Ego wrote:
Feynman was a truly great teacher. He prided himself on being able to devise ways to explain even the most profound ideas to beginning students. Once, I said to him, "Dick, explain to me, so that I can understand it, why spin one-half particles obey Fermi-Dirac statistics." Sizing up his audience perfectly, Feynman said, "I'll prepare a freshman lecture on it." But he came back a few days later to say, "I couldn't do it. I couldn't reduce it to the freshman level. That means we don't really understand it."
However!
What's interesting here is that Feynman drew his demarcator of "our" understanding at the freshman level. Why not the 9th grade level? Or the 3rd grade? Or pre-school?
Does it also stand to reason that if Feynman or Einstein couldn't explain force equals mass times acceleration to a 1st grader, then we don't really understand Newton's second law? If we can't explain how to count to 100 to the average 2-year old, then we don't understand counting because we can't explain counting "simply" enough. I don't think so.
To me the choice of the freshman demarcation for statistical physics strongly suggest that pedagogical reach between the teacher and the student has real limits. It also suggests that the inability to simplify concepts also has limits because some subjects can't be simplified indefinitely (all the way down to two year olds). A great teacher like Feynman had a bigger pedagogical reach whereas your average professor is satisfied if he can explain statistical physics to "sophomorons" (where this subject is usually taught AFTER students have learned quantum mechanics, something freshmen usually do not know very much about). The measure of that pedagogical reach in the intellectual domain is described by the Wheaton scale. For content of a given complexity, there's a pedagogical range where this content can be explained. Having a better understanding or being a better teacher increases the range, but outside that range, it is hopeless.
If one accepts that subjects have a range and that teachers have a range, it explains why we have first grade teachers and not university professors teach 1st graders and vice versa. It also explains why 1st graders are taught 1st grade topics. When I was in 1st grade, I was subjected to a horrible pedagogical experiment called "New Math" which was the mathematical analogy to trying to construct a building by starting with the roof presuming that it would somehow hold itself up in mid-air.
https://en.wikipedia.org/wiki/New_Math
The attempt was to teach the fundamentals of abstract set theory (usually a subject reserved for 2 and 3+ year college students, and for good reasons, as it was eventually realized) so we talked about open and closed sets, subsets, interactions, and unions. There were two problems with this approach. The first problem was that set theory is not really in any way relateable to the experience (practical and theoretical) of 1st graders. Talking about lions and monkeys on a velcro board and calling the set a fence which could be open or closed didn't help a lot. The teachers were relatively clueless as well, university level math not being something they had ever studied.
Here's Feynman on New Math:
Feynman wrote:
If we would like to, we can and do say, 'The answer is a whole number less than 9 and bigger than 6,' but we do not have to say, 'The answer is a member of the set which is the intersection of the set of those numbers which are larger than 6 and the set of numbers which are smaller than 9' ... In the 'new' mathematics, then, first there must be freedom of thought; second, we do not want to teach just words; and third, subjects should not be introduced without explaining the purpose or reason, or without giving any way in which the material could be really used to discover something interesting. I don't think it is worth while teaching such material.
I don't think first graders make for a good analogy for all grades of teaching nor for all concepts. You can't teach Fermi-Dirac statistics to freshmen using big words and expect their little brains to work out the details. It's cute when kids use big words, but it's also clear (like from the video) that their understanding is no deeper than a few sentences in a dictionary. This video is mainly cute because you're hearing what's pretty much the average level of adult comprehension when it comes to the universe coming out of the mouth of a 9-year old. On an absolute scale of knowledge, it's not remarkable.
I don't think kids have a problem with being put in boxes (or grades). I think it's the adults who have problems insofar they're put in boxes if they feel those boxes are below their "paygrade". Most adults have an understanding of the Earth and its relation to the galaxy which is slightly worse than that 9-year old. It's when we take those adults and tell them that their
functional literacy or understanding of the universe corresponds to a 4th grade level that they get pissy and start questioning the veracity of the valuation scheme rather than themselves.
Kids are better accepting that they might not know everything or indeed that they might know very little without feeling bad about it. Adults, on the other hand, are better at rationalizing why something is useless or wrong insofar they don't understand it or don't get the expected results.
So, here's another issue.
In the US 42% of all adults do not believe in evolution. If we take Einstein literally, this should be a problem of not being able explain evolution simply. However, basic evolution is pretty damn simple to explain. It's not that those 42% can't understand evolution, rather it's that they
won't understand it. Unlike 1st graders who will are eager to fill in blanks, these creationists will actively resist knowledge they disagree with or which doesn't fit into their world-view.
In conclusion, what I found remarkable about this thread to the point it almost blows my mind is not the range of viewpoints when it comes to ERE (extreme frugality, nomadism, 100% self-sufficient, ... ), that has happened before in another long and similar thread about how "you" see ERE:
Do you really understand ERE?. A wide range was to be expected.
What I find remarkable is that not only did a couple of people INSTANTLY grasp the Wheaton table concept, but (and that's the remarkable part) they understood it 100% or one-to-one exactly how I see it from Day One without any need for further clarification or further explanation.
(It was as if you go to random country and speak a few words in English and discover to your surprise that someone else seemingly possesses a full and fluent vocabulary of English despite the fact you only spoke a few words "How are you?" and at no point used the assistance of a dictionary of a universal translator. That obviously can't be random and the only explanation is that there are people out there who already speak English just as you do without any of you having to spend any time elaborating on a grammar or a vocabulary. Here "speaking English" is the metaphorical analogue for "Wheaton table". It's pretty obvious that some clearly does speak the language of Wheaton and tables well enough already so that only a few words is needed to make the [Vulcan Mind Meld] connection.)
What's equally remarkable is that everybody who didn't instantly grasp it immediately haven't budged a millimeter. In the metaphorical sense, they refuse the acknowledge the existence of the "Wheaton table" language despite it being able serve as a perfect communication line (language that describes the pedagogical challenge) between a few people. Now, if it had required a development of a grammar and a vocabulary, I could see why some would argue that neither is perfect. However, in this case it seems that for some it was already perfect from the get go.
PS:
Fun story: In grad school, I actually figured out a simple explanation [of Fermi-Dirac statistics] and started using it as the main ingredient in my conference talks. It landed me a couple of invitations to present at general colloquia from people (full professors) who came up after my talk(s) saying it was the clearest presentation they'd ever seen. I even gave a two hour long lecture at a summer school (where you drag a bunch of phd students to some maintain top and have some experts give them insight). Usually this "honor" (extra work load, really) is reserved for senior scientists. Certainly not grad students. => Just because one of the demi-gods of physics can't do it in a couple of days, it doesn't mean that some phd student can't do it in a few weeks. (PS: I might have cheated slightly. Before this, I spent a few months seriously thinking about and writing an article about thermodynamics for the "intelligent layman". You can read the result
here.)
(*) My field had to do with the behavior of a fully ionized gas on neutron stars and thus involved both electrons (Fermi-Dirac distributed) and atomic nuclei (Boltzmann distributed) and how the different distributions would lead to explosion by compression.
