Filter This month

Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

Comment author: Dacyn 15 February 2018 12:34:54AM *  1 point [-]

I don't know much about Clifford algebras. But do you really need them here? I thought the standard formulation of abstract quantum mechanics was that every system is described by a Hilbert space, the state of a system is described by a unit vector, and evolution of the system is given by unitary transformations. The Born probabilities are concerned with the question: if the state of the universe is the sum of where are orthogonal unit vectors representing macroscopically distinct outcome states, then what is the subjective probability of making observations compatible with the state ? The only reasonable answer to this is , because it is the only function of that's guaranteed to sum to based on the setup. (I don't mean this as an absolute statement; you can construct counterexamples but they are not natural.) By the way, for those who don't know already, the reason that is guaranteed to sum to is that since the state vector is a unit vector,

Of course, most of the time when people worry about the Born probabilities they are worried about philosophical issues rather than justifying the naturalness of the squared modulus measure.

In response to Be secretly wrong
Comment author: Sengachi 03 February 2018 08:07:46AM 1 point [-]

"Not if they change their minds when confronted with the evidence."

"Would you do that?"


This is where I think the chain of logic makes a misstep. It is assumed that you will be able to distinguish evidence which should change your mind from evidence that is not sufficient to change your mind. But doing so is not trivial. Especially in complicated fields, simply being able to understand new evidence enough to update on it is a task that can require significant education.

I would not encourage a layperson to have an opinion on the quantization of gravity, regardless of how willing they might be to update based on new evidence, because they're not going to be able to understand new evidence. And that's assuming they can even understand the issue well enough to have a coherent opinion at all. I do work pretty adjacent to the field of quantized gravity and I barely understand the issue well enough to grasp the different positions. I wouldn't trust myself to meaningfully update based on new papers (beyond how the authors of the papers tell me to update), let alone a layperson.

The capacity to change a wrong belief is more than just the will to do so. And in cases where one cannot reliably interpret data well enough to reject wrong beliefs, it is incredibly important to not hold beliefs. Instead cultivate good criteria for trusting relevant authority figures or, lacking trusted authority figures, simply acknowledge your ignorance and that any decision you make will be rooted in loose guesswork.

Comment author: cousin_it 27 January 2018 09:36:08AM *  1 point [-]

What a beautiful comment!

Every once in a while I wonder if something like Eliezer's Lawful Creativity is true - that creativity can be reduced to following rules. And then I come across something like your comment, where a non-obvious "jump" leads to a clearly true conclusion. For humans trying to create new stuff, practicing such "jumps" is at least as important as learning the rules.

Comment author: pjeby 22 January 2018 09:46:37PM 1 point [-]

I think that using the word "valuing" adds back in confusion that this trichotomy is trying to remove. Wanting is the axis of urgency to act or not act, liking is the axis of feeling enjoyment or suffering, and approving is the axis of feeling morally elevated or disgusted. These are independent axes that can exist simultaneously regardless of time, and which are only made more vague by lumping them together as "valuing".

(Notably, one's experience can be placed simultaneously on all three axes: it is not necessary for these experiences to be separated in time. You can approve or disapprove beforehand and during, not just after. You can want while doing, as well as beforehand.)

In response to comment by RobbBB on Causal Universes
Comment author: Caspar42 16 February 2018 05:09:26PM 0 points [-]

(RobbBB seems to refer to what philosophers call the B-theory of time, whereas CronoDAS seems to refer to the A-theory of time.)

Comment author: jrincayc 12 February 2018 03:31:33AM 0 points [-]

I have used Lulu to print the book, instructions are at: Or you could print it somewhere else that allows you to print a 650 page 8.5 by 11 inch book. (If you try it with a different place, let me know) I have read through the entire printed version and fixed all the formatting issues that I found in the beta7 release in the new beta8 release.

