Music, Math, and trees   Lee E. Frelich
  Mar 09, 2006 15:37 PST 

Bob et al.:

I am coming back in time for the Brahms festival Saturday evening with the
Minnesota Orchestra, when I hear symphonies 3 and 1. Last week they did 2
and 4. First time I ever heard all four symphonies in a two week
period. In my mind they all correspond to a different type of forest:
black spruce, white spruce and birch, sugar maple and hemlock. I will
check my e-mail Saturday to see if you can guess which symphony is which
forest type.

Lee
Impractical questions for measuring and numbers experts   Pamela Briggs
  Mar 11, 2006 13:00 PST 

Dear math fans --

From what I understand, aside from the practical value of statistics,
you get natural satisfaction from computing averages, comparing figures,
and such. I was wondering whether your love of numbers extends into
other areas -- nonpractical intellectual, emotional, and sensual realms.

As a creature of words, I enjoy language on many levels. Sometimes I
write for myself, for no purpose, surrounding myself with words. I
enjoy learning about and comparing world languages. I love anagrams,
puns, and wordplay from juvenile to sophisticated. As a graphic
designer, I like experimenting with how words look in different fonts.

Some words are majestic or awful when I hear or read them. Some words
feel good to say. For some reason, hearing or saying the word "bee"
cracks me up. I had a college friend who hated to hear the word
"rubble." Then there's the old comedy principle that words with a "k"
sound are inherently funny. (Remember Bugs Bunny taking "a wrong turn
at Albuquerque," or Homer and Jethro singing "The Battle of
Kookamunga"?)

So how is it for you? When you're nestled all snug in your bed, do
equations, not sugarplums, dance in your head? Are some numerals more
fun than others to see, hear, or write? Do you smirk at a European "7"?
Do you like pi? Do even numbers irritate you? Is it satisfying to
round numbers to the nearest hundredth decimal? Are some numbers
funnier than others? Do you like numerical trivia?

Do you look at a tree and admire its shapes and curves, or its divisions
of trunks, branches, and twigs, as expressions of a mathematical
formula?

Do you play with the magical properties of nine?

Do you grin when you're calculating something and come up with a
repeating decimal, or does it drive you nuts to have to put a bar over
those digits?

When you hear the word "five," do you visualize five heavy, satisfying
blocks in a row, equidistant? Or when you hear "six," do you see a neat
triangular pile of circles -- from bottom to top, rows of three, two,
one?

Is there beauty in balancing equations?

When you're out in the field, do you punch "58008.40" into your
calculator and show it to your buddy upside down for a cheap laugh?

I've read that some mathematical geniuses can enjoy a conversation of
simply reciting numbers. One person gives a prime number, and they
savor its unique quality for a while, until the other person gives
another number.

Does any of this resonate with you?

Pamela

http://pamelabriggs.com/
RE: Impractical questions for measuring and numbers experts   Ernie Ostuno
  Mar 12, 2006 15:04 PST 

In reference to the "visualizing of numbers"; for many years I have
equated colors to numbers. Don't ask me why, since there is no practical
application of this scheme that I have ever used. Here is the
number/color association:

0 : clear, transparent, no color
1: white
2: maroon
3: gold
4: scarlet
5: black
6: gray
7: silver
8: blue
9: brown

The weird thing is I don't ever remember consciously picking those
colors for each number. It's as if they were always associated with each
other in my mind.

So I visualize a string of numbers such as 3/12/06 as being a "rainbow"
of gold/white/maroon/transparent/gray/

One possible practical application of this would be to help memorize a
string of numbers such as phone numbers and lock/safe combinations, but
I have never done so, finding it easier to equate those number groups to
months and years. Using this method, a phone number such as 392-4871 can
be thought of as "March, 1992" - "April 8, 1971". For some reason I find
this method more useful than the color method.

Ernie
Back to Pamela on numbers   Robert Leverett
  Mar 13, 2006 06:13 PST 

Pamela,

   Wow! You've given us inveterate number crunchers quite a challenge, a
heavy duty assignment. Let's see, we are to look beneath the
surface-wise aspects of our tree-based compulsions and hunt for the
sources/origins of our interest in numbers, for the deeper meanings.

