There is an infinite number of increments of time; that is, every second can be divided in half, and its half divided in half, and so on. There is therefore an infinite number of time increments that are not midnight. Does that mean that it is never midnight? If not, then what percentage of the time is it midnight?
http://plato.stanford.edu/entries/spacetime-supertasks/
As an instance of the second sort of processes we referred to above, those about which no consensus has been reached as to whether they are supertasks, we can take the process which is described in one of the forms of Zeno’s dichotomy paradox. Suppose that initially (at t = 12 A.M., say) Achilles is at point A (x = 0) and moving in a straight line, with a constant velocity v = 1 km/h, towards point B (x = 1), which is 1 km. away from A. Assume, in addition, that Achilles does not modify his velocity at any point. In that case, we can view Achilles’s run as the performance of a supertask, in the following way: when half the time until t = 1 P.M. has gone by, Achilles will have carried out the action a1 of going from point x = 0 to point x = 1/2 (a1 is thus performed in the interval of time between t =12 A.M. and t = 1/2 P.M.), when half the time from the end of the performance of a1 until t* = 1 P.M. will have elapsed, Achilles will have carried out the action a2 of going from point x = 1/2 to point x = 1/2 + 1/4 (a2 is thus performed in the interval of time between t = 1/2 P.M. and t = 1/2 + 1/4 P.M.), when half the time from the end of the performance of a2 until t* = 1 P.M. will have elapsed, Achilles will have carried out the action a3 of going from point x = 1/2 + 1/4 to point x = 1/2 + 1/4 + 1/8 (a3 is thus performed in the interval of time between t = 1/2 + 1/4 P.M. and t = 1/2 + 1/4 + 1/8 P.M.), and so on. When we get to instant t* = 1 P.M., Achilles will have carried out an infinite sequence of actions, that is, a supertask T = (a1, a2, a3, . . . , an, . . . ), provided we allow the state of the world relevant for the description of T to be specified, at any arbitrary instant, by a single sentence: the one which specifies Achilles’s position at that instant. Several philosophers have objected to this conclusion, arguing that, in contrast to Thomson’s lamp, Achilles’s run does not involve an infinity of actions (acts) but of pseudo-acts. In their view, the analysis presented above for Achilles’s run is nothing but the breakdown of one process into a numerable infinity of subprocesses, which does not make it into a supertask. In Allis and Koetsier’s words, such philosophers believe that a set of position sentences is not always to be admitted as a description of the state of the world relevant to a certain action. In their opinion, a relevant description of a state of the world should normally include a different type of sentences (as is the case with Thomson’s lamp) or, in any case, more than simply position sentences…*
{Too large of a cite, IMHO. I trimmed it. --Gaudere}
[Edited by Gaudere on 03-18-2001 at 12:36 PM]
Or you could just look at your watch.
Thanks, Brian, for contextualizing the debate, which I failed to do. With which of the philosophers do you agree, and why?
JonScribe, what percentage of the time is it midnight by your watch?
Well, does a line exist? It has no width. How about a dot?
Midnight is a theoretical object; a boundry.
BTW, Libertarian - welcome back.
Thanks.
Thanks a lot. Now I have to stay up half the night tonight, contemplating this question. Stephen Hawking did the same thing to me at one point. Damn you!
-L
how does this apply to Cinderella?
By agreeing that there is a such thing as time, you negate the argument.
Time is a system of measurement that constantly moves forward. Dividing an increment of the whole by half again and again does not stop the forward flow. A second will always take the same exact amount of time as the last one did and the next one will, no matter how many times it is broken up.
1 second, halved again and again for infinity, when added back up again, still equals 1 second.
By the standards of time we are taught and live by, midnight is essentially 12:00 A.M. (that is: 0:00:00 until 0:00:59), so the percentage of time it is midnight is equal to what 1 of how ever many minutes there are in a 24 hour day is.
Allesan, thanks for the welcome. Are you saying that midnight is to time as a photon is to light?
SexyWriter, sorry about your anxiety. Stephen Hawking? Very undeserved, I’m afraid.
SoulMurk, do you disagree that there is such a thing as time? If so, which time, all of them? The time that is a dimension? The time that is a ratio of rate and distance? Or something else? You make a good point, but I think different people are “taught to live by” different concepts of what is midnight. Computer programmers might think of midnight as from 00:00:00 to one clock cycle later (depending on the density of capturable cycles), rather than from 00:00:00 to 00:00:59, since that is when their equality comparison operator would gate as false. Still others might think of midnight as a moment, or boundary, like Alessan seemed to imply. In other words, what exactly is it that you think might not exist?
Spritus? Father Mentock?
Actually, time can’t be divided in half infinitely. Eventually, you come up to Planck Time, which is 10[sup]-43[/sup] seconds. time can’t be any shorter than that. It’s one o’ them quantum physics things. 
