The Universe of Discourse

Sun, 02 Apr 2006

Here are some notes on posts from the last month that I couldn't find better places for.

• In my close attention to the most embarrassing moments of the Indiana Pacemates, I completely missed the fact that Pacemate Nikki, the only one who admitted to farting in public, also reports that she was born with twelve fingers.

• Regarding the manufacture of spherical objects, I omitted several kinds of spherical objects that are not manufactured in any of the ways I discussed.

• One is the gumball. It's turned out to be surprisingly difficult to get definitive information about how gumballs are manufactured. My present understanding is that the gum is first extruded in a sort of hollow pipe shape, and then clipped off into balls with a pinching device something like the Civil-War-era bullet mold pictured at right. The gumballs are then sprayed with a hard, shiny coating, which tends to even out any irregularities.

[ Addendum 20070307: the bullet mold at right is probably not used in the way I said. See this addendum for more details. ]

• Glass marbles are made with several processes. One of the most interesting involves a device invented by Martin Frederick Christensen. (US Patent #802,495, "Machine For Making Spherical Bodies Or Balls".) The device has two wheels, each with a deep groove around the rim. The grooves have a semicircular cross-section. The wheels rotate in opposite directions on parallel axes, and are aligned so that the space between the two grooves is exactly circular.

The marble is initially a slug of hot glass cut from the end of a long rod. The slug sits in the two grooves and is rolled into a spherical shape by the rotating wheels. For more details, see the Akron Marbles web site.

Fiberglas is spun from a big vat of melted glass; to promote melting, the glass starts out in the form of marbles. ("Marbles" appears to be the correct jargon term.) I have not been able to find out how they make the marbles to begin with. I found patents for the manufacture of Fiberglas from the marbles, but nothing about how the marbles themselves are made. Presumably they are not made with an apparatus as sophisticated as Christensen's, since it is not important that the marbles be exactly spherical. Wikipedia hints at "rollers".

• The thingies pictured to the right are another kind of nearly-spherical object I forgot about when I wrote the original article. They are pellets of taconite ore. Back in the 1950s, the supply of high-quality iron ore started to run out. Taconite contains about 30% iron, but the metal is in the form of tiny particles dispersed throughout very hard inert rock. To extract the iron, you first crush the taconite to powder, and then magnetically separate the iron dust from the rock dust.

But now you have a problem. Iron dust is tremendously inconvenient to handle. The slightest breeze spreads it all over the place. It sticks to things, it blows away. It can't be dumped into the smelting furnace, because it will blow right back out. And iron-refining processes were not equipped for pure iron anyway; they were developed for high-grade ore, which contains about 65% iron.

The solution is to take the iron powder and mix it with some water, then roll it in a drum with wet clay. The iron powder and clay accumulate into pellets about a half-inch in diameter, and the pellets are dried. Pellets are easy to transport and to store. You can dump them into an open rail car, and most of them will still be in the rail car when it arrives at the refinery. (Some of them fall out. If you visit freight rail tracks, you'll find the pellets. I first learned about taconite because I found the pellets on the ground underneath the Conrail freight tracks at 32nd and Chestnut Streets in Philadelphia. Then I wondered for years what they were until one day I happened to run across a picture of them in a book I was reading.)

When the pellets arrive at the smelter, you can dump them in. The pellets have around 65% iron content, which is just what the smelter was designed for.

• Regarding my assertion that there is no way to include a menu of recent posts in the "head" part of the Blosxom output, I said:

With stock Blosxom, however, this is impossible. The first problem you encounter is that there is no stories_done callback.

Todd Larason pointed out that this is mistaken, because (as I mentioned in the article) the foot template is called once, just after all the stories are processed, and that is just what I was asking for.

My first reaction was "Duh."

My second reaction was to protest that it had never occurred to me to use foot, because that is not what it is for. It is for assembling the footer!

