Comment by westoncb | Hacker News Reader

Comment by westoncb | Hacker News Reader

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If you are going to be an expert in one thing, and then augment with ancillary knowledge from other fields, you have to pick a subset of knowledge to learn from the other fields (if you weren't just learning this subset, you would also be an expert in the other fields). It looks to me like you are advocating one specific type of subset, which is something like implementation knowledge or foundations: math for physics, greek/latin for classical literature.

Not to say that's incorrect, but I would be curious to hear why you believe that's the most important subset to go after. Personally, I see foundations as critical for the field that you're going to be an expert in, but if you're picking up ancillary fields, I believe the question is more open (of course you shouldn't be totally ignorant of foundations, but...).

As an example of another subset you could take—which I think is fairly common and perhaps well-justified—meta-knowledge. That seems to be what you're complaining about with folks who are probably of a more philosophical bent who claim to be Bayesians, but don't know MCMC sampling (again, this is knowledge of a particular implementation of Bayesian ideas)—they focus instead on something more like a philosophy of probabilistic thinking, and so what's important to them is the relation of Bayesian probability to frequentist probability. They have no interest in performing calculations in either (doing so could help their goal of course, but it is not their end goal).

So if you have to pick a subset (of knowledge of some field), should it be more about how the field relates to other fields, or should it be more about the foundations of the field? IMO it should probably be taken on a case-by-case basis, but perhaps more often than not it's knowledge about how fields relate to one another that ends up being more useful in your ancillary picks (that totally depends on what you're doing with the knowledge though).

Thanks for the interesting post - however, I respectfully disagree with the example you've picked out.

How can you do intelligent philosophy about probability if you don't have a good detailed understanding of what probability is?

To make a concrete example: the best philosophers of logic (Kripke, Ruth Barcan Marcus, Quine, etc) were also superb logicians with an excellent understand of logic itself. Regardless of how you feel about his atheism, Richard Dawkins is in my mind the best philosopher of biology currently alive, and his first two books (Selfish Gene and Extended Phenotypes) are masterworks. Certain concepts in physics are much clearer when formulated in math - and you can only really explain them clearly once you are firmly grounded in the math. Speaking for myself, I've never met someone who I would describe as having a fantastic understand of QM yet skipped the formal mathematical training to deeply understand the equations.

> How can you do intelligent philosophy about probability if you don't have a good detailed understanding of what probability is?

There is more than one way to answer the question of 'what probability is'; you are advocating for an inductive approach where the general category is arrived at through exposure to particular instances; another approach is to work within a more general framework which expresses different types of probability theories as configurations of more general types. Granted, one must start inductively in order to get the general framework I speak of—but such frameworks are now in place, so it is not necessary for everyone who wants to compare theories of probability to proceed inductively. Then again, if your expertise is philosophy of probability you should do it anyway—but that brings me to the other point I wanted to make, which is: in my original post I was not referring to philosophers of probability, since that would be their expertise; instead I was referring to ancillary knowledge and whether someone acquires foundational or 'philosophical' (i.e. meta) knowledge of these ancillary fields.

As for whether there can be value to knowing about something like QM without knowing the math behind it, consider Feynman's preface to Q.E.D (the edition he wrote for the layman [well, transcription of lectures technically]). In it he describes the six years of training required in order to actually perform the mystical rites of physics, but knowing what the rites are about and what purpose they serve etc. is also valuable, which is why he wrote the book/gave the lectures (sorry, trying to give a rough quick summary, but the analogy he presents in the preface is the best explanation I've seen).

But that's exactly my point. Feynman was only able to give such a clear explanation because he really understood QM inside out.

If you want to describe yourself as someone who can read and appreciate Feynman's books - that's completely fine with me. However, I hope we can agree that reading Feynman's books (the ones for laymen at least) is not enough to call yourself a polymath.

> However, I hope we can agree that reading Feynman's books (the ones for laymen at least) is not enough to call yourself a polymath

Of course not. However, first off, the reason I brought up the specific book of Feynman's wasn't because I believe reading it gives you anything special—I was just referencing an argument that Feynman makes in the preface.

Secondly, I'm addressing what I see as an impossibility in what it appears to me that you're advocating for:

> I've never met someone who I would describe as having a fantastic understand of QM yet skipped the formal mathematical training to deeply understand the equations.

That quote sums up what I'm talking about. Another way of stating it, at the level of generality of the greater question at hand here: "no one who is not an expert in field X understands field X as deeply as someone who is an expert in field X" —since people generally already know that, the more useful question is, "If I'm going to learn some things about field X, even though I'm an expert from field Y and not field X—which things from field X should I focus on?"

I think part of our disagreement here comes from what one pictures the person with knowledge of many fields doing with that knowledge. Are they working professionally as a philosopher and then on the weekends as a physicist? If so, they have to be an expert equally in both. Or, is there something that can be added to their philosophy work by having fairly in depth knowledge of say, physics, linguistics, psychology, history, and literature? If you are going for this second thing, the way you pick up knowledge from the ancillary fields is different from if you're going for the first thing.

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