Trigonomotastic

After a two month hiatus from learning anything new, the summer session careened into view.  MATH 140: Introductory Mathematical Analysis started over two weeks ago, and only just now, today, do I have time to take a breath.  Initial observation: summer class timelines are not to be taken lightly.

This is the course in which we finish up the algebra begun in MATH 120, and we start trigonometry.  How did I not know that trigonometry was just Super Fantastic Geometry?  I vaguely remember enjoying geometry in high school, although my only concrete memory is the gift of a pencil that said, “A logarithm is an exponent.”

IMG_20160713_131948In trigonometry, we’re learning how to calculate the speed of airplanes, the velocity of tsunami waves, and the ascent of hot air balloons.  We can also calculate a ship’s bearings and a satellite’s orbit.  Of course, algebra is simmering under the surface of it all: even if I get the concept and pick the right formula, I can’t complete the calculation without stupid PEDMAS poking me in the eye again.*  But the ability to look at a triangle on the page and see movement and change in the physical world is powerful.  I am in love.

The ability to see movement and change through language is powerful too, and it’s one reason I was an English major from the get-go.  These days, I write a lot of things without knowing my words’ trajectories once launched.  This blog is one of those things.  Many of my social media posts are these things, too.  Someone blocked me last week because of a comment I made related to #BlackLivesMatter and the Dallas sniper.  Now that I’m blocked, I can’t access the comment to delete or amend it, I can’t respond, and I can’t see what anyone else has written.  That ship has sailed, and in which direction I have no idea.

Who knows what other trajectories my writing has taken or what kind of change I have effected, I hope more often for better than for worse.  But in just two short weeks of trigonometry, this power pops all over again, clearly and consistently. I am excited to have been reminded that it is sometimes possible to see a large chunk of the world on a relatively small piece of paper.

*Look! I just tried to express a relationship between algebra and trigonometry, which I couldn’t have done six months ago.  Related: I still don’t know what calculus means.

3 is a 0 of multiplicity 2

In a graph, when you touch or cross the x-axis, you can call that point “a zero.”  If whatever you’re drawing crosses the x-axis at “3,” then “3 is a 0.”  And “multiplicity” determines the shape of the thing you’re drawing at that point on the graph: the even numbers are parabolas, odds are dog-legs, and a “one” is a plain old line. “Multiplicity 2” means that at the point your thingy touches the x-axis, it does so in the shape of a parabola.  And although my class hasn’t gotten to this yet, I also know that it’s possible to have imaginary zeros.  I don’t know what you do with imaginary zeros.

multiplicity

Multiplicity has been a favorite word of mine since I was introduced to Bergson and Deleuze.  But I usually use the word in a sloppy way, as in: “we should have a multiplicity of voices represented in the literary canon.”  That’s a terrible thesis.  Bergson (who was a math whiz before he became a philosopher) wrote about both quantitative and qualitative multiplicities in much more precise, interesting ways.

Qualitative multiplicity is found in a singular experience that can’t be juxtaposed against another one.  One of Bergson’s examples is to imagine the stretch and elasticity of an elastic band. “Bergson tells us first to contract the band to a mathematical point, which represents ‘the now’ of our experience. Then, draw it out to make a line growing progressively longer. He warns us not to focus on the line but on the action which traces it”(from the Stanford Encyclopedia of Philosophy).  The duration of the stretch, the inherent tension, the smooth transition from point to line, the experience of it all: these elements contribute to the qualitative value of the multiplicity more than a static image (such as a graph of a trajectory like the one above) can preserve.

20160327_215900So there’s math + philosophy. And also + art: in Findings on Elasticity, editors Hester Aardse and Astrid Alben write, “Elasticity has no inhibitions.  Science has no inhibitions…As science continues to shamelessly stretch knowledge as far as it will go, unburdened by inhibitions, so art, in its limitless ways of expressing human experience, often confronts our inhibitions and suggests where we should put them.”  It’s a wonderful book full of experiments and installations and inventions exploring (it seems to me) the question: How do we authentically record, document, preserve, share, communicate our experience of the qualitative multiplicity of elasticity?

