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07/31/09 -- Vol. 28, No. 5, Whole Number 1556
Table of Contents
Acknowledgement (comments by Mark R. Leeper):
This week's MT VOID is brought to you by the Pre-Owned-Humvee Owners Exchange.Buy a used Humvee today. Humvee: because you never know. [-mrl]
Make Love, Not War (comments by Mark R. Leeper):
Americans have this bugaboo about sex. We do not mind violence in films, but we are really uptight about sex. I am as bad as anyone I guess. We are watching this program "Jurassic Fight Club" that is about paleontology and longs extended sequences of dinosaurs fighting. I admit it. I enjoy it more than the European equivalent which I assume would be "Jurassic Love Nests" or "The Jurassic Dating Game". [-mrl]
Birds Losing Dinosaur Status (comments by Mark R. Leeper):
For years I have been tickling children's imaginations by telling them that the dinosaurs did not really die out. There are still dinosaurs that walk the earth. Then while they are imagining scenes out of THE LOST WORLD with dinosaurs fighting in some remote place I tell them that birds are dinosaurs. If it is around Thanksgiving I might throw in first that they are going to be eating dinosaur soon. The connection of dinosaurs and birds are one of the fun facts of science. And it is sort of easy to picture an ostrich and say that this looks a lot like an allosaurus. In fact, nature actually reinvented something that behaved a lot like the tyrannosaurus but was actually a much later bird. They had the tongue-twisting name of phorusrhacid. I wrote about them in 2007:
See http://www.fanac.org/fanzines/MT_Void/MT_Void-2612.html#4
The last time I was at the American Museum of Natural History (sadly quite a while ago) when I saw their (then) new exhibit on cladistics (a fancy word for putting all species in an evolutionary tree) they openly declared that birds really are dinosaurs whether we call them that or not. It has become just one of the accepted facts that birds are the surviving remnants of dinosaurs. It is so accepted that I no longer get such a good reaction from kids, most of whom already know that birds are dinosaurs. Now if I want to tell them something they do not now know I have to go to the other side of the argument and say birds really are not dinosaurs after all.
It would be easy to say that dinosaurs and birds are close relatives and that they share similar behavior. Sadly there seems to be new evidence that birds are not really dinosaurs, in spite of a lot of anatomical similarities. The evidence now suggests that birds and dinosaurs really are probably descended from a common ancestor that predated dinosaurs.
The insight arises over bird lungs. Flying is hard work and birds need a lot of oxygen for the strength to accomplish the feat. Breathing as hard as a bird does is very hard on the lungs. One bird will use as much oxygen as twenty cold-blooded lizards. If their lungs collapsed in flight, the animal would be less likely to be classified as a "bird" per se and more likely as simply a "falling object." It would be bad for the bird. Luckily that does not happen. The lung gets support from the thighbone and the thighbone does not move in a bird the way it does in other animals including dinosaurs. In fact, birds are the only class of land animal with fixed thighbones. It was thought that birds were descended from theropods like the Allosaurus and the Tyrannosaurus, but they have movable thigh bones. Perhaps even more cogent is that fact that birds seem to have predated the type of dinosaur they were supposedly descended from.
This has all been announced by zoologists at Oregon State University: http://www.world-science.net/othernews/090610_dinosaur.htm
It is suggested that both birds and dinosaurs are both descended from thecodonts. They are lizards that looked vaguely dinosaurian. But they were not true dinosaurs.
