|
05/22/2003
Twin Verses
At last Friday’s afternoon concert by the New York
Philharmonic Orchestra, the first number was a short
composition, “Ceremonial: An Autumn Ode for Orchestra with
Sho”, by Japanese composer Toru Takemitsu. Mayumi Miyata
was the sho soloist. Neither Ms. Miyata nor the sho rang a bell
with me and, from my seat in the second tier and less than
perfect eyesight, both remained a mystery after the concert. I
had no idea what she was playing except that she was blowing
into something held in front of her face and it appeared that two
antennae were sticking up from it.
Not until I got home and visited the Web site mode.com did I
realize that I should have recognized Ms. Miyata. At the 1998
Nagano Olympic Winter games opening ceremony, she
performed the Japanese national anthem. On another Web site,
jtrad.Columbia.jp, I found a picture of the sho. It’s an odd
instrument, described as being harmonica-like and producing a
“cloud of sound”. The sho has 17 pieces of bamboo of various
lengths (the “antennae”) protruding from a “bowl” of Japanese
cherry or cypress in a cover of water buffalo horn. You blow
into an opening in the bowl, and finger holes in the bamboo
sticks to produce different chords.
I think the Philharmonic missed a theatrical opportunity.
Traditionally, the sho is heated over a charcoal fire to remove
any traces of moisture prior to a performance. I envision a
“tuning up” of the sho over a fire in a little hibachi on stage
while the concertmaster leads the orchestra in its own, more
conventional tuning up process.
The strangeness of this instrument pales when compared to a
claim I’ve seen recently. You should be particularly interested in
this claim, namely, that somewhere out in space you have an
identical twin. Not only that, but at this very moment, he or she
is reading a column by a Dr. Bortrum! Similarly, I have an
identical twin who wrote that column under the pen name of Dr.
Bortrum. I am just as shocked and as skeptical as you are. To
tell the truth, I had heard of this absurd notion before and, in fact,
mentioned it in my column of September 4, 2001. At the time, I
don’t recall reading that my twin was following my exact
behavior pattern. In any case, I felt that the idea was as goofy as
it sounded.
I’m somewhat less skeptical after reading an article in the May
2003 issue of Scientific American by Max Tegmark titled
“Parallel Universes”. Tegmark is a professor of physics and
astronomy at the University of Pennsylvania and an expert in
cosmic background radiation and galaxy clustering. Tegmark is
treading dangerous ground. A visit to his upenn.edu Web site
cites the case of Giordano Bruno. Poor Bruno was burned at the
stake in 1600 in Rome, proclaimed a heretic, possibly for his
proposal that the universe is infinite and contains an infinite
number of worlds, all inhabited by intelligent beings. Awfully
close to what Tegmark is claiming!
Tegmark bases his work in part on the results of NASA’s
WMAP mission on the cosmic background radiation that I
discussed in my column dated February 27, 2003. He combines
these results with galaxy survey data to make two key
assumptions. First, space is infinite; no matter how far out in
space you go, there’s more space out there. The WMAP
evidence that space is flat, not curved, bolsters this assumption.
Second, on a grand scale, matter is distributed uniformly
throughout space. Tegmark shows remarkably consistent data
combining WMAP results with galaxy surveys that show
uniform matter distribution throughout the universe visible to us
with our telescopes. He simply assumes that this same condition
holds in the endless space that we can’t see.
The space that we can see is called the “Hubble volume”. This is
“our” universe. Here on Earth, with our telescopes, we can see
roughly 10^23 miles around us in every direction. (10^23 is the
notation I have to resort to, lacking superscript capability.
Einstein’s famous equation would be E = mc^2 in this notation.)
The number 10^23 is a 1followed by 23 zeros. If you convert
this number of miles to light years, it turns out to be 42 billion
light years. This number might surprise you, as it did me, since
the universe is only 14 billion years old. However, Tegmark
says the larger number is due to cosmic expansion. I’ll have to
take his word for that. Whatever, our universe is big!
Tegmark calls his calculations on what follows from these two
assumptions “trivial”! Actually, I worry that the approach he
uses is too simple, especially since I can almost understand it!
I’m heartened to find that he implies that the same results can be
derived from more sophisticated analyses. While his math may
be simple, his numbers are humongous! For example, a key
calculation is to take the total number of particles in our universe
and then calculate the number of possible ways of arranging
those particles. He uses as the number of particles in our
universe 10^118 or a 1 with 118 zeros after it!
Why does Tegmark want to calculate the number of ways of
arranging this number of particles? The number of possible
arrangements is the number of possible different universes,
including the number of possible forms of life and including you
and me. I have no idea whether his calculation is correct but his
number of arrangements turns out to be roughly 10^10^118.
When you get a number raised to the power of a number raised to
a power, the result can be truly out of sight. (Let me illustrate a
simple example. 10^2 = 100 while 10^10^2 = 10000…….000
[100 zeros]) In this case of our universe, this is a 1 with the
number of zeros after it being the number 1 with 118 zeros after
it! Let’s just call that number “HUGENUMBER”.
HUGENUMBER then is the number of possible arrangements of
all the particles in our visible universe, our Hubble volume. Now
it’s time for us to think, as they say, “outside the box”. Let’s
pretend our Hubble volume is a ball. Now let’s make balls of
each possible other arrangement of the particles in a Hubble
volume. The number of different balls will be HUGENUMBER.
Let’s now make a box just big enough to hold all these different
balls. Let’s make it a spherical box and float it out in space.
What if we go outside the box? If all space is uniform, we’re
going to encounter other balls (universes) all around our box.
Remember we’ve got balls of all possible arrangements in the
box. So, if we go outside the box and look at any ball it has to be
a duplicate of one of the balls in the box! If that ball in the box is
our universe, everything in the duplicate ball outside the box is
the same and you and I are doing precisely out there what we’re
doing at this moment in the box!
Tegmark even calculates the average distance we would have to
travel to meet ourselves in another Hubble volume that looks
exactly like ours. The answer in miles is no more than about
HUGENUMBER divided by about a thousand, still a huge
number! We won’t meet any twin universe in our lifetime!
This collection of universes, or Hubble volumes, that surround us
is called a “multiverse”. What I’ve been discussing is what
Tegmark calls the simplest “Level I” type of multiverse. I hate
to mention it but Tegmark also considers the possibility that
there may be other levels of multiverses. I’m not going to touch
that one except to say that it’s possible that there are multiverses
floating around in empty space and, if so, I assume there must be
twin multiverses. If that’s the case, HUGENUMBER will be
peanuts compared to the numbers for twin multiverses!
If all this is true, it occurs to me that there also must be universes
out there where you and I are being born, others where we’re
going to college, etc. Furthermore, doesn’t it also follow that
there are universes where our parents or their ancestors are alive,
where Galileo is peering through his telescope, etc. I should
point out that HUGENUMBER applies to finding our twin
Hubble volume, our whole universe. Actually, we don’t have to
have a whole universe be exactly the same arrangement for our
twin to exist. We just have to have a volume large enough that
one of the possible arrangements in that small volume includes a
sun and planets and an earth. Thus, Tegmark calculates that we
won’t have to go nearly so far to find our twins. Even so, “not
nearly so far” corresponds to a dauntingly large (10^10^28)
miles away.
Tegmark makes the point that our twins may depart from our
behavior here on Earth. Hey, maybe somewhere one of my
many twins is living my childhood dream of playing left field for
the Philadelphia Athletics, who did not move to Oakland after
all! Or, maybe he’s all set for the ice skating competition at the
Nagano Olympics as soon as a Mayumi Miyata finishes playing
her sho!
Allen F. Bortrum
|