These notions of multiplicity-via-elasticity (math, philosophy, art) relate to the nomadic paths of protest librarians and the (often surprisingly divergent) paths of the libraries’ physical collections of books.  The question is, how do these trajectories represent both quantitative and qualitative multiplicities, and how can they be recorded in a meaningful way.  This is a project to root around in over the summer.

PS: This article about an exhibit called “Design and the Elastic Mind” randomly passed through my Facebook feed just as I posted this entry: Curator Forced to Kill Out-of-Control Bio-Art Exhibit

 

Things are linearly sloping up.

In the 1970s, I drew buttons and flashing lights on a cardboard box, cut slots on each end, and called it a computer.  You could write a question on a card, drop it into the entry slot, and it would come out the other end with the answer to your query.  The catch (a doozy): I had to write the answer on the card before you dropped it into the computer, since nothing actually happened on the inside of the box.

In math class, we’ve reached the chapter on functions. Functions do the kinds of things I very much wanted to make happen inside my cardboard computer. They are all about inputs and outputs: f(x) = [something crazy like 3x + 2].  f(x) — which is a fancy way to say y — is dependent on the input of x.  If you input something as “x” and only one thing is output at the other end, then it’s a function and you can happily plot x and f(x)  on a graph.

The linear model that we learned about last fall in statistics is closely related to all of this (or so it seems to me).  The lineaLinearModelr model includes a slope (of a line), a y-intercept, and a relationship between dependent and independent variables.  They all work together to help predict the locations of dots on a regression analysis graph.  And I do love graphs.

 

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This floated through my Facebook feed last week.  I can’t find a source for it.  But it makes about as much sense as linear models do when you don’t know algebra.

Understanding dependent and independent variables about killed me last semester, and they’re doing a number on me again.  But the cause/effect is clearer this time around.  My hat’s off to everyone who has to teach stats to someone like me, someone who doesn’t know what an algebraic function is.  I think this must have been the same kind of frustration as playing Mad Libs with someone who doesn’t know a noun from a verb from a postmodern platitude.

I feel triumphant in making this connection between functions and linear models (even if I still have some of it wrong).  And I am excited to think about how the spatial mapping of data (as dots) and relationships (as lines and slopes) is a much stronger undercurrent than I realized.  Maybe I should have known it.  But I didn’t.  But now I do.  So that’s progress, with the slope of my own linear progression again pointed upward and onward.

Confessionals, boy-crazy and otherwise

First:  I did not fail the test.  Nope.  Not a failure.  Not today.  Voice of reason: Although I am happy to have passed, it was a genuine surprise.  So clearly I have no idea how to self-assess my abilities in this course.  File that away as something to think about post-celebration.

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Hot X: Algebra Exposed!  By Winnie from Wonder Years.

Second: I made progress on my black-hole tendencies.  I asked two questions in class, and I bought a new book.  Yes, this book.  Yes, the cover pumps a personality quiz and “boy-crazy confessionals.”  But Winnie-from-Wonder-Years’s tone is so much more likeable than my $400 course textbook.  The blurb promises that she “shows you how to ace algebra and soar to the top of your class–in style!”  The pep-talk to us girls (tween or otherwise) about being able to do math is a bonus.

Third: We started graphing things this week.  MY OPTIMISM IS RENEWED.  I love graphing.  I love graph paper.  I love charts and tables.  And grids.  It’s the whole reason I became a girl-scout as a kid: selling cookies meant I had control over the most magnificent, color-coded spreadsheet that a 1980’s 10-year old could hope for.  And when we planted a garden, we went the square-foot gardening route because it required a grid.  And crossword puzzles: a favorite pass-time.  So many tiny little boxes.  I use graph paper all the time, but using graph paper for its intended purpose brings a special kind of joy.

Finally: I’m not funny.  I know it.  Last week, a stranger commented that this blog was interesting but not funny.  Being interesting can be hard, so I’ll take that as a win and continue to forge ahead.  Onward and upward, everyone, mechanical pencils at the ready.  It’s a whole new week.