Umberto, I wonder if this is not the time and place to apply a bit of
chaos theory. Since pig canines grow as segments not of simple arcs but of
spirals, one should be able to treat them as Stephen Jay Gould et
colleagues long ago treated coiled snail shells, and so forth. In other
words, the older the pig the farther out on the spiral the base of the
tooth should lie. You could set the tooth on the spiral even if all you
had was just a chunk of it, broken at both ends. And I would be willing to
bet you that the distances between successive coils of the spiral upon
which the pig tusk grows will turn out to be elements in the Fibonacci
series, as they are for other natural coils.

Over the years, I have been inspired again and again by Gyorgy Doczi's
"The Power of Limits: Proportional Harmonies in Nature, Art, and
Architecture", and I await the day when somebody develops an easy-to-use
(and hopefully downloadable!) algorithm to apply Mandelbrot's very simple,
elegant equation for calculating the fractal number of a squiggly line.
Mandelbrot told me himself, when I long ago wrote to him about it, that he
didn't think that the squiggly line represented by, say, the silhouette
outline of a femur, would turn out to have a unique fractal number; but
even if it did not, I can think of twenty practical ways around that so as
to still enable it to be a useful descriptive and analytical technique.

I frankly hate measuring bones and teeth. We cannot get "there" from here,
you see, no matter how eloquently you have argued, Umberto, for the
necessity of quantification in zooarchaeological studies. After all, it is
only statistics and the mis-use of statistics, at that. But it's the tone
of the times, the Giant of the Age as C.S. Lewis would call it, and we are
all enthralled in the Giant's dungeon.

We "cannot get there from here" because no number can describe shape, and
there is no exact formula for any curving figure, nay though you tell me
that there is Pi; for I will reply that there is a reason why Pi is called
an "irrational" number. You will be able to argue me out of this only when
the supercomputer resolves Pi, to however many gazillions of places. Pi
helped the old Egyptians order the right amount of lumber, within a couple
of inches or board-feet, when they wanted to build a roundpen for a
ceremonial bullfight. And calculus, in all its many forms dependent upon
the limit-function, can calculate "to infinity", which means, however, not
only "infinitely close" but also paradoxically and inesecapably,
"infinitely far away". We cannot get there from here; it is the Giant of
the Age but also the Giant's Stairway Conundrum and we are trapped there,
albeit at a higher geometric level, than the Flatlanders. Maybe in the
next plane of existence we will be allowed to precisely calculate curving
figures in the same sense that we can precisely calculate a triangle, a
rectangle, or a square, that is, without the use of a "fudge factor"
(synonym of "irrational number").

Meanwhile, though, if I have to measure stuff in order to maintain my
reputation as a properly-trained and societally-well approved so-called
'hard' scientist, I'd rather be using fractals, because they're pretty and
elegant and kaleidoscopic, even though they're just as much limit
functions as Fourier Chains or Stretch Calculus. So maybe there will be
somebody on this list who is a real mathematician, tolerant of this old
screwball who only whips out the calipers in order to conform, while
knowing all the time in my heart of hearts that the best way to compare
skulls or teeth is to make GOOD SCALE DRAWINGS and then let the world's
most powerful shape-processor, the trained human brain, do all the
analyzing that will ever be worth a hoot.

I would measure the boar's tusks, though, Umberto, after making a spiral
template, because I do want to know how far apart the spirals are and
where on it the particular specimen lies, for I don't think my eye is as
good as millimeters as to calibration. Cheers -- Dr. Deb

> Dear Fiona,
>
> I suspect that you will find that pig canines are very difficult to
> measure.
> Male canines in particular, due to their open roots, do not provide
> reliable
> lengths and, even in females, lengths can only be measured when the tooth
> is
> isolated and unworn. Cross section measurements are equally problematic as
> it
> is difficult to define at what level the measurement should be taken. The
> base,
> which is often used as a reference point in other teeth, is of little use
> in
> male canines as it grows constantly and is often broken. I guess that
> weight
> may theoretically be one way round, but then you'll have to be sure that
> the
> tooth is 100% complete and that, being hollow, it does not contain any
> soil or
> concretions - and, even then, different levels of mineralisations can
> affect
> the result.
>
> Should anybody have a well tested suggestion about how to reliably and
> consistently measure pig canines I'd be interested to hear.
>
> Cheers
> Umberto
>
>
> --
> Umberto Albarella
> Department of Archaeology
> University of Sheffield
> Northgate House
> West Street
> Sheffield S1 4ET
> United Kingdom
> Telephone: (+) 44 (0) 114 22 22 943
> Fax: (+) 44 (0) 114 27 22 563
> http://www.shef.ac.uk/archaeology/staff/albarella.html
> For Archaeologists for Global Justice (AGJ) see:
> http://www.shef.ac.uk/archaeology/global-justice.html
>
> "only when the last tree has died and the last river been poisoned
> and the last fish been caught we will realise we cannot eat money"
>
>
>