Simplicity is not natural. Over-complication is the default, people assume social reasons are the main reason for over-complication but I think it’s an unparsimonious and false model.
But I think the most common lay model of overcomplication is wrong. I think a lot of people have a natural tendency/theology of “simplicity” that I covered in the plain language section of my writing styles guide, something like:
The truth is simple and obvious. Smart alecs try to overcomplicate things, either due to personal insecurities or institutional/social reasons (can’t get tenure/promotions from doing easy things),
Because the truth is obvious, anybody can find it. Children often find it first. They haven’t learned to complicate things.
I disagree. I think the reason things are (over)complicated are due more to a combination of “territory” and cognitive reasons than due to social or institutional reasons.
Put a different way, I think finding the truth is often hard. And once you do find the truth, finding a simpler way to express the same truth is also hard (and requires significant cognitive effort, parallel searches, and in some cases significant serial time).
Calculus went from something that the greatest minds of Newton’s generation could barely understand to something that’s a rite of passage for smart high-schoolers. I think the difficulty change is mostly due to coming up with better explanations, pedagagogy, and advances in the conceptual technology of intermediate steps, not due to social reasons like people being too arrogant to understand the deep truths of calculus.[1]
I don’t currently have a great model of why simplicity is difficult. Two models I’m playing around with are the Lottery Ticket Hypothesis-adjacent models and Grokking-adjacent models. (I currently think the former is more plausible).
I’m not saying people never overcomplicate things for non-epistemic reasons. Motivated reasoning, for example, is a real, commonplace, and persistent problem (see here for an example). But in situations where nobody proffers a good explanation (rather than just some people “mysteriously” not understanding obvious concepts, or running interference), I think the more parsimonious explanation is a combination of the lack of skill and lack of motivation/effort/serial time invested so far in coming up with a better explanation, rather than that the good explanations are out there and individual or institutional factors actively hide it.
(This is also another angle in which I disagree with the implicit telos of the midwit meme).
No, and my understanding is that this is a major reason why Europe became the analysis powerhouse during the 1800s. Leibniz had the better notation and pedagogy, so far more people in Europe could understand calculus than in England (who mostly closed ranks around defending Newton as the discoverer with the superior notation).
This is why in analysis courses everything is named after a french person.
I don’t know about the age distribution at which people were able to understand Leibniz, sadly, but I’d bet it was much lower than in England, and I would not be surprised if you in fact had smart aristocratic 16-17 year olds learning about it in university,
Scientists worry a lot that their work will be ignored, which causes them to immitate the style and form of previous impactful works, which explains Newton’s choice of Latin and his choice of proofs in the geometric tradition to present results that he came up with using more calculational and more analytic methods. When I read Principia I felt the author was trying to explain clearly and as simply as possible, but sticking to established expository forms to avoid the work’s being rejected due to too much novelty.
I agree it is possible Newton was trying his best to explain his work, and you probably know better than I do since you’ve read it. However the claim is consistent with my understanding of his personality and is supported second-hand by William Derham’s claim that
These Controversies with Leibnitz, Hooke, & Linus, & others about Colours, made Sir Isaac very uneasy; who abhorred all Contests, accounting Peace a substantial Good. And for this reason, namely to avoid being baited by little smatterers in Mathematicks, he told me, he designedly made his Principia abstruse; but yet so as to be understood by able Mathematicians, who imagined, by comprehending his Demonstrations, would concurr with him in his Theory.
Note that this may be reasonable. If you make a scientific or mathematical discovery, it may be right to confine it in the language specialized to that field so that the relevant scientific or mathematical communities can discuss it with minimal outside noise, however Leibnitz and Hooke were able mathematicians, so if his goal was to write the theory so that even them or their followers couldn’t understand, then that is a different story.
As for the Latin question, regardless of why Newton wrote the Principia in latin, that is definitely a social factor rather than a “we understood calculus more as a society and could therefore explain it better than he could” factor.
I think people overcomplicate explanations because they don’t arrive to the truth immediately (e.g. by enumerating all possible answers, ordered by length) but basically by semi-randomly walking in a maze of hypotheses and finally stumbling upon the truth—so their path is not necessarily the shortest path.
(Later people travel the maze more, and notice shortcuts.)
Like, someone considers an option A, it is wrong, but seems kinda correlated. So afterwards they try “A and B”, and it works. They don’t notice that B alone would have worked too, because they are coming there from A.
(But later someone is too lazy and tried B alone, or they forget the A part, and they find out it works anyway.)
Sometimes you just find a better perspective. For example, imaginary numbers were invented as solutions to polynomials, but if you think about them as 2D coordinates, it is much easier. That’s because when people tried to solve polynomials for the first time, it wasn’t obvious that the answer will be somehow two-dimensional, but it turned out that it is. Starting with two dimensions is intuitive, then you add the geometric interpretation of complex multiplication (multiplying by i means doing it rotated by 90 degrees) and you are done.
