Math Is Fun Forum

Do you believe in reincarnation?

With

It's the same as

Using integrals rules:

So we get

Another, more graphical way to look at it is you're finding the area under the line

I think it's far more important to exist than to have a purpose.

We exist. It feels awesome.

On the mathworld page it gives

You're given

So you can solve for h.

If you want to derive the formula you need to know about integral calculus and volumes of revolution

I think 'life' as we know it is really 'biological potential energy'

If you think back to the very first 'living' cell, how did it come about? Molecules arranged themselves in such a way as to create a structure that is self-sustaining - a structure that prefers life to death. Eventually this structure became more complex and evolved into the different species we see, but it must still operate on the same basic principles.

So I think our consciousness is actually a manifestation of this biological potential energy, and it is hardwired into our brains.

So if we were to create robots with the same basic operating principles, they would be just as 'alive' as we are.

I don't know exactly know why we are here to witness the universe, but I think that's how consciousness emerges.

Thanks bobbym and gckc123,

I was asking because I had a similar probability density function which I thought had an expected value of infinity, but it turns out it was my calculator's fault that it was coming out as undefined!

But yeah, Cauchy distribution is quite counterintuitive... I was always taught that an even graph will have its mean at the middle.

Thanks gckc123!