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  • Joseph Nebus 6:00 pm on Tuesday, 17 January, 2017 Permalink | Reply
    Tags: capitals, , , United States,   

    48 Altered States 


    I saw this intriguing map produced by Brian Brettschneider.

    He made it on and for Twitter, as best I can determine. I found it from a stray post in Usenet newsgroup soc.history.what-if, dedicated to ways history could have gone otherwise. It also covers ways that it could not possibly have gone otherwise but would be interesting to see happen. Very different United States state boundaries are part of the latter set of things.

    The location of these boundaries is described in English and so comes out a little confusing. It’s hard to make concise. Every point in, say, this alternate Missouri is closer to Missouri’s capital of … uhm … Missouri City than it is to any other state’s capital. And the same for all the other states. All you kind readers who made it through my recent A To Z know a technical term for this. This is a Voronoi Diagram. It uses as its basis points the capitals of the (contiguous) United States.

    It’s an amusing map. I mean amusing to people who can attach concepts like amusement to maps. It’d probably be a good one to use if someone needed to make a Risk-style grand strategy game map and didn’t want to be to beholden to the actual map.

    No state comes out unchanged, although a few don’t come out too bad. Maine is nearly unchanged. Michigan isn’t changed beyond recognition. Florida gets a little weirder but if you showed someone this alternate shape they’d recognize the original. No such luck with alternate Tennessee or alternate Wyoming.

    The connectivity between states changes a little. California and Arizona lose their border. Washington and Montana gain one; similarly, Vermont and Maine suddenly become neighbors. The “Four Corners” spot where Utah, Colorado, New Mexico, and Arizona converge is gone. Two new ones look like they appear, between New Hampshire, Massachusetts, Rhode Island, and Connecticut; and between Pennsylvania, Maryland, Virginia, and West Virginia. I would be stunned if that weren’t just because we can’t zoom far enough in on the map to see they’re actually a pair of nearby three-way junctions.

    I’m impressed by the number of borders that are nearly intact, like those of Missouri or Washington. After all, many actual state boundaries are geographic features like rivers that a Voronoi Diagram doesn’t notice. How could Ohio come out looking anything like Ohio?

    The reason comes to historical subtleties. At least once you get past the original 13 states, basically the east coast of the United States. The boundaries of those states were set by colonial charters, with boundaries set based on little or ambiguous information about what the local terrain was actually like, and drawn to reward or punish court factions and favorites. Never mind the original thirteen (plus Maine and Vermont, which we might as well consider part of the original thirteen).

    After that, though, the United States started drawing state boundaries and had some method to it all. Generally a chunk of territory would be split into territories and later states that would be roughly rectangular, so far as practical, and roughly similar in size to the other states carved of the same area. So for example Missouri and Alabama are roughly similar to Georgia in size and even shape. Louisiana, Arkansas, and Missouri are about equal in north-south span and loosely similar east-to-west. Kansas, Nebraska, South Dakota, and North Dakota aren’t too different in their north-to-south or east-to-west spans.

    There’s exceptions, for reasons tied to the complexities of history. California and Texas get peculiar shapes because they could. Michigan has an upper peninsula for quirky reasons that some friend of mine on Twitter discovers every three weeks or so. But the rough guide is that states look a lot more similar to one another than you’d think from a quick look. Mark Stein’s How The States Got Their Shapes is an endlessly fascinating text explaining this all.

    If there is a loose logic to state boundaries, though, what about state capitals? Those are more quirky. One starts to see the patterns when considering questions like “why put California’s capital in Sacramento instead of, like, San Francisco?” or “Why Saint Joseph instead Saint Louis or Kansas City?” There is no universal guide, but there are some trends. Generally states end up putting their capitals in a city that’s relatively central, at least to the major population centers around the time of statehood. And, generally, not in one of the state’s big commercial or industrial centers. The desire to be geographically central is easy to understand. No fair making citizens trudge that far if they have business in the capital. Avoiding the (pardon) first tier of cities has subtler politics to it; it’s an attempt to get the government somewhere at least a little inconvenient to the money powers.