   Since my minor in college was mathematics, a personal interest is
implied, but from what direction and to what ends? Do I even know? Then
there is John Eichholz and there is Howard Stoner. Both are
mathematicians with, I'd think, plenty to share with us on the subject
of their mutual focus. I suspect that my good friend Don Bertolette
could weigh in with an interesting analysis of his personal relationship
to numbers. He is very much into nuances. And I would expect Lee
Frelich's intimations to raise the bar for all of us. Music =
mathematcis, eh, Lee? Any string theory in there? What's the vibration
rate for the note A, 442 or some such value?

   Regardless of the input of others, I accept your challenge. But
before turning to the science of patterns, which is what mathematics is,
let me once and for all clear up some confusion. Pi are NOT square. Pi
are round. Leastwise all th ones I ever et wus. Oooh, I can hear the
groans all the way to the distant corners of ENTSLAND. Another one like
that from me and we may lose members.

    But, to begin with my story, my fascination is first and foremost
with patterns, spatial and temporal. Infinite series fascinate me and
how certain series spring up in the darndest places. Of course, many
infinite series are highly practical. For example, if I forget my
trigonometry tables and need a quick sine or cosine of an angle, there
are the infinite series:

   sine(a) = a - a^3/3 + a^5/5 - a^7/7 + a^9/9 ...........

   cosine(a) = 1 - a^2/2 + a^4/4 - a^6/6 .................

where a is measured in radians as opposed to degrees. Fascinating! All
that meaning accumulating in the sequence of terms. Who'd a thunk it!

    Monica recently signed me up in the Scientific American book club. I
now have highly readable books on the history of Pi, zero, e, and
imaginary numbers. One of the books deals with the history of infinite
series. I'm suddenly waist deep in the history of numbers. Ahh, all the
better to further our ENTS field of mathematics - which is as you will
no doubt remember, "twigonometry". But, you may have forgotten its
extensive use of logarithms.        

    Boy, this early morning coffee is good!

Bob
Re: Back to Pamela on numbers   Lee E. Frelich
  Mar 13, 2006 07:40 PST 

Bob:

Yes, music is math, and trees are math, and everything is math. Math is
the simplest of all sciences and that is why you can use it to abstract
everything else in the world.

I find string theory very similar to ecology. Fundamental particles that
make up atoms and all matter are made up of vibrating strings, which it
turns out are actually like little rubber bands and membranes in 11
dimensions. Most ecological analyses have at least 11 dimensions (although
we only present 2 or 3 to the public) and they are also fuzzy and
constantly changing with many shapes, like the physicists string theory.

BTW, concert A is 440 vibrations per second, not 442.

Lee
Back to Lee on numbers, music, the cosmos, and whatever   Robert Leverett
  Mar 13, 2006 08:14 PST 

Lee,

    Ah yes, 440. I was using the RD 1000 to measure A. Should've used
the Macroscope 25.

    BTW, I'm going to need more time on the puzzle you gave me last week
on those four forest types versus the four Brahms symphonies - which
matches which. Unfortunately, I haven't heard any of the Brahms
symphonies for a couple of years. I'll need to go out and get CDs of
them before making a concerted effort. In the meantime maybe others
would like to come forward with their match ups.

   Do you often match symphonies to forest/landscape types? We started a
discussion of this type once before. It's a pretty fascinating area to
explore, regardless of what the composers of nature sounding music may
have had in mind. From your perspective, which composer's or composers'
music most clearly carries the feel and textures of nature? Alexander
Borodin's "On the Steppes of Central Asia" immediately sends me to those
places. His Prince Igor opera is a favorite and conjurs images of Russia
for me. Did you know that Borodin was a PhD organic chemist? He lived a
pretty amazing life. http://www.geocities.com/cahmn/Essays/Borodin.htm

Bob


    Monica and I are often discussing the emotional impacts of various
types of music - she as the professional and me strictly as an amateur.
Which is the music of the trees?