Comment author: BentleyDavis 10 February 2018 11:18:12PM 0 points [-]

Hello everyone, I hope you don't mind me joining in on this 8 year old post. I've been working on ideas like this since 2012 and just found this. My current experiment is Reason Score where I am working on a way to measure the reasonableness of a claim based on the pro and con claims added to it. This will hopefully reduce cognitive biases by forcing people to add reasons to affect the score instead of votes. In the least it will encourage people to think through their claims.

It's not documented well so it might be best if someone has some time to debate me on a topic and see if it provides benefit. Any takers?

Comment author: trickster 10 February 2018 07:10:12PM 0 points [-]

I think that you can't count most of the Chinese as non-communist. Centralized propoganda is a strong weapon and shouldn't be discounted. When people first start doubting church dogmas- in most part they developped a some kinds of heresy, not an atheism. So, they doesn't believe in offical religion, but for outer observer point of view - they beliefs was almost indistingushable from offical dogma. And in the example with Soviet Union- communist party still exsicte tin Russia. It's influence slowly dyied out, but right after the disintegration of Soviet Union they have a really good chance to win elections

Comment author: trickster 10 February 2018 06:51:02PM 0 points [-]

It's worth pointing that phrase "atheism is also a religion" is essentially an accusation. So, the notion that religion is a bad stuff is so ingrained even in beliviers mind, if they think that phrase "you have a religion" can be used as an acusation

Comment author: thecleeds 04 February 2018 01:10:47PM 0 points [-]

What bugs me about this article is that we have 'half silvered mirrors'. By definition they divert half and allow half through. Like the one at 'A'. But then suddenly, with the one at 'D' we get "And what D does to a photon, depends on the angle at which the photon arrives" - so not a half silvered mirror, but something else, with no explanation of how or why the angle affects the outcome.

As a layperson whose understanding changed from billiard balls to waves to probabilities I suspect there is no 'reality' that everything can be reduced to - and I certainly don't think 'amplitudes of configurations' will be it. Even if the description is useful, they do not actually exist, just as billiard balls and the rest are just useful-at-times descriptions.

Comment author: Sengachi 03 February 2018 06:37:51AM 0 points [-]

Hmm. I don't think it's not useful to practice looking at the truth even when it hurts. For instance with the paperwork situation, it could be that not fixing the paperwork even if you recognize errors in it is something you would see as a moral failing in yourself, something you would be averse to recognizing even if you allowed yourself to not go through the arduous task of fixing those mistakes. Because sometimes the terminal result of a self-evaluation is reducing one's opinion of oneself, being able to see painful truths is a necessary tool to make this method work properly.

That said, I do think this is a much more actionable ritual than just "look at the painful thing". It also serves better as a description of reality, encompassing not just why certain truths are painful, but also how they become painful. It establishes not just a method for coping with painful truths and forcing confrontation with them, but also for establishing mental housekeeping routines which can prevent truths from becoming painful in the first place.

This has been a topic I started thinking about on my own some months ago (I even started with the same basic observation about children and why they sometimes violently reject seemingly benign statements). But I think my progress will be much improved with a written document from someone else's perspective which I can look at and evaluate. Thank you very much for writing this up. I really appreciate it.

Comment author: Sengachi 03 February 2018 06:12:30AM *  0 points [-]

Just so you all know, Clifford Algebra derivations of quantized field theory show why the Born Probabilities are a squared proportion. I'm not sure there's an intuitively satisfying explanation I can give you for why this is that uses words and not math, but here's my best try.

In mathematical systems with maximal algebraic complexity for their given dimensionality, the multiplication of an object by its dual provides an invariant of the system, a quantity which cannot be altered. (And all physical field theories (except gravity, at this time) can be derived in full from the assumption of maximal algebraic complexity for 1 positive dimension and 3 negative dimensions). [Object refers to a mathematical quantity, in the case of the field theories we're concerned with, mostly bivectors].

The quantity describing time evolution then (complex phase amplitudes) must have a corresponding invariant quantity that is the mod squared of the complex phase. This mod squared quantity, being the system invariant whose sum describes 'benchmark' by which one judges relative values, is then the relevant value for evaluating the physical meaning of time evolutions. So the physical reality one would expect to observe in probability distributions is then the mod squared of the underlying quantity (complex phase amplitudes) rather than the quantity itself.