I have to commiserate with birds. Suppose you are a rooster at a cock tail-party. You happen to mention nonchalantly in passing that your line of descent goes back to the DINOSAURS. Well, the other birds look up. That gets a little respect. Other roosters get out of your way. (Of course if you are descended from a dinosaur the other roosters are also. But they don't realize that. Chickens are not very smart birds.) But it is impressive to say you are a dinosaur. To say you are descended from thecodonts does not have nearly the same cachet. [-mrl]
Units in Physics (letter of comment by Warren Montgomery):
In response to Mark's comments on units in physics in the 07/24/09 issue of the MT VOID, Warren Montgomery writes:
The discussion on units reminded me of my graduate student days. Six of us sharing two offices with a small "terminal room" (remember those?) in between would often meet in the terminal room on a dull afternoon and discuss stuff like that (as well as everyone's latest sci-fi readings). One day one of my office mates set out to analyze the significance of "miles/gallon", and discovered it was in the same units as inverse acres. He thought that was an interesting coincidence, since with the right constant multiplier you could relate the number of acres required to grow the bio-fuel crop needed to propel a vehicle a fixed distance to its mileage. (We were also very fond of discussing the implications of curved space-time and whether it could be exploited to speed up the process of completing our dissertations. :-) [-wm]
Perpetual Motion Machine? (letter of comment by Robert Stampfli):
In response to Mark's comments on units in physics in the 07/24/09 issue of the MT VOID, Rob Stampfli writes:
Yes, Mark proves that energy has the right units to fit Einstein's famous formula, but that's the trivial part. The "and this speed turns out to be the speed of light" is the part where the and-then- some-magic-occurs gets translated into the-genius-of-Einstein- happens.
I recently was contemplating a thought experiment of my own that I stewed about some weeks ago, and which I'll throw out for general discussion:
Suppose you have a car. If you accelerate the car from 0 to 30 MPH, you use a certain amount of fuel. Neglecting frictional losses, if you accelerate that same car from 0 to 60 MPH, you'll use four times the fuel--it takes four times the energy to do this, right? (And, you'll similarly get four times the heat out of the brakes if you make the car stop from 60 MPH than you will if you make a stop from 30 MPH.)
Now, suppose you have a rocket sled that runs on a rail besides that car. If you fire the rocket for a certain period of time, you'll accelerate the sled from 0 to 30 MPH. But, if you fire the rocket twice as long, the sled will accelerate to 60 MPH (again, neglecting frictional losses). Same mass. F=ma. Right? And, thus, you'll achieve the same result as the car, using only two times the energy, not four. (In the first case, the energy consumption varies with the square of the speed, whereas in the second case it varies linearly with the speed.)
So, it appears we have a paradox: Where is the discrepancy? Or, have I just invented a perpetual motion machine?
Inquiring minds want to know! [-rs]
Mark responds:
I have not analyzed the whole thing, but I think at least one part is wrong. Assuming perfect conditions it should take twice as much fuel to take a car 0 to 60 MPH as from 0 to 30 MPH, not four times as much. Consider a rocket in space. It is standing still. It takes F fuel to take it from 0 to 30. The rocket turns off. It is now in a new inertial frame of reference. Compared to the first frame of reference it is traveling at 30 MPH, but compared to its current self it is traveling at 0 MPH. It now fires the rocket again burning F fuel. When the rocket turns off the rocket is in a new inertial frame of reference. From the previous frame of reference it is traveling at 30 MPH. From the initial frame of reference it is traveling at 60 MPH. But it has expended 2F fuel. [-mrl]
And Rob replies:
I'm fairly sure the car obeys a 4X consumption rule, as the formula for its kinetic energy would be "ke = (1/2) * m * v^2" and thus its KE at 60 MPH would be 4x that at 30. You can also observe this from considering how the car brakes: It takes 4 times as long to stop from 60 MPH as 30, presuming constant brake pressure. Or looking at it another way: the rotors would sweep out 4x the linear distance over the brake pads, and therefore the stop would dump 4x the heat into them, right?
Of course, KE doesn't make any sense without the presence of another object, or a frame of reference. With the car, this is obviously the earth. With the rocket-on-rails, I'd think you could claim a similar frame of reference.
