Lib very conveniently (for the purposes of this prankster) neglected to assign us to a fixed point on the surface of the planet. Therefore, I reserve the right to answer the question in terms of a constantly moving point of observation.
A thought exercise*: Take your spacecraft out for a spin around the galaxy, and find a planet you’d like to observe. You will note that the sunlit portion of the planet has two terminators, both constantly shifting with respect to a local observer on the ground (who will view the surrounding conditions as either sunrise or sunset, depending on which terminator the local is observing). Halfway between the terminators is an imaginary point which we will, for the sake of convention, call the MERIDIAN, also constantly shifting with respect to the local observer (who will be quite justified in setting his or her chronometer to NOON). At the antipodal point to this meridian, is Midnight.
Back to Earth.
Because the terminators never stop existing, a meridian exists 100% of the time.
Therefore, antipodally speaking, a point where it is midnight also exists for 100% of the time.
Q.E.D.
I make it a thought experiment because most people, of course, don’t have access to a spacecraft that they can just take out for a spin aroung the galaxy. If any of you actually DO have such access, can I borrow it next Saturday night? I promise to fill up the tank.
You might enjoy reading these threads. The first really seems more up your alley than mine. The second is a revival of our epistemological ravings: complete with an Ayn Rand lover, no less.
Yes, there is the 1-minute increment, 1-second increment, … infinitely smallest increment.
Deceivingly correct. More precisely it should read “There is therefore an infinite number of infinitely smallest increments that are not midnight.” There are a finite number of 1-minute or 1-second increments and you can measure them
If you choose to measure time useing some cumbersome method. you might end up with a problem. For example: One afternoon friends came over to my place to watch the Super Bowl. I knew I could pace myself drinking beer and I could chug two an hour, and I wanted to have everyone out by midnight. So all I had to do was fill my cooler with the proper number of beers and when it became empty it was time to go. The party started at 5:00 and to make a long story short after an undetermined number 16oz Slitz Malt Liquors I passed somoveee out. I didn’t wake up till 8:30 the next morning! Wondering what time I passed out I glanced over in my cooler to count the number of remaining beers, it was empty. Did I make it to midnight? Did those guys leave and take my beers?
Regardless of the increment of time we use as a measure the answer is the same and Alessan has given us that
I think everyone here has covered it well enough, but what the hell. Nothing like throwing my muddled two cents in.
Zeno’s paradox looks at motion wrong, and this midnight paradox does the same thing (only with time instead of distance).
Whether or not motion or time is quantized we move along it at a continuous rate (in the zeno problems)(either piecewise continuous or continuously continuous, lol). Thus, when we observe the “paradox” it is because we are constantly changing the perspective, and so each “half step” for motion or “half increment” for time is really its own perspective. If we infinitely change the way we look at a problem it should come as no suprise that we also don’t come up with an answer that makes sense. Once we agree on the rate of change, the problem disappears.
Nice to see you posting, Libertarian. Why the long absence?
Regarding Midnight - when I was younger we knew exactly when midnight was since the local Diner had specials on after Midnight. Therefore it exists. Sort of “I eat, Therefore a.m.”
Well, for my watch, it’s midnight for 0.001160093% of the day. If I had a watch without a second hand, it would be midnight for 0.0694444% of the day. However, over at NIST, and the USNO, it is only midnight for a very small fraction of the time it is on my watch, since they keep track of time to a billionth of a second.
Precision is a matter of choice, and capability. Back when there were twelve hours in a day, midnight was one third of the night, although the length of time varied. Noon, was a twelfth of the day, but the night was just divided up into “watches” and there were usually only three of them.
I suppose if you divided the day into Planck intervals, and then figured the percentage from that, you would have a fairly unassailable limit for the “duration” of midnight. The definition of the Planck interval includes an assumption that no interactions between quantum forces or objects can occur in less time. Of course, you really couldn’t designate a particular Planck Interval to be the specific one that was midnight, because you are not the USNO, or NIST, and by legal definition, their opinion is right, and you are only right if you agree with them. Since you cannot compare your answer with them during the interval, you can’t be sure. I suppose that is pretty much the same thing as saying it is never really midnight exactly. (Except at that one place, in Maryland, or another one in Paris.) (Hmmmm. Probably not in both, though, since they cannot agree to the limit of a Planck interval, except by coincidence.)
Along the same lines, also from Stoppard (but a bit darker):