Bob
RE: Back to Pamela on numbers   Monica Jakuc
  Mar 13, 2006 08:57 PST 

Dear Lee,

You're absolutely right that concert A is 440 cylcles per second, but
some orchestras today do go higher, to 442, or even 444. Conductors
like the brighter sound produced by the strings. This is a real hazard
for wind players, however. I'm told that some new flutes are pitched
higher than 440 to deal with this new situation.

When I play classic period music on fortepiano I play at A 430 or A 435
for my 6 1/2 octave fortepiano. Pitch wasn't really standardized until
pretty recently: in the baroque period anything from A 392 to A 450
could be encountered.

Did you know that Bartok based all of his music on the Fibonacci series
(or so a musicologist named Lendvai says)?

Well, we're straying from topic here.....

Monica
Re: Back to Lee on numbers, music, the cosmos, and whatever   Lee E. Frelich
  Mar 13, 2006 11:31 PST 

Bob:

I always match up music with trees, forests, or something in the natural
world (for example Dvorak Symphony #8 doesn't match up with trees, but it
has an elephant call in the last movement--if it wasn't for that I would
always have #7 and #8 mixed up).

Its pretty clear that Brahms used forests as inspiration for his music, he
is well known for his hikes in local forests around Vienna as well as
summer trips to the mountains.
A clue you can use for lining his symphonies up with forest types is the
way they fall into two pairs (2 and 4 vs 3 and 1), which is the way the MN
Orchestra presented them (the commonly used grouping of 1 and 2 vs 3 and 4
doesn't make any sense other than its in numerical order).

Lee
RE: Impractical questions for measuring and numbers experts   Pamela Briggs
  Mar 13, 2006 18:43 PST 

Dear Ernie --

This is wonderful! I love knowing this. Thank you.

Does it work the other way when you see colors? I wonder if you saw the
shirt I'm wearing, it would make you think of 1685.

I'm going to try your phone number-memorizing technique, too.

Pamela
Trouble with numbers   John Eichholz
  Mar 13, 2006 18:49 PST 

Pamela,

I always liked the Fibonacci series1,1,2,3,5,8,13,21,34,55 and so on.
They appear often in nature. Prime numbers are a gas. I am also
facinated, having passed that age, that 42 is a highly complex number
(2*3*7) while 43 is prime. Did you know that e^(i*pi())=-1? That is
pretty freaky, since both e and pi are transcendental (the root of no
polynomial equation of any order) and i is imaginary. But hey,
mathematicians have a very vivid imagination. One more neat thing. If
you consider the group of integers modulo 3, you can say with all
honesty not only 1+1 = 2, but also 2+2 = 1. I guess that resin-ates
with me. I like a real simple concept, and there is nothing like
chopping off all those extra numbers and just dealing with a handful.
Give me the integers modulo 7, give me 0,1,2,3,4,5 and 6, and forget
about the rest of them. It is all still there. 4*5=6, 5/4=3, 2*2*2=1,
or add them all up and get nothing, 1+2+3+4+5+6=0.   Ahh, the simple
life! As for having a conversation reciting numbers, that sounds more
like being a cashier than anything else.

John
RE: Trouble with numbers   Roman Dial
  Mar 13, 2006 23:53 PST 

Pamela and John,

Pamela, John's email here delights me. These are all neat things that he
has written -- I, too like the Fib series and when I have to build
shelves in my house I often space them using pieces from the Fib
sequence (like 3 shelves that are 8, 13, and 21 inches apart). And
Euler's Equation relating Pi, i, e, -1, and 0 is wonderful, beautiful,
elegant, and mysterious. Also fun to derive for other people and share
in its delight.

When I drive long distances sometimes I search for primes in my head to
stay awake....I am also, I confess, a bit, just a wee bit superstitious
about numbers. I like 7, but like 14 more. Three is good, too. When I
was a mountain climber in my youth, an activity with weather and other
chancy events impotant, I looked for signs in numbers before my climbs.
I made sure to carry multiples of 7 in crabiners and slings and other
gear. I avoided 13, of course. Why believe in luck when you can rely on
it? For example, 21, 35, 42 were all great years in my life (but so were
9, 18, and even 26 -- go figure).

