How Isaac Newton discovered the binomial power series
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How Isaac Newton discovered the binomial power series
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Re: How Isaac Newton discovered the binomial power series
#2"How Isaac Newton Discovered the Binomial Power Series"
Current title ("Isaac Newton Discovered the Binomial Power Series") implies something rather different :)
Re: How Isaac Newton discovered the binomial power series
#3" How Isaac Newton Discovered the Binomial Power Series" Current title ("Isaac Newton Discovered the Binomial Power Series") implies something rather different :)
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.
Re: How Isaac Newton discovered the binomial power series
#4I 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.
Re: How Isaac Newton discovered the binomial power series
#5" How Isaac Newton Discovered the Binomial Power Series" Current title ("Isaac Newton Discovered the Binomial Power Series") implies something rather different :)
Rehowed. Thanks!
Re: How Isaac Newton discovered the binomial power series
#6" How Isaac Newton Discovered the Binomial Power Series" Current title ("Isaac Newton Discovered the Binomial Power Series") implies something rather different :)
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.
Re: How Isaac Newton discovered the binomial power series
#7I 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 were surprising, interesting, novel, and worth a PhD.
The problem was that in the first version I explained far too clearly all my thinking, and how I came to the results. As a result, it all seemed obvious and inevitable.
To publish, results need to be novel, surprising, or otherwise "worthy", and if you explain too clearly how you got there, your results can easily be dismissed as "trivial".
Beware of explaining things clearly.
Re: How Isaac Newton discovered the binomial power series
#8I 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…
That sounds like a profoundly immature external examiner. Any seasoned person here is aware of this effect.
In my view the "logical sciences" all aim for triviality: the hardest thing is to specify the problem in such a way that the solution is trivial. All the work is done, precisely, so that it is trivial.
Re: How Isaac Newton discovered the binomial power series
#9I 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 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 as a lifesaver critical to the business and my name is mentioned in the Daily Standup the next day.
Explaining how we work trivializes our work. It's better to remain mysterious.
Re: How Isaac Newton discovered the binomial power series
#10I 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…
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').