It's not appropriate for Ylem to expect a real-world example of every little fact in mathematics as is possible in relatively basic physics (not that it wasn't groundbreaking at the time, but it's taught to first year undergrads). It's a little involved to understand all the characters involved and their significance. I suppose the significance of the exponential function is the first stumbling block, basically it's important because it's rate of change is equal to itself, so here's one example:

Suppose something changes at a rate proportional to itself, for example, with continuously compounded interest, the amount of interest you get per time unit is proportional to the amount of money you have at that time -- so say you had $10,000 at 5% continuous interest -- in 10 units of time, it can be shown you will have $(10,000*exp(.05*10)).

We could equally well talk about radioactive decay, which is essentially the same, but with a negative rate -- the math doesn't care what it's talking about, it works for phenomena that works similarly, and the number e comes up in tremendously many other mathematical applications. It's important to realize math is not applied to anything in particular, its strength comes from its generality.

Most people probably understand the what pi, sin, cos, and i are and some things they're good for, and so the end of the story is that this formula reveals a way to turn a problem about e into a problem about sin, cos, and i which we have some good tools to deal with. Otherwise, we can turn a problem about i, sin, and cos into a problem about e, which gives us access to another set of tools. Sometimes one or the other form is more convenient, that's the extent of its value. Mathematics is simply more underwhelming to the casual observer than the sciences.

This post was edited by N1ccolo on May 5 2013 01:43am

Is it common to love your enemies? Never knew that.
Is it common to do good to those who hate you? Never knew that.
Is it common to turn the other cheek when you are struck? Never knew that.
Is it common to give when anybody asks and when somebody takes something that belongs to you, you don't demand it back? Never knew that.

Luke 6:27-42 http://www.biblegateway.com/passage/?search=Luke+6%3A27-42&version=NIV

The reading we did on Sunday.

Now explain to me how you can do that kind of love without ever hearing about Jesus? Even as Christians we find it hard.

no, it is not common that people live by those ideas/principles
just have a read of the posts following your previous post and you will notice different views on those principles by religious (including self-styled christian) people
btw, i did not say that those are commonly adhered to ideas/principles but that those ideas/principles are common in quite a few cultures/religions
as said before, it would be good if you read up on something else in that context, eg buddhism
it is always amusing to see chirstians wanting to mount the moral high horse but not living by underlying ideas/principles, do you?

You say what you said. I hear: "You can't show that much love without hearing about Jesus."

the mentioned ideas/principle were known well before the christian era - you proved your lack of knowledge again, so i have to say:
wash your ears
who in the last hundred years lived the most christian life?
of all the more commonly known people my nomination would have to be: ghandi

IMO, its pretty but worthless if it dosnt.

This post was edited by Ylem122 on May 6 2013 04:33am

do you admire the mathematics behind the theory of relativity? unfortunately the end result of those calculations provides the real-world example
and that is true for many mathematical facts, they don't have simple 'real world' examples because mathematics in themselves are not really concerned with the real world
this is not to say that mathematical facts do not help to explain real-world facts or that mathematics don't get inspired by some real world problems
let me give you something else which is 'pretty':

consider a very tiny segment of the real line and the collection of numbers contained therein
now take the collection of all 'things' in the known universe
and those are not more than the above collection of numbers
that's something for you to ponder upon

I'm assuming that this 'Christian era' started after Jesus died on the cross? Also, this 'Christian era' is continuing and continuing strong up to this very day?
If I need to study some other religion, we all know that they are good on the outside. Yet what they stand for is not right - earning your way into salvation.
Besides, have you ever noticed how the Muslims like to riot when somebody takes a stab at them? I suppose that is your idea of principle.

It seems to me that you believe that the examples I gave above were 'well known' before the 'Christian era' which I assume that you mean when Jesus came.
Nice try pulling that one out of your ass but I saw right through that one. You think that people lived by those ideas/principles before Jesus came along?
If that is the case why is it such a shock when Jesus says to love your enemies? If people were living by those ideas/principles then it wouldn't have come as a shock.

The fact that it did shock everyone means that those ideas/principles were unheard of before that time. I have to say that you have no logic the way you put it.

Jesus didn't live in a society that saw turning the other cheek as moral. Just look up Buddhism, and you'll see that the Buddha said pretty much the same things. The Buddha's teachings also came as a shock to the Hindu community.

how can you be so ignorant about anything which has not to do with the bible?



where is your proof that people went into shock even in that area (source outside the bible will do) when hearing those ideas/principles?
i have to say that you utterly lack in knowledge, no need to even mention where you logic is positioned