When I was a grad student in math I disdained stats, but then when I
became a PhD student in biology I fell in love with stats and now revel
in analyzing data, which is not so much math as using math to find
patterns, I uess. Lately I have actually started to enjoy just the logic
involved in managing and manipulating data bases.

Indeed, one thing that draws me to ENTS is the kindred spirit feeling I
have for those who mix numbers and natural history.

Roman
RE: Impractical questions for measuring and numbers experts   Monica Jakuc
  Mar 14, 2006 07:18 PST 

Dear Pamela,

When it comes to numbers, you certainly have my sweetheart's number.
Notice how, in a recent email, he calls 80 a hefty number.

He walks around with formulas and numbers (and trees) in his head.
Sometimes he doesn't even hear what I've been saying. I notice it most
when his glazed look of abstract thinking suddenly become focused. When
I ask him what number he was thinking of, he gets a sheepish look on his
face. Then there’s all the stuff around the house that he never notices
to clean because he's too busy with the math in his mind.

I have also noticed that, in conversation, Bob always relaxes with a
smile when we can finally put a number on something, accompanied by
mutterings like, "Well, we're finally getting somewhere."

We do engage in humor with numbers. Some of it I won't mention here. But
on the lighter side, sometimes one of Bob's numbers gets away and he has
to go searching for it. One of those lost numbers has become a pet of
ours. Evidently, it finally came home, and curled up underneath the
133-ft pine in my backyard. That number followed us to Cook Forest, and
started cavorting with the trees there. It stayed for an extra week
before coming back home.

Since then it has met a mate and they had a baby (3). 3, of course, has
grown, and is now 3.6. Discretion dictates that the two numbers that
gave birth to 3 shall remain anonymous.

Monica
RE: Impractical questions for measuring and numbers experts   Monica Jakuc
  Mar 14, 2006 07:25 PST 

Pamela and Ernie,

I too love the idea of associating colors with numbers. It reminds me
of the fact that many musicians, including myself, associates colors
with keys: E Major is green for me. As far as I know, there is no
consistency to which colors go with which key.

There is also the phenomenon of of people who hear in color: Russian
composer Alexander Scriabin was one of those.

Monica
Pi   Robert Leverett
  Mar 14, 2006 11:38 PST 

ENTS:

   Continuing our digression into mathematics and the world of numbers,
the following is presented courtesy of John Knuerr.

=================================================
Written in the USA </wiki/USA> date format, March 14 is an unofficial
celebration for Pi Day derived from the common three-digit approximation
for the number ๐: 3.14. It is usually celebrated at 1:59 PM (in
recognition of the six-digit approximation: 3.14159). Some, using a
twenty-four-hour clock </wiki/24-hour_clock> rather than a twelve-hour
clock, say that 1:59 PM is actually 13:59 and celebrate it at 1:59 AM or
3:09 PM (15:09) instead. Parties have been held by the mathematics
</wiki/Mathematics> departments of various schools around the world.
================================================

Bob
RE: Impractical questions for measuring and numbers experts   Ernie Ostuno
  Mar 15, 2006 14:25 PST 

Pamela,

Strangely enough, it doesn't work in reverse for me. In fact, when you
mention clothes and 1685, I picture you decked out in period costume
from the court of Louis XIV.

Ernie
Trees and music   Lee Frelich
  Apr 30, 2006 16:52 PDT 

ENTS:

I discovered a few additional pieces of music related to trees while
listening to the radio:

Robert Schumann, Forest Scenes, a work for solo piano. To get this one
ready for performance would be a lot of work for our piano playing ENT, Monica.

Weber. Der Frieschutz (or something like that, I am not that good with
German), an opera where many of the characters are foresters (which
actually means a lot in Germany), and among other complications in the
plot, all of the foresters in the region compete in a target-shooting
competition, and the one who wins gets to marry the king's daughter.

Lee
RE: Trees and music   Monica Jakuc
  May 01, 2006 07:48 PDT 

Dear Lee and Bob,

Of course, I've played some of the Forest Scenes of Schumann, though not all of them. The "Haunted Spot" is interesting, as well as the "Prophet Bird" and the "Lonely Wildflower." It's been on my list of things to do to learn them all for some time.

Yes, Freischutz is pretty wild.....

Monica