Hey I have an essay to write for my physics class but I'm not sure where to start... here's the question:

'the world would be a better place if we fully understood the exponential function'

i've tried searching the internet but i've found nothing...everyone seems to fully understand the exponential function!

if someone could point me in the right direction i would really appreciate it!

thanks!

i don't think the question is technical in nature...you could just use population as an example and the problems of overpopulation. stuff like that...or how rumors spread or something like that

exponential functions are used to create real world models, like population growth

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Originally posted by AnotherWay83 i don't think the question is technical in nature...you could just use population as an example and the problems of overpopulation. stuff like that...or how rumors spread or something like that

well i'm not so sure if it's not technical... he said in the lecture notes that one of the greatest flaws of humanity is that we don't fully understand the exponential function... what i think i need to figure out is how and why we don't understand it.

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Originally posted by stevebutabi 'the world would be a better place if we fully understood the exponential function'

This is an arguement that dates back to teh stone age. It is not actually how long the exponential funtion is, it is how you use it that counts.

exp(z)= e^Z

If you had a bon3r for 24 hour a day you would be unable to pee & would get sore. If you get 2 straight men together you instantly get 2 floppy fellows. You will notice that those 2 floopy fellows will never touch. This is important because of the following google searche:

http://mathworld.wolfram.com/ExponentialFunction.html

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so what you are saying... i think... is that the world would in fact not be a better place if we could fully understood it? and that the fact we can apply it to real life stuff is the most important thing?

quote:

Originally posted by stevebutabi so what you are saying... i think... is that the world would in fact not be a better place if we could fully understood it? and that the fact we can apply it to real life stuff is the most important thing?

Yerrr, find as many real life applications as you can & then focus on the biggest & most important schlong. Instant soft on.

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Originally posted by stevebutabi so what you are saying... i think... is that the world would in fact not be a better place if we could fully understood it? and that the fact we can apply it to real life stuff is the most important thing?

What I don't understand is which part of the exponential function "we" do not understand (no pun intended)...

It's a pretty basic function, which can be "easily" calculated numerically. It is well defined, it's pretty simple to deriver and integrate and unlike some other constants, 'e' can be approximated very good.

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quote:

Originally posted by cviper What I don't understand is which part of the exponential function "we" do not understand (no pun intended)... It's a pretty basic function, which can be "easily" calculated numerically. It is well defined, it's pretty simple to deriver and integrate and unlike some other constants, 'e' can be approximated very good.

In essence, there are many things unknown about the exponential function, which mostly have to do with its holomorphic behaviour, even though its an 'entire' function. All things in math are inter-related, thus one could relate it to the Riemann hypothesis, the Gudermannian function, or quite simply to Euler's constant e, itself.

Even though e can be approximated at rapid convergence, its appearance throughout mathematics if very surprising and enigmatic. For instance, the ratio 1/e is related to the number of derrangements in an ordered set of numbers, even though combinatorics is a discrete subject.

Also look at problems in elementary calculus such as Steiner's problem, etc.


The report I would do would be related to abstract algebra and a function known as the Mobius Inversion, which is closely tied, like abstract algebra itself, to combinatorics, and the derrangements thing. The nature of this function is highly group theoretic (having to do with group theory, which seems to be a popular topic these days) and is not very difficult to grasp, unless you dwelve into the actual mathematics of it. Anyway, this function allows the computation of certain difficult combinatorial problems. For instance, it is a more general case of the Euler totient function, which basically counts the number of numbers relatively prime to a given number. In this way, the function is tied to number theory. It also counts the number of arrangements of rooks on a chess board, with forbidden propositions, etc. Read up on the Mobious inversion and study its relation to Euler's constant, and Stirling formula, etc.

There is ton's of material on this stuff, but hopefully you have access to a university library, as the information available on the internet is usally rather concise.

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quote:

Originally posted by eulerfx In essence, there are many things unknown about the exponential function, which mostly have to do with its holomorphic behaviour, even though its an 'entire' function. All things in math are inter-related, thus one could relate it to the Riemann hypothesis, the Gudermannian function, or quite simply to Euler's constant e, itself. Even though e can be approximated at rapid convergence, its appearance throughout mathematics if very surprising and enigmatic. For instance, the ratio 1/e is related to the number of derrangements in an ordered set of numbers, even though combinatorics is a discrete subject. Also look at problems in elementary calculus such as Steiner's problem, etc. The report I would do would be related to abstract algebra and a function known as the Mobius Inversion, which is closely tied, like abstract algebra itself, to combinatorics, and the derrangements thing. The nature of this function is highly group theoretic (having to do with group theory, which seems to be a popular topic these days) and is not very difficult to grasp, unless you dwelve into the actual mathematics of it. Anyway, this function allows the computation of certain difficult combinatorial problems. For instance, it is a more general case of the Euler totient function, which basically counts the number of numbers relatively prime to a given number. In this way, the function is tied to number theory. It also counts the number of arrangements of rooks on a chess board, with forbidden propositions, etc. Read up on the Mobious inversion and study its relation to Euler's constant, and Stirling formula, etc. There is ton's of material on this stuff, but hopefully you have access to a university library, as the information available on the internet is usally rather concise.

wow thanks for such a thoughtful answer...

the thing is though my class is physics 101... i'm not so sure if the question is asking me to go into stuff like abstract algebra

do you think you could give me a more general idea of how the world would be a better place if we more fully understood the exp function?

i mean xenocreator says the world would not in fact be a better place if we fully understood it

"e" has revealed itself in relation to so many phenomena, as mentionned by many in this thread, so imagine what remains to be discovered about the relation between this transcendent (pun intended) number and nature.

so the world would, in fact, be a better place if we understood it... ok sounds good to me, thanks