    There’s exceptions, of course. Boston is the obviously important city in Massachusetts, Salt Lake City the place of interest for Utah, Denver the equivalent for Colorado. Capitals relocated; Atlanta is Georgia’s eighth(?) I think since statehood. Sometimes they were weirder. Until 1854 Rhode Island rotated between five cities, to the surprise of people trying to name a third city in Rhode Island. New Jersey settled on Trenton as compromise between the East and West Jersey capitals of Perth Amboy and Burlington. But if you look for a city that’s fairly central but not the biggest in the state you get to the capital pretty often.

    So these are historical and cultural factors which combine to make a Voronoi Diagram map of the United States strange, but not impossibly strange, compared to what has really happened. Things are rarely so arbitrary as they seem at first.

     
    • Matthew Wright 6:49 pm on Tuesday, 17 January, 2017 Permalink | Reply

      New Zealand’s provincial borders were devised at much the same time as the midwestern and western US and in much the same way. Some guy with a map that only vaguely showed rivers, and a ruler. Well, when I say ‘some guy’ I mean George Grey, Edward Eyre and their factotum, Alfred Domett among only a handful of others. Early colonial New Zealand was like that. The civil service consisted of about three people (all of them Domett) and because the franchise system meant some voting districts might have as few as 25 electors, anybody had at least a 50/50 chance of becoming Prime Minister.

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      • Joseph Nebus 3:45 pm on Saturday, 21 January, 2017 Permalink | Reply

        I am intrigued and delighted to learn this! For all that I do love maps and seeing how borders evolve over time I’m stronger on United States and Canadian province borders; they’re just what was easily available when I grew up. (Well, and European boundaries, but I don’t think there’s a single one of them that’s based on anything more than “this is where the armies stood on V-E Day”.)

        Would you have a recommendation on a pop history of New Zealand for someone who knows only, mostly, that I guess confederation with Australia was mooted in 1900 but refused since the islands are actually closer to the Scilly Isles than they are Canberra for crying out loud?

        Liked by 1 person

    • Matthew Wright 8:43 pm on Saturday, 21 January, 2017 Permalink | Reply

      Europe has had so many boundary changes since Roman times that I wouldn’t be surprised if there’s a tradition for governments to issue people with an eraser and pot of paint to update their maps – and, no question, their history IS the history of those boundary changes. Certainly it explains their wars…

      On matters NZ, I wrote just such a book – it was first published in 2004 and has been through a couple of editions (I updated it in 2012). My publishers, Bateman, put it up on Kindle:

      It’s ‘publisher priced’ but I’d thoroughly recommend it! :-) The parallels between NZ’s settler period and the US ‘midwestern’ expansion through to California at the same time are direct.

      The reasons why NZ never joined Australia in 1900 have been endlessly debated and never answered but probably had something to do with the way NZ was socially re-identifying itself with Britain at the time. The British ignored the whole thing for defence/strategic purposes, deploying just one RN squadron to Sydney as the ‘mid point’ of Australasia. Sydney-siders liked it, but everybody from Perth to Wellington was annoyed. I wrote my thesis on the political outcome, way back when.

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      • Joseph Nebus 6:19 am on Saturday, 28 January, 2017 Permalink | Reply

        Aw, thank you kindly! I’d thought you might have something suitable.

        The organizing of territory that white folks told themselves was unsettled is a process I find interesting, I suppose because I’ve always wondered about how one goes about establishing systems. I think it’s similar to my interest in how nations devastated by wars get stuff like trash collection and fire departments and regional power systems running again. The legal system for at least how the United States organized territory is made clear enough in public schools (at least to students who pay attention, like me), but it isn’t easy to find the parallel processes in other countries. Now and then I try reading about Canada and how two of every seven sections of land in (now) Quebec and Ontario was reserved to the church and then I pass out and by the time I wake up again they’re making infrastructure promises to Prince Edward Island.

        I’m not surprised that from the British side of things the organization of New Zealand and Australia amounted to a bit of afterthought and trusting things would work out all right. I have read a fair bit (for an American) about the British Empire and it does feel like all that was ever thought about was India and the route to India and an ever-widening corridor of imagined weak spots on the route to India. The rest of the world was, pick some spot they had already, declare it “the Gibraltar of [ Geographic Region ]” and suppose there’d be a ship they could send there if they really had to.

