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August 21, 2009 / Brittany Hendrick

Synecdoche in science: A mathematical explanation on why I favor the paisley pattern

Not long ago, I’d described an abstract concept to a guy– whose cute face and presence I liked very much at the time — about the universe. (9/14/09 update: Holy shit. He looks like a scabies-infested, sewer-dragged rat hung out to dry in the middle of winter in downtown Chicago. I wouldn’t touch that bedraggled, self-destructive mess even if he were to be quarantined by the CDC, gilded by the Department of Treasury, and delivered to my doorstep via Air Force One.)

I very rarely “go there” with people, because, hey, what’s the point– the last time I displayed beyond-basics scientific knowledge, I was looked upon negatively: I was accused of cheating at Trivial Pursuit because I legitimately identified the six flavors of quarks.

Geez, I was just answering the question put to me. I took two years of Physics in high school, so I might know a little bit about quarks. I don’t claim to be a physicist or mathematician, but I think I can grasp an abstraction and terminology without knowing how to work a formula. I didn’t know I was supposed to play dumb. I digress…

There was a reason I brought up such lighthearted conversation with a practical stranger (aren’t I fun!), which will be apparent by the end of this post.

I said to him, “The universe is just matter being pushed around. It’s like that numbers puzzle with the tiles: you move them around, trying to find order. And each tile has another set inside it, and so on.”

Little did I know that what I expressed to my once-rapt audience is a property of fractal geometry called self-similarity.

My analogy may have a hole, because the numbers puzzle IS solvable with the use of logic; order can occur somewhere– but not everywhere, not wholly, because there is ANOTHER disordered set within one tile, which continues infinitely (I’m not a mathematician, so I can only assume infinity). Furthermore, even with order present there can still be chaos– most people do not know how to solve the puzzle logically, and instead haphazardly push around the tiles until they reach that satisfactory string of consecutive positive integers.

But the concept of “order vs. chaos” is irrelevant and sub-categorical to “self-similarity.”

Last night, I happened to catch a bit of a program on PBS. I don’t know if the program was about only fractal geometry or other things in addition to it. I missed the beginning– and the end, because I fell asleep (why did this have to come on at 1:00 a.m.?)– but I tuned in at just the right part.

Fractals occur naturally in the physical world: in mountain ranges, coastlines, tree branches, leaves and countless other things. Of course, properties of these entities are measurable (graphing points), which means a number theory/formula may be applied. This goes beyond Euclidian, or plane, geometry, which is what we learn in high school.

The easiest demonstrable example of fractals in nature is the snowflake.

That makes sense to me. Yet I about fell off the couch when [Benoit] Mandelbrot’s set was explained. I got so excited, a tear fell down my face. This theory best depicts how I like to try to envision the expansion of the universe (though, I don’t think Mandelbrot’s theories are applied as such, apart from adding doubt to Big Bang theory). Spiraling galaxies upon galaxies, expanding, yet allowing concurrent cyclical paradoxes.

Stay with me! Here are magnifications of the set, with the spirals visible:

It appears that Mandelbrot’s set also integrates a concept called strange loops, innovated by Douglas Hofstadter and his book, Godel, Escher, Bach: Eternal Golden Braid (aka GEB), which I often reference to explain how seemingly unrelated events are connected cyclically. Even though you are moving chronologically through life, a new event– it could be a word, an object, a person– links to a past event, as if you’re right back where you started. My application of strange loops may be bastardized, but I like it. Artist M.C. Escher was a genius at exemplifying the strange loop phenomenon on paper– except I don’t think the term strange loop existed at that time.

Which brings me back to The Stranger who, strangely, did not feel like a stranger at all. Which is why I felt I could discuss Theoretical Cockamamie with him. A couple hours earlier, I’d made a frustratingly ill attempt at explaining to him how I interpret strange loops, and how I apply them to my life.

“Does that make any sense?” I asked, exasperated, ready to receive a look of confusion.

“Yes,” he said.

Of course, he could have been lying to me. In fact, he probably was. Maybe he was trying to impress me. But he never attempted to gain anything from me. So even if he said “no, I don’t understand,” the outcome would’ve been the same. To this day, the reason for his false affirmation is not yet clear to me.

Whether he was honest or not, The Stranger’s understanding allowed me to bring up the numbers puzzle theory with ease later on.

There was a topic of our conversation, independent from the Cockamamie, that surprised me: The Stranger wasn’t familiar with Bertrand Russell and his work.

Now, lots of people don’t know about Bertrand Russell. But there are TWO HUGE reasons why The Stranger should have known of Russell. That’d be like me never hearing of Henry David Thoreau; or a Buddhist not knowing about Siddhartha. Maybe The Stranger was lying again, testing me to see if I really know who Bertrand Russell is. Maybe he was trying to un-impress me; well, I wasn’t going to hold it against him or think he’s stupid over it. Besides, my point in mentioning Russell here is this:

In my research of fractals, Bertrand Russell’s name popped up as someone who showed early interest in its mathematics.

strange loop!

The Stranger has taken to incorporating paisley in his belongings… which kind of creeps me out… because we never discussed, uh, fashion (Did I mention that he looks like a powerbottom pedobear on a cloudy day, who dresses like he’d won a $200 $50 shopping spree at dELiA*s (R.I.P.).

strange loop!

 

… and it’s obvious that he was playing a game with me. I was just a trivial pursuit.

strange loop!

So, I’m right back where I started. I didn’t know I was supposed to play dumb.

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One Comment

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  1. Lisa Brower / Aug 27 2009 12:05 am

    That is a really interesting post. I want to see the show you referenced. Truthfully, I don’t know much about anything you said, including Bertrand Russell, BUT it sounds interesting enough after you explained it to want to learn about it. Must go Google fractals and B.R.

    Like

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