Professor Ed Copeland shows a proof by Joseph “Voldemort” Fourier that e is irrational.
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Ed Copeland is a physics professor at the University of Nottingham.
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Conjecture: Neil Barnes is a descendant of Joseph Fourier.
The greater question is not what is e but where is e. This number only exists within the confines of a perfect symmetrical number grid that has no physical approximation. It is a number that can only ever describe other numbers. It is nothing and yet these capable people give it great importance. In math, the most telling descriptor used is the British use of "not" in place of zero. This says it all. Zero is the trap blocking these great minds from better understanding. Math cannot be symmetrical if it is to represent what is physical. You want to know the problem with a perfect circle? It doesn't exist. In the end it is better to admit we didn't make ourselves and we cannot know most things and that is alright.
One practical use case is the perfect speedometer meter
How do we know that e is a female number? Because it's completely irrational.
We don't need to prove it. Look at how it acts. That's proof enough.
9:01 Missed an opportunity to say "R for the 'rest' of the proof"
I'm sure if he had more time to think he could have thought of an answer to the question at 3:13 . But the fact that the derivative of e^x is itself is IMMENSELY important! It's required to solve Ordinary Differential Equations (ODEs) which are EVERYWHERE in physics. If we as a species never figured out that the derivative of e^x is itself, you couldn't be reading this sentence because your phone wouldn't exist, your computer wouldn't exist, you wouldn't have a car, you wouldn't even have electricity.
Professor Ed saying "I don't know why its useful" is possibly my favourite part of any Numberphile video ever heh
Why cant we use the same logic to demonstrate that gamma is also irrational ?
"And it goes on forever and ever and ever". What is this, story time for 5 year olds? We get it.
honestly, even after watching this neat and comforting presentation several times now by stumbling upon it here and there, the irrationality of e does still feel eerie and unsettling 🙂
e is important because of the change of base formula. There are a lot of things in the world that grow exponentially and by using the change of base formula, we can make calculus a lot easier
The continued fraction expansion is a constructive proof of its irrationality. More setup, but more motivated. Worth an episode itself
Єто число придумали древние русские, как и все числа и Менделеев русский!
I'm surprised Prof Ed had a hard time finding signficance for the ubiquity of e^x at 3:40 . e^x is important because it defines a quantity which changes in value depending on how much of it there is/was. It's a fundamental in nature. For example, the growth of cells in a petri dish depends on how many cells there are to divide. e is just the simplest number to define this relate but in general you'd have the growth formula N'=kN and you'd have (e^k)^x which could be anything to the power x say 2 if k=ln2 and this would mean the N cells double every period x. You could also have k=-ln2 which would describe for example the number of radioactive nuclei remaining every x half lives
This “theoretical physicist” is unable to say why it’s important to know which function in lower level calculus is its own derivative?
To me, this doesn’t bode well for the physics PhD program at Newcastle upon Tyne.
Early on he says he tells people that e is the only number that is its own derivative. I wish he’d stop that.
The notion of a derivative that is most commonly recognized by the most likely viewers is the one he describes after he says that, and using that notion of a derivative, the derivative of a constant function is always zero. Most viewers probably identify a number with the constant function whose value at every element of its domain is that number, so they think of the derivative of a number as zero. Clearly this means he’s wrong and then he goes on to do something different from what he said. Think about that for a moment. He says differentiation of this number e yields e but in the video he doesn’t differentiate the number e. The abuse of terminology of this kind is one of the reasons that it’s so difficult to explain concepts to people who’ve learnt from someone who talks this way; when the “students” have been exposed to a cacophony of levels of rigor in their mathematics classes without a careful explanation of the fact that it is a cacophony of levels of rigor, a teacher who tries to help students learn to be rigorous faces an uphill battle.
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Towards a neophyte, I think defining e trough its definition with the differentiation staying the same may not be the clearest explanation.
I lprefer introducing e as the number value you reach towards when computing (1+1/n)ⁿ as n→∞ .
*A proof that e is e rational