Desription and arguement - el Infinite

Quantum Heraclitus:

No it cannot. It is the product of an infinite series of divisions (ideal). It has no size except "infinitely small".

To ape Wittgenstein: What is North of the North Pole? What is smaller than the infinitely small?

It is beneath all of those.

 

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lim f(x)=1/x as x approaches infinity = 0
lim g(x)=x as x approaches infinity = infinity
lim f(x)*g(x) as x approaches infnity= 1

Apply to Ben's camera example:
x=Frames per second of camera
f(x)=exposure time of a single frame
g(x)=number of frames (assuming one shot immediatly after the other, think video camera) captured in a 1 second interval
f(x)*g(x)=temporal periode represented by these frames

Thus, as you can see, as we increase the rate of the shutter, we are still able to capture the entire periode of time even when the camera is so perfect so as to allow no exposure time whatsoever (an infinite number of frames per second.)

Contrarily, if I have a bunch of sheets, of thickness 0, the limit of the sum of all n=0 (thickness of each sheet) for i=0 to i=x (counting each sheet) as x approaches infinity, will always = 0. (That is, gathering more sheets will never give me a volume.)

You know, this question sounds like: "What's 0/0 ?"
I could argue that lim x/x as x approaches 0 = 1, and hence, 0/0=1
Or I could argue that lim 0/x as x approaches 0 = 0, and hence, 0/0=0. etc...

The answer of course to 0/0 is indeterminant: you need the context of the problem that the term appears in. Hence: perfect video cameras can make movies, but perfectly thin sheets can never form a brick.
Though, I could slice a brick into an infinite number of infnitly thin sheets which would have a volume equal to that of the original brick! (see the first set of equations, where x is the number of cuts, and go from there.)

But, back to what Ben originaly said, there is no such thing (physcialy) as a perfectly thin sheet, nor a perfect camera, etc... In physics and engineering, one compromises a certain degree of accuracy for simplicity. No need to drag the gamma factor into play if your measuring the length of time of a car ride, despite the fact that Newtonian mechanics are truly only valid when the speed is 0. In this case, we have said "The car is going so slow, that it's speed might as well be 0 for the purpose of computing gamma."

-Andrew

 

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the north pole is a finite resolution is it not, so nothing is beyond the finite resolution.

why limit infinity PJ?
as you are determining an impossible to determine value?

 

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so the use of the notion infinity is always paradoxical. damned if you do and damned if you don't sort of thingo...

 

PJ,
What makes something finite in the contrext of our discussion?
How is finite different from infinite?

 

Quantum Heraclitus:

The analogue to the infinitely small still stands. To ask "what is smaller than that which is smallest?" is irrational when the answer to "the smallest" is "infinitely small".

I've given a value: More than nothing, less than any (other) number. The product of infinite division.

Any finite number is countable given finite time.

Any infinite number is not countable given finite time.

 

You will notice by rereading the OP that I am not asking how many slices make a brick. I am asking how many slices can fit into the volume of a brick.

This is a big difference.
If you give a slice a given thinness then a finite number of slices will fit into the volume of the brick? yes?
If you quantify infinity to a given thinness then this is what you are doing applying a finite value to and infinite value. Therefore PJ's infitesimal smallest segment [slice] will not fit within the volume infinitely as the segment [slice] is no longer infinitely small as he has clearly stated that it is the smallest one can go. Therfore it is finite and not infinite.

If you give a slice zero thickness then there is no doubt that an infinite number of slices would fit into the volume of a brick.

An infinitely small slice will fit infinitely also as long as it is never quantified as being the smallest.

Is this arguement logical?
Is it rational?

If not why not?

 

The relevance to Zeno's metaphor IMO is that the hare may never overtake the tourtise but he has to keep trying to do so. A soon as he stops trying the paradox fails. And the solution becomes finite.

In philosophy this is why perfection can never be achieved or a perfect circle can never be drawn but the trying to do so is what counts.

 

Quantum Heraclitus:

Actually, you'd never reach the thickness of the brick: 0 * 0...

If he stop trying, then he fails.

 

re- read post 27
not interested in making a brick...just how many slices can fit into the volume of a brick

 

Quantum Heraclitus:

It is infinitely small: It is smallest than any number, but larger than zero. Any number/infinity = infinitely small. As such, you're wrong that there'd be a finite amount within any finite segment. No, there'd be an infinite amount of these slices.

That is absurd: It would have to be smallest in order to be infinitely small.

 

I think I'll have another beer.

 

What brand?

 

rather a malt whiskey my self....but beer is good

 

So in the year 2100 are we still going to be debating this issue?
If yes then this is good and helps prove infinity. If no then the hare has given up....

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yeah I know we should be both dead and buried and that is exactly my point...

 

BA DUM DUM PSHHHHHHHHHH! *Rimshots.*

 

back in 6 hours for more....uhm....fun

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Alright, the problem is, that you have ill-defined the problem.

Prince James is talking about slices of 0 thickness, while Quantum Quack is talking about slices of infinite thinness. There is a difference.
Slices of 0 thickness always have 0 volume, no matter how many you have, because they have been defined in 2-dimensional space
While slices of infinite thinness have a non-zero volume, as the number of sheet's approaches infinity, because they have been defined in three dimensional space.

The former is a single limit, the latter is a 2-limit problem for multivariable calculus.

Try creating a more meaningfull situation.
-Andrew

 

1=1

I would like to introduce Information Theory, and the definition of the clear and defineable difference between data and information.

In this stuation we seek to garner knowledge on how many slices of immesurably small size will fit into a measurably hefty 12" brick. Conversely, given that we at all wish to come to a helpful number, however mindblowingly large, that the brick must, by the end of the thought experiment, be divided. Such is this a criteria for finding information from the given data, and that unless we dont care whether we find the answer, that the size of the slice must conform and equal x>0 and hence a foreseeable answer will arise...

BUT if in fact we dont actually care and that one (1) is in fact indefinite (say 1.000... recurring to the nth and utterly unhelpful degree) then even if one were to ask how many inches are there along a 12" brick we must answer "I dont care.". Seeing as this makes total sense, most teenagers are actually the universal equivalent to God, who clearly does not care the slightest whether a brick has any decisive power over its fate... which IMO is highly maleveolent.

Seeing this my heart felt a twang and i wanted to care about the 12" brick and so thought, if 1=1 in any sense that x=x then 1 [x] must be a defineable answer. And given so, maintaining clear reasoning and the will to live... we MUST have an answer.

For if not the poor little brick doesnt actually exist. And nor do we.

 

...

I'm going to go smoke some opium now, Benjimania.