Definitely check out the paper for this one (link in the description). Even in a video this long there's so much cool stuff in there that we didn't have time for! I might make a more technical follow-up video myself if people want that

Then people say philosphy is useless...this is pure formal epistemology, and it really shows in the references section of the paper BTW (Carnap, Priest, Hintikka, etc...)

This is what’s been missing from recent computerphile videos. Rob!

>"spherical chickens in a vacuum" I always heard this expressed as "spherical cows on a frictionless surface".

i love this guy. More of him please. Computerphile used to do videos on real world stuff like cross site scripting (tom scott is dope) and like more feet on the ground real world programming things, not so etherial. This guy is more in the weeds, which i like.

Great video. One small caveat: the agents must be risk neutral and have a discount factor equal to one, for the conclusions in the video to be right (otherwise, for instance with risk-averse rational agents with a discount factor smaller than one, a 50% bet would be traded at LESS than 0.5, and vice-versa). Really love all Rob Miles' videos!

P.S.A.: There's an abridged version (from 131 pages down to 20) of the paper on logical induction. The link to it is given in the original article (see Description)

Get this genius a glass of water when you interview him next.

The guy writes on toilet paper sheets and all.. but then he rolls the dice, and out of nowhere, the dice turns green! We can see it's trajectory in slow-mo UNDER THE CUP! Blew my mind! Direct thumbs up!

Computerphile needs infinitely more theory/math videos.

This is a topic I've thought about for a long time. I'm excited to learn the theory.

FYI here's a full lecture where one of the co-authors of the paper talks about it in more depth: watch?v=UOddW4cXS5Y It's a great talk, I highly recommend watching it before trying to read the paper, which is quite technical.

Sounds like you need a device to throw ink at the page, to bypass friction with the delivery device. ink-jet-pen?

This video explained so much more than the title promised it would. I just learned a lot. Thank you!

"we're not going to get too far into it" (looks at the video length) -rrr-right

Probably one of my favorite computerfile videos.

So what you're saying is now's a good time to buy Bitcoin?

Amazing channel! Keep up the great work!

Thanks Rob I enjoy listening to your explanations

It is now my life's goal to qualify all of my initial thoughts on solving a problem as "in a 'spherical chickens in a vacuum' sort of way"

Little correction: The price of futures does not actually depend on the expected future price. It is only a function of the current price and interest rates. That is the case because the predicted future price of the good is already reflected in the current price. If you would predict the price to go up in the future, you could also buy the good now and sell it in the future. By "no arbitrage" assumption, the expected value of doing this and selling a futures contract must be the same. As such the price in a futures contract will just be the current price plus interest for the time period.

Rob Miles! My favorite presenter.

This is so interesting, wish the video was a bit longer. I think he was about to talk about how the algorithm reacts to paradoxes

Very happy to find this video!

What's on that bookcase? Sapiens - Yuval Noah Harari Soonish - Zach Weinersmith Run Program - Scott Meyer

Just wanna say thanks for your videos, always look forward to them!

I love it! Really fascinating.

The graphics were cool in this video

Very difficult topic to explain. Well done!

Very very interesting, great video! It is pure gold. Since the term is dropped multiple times, the rational choice theory has its limits. Individual entirely rational actions can lead in sum to irrational outcomes.

The Dutch invented shipping insurance. It's a Dutch Book because if you set the numbers right the sponsor makes a profit regardless - either the trades work or they claim it from the insurer. The original was 'I always win', not 'I always lose', but in probability that's kind of the same concept, just flipped.

Great video!

Super interesting from a mathematical and computer scientist's point of view. Problem I already see is that with those contracts people blow a bubble of unrealistic prices for real goods by gambling. That leads to increasing prices for food and other real and basic resources so that people who already have hardly enough for a living (in developing countries for example) have to pay even more just to survive.

Love you Rob!

One way or another, I don't think the predicted jet fuel prices from last year are holding up right now ;) Also, great video!

This was really well explained!

What a legend! He has Soonish on his bookshelf! AI isn't my area but this paper looks like a really interesting. Thanks for bringing it to my attention CP.

