Career, Physics and Goals (was: Artificial General Intelligence Speculations)

Yeah that’s a factor.

So consider:

define f(x): 2x >= 100

The domain (allowed inputs) is integers.

So you can use 50 as a base case and inductively prove that f is true for the range {50…∞}.

But someone says “our process has to start at 1” or “we need proofs that apply to all natural numbers; give me one of those”. How can you make an inductive proof to satisfy them? It will not be perfect depending on the exact use case (since literally f is not true for e.g. 10), but there is something you can do that might solve their problem.

Also, can you imagine any scenarios where they are making a reasonable request?

There are certainly scenarios where it is not very reasonable. E.g. you get hired at the CIA and they say “our policy here at the CIA is we only record proofs about all natural numbers in our proofs database, cuz we thought if we put in just any proof we’d run out of disk space, so we needed a way to limit things”. Stupid government red tape… Nevertheless, you could do something to get a proof related to f into their database.

Answering this stuff helps connect induction to other concepts and also would demonstrate some flexible understanding that most high school students don’t have even if they are able to do some standard induction problems on their math tests. This is not meant to be very hard or long if you know the other relevant concepts I have in mind (which I think lmf does).

I have read material on several parts of physics. The material I have read on string theory is among the worst stuff I have read. The people who write about string theory don’t seem to be particularly interested in quantum theory or general relativity, or in explaining the problems they’re trying to solve. Their material reminds me of this quote from DD in a talk he gave called “Apart from universes” [1, 2 Chapter 18]:

There’s a related and even worse spanner in the works of elementary particle physics: particles (or fields, strings, or whatever) are supposed to be fully quantum-mechanical entities. But the people who work on them only ever construct classical, single-universe theories. Why? Because they think that the quantum part of the theory necessarily has to be trivial. It is assumed that in order to discover the true quantum-dynamical equations of the world, you have to enact a certain ritual. First you have to invent a theory that you know to be false, using a traditional formalism and laws that were refuted a century ago. Then you subject this theory to a formal process known as quantization (which for these purposes includes renormalization). And that’s supposed to be your quantum theory: a classical ghost in a tacked-on quantum shell.

define g(x) : f(x + 49),

then you can inductively prove g is true for {1,…,∞}

Well, I think stuff like that could be needed for formal proof assistants like coq. E.g. I think it would be completely reasonable to use the formal defn I gave (the one that only worked for predicates holding for all natural numbers) to define induction for the computer, then whenever you want to use it in a proof you have to modify your input predicate so that it fits.

I was going to define two new functions: one to map between sequences, and then one to compose the first two functions. But sure, your way works too.

Doing that shows how induction can be connected with other concepts (in my version, they are explicitly mapping and composing). Some people can do that and some can’t (or maybe only with guidance/hints/etc.). It’s a way people’s knowledge varies.

Similarly, some people find such things easy, intuitive, kinda fun. Others find it burdensome work to be avoided unless there is a clear purpose. The first group have a much better chance to accomplish stuff that’s creative.

Some people have rigid ideas like induction must work for all natural numbers. They might think you must use mapping and composing, or some other conversion method. But that’d be a bad way to conceptualize the issues. It’s good to be able to induce for 50+ directly without requiring extra steps, extra tacked on complexity which usually isn’t useful.

Make sense, agree?

This much I agree with. String theory people often don’t have great explanations of why they are solving the problems they are trying to solve, and even when they do they often don’t explain it clearly.

There’s a related and even worse spanner in the works of elementary particle physics: particles (or fields, strings, or whatever) are supposed to be fully quantum-mechanical entities. But the people who work on them only ever construct classical, single-universe theories. Why? Because they think that the quantum part of the theory necessarily has to be trivial.

Deutsch is just dead wrong about this.

I don’t know exactly what a “fully quantum mechanical” entity is, but I don’t think that the particles in QFT count (nor do I think strings or branes count, but that’s a more complicated discussion). Particles arise when you try to write your path integral as an asymptotic series in ħ, so the assumption that quantum effects are small is built into the whole formalism of perturbative QFT.

People who work on this stuff simply do not think that “the quantum part of the theory necessarily has to be trivial.” I thought that every theorist knows that this quasi-classical / perturbative way of studying QFT is not the whole story. Non-perturbative QFT is a huge area of study: almost everyone who calls themselves a string theorist works on some aspect of non-perturbative QFT, and “non-Lagrangian” field theories (i.e. quantum field theories with no classical limit) show up all the time.

The methods for studying non-perturbative QFT are more limited, so a lot of things about it are very mysterious. There’s not a lack of interest, though!