I have delved into this a bit more deeply than I indicated in the post, but don't claim to understand it completely yet. If you want to think about it some more, stop reading here. But, if you'd like to hear the rest of my story, feel free to read on:
I think part of the solution lies in the fact that the rocket engine is doing more than just accelerating the rocket. It is also putting an equal amount of energy (from the perspective of someone on board the rocket) into its exhaust gases. When I set up the problem, I never said that the energy expended by the rocket engine was the same as the car engine. Indeed, it is empirically much more, as the rocket is quite inefficient at slow speeds. As the rocket accelerates, at least from our frame of reference on the ground, more energy winds up being fed into the rocket, and less into its exhaust gases. See http://en.wikipedia.org/wiki/Kinetic_energy and http://en.wikipedia.org/wiki/Oberth_effect.
However, this begs the question: at some point, the v^2 term, which is essentially unlimited, has to win out -- at some point the delta-KE imparted to the rocket has to become greater than energy being produced by the rocket engine, which is limited, right? And that's impossible!
Except! Except that the rocket is losing mass as it accelerates, so the delta-KE is always somewhat less than a strictly v^2 calculation, because of the declining m term. My working theory is that, for a given rocket engine, you'll always run out of mass before you can achieve a speed whereby the delta-KE imparted to the rocket exceeds the energy being produced by the rocket engine.
But, jeez, how to prove that mathematically!
Anyway, thanks for listening. [-rs]
General Motors (letter of comment by Victoria Fineberg):
In response to Mark's comments on General Motors in the 07/24/09 issue of the MT VOID, Victoria Fineberg writes, "To extend Mark's pun, GM did not shift gears, because it was asleep at the wheel and failed to kick the tires." [-vf]
Fuel Economy Versus Emissions (letter of comment by Pete Brady):
In response to Mark's comments on units in physics in the 07/24/09 issue of the MT VOID, Pete Brady writes, "You talked about miles per gallon in the context of measuring a car's performance with many variables. Here is a simpler test, one that applies directly to me and my 2001 Buick LeSabre. The Buick, with 90,000 miles on it, still gets 32 miles per gallon in highway driving. So, I guess I'm being a pretty good citizen driving it and saving burning up Mideast fuel. The problem is, the engine in the car is no longer manufactured because it would not meet current emission standards. It's okay for me to have it in that car, but I can't buy a new car with that engine in it. A new Buick, which costs a bundle, has a better engine for emissions, but gets only 25 miles per gallon. Let's assume I didn't have to worry about the cost of buying a new car. My question is, should I continue to drive the fuel-efficient car with poor emissions, or replace it with a guzzler with good emissions?" [-ptb]
Mark replies, "Well, the problem may be just that Buick is no longer making a car appropriate for our times. I cannot blame you for loyalty to one car brand. I have always bought Toyota Corollas. Certainly in Detroit it had the reputation for not being a very good car and Toyota drivers kept the secret that it was an extremely well-designed car. I get 25 to 30 miles per gallon in the city and 42 miles per gallon on the highway with good emissions." [-mrl]
This Week's Reading (book comments by Evelyn C. Leeper):
The Connectivity of the Library of Babel (Part 1)
"El universo (que otros llaman la Biblioteca) se compone de un número indefinido, y tal vez infinito, de galerías hexagonales, con vastos pozos de ventilación en el medio, cercados por barandas bajísimas. Desde cualquier hexágono se ven los pisos inferiores y superiores: interminablemente. La distribución de las galerías es invariable. Veinte anaqueles, a cinco largos anaqueles por lado, cubren todos los lados menos dos; su altura, que es la de los pisos, excede apenas la de un bibliotecario normal. Una de las caras libres da a un angosto zagu n, que desemboca en otra galería, idéntica a la primera y a todas. A izquierda y a derecha del zaguan hay dos gabinetes minúsculos. Uno permite dormir de pie; otro, satisfacer las necesidades finales. Por ahí pasa la escalera espiral, que se abisma y se eleva hacia lo remoto. ... 'La Biblioteca es una esfera cuyo centro cabal es cualquier hexágono, cuya circunferencia es inaccesible.'"