25:47 I'd point out that by "loads of money" you mean infinite money (as time approaches infinity). You can in fact make loads of money for very high but finite values of "loads", because this efficient trader is very slow. It does a lot of things "in a timely manner" based on a definition in the paper, but the definition of "timely manner" is not very timely. For example, you could make a lot of money by buying a lot of "The thousandth digit of pi is 9" and selling a lot of shares for every other digit. You couldn't get *unboundedly* high amounts of money because the inductor would eventually learn that the thousandth digit is 9, but you could probably get a lot in the meantime because until it ends up figuring out you're right it'll value all of those at $0.10.

One technical correction. "Most" futures contracts (as in most kinds, not most contracts) actually settle. If you forget to close out your contract (purchase an offsetting contract), you could find yourself the proud owner of a tank car of orange juice. Joy! Now what?* Of course, the way out is to close out your contract before the settlement date. * That's basically the evidence the SEC (CFTC?) used in their case against the Hunt brothers in 1980 -- they held their contracts (LOTS of them) to maturity.

17:50 According to Gödel there might be statements which can't be proved or disproved in a finite amount of time. An example could be Riemann's hypothesis about the roots of his zeta function. So the confidence value would be 1 - but w/o provability.

This is exactly why some Bayesians say that no probability is without prior. The only way to deal with probabilities on this sort of level is to be very explicit about what you know and don't know when you model your current state of knowledge.

When you say probability theory doesn't include a framework for including beliefs, that may be true for traditional frequentist probably theory, but it is absolutely a big part of Bayesian probability theory. For a *really* good treatment of Bayesian probability theory I'd highly recommend Jaynes' book "Probability Theory: The Logic of Science". He makes a big point of pointing out that probabilities should be treated as degrees of belief which absolutely depend on a person's knowledge and he lays out all the mathematics needed for "updating one's belief" when you get more information or discover something by analyzing it (like in your square root example). This rule is simply Bayes theorem.

Amazing ! Love it ! This concept is just super duper cool I'm so excited to read the paper now :3

I can not literally imagine that the computers we use are result of countless transitions and one of those transition is just pure mathematics.

Miles is so smart, it literally hurts me to listen with full attention for too long at a time.

Amazing video also estimates :D

Maybe I’ll try to peek at that paper (my old brain is hurting already). But it seems to me that formal specifications and rational choice theory are good but limited; they only work to the extent of one’s understanding of the universe of discourse (even if you were logically omniscient). But it seems like the unaccounted for possibilities are a pretty serious concern in these cases - I guess I’m just restating the basic problem of induction. Which isn’t to say that it’s not useful to try and optimize what can be done re. what we do know and the limited resources available to process that knowledge (I am a card carrying Bayesian) just that a dose of humility re. any conclusions seems useful.

is there an implementation of explained algorithm?

Mathematician vs doubling cube: "Oh, powers of two".

just a question why do they always write on that dot matrix paper with green lines on it...I've never seen that paper before.

22:00 Almost made me choke from laughing while eating... I love Rob's tangents!

Do, would the AI become a Laplace's Demon if you let It to know more?

in the part about the gathering evidence and accumulating enough beliefs to narrow your probability down, I actually sort of see it like a -- imagine a hologram to be your understanding of the thing. you see the hologram by perceiving many images of it from many different angles, each helping you to formulate a better understanding of what is being shown (for me, probabilities are not really like numbers, but more like blurry images that slowly make more and more sense with time), so even if you perceive it from all angles, you can never really "see" the hologram for what it really is. the more angles I see of it, it'll create a sort of meta-logical understanding of what it really is which I can now apply to things of similar nature. so, how do you notice things of similar nature? well, I guess you could recognise aspects of details of the thing, but I personally "feel" it, and then the similar aspects start to show themselves. what I'm trying to say is, while watching this video, I'm realising that I perceive things a bit backwards. like he said, the probability theory assumes logical omniscience and so therefore, if the pattern is not understood, it cannot be recognised. the brilliance to my approach is actually the assumption that never is it possible to perceive the whole thing at once (omniscience), and so therefore a gradually sharper understanding of what's happening in the image, allows for that continual revelation of what the probability really is, that logical omniscience assumes.

As a fan of MassEffect this explanation reminded me a LOT of how the Geth build a "Consensus" among them, and the more there are that communicate, the better they work. Let's just hope we don't create something exactly similar and they exile us from the planet :D

where is the video where he talks about - should and is as ways to describe what is and what we want - he was talking about always needing two shoulds in order to express a wish in order to state a logic construct for comeing up with that wish!?? would really like to watch that video again. got stuck with me

If you can't use 1 or 0 probability, then it's ensuring the logic will fail because of the Halting Problem, instead of having limiting "Renormalization" boundaries, (I guess that's the logical objective of calculating probabilities in the first place). Very interesting discussion, thank you.

