Learning Strategies

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Labels: books, Dorchester, food, life, linguistics, math, model railroads, movies, teaching and learning, technology, travel, Weston

One of my students asked me why I haven’t yet posted any photos of the model railroad I’m building. One answer is that it’s still in such an early stage that I don’t have much to show yet. Another answer is that I’m intimidated by videos like the stunning Route 6 HO Scale Model K-Car Trip around Philadelphia, which is so much like the urban, transit-oriented layout I am trying to accomplish (except for being Philadelphia rather than Boston) and yet so far from what I am really going to achieve.

But I’ll bite the bullet soon and will show some of my progress.

Labels: model railroads

Take a close look at the yellow bars in this bar chart:

Much to my surprise, it turns out that subway fares in Boston have remained nearly unchanged for 110 years when adjusted for inflation, especially when you ignore the short-lived drop to ten cents in 1950. This chart comes from a fascinating document entitled “Report on the Proposed 2007 MBTA Fare Restructuring and Fare Increase,” published by the MBTA in July of 2006.

Why am I so unusually interested in this geeky document? Perhaps it’s because I’m a math teacher — or maybe it’s because I’m building a model railroad based loosely on the T, though I think there’s a lurking variable there that explains both phenomena. In any case, the general public should also become aware of it, especially with all the recent complaints against the MBTA. Many, perhaps even most, of those complaints are certainly justified, but isn’t it interesting that the fare hasn’t actually risen significantly in real dollars in over a century? Using my trusty TI–83 Plus calculator, I computed a linear regression for the data, with years since 1900 as the input values and the fares in 2005 dollars as the output values, excluding the anomalous dip in 1950. The slope indeed turned out to be indistinguishable from zero — actually 0.0013 to two sig figs. Even when I included the 1950 fare it was still only barely higher, being 0.0017. The correlation coefficient wasn’t good, but it’s still quite compelling that the best-fit line should be nearly flat.

Labels: Dorchester, math, model railroads

Just got back from the Boston Trolley Meet (actually held in Somerville, not Boston). This event, sponsored by the Boston Chapter of the National Railway Historical Society, offered a combination of layouts, dealer tables, and field trips. The actual exhibit provided a good balance between “real” trolleys (mostly historical material on the prototype) and model trolleys (mostly layouts and rolling stock). Unfortunately the layouts focused almost entirely on the trolleys themselves, with very little in the way of scenery or structures, and the rolling stock was almost all very expensive, so I didn’t buy any. (I’m not in the market for a $300 trolley car.) It will still useful — and fun — to look through the various books, posters, maps, and DVDs, and to see how the various layouts presented working models of trolleys in tight spaces.

Labels: model railroads

I guess Kalmbach didn’t have 100 fingers:

Labels: math, model railroads

Actually, I never knew you, sad to say. For 15 years now I have been intending to meet George Sanborn and talk with him about the MBTA (since my model railroad layout is based loosely on the MBTA of 1969). But I kept putting it off, and now it’s too late. Adam Gaffin’s remembrance, titled “Remembering Boston's train man,” links to Dirty Water and to Commute-a-holic. Read the comments to Gaffin’s post, and the various links in the original post and within the comments. As SwirlyGrrl says in her title to her otherwise blank post, “He will ride forever ’neath the streets of Boston.” Why did I keep thinking that I could always talk with him next year?

P.S.: I have just been told about the Globe’s article on George Sanborn. Read that too.

Labels: life, model railroads

This morning I went to the Spring Open House of the South Shore Model Railroad Club in Hingham, MA. Despite the excessive number of young children present, it was an excellent layout, with a reasonable but small quantity of vendors as well. The layout was well worth seeing, especially the structures and scenery. I especially liked the urban scenes, including a semi-covered track entering a city. The nearby harbor was less than completely effective, but water is especially difficult to model convincingly. I’m certainly not going to try to become a member, as their requirements include attending 18 meetings within a period of nine months! So I suppose it fits into the category of “a nice place to visit, but I wouldn’t want to live there.” I do, however, plan to return for a longer visit for their next open house in the fall.

Labels: model railroads

OK, so why on earth should you care about a review of a model railroad show? More generally, most of my readers aren’t the least bit interested in model railroading, so why should they bother reading this post? The answer is that any performance — whether it be a play, a concert, a translation, or a model railroad — requires a passing grade on the creation of a willing suspension of disbelief, and this weekend’s exhibit by the Northeast NTRAK Modular Railroad Club at the National Heritage Museum in Lexington, MA, did poorly on the test.

