Tagged: New Jersey Toggle Comment Threads | Keyboard Shortcuts

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

    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.

      Like

      • 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.

      Like

      • 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.

        Like

  • Joseph Nebus 3:00 pm on Monday, 18 April, 2016 Permalink | Reply
    Tags: , , , dot products, , New Jersey, NJIT, , ,   

    A Leap Day 2016 Mathematics A To Z: Vector 


    And as we approach the last letters of the alphabet, my Leap Day A To Z gets to the lats of Gaurish’s requests.

    Vector.

    A vector’s a thing you can multiply by a number and then add to another vector.

    Oh, I know what you’re thinking. Wasn’t a vector one of those things that points somewhere? A direction and a length in that direction? (Maybe dressed up in more formal language. I’m glad to see that apparently New Jersey Tech’s student newspaper is still The Vector and still uses the motto “With Magnitude And Direction’.) Yeah, that’s how we’re always introduced to it. Pointing to stuff is a good introduction to vectors. Nearly everyone finds their way around places. And it’s a good learning model, to learn how to multiply vectors by numbers and to add vectors together.

    But thinking too much about directions, either in real-world three-dimensional space, or in the two-dimensional space of the thing we’re writing notes on, can be limiting. We can get too hung up on a particular representation of a vector. Usually that’s an ordered set of numbers. That’s all right as far as it goes, but why limit ourselves? A particular representation can be easy to understand, but as the scary people in the philosophy department have been pointing out for 26 centuries now, a particular example of a thing and the thing are not identical.

    And if we look at vectors as “things we can multiply by a number, then add another vector to”, then we see something grand. We see a commonality in many different kinds of things. We can do this multiply-and-add with those things that point somewhere. Call those coordinates. But we can also do this with matrices, grids of numbers or other stuff it’s convenient to have. We can also do this with ordinary old numbers. (Think about it.) We can do this with polynomials. We can do this with sets of linear equations. We can do this with functions, as long as they’re defined for compatible domains. We can even do this with differential equations. We can see a unity in things that seem, at first, to have nothing to do with one another.

    We call these collections of things “vector spaces”. It’s a space much like the space you happen to exist in is. Adding two things in the space together is much like moving from one place to another, then moving again. You can’t get out of the space. Multiplying a thing in the space by a real number is like going in one direction a short or a long or whatever great distance you want. Again you can’t get out of the space. This is called “being closed”.

    (I know, you may be wondering if it isn’t question-begging to say a vector is a thing in a vector space, which is made up of vectors. It isn’t. We define a vector space as a set of things that satisfy a certain group of rules. The things in that set are the vectors.)

    Vector spaces are nice things. They work much like ordinary space does. We can bring many of the ideas we know from spatial awareness to vector spaces. For example, we can usually define a “length” of things. And something that works like the “angle” between things. We can define bases, breaking down a particular element into a combination of standard reference elements. This helps us solve problems, by finding ways they’re shadows of things we already know how to solve. And it doesn’t take much to satisfy the rules of being a vector space. I think mathematicians studying new groups of objects look instinctively for how we might organize them into a vector space.

    We can organize them further. A vector space that satisfies some rules about sequences of terms, and that has a “norm” which is pretty much a size, becomes a Banach space. It works a little more like ordinary three-dimensional space. A Banach space that has a norm defined by a certain common method is a Hilbert space. These work even more like ordinary space, but they don’t need anything in common with it. For example, the functions that describe quantum mechanics are in a Hilbert space. There’s a thing called a Sobolev Space, a kind of vector space that also meets criteria I forget, but the name has stuck with me for decades because it is so wonderfully assonant.

    I mentioned how vectors are stuff you can multiply by numbers, and add to other vectors. That’s true, but it’s a little limiting. The thing we multiply a vector by is called a scalar. And the scalar is a number — real or complex-valued — so often it’s easy to think that’s the default. But it doesn’t have to be. The scalar just has to be an element of some field. A ‘field’ is a ring that you can do addition, multiplication, and division on. So numbers are the obvious choice. They’re not the only ones, though. The scalar has to be able to multiply with the vector, since otherwise the entire concept collapses into gibberish. But we wouldn’t go looking among the gibberish except to be funny anyway.

    The idea of the ‘vector’ is straightforward and powerful. So we see it all over a wide swath of mathematics. It’s one of the things that shapes how we expect mathematics to look.

     
  • Joseph Nebus 10:04 pm on Tuesday, 15 April, 2014 Permalink | Reply
    Tags: , New Jersey, New Jersey Devils, ,   

    The Most Unlikely NHL Playoff Upsets of the Last Five Years 


    Nick Emptage, writing for puckprediction.com, has the sort of post which I can’t resist: it’s built on the application of statistics to sports. In this case it’s National Hockey League playoffs, and itself builds on an earlier post about the conditional probabilities of the home-team-advantaged winning a best-of-seven series, to look at the most unlikely playoff wins of the last several years. Since I’m from New Jersey I feel a little irrational pride at the New Jersey Devils being two of the most improbable winners, not least because I remember the Devils in the 1980s when the could lose as many as 200 games per eighty-game season, so seeing them in the playoffs at all is a wondrous thing.