*Bringing the 'wisdom of markets' into AI research (and codifying it) intuitively seems like something that will be a game changer. It just makes sense, as it's how the world (and many natural systems within it) work.*

20:00 I now understand why futures markets are a thing.

I guess that logical induction must be perfected before they continue developing self driving cars. There are so many variables in such a short amount of time that it will have for computations.

7:53 Time 10:10 Seeing part of the process eliminates some wrong answers. 17:20 Well-Calibrated 19:02 Prediction Markets

class Task extends Goal { // you have the robot inherit you're overall goals so that they don't obstruct those while pursuing specific task }

Can you do a video on honeypots, honeynets, and honeyfarms?

There are not enough serious videos about computer intelligence

Does having a bunch of algorithms trading their predictions on a market have any better or worse or different consequences than doing Bayesian inference on their validity?

Going into 2021, where are we at with this?

27 quality minutes!

Whats hillarious about this is that instantly beeing able to process the stuff around you, is the semipossible superpower of sherlock holmes.

Isn't converging on a probability of 0 or 1 in contradiction to nondogmatism as it is essentially an approximation? To make an estimation of what an estimation is would seem to indicate an inaccuracy rather than an imprecision or a problem with applicability not application.

I love how Rob explains these papers.

I'm skeptical this approach works well in presence of randomness. Take a problem where a nondeterministic T machine is much faster than a regular one. Now consider betting on such a problem in presence of randomness. In such a case you can't have a condition about market not being beatable since someone could always get lucky and verify the answer.

Dutch was the term used for most germanic communities 100-300 years ago in the USA. This is still the case with the Pennsylvania Dutch, who in turn refer to all that is outside their community as "English".

what does this say about the nature of uncertainty, i mean is it an artifact of our ignorance, or is there something inherent in the physical processes that makes it so?

Do I understand correctly? The minds which are thinking towards AGI safety engineering are using the paradigm of neoliberal commodity markets as the mathematical instrument for ‘value alignment’ in a formal system of reason. i.e a google adwords algorithm trading cheap reasons instead of cheap adverts. What are the other predicates of this system that aren’t philosophically grounded in Classical economic theory?

Thanks for another great video with one of my favorite "mad scientists" (no offence ;). And I feel I have to add that I to prefer the "long form" where the expert is allowed take their own, sometimes meandering, way to expand and explain their topic, and You only "gently steer" with Your question. Jolly good job Sir :) Best regards.

The none dogmatism property is interesting, nice word to use instead of agnosticism.

23:24 super cool if every trader would affect the system equally. Reality is that the ones who will bet more, will affect the price more, and if her/his prediction is off, then humanity's predictions is off. Anyway, the video was great, thanks :)

This reminds me of TRON where the various programs compete against each other to see which one is fittest or something.

SUMMARY OF THE PAPER courtesy of CHATGPT Here are some notes on the "Logical Induction" paper: Introduction: The paper introduces the concept of Logical Induction as a new framework for reasoning about uncertain or unknown information. Background: The authors provide a brief overview of traditional induction methods based on probabilities and their limitations. Logical Induction Framework: The framework is described in detail, including its mathematical foundations and the rules for making predictions based on past observations. Advantages of Logical Induction: The authors argue that Logical Induction provides several advantages over traditional induction methods, including greater accuracy and flexibility. Applications: The authors discuss potential applications of Logical Induction in fields such as machine learning and artificial intelligence. Conclusion: The paper concludes by summarizing the benefits of Logical Induction and its potential for advancing the field of reasoning about uncertain information. --------------- HOW IS THE LOGICAL INDUCTION FRAMEWORK IN THE PAPER DIFFERENT FROM TRADITIONAL LOGICAL INDUCTION --------------- The Logical Induction framework proposed in the paper is different from traditional logical induction in several ways. Integration of Induction and Deduction: Traditional logical induction is based solely on logical deduction, while the Logical Induction framework proposed in the paper combines elements of both induction and deduction. Mathematical Rules: The Logical Induction framework is based on a set of mathematical rules, which define how to make predictions based on past observations. This is different from traditional logical induction, which relies on formal logic and inference rules. Flexibility: The Logical Induction framework is more flexible than traditional logical induction, as it allows for the incorporation of uncertain or unknown information into predictions. Accuracy: The authors argue that Logical Induction provides a more accurate approach to induction compared to traditional methods, as it takes into account both the logical relationships between variables and the empirical evidence from past observations. Overall, the Logical Induction framework in the paper represents a departure from traditional logical induction, offering a more comprehensive and flexible approach to reasoning about uncertain information.