It didn’t help that the adults at the show were outnumbered by the 4- and 5-year-olds. I suppose it’s nice to see that there are still young kids who are interested in model railroads — maybe there’s a future to the hobby after all — but it made it hard to concentrate. Actually, however, made it did help in the suspension-of-disbelief department, since the young kids tended to ooh and aah loudly about the trains and the bridges, not the quality of the representations, thus encouraging belief in the reality of the model. Otherwise the issue was the constraints imposed on modules that can be interchangeably connected mean that the total layout looked like what it was: a sequence of unrelated modules. There was no overall theme, no sense that this could be a real layout. Sure, a canyon or a truss bridge or an industrial area might look authentic, but it’s not part of an authentic whole. It all reminds me of the typical Algebra II course, which consists of several vaguely related modules instead of a unifying theme — in other words, instead of a course. A model railroad should reflect some consistent big ideas; it shouldn’t just be independent modules that happen to meet at each end.

Labels: model railroads

In my review of Transit Maps of the World a couple of days ago, I made the following observation:

I have to admit that it will appeal strongly only to readers who are fascinated both by cartography and by railroads, and mostly to those whose railroad interests are focused on urban transit. I am a member of that small band.

I’m delighted to learn that I was wrong about the narrowness of the audience. The author has written to me from across the Pond and has let me know that “it reached number 110 on the general Amazon Sales Ranking and as high as Number 1, 2 and 5 in categories like Mass Transit, Atlases and Travel books.” That’s wonderful!

Labels: books, model railroads

OK, this is just one example. It’s purely anecdotal evidence, and therefore it doesn’t prove anything. But it’s still indicative of a problem with adult attitudes toward math. A bit of background first: if you don’t have the good fortune to be a model railroad enthusiast, you will need to know that “HO Scale” (not gauge) is 1/87 and that “N Scale” is 1/160. Now here’s the quick anecdote:

A participant in the HO Railroading Yahoo newsgroup asks the following:

Is there any known formula for converting a N-Scale track layout to a HO track layout?

Where do I begin in explaining why this question bothers me so much? The most obvious reason is the writer’s inability to deal with fractions, even when he has a computer and therefore a calculator; he clearly can’t figure out what operation to perform on 1/87 and 1/160. Some of my ninth-graders in Weston couldn’t do that either, so I suppose it should neither surprise me nor bother me. But the main reason the query upsets me is the opening five words. “Is there any known formula?” Most formulas are the wrong way to go, as they tend to replace thinking with algorithms. Sometimes we do need formulas, but why look for one here? Surely an experienced model railroader knows that multiplying N-scale lengths by 160 gives you real-life scale (prototype, as we call it). And then dividing the real-life lengths by 87 gives you HO scale. Who needs a formula?

Labels: math, model railroads, Weston

This gorgeous book — I might even call it stunning — must have a rather limited audience. Although I’m tempted to add it to my list of favorite books (see my profile in this blog), I have to admit that it will appeal strongly only to readers who are fascinated both by cartography and by railroads, and mostly to those whose railroad interests are focused on urban transit. I am a member of that small band.

The full title of the book is Transit Maps of the World: The World’s First Collection of Every Urban Train Map on Earth. Wow! Author Mark Ovenden and editor Mike Ashworth have done an amazing job of compiling the comprehensive collection described in the subtitle. The frontispiece promises beautiful cartography within, and the book delivers on the promise. (But there is one small glitch. What the frontispiece shows is a stylized map that at first glance looks like the London Underground, but a second glance shows that the “stations” are really cities. These are all the cities represented by maps in the book, and they’re linked together by fanciful subway lines. The commentary says this:

This captivating diagrammatic view of the cities included in this book is in the style of Harry Beck’s classic London Underground diagram. It was conceived by the author and executed at LS London by Alan Foale, who is responsible for updating the London diagram. It is also available as a full-size wall poster from London’s Transport Museum shop or online.

But, alas, I searched through the London [no “’s”] Transport Museum site to no avail.)

Anyway, among the treats awaiting the specialized reader are beautiful contemporary maps from hundreds of cities, historical maps for many of them, great photographs of stations and transit vehicles, and crisp explanatory text. Among the most attractive maps are those of obvious cities (e.g. London, New York, Boston, San Francisco, Montreal), those of less obvious cities (e.g. Madrid, Budapest, Barcelona, Hamburg, Hong Kong, Osaka), and those of thoroughly unobvious cities (e.g. Bucharest, Kiev, Prague, Cairo, Stuttgart). The blurb from The Guardian points out that the explanatory text provides a lot of background on the history of mass transit and remarks that this book is “the ideal gift for the most challenging relative.” Well, I suppose...as long as your most challenging relative is an urban-transit-and-cartography enthusiast.

