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How Isaac Newton discovered the binomial power series

quantamagazine.org

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Re: How Isaac Newton discovered the binomial power series

#11

Post by vmilner »

dotancohen wrote: post #9
ColinWright wrote: post #7

Earlier quoted context omitted.

There's a reason they don't. I failed my PhD first time around, with the external examiner recommending I not even go to the viva stage, saying that the results were obvious and trivial, not worthy of a PhD. He recommended I be given a Masters and not even permitted to re-write or re-submit. My internal examiner insisted we go to viva , wherein I managed to convince them (unaware of all the above) that the results we…

I have a similar experience in industry (software development) that I relive weekly, but I never learn. When I help someone solve a problem, I like to show them how I got to the solution. In the end, my hour invested was "we did it together" and not appreciated by anyone, least of all the manager. But on the few occasions that I just bang out a function quickly for somebody because I don't have the time, I'm hailed a…

     Mr. Jabez Wilson laughed heavily. “Well, I never!” said he. “I thought at first that you had done something clever, but I see that there was nothing in it after all.”

     “I begin to think, Watson,” said Holmes, “that I make a mistake in explaining. ‘Omne ignotum pro magnifico,’ you know, and my poor little reputation, such as it is, will suffer shipwreck if I am so candid. 

        - "The Red Headed League", (The Adventures of Sherlock Holmes)

Re: How Isaac Newton discovered the binomial power series

#12

Post by plopilop »

ColinWright wrote: post #7
ironSkillet wrote: post #4

I love articles like this. I wish more research papers and textbooks actually explained how people came up with their ideas/proofs in the first place.

There's a reason they don't. I failed my PhD first time around, with the external examiner recommending I not even go to the viva stage, saying that the results were obvious and trivial, not worthy of a PhD. He recommended I be given a Masters and not even permitted to re-write or re-submit. My internal examiner insisted we go to viva , wherein I managed to convince them (unaware of all the above) that the results we…

I clearly despise academics (and the papers they write) who think that everything should look novel by hiding your thought process.

Sadly, especially in fields where conferences are favored over journals, this seems to be common: you only have a single chance of impressing the reviewer, so you lose little by hiding your thought process, and if possible make your result look more complicated that it actually is.

Many papers I read look needlessly complicated, and I cannot help but wonder why the authors chose this style. I've already been rejected because reviewers found my contributions too simple, however I'd say that the majority prefer to highlight the fact that the paper is "easy to understand". (Of course, sometimes you also need to get told that your contributions are minimal).

Sometimes, I wonder if I have this point of view because some academics like to hide their simple result under a mountain of useless rigor, or because I'm not smart enough to comprehend the necessity of the above rigor and I'm just a dumb engineer who chanced into research. I'd say both are true, but usually not at the same time: some papers are clearly hiding a small contributions, while some are just above me.

Re: How Isaac Newton discovered the binomial power series

#13

Post by ColinWright »

mellosouls wrote: post #6
contravariant wrote: post #3

Earlier quoted context omitted.

If I recall correctly HN automatically removes words like 'How' from the title (I think it also removes 'Why', not sure if it removes all interrogative words) Technically the current title is not false.

Yeah I thought it might be an automatic thing.

Interestingly, if,after submission and the initial word stripping, you then edit the title, you can restore it yourself.

Re: How Isaac Newton discovered the binomial power series

#14

Post by ColinWright »

contravariant wrote: post #10
ColinWright wrote: post #7

Earlier quoted context omitted.

There's a reason they don't. I failed my PhD first time around, with the external examiner recommending I not even go to the viva stage, saying that the results were obvious and trivial, not worthy of a PhD. He recommended I be given a Masters and not even permitted to re-write or re-submit. My internal examiner insisted we go to viva , wherein I managed to convince them (unaware of all the above) that the results we…

Oh now I'm actually curious, I have a weak spot for explanations that make surprising results seem inevitable. Much better than articles that make stuff sound fancy to make it more convincing (e.g. I've seen articles that used $r^n \pi^(n/2) / \Gamma(n/2 + 1)$ instead of the more sensible 'volume of an n-sphere').

There's a balance to achieve between presentation of a NEW RESULT vs simple obfuscation. Achieving that balance depends in understanding your audience and adapting your style appropriately.

The "understanding your audience" bit is repeated again and again and again, but seems never to be heard or heeded.

To be fair, most PhDs in Pure Maths don't contain earth-shattering, field altering results. Mostly they are small things that are genuinely new, but not very substantial. The author then has to make it clear which wide they fall in the tension between "trivial observation" and "genuine progress". I didn't do that the first time.

