spacer1

Jayjay,
I think it is safe to assume time (or motion) is continuous. I think your problem arises where you equate our descriptions of reality with reality itself. In reality there is no "state" because there is no break in the continuum of time. The only "state" which exists is that which exists in our mind, where we can work in short-term memory with concepts drawn from our prior experiences. This is only an artificial stoppage in the continuous flow of time, however, created by our minds.

There is no actual t0, t1, t2,...., these are just boundaries or positions you have ascribed to reality, so as to describe a part of that reality to others.

Jayjay

I disagree. Even if time is continuous, we can still point out a particular moment in time, just like we can point out a particular number from a continuum of real numbers. I fail to see why the analogy between continuous time and real numbers doesn't work out.

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Jayjay,
Basically, because real numbers only exist in our minds, whereas reality doesn't. You can do anything you like with a continuum in your mind. You can stop it, chop it, cover it in chocolate, or give it golden wings. However, since reality isn't just in our minds, but actually surrounds us, where we are within it rather than it being within us, then we can't do whatever we like to it in the same fashion. We can imagine a "state" but such a state is bounded and, therefore, artificial, whereas reality flows continuously. Unless you believe our minds cause planetary motion.....?

xorbie

I think you are looking at the problem from the wrong viewpoint... states do not cause one another, rather the states are the initial conditions in a function that determines what the next state will be. For instance, if the function f determines an object's position, then we can just say f(t) = t^18 + ln(t) + tan(t) or whatever other hideous thing you want, the point is that this still determines an objects position for any and all t, even if time itself is continuous. I think this is a lot like calculus, in which we can calculate the areas of entire integrals without taking into account every single point.

However, I do think that the whole conversation is meaningless as both time and distance (I believe) are quantized and thus discrete in nature.

Jayjay

What do you mean by "bounded" in this case?

I don't see how that follows. I'm not claiming that our minds cause anything, in fact I'm not even assuming that there are "minds" in the timelines I'm trying to figure out.

spacer1

Jayjay,
Well, firstly, you're discerning the concept of time from the rest of reality. And secondly, you are defining points along that continuous timeline, which, I argue, do not exist within reality.
Are you speaking of time as the motion of the planets, as we know time to be in reality, or are you speaking of time as some abstract mathematical concept?

Jayjay

Interesting points... I have to sleep on these ideas.

scumble

Our measurement of time is based on counting events. It's just that at our scale of perception, it appears to be continuous.
It's a bit difficult to talk about time if nothing happens for there to be a time between. If there weren't a lot of regular phenomena to observe, it would be difficult for us to find a standard of time.

jpbrooks

Good point and good question!
Space is continuous because the lengths, widths, and depths/heights can have irrational (for example, the length of a diagonal of a square whose sides have an integral length) as well as rational numerical values. The cardinality of points in space is thus equal to that of a "continuum".

jpbrooks

The "structure" (for lack of a better term) of causality in the real world is very complex. There is (usually) no isolated line of causes and effects (where there is one cause for each effect) for physical processes in the real world. So, since in the real world effects can have more than one cause, causality can be continuous.