There are two things wrong with this protest. First, it isn't a true statement of history. It never occurred to me to use foot, true, but not for the reason I wanted to claim. The real reason is that I thought of a different solution first, implemented it, and stopped thinking about it. If anything, this is a credit to Blosxom, because it shows that some problems in Blosxom can be solved in multiple ways. This speaks well to the simplicity and openness of Blosxom's architecture.

The other thing wrong with this protest is that it assumes that that is not what foot is for. For all I know, when Blosxom's author was writing Blosxom, he considered adding a stories_done callback, and, after a moment of reflection, concluded that if someone ever wanted that, they could just use foot instead. This would be entirely consistent with the rest of Blosxom's design.

M. Larason also pointed out that even though the head template (where I wanted the menu to go) is filled out and appended to the output before the article titles are gathered, it is not too late to change it. Any plugin can get last licks on the output by modifying the global $blosxom::output variable at the last minute. So (for example) I could have put PUT THE MENU HERE into the head template, and then had my plugin do: $blosxom::output =~ s/PUT THE MENU HERE/\$completed_menu/g;

to get the menu into the output, without hacking on the base code.

Thank you, M. Larason.

• My article on the 20 most important tools attracted a lot of attention.

• I briefly considered and rejected the spinning wheel, on the theory that people have spun plenty of thread with nothing but their bare fingers and a stick to wind it around.

Brad Murray and I had a long conversation about this, in which he described his experience using and watching others use several kinds of spinning tools, including the spinning wheel, charkha (an Indian spining wheel), drop spindle, and bare fingers, and said "I can't imagine making a whole garment with my output sans tools." It eventually dawned on me that I did not know what a drop spindle was.

A drop spindle is a device for making yarn or thread. The basic process of making yarn or thread is this: you take some kind of natural fiber, such as wool, cotton, or flax fiber, which you have combed out so that the individual fibers are more or less going the same direction. Then you twist some of the fibers into a thread. So you have this big tangled mass of fiber with a twisted thread sticking out of it. You tug on the thread, pulling it out gently, while still twisting, and more fibers start to come away from the mass and get twisted into the thread. You keep tugging and twisting and eventually all the fiber is twisted into a thread. "Spinning" is this tugging-twisting process that turns the mass of combed fibers into yarn.

You can do this entirely by hand, but it's slow. The drop spindle makes it a lot faster. A drop spindle is a stick with a hook stuck into one end and a flywheel (the "whorl") near the other end. You hang the spindle by the hook from the unspun fiber and spin it.

As the spindle revolves, the hook twists the wool into a thread. The spindle is hanging unsupported from the fiber mass, so gravity tends to tug more fibers out of the mass, and you help this along with your fingers. The spindle continues to revolve at a more-or-less constant rate because of the flywheel, producing a thread of more-or-less constant twist. If you feed the growing thread uniformly, you get a thread of uniform thickness.

When you have enough thread (or when the spindle gets too close to the floor) you unhook the thread temporarily, wind the spun thread onto the shaft of the spindle, rehook it, and continue spinning.

A spinning wheel is an elaboration of this basic device. The flywheel is separate from the spindle itself, and drives it via a belt arrangement. (The big wheel you probably picture in your mind when you think of a spinning wheel is the flywheel.) The flywheel keeps the spindle revolving at a uniform rate. The spinning wheel also has a widget to keep the tension constant in the yarn. With the wheel, you can spin a more uniform thread than with a drop spindle and you can spin it faster.

I tried hard to write a coherent explanation of spinning, and although spinning is very simple it's awfully hard to describe for some reason. I read several descriptions on the web that all left me scratching my head; what finally cleared it up for me was the videos of drop spinning at the superb The Joy of Handspinning web site. If my description left you scratching your head, check out the videos; the "spinning" video will make it perfectly clear.

The drop spindle now seems to me like a good contender for one of the twenty most-important tools. My omission of it wasn't an oversight, but just plain old ignorance. I thought that the spinning wheel was an incremental improvement on simpler tools, but I misunderstood what the simpler tools were.

