I hope you do - mathematics can actually save you from a great deal of heartache if you allow it to do so.
How did I come to love mathematics? First, I want to say that though I love mathematics dearly, I distrust its love for me, and I worry about it becoming fickle in some measure with imaginary numbers or maybe getting non-Euclidean on me or something like that. And as you have probably experienced, mathematics, like any good tool, also makes an excellent bludgeon.
All that aside, my love for mathematics began one day when the band rehearsed a new song I had written, and the arrangement process had begun. The chorus misbehaved itself in a dreadful way, it sounded wispy and pale. I tried using every exhortation and comparison that I could conjure up to address this issue, but everybody seemed to think the chorus worked just fine. “But it doesn’t soar!” I said. “It needs to be a vulture on a beach; it needs to transform from something strange but plain to something magnificent and preternatural.” Or, “It’s like the chorus has got to find the crack that opens up the other dimension, and put a wedge in there so we can pull every one through!” These kind of analogies used to drive everybody crazy after a while and I knew it. So I tried making more specific suggestions like asking the bass player to play a third off the root or the drummer to toss in a little double time beat. We worked up a couple of vocal harmonies, I changed my guitar parts, still to little avail. We decided finally to call it a day, and arranged to meet again the next day. I looked into booking the room again, and needed to select one of two storage rooms for the night.
One room was 7X7. The other was 10X4. I said I’d have the larger one.
The guy behind the desk said: Which one is that?
It seemed obvious to me that the 7X7 room was the larger of the two. But some one suggested that since both of the footage dimensions add up to a total of 14, they would be the same size. That’s not true. I hastily scratched out the formula for volume on the back of a set list I had in my purse:
Volume in cubic feet = Length (ft) X Width (ft) X Height (ft)
Volume 1 = 7ft X 7 ft x 6 ft = 294 cubic feet
Volume 2 = 10 ft X 4 ft X 6 ft = 240 cubic feet
So the 7X7 room was 54 cubic feet larger than the 10X4 room.
There you have it. The Glorious Answer and no doubt about it, no arguments, no vagaries, no shades of grey. In a life full of nuance, in a business where no one really says what they mean in the first place, and where words so often fail, such a delicious moment of absolute certainty made me shiver with delight. I happily abandoned my prejudice against mathematics (for that moment anyway - though I strive to keep the faith), and have made every attempt to proselytize in its honor ever since.
Now. Go forth and multiply.
December 31st 1997
Cyril Wong : What do you think is the most important development in modern physics?
As a dilettante physicist, I am most excited about the possibility of a grand unification theory that successfully reconciles quantum mechanics theory with the theory of relativity. As a mortal who fears death, I am excited by the nonlocal nature of subatomic particles and the larger implications of this theory by John S. Bell. I’m going to quote Larry Dossey, M.D. for the rest of this - the nonlocal theory
“...predicts that if two subatomic particles once in contact are separated to some arbitrary distance, a change in one is correlated with a change in the other - instantly and to the same degree. There is no travel time for any known form of energy to flow between them. Yet, experiments have shown these changes do occur, instantaneously. Neither can these nonlocal effects be blocked or shielded - one of the hallmarks of nonlocality.”
He goes on to state
“Nonlocal mind is a term I introduced in 1989 to account for some of the ways consciousness manifests, ways suggesting that it is not completely confined or localized to specific points in space or time.”
He supports his claim by citing Nobel physicist Erwin Schrodinger’s beliefs that mind by its very nature is singular and one, but that consciousness is ultimately a unified field. Plainly, the next logical step is to hypothesize (as David Chalmers, a mathematician and cognitive scientist form the University of California at Santa Cruz has done) that consciousness is fundamental in the universe, perhaps on a par with matter and energy and that it is not derived from, nor reducible, to anything else. Thus, the statistically substantiated effectiveness of such abstract and subjective endeavors as prayer intervention, creative visualization, and the like. Another associated study that attempts to look consciousness as its own entity are the famous crossword puzzle learning experiments where puzzles that had been published in newspapers were significantly easier for people to solve than they had been before they were published, and than were the control puzzles that never were published. Fascinating stuff.
If you have ever faced death, if you have held a dying creature in your arms as I have, you know that a life force does not simply evaporate. My simple peasant belief is that the universe would not squander something so valuable as all of the learning that is achieved over the course of a lifetime. It wasn’t so long ago that we learned that matter and energy could not be created or destroyed, that when one or the other appears to be lost, it has simply transformed into something else. That applies to consciousness in my weird doctrine. I feel that physics holds the ultimate key to the really big questions that mankind has been asking since we slithered out of the ooze.