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  • Joseph Nebus 6:00 pm on Thursday, 3 March, 2016 Permalink | Reply
    Tags: flags, , , United States   

    Stars On The Flag 


    The United States flag has as many stars as the country has states. For a long while star arrangement was up to the flag-maker, with no specific rule in place. This is where the occasional weird and ugly 19th century flag comes from. But the arrangement has got codified. It’s to be stars in rows, or at least staggered rows.

    It’s easy to understand how to arrange 48 stars, which the flag had for a while. Or 49 stars, which it had almost long enough to get a new flag made. 50 stars, which it’s had for longer than 48 now, are familiar from experience. But a natural question is how to arrange an arbitrary number of stars? And courtesy the MTBos Blogbog, linking to essays about mathematics, I don’t have to answer it myself.

    Experience First Math reviewed the problem recently. You can find a pattern by playing around, of course. It’s not very efficient, but we don’t need new flags very often. We don’t need to save time on this.

    And uniformly spacing stuff can be a hard problem. For example, no one knows what is the most uniform way to put thirteen spots on the surface of a sphere. We’re certain that we’re close, though.

    This is a simpler problem. We have to fit stars in a rectangle. The stars have to be arranged in rows, or in staggered rows. Each row can’t be too much bigger or smaller than its neighbors. And with that, a little bit of factoring and geometric reasoning and counting produces a lovely result: how to generally arrange stars.

    Well, almost generally. There are some numbers that don’t work with alternating rows. We’ve seen this before. There were some ugly compromises necessary to have a 44-star flag, in the 1890s, or the 36-star flag in 1865. But with this alternating-rows example, we’ve got a hint to working out other nearly-staggered and nearly-alternating row patterns.

     
    • Matthew Wright 6:47 pm on Thursday, 3 March, 2016 Permalink | Reply

      New Zealand’s flag has four stars, representing the Southern Cross, and we might be losing those if a flag change referendum under way just now votes for an alternative.

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      • FlowCoef 3:07 am on Friday, 4 March, 2016 Permalink | Reply

        Both the current one and the possible alternate both have the four star pattern on them.

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        • Matthew Wright 4:35 am on Friday, 4 March, 2016 Permalink | Reply

          Yes, however I have been trying to ignore the new one.

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          • Joseph Nebus 8:38 pm on Friday, 4 March, 2016 Permalink | Reply

            I am intrigued … hm.

            Well, if Wikipedia’s not leading me wrong and I’m looking correctly at what it calls the designs by Mike Archer … they’re not bad, I suppose. I feel old-fashioned enough to not be perfectly comfortable with curves in flags, except those that surround Great Seals and the like. I’m from New Jersey, which just plants its seal on a buff background. I imagine it didn’t take a lot of design imagination to do, but it looks thick with symbolism and dignity and all.

            Liked by 1 person

  • Joseph Nebus 7:33 pm on Wednesday, 1 April, 2015 Permalink | Reply
    Tags: , , , ideal gas, , , , , United States,   

    My Mathematics Blog, As March 2015 Would Have It 


    And now for my monthly review of publication statistics. This is a good month to do it with, since it was a record month: I had 1,022 pages viewed around these parts, the first time (according to WordPress) that I’ve had more than a thousand in a month. In January I’d had 944, and in February a mere 859, which I was willing to blame on the shortness of that month. March’s is a clean record, though, more views per day than either of those months.

    The total number of visitors was up, too, to 468. That’s compared to 438 in January and 407 in short February, although it happens it’s not a record; that’s still held by January 2013 and its 473 visitors. The number of views per visitor keeps holding about steady: from 2.16 in January to 2.11 in February to 2.18 in March. It appears that I’m getting a little better at finding people who like to read what I like to write, but haven’t caught that thrilling transition from linear to exponential growth.

    The new WordPress statistics tell me I had a record 265 likes in March, up from January’s 196 and February’s 179. The number of comments rose from January’s 51 and February’s 56 to a full 93 for March. I take all this as supporting evidence that I’m better at reaching people lately. (Although I do wonder if it counts backlinks from one of my articles to another as a comment.)

