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A matter of expression

I was visiting with my esteemed colleague Luigi Costantini in Italy – practicing safe social email-distancing of course – and the topic of expressions came up.

Namely, how the internet has influenced symbology.

Our topic was Refractive index, which happens to pair nicely with a glass of Chianti. Stated in “Boringlish” (the official language of Yawnland) refractive index measures the bending of a ray of light when it passes from one medium into another – where i is the angle of incidence of a ray in vacuum perpendicular to a medium’s surface, called the normal, and r is the angle of refraction.

Refractive index n can be defined as the ratio of the sine of the angle of incidence to the sine of the angle of refraction:

n = sin i / sin r

Image credit: Particle Tech Labs

So far so good.

Refractive index n can also be expressed as the velocity of light c of a given wavelength in empty space divided by its velocity v in a substance. That expression is classically notated like this:

Hold on a minute. Something’s wrong. I want to email this to my little brother, but can’t seem find that old classical chalkboard notation (c over a line over a v) anywhere on my computer for email-typing. Oh well. I suppose I’ll modernize it to n = c/v

The ordinary and the extraordinary

Without getting into an exposition on birefringence  – which calls for a heartier red wine (from the Yawnland valley) – in certain materials refractive index n depends on the polarization and propagation direction of the light rays. Light with linear polarization perpendicular to the optical axis of the medium will experience ordinary refractive index while light polarized in parallel will experience extraordinary refractive index.

In classical notation, the Greek letters omega and epsilon were used to identify n ordinary (omega small case) versus n extraordinary (epsilon).

Away from the chalkboard, however, there are computer fonts which don’t include Greek characters. When omega and epsilon present themselves, applications using those fonts become disoriented and confused and wind up showing them as n?= and n?= which is a #fail.

Subscript substitute

Okay. We can overcome that problem by employing common Latin characters, combined with subscript so that n ordinary values are indicated with subscript “o” and n extraordinary with subscript “e”.

Hey hey! Now these expressions appear properly in all fonts throughout the western world. They are even used on the Refractive Index Wikipedia page, which kinda makes them internet-official.

Oops, we did it again.

Guess what? Globalization is a real thing. It turns out, while superscript and subscript are groovy and copacetic in the western world, the internet goes east, south and north too. So, applications which convert Latin characters to non-Latin script alphabets recognize the characters, but don’t capisce subscript… Aye yai yai.

The virtual “reality”

To accommodate the world’s vast array of devices, languages and applications, n ordinary and extraordinary are being expressed like this.

And if RI or n is used in a preceding sentence it gets shortened to this, even.

The irony?

In an effort to advance scientific communications we have reduced these beautiful, florid symbols – paying homage to great ancient civilizations – to coarse common letters. In effect, we have diluted the most complex scientific formulas into… Wait for it… The least expressive expressions.

Read that last sentence again.

I’m having another Chianti. Cheers.

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