The charkha, by the way, is an Indian configuration of the spinning wheel; "charkha" is just Hindi for "wheel". There are several varieties of the charkha, one of which is the box charkha, a horizontal spinning wheel in a box. The picture to the right depicts Gandhi with a box charkha.

• Doug Orleans asked whether I had considered the key. I hadn't, but I think it's exempt from consideration for the same kinds of reasons as those I cited for the remote control: any particular key serves not a general door-opening function but a specific one. Not that keys aren't important, but rather, they seem to be outside the scope of this particular discussion.

• Mike Krell asked why I would list the radio on my third-tier list and omit the computer. Obviously, the question is not one of usefulness or of importance, but of whether the "computer" is a "tool" in the original sense of the list, or whether it is disqualified by reason of being too general, too abstract, too complex, or something like that. I made several arguments, most of which I think he refuted.

My initial answer was that computers are disqualified for the same reason that remote controls are: people do carry calculators, cell phones, personal organizers, handheld GPS devices, and (if they work for FedEx) package tracking gizmos. All of these are tools that incorporate computers, but they don't really seem to be merely different forms of the same thing. Each one is a tool, but "computer" is not, similar to the way that the microscope and the telescope are different tools, and not merely variations of "the lens".

Perhaps so, but then I had a fit of insanity and asserted that people do not walk around toting general-purpose computers in case they happen upon some data that needs processing. M. Krell very gently pointed out that yes, they do exactly that: "I see them every time I fly on an airplane, breaking them out to process some data for work (or play) as soon as the flight attendant says it's OK." Whoops. Quite so.

M. Krell suggested that by restricting the definition of "tool" to devices that perform a single specific function or a few such functions, I have circumscribed the definition of "tool" in an arbitrary way that "does not accurately reflect the realities of our current Information Age". Okay.

• Jon Evans said "Everyone always forgets the hoe." I did indeed forget the hoe. Not quite a knife, not quite a shovel...

• Regarding the start of the year prior to 1751, when it was moved from 25 March to 1 January. You may recall that I had a series of articles (1 2 3 4) in which I was concerned that Benjamin Franklin might be only 299 years old, not 300, because of confusion about just what year was meant in discussions of the date "6 January 1706". (The legal year 1705 ran from 25 March 1705 through 24 March 1706.) This ambiguity was confusing at the time as well. It makes little difference to my life whether Franklin is 300 years old or only 299, but if you were a person living in 1706, you might like to be sure, when someone said they would pay you fifty shillings on 6 January 1706, when the payment would be.

It seems that baroque authors had a convention to disambiguate such dates. Here's a quote from William Derham's 1726 introduction to Robert Hooke's notes on the invention of the barometer:

To this I W.D. shall add another Remark I find in the minutes of the Royal Society, February 20. !!167^8_9!!, viz.
And similarly, from Richard Waller's summary of The Life of Dr. Robert Hooke:

…they prosecuted their former Inquiries, their first meeting at Arundel house being on the ninth of Jan. !!166^6_7!!.
• * In an earlier post, I referred to "Ramanujan's approximation to π":

$$\cfrac{1}{1+ \cfrac{e^{-2\pi}}{1 + \cfrac{e^{-4\pi}}{1 + \cdots}}} = \left( \sqrt{\frac{5+\sqrt5}2} - \frac{\sqrt5-1}2 \right) e^{2\pi/5}$$ But this isn't the formula I was thinking of; I showed the wrong formula! It's obviously not an approximation to π. The approximation formula I was thinking of is no less astonishing:

$${1\over\pi} = {\sqrt8\over9801} \sum_{i=0}^\infty { (4i)! (1103 + 26390i) \over (i!)^4 (396)^{4i} }$$

• Finally, in my article on the 20 most important tools, I said that I didn't think I knew anyone who had used a gas chromatograph; Geoffrey Young pointed out that he had used one.