Freely translated (by me):
"The universe (that others call the Library) is composed of an indefinite, and perhaps infinite, number of hexagonal galleries, with vast ventilation shafts in their centers surrounded by low railings. From each hexagon one can see the lower and higher floors--without end. The arrangement of the galleries is fixed. Twenty shelves, with five long shelves per side, cover all the sides except two; their height, that is that of the level itself, is scarely more than that of the average librarian. One of the free faces opens on to a narrow vestibule, that leads to another gallery, identical to the first and to all the others. To the left and to the right of the vestibule there are two tiny rooms. One permits sleeping standing up; the other, satisfying the "final necessities" [i.e., a latrine]. Through it also passes a spiral staircase, that goes down into the abyss and up to the remotest levels. ... 'The Library is a sphere whose precise center is any hexagon, and whose circumference is inaccessible.'"
(The latter is an obvious reference to Blaise Pascal's description/definition of Nature/the Universe: "It is a infinite sphere, the center of which is everywhere, the circumference nowhere." [Pensées, 1670] But Borges himself wrote [in the essay "Pascal's Sphere", 1951], that Pascal started to write "effroyable"--"a frightful sphere....)
When attempting to determine the topology of the Library, one thing immediately strikes the reader: Borges has failed to account for one of the six sides of each hexagon. Four have shelves, one has a vestibule, but what of the sixth? Well, a moment's thought will lead one to the conclusion that it too must lead to another hexagon, since only one exit in each hexagon would result in an infinite number of two-hexagon columns, each completely cut off from any hexagon outside that column. The assumption, however, seems to be that every hexagon is accessible from every other hexagon, and for this, two doors in each hexagon are required. (Well, not quite--see below for another way to account for this.)
But is this interpretation sufficient? Yes, although the resulting topology does not appear to be what Borges envisioned. For every hexagon to be accessible from every other hexagon, if only (a maximum of) two exits are allowed per hexagon, then it appears that the layout must be in effect a spiral. Choose a hexagon as the starting point. Exit into any adjoining hexagon, then circle the first one clockwise, creating doorways, until one would be re-entering a hexagon already visited. At that point, choose the wall to the left of the one you would have chosen and go through that one, then circle again clockwise around all those hexagons already visited, and so on. This will allow you access to every hexagon eventually, and by use of the staircases, to every hexagon on every level.
The problem with this is that it in effect makes each floor of the Library a single infinitely long room with one fixed end. This does not appear to be how Borges wanted the reader to picture the Library. And indeed, the necessity to select a starting hexagon-- which will have only one exit instead of two--violates both the statement that all hexagons are identical and that any hexagon may be considered the center of the Library. (There will be more on this next week.)
(As an aside, one might marginally improve the connectivity by alternating clockwise and counter-clockwise traversals on alternating floors, but that does not change the linear layout of a given floor.) (There will be more on this also next week.)
Now, I have assumed that the connections to other hexagons are "dimensionless"--basically an opening in a wall. In a Usenet posting from 1984, Donn Seeley started with different assumptions:
"[Let] us assume that the Library fills space; it extends to an arbitrarily large distance in all directions in three dimensions (or more?). Let's assume that the second 'free side' of a hexagon opens onto another gallery directly, without passing through a hall with a staircase. Without this assumption it would be difficult to establish an arrangement compatible with the first assumption. Next, let's assume that given sufficient time, it is possible to travel from any hexagon to any other; this is implied but not stated in the course of the story. Finally, to make tiling convenient, let's assume that the halls which contain stairwells are hexagonal in shape and the same size as the book hexagons. We can explain the narrowness of the corridor by the fact that the bedrooms and bathrooms and stairs take up most of the floor space. We can even put the stairs in the same position as the central ventilation shaft of the book hexagons (they were pre- fabricated!)."