To explain it in a different way, because I suspect the one way is not adequate without an understanding of the math.

Clifford Algebra objects (i.e. the actual constructs the universe works with, as best we can tell) do not in of themselves contain information. In fact, they contain no uniquely identifiable information. All objects can be modified with an arbitrary global phase factor, turning them into any one of an infinite set of objects. As such, actual measurement/observation of an object is impossible. You can't distinguish between the object being A or Ae^ib, because those are literally indistinguishable quantities. The object which could be those quantities lacks sufficient unique information to actually be one quantity or the other. So you're shit out of luck when it comes to measuring it. But though an object may not contain unique information, the object's mod squared does (and if this violates your intuition of how information works, may I remind you that your classic-world intuition of information counts for absolutely nothing at the group theory level). This mod squared is the lowest level of reality which contains uniquely identifiable information.

So the lowest level of reality at which you can meaningfully identify time evolution probabilities is going to be described as a square quantity.

Because the math says so.

By the way, we're really, really certain about this math. Unless the universe has additional spatial-temporal dimensions we don't know about (and I kind of doubt that) and only contains partial algebraic complexity in that space (and I really, really doubt that), this is it. There is no possible additional mathematical structure with which one could describe our universe that is not contained within the Cl_13 algebra. There is literally no mathematical way to describe our universe which adequately contains all of the structure we have observed in electromagnetism (and weak force and strong force and Higgs force) which does not imply this mod squared invariant property as a consequence.

Furthermore, even before this mod squared property was understood as a consequence of full algebraic complexity, Emmy Noether had described and rigorously proved this relationship as the eponymous Noether's theorem, confirmed its validity against known theories, and used it to predict future results in field theory. So this notion is pretty well backed up by a century of experimental evidence too.

Tl;DR: We (physicists who work with both differential geometries and quantum field theory and whom find an interest in group theory fundamentals beyond what is needed to do conventional experimental or theory work) have known about why the Born Probabilities are a squared proportion since, oh, probably the 1930s? Right after Dirac first published the Dirac Equation? It's a pretty simple thing to conclude from the observation that quantum amplitudes are a bivector quantity. But you'll still see physics textbooks describe it as a mystery and hear it pondered over philosophically, because propagation of the concept would require a base of people educated in Clifford Algebras to propagate through. And such a cohesive group of people just does not exist.

Comment author: Caspar42 02 February 2018 04:03:03PM 0 points [-]

I tried to run this with racket and #lang scheme (as well as #lang racket) but didn't get it to work (though I didn't try for very long), perhaps because of backward compatibility issues. This is a bit unfortunate because it makes it harder for people interested in this topic to profit from the results and submitted programs of this tournament. Maybe you or Alex could write a brief description of how one could get the program tournament to run?

Comment author: MathieuRoy 27 January 2018 09:48:24AM 0 points [-]

the link is broken

Comment author: cousin_it 23 January 2018 10:33:15AM *  0 points [-]

How come we never see anything physical that behaves like any of of the non-standard models of first order PA?

Qiaochu's answer: because PA isn't unique. There are other (stronger/weaker) axiomatizations of natural numbers that would lead to other nonstandard models. I don't think that answer works, because we don't see nonstandard models of these other theories either.

wedrifid's answer: because PA was designed to talk about natural numbers, not other things in reality that humans can tell apart from natural numbers.

My answer: because PA was designed to talk about natural numbers, and we provably did a good job. PA has many models, but only one computable model. Since reality seems to be computable, we don't expect to see nonstandard models of PA in reality. (Though that leaves the mystery of whether/why reality is computable.)

Comment author: trickster 21 January 2018 05:58:27PM 0 points [-]

''Assign a dollar value to punitive damages''' - does this corelated with the ammount of money, that peoples, who responded to this earn? It look plausible that people who earn more can assign a highely money punishement for body harm