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Dad • 09/23/03 • 5:25 PM:

For the record, Dad didn’t “sorta have it,” he had it. Admittedly, Dad’s explanation wasn’t good enough to immediately convince David, but to his credit, Dave did get it later, after meditating on the problem for a while. I can’t confirm that he used only his brain.

AJ • 09/23/03 • 9:37 PM:

First off, it is incorrect to say we ‘lose’ those four minutes. It’s not like bosses the world over are yelling at employees for leaving at 5:00 when “it’s only 4:56 earth rotation time!” You then say that we perceive that the earth rotates every 24 hours, which I suppose is more or less true. I obviously have to assume that the same time system used to decide the earth takes 23.56.04.10 to rotate is the same standard 24-hour system we use to keep track of time. We still go through each ‘day’ defined as a 24-hour increment, but as you have pointed out one of these ‘days’ is clearly not equivalent to one earth rotation. So the question must boil down to what the heck a day actually is.

Therefore, I’ve come to the conclusion that the best way to solve this problem will be to walk through a typical day in my life and then go back and eliminate all the parts that I can’t relate to the rotation of the earth. A quick brainstorm shows that pretty much none of my typical day has any apparent relation to the rotation of the earth, so I guess I’ll scratch that and instead embark a new roller coaster on the road to solutionville. Although, I’m pretty sure the earth doesn’t rotate at a constant rate we’ll also have to assume that it does for this problem (or at least that the mean value of the earth’s various rotational speeds approaches this given time per rotation).

Since the earth is orbiting the sun as well as spinning around its own axis, it actually takes more than a 360-degree rotation for the same spot on the earth to point perpendicular to the sun again. Draw a diagram if you don’t believe me. It does, however, take 24 hours to do this. Actually it takes CLOSE to 24 hours to do this. 24 hours is just a good mean value for each of the separate rotations the earth makes each ‘year.’ It works out to be a convenient time system that humans can use to spend most of their life living in daylight.

It should be noted that, sort of like the time I choose to go to and leave work, the time of day that the sun rises and sets changes every day of the year. Assuming that the earth would rotate once every 24 hours exactly, this would still happen. It has to do with the tilt of the earth during its rotation and probably with the orbital pattern, but lets avoid how much I forget about why that happens. Just suffice it to say that this varying sun-rise/set time can be explained by the earth tilt and seasons. It can also be explained by the fact that it takes a different amount of degrees (but always over 360) to be perpendicular the sun again depending on where the earth is on its elliptical orbit. As a meaningless side point, the change in day length kind of messes up that “living in daylight when using the same schedule” thing. So some ruling maniac who realized this schedule was the most important thing in life invented daylight savings to fix that problem.

I admit I had thought about this a lot (while at work) and come up with an answer based solely on the changing sun-rise/set times and seasons covering up the four minutes. I realized there was a flaw in this theory though, because the four minutes always disappear. The days, on the other hand, get longer throughout the year - then they get shorter. So while half the year, it’s possible the seasons would hide these departed minutes, the other half of the year they would actually magnify the amount of time lost. Because I don’t have the free time that a retired chemical engineer obviously does to solve such conundrums, I did some research. One stupid astronomer not so stupidly answered many great questions, but than tried to explain that the four minutes were fixed by leap year and you shouldn’t lose sleep over it. It’s possible he assumed that the people with littler brains than him were asking him another dumb question and so he didn’t bother to answer the question while he was awake. This, of course, resulted in him failing to turn on his magnificent super powered brain robot that obviously answered all the other questions. I did learn in my research that during the earth’s rotation around the sun it changes the speed at which it does so because of the elliptical orbit. That is interesting, if not full-on radical. Anyway, the moral of this paragraph is that I cheated by looking for an answer without the flaw mine obviously had even though David explicitly told me not to do so. I don’t feel bad though because I’m convinced that I could have figured it out on my own since it’s such a simple answer and someone once told me that I’m pretty simple.

Then again, I couldn’t solve the probability problem on my own until I was re-educated in probability by my friend, who first explained that I was solving the wrong problem - I thought the host didn’t always show you a goat door, but randomly picked one of the other two - oh, and I was solving it wrong anyway (in my defense, my approach was right, I just made a slight miscalculation). Anyway, my friend Chris is pursuing a PhD in some crazy scheme to give computers vision and at the same time working on a masters in math (a second masters because already having one in EE is clearly not good enough). Nevertheless, despite not having Marilyn’s 20 gazillion or whatever IQ, he was able to explain that the probability is 1/3 for both doors in my problem and 1/3 and 2/3 in Pat’s to me.

