THE MT VOID
Mt. Holz Science Fiction Society
07/31/09 -- Vol. 28, No. 5, Whole Number 1555
C3PO: Mark Leeper, mleeper@optonline.net
R2D2: Evelyn Leeper, eleeper@optonline.net
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Topics:
Acknowledgement (comments by Mark R. Leeper)
Make Love, Not War (comments by Mark R. Leeper)
Birds Losing Dinosaur Status (comments by Mark R. Leeper)
Units in Physics (letter of comment by Warren Montgomery)
Perpetual Motion Machine? (letter of comment
by Robert Stampfli)
General Motors (letter of comment by Victoria Fineberg)
Fuel Economy Versus Emissions (letter of comment
by Pete Brady)
This Week's Reading (The Connectivity of the Library of
Babel [Part 1]) (book comments by Evelyn C. Leeper)
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TOPIC: 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]
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TOPIC: 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]
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TOPIC: 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]
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TOPIC: 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]
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TOPIC: 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]
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TOPIC: 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]
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TOPIC: 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]
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TOPIC: 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
numero indefinido, y tal vez infinito, de galerias hexagonales, con
vastos pozos de ventilacion en el medio, cercados por barandas
bajisimas. Desde cualquier hex gono se ven los pisos inferiores y
superiores: interminablemente. La distribucion de las galerias 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 zaguan, que desemboca en otra galeria,
identica a la primera y a todas. A izquierda y a derecha del
zaguan hay dos gabinetes minusculos. Uno permite dormir de pie;
otro, satisfacer las necesidades finales. Por ahi pasa la escalera
espiral, que se abisma y se eleva hacia lo remoto. ... 'La
Biblioteca es una esfera cuyo centro cabal es cualquier hexogono,
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
hexgaon, 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." [Pens‚es, 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 abime" ("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]
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Mark Leeper
mleeper@optonline.net
The deeper the experience of an absence
of meaning -- in other words, of absurdity --
the more energetically meaning is sought.
--Vaclav Havel