Unfortunately a few of the maps did not scan well and are decidedly fuzzy. If they were printed in a larger size they might have been easier to read, but then I suppose the fuzziness would have been more obvious.

Finally, as I observed in a much earlier post (two and a half years ago in fact), my interests in cartography and model railroading share something with my interests in certain parts of mathematics: representation. Although Transit Maps of the World doesn’t deal with model railroading per se, the two topics are deeply intertwingled for those of us who model urban transit. And transit maps are especially interesting for math teachers and mathematicians, not because they are scale model of reality (similar, as we say in geometry) but precisely because they are not scale models. Riders almost always want a map to be topographically correct, but they don’t want it to be made to scale. Indeed a scale map of an urban transit system would be nearly impossible to use: either it would be much too tightly crammed together in the downtown area, or the entire map would need to be much too big. Applied geometry isn’t as simple as they taught you back in ninth grade (or tenth grade, if you’re above a certain age).

Labels: books, model railroads

How tall is a tree? What color is a rock? These may sound like silly questions, but they have thrown themselves in my face as I build my model railroad. In the process, I’ve discovered a couple of facts that confirm what Chris Fehl taught me in a drawing workshop that I described ten months ago: when I think I can’t draw, the truth is that I’m not seeing. Here are the facts:

1. Trees are tall. Yeah, I know, that’s obvious. But until I got out and really looked at trees that are next to houses, I never truly realized that most of them tower over the houses. Trees on model railroads don’t look right because they aren’t tall enough. (On the other hand, the viewer’s eye is at a different level when standing on a street compared to looking at a model railroad.)


2. Rocks are some undescribable combo of gray and brown. I can’t yet figure out how to make them look realistic, but it quickly became clear that I needed to look closely at actual rocks.

My goal is to make rocks that look like this model. But before I build more terrain and scenery, I need to see the real world. The modeled must precede the model.

Labels: model railroads, teaching and learning

Is model railroading an art, or is it a craft? Or is it just a hobby, as most people believe? Surely some would admit that it’s not only a hobby but also a craft, and perhaps there’s someone somewhere who thinks it’s an art.

If it’s an art, you should see it in museums, right? Well, I almost saw it in a museum today — and if it weren’t for the storm, I would have. But there was no way I was going to drive to Lexington at midday today. Our excellent National Heritage Museum was sponsoring an unfortunately timed model railroad exhibit sponsored by the HUB Division of the National Model Railroad Association. But I missed it.

Of course I could console myself by assuming that it probably wasn’t very good anyway. There’s at least some evidence to support this sour-grapes theory: as I reported last year, I was disappointed by their 2006 show in Marlborough. But my complaint about that one was that it was too commercial, and it seemed likely that one at the National Heritage Museum wouldn’t be. Oh, well.

But I’ve been to three other model railroad shows this year that were (at least partially) successful from my point of view. One showed model railroading as a hobby, one as a craft, and one as an art. Let’s start with the hobby first. Greenberg’s Train and Toy Show is a 30-year-old tradition that ropes in the whole family by not limiting themselves to model railroads (as you can tell from the name). This was my first visit — on November 18 in Wilmington, MA — and I was pleasantly surprised. Although there was a lot of junk, and too many tables were selling the same merchandise, there were also several high-quality layouts and a few choice vendors. It was definitely worth going to, as long as I was willing to invest a few hours to sort the wheat from the chaff.

Next comes the craft. The New England Prototype Modelers Meet — on June 3 in Collinsville, CT — was very impressive, but unfortunately over my head. No problem with chaff here! Just the opposite: I was clearly an amateur among professionals. There was amazing attention to detail, as you can see from the photo gallery. I can hold out this level of craft as an ideal, but I’ll never come close to it.

Finally, model railroading as art. The DeCordova Museum in Lincoln is hosting an elaborate exhibit called Trainscape, in which 12 artists created original works of art, all interacting with and linked by a fully functioning model railroad that passes through them:

Trainscape addresses a vital issue in the art of the early twenty-first century. Currently, many artists are actively engaged in the creation of imaginary worlds, not only with sculpture and installations, but also with painting, drawing, and photography. This impulse reflects philosophical ruminations about alternate realities, escape from the current world situation, and the use of place as an emotionally expressive device. A major theme within this exploration of parallel universes is a wide expansion of the idea of landscape sculpture (as opposed to the far more familiar “landscape painting”). Trainscape presents many alternative worlds, united only by the physical — and often conceptual — presence of the trains that travel throughout the exhibition.

