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  • Joseph Nebus 6:00 pm on Tuesday, 28 February, 2017 Permalink | Reply
    Tags: , , , Julian Dates, , mystery science theater 3000, US Naval Observatory   

    How To Work Out The Length Of Time Between Two Dates 


    September 1999 was a heck of a month you maybe remember. There that all that excitement of the Moon being blasted out of orbit thanks to the nuclear waste pile up there getting tipped over or something. And that was just as we were getting over the final new episode of Mystery Science Theater 3000‘s first airing. That episode was number 1003, Merlin’s Shop of Mystical Wonders, which aired a month after the season finale because of one of those broadcast rights tangles that the show always suffered through.

    Time moves on, and strange things happen, and show co-creator and first host Joel Hodgson got together a Kickstarter and a Netflix deal. The show’s Season Eleven is supposed to air starting the 14th of April, this year. The natural question: how long will we go, then, between new episodes of Mystery Science Theater 3000? Or more generally, how do you work out how long it is between two dates?

    The answer is dear Lord under no circumstances try to work this out yourself. I’m sorry to be so firm. But the Gregorian calendar grew out of a bunch of different weird influences. It’s just hard to keep track of all the different 31- and 30-day months between two events. And then February is all sorts of extra complications. It’s especially tricky if the interval spans a century year, like 2000, since the majority of those are not leap years, except that the one century year I’m likely to experience was. And then if your interval happens to cross the time the local region switched from the Julian to the Gregorian calendar —

    So my answer is don’t ever try to work this out yourself. Never. Just refuse the problem if you’re given it. If you’re a consultant charge an extra hundred dollars for even hearing the problem.

    All right, but what if you really absolutely must know for some reason? I only know one good answer. Convert the start and the end dates of your interval into Julian Dates and subtract one from the other. I mean subtract the smaller number from the larger. Julian Dates are one of those extremely minor points of calendar use. They track the number of days elapsed since noon, Universal Time, on the Julian-calendar date we call the 1st of January, 4713 BC. The scheme, for years, was set up in 1583 by Joseph Justus Scalinger, calendar reformer, who wanted for convenience an index year so far back that every historically known event would have a positive number. In the 19th century the astronomer John Herschel expanded it to date-counting.

    Scalinger picked the year from the convergence of a couple of convenient calendar cycles about how the sun and moon move as well as the 15-year indiction cycle that the Roman Empire used for tax matters (and that left an impression on European nations). His reasons don’t much matter to us. The specific choice means we’re not quite three-fifths of the way through the days in the 2,400,000’s. So it’s not rare to modify the Julian Date by subtracting 2,400,000 from it. The date starts from noon because astronomers used to start their new day at noon, which was more convenient for logging a whole night’s observations. Since astronomers started taking pictures of stuff and looking at them later they’ve switched to the new day starting at midnight like everybody else, but you know what it’s like changing an old system.

    This summons the problem: so how do I know many dates passed between whatever day I’m interested in and the Julian Calendar 1st of January, 4713 BC? Yes, there’s a formula. No, don’t try to use it. Let the fine people at the United States Naval Observatory do the work for you. They know what they’re doing and they’ve had this calculator up for a very long time without any appreciable scandal accruing to it. The system asks you for a time of day, because the Julian Date increases as the day goes on. You can just make something up if the time doesn’t matter. I normally leave it on midnight myself.

    So. The last episode of Mystery Science Theater 3000 to debut, on the 12th of September, 1999, did so on Julian Date 2,451,433. (Well, at 9 am Eastern that day, but nobody cares about that fine grain a detail.) The new season’s to debut on Netflix the 14th of April, 2017, which will be Julian Date 2,457,857. (I have no idea if there’s a set hour or if it’ll just become available at 12:01 am in whatever time zone Netflix Master Command’s servers are in.) That’s a difference of 6,424 days. You’re on your own in arguing about whether that means it was 6,424 or 6,423 days between new episodes.

    If you do take anything away from this, though, please let it be the warning: never try to work out the interval between dates yourself.

     
    • elkement (Elke Stangl) 9:31 am on Friday, 3 March, 2017 Permalink | Reply

      And I figured the routine date and time conversion mess you face as a software developer is a challenge ;-) …

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      • Joseph Nebus 4:53 am on Saturday, 11 March, 2017 Permalink | Reply

        Oh you have no idea. In that one ancient database was designed with every column a string, and dates entered as literally, eg, ’03/10/2017′. That string of text. Which was all right when the date just had to be shown on-screen but then I had said it should be easy to include a date range, unaware of just what was in the database. Also, that there are so many mistakes too. Or people entering 00/00/0000 when the date wasn’t available.