More Rob, please.

check bayesian stuff thats also a good logical induction with uncertainty

I have a problem with the probability relationships as presented, compare 13:30: P(A), P(B), and P(A and B)

Oooh, I see that copy of Iain M Banks' "Consider Phlebas" on the shelf... nice.

Lem "Summa Technologiae" on shelf.

Make a video on how to think in recursion

It seems to be a sieve for AI models. Bad predictors can’t pass through the (50% accuracy) grid. Seems a bit like Kalman filtering from feedback control theory.

As a framework for producing safe AI (and I do not know how to code this) how about making the primary goal of the AI "minimize the impact of actions on the world in the process of achieving a task." This might make its utility more difficult to realize, but it should be safer. By "impact" I mean an increase of entropy. A human body is more organized than a smear on the floor (stepping on a baby to make tea). Converting a human body into crystalline forms of its constituents produces more entropy in the form of heat than leaving it alone.

and that why u need to remember.......remember as much as u can anyway

So you're making the Dunning-Kruger-Effect measurable :D

I've never forgot about htis guy since the "difference between a difficult problem and a very difficult problem...".

A useful demonstration of the Guess-the-Digit problem is to ask "What is the 10th decimal digit of 1/7?" The naive approach is to state that it must be one of the ten possible decimal numbers, and so the probability that it is the number, 1, is 10.00%. However, a little logical induction shows that the decimal digits of a fraction are always one of only seven possible choices: 01,2,4,5,7,8 And so the probability of the 10th digit of 1/7 being 1 is closer to 14.28% than it is to 10.00%. Furthermore, unless the first digit is the number, 0, then of those remaining six, the digits *always* proceed in the following sequence: 1,4,2,8,5,7 And so it is trivial to calculate that the 10th decimal digit of 1/7 is 8; the probability that the 10th digit of 1/7 being 1 is closer to 0% than it is to 14.28%. (Incidentally, this sequence is true for every fraction, n/7.) This truth is a consequence of the Discrete Logarithm Problem.

Perhaps the last criteria that things that cannot be proven do not take values of 0 or 1 is not that obvious. It's my understanding that Goedel's incompleteness theorem implies that there exist some statements that cannot be proven to be true/false. It seems to me like this supports the criteria because if something is not provable then you don't know whether it is true or false and therefore cannot assign definite 0/1 values to the statement.

The paper uses the qualifier "efficiently computable" so often that it doesn't really prove whole lot if the class of efficiently computable trading strategies is too small. Also the enumeration technique it uses is completely impractical.

Had a brain freeze watching this. At one point my brain slammed the door and shouted through the letter box, come back Tomorrow.

reasoning.... that thing that would be really nice if more people did do...

1 and 0 are not really probabilities: when you try to convert them to fractions you get 1/infinity or 1/1. True certainty (or 1 in this case) isn't really a prediction or a relation to the real world any more, because there's literally no possible observation you could make which could change it, not even direct observation.

What about undecidability? I assume an AGI would be Turing Complete. There is in general no decision procedure for a Turing Complete system's operation, so all the talk about proving theorems about an AGI's behavior seems vacuous.

Try wearing Bluetooth headphones at max volume and listening to the ending without going deaf

This is more of a meta-question or something, because it's not a about the paper's content, but the paper itself and the publisher---but I still think it's an important question: Is this published in a peer-reviewed journal? I know that MIRI has had some... _issues_... with that in the past. I don't see any journal info in the paper's title, so can we assume that it isn't peer-reviewed? More generally, does the Machine Intelligence Research Institute (formerly the Singularity Institute) still have little to no credibility, or have they improved? I haven't been keeping up with Yudkowsky's attempted "machinations" recently; is he still trying to form a cult and take over the world or whatever? Or did he (re?)-gain sanity? How much influence does he still have at MIRI? Is he still in charge?

Thank you for scaring me with a superabstract paper. If you are all fancy for AI, you should probably consider to learn about didactics in the first place.

I think it was a 3. Also, this video was really cool.