(#5) Sometimes reading stuff here makes my brain smoke. I think this is good in the same kind of way doing lunges when you haven’t for years and then not being able to walk for a week is good. For me the only other time my brain smoked was the last 2 weeks of certain semesters (all of them) in college when I did all the work for the entire semester and then jedi-mind tricked my professor’s to just grade it and not worry about it being months late. I’m always surprised at how I managed to do this while at the same time being trapped in a place that was at least adjacent to, if not in, some chamber of hell – NJIT.

Dan • 09/28/03 • 8:42 PM:

i pretty much figured it out, and maybe i’ll explain how i got to the answer, but for now,

look at this.

Patrick • 09/29/03 • 12:45 PM:

First of all, we should understand that a “day” is 24 hours. Otherwise we’d just be calling 23h 56m 4.1s “24 hours” or however else we’d choose to divide it up. But, if we posit an earth that doesn’t rotate on its axis, then we see that there would still be one “day” per year because the sun would seem to rise and set once (as the earth goes around it). That “day” gets divided up into all the other days of the year since the earth is rotating on its axis as well as revolving around the sun. So I think the teaser is interesting, but kind of dishonest. A day is a day is a day.

David • 09/29/03 • 1:08 PM:

My point/question is why are the values different? The question is what is a DAY? My point Pat, is that the definition is somewhat flawed, as seen in your comment and in dictionary.com’s definition - “The 24-hour period during which the earth completes one rotation on its axis.” See, one rotation IS NOT 24 hrs. The other question is - Mathematically how can you show that rotating once at 23.56.04 matches perfectly with our day experience being 24 hours. Of course it has to be, but prove it!

The answer, which nobody has proven/shown yet is below - don’t read if you want to figure it out on your own.

Seeing as the earth rotates and revolves, it moves a little bit in its orbit each day around the sun - basically 1/365th of the way. Therefore, we must rotate 1/365th PAST the one rotation point of the earth in order for that exact spot, say Whippany, NJ to be alined to the sun again. So, one rotation is 23 hrs. 56 min and 4 seconds - the extra rotation is the piece of the pie if you will (dividing earth’s orbit into 365 pieces - very close to the 360 degrees of a circle - although Kepler showed us it’s really an ellipse). Turns out that 1/365th of a day is equal to 24 hrs * 3600 seconds/hr = 86400 seconds each day/365 = 236.7 seconds which when you divide by 60 seconds/min = 3.94 minutes. Booyah.

The ‘missing’ time (subtract that number from 24 hours and you get the earth’s time of rotation). By the way, I know the time isn’t really missing, but it still is interesting to think about.

AJ • 09/29/03 • 2:35 PM:

David, either you didn’t read my post because it was too long or you wanted me to write it in a more confusing way like you did. Or maybe when you say nobody has proved you mean noMADDENbody. Anyway it’s explained in my third paragraph of the first post. The 1/365th of the way around the sun is also pretty close to 1 degree of rotation (there are 360 in a circle) which is one reason why a year is 365 days. The extra time (between 24 hours and 23.whatever) to rotate to the sun again is due to the earth traveling around the sun as well as around it’s own axis. In other words, it takes about 361 degrees of rotation around the earth’s axis to get to face the sun again because it is also moving around the sun. But in more words, it doesn’t always take the same amount of degrees to rotate to face the sun because (like you said) the orbit around the sun is elliptical. Sometimes it’s more sometimes it’s less (than 1/365th of the way - depending on how close you are to the sun). Think about it more and you’ll figure it out. Or draw the diagram like I said. Or go here or here.

AJ • 09/29/03 • 2:47 PM:

Or don’t go there or there because my hrefs aren’t working for whatever reason. Here are the links I was trying to list

David • 09/29/03 • 3:09 PM:

AJ,

Yes, yours was too long. Also, I didn’t see any mention of 361 degrees in there. You’re right -you knew it, you win. But still, more math to prove it - like the 1/365th of a day is ~ 4 minutes. I know you know this. But that’s all I was pointing to with ‘nobody’. Maybe noMAHALICbody? :)

And by the way, I don’t need to draw a diagram, I used rolls of toilet paper and made a MODEL of the sun - earth revolution/rotation system. Really, I did. All I need is mental imaging. It was during that wedding reception I mentioned earlier.