It is assumed that in order to discover the true quantum-dynamical equations of the world, you have to enact a certain ritual. First you have to invent a theory that you know to be false, using a traditional formalism and laws that were refuted a century ago. Then you subject this theory to a formal process known as quantization (which for these purposes includes renormalization). And that’s supposed to be your quantum theory: a classical ghost in a tacked-on quantum shell.

Since perturbative QFTs have classical limits, it’s not problematic at all that one starts with a classical field theory (there’s some extra wiggle room that comes up in one’s choice of renormalization scheme; different renormalization schemes would lead to different perturbative theories). Not every quantum theory can be obtained in this way, but I don’t think that theorists forget that.

Yes and yes.

Now that we clarified stuff more, want to try explaining trig more?

Okay.

It seems odd to me that you say you don’t understand something and then continue to write without asking questions. A longer explanation of what DD is talking about can be found here:

I’ll read the paper. Looks cool and completely different from the approaches to QFT that I’ve seen before.

Okay sure. Here’s how I should have begun an introduction to trigonometry (rather than regurgitating SOHCAHTOA in 20 seconds):

As you go around a circle, your position on the circle is entirely determined by the angle theta that you’ve swept out. Just like how on a clock, you could tell what time it is if only you knew what angle the hour hand and minute hand are each making with the vertical “12” mark. The sine and cosine functions allow us to convert between an angle theta, and the x,y (“cartesian”) coordinates of the point on the circle which is found at angle theta. In the clock analogy, imagine that we put the hands of the clock on some graph paper. Then if we knew the angle of the minute hand and its length, the sine and cosine functions would allow us to determine which square cell the tip of the minute hand is in. [Insert picture here]

To define these functions precisely, we first choose as a convention the following way of defining the angle: we measure the angle between a ray going out from the origin and the +x axis, and an increase in the angle corresponds to a rotation of the ray in the counterclockwise direction. [Insert picture here]. Then, we define two functions sin(theta) and cos(theta) as follows: the x,y coordinates of the point on the circle centered at the origin of unit radius at angle theta are ( cos(theta), sin(theta) ). Note that these functions are well-defined (they take a single value at any given theta), and that they are necessarily 2*pi periodic. Also note that if we had defined theta in a different way (say by letting it increase in the clockwise direction and start at the -y axis, or by letting the circle have radius 2 and be centered at (1,1)), we’d get different functions, though we wouldn’t lose any essential information; they would just be translations or inversions or rescalings of what we just defined.

Why do we care? Speaking very generally, knowing how to convert between these two descriptions of geometry is important because sometimes things are easier to understand or compute in the angular description, and sometimes it’s easier in the cartesian description. Also, there are a lot of problems that you didn’t know how to solve in geometry that trig will enable you to solve easily (or to say it a bit more precisely, it will allow you to easily reduce such geometry problems to already-solved problems like finding the first three digits of cos(7 * pi / 16)). There are many more reasons why trig is important (like how (cos,sin) is the fundamental example of a covering map, like Fourier transforms, etc), but they won’t come up until later in your education so I can’t motivate them properly now.

I think that most of the standard trig facts can be derived from this starting point. The next thing I’d do would be to explain how to determine the cartesian coords of a point on a circle of any radius by rescaling, and in the same breath I could derive the SOHCAH rules for right triangles. Then I’d explain how to compute sine and cosine for certain special values of theta like pi/4, how to derive certain properties like antisymmetry under translation by pi, then I might show them a numerical plot of sine and cosine and check that it is consistent with the properties we’ve derived, etc etc.

I think it would be good for me to state the following facts explicitly so that I can’t evade them later if someone criticizes my explanation:

  • Writing this explanation took much more effort than the last one (in total I think it was about ~1.5 hours of writing, plus something like ~1hr of thinking about it over the past couple days).
  • My least favorite paragraph of the explanation I gave is definitely the first one (where I describe the general idea), but I don’t know exactly what I dislike about it or how to improve it.
  • Overall I am fairly satisfied with what I wrote.

Would you agree that that amount of time indicates lack of mastery? And that it’s partly lack of mastery of trig concepts, rather than only of writing?

BTW, placing a low value on writing is a systemic error in math and physics related to anti-conceptual attitudes. Writing in a language like English is humanity’s best general tool for dealing with concepts/ideas. Being able to explain concepts in words is a big part of how people learn them, think about and discuss them, improve them, etc. It also helps with remembering without memorizing.