     
  • Joseph Nebus 10:18 pm on Friday, 5 April, 2013 Permalink | Reply
    Tags: , , , , New Jersey   

    Reading the Comics, April 5, 2013 


    Before getting to the next round of comic strips that mention mathematics stuff, I’d like to do a bit of self-promotion. Freshly published is the book Oh, Sandy: An Anthology Of Humor For A Serious Purpose, edited by Lynn Beighley, Peter Barlow, Andrea Donio, and A J Fader. This is a collection of humorous bits, written out of a sense of needing to do something useful after the Superstorm. I have an essay in there, based on the strange feelings I had of being remote (and quite safe) while seeing my home state — and particularly the piers at Seaside Heights, New Jersey — being battered by a storm. The book is available also through CreateSpace.

    Jenny Campbell’s Flo and Friends (March 23) mentions π, and what’s really a fairly indistinct question for a tutor to ask the student. “Explain pi” is more open-ended than I think could be useful to answer: you could write books trying to describe what it’s used for, never mind the history of studying it. After all, it’s the only transcendental number with enough pop cultural cachet to appear routinely in newspaper comic strips; what constitutes an explanation of it? Alas, the strip just goes for the easiest pi pun to be made.

    Scott Hilburn’s The Argyle Sweater (March 25) returns to the gimmick of anthropomorphized numerals. It’s a cute enough joke; it’s also apparently a different pair of 1 and 2 from earlier in the month. I do wonder what, in this panel’s continuity, subtraction might mean. Still, Hilburn is obviously never far from thinking of anthropomorphized numbers, as he came back to the setting on April 3, with another 2 putting in an appearance.

    (More …)

     
    • BunnyHugger 6:13 pm on Tuesday, 9 April, 2013 Permalink | Reply

      Rollercoaster Tycoon having been written in machine code is why Mac folks never got to have it. :(

      Like

      • Joseph Nebus 5:19 am on Tuesday, 16 April, 2013 Permalink | Reply

        Yeah, and that’s a pity. I suppose the programmer figured he was getting a more responsive game from it, but I can say confidently that any possible gain in speed he got from using machine code rather than a higher-level language was tiny compared to what improved hardware has gotten us.

        Mostly I’d really, really like a version of Roller Coaster Tycoon that could be played on the iPad.

        Like

  • Joseph Nebus 11:23 am on Wednesday, 12 December, 2012 Permalink | Reply
    Tags: , , , , New Jersey   

    How Big Was West Jersey? 


    A map of New Jersey's counties, with municipal boundaries added.

    A book I’d read about the history of New Jersey mentioned something usable for a real-world-based problem in fraction manipulation, for a class which was trying to get students back up to speed on arithmetic on their way into algebra. It required some setup to be usable, though. The point is a property sale from the 17th century, from George Hutcheson to Anthony Woodhouse, transferring “1/32 of 3/90 of 90/100 shares” of land in the province of West Jersey. There were a hundred shares in the province, so, the natural question to build is: how much land was transferred?

    The obvious question, to people who failed to pay attention to John T Cunningham’s This Is New Jersey in fourth grade, or who spent fourth grade not in New Jersey, or who didn’t encounter that one Isaac Asimov puzzle mystery (I won’t say which lest it spoil you), is: what’s West Jersey? That takes some historical context.

    (More …)

     
  • Joseph Nebus 12:20 am on Wednesday, 23 May, 2012 Permalink | Reply
    Tags: , , , , coefficients, House, , , New Jersey, ,   

    How Big Charlotte Was In 1975 


    [ I cannot and do not try to explain it, but yesterday was a busier-than-average day around these parts, with a surprising number of references coming from an Entertainment weekly article about the House series finale for some reason. In this context a “surprising” number is “any number other than zero” since I don’t know why anyone would go from there to here. I watched House, sometimes, sure, and liked it, but kind of drifted away when there was other stuff to do, you know? ]

    That’s enough time spent establishing the heck out of the idea of a polynomial. Let’s actually put one in place. My goal back when was estimating what the population of Charlotte, North Carolina, was around 1975. I had some old Census data from 1970 and 1980 giving its population on the first of April, the earlier year, as 840,347; and the first of April, 1980, as 971,391.

    (More …)

     
  • Joseph Nebus 12:53 am on Wednesday, 25 April, 2012 Permalink | Reply
    Tags: , , Delaware, , , NC, New Jersey, popcorn, , , South Amboy, south amboy new jersey   

    Life In North Carolina 


    [ I’m grateful to all for the help in reading my pages here. I’ve not quite reached 3,000 hits, but it’s within sight. If you do know of people who might be interested in either what I’m doing now — and it should be clearer after today’s post — or articles I’ve written in the past, please let them know, or let me know if I could be doing better at reaching interested audiences. ]

    I left off the list of places I’d lived the city of Charlotte, North Carolina. There’s justice in my doing so. We lived there only for a couple years, when I was extremely young. I have only a few memories of the place, most of them based on the popcorn machine they had in my preschool program. I don’t know what else I got out of that, but I certainly appreciated seeing popcorn pop. Also I had two brothers born then. But, mostly, I can’t say that Charlotte made much of an impression on me. I couldn’t identify any major features of it from memory, and challenged to point to it on a map I might point at Delaware instead, or wander off to find a soda. Plus, I last lived there somewhere around 1975. I can accept that the population of South Amboy, New Jersey, may not have changed very much since the mid-1970s, but not that Charlotte’s hasn’t.

