you see anticommutaters.
Would be great to get an um, um, um edited-down version of this. Like might save like, like, you know 30 minutes.
Although there may not be a singular algorithm (ie.NP-Complete) which can reduce all NP runtime algorithms to a Polynomial runtime, there indeed exists at least one algorithm for every NP algorithm which can reduce its runtime to Polynomial runtime, given adequate constraints. For example the famous BPP problem can be reduced to a Polynomial runtime algorithm if sufficient constraints are added to the problem to narrow its solution space. If these heterogeneous algorithms which individually reduce their problem set runtime complexity to P, are combined into a solution set, NP*, then collectively they can cover all NP runtime algorithms which cannot be reduced to P.
How are you going to confirm that a finite list of algorithms is capable of addressing an infinite list of potential variations of input data?
In Complexity Theory we refer only to the way an algorithm's runtime complexity can be expressed relative to another algorithm, not to the actual number of algorithms in existence, which is in fact innumerable. Analyzing The Traveling Salesman (TSP) algorithm, and the Box Packing Problem (BPP) algorithm for example are NP-complete algorithms, which means they share the special property in Complexity Theory which states that these are actually expressions of the same algorithm; such that proving one NP-complete problem can be reduced to Polynomial runtime actually proves all of them can be reduced to the same Polynomial runtime complexity, being they are all expressions of the same NP-complete algorithm. NP-complete problems are considered the hardest and most difficult problems in NP, having exponential runtimes and even higher. The challenge, which I argue is true in all cases, is that applying a unique knowledge to one NP-complete algorithm's dataset, such as to the BPPs solution set, where in a specialized case, the height of all boxes are integer multiples to the box's width (allowing the packing algorithm to be optimized by calculate the box's rotated dimensions as well as the number of boxes that fill its same space, in a single step) allow it to be removed from NP and added to the set of Polynomial runtime algorithms. And that this application of specialized knowledge can be repeated for every variation of NP-complete problems in NP until the entire set is covered.
@@abdulshabazz8597 Yeah you're not saying anything I didn't understand the first time. But once again you're missing a crucial step. Lets take the travelling salesman as an example.
Step 1. You find a way of optimising it for certain finite types of input data with particular characteristics. Great. And through reduction, you use it to solve all other NP complete problems such as Boolean Satisfiability (SAT). But it only works on finite types of SAT input data with particular characteristics.
Step 2. You find another 100 of these travelling salesman algorithms and now you can solve a hundred classes of NP input data across all NP complete problems. You tell the world that you've solved P=NP but frequently people find that your solution disappoints. A scientist hoped to use the Clique Problem to find the best combination of molecules for a new drug. But none of your 100 algorithms is ideal for the specific characteristics of the scientist's data (after he reduces his graph from the Clique Problem into a form compatible with the Travelling Salesman).
Step 3. ???? How do you solve this issue so that it doesn't happen repeatedly until the end of time? What I mean is, how can you claim your solution would solve P=NP if this scientist is still stuck in the same situation that already exists today? Your solution doesn't change anything. People are already using these techniques that you speak of and it is inadequate. You have suggested nothing unique that might change the outcomes.
Oh wow if you program a ball park answer into a program designed to find that answer makes it run faster...
Why isn’t a theoretical human predictor impossible bc of the Halting Decidability Problem?
Sometimes I think I'm smart and then I listen to this podcast and I realize I'm not.
I had no idea that there was a consistent version of quantum mechanics in real numbers...
At 47:00 if the amplitudes are reality, and our measurement is just our local perception in our own universe, then how come we live exactly in the universe where the measurements comply with the probabilisitic predictions? Most universes would have to be measuring something that does not comply with the probability of measurements, wouldn't it?
Like if the distribution of measurement outcomes in our universe is precisely aligned with the probability of measuring them, then other universes would be getting a different distribution, and they would not be predictable, wouldn't they?
How come I never hear this question addressed by people who think that many worlds is plausible?
OK, well he kind of brushes it off at 1:05:00 and I'm not sure I'm convinced. The problem of many worlds is not just that we don't know why we see these probabilities, it's that every other universe would just see noise. Why are we the only ones who see a determinate probability distribution? If the other universes were selected at random at each branch at least. So in order for many worlds to make sense, you have to assume that specific probability distributions are somehow routed to just the right universe every time for these other universes to have deterministic physics...
Brillant presentation of the Problem class. Why is this guy continuously wiggling with 2 Hz? Doubt that brain, turing maschine and physics were eqivalent, so the conclusion on FREE will.
