A math formula is one of the objectively simplest ways of expressing something. But it's not easily understood unless you know the math well, thus violating Gruber's rule. Feynman was honest about this, because magnetism can be explained very simply, but not in any familiar way to things most people already know about.
At least as good as math (and capturing the objective complexity better I think) is a working program. "What I can't program, I don't understand."
When people ask for a simple explanation, they usually expect it to be easy for them too, because we all want simple and easy at the same time, even though only one of those is objective. If your reply to "how do magnets work?" is to start by writing down Maxwell's equations, you're gonna get crap for it, but someone who uses the fake rubber band analogy will be well received. But who really understands magnetism better?
But I think that's the deeper point of the "if you can't explain it, you don't understand it": Sure, you can write down the equations, but then what exactly have you done? You wrote down some string of characters and showed that it can be derived from some other strings of characters by applying a series of arbitrary-looking rules. By itself, that doesn't tell anything. It's only when you manage the connect formula to the part of reality that it tries to describe - and connect that part to the rest of reality - that it gains any sense.
Trying to explain a concept in "simple terms" forces you to view it in terms of its connection to other, well-known phenomena.
> You wrote down some string of characters and showed that it can be derived from some other strings of characters by applying a series of arbitrary-looking rules.
That's what it looks like if you only look at the formula. (And why I'd say that formulas are not an "objectively simple way of expressing something*)
If you can somehow keep in mind what the formula is supposed to represent, the operations on characters will let you find some insight about that thing and will stop standing only for itself.
The point is that the term "simple" is inherently subjective - there are plenty of concepts that are simple and intuitive once learned, but are hard to learn.
Also, mathematical formulas are essentially a different language. If people don't speak it, then it's a moot point.
I'd say we do it quite well, just not in in higher brain parts. We find it hard to integrate 'intuition' with the later 'reasoning' parts, instead, it just biases the logic.
Well an equation is certainly the more precise way of describing something, but not really the simplest. My most vivid memory of this is my Automata class; the instructor led with the equations before describing in plain language. Take push down automata as an example [1]. The equations are found in the formal definition, but the informal definition is much clearer.
An equation is compressed, which helps give it its precision, and can create an illusion of simplicity. Just like "a witch did it" is compressed, but if you expand it all of the complexity is inside "witch" and "it", and as you expand "it" you might arrive at some true simplifications in the untwisting sense like physical laws that make you wonder about the need for "witch"... But even if you expand the math it's still all together one of the simplest ways to describe something. That's why I like programs more, there's less implicit compression and it's easier to expand things you aren't familiar with. And there's the formalization of Kolmogorov complexity you can use for things.
As you say, informal explanations are great for understanding and bringing clarity, a lot of the time they're just used to help expand the unfamiliar math, but also a lot of the time they trade off precision, conciseness, or accuracy. At worst they complicate things with twists and relations in the informal explanation that don't exist in the real deal. Sometimes that might be helpful in the same way technically unrelated mnemonics are but it's important to point them out.
The conflation of simple, easy, concise, precise, clear, intuitive.. is the root of the issue when discussing what makes a good explanation.
That's because those things are inherently tied. It's not about taking your time and making the layman an expert to understand some hard topic. It's about being able to relate it to them in simple terms.
Obviously, if you use the "hairy" physics etc terms, then the layman wont understand your explanation, because he is not familiar with them.
Unfortunately, that is what is expected more commonly these days where the audience being presented to a.k.a layman aren't users or domain experts or people who know whats going on. They're management "experts" tasked with getting "resources" to "get things done".
I've seen people from my domain making ridiculous, inaccurate analogies and oversimplify to hide the inherent challenges that a task usually involves. And they get away with that because they aren't the ones actually building the product. They just have to sell it. And the one's they are selling to aren't/won't be using the product either, they will tell someone else to use it.
Well he made that statement in 1965, and then wrote QED, which is a layman's explanation of his Nobel Prize work, in 1985. So perhaps he set out to prove himself wrong.
QED does explain quantum electrodynamics without any calculus or other math (for example, he uses imaginary clocks as a way to explain wave interference), but I think if the average person read it they wouldn't walk away with even a partial understanding of it.
Some parts of physics might stretch the ELI5 to its limits. I like to explain science to my non-science friends, but I'm always hitting the issue that parts of the specialized knowledge become intuitive, and then it's difficult to go back. Say, my understanding of how electrons behave in matter is a category on its own (let's call it quantum), and it's difficult to translate to common terms.
The more I try to learn physics, the more I need to see the mathematics to understand the ideas. Without the math, I don't believe it is possible to break beyond the surface 'armchair' level of understanding.
I started by building an intuitive understanding of advanced physics before I really dug into the math. It is absolutely possible. That being said, I did have a very good understanding of advanced mathematical concepts to start with, so I could think intuitively about things like high-dimensional spaces and eigenfunctions.
If one assumes that things at the edge of human understanding and thus most worthy of such a prize are understood only incompletely by those who understand them best, it is both consistent with Feynman's maxim and not at all a sign of hubris.
It's not just some hard physics that have trouble with the ELI5 / "should be able to explain it" concept.
This is also true for literature, poetry, non-analytical philosophy etc. And there the challenges are not about the complexity of the subject, but about its subtlety, and how one needs historical context and/or certain life experiences (or even proclivities) to be able to grasp a particular piece of work.
It's not so much life experiences, but prior knowledge and familiarity.
Taking mathematics as the operative example. A lot of deep theorems are trivial when you fully understand all relevant definitions. These proves cannot be stated 'in simple terms' because it took a stack of non-simple definitions to even formulate such a theorem.
Explaining the entirety of the stack gets hard when the stack gets deep. For example, a lot of math gets really hard to explain when the concept of the real numbers being 'uncountably infinite' whilst the rationals are 'countably infinite' isn't obvious.
(Highly recommend the whole Feynman series, which is excerpted from an interview video called The Pleasure of Finding Things Out, which is also spectacular)
I run into this all of the time when explaining what I'm doing at work as a programmer. It's not that I couldn't explain why my merging workload increased due to the increased code collisions from my coworkers working in the same files, and how dividing my current assignment in two so I could check in code would reduce this. It's doing that in a normal conversation under time and attention constraints which is the problem.
In one of his books he told this story as follows, a cab driver watched him on TV and said to him "I cant believe you actually tried to explain what did you found." Then Feynman said "Well, what would you say?" Cab driver "If i could explain it in 2 min. then it would not be worthy." Afterwards Feynman used that line. I might be wrong though, but pretty sure he told a story like this.
I don't see this as evidence the other statement is false. If it was something he understood well enough at the time he was earning the prize, it wouldn't have been groundbreaking work worthy of the prize. Gaining that understanding or paving the way for that understanding is what's prize-worthy.
They are both right. Something's can't be dumbed down enough to explain to everyone, but you can always explain the concepts. An example could be comparing an interface to a chocolate cookie recipe, when explaining it to your grandmother.
She'll still have no idea what an interface actually is, but she'll have a good grasp of the concept.
Neither if he was speaking about Quantum Mechanic. Feynman probably paraphrasing Bohr:
"If you think you understand quantum mechanics, you don't understand quantum mechanics."
"Hell, if I could explain it to the average person, it wouldn't have been worth the Nobel prize." [1]
Showing a limitation of the maxim or Feynman's hubris?
[1] https://en.wikiquote.org/wiki/Richard_Feynman