Silly Questions? Sensible Answers!

[David Franklin]

It doesn't exactly help that both the Kronecker delta and the Dirac delta both rely on a number which doesn't actually exist

In what way does the Kronecker delta rely on a number that doesn't exist?

[Ghost]

In what way does the Kronecker delta rely on a number that doesn't exist?

i - is an imaginary number which doesn't exist

I have no idea how to quote the thing on the Forum so this will have to do

Take care,
Christopher

[David Franklin]

i - is an imaginary number which doesn't exist

But the "i" in the definition of the Kronecker delta has nothing to do with sqrt(-1).

[Ghost]

This is getting kinda existential with all these infinities

What's the sound of one hand clapping?

Be Well,
Christopher

Anyway infinity is really more a belief than a number
*ducks*

[philsmove]

I just love this forum, were else in the world will you find, the Kronecker delta and superman’s underpants on the same thread

[Ghost]

I just love this forum, were else in the world will you find, the Kronecker delta and superman’s underpants on the same thread

Plus if anyone asks what you did over the weekend.............

Be Well,
Christopher

[Baruch]

What's the sound of one hand clapping?

{Baruch, sitting peacefully at Ghost's feet, wordlessly thrusts one hand forward.}

[El Salsero Gringo]

Yup - though I personally feel it extends across the board. There's a quote from Star Trek where a Vulcan looks down his nose and says
"You actually believed Quantum Physics?! "

Well if an actor in pointy ears says so...

Given that science rubbishes it's own theories on a fairly regular basis and given how wild some quantum physics is, I fully expect a lot of it to be regarded as madness in about 50 years time. I could of course be wrong.

Ya don't say!

i - is an imaginary number which doesn't exist

Misconception: just because it's labelled 'imaginary' - doesn't mean it doesn't exist. It's as real as the number -1, or 3. (But still not relevant to the Kronecker delta...)

[DavidY]

I never liked resorting to the infinite.

Homework: lookup the Kronecker delta and the Dirac delta.

So a Dirac delta function is zero everywhere except at the origin, where it's infinite, and the integral across everywhere is 1?

If you take two Dirac deltas & add them together, you presumably get a new function that's zero everywhere except the origin, where it's infinite, and the integral across everywhere is 2.

But the infinity at the origin of the double function is presumably twice as big an infinity than the regular infinity of just one on its own? But how can you get bigger than the first infinity?

The rate of change of momentum - the force applied to the wasp (and so to the train) - can be considered infinitely large but in fact of zero duration.

But in the real world, not even Richard Branson would claim his trains apply infinite forces to anything (although I can see he might claim that some events are of zero duration ).

An alternative thought experiment is this: consider replacing the train windscreen with a springy material (eg. from a trampoline).*

The wasp hits the trampoline and the deflection is much more noticeable. The part of the trampoline hit by the wasp is going at a different speed to the rest of the train, until it springs back to its original position. I'll assume the wasp is still squidged** onto the trampoline rather than bouncing off.

In the real train there's still a deflection when it hits the windscreen ('cos of the equal and opposite forces), but it's much less noticeable.

I think the essential maths stay the same as the original problem. You don't need infinities to visualise it, but I don't think it changes anything about conservation of momentum.

* Note to readers: do not try this at home - driving a train at 140mph with a trampoline instead of a windscreen is dangerous and should only be attempted by trained professionals.

** It's a thought experiment wasp - no wasps were harmed in the making of this post.

[pjay]

"Which foot should I step back on in a First Move?"? DJ, where are you

So, if either foot could be correct... then why isn't it post-modern jive ?

[pjay]

But how can you get bigger than the first infinity?

But that is easy... first year math (25.101 at Auckland uni - I can't believe I remember that number)...

Consider:

y = 2z

as z tends to infinity, y tends to 2x infinity... in which case we can say that

as z tends to infinity:

z - y = infinity
y - z = negative infinity

Besides, what's with the concept of infinity being big? Surely it just refers to an inability to measure...

If two trains are travelling towards each other and every second the distance between them halves, what is the distance between them as time tends towards infinity?

* Note to readers: do not try this at home - driving a train at 140mph with a trampoline instead of a windscreen is dangerous and should only be attempted by trained professionals.

[David Franklin]

I never liked resorting to the infinite.So a Dirac delta function is zero everywhere except at the origin, where it's infinite, and the integral across everywhere is 1?

Loosely speaking, yes. But that's certainly not the definition. You can either consider a limit of functions (e.g. lim_{n->oo} abs(x)^((1-n)/n)/n), or take a functional approach where essentially you say "I know what it does but I won't try to define it at zero". Neither approach has you adding infinities.

If you want to avoid the whole infinities thing with the wasp, imagine it has a spring shock absorber on the front. Then the forces are always finite (providing it's a good enough spring, at any rate), and the change in the train speed will be negligable.

[Ghost]

{Baruch, sitting peacefully at Ghost's feet, wordlessly thrusts one hand forward.}

In less than a day you've answered
does the lady you step back on the left foot or the right for the first move?
are we talking about the first step back, or the second step back ;-)
what's the meaning of life?

And now What's the sound of one hand clapping?


Christopher

[Baruch]

Is this a question

[Ghost]

Ok before I even start - in no way am I taking any of this seriously

Well if an actor in pointy ears says so...
Ya don't say!

I refer you to my quote about being a penguin and MsFab's eloquent response

Misconception: just because it's labelled 'imaginary' - doesn't mean it doesn't exist. It's as real as the number -1, or 3.

There are real numbers and imaginary numbers. It's the same reasoning that 1 isn't a prime number because a prime can only be divided by 1 and itself.

(But still not relevant to the Kronecker delta...)

It is strange though, that given that i means imaginary number, and that there are a lot of other letters, both western and greek to chose from, that it's used

At this point I suspect the arguement now comes down simply to belief if you're not a mathematician. I'd be surprised if non-mathematicians are following the arguements put forward - I mean look at the Kronecker delta!

I have to admit I am finding the arguements funny though - shock absorbers on a wasp

WayaayBird - please - more questions

Take care,
Christopher

[Ghost]

Is this a question

Yup - unfortunately it's bad typing - you left off the ?

Take care
Christopher

[Baruch]

Yup - unfortunately it's bad typing - you left off the ?

'Twas deliberate

OK then - what is the mass of 1 cubic centimetre of material from the centre of a black hole?

[Ghost]

'Twas deliberate

Was it

OK then - what is the mass of 1 cubic centimetre of material from the centre of a black hole?

Argggggggggggh. You'll have the scientists at it again

Depends how much stuff is in there.

Be Well,
Christopher

[philsmove]

'Twas deliberate

OK then - what is the mass of 1 cubic centimetre of material from the centre of a black hole?

I think - at the centre of the 1 cubic centimetre of the black hole will be a singularity, a singularity has a finite mass but an infinitely small volume and infinitely large density. so its density is undefined.

edit so I think its mass maybe its easier to try to understand women

[doc martin]

There are real numbers and imaginary numbers. It's the same reasoning that 1 isn't a prime number because a prime can only be divided by 1 and itself.

What's real about real numbers? Could you point out a one for me?

It is strange though, that given that i means imaginary number, and that there are a lot of other letters, both western and greek to chose from, that it's used

Except sometimes they use j for the square root of -1.