AJ • 09/29/03 • 4:49 PM:

WOOHOO!
I figured saying it was 361 or 24 hours and showing the math for that wasn’t really answering right since it only averages out to something close to that. Remember, the ellipse makes it vary along the orbit? I did say that it always takes more than 360 degrees though.

All Pat Jr needed was mental imaging at the reception, but you were Doubting David there (as you mentioned earlier). I like your explanation anyway. It’s more thorough. Mine is just rambling in an attempt to show my sluggish thought process and my constant tangents into something I think is funny, but probably isn’t. You win instead. I forfeit. MIHALIC has two I’s not two A’s.

Dad • 09/29/03 • 6:07 PM:

By the way, this problem is similar to the plot device used by Jules Verne in Around the World in Eighty Days. Phileas Fogg travels generally eastward around the world and counts 80 days as he goes, but forgets to subtract the “extra” day he caused to happen because he was always moving toward the sun. At first, he thinks he’s missed the deadline, but then finds out that only 79 days have actually passed in his beloved England. Modern readers might note that he simply forgot to subtract a day when he passed over the International Date Line. The date line was well known even during Verne’s time, but like today, most people didn’t give it much thought.

David • 09/29/03 • 10:17 PM:

eh jay,

Sorry about the name misspelling. My bad.

How about we tie?

By the way, does anybody remember the X-Files episode titled, “Tempus Fugit”? The one where Fox ‘loses’ 9 minutes and aliens/or the government hijacks an airplane in midflight? I do. Also, a ways back I finally looked up what tempus fugit meant - ‘time flies’ here’s what looks like an interesting webpage

Patrick • 10/01/03 • 12:27 PM:

I first learned the term tempus fugit from the Yes song of that name. I intuited the meaning because although the song’s title is “Tempus Fugit,” there is no mention of the phrase within the song. Instead, there is the phrase “time flies,” although it is not in a prominent position like a chorus or anything. It is only said in passing. Also, this songs is on the album Drama, where Trevor Horn does the singing instead of Jon Anderson, the regular singer. I didn’t really notice the difference until John Anderson (of Whippany) told me. Even then I didn’t believe him. Trevor Horn went on to fame with “Video Killed the Radio Star,” in his band The Buggles, which was really just him and Geoff Downes on keyboards (Downes also played on that one Yes album). That was the first video played on MTV (for all you trivia buffs). Downes later formed Asia with Steve Howe (also of Yes) and Carl Palmer (of Emerson, Lake, and Palmer) and John Wetton (of King Crimson, which also at one time included Greg Lake of Emerson, Lake, and Palmer). Man, those English bands were cross-pollinating like orchid growers! In any case, we didn’t have MTV back then, so if we wanted to see The Fixx singing “One Thing Leads to Another,” or Asia singing “Don’t Cry,” or Triumph singing “Fight the Good Fight,” we had to go to the McBrides. I don’t know why Mom dragged us all over to see Kathleen’s friend, but it was OK because we could watch MTV. Those were the days when MTV still played music videos. Man, how time flies…

David • 10/01/03 • 6:35 PM:

Beautiful memories. As I read Pat’s last comment I got all pumped and the chills thinking about just those videos at the McBrides - specifically “Don’t Cry” - Love it! and The Fixx are awesome too! Watch out for the doberman’s!

Dan • 10/01/03 • 7:20 PM:

the doberman’s what?

“Don’t Cry” is one of those songs that wreaks havoc on my emotions systems. You know, there’s a couple songs (“Nobody Gonna Break My Stride” is the other for me) that you heard when you were a little kid, loved them, had all but disposed them from your memory, then WHAM! 15 years later you hear it and you feel like you’re 8 again. Time flies. (and WHAM! had “Last Christmas,” which is pretty good too.)

David • 02/25/05 • 9:36 AM:

Whether you’ve got 24 hours or 23hrs 56 mins - this is the quote for you.

“Don’t say you don’t have enough time. You have exactly the same number of hours per day that were given to Helen Keller, Pasteur, Michaelangelo, Mother Teresa, Leonardo da Vinci, Thomas Jefferson, and Albert Einstein.” -H. Jackson Brown, Jr., writer (from today’s AWAD)

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