Comment by knzhou | Hacker News Reader

Comment by knzhou | Hacker News Reader

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Explaining the Standard Model clearly and correctly is just really hard! I've tried, a lot. Costless simplification is impossible, because the mathematical form it's usually written in is already the simplest, clearest, and most concise way we know to describe it. (If there were a better way, we'd be using that instead!)

Anything simpler necessarily sacrifices correctness. Metaphors are great, but it's clunky to explain when the metaphor stops working or becomes actively harmful to understanding. For example, adding a 4th neutrino that is otherwise identical to the other 3 would break the Standard Model would violate anomaly cancellation, making the model mathematically inconsistent. But explaining from scratch what an anomaly is or why they need to cancel would require a ton of vague, fragile metaphors layered on top of each other, at which point I'm not sure what value it would provide.

Imagine explaining how a CPU works on the silicon level to somebody from the 18th century. It's the same problem -- it's hard to say anything that isn't the length of a full textbook, or completely misleading, or bordering on woo. I've written and then thrown away a lot of attempted explanations because of this.

> Anything simpler necessarily sacrifices correctness.

But not clarity.

This is the crux of the problem. Mathematicians, and by extension, theoretical physicists are under the impression that the most terse, most technical, most "correct" (by some abitrary definition!) definition is the only one that matters, and that nothing else should ever stain their lips.

Take a tour of any abstract mathematical topic on Wikipedia. It's a travesty.

Nothing at all can ever be understood from those pages by even an extremely intelligent person who doesn't already know the topic.

Do you see the issue? You have to already understand to gain understanding... err... of a thing you don't understand, hence the need for a Wikipedia page. If you understood it, then as a "quick reminder reference" the Wikipedia page might be useful, but then the audience is a few hundred people.

There is absolutely no difference between this idiotic behaviour of mathematicians, and the insistence of English priests in the middle ages of sticking to Latin for theology. NONE.

If you argue this point, first explain to me why physics is done with Greek letters.

I bet whatever you say will be indistinguishable from the arguments made by those priests.

> Imagine explaining how a CPU works on the silicon level to somebody from the 18th century

I could do this, no problem. It would take about 20-30 hours of talking and something to scribble on, but I could do it.

I would use analogies with things they already understand, such as the hydraulic control lines of steam-powered machinery, and explain that electronic transistors (called 'valves' back in the day!) are just like the hydraulically or pneumatically controlled valves they use every day in industry. Just more of them, faster, and smaller.

See, it's not that hard.

> I've written and then thrown away a lot of attempted explanations because of this.

Try using geometric algebra instead of the mishmash that is vector algebra. Try avoiding complex numbers. Try to avoid Greek letters. Try to avoid mixing ten branches of mathematics just to shave off a few letters in an equation somewhere. Try using an analogy with things the audience might already be familiar with.

Try harder.

And then you end up with explanations like "Gravity is like a deformation of a rubber sheet". Completely misleading. In a similar case (not physics), I literally wasted years on trying to understand something correctly because I wriggled from analogy to analogy instead of putting effort into learning it correctly.

> I would use analogies with things they already understand, such as the hydraulic control lines of steam-powered machinery

How many people from the 18th century knew how those worked? You would be talking to an elite engineer. And even then you would first have to explain to them how you can represent numbers and numerical operations with those valves. I am pretty sure that if you take a today's elite engineer and take the time to explain him the basics correctly, he would be able to understand theoretical physics. That's what's happening in universities every day.

> If you argue this point, first explain to me why physics is done with Greek letters.

There are probably some historical reasons for that, but today it's just because you are quickly running out of latin letters in complex equations, at least that's my opinion :)

> And then you end up with explanations like "Gravity is like a deformation of a rubber sheet".

If you haven't read Eistein's "Relativity : the Special and General Theory", I strongly recommend you do.

It's a book aimed at laypeople, that requires only a basic (1st undergrad semester) understanding of calculus and vectors (not vector calculus, not linear algebra, just vectors). Yet, it's precise and correct, sacrificing conciseness to get easiness to understand - like every teaching book should.

So, no. It's perfectly possible to explain it without the bad analogies.

Special relativity is well-known for having the least prerequisites of any modern physics subject. Yes, you can explain it with just calculus and vectors. That's precisely what we already do in university courses.

But the complaint that started this whole thread is "why can't physicists explain why it's hard to add in extra neutrinos to the Standard Model?" Understanding the reason requires 2-3 semesters of relativistic quantum field theory, a subject which in turn requires relativity, quantum mechanics, and classical field theory.

Seriously, any resource that legitimately explains all of this, without bad analogies, and assuming no prerequisites, would end up precisely as hard to read (or likely harder) than the ~10,000 pages of textbook people currently study. The textbooks have already been optimized for ease of learning, there is no magic way to make a hard thing easy.

If you argue this point, first explain to me why physics is done with Greek letters.

Because there are not enough letters in the Latin alphabet? You could of course use words instead of single letters, but I think most people that do numeric computing would agree that the transliteration of formulas into programming language syntax using ASCII makes things less readable.

Using different alphabets (we don't just use Greek, there's also Fraktur, bold letters, etc, though physicists tend to prefer markers like vector arrows, dots, hats, ...) allows for a compact way to namespace symbols.

If I do linear algebra and see an expression like

    A u = λ v + μ w

I'll know immediately what type of quantities the various symbols conventionally denote.

Conventions where the same letter means the same thing in different pieces of work, are useful. There aren't enough latin letters to go around. Hell, there aren't even enough greek ones. Maybe we should start using unicode emoticons next?

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