Figure Not To Scale

Welcome to Figure Not To Scale.  Here are some examples of out-of-scale figures:

I once walked into a pizzeria and asked for “Two slices please”, but held up three fingers.  I wanted to see which I got.

I got a smirk, but didn’t flinch.  Only two slices, though.  I wondered why.

How many would you have given me?

I teach SAT classes.  I don’t much like it, but sometimes the kids are fun.  Many problems feature a diagram that would seem to be a simple shape such as a square, but don’t be fooled for it is ‘not to scale’.  Trusting the image will lead you astray, only by submitting to the textual logos can the answer be found.

There is one particular problem where the logos is insufficient.  A square is pictured.  Assuming that the square is a square will lead to the wrong answer.  Assuming that it is a rectangle will yield the correct one.  However, the text that describes the problem is not rigorous enough to specify a rectangle rather than any other four sided shape, and so in actuality the problem is ambiguous and unsolvable.  The test-makers have fallen into their own trap.

It is subversive to out-logos the logos-police.  To see that their square-rectangle could actually be a rhombus, or a giraffe, is to dance within the one degree of freedom that is left, and even that by accident.  This is at least one of core elements I envision for this blog:

To reach the fault-line of the imaginary and the symbolic, and through small disruption trigger widespread tremors of a ground that seemed solid, but is yet living, evolving, and writhing.

If the image can’t be trusted completely, how are we to know which facets of it to take seriously?  How can we know that we must assume the angles are shown correctly but the sides aren’t?  Why have a picture at all?

In mathematics, we study the subtle gradations of ambiguity.  Indeed, mathematics makes even ambiguity un-ambiguous.  This is done most poetically in Klein’s “Erlangen Program”, which established an ambiguity-hierarchy of geometries.  Euclidian figures are ambiguous only as to their position and rotation, that is, if you rotate the figure or slide it across the page it is still the ‘same’ figure.  In more abstract geometries, such as conformal or topological, more warping is allowed.  For example, angles may change and so the figure becomes more visually ambiguous, more text and less image, because any depiction of it illustrates a particular angle and not another.  Indeed, this draws attention to the symbolic element inherent in all images, all of them implying certain ambiguities/abstractions beyond the pictured specimen.  In topology, only continuity is safe; figures may be stretched and warped forever, only no new holes are allowed.

I wish to creatively reconfigure the implicit symbolic element in the image, and thus bring it to awareness.  This, as far as I can tell, was Lacan’s goal as a clinician.

This standardized test expects us to know precisely where we are in the ambiguity-hierarchy, to be able to orient ourselves properly within consensus-ambiguity, standardized abstraction. Another element of this blog:

To articulate the cascading geometries of ambiguity. 

To seek the most rarefied topology of logos can have several goals.  Most academic philosophy aims only to distill, to stand at the top of Mount Erlangen and look down from Thought to more concrete thoughts.  It lives in the thin air of the clouds.  Great art reduces the logos to its more ethereal ligatures only so as to have less to leave behind.  Its aim is upwards from Mount Parnassus to the stars.  I do not wish to be cloud, but rather an aurora.

But why illustrate the ‘square’ at all?  It is clearly not to aid the test-taker.  On the contrary, it is meant to promote confusion.  But this confusion is of a very specific form, and has a very specific agenda.

We are meant to have our loyalty to text challenged! The test forces us to ignore the beguiling image in favor of the text.  Only youth who have given up their imagistic gratification will succeed.  Only those who have accepted the substitute satisfaction of the logos and forsaken the world of images, those who care more for rules than dreams, more for grammar than smiles and tears, are deemed worthy of college.

I’d like to know why, and what this means.  I’d like to know how it has to do with math, the ultimate rules, and mythos, the keeper of dreams, and I’d like to find their points of contact.

Had I been questioned at the pizzeria, about my three fingers, my response would have been simple.  ”This is not three fingers!  I’m just showing you two slices.”