The use of a miniature railroad enables DeCordova Museum to effectively present twelve separate works of contemporary installation art in a limited space, and to allow these works to be considered both separately and in juxtaposition. The miniature is also the perceptual cousin to the colossal. Tiny objects and images demand close examination, so that they fill one’s optical field in much the same way as very large visual phenomena. This close looking at small things allows for deep mental immersion as well. Trainscape thus provides enveloping journeys to cities, mountains, deserts, technological landscapes, and places of pure imagination.

Certainly their words, not mine, and surely not the way most of us think of model railroading, but it dramatically emphasizes the idea of miniature worlds and alternative representations. It’s there only through January 18, so be sure to go soon!

Labels: model railroads

According to the New York Times and NPR, wealthy online gamers are outsourcing the playing of games to Chinese workers! At first glance this sounds ridiculous: surely people who play online games enjoy playing them, so it makes no sense to outsource that activity. It still sounds somewhat ridiculous, but it turns out that there’s a method to this madness. From the NYT article:

...affluent online gamers who lack the time and patience to work their way up to the higher levels of gamedom are willing to pay the young Chinese here to play the early rounds for them.

“For 12 hours a day, 7 days a week, my colleagues and I are killing monsters,” said a 23-year-old gamer who works here in this makeshift factory and goes by the online code name Wandering. “I make about $250 a month, which is pretty good compared with the other jobs I’ve had. And I can play games all day.”

...

As they grind through the games, they accumulate virtual currency that is valuable to game players around the world. The games allow players to trade currency to other players, who can then use it to buy better armor, amulets, magic spells and other accoutrements to climb to higher levels or create more powerful characters.

I guess if you can hire someone to build your model railroad layout for you, you can also hire someone to play games for you. That’s logical, isn’t it?

Labels: life, model railroads, technology

What is model railroading? Sure, it’s a hobby, but all sorts of disparate activities are admitted into the big hobby tent; some are sports, some are arts, some are crafts. All of them are leisure activities that one does for fun rather than for profit. So cooking, for example, is a hobby for some, a job for others, a profession for a few. Model railroading, as I said, is a hobby — very, very few make a living from it! — and it encompasses a remarkable number of crafts and technologies.

Some model railroaders are really toy train enthusiasts; they “play with trains” as adults, having enough of a layout to be able to enjoy operating their not-particularly-realistic trains without worrying about scale realism or scenery. At the other extreme are the true railroad modelers, who can be fanatical about scale accuracy, faithfulness to the prototype, and detailed scenery and structures. There’s a whole huge range in between. But almost everybody finds himself (or occasionally herself) spending time on a wide variety of crafts, some of which may be more enjoyable than others, and all of which can turn out to have the side benefit of being educational and absorbing. There’s construction of benchwork, buildings, roads, terrain, and scenery; there’s the sometimes complex task of wiring an entire layout; there’s the artistry involved in creating backdrops and scenic details, as well as the routine painting of almost everything; there’s laying and ballasting track; there’s controlling the trains, with or without the aid of a computer. And there’s a large side of the hobby that I have very little to do with: realistic operation of a railroad, completing with timetables, picking up cargo, switching, and delivering the cargo. Quite an amazing variety of crafts for one hobby!

“Model railroading today is a great exercise in systems integration,” says joe.daddyo in the Layout Construction Yahoo newsgroup.

Labels: model railroads

In HO scale model railroading, tracks always used to have rails that are 0.100 inches high, even though that’s not strictly to scale. Many model railroaders — mostly those who interpret the word “model” strictly — favor the newer versions, called Code 83 and Code 70 because they’re 0.083" and 0.070" respectively, which are more prototypically accurate than 0.0100". On several of the model railroading newsgroups a fierce discussion breaks out periodically on this subject, usually about Code 100 vs. Code 83. Here are some of the remarks:

I can think of almost no good reason whatsoever to continue to buy, or plan to use code 100 in HO, save for compelling economic reasons, or for trackage that is not modeled and is out of view.

The way I look at it is that code 100 is more then 20% larger then code 83. If I had a boxcar or building that was 20% larger then it should be, it would be out of scale and not look right on my layout. I'm not a perfectionist when it comes to these things, but buying code 83 was a no-brainer for me.

Sure [code 100 track] is more durable, if you like to run your trains on 'I' beams...

Code 100 looks really weird after working with code 83/70/55. You can spot it a mile away in photo of models. No matter the cost or minor (theoretical) structural benefits, don't use code 100. Just my humble opinion.