    The mathematics blog starts the month at 22,837 total views, and with 454 WordPress followers.

    The most popular articles in March, though, were the set you might have guessed without actually reading things around here:

    I admit I thought the “how interesting is a basketball tournament?” thing would be more popular, but it’s hampered by having started out in the middle of the month. I might want to start looking at the most popular articles of the past 30 days in the middle of the month too.

    The countries sending me the greatest number of readers were the usual set: the United States at 658 in first place, and Canada in second at 66. The United Kingdom was a strong third at 57, and Austria in fourth place at 30.

    Sending me a single reader each were Belgium, Ecuador, Israel, Japan, Lebanon, Mexico, Nepal, Norway, Portugal, Romania, Samoa, Saudi Arabia, Slovakia, Thailand, the United Arab Emirates, Uruguay, and Venezuela. The repeats from February were Japan, Mexico, Romania, and Venezuela. Japan is on a three-month streak, while Mexico has sent me a solitary reader four months in a row. India’s declined slightly in reading me, from 6 to 5. Ah well.

    Among the interesting search terms were:

    • right trapezoid 5 (I loved this anime as a kid)
    • a short comic strip on reminding people on how to order decimals correctly (I hope they found what they were looking for)
    • are there other ways to draw a trapezoid (try with food dye on the back of your pet rabbit!)
    • motto of ideal gas (veni vidi v = nRT/P ?)
    • rectangular states (the majority of United States states are pretty rectangular, when you get down to it)
    • what is the definition of rerun (I don’t think this has come up before)
    • what are the chances of consecutive friday the 13th’s in a year (I make it out at 3/28, or a touch under 11 percent; anyone have another opinion?)

    Well, with luck, I should have a fresh comic strips post soon and some more writing in the curious mix between information theory and college basketball.

     
    • scifihammy 7:21 am on Friday, 3 April, 2015 Permalink | Reply

      It’s fun to look at our stats :) Though I never understand that a post I have spent a lot of time and effort on passes by hardly noticed, and one I have quickly written in minutes is suddenly my most viewed! I guess all part of the fun! :)
      Nice to find someone else who likes numbers :)

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      • Joseph Nebus 5:04 pm on Saturday, 4 April, 2015 Permalink | Reply

        I’ve almost had to give up on guessing what people will and won’t like. I suppose I could try searching what kinds of subjects produce the most response — in readers, in likes, and in comments — and try to aim for that, but I’m not quite up to that challenge yet.

        Anyway, I’m glad that you’re enjoying my little work here.

        Liked by 1 person

        • scifihammy 5:51 pm on Saturday, 4 April, 2015 Permalink | Reply

          I blog for my own amusement really. I just think it is funny what is noticed or not :)
          I don’t understand all you write – but I do like maths :)

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    • Planetary Defense Commander 7:05 am on Tuesday, 7 April, 2015 Permalink | Reply

      I was a little sleepy when I read this, and my thought was “Chances of consecutive Friday the 13ths? Zero, because the next day will be the 14th.”

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      • Joseph Nebus 10:06 pm on Wednesday, 8 April, 2015 Permalink | Reply

        You’d think that would be reassuring, but I believe Churchy La Femme has at least a couple months worried about there being no end of 13ths in the month. (He’d be reassured that Friday the 13th comes on a Monday this April, though.)

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  • Joseph Nebus 12:15 am on Friday, 20 April, 2012 Permalink | Reply
    Tags: American English, , British English, Canada, Costa Rica, , , , Germany, , Malaysia, picture of a trapezoid, , , South Africa, trapezium, , United Kingdom, United States   

    Something I Didn’t Know About Trapezoids 


    I have a little iPad app for keeping track of how this blog is doing, and I’m even able to use it to compose new entries and make comments. (The entry about the lottery was one of them.) Mostly it provides a way for me to watch the count of unique visits per day, so I can grow neurotic wondering why it’s not higher. But it also provides supplementary data, such as, what search queries have brought people to the site. The “Trapezoid Week” flurry of posts has proved to be very good at bringing in search referrals, with topics like “picture of a trapezoid” or “how do I draw a trapezoid” or “similar triangles trapezoid” bringing literally several people right to me.

    (More …)

     
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