Quantized values

[Aussie Objectivist]

A quantized value is something that can exist only in specific quantities.

For example, electric charge. The fundamental unit for electric charge is that on an electron; every charge is merely a whole number of electron charges. (The charges dealt with in daily life are so large that electrical charge appears to be a continuous variable).

Time is not a discrete/quanitized value.

Neither is distance. Now this is where I am confused...

Take two points, A and B, that exist in space a certain distance apart (say, 1 metre, although that's completely arbitrary). No matter what their distance apart, there will always exist an infinite number of points between A and B. Thus, for an object at A to move to B, it must pass through an infinite number of points before it can ever reach B...

But infinity, by definition, is beyond measurement. Thus, how can the object at A ever reach B? (Since it has to pass through an immesurable amount of points)

Similarly, take two instants in time; t=0 and t=1 (second). There is an infinite number of instants between t=0 and t=1, therefore how can time ever "reach" t=1?

I think the solution to these problems is associated with "space-time" which is generally considered to be another dimension.

Somebody enlighten me.

[y_feldblum]

This problem is known as Xeno's Paradox.

The philosophical answer is: you're context-dropping.

The simple answer is, to go from A to B at velocity V one would require time T = (B - A) / T.

One goes halfway to B and takes duration T/2 doing so.

One then goes half the remaining distance, taking T/4 doing so.

One then goes half the remaining distance, taking T/8 doing so.

Etc.

Keep in mind that the time for each leg of the journey keeps changing.

So, one travels the entire distance, taking T/2 + T/4 + T/8 + .... I will prove that the sum of the infinite series here is T.

Sum = T( 1/2 + 1/4 + 1/8 + ... )

2*Sum = T( 2/2 + 2/4 + 2/8 + 2/16 + ... )

= T( 1 + 1/2 + 1/4 + 1/8 + ... )

2*Sum - Sum = Sum = T*1 + (T*1/2 - T*1/2) + (T*1/4 - T*1/4) + (T*1/8 - T*1/8) + ... = T

One can do the same thing switching time and distance.

"Spacetime" has absolutely nothing to do with Xeno's Paradox or infinite series. Spacetime is a kind of non-Euclidean geometry.

[danielshrugged]

More fundamentally, I'd say you're confusing metaphysics and epistemology. We can divide distance and time up infinitely in thought. That does not mean that an infinite number of locations exist in reality, metaphysically, between any two distances.

Aristotle, in answering Zeno's paradox, first gives something that sounds much like y_feldblum's answer. But later, at 239b of the Physics, he says:

Zeno's reasoning, then, misses the mark: for he says that if everything is always at rest when it is at a place equal to it, while what is changing place is always doing so in the now, the flying arrow is motionless. But this is false, for time is not composed of indivisible nows, just as no other magnitude is.

Sachs, commenting, says:

The whole motion with its continuity is the primary datum of experience, and points and nows are derivative from it.

[Evangelical Capitalist]

Actually, space and time are quantized values too.

Planck Length and Planck Time