Simplicity is not natural. Over-complication is the default, people assume social reasons are the main reason for over-complication but I think it’s an unparsimonious and false model.
I dislike overcomplication and spend a significant amount of my time on trying to come up with more simple understandings or portrayals of topics that other people find complicated.
But I think the most common lay model of overcomplication is wrong. I think a lot of people have a natural tendency/theology of “simplicity” that I covered in the plain language section of my writing styles guide, something like:
I disagree. I think the reason things are (over)complicated are due more to a combination of “territory” and cognitive reasons than due to social or institutional reasons.
Put a different way, I think finding the truth is often hard. And once you do find the truth, finding a simpler way to express the same truth is also hard (and requires significant cognitive effort, parallel searches, and in some cases significant serial time).
Calculus went from something that the greatest minds of Newton’s generation could barely understand to something that’s a rite of passage for smart high-schoolers. I think the difficulty change is mostly due to coming up with better explanations, pedagagogy, and advances in the conceptual technology of intermediate steps, not due to social reasons like people being too arrogant to understand the deep truths of calculus.[1]
I don’t currently have a great model of why simplicity is difficult. Two models I’m playing around with are the Lottery Ticket Hypothesis-adjacent models and Grokking-adjacent models. (I currently think the former is more plausible).
I’m not saying people never overcomplicate things for non-epistemic reasons. Motivated reasoning, for example, is a real, commonplace, and persistent problem (see here for an example). But in situations where nobody proffers a good explanation (rather than just some people “mysteriously” not understanding obvious concepts, or running interference), I think the more parsimonious explanation is a combination of the lack of skill and lack of motivation/effort/serial time invested so far in coming up with a better explanation, rather than that the good explanations are out there and individual or institutional factors actively hide it.
(This is also another angle in which I disagree with the implicit telos of the midwit meme).
People being individually smarter via better nutrition and and lower parasite load also plays a role, but I think lower
It shouod be noted that Newton did in fact intentionally (or so I’ve heard) write his Principia to
Be in latin, so that only the higher classes could read it
Be written in an impenetrable style, so that only the very smart could understand it.
Therefore I think its wrong to say there were no social reasons why calculus was overly complicated early on.
Do you think the same issues were relevant for Leibniz?
No, and my understanding is that this is a major reason why Europe became the analysis powerhouse during the 1800s. Leibniz had the better notation and pedagogy, so far more people in Europe could understand calculus than in England (who mostly closed ranks around defending Newton as the discoverer with the superior notation).
This is why in analysis courses everything is named after a french person.
I don’t know about the age distribution at which people were able to understand Leibniz, sadly, but I’d bet it was much lower than in England, and I would not be surprised if you in fact had smart aristocratic 16-17 year olds learning about it in university,
Scientists worry a lot that their work will be ignored, which causes them to immitate the style and form of previous impactful works, which explains Newton’s choice of Latin and his choice of proofs in the geometric tradition to present results that he came up with using more calculational and more analytic methods. When I read Principia I felt the author was trying to explain clearly and as simply as possible, but sticking to established expository forms to avoid the work’s being rejected due to too much novelty.
I agree it is possible Newton was trying his best to explain his work, and you probably know better than I do since you’ve read it. However the claim is consistent with my understanding of his personality and is supported second-hand by William Derham’s claim that
Note that this may be reasonable. If you make a scientific or mathematical discovery, it may be right to confine it in the language specialized to that field so that the relevant scientific or mathematical communities can discuss it with minimal outside noise, however Leibnitz and Hooke were able mathematicians, so if his goal was to write the theory so that even them or their followers couldn’t understand, then that is a different story.
As for the Latin question, regardless of why Newton wrote the Principia in latin, that is definitely a social factor rather than a “we understood calculus more as a society and could therefore explain it better than he could” factor.
I think people overcomplicate explanations because they don’t arrive to the truth immediately (e.g. by enumerating all possible answers, ordered by length) but basically by semi-randomly walking in a maze of hypotheses and finally stumbling upon the truth—so their path is not necessarily the shortest path.
(Later people travel the maze more, and notice shortcuts.)
Like, someone considers an option A, it is wrong, but seems kinda correlated. So afterwards they try “A and B”, and it works. They don’t notice that B alone would have worked too, because they are coming there from A.
(But later someone is too lazy and tried B alone, or they forget the A part, and they find out it works anyway.)
Sometimes you just find a better perspective. For example, imaginary numbers were invented as solutions to polynomials, but if you think about them as 2D coordinates, it is much easier. That’s because when people tried to solve polynomials for the first time, it wasn’t obvious that the answer will be somehow two-dimensional, but it turned out that it is. Starting with two dimensions is intuitive, then you add the geometric interpretation of complex multiplication (multiplying by i means doing it rotated by 90 degrees) and you are done.