You can explain it classically, but simply do need faster than light physics where entangled systems do interact faster than light, but ofc it is something rather special to achive without breaking everything. The superluminal structure has to add in the appropriate interactions to explain entanglement but also preserve potentials and all the standard stuff, and incidentally explain dark energy and dark matter and pretty much everything at once, or its a faliure, because ot would make absolutely no sense to try to do it piece meal, there cannot be for example electro magnetism with no strong force, or weal force, because if you are looking for an underlying structure that requires superluminal interactions to give you the right predictions, then every subliminal force has to emerge simultaneously from the same structure or it wouldn't make any sense at all. A bit like trying to invent the aether before you even know what it is supposed to be doing, which is kind of what the late 19th century project got wrong, there is no way to get part of the structure, if you can indeed explain everything in a classical fashion then everything needs to be included, making a mechanical model of e and m doesn't really help that much loldx. Either you take all the known phenomena seriously or you give up.
1:33:20 I did 2^330 on my solar powered CASIO calculator and it took less than a second :)
the rational move isn't one-box or two-box, it's destroy the predictor, that's just to much power to accept existing
I disagree with Scott Aaronson's critique of Wolfram...to my view Wolfram is attempting to illustrate a fundamental problem about philosophical questions about consciousness in the context of decidability.
And does so by posing the case of all possible computation relative to all possible conscious states.
And then demonstrating that if we pose the question of what is consciousness?
Then that will necessarily entail the issue of decidability if we wish to have some objective metric by which to varify that answer.
This can have all sorts of implications about deep mathematical proofs like incompleteness relative what is possible in reality and what is possible to effectively compute.
And to my view it is highly relevant to the goals of AI development.
So in a similar fashion I will point out that Aaronson alludes to a no-go theorem...but has failed to demonstrate that, at least in terms of the ruliad postulate by Wolfram.
Aaronson's demeanor reminds me of John Madden during his sports commentator career.
It seems to me that _perfectly_ predicting the brain's future states is equivalent to uploading a brain.
A well known category of problem, often cited as to perfectly predict the weather on Earth you would literally need another Earth replica simulation, a whole category of complexity for this and forget the name
Computational irreducible
Wrong. When regular people talk about uploading the brain it is usually within the context of a desire to overcome death: for the consciousness to continue forever. But there is a massive flaw. Lets say I create a machine to predict your brain's future states. Is your consciousness now in my computer? Can you experience the simulation in my software? No. So why would you think that there was any personal benefit to you in having your brain "uploaded"? If you consciousness is not there now, then why would it be there after your body dies? The only thing that will happen is after you die, your family will believe that the AI is actually you and then OpenAI who created the AI will profit by getting the AI version of you to sell your family's personal data to Microsoft's ads team.
P=NP
You are correct.
Ofc you say otherwise locality is violated, but in what way it is violated is important, the protocols for testing bell without subliminal interactions serving this role i outlined is simple just do one soace lile separated bell test and you are done, but with superluminal interactions between spins of roughly this kind you need to understand a much more complicated protocol and also btw the protocol doesn't allow you to ever do an experiment that rules out that entanglement has a maximum speed, the only possible results is to probe for it, and find a violation of lorentz symmetry with respect to quantum mechanical predictions for spin correlations like this, or not to find it, but proving there is no such symmetry breaking and entanglement doesn't break lorentz symmetry can't be done experimentally witha finite experiement. Imagine that i told you that one of the definitions of simultaneity is real and the others are just a consequence of an approximate symmetry, and the only way to find the real now is to do a bell test, and i tell you that within some tolerance epsilon your bell test would stop violating bells inequality, for some definition of simultaneity. Well then deoending on the epsilon you need to probe the whole range of definitions of simultaneity that can be real and i will leave the problem as an exercise to the reader, if i told you that this experiment could find a violation of lorentz symmetry, then how many measurements would you need to do to confirm that i am lying to you about it, aka how hard is it to prove the negative. It turns out to not be a closable loophole. But you can figure that out for yourself, its quite simple, just assume there is a surface of simultaneity along which the results will be different and make a protocol to rule it out.
I believe in new physics, but the only postulate I have is that randomness vs determinism is a false dichotomy.
To my view a predetermined universe is one in which each event is unique relative to all other causal relationships, and that is basically the same thing as randomness as you move along a worldline.
The only mechanism I can think that might address something like that is if the "past" of a temporal dimension is converted to a spatial dimensionality.
But I cannot concieve of any computational method to demonstrate that.
Also I am not so sure manyworlds and multiverse theories are disparate or distinct things, one could easily speculate that events that have different outcomes in one of the many worlds could cause variation in physical constants that result in a multiverse, and that there are an infinite amount of multiverse caused by variations, and infinite amount of manyworlds that maintain the same values of physical constants.
But I am a laymen so I am not sure how one would address that rigorously.
@11..00 at last the halting problem explained to a layman like me
Twentieth century not 19th century. It is a big theorem in algebraic topology. That is about spheres with spanning vector field.
17:50 your decision didn’t effect what’s in the box, the predictors prediction that was made earlier effected it.
Curt is not satisfied, just like me, only I went my own way, free will. Turing gave us computational physics but we squander the window and prosecuted Turing.
He should have explained that you can clone a known state. What you cannot do is to clone a state that is not perfectly known.
Is free will really about predictability? If we have truly random influences, that's not really "free will" to most.