I really do love the hard sciences and it is SO DIFFICULT to discuss these flights of thought with anyone I know. For example, I was so agitated when I discovered the superstring theory, physicists think that this hypothesis will finally provide a method for uniting the disparate theories of quantum mechanics and relativity. Imagine ! One unified field theory, the most elegant equation in the history of the universe. I tried to share my enthusiasm with strange results. People would tend to think I'm showing off, or get intimidated by the material, or bored. So now I just read my science books at home alone in my bedroom and don't talk about it, just as if I were reading pornography.
Calculus needs a great big spanking. If you consider when you're doing calculus that Newton invented it all himself, you realize that if one man can create this whole mathematical branch, that it should be possible for one person to learn it. But then, I had a really good tutor. I still didn't like calculus, though, I hadn't made friends with math yet. You know, people come to me with their story problems. "We have to 50 yards make plastic out of compound x that expands at the rate of 39% and compound y that expands at the rate of 70%. How much in liters of each?" (I actually gave him the right answer.) How many gallons are in my pond? How big is my irregular pentagonal lot? I can answer these questions. I can give you an answer that is irrefutable if I haven't screwed something up, and math graciously provides many ways to refute wrong answers.
Not like writing a song or even arranging it. Should we change the strings sound to piano? Who knows? You're winging it. Every minute, every second you're taking a chance. Even when it's a song you've played a zillion times, that's when the little thing starts that says "oooh, a really trippy out of key solo would sure be fun to play here, or maybe I should beat my guitar with a stick." Then the other voice comes in and says "wrong. so wrong." but you know, it's really not. It's never wrong, it's always just an opinion.
I think both of these regions of human endeavor are important and exciting, but math has gotten a reputation for being rigid and boring because of bad instructors. Now, interestingly, there has been a very strong correlation made between early musical training and math aptitude. When you think about it, the connection is obvious.
I disputed that there was an obvious connection...
What is music, though, but groups of tones (and these have to be defined mathematically for any kind of precision) that have been manipulated according to a specific modality and regulated by a numeric designation in time? A child studying the piano can clearly see that each note has a numeric designation in its key, the numbers one and eight of the scale belonging to the key of that scale. Each composition starts with a time signature that breaks up time (which is equivalent to life itself) into little pieces that go by in counts of (usually) four or three. Notes are divided up into whole notes, quarter notes and such, and they have to fit in the slice of time designated for them. You have to start any musical combo out with a count down of some sort. All of this counting and dividing and three part harmonies and sevenths and the like is easy to absorb, it's integral to the process that humankind has exhalted for eons, playing and enjoying music. What happens is that numbers and their uses are employed naturally and pleasurably as an essential part of music, and therefore numbers and their ways are not frightening strangers when they are encountered later in a totally different context. This reasoning is simply conjecture on my part. But I have read studies that confirm the math and music connection, and we've known about it since the '50's. Last place I noticed a mention of this was in How to Raise a Brighter Child by Joan Beck.
What about those stage tricks like lightning calculation ? I tried to learn some of it but...
Oh, I'm bad at that cute stuff too. My brain is too full of trivia for one thing. I think it's that fancy shmancy math stuff where all of a sudden "everything gets crossed out and the answer is magically 8" - that's probably another reason people hate math. I still get queasy thinking of the "Huh?" that I feel looking up at some white chicken scratches on a chalk board behind some verbally impaired teacher gazing smilingly down at me as if they had just offered me a communion wafer or something.
Real math goes more like: Here are the rules. You can use these rules to find out any answer. You can use these formulae now that you understand the rules, because they're just little things that we've figured out using the rules. Now that you're good at the formulae, here are a couple of other cool shortcuts.
Another way to make people hate math is to use it as a donkey to carry around a really stupid proposition like the movements of the planets and stars when the earth is the center of the universe. They actually made all kinds of calculations in the pre-Renaissance days to predict the movements of these heavenly bodies doing all kinds of fishy spirals et cetera, and when the planets didn't do what they expected, they blamed the math. That sort of thing still goes on all the time, too. It's why people don't trust math. But they should, math is by nature the purest, cleanest method of thought available to our species.
>Space-time descriptors, I guess, is about the "space-time fabric" etc...