As you can see, Seeley makes one major change in his assumptions from mine: he assumes that the vestibule/closets/staircase area forms a hexagon of its own, the same size as a book-filled hexagon. But as I noted (in e-mail) at the time, I do not think that Borges's description warrants that assumption.
For one thing, the description of the vestibule is that it leads to another gallery (not that it is another gallery), and that the staircase passes through the vestibule itself. The second objection is that having galleries which have the closets, staircases, and multiple exits of their own, but no books, violates the statement that each gallery is identical to all the others.
He then additionally postulates that the sixth side of the hexagon as a "simple" door into an adjoining (book-filled) hexagon. While it does eliminate the need for multiple sleeping rooms and latrines accessible from each hexagon (thus allowing for more book-filled hexagons), and does provide some explanation as to why Borges did not describe the sixth side, the asymmetry of the layout is unsettling.
(Given his conditions, by the way, Seeley was able to design a method of connecting all the hexagons that did not rely on a unique starting point.)
Seeley is at least more accurate than Shirley Neuman, who said at the opening of the Walter C. Koerner Library at UBC: "Four sides of each hexagon hold five rows each of identical bookshelves. One side is bounded by a low railing overlooking an airshaft.... The sixth side of the hexagon opens onto a modest hall, which leads transversely to other hexagons, and vertically by means of a spiral staircase to hexagons above and below."
This is just wrong. The airshaft is in the center of the hexagon, with the railing all the way around the shaft, not merely on one side of the hexagon. And the "modest hall" of Borges's description leads to a single other hexagon, not multiple ones.
As I noted above, though, there is another way around some of these problems. That is by simply assuming that the hexagons are actually free-standing. In other words, while the Library as a whole fills space, the hexagons do not. Instead, one may suppose that there are narrow passages that surround each hexagon and separate it from the other hexagons. Think of the interior walls of a house. We think of the rooms as filling the house, but in fact, there is some space between the walls of two adjoining rooms. If we expand this space to be wide enough to allow the librarians to walk through them, then they could access any room by using the passageways to get to the entrance of the room they wish to access. (When I worked at Bell Labs in Holmdel, there was indeed a wide enough space between two "adjacent" aisles to allow people to walk along this space to work on the wiring to the offices on either side.)
While it is true that this set of passageways (or rather, one giant inter-connected passageway) is not described in the original story, it is the sort of thing that could easily be over-looked in the description--just as you don't talk about the intra-wall space when describing your house.
I found this idea quite attractive, so it was very disappointing to read in JORGE LUIS BORGES: A WRITER ON THE EDGE by Beatriz Sarlo (ISBN-13 978-0-86091-635-2, ISBN-10 978-0-86091-635-9), "As Borges himself declared in an interview, his first spatial idea for the Library of Babel was to describe it as an infinite combination of circles, but he was annoyed with the idea that the circles, when put in a total structure, would have vacant spaces in between. He chose the hexagon for its perfect simplicity and its perceptive affinity to the circle." (The interview is in BORGES Y LA ARQUITECTURA by Christina Grau, Madrid 1989.) So the idea of intra-wall space, regrettably, has to be discarded.
(For the non-lit-theory trained reader, Sarlo has an unfortunate tendency to drop terminology like "en ab&icarat;me" ("in the abyss", typified the view when standing between two mirrors facing each other--an archetypal Borgesian image!) and "als ob" ("as if", connected to "willing suspension of disbelief").)
As I mentioned, next week I will be saying more about a couple of my conclusions and how they may be incorrect, based on my reading of THE UNIMAGINABLE MATHEMATICS OF BORGES' LIBRARY OF BABEL by William Goldbloom Bloch. [-ecl]
Mark Leeper
mleeper@optonline.net
Quote of the Week:
The deeper the experience of an absence
of meaning -- in other words, of absurdity --
the more energetically meaning is sought.
--Vaclav Havel
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