A common reaction among civilians is to wonder why these enthusiasts care so much, but that’s not really a fair question: after all, I don’t ask why Red Sox and Patriots fans care so much, even though I don’t understand it. My question is to ask whether it’s this difference of 0.017" (about one sixtieth of an inch!) is really so visible to the naked eye. I have trouble believing that it is. On the other hand, code 100 is 20% larger than code 83, so maybe the difference can actually be perceived.

Labels: math, model railroads

Over the weekend I squeezed in two more model railroad shows. The Marlborough one was OK, but disappointing. The Roslindale one was definitely worth while. Both will repeat in future years, so if you’re interested in model railroads I recommend the latter but not the former.

In Marlborough I attended the National Model Railroad Association HUB Division, New England Model Train Expo, which had a couple of good layouts and a lot of commercial vendors. Mostly it was the same set of products over and over again, from table to table. There was almost nothing that I hadn’t seen elsewhere. There were too many commercial vendors and not enough artistry. Most disappointing was the lack of realistic detail in the layouts: while I don’t expect strict adherence to prototype (a.k.a. “rivet-counting”) in a show like this, I do think that scenery and structures should at least show a little attention to realism. We need the willing suspension of disbelief, as they say in the English classroom. And did I mention that there were too many commercial vendors?

Roslindale was a different story altogether. The Bay State Model Railroad Museum, a merger of the Massachusetts Model Railroad Society and the Bay State Society of Model Engineers, holds an open house several times a year. Packing four layouts into a small space, they are almost the opposite of what I saw in Marlborough, showing attention to detail at every level. The terrain, the scratchbuilt urban structures, the trolleys, and the weathering of all structures and railroad cars were particularly impressive. But so was everything else, really. Check out the links at the right edge of their webpage under Scale Layouts. And go visit them at the next open house, on March 3 and 4.

Labels: model railroads

Barbara and I spent an enjoyable couple of hours yesterday visiting the MIT Museum and the Tech Model Railroad Club (TMRC). Go see both of them!

MIT’s small museum is currently showing five exhibitions:

• a fascinating collection of holograms — always amazing to look at, and claiming to be the world’s largest such collection


• an informative multimedia show about robotics and AI, complete with actual models, videos, and info about the real people behind the development of the robots (no, it’s not science fiction)


• a well-done exhibition about Harold “Doc” Edgerton, the renowned inventor of the strobe, including a large blow-up of his famous milk drop photo — worth seeing if it isn’t old hat to you


• a captivating and truly amusing set of kinetic sculptures by Arthur Ganson (are they art? are they engineering?)


• a wonderful history of MIT called Mind and Hand, of interest not only to MIT folk but also to anyone whose life includes education or technology

Actually, there were six exhibitions. Somehow we missed Tech’ing it to the Next Level. Obviously I’ll have to go back to see it if it’s still there (I don’t know how we could have failed to notice it), since it’s all about educational innovation using technology.

Now, onto the model railroad layout. TMRC is well-known in certain circles as being the originator of the term hacker —not in the current sense to which the media have perverted the term (for which cracker is the approved term), but in the sense of “a person who enjoys exploring the details of programmable systems and how to stretch their capabilities, one who programs enthusiastically (even obsessively) or who enjoys programming rather than just theorizing about programming, one who enjoys the intellectual challenge of creatively overcoming or circumventing limitations.” It’s no coincidence that these meanings arose out of TMRC, whose exhibit suggests “MIT” as much as it suggests “model railroading.” In contrast to the majority of the highly detailed layouts that one is likely to see elsewhere, this one emphasizes the technology more than the illusion of reality. Exposed wiring is a virtue, not a defect. Seeing the scaffolding is fine. Roads don’t need drains, mailboxes, or fire hydrants. But there are many cool high-rise buildings, including one that lets the viewer can play Tetris on it (the controls turn the lights in the building’s rooms off and on appropriately, producing a Tetris game through the windows). There are excellent demonstrations of how to handle tracks and roads on multiple elevations. And don’t forget the ads for the breakfast food for which MIT has been famous for decades: Apple Gunkies, “rhomboidal pellets of true fruit goodness.”

Labels: life, model railroads

Two upcoming model railroad shows:

1. Tech Model Railroad Club, Saturday, November 18, at the MIT Museum, 265
   Massachusetts Avenue, Cambridge MA, Room N52–118, 2–5 and 7–10. Free!


2. National Model Railroad Association HUB Division, New England Model Train Expo, Saturday-Sunday, December 2–3, 10–4 at Best Western Royal Plaza Trade Center, Marlborough MA. Not free (but not expensive, especially for kids).

I will be at both, and I hope to see some people I know. Brief reports will follow.

Labels: model railroads

It takes a certain kind of person to be interested in the sociology of model railroading...

Labels: model railroads