[Insert picture here]

What’s the reason for omitting pictures? That also seems like it indicates lack of relevant mastery. In other words, you find something hard or burdensome about including the pictures. The process is not easy/intuitive/automatic for you. That seems problematic because working with diagrams on computers is a relevant useful skill for your fields. (Related, I noticed you didn’t use any MathJax in this post or IIRC previously, which could indicate a lack of mastery of LaTeX, which also seems relevant to your fields.)


Also, do you agree that trig is a relevant building block to your field, and something you should be good at?


The big picture is that, while you know some stuff about how it works, I think the concepts and writing are both kinda a mess. It’s not well-organized, streamlined knowledge. It has “code smells” if you know that term. This is different than wrong and is compatible with doing the calculations correctly for tests.

I want to start with the above, not explain this part more yet, but I didn’t want to leave out an overall comment entirely.

Yes, the fact that I spent so much time indicates lack of mastery of something.

I don’t know how to separate out lack of mastery of trig concepts from lack of other sorts of mastery, so I can’t answer the second question.

This lack of interest in clear writing is something that has always bothered me about my field. People are much better rewarded for getting the right answer than they are for giving clear explanations. I can see how that’s an anti-conceptual attitude.

This may surprise you, but I think I have always placed a higher value on explanations than any of my math/physics peers (the ones that I’ve met at least), and many of my professors (though that’s harder to judge). Now I’m starting to think that I haven’t done it enough.

I think you are wrong about me lacking relevant mastery here.

I use TeX all the time, I take notes in it, I do my homework in it, and I am comfortable with it. I figured that this forum might support TeX equations because I think I saw Max using it earlier, but I didn’t care enough to look into it because none of the math I’ve had to type here is notationally complicated.

Regarding pictures (edit: new thoughts caused me to make significant changes to this section like an hour after I wrote it),

  1. I had resolved not to look anything up when I wrote my explanation, so I didn’t want to go find suitable images from Wikipedia or somewhere else on the internet. I think that they would be easy to find b/c it’s such a common topic, and if I had an image I wanted I could insert it into my forum post in like 20 seconds with no thought.
  2. I normally could make a digital drawing really easily too, but I got a new computer a few days ago and still have to set some things up, and I guess I didn’t think it was worth the bother in this case.
  3. TikZ diagrams are relevant for my field, but I haven’t learned TikZ yet because I have not yet written anything that requires me to make a custom diagram (so there is a lack of mastery here but not an important one—yet).

Yes.

Okay, I await your elaboration.

Actually, I guess I could have drawn something on a piece of paper and taken a picture really easily, but I didn’t do that. The question I then need to ask myself is: If it’s easy for me to put pictures in my post, and if my goal in writing that post was to make as clear an explanation as possible, why didn’t I put pictures in my post?

I think that the answer to that question is that I just didn’t think much about the costs or benefits of adding pictures. I don’t think I even considered adding real pictures. I was being irrational, because in hindsight I do think that pictures would add a lot to the explanation I gave.

This is still not a lack of mastery, though. At least not a lack of mastery wrt computer images or TeX.

When I parenthetically wrote:

could indicate a lack of mastery of LaTeX

that is not wrong if, in this case, there is no lack of mastery.

The thing I was claiming was that it was worth mentioning (as an aside) given the evidence available to me. After seeing your reply, I stand by that.

What I said about images could also be accurate even if your reply is correct. So I’m concerned that you’re not noticing the difference when I say one thing instead of another kinda similar thing.

Not considering something does show lack of mastery. It means the ideas aren’t integrated well enough into your life/thinking. Easily recognizing opportunities to use something is part of mastering it.

In short, mastery includes everything necessary to use something in your life and to connect it with your other ideas and your actions.

Why didn’t you mention this earlier when I was saying there were systemic issues in your field and you said that I was biased instead of volunteering this opinion of yours that a major systemic issue exists in the field?

BTW, you didn’t respond to my denial re bias, so I don’t know if you changed your mind or what.

Why would it surprise me? It is on-theme/on-message for what I have been saying in this topic. It’s the kind of thing I was trying to tell you. Did I say something that clashes with it or shows potential ignorance of it?

I think I had it filed away as a different category of error, so it just never came to mind. I think I saw it as like “here’s this slightly annoying cultural thing in my field that makes lectures more boring and makes some papers harder to read,” rather than “here’s this evidence of an anti-conceptual attitude in my field that could affect the actual physics.”

Sure, I changed my mind. By the way, I think I did respond in some sense because I liked the post. If there was something you said in your post that I had a significant disagreement with, I wouldn’t have liked it.

Because in the whole thread you have been talking about how I don’t put enough value on explanations and concepts. I’m saying that you might be surprised to know that I think I’m better about it than so many others in my field, as opposed to me being an average representative.

(I also figure you probably aren’t actually all that surprised, given that we have had conversations and that you know that I’m interested in philosophy. I was saying “this may surprise you” in kind of a tongue-in-cheek way.)

I’m posting as a practice activity (improve posting frequency) and to check my understanding. Not meant to disturb the discussion.

I think that @lmf could value explanations and concepts more than most in his field but still undervalue them. Like a person could be bad at X and the entire field could be really bad at X. In that case the person would be better than most in his field at X but still bad at X.

1 Like

I don’t know if you want this feedback, but this wording reads to me as passive-aggressive. It’s a cumbersome wording (“seems odd to me”) and an indirect (passive) way to criticize an error (aggressive).

A more direct version, just as an example for comparison, would be: You say you don’t understand this, so it doesn’t make sense to comment on it, particularly with a strong opinion. Commenting is implicitly premised on understanding the thing you’re commenting on. A better way to deal with not understanding something is to ask questions about it.

Another reason I thought it could be passive-aggressive is that I saw a trigger for that type of response. The trigger was the arrogant, aggressive, non-tentative comment that you were replying to:

Deutsch is just dead wrong about this.

And that was actually part of a pattern. Earlier in this thread, lmf was similarly dismissive of DD’s ideas about physics, in favor of his own:

but that’s simply false.

If you were offended by these comments, or disliked or disagreed with them, there are better ways to handle them, like commenting directly on what you think is objectionable about them.

If there was some other cause in this particular case rather than being passive-aggressive, then your text miscommunicates, which is also bad. One enabler of this kind of miscommunication is being capable of being passive-aggressive, rather than having automatized awareness of the issue and its problems – that enables writing stuff that sounds passive-aggressive, with the wording intuitively seeming normal instead of you noticing the problem, even when actually something else is going on.

A difficulty with this kind of writing (both the passive-aggressive sentence and the arrogant sentences) is people often intuitively know what it means but don’t explicitly, consciously know what they are reacting to and why. People often get impressions, emotions and intuitions, based on their subconscious and automatized knowledge, without knowing exactly what happened. That makes it hard for them to address the issues directly or specifically. That’s one of the things that happens to me: People feel like I’ve been mean to them, and then when I ask for a quote with an explanation of what was mean about it, they can’t give one. But they still have the feeling and general negative impression. They often fail to problem solve that themselves and also don’t ask for help with that problem solving process (they often also reject help if I offer it, claiming that the problem is solved as a way to end the discussion. They say this when they have not automatized better knowledge; they just reached a conscious conclusion that they were wrong and then tried to suppress their feelings that they regard as irrational and perhaps also static memes). This kind of thing causes a lot of trouble and is one of the ways people end up failing.

BTW, I am interested to see some continuation/resolution to the debate about string theory. There appears to be a substantial disagreement between two people who both have some relevant expertise.

1 Like

I finally got around to doing this. I recorded every “trivial” mistake I made in a ~2hr period of doing calculations. To be clear, these are the types of things I was referring to earlier as “arithmetic mistakes,” even though strictly speaking they are mostly not arithmetic mistakes.

For all the things I’m about to mention, I did them in my head, wrote the answer down, and then noticed an error a little bit later. These were small parts of much longer calculations. I happened to notice all these errors before they propagated very far so they were easy to fix.

I was doing what I consider a medium amount of error correction. I wasn’t rushing, but I wasn’t being particularly careful either.

Here’s my log of all my “trivial” mistakes:

  • On one line, I had a 1/2 factor sitting next to some quantity X, and then I evaluated X and it contained a factor of 1/4. On the next line I intended to combine these factors, which should have resulted in a 1/8, but for some reason I wrote 1/4 instead.

  • There was a b^{-5/2} in my answer and I accidentally wrote b^{5/2}

  • There was a b^{-1} that I accidentally wrote as b (not directly related to above error)

  • I had to do evaluate an integral of the form \int_0^\infty e^{-(a + b)x}dx, and I forgot about the a and wrote the integral as 1/b instead of 1/(a+b)

  • I took the x derivative of e^{a x} and wrote it as a rather than a e^{a x}

  • I had an expression of the form (e^{-a x} - e^{-b x}) that I needed to Taylor expand to first order in x, and I wrote (a - b)x rather than (b - a)x

I would be very interested to know if you (@Elliot presumably) can think of a way that a conceptual deficiency could be causing some of these errors, or if there is some extra info I could provide (or extra experiments I could do) that could reveal that. My operating theory up til now has basically been that the unaided human brain (or at least my unaided human brain) can’t avoid errors like these.