I do not disagree that there is such a thing as time, no.
Time is a very handy system of measure, but that is all it is, a system; a theory. Debating whether or not midnight is actually midnight, or a perceived boundary, is a philosophical matter, and getting off of the original OP.
I personally do not ever wear a watch, nor (other than that 8 hour stretch of the day while at work) do I check what time the clock reads on a regular basis. I did not mean to allude that I did not believe in the concept of time, merely that I did not subscribe to being ruled by what time the clock read.
In attempting to answer your original questions, I referred to the basic system that we are all taught in 1st grade. Though there may be several ways of interpreting this basic system (i.e. your reference to programming), time is a universal concept, agreed upon anywhere.
1 second in France takes the exact same amount of time as 1 second in Guatemala. 1 second to a juggler is the exact same as 1 second to a computer programmer. Computers may understand time differently than a human and need to be programmed accordingly, but that does not change the fact that 1 second is 1 second, or what period of time midnight actually is.
Delighted to see you here again Libertarian.
I have little to add here except a quote from Jumpers by Tom Stoppard:
Greetings, Jab. Them quantum physics things can indeed perplex. Particularly since we do not know at this point, and possibly might never know, whether their quanta are in fact quanta. Has the study of subquantum physics yet begun?
Let’s agree, nevertheless, to work with Planck time as though it were the final word, much as we would have worked with Newtonian gravity in the eighteenth century. The percentage of time that it would be midnight, then, would be the number of cycles from midnight to midnight, divided by the sum of all Planck times, times one-hundred. Do you know whether the sum of all Planck times is infinite? That is, do you know whether the universe is eternal?
SoulMurk, I think of midnight much in the same way that Alessan does, except that I think of it as analogous to the peak of a wave. That is, a moment (like midnight) is to time as a particle (like a photon) is to a wave. Therefore, it is midnight once per each day cycle, and is never midnight for the duration of any day cycle. The percentage of time that it is midnight could then be derived if we accepted Planck time as axiomatic, and knew how many Planck times (perhaps Jab knows) were in a day’s cycle, irrespective of how many day cycles there are, were, and will be. This would be true even if there are infinitely many cycles. (I don’t believe there are.)
Picmr, thanks. Delighted to be here, if only for a brief visit.
D’oh. Barring careless math, it occurs to me that there would be 8.64 X 10[sup]47[/sup] Planck times in a day cycle. Midnight, then, would be roughly 1.157407 x 10[sup]-46[/sup] percent of the time. Did I do that right?
Where ya been?
This reminds me of the riddle I was told in grade school about the frog jumping across the road.
If the frog jumps half-way across the road, and then half-way again, and then half-way again, and each succeeding jump is half of the distance left to complete his trip across the road, does he then ever reach the other side?
I came up with two answers:
a) Yes, because althought you can keep dividing the distance in half to infinity, the frog is too large to jump an infinitesimally small amount, so he would reach the other side because he would not be able to prevent himself from doing so.
b) No, because while his poor brain was trying to figure this out, a sixteen wheeler rushes by and squashes him flat.
I find these sorts of questions to be, in a way, artificial. The measures of time and space are tools for human convenience and, of necessity, these measures are limited by our capacity to understand what they are actually measuring.
I forgot my sig, which I have seldom used since Libertarian’s hiatus from the board.
WRONG. “MDJ KO ANA HEY” (Urdu).
Spidey, “…these measures [of time and space] are limited by our capacity to understand what they are actually measuring”. Profoundly beautiful, thank you.
(By the way, God, too, says, “I Am”. Is that sufficient for you?)
I think the only good answer to the question “what percentage of the time is it midnight” is 0%. That answer doesn’t imply that it’s never midnight (“it’s never midnight” is a contradiction in terms), it just reflects the fact that intervals like seconds have positive duration while moments like “midnight” do not.
These are all fairly simple concepts once you’ve taken either some calculus or some statistics.
(I’m deliberately ignoring Planck, partly because I’m not a physicist but mostly because I was under the impression that quantum limits like Planck Time were just limits on what we could measure, not limits on the nature of time itself.)
To answer your question regarding me, I am a finitist. I think time is a comprehension of space and causality, without which would be impossible. It is somewhat artificial, because we assume it is constant. Time stops being a comprehension tool whenever we suspend it to play with infinity–which is in-de-finity to me. We had a thread on it a few weeks ago.
One of us threw a decimal place. I get 1.157407 x 10[sup]-48[/sup] if time is quantized and Planck time is the smallest increment.
If time is not quantized, then mathgeek is correct. The percentage of time that is midnight is 0. This does not bar midnight from occuring. The probability of any point occurence over a continuous field is zero.
As promised in the thread mentioned I will now chuckle at BrianBunnyhurt. (Okay, technically he did not put “infinity” in quotation marks, but I find in-de-finity to be equally amusing.)