        Liked by 1 person

  • Joseph Nebus 9:46 pm on Friday, 17 January, 2014 Permalink | Reply
    Tags: , , , mystery science theater 3000, ,   

    What’s The Worst Way To Pack? 


    While reading that biography of Donald Coxeter that brought up that lovely triangle theorem, I ran across some mentions of the sphere-packing problem. That’s the treatment of a problem anyone who’s had a stack of oranges or golf balls has independently discovered: how can you arrange balls, all the same size (oranges are near enough), so as to have the least amount of wasted space between balls? It’s a mathematics problem with a lot of applications, both the obvious ones of arranging orange or golf-ball shipments, and less obvious ones such as sending error-free messages. You can recast the problem of sending a message so it’s understood even despite errors in coding, transmitting, receiving, or decoding, as one of packing equal-size balls around one another.

    A collection of Mystery Science Theater 3000 foam balls which I got as packing material when I ordered some DVDs.

    The “packing density” is the term used to say how much of a volume of space can be filled with balls of equal size using some pattern or other. Patterns called the cubic close packing or the hexagonal close packing are the best that can be done with periodic packings, ones that repeat some base pattern over and over; they fill a touch over 74 percent of the available space with balls. If you don’t want to follow the Mathworld links before, just get a tub of balls, or crate of oranges, or some foam Mystery Science Theater 3000 logo balls as packing materials when you order the new DVD set, and play around with a while and you’ll likely rediscover them. If you’re willing to give up that repetition you can get up to nearly 78 percent. Finding these efficient packings is known as the Kepler conjecture, and yes, it’s that Kepler, and it did take a couple centuries to show that these were the most efficient packings.

    While thinking about that I wondered: what’s the least efficient way to pack balls? The obvious answer is to start with a container the size of the universe, and then put no balls in it, for a packing fraction of zero percent. This seems to fall outside the spirit of the question, though; it’s at least implicit in wondering the least efficient way to pack balls to suppose that there’s at least one ball that exists.

    (More …)

     
    • Chiaroscuro 6:59 am on Saturday, 18 January, 2014 Permalink | Reply

      Without knowing the mathematical definition, I’d figure a ‘packing of spheres’ involves an arrangement such that:
      #1 There are no spaces/holes in the packing arrangement large enough so that a sphere could fit into a empty space.
      #2 Each sphere touches at least one other sphere.

      The Tetrahedral packing would seem to follow this; I’m.. not sure about the others.

      –Chi

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      • Joseph Nebus 5:33 am on Monday, 20 January, 2014 Permalink | Reply

        I admit not knowing what’s actually considered standard in the field. The requirement that each sphere touch at least one other seems hard to dispute; after all, otherwise, you might have isolated strands that don’t interact in any way.

        That there not be any gaps big enough to fit another ball in seems like it might be a fair dispute. I could imagine, for example, the problem of a sparse packing being relevant to the large-scale structure of the cosmos, as it seems to have some strands of matter and incredible voids.

        I wouldn’t be surprised if there’s a term of art for packings without such gaps and packings with, though I don’t know what that might be (although “sparse packings” seems like the sort of thing that might be used).

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    • elkement 1:26 pm on Monday, 20 January, 2014 Permalink | Reply

      My perspective on that packings is that of solid-state physics – so I would suppose that real-life packings would need to be stabilized by electromagnetic forces between these “particles”, not so much by gravity.

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      • Joseph Nebus 12:39 am on Wednesday, 22 January, 2014 Permalink | Reply

        I think you’re probably right that in this sort of problem, at least for solid-state physics, gravity wouldn’t be a consideration and it’d just be the pairwise interactions of the balls themselves that matters.

        There’s a couple things people might mean by stability, with the one most relevant to the mathematics problem probably being how little displacements of the balls affect whatever force holds one ball to its neighbors. If you were trying to build a model of one of these out of styrofoam and toothpicks to show off in the mathematics library, stability with respect to gravity probably matters more.

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    • Gerry 11:20 pm on Wednesday, 13 April, 2016 Permalink | Reply

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