Re: How Isaac Newton discovered the binomial power series

#15

Post by vmilner »

ironSkillet wrote: post #4

I love articles like this. I wish more research papers and textbooks actually explained how people came up with their ideas/proofs in the first place.

Check out

https://www.amazon.com/Mathematics-Its-History-Undergraduate...

which goes through the history of maths while actually _doing_ some maths at undergraduate level.

Also the lectures based on it by N J Wildberger

E.g. https://www.youtube.com/watch?v=HRD9X-2Bmdw&t=2692s

Re: How Isaac Newton discovered the binomial power series

#16

Post by yolo3000 »

ColinWright wrote: post #7
ironSkillet wrote: post #4

I love articles like this. I wish more research papers and textbooks actually explained how people came up with their ideas/proofs in the first place.

There's a reason they don't. I failed my PhD first time around, with the external examiner recommending I not even go to the viva stage, saying that the results were obvious and trivial, not worthy of a PhD. He recommended I be given a Masters and not even permitted to re-write or re-submit. My internal examiner insisted we go to viva , wherein I managed to convince them (unaware of all the above) that the results we…

Haha. This reminds me how I was failed an exam for electronic circuits in university. The teacher was giving us some brief formulas without going over why the formulas made sense. When it came to solving the problems in the exam, I used the unpacked formula step by step (that's how I studied it to prep up) and came to a good result. He failed me and told before everyone that one student (me) detailed the solution in too many steps, and you don't do that. Funny thing is that the colleague behind me, who copied what he could see from my paper, passed the exam. He didn't copy all the details :))

Re: How Isaac Newton discovered the binomial power series

#17

Post by laichzeit0 »

Well this flies in the face of everyone who thinks the biggest stumbling block to learning mathematics is the “obscure notation”. There’s nothing obscure in this discovery, but there is genuine invention involved. Something more than can be taught by rote, or using different notation.

Re: How Isaac Newton discovered the binomial power series

#18

Post by TheAceOfHearts »

ColinWright wrote: post #7
ironSkillet wrote: post #4

I love articles like this. I wish more research papers and textbooks actually explained how people came up with their ideas/proofs in the first place.

There's a reason they don't. I failed my PhD first time around, with the external examiner recommending I not even go to the viva stage, saying that the results were obvious and trivial, not worthy of a PhD. He recommended I be given a Masters and not even permitted to re-write or re-submit. My internal examiner insisted we go to viva , wherein I managed to convince them (unaware of all the above) that the results we…

Sometimes the result of thousands of hours of work and thinking end up being summed up in a few sentences. Newton's 3 laws are a perfect example.

Carmack recently said that all the key ideas to create AGI will probably fit in a couple pages, with a basic implementation only being only a few thousand lines of code. I'm very much inclined to believe him.

Once you know how the trick is done, of course it'll seem obvious. But if it was so obvious why didn't you come up with it yourself?

Some people feel the need to write incredibly long texts to explain what they're doing, because it makes the topic seem more complicated.

Re: How Isaac Newton discovered the binomial power series

#19

Post by P999999967 »

ColinWright wrote: post #7
ironSkillet wrote: post #4

I love articles like this. I wish more research papers and textbooks actually explained how people came up with their ideas/proofs in the first place.

There's a reason they don't. I failed my PhD first time around, with the external examiner recommending I not even go to the viva stage, saying that the results were obvious and trivial, not worthy of a PhD. He recommended I be given a Masters and not even permitted to re-write or re-submit. My internal examiner insisted we go to viva , wherein I managed to convince them (unaware of all the above) that the results we…

The problem was not that you explained your reasoning but that you did so inappropriately for your intended readers. This is explained clearly in Lawrence McEnerney's Leadership Lab courses: https://www.youtube.com/results?search_query=Lawrence+McEner...

Re: How Isaac Newton discovered the binomial power series

#20

Post by tpoacher »

ColinWright wrote: post #7
ironSkillet wrote: post #4

I love articles like this. I wish more research papers and textbooks actually explained how people came up with their ideas/proofs in the first place.

There's a reason they don't. I failed my PhD first time around, with the external examiner recommending I not even go to the viva stage, saying that the results were obvious and trivial, not worthy of a PhD. He recommended I be given a Masters and not even permitted to re-write or re-submit. My internal examiner insisted we go to viva , wherein I managed to convince them (unaware of all the above) that the results we…

Alas, I have reached exactly the same conclusion over the years.

You need to strike the right balance between not obfuscating too much such that the reader ragequits in frustration, versus obfuscating things just enough so that the reader has to put a bit of "work" before the insight hits home, lest they fail to appreciate how much effort getting to that insight took in the first place, and dismiss it for a trivial one.

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