Ding! Yes, this whole thing is pretty weird, that we can never catch up with the speed of light because time slows down as we accelerate. This makes time travel seem almost plausible. You know Stephen Hawkins said an interesting thing about time travel, that humankind will obviously never figure out how to travel backwards in time, because if we did eventually figure out how to travel through time, we would certainly apply the science. And where are the tourists (from the future)?
>Renormalization of infinities - definitely a maths thing, maybe to do with that "different types of infinities" thing (aleph one,two, three) etc ?
Yes. I don't know about aleph 1,2,3 - but renormalization of infinities boils down to infinity minus infinity equals zero. A lot of physicists thought this was a parlour trick, that maybe you could cancel an infinitely small amount on either side of the equation, but an infinitely large amount shouldn't work. Turned out that it does though, after some rocky moments with weak-interaction and W-particles which initially looked non-renormalizable. It took a computer to prove that the infinities here could be renormalized, and the gentleman who did so was a 24 year old Dutch man.
>Theraminaylic guitars - The theramin is a musical instrument invented by a Russian who did so accidentally, while working on radios. Famous for its use in the Beach Boys' "Good Vibrations" - there's a documentary movie about it, which is quite good I've heard.
This designation was selected by Rick for himself, and indeed does nod at the Theramin, the laylic comes from the song Layla by Derek and the Dominos - the guitars in the end vamp which howl in the really high registers was kind of what he was doing sounded like.
Celestial mechanics - physics again. Is that about how stars work ? Or how they move ?
This is the title of a book written by Pierre Simon Laplace in the early 1800's which postulates that if the movements of every atom at the beginning of time were known, all of the future events which followed could be determined mathematically. This is Newtonian determinism at its peak. Apparently Napoleon asked Laplace what role the Creator plays in this scenario, to which Laplace replied "I have no need for that hypothesis".
Chandrasekhar limiting : This was my favourite one ! The C. limit is a constant mass reference; if a star masses more than this it will go supernova at the end of its life...I think.
My favorite too! Especially if you know Bryce. He really can push a song as far as it will go making it shine as bright as it can until it cain't shine no mo. My recollection is that after the limit the star becomes a black hole, though, this could be after a supernova, I can't quite remember, and I remembered that whole deal from a library book.
E.Bowa virus - play on words between the EBow (check out www.ebow.com) and the Ebola virus, which the media just *loved*, 'cos they could predict wide-scale disasters and scare people into watching their stations.
You got it! Did you read the Hot Zone? I enjoyed that book, not great though, but ok.
General & Special Relativity : Mr Einstein here - did you know he worked out Special Relativity while he was quite young ? He was either 16 or 21...nah, that can't be right, can it ? Amazing guy...
Einstein is my dude! Did you know he was on Marilyn Monroe's list of fantasy sex partners? He was actually 26 as I recall. My favorite Einstein quote (needs some background info): An experiment was held in Brazil and Africa in 1919 during a total eclipse. Einstein's theory predicted that a light beam's path should bend as it passed by the sun, and the sun's matter/energy could warp space-time. The deflection if starlight around the sun would verify these ideas. Sure enough, there was a significant measurable bending of starlight which verified the theory. When a first year student asked Einstein what his response would have been had the experiment failed he replied "Then I would have been sorry for the dear Lord (for creating a flawed universe - dt) but the theory is correct."
Yes, even Einstein didn’t want to commit to quantum mechanics until he could find a way to see it working with relativity ("God does not play dice"). Problem was, we just didn’t have the cosmology information available at the time. He was trying to spell eon without any vowels. Given his ability to visualize and postulate the workings of relativity, (and doing this in any non-simplistic way is really hard for me), I can see how he would keep trying. He had already defied the limits of Newtonian physics. Poor man, for years thereafter just trying to *think* hard enough, if he could just see this all working together - and he got pretty close, too, to our current superstring theory with the little he had to work with, though a lot of people dismissed it as lunatic ravings of a beaten man.
On the other hand, pseudo-science and other fraudulent bastards promise an easy answer "Only 5 bucks a minute and I'll tell your future" and millions believe them ! It's sad that such transparent fakery succeeds.
People need faith in their lives. I know I do, I had to invent a religion for myself of which I am now a devout follower. Loosely based on Greek Mythology, native American legends, Buddhism, and of course relativity/quantum mechanics and other science.
I was *deeply* disappointed to see Nichel Nichols (Lt. Uhura in the old Trek) promoting one of these psychic hotline things - what a terrible message to send to people who admire her work as a rational woman of the future...
Yes, she deeply influenced a lot of black women in particular. Thankfully, the sad depths to which people can sink to make a buck at the end of their careers does not negate the good they did.