## The algebrista

If you like geeky TV shows, I particularly recommend Bones s06ep08 entitled “The Twisted Bones in the Melted Truck”. The title alone should convince the best of you who know that it is impossible to twist bones because *bones don’t melt* ! But these guys are the specialists, so they will really find twisted bones and even provide a scientific explanation to that [1]. What’s even stronger is that they untwist them just for your pleasure. Check this out !

*ALL THE RIGHTS OF THE CLIPS BELONG TO THE CHANNEL FOX. This video is used for comment purpose of Bones season 6 episode 8 where it is stated that Gerolamo Cardano wrote a set of mathematical equations to describe the skeleton system. Believing that comment and critique are at the very core of the fair use doctrine as a safeguard for freedom of expression, we claim it is a fair use under copyright law.*

I should confess that I wasn’t familiar with Gerolamo Cardano prior to this. Cardano is a famous algebraist known for his publication of the solutions to the cubic and quartic equations. And as there is no general algebraic solution to polynomial equations of degree five or higher [2], Cardano couldn’t do more. Besides he was the first to publish the use of complex numbers in calculations even if he did not understand their properties. Among his many other contributions, he invented the Cardan shaft with universal joints and published the horoscope of Jesus… Concerning the set of mathematical equations written by Cardano to describe the skeleton system mentioned in this episode of Bones, I found no reference of their existence.

If Cardano didn’t publish such equations, why did the scriptwriters made reference to him there ? They have obviously done some research, but maybe it’s a confusion due to the fact that in Biomechanics, angles named “cardan angles” can be used to describe the kinematic of the limbs [3]. Another plausible explanation can be found looking for the etymology of the word “algebra”. It comes from Arabic al-jebr and refers to the setting or the straightening out of broken bones, to the “reduction” of a fracture. In Spanish “algebrista” still designs a bonesetter. In Mathematics, the word has been introduced in 820 by al-Khwārizmī to describe the operations of “reduction” and balancing, i.e. the cancellation of like terms on opposite sides of the equation* *[4]. Nowadays one still talks of “reducing” fractions to lowest terms. Knowing this, Cardano’s 1545 book title *Artis Magnæ, Sive de Regulis Algebraicis* could be translated by *About The Great Art, or The Rules of Bone Setting*… (Mmmmh…) A bit too subtle maybe?

**Notes**

- See K. Killgrove comments about that.
- Abel’s impossibility theorem
- S. J. Tupling and M. R. Pierrynowski, “Use of cardan angles to locate rigid bodies in three-dimensional space”, Medical and Biological Engineering and Computing, Vol. 25, Nb. 5, pp. 527-532, 1987.
- C. B. Boyer and U. C. Merzbach, “A History of Mathematics”, second edition, John Wiley & Sons, 1991, ISBN0471543977.

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