    (More …)

     
    • Chiaroscuro 4:53 am on Wednesday, 25 April, 2012 Permalink | Reply

      I’m pretty sure what this simplest possible interpolation would be; and will even predict what the next interpolation would be; let me take my fun little stabs at such in the vague belief that my comments make your essays stronger. Or at least longer.

      The easiest interpolation, given just the current information, would be (840,347 + 971,391)/2. We’re taking 1975 as a midpoint between 1970 and 1980, which it is on a strictly linear scale, 5 each way. The answer to the 1975, in that fashion, would be 905,869. For something like 1973, you’d look at 30% of 840,347 and 70% of 971,391. Or, in another way, you’re moving up 10% of the difference between the two numbers given (131,044) each year.

      That assumes that the rate of population growth over ten years was a flat 13,104.4 people each year. That’s slightly unlikely; It’s more likely that the growth rate was closer to a constant percentage, say, 1.5% (A rough guess) each year. Now that’s a little more complex to calculate; how do you account for the increase on the increase on the increases?

      ..well. That part of my prediction I’m certainly not going to spoil.

      Like

  • Joseph Nebus 1:45 am on Tuesday, 24 April, 2012 Permalink | Reply
    Tags: Action Park, appalachian mountains, Benjamin Franklin, Brooklyn, Bruce Springsteen, , , James Madison, New Jersey, New York City, numerical methods, Philadelphia, ,   

    Dense Places I Have Lived 


    [ I don’t wish to be too shameless here, but I’m closing in on 3,000 visitors to my little blog here. Can we get there? Kindly pass on a reference to people you think might be interested; if I matched my most-popular-ever day I’d reach 3,000 tonight easily. ]

    I’ve lived almost my entire life in New Jersey, which has its effects on my world view; for example, it produces an extreme defensiveness about the state — really, has there been a fresh Jersey Joke since Benjamin Franklin’s quip about it being “a barrel tapped at both ends”, and they’re not even sure it wasn’t James Madison who said that instead, if anyone ever did? — and a feeling that one should refer to Bruce Springsteen as “Bruce”, as if we’d ever knowingly been in the same zip code simultaneously. Add to that not understanding what is wrong with other states that you’re forced to pump your own gas, and not being able to get a cackling laughter and a voice-over announcer wailing “Rrrrrrrrraceway Park!” out of the head, and you’ve got a first sketch of my personality. (I seem to have missed going to Action Park. My father insists he took me there; I grant he may have taken my siblings, but I don’t remember ever getting there, and the fact I have all my limbs suggests I never did go there.) But there are some other impressions that one gets from growing up in New Jersey.

    (More …)

     
    • BunnyHugger 12:56 am on Wednesday, 25 April, 2012 Permalink | Reply

      Lansing, MI: 3,175

      That compared with Jackson, NJ pretty well wins me the argument with someone you know that almost certainly inspired this post!

      Like

      • Joseph Nebus 12:22 am on Thursday, 26 April, 2012 Permalink | Reply

        It certainly does, and yes, Lansing makes Jackson look particularly deserted. Of course if we compare downtowns, we have to handicap things by how Jackson’s downtown is in some other municipality altogether, or else is the midway at Great Adventure.

        Like

    • Chiaroscuro 4:03 am on Wednesday, 25 April, 2012 Permalink | Reply

      That would put Lansing about 15% denser than Piscataway. Which.. have I ever been to Piscataway? I can;t recall.

      Like

      • Joseph Nebus 12:24 am on Thursday, 26 April, 2012 Permalink | Reply

        It’s hard to say. It would be at a natural point to jump off the Turnpike — exit 9, the Raritan Toll Plaza — for a break or something to eat or just to stretch. But then you’d have to pass through the Brunswicks and go across the Raritan again to get into Piscataway. On the other hand, there are a lot of restaurants, of the strip mall, chain, and grown-up varieties that way.

        Oh, here’s an easy way. Have you got off the Turnpike at the Raritan toll plaza and made it to a White Castle? The most convenient one to there is in Piscataway (although the next nearest is around the Menlo Park Mall/Woodbridge Center mall, around Edison and Woodbridge).

        Like

c
Compose new post
j
Next post/Next comment
k
Previous post/Previous comment
r
Reply
e
Edit
o
Show/Hide comments
t
Go to top
l
Go to login
h
Show/Hide help
shift + esc
Cancel
%d bloggers like this: