Tuesday, March 15, 2016

Timurlengia’s failed proof of the Urysohn Metrization Theorem

The scientific world is abuzz with this late-breaking discovery, of a small but “brainy” ancestor of the giant, feared  Tyrannosaurus rex:

Fossil Hints T. Rex Got Smart Before It Got Big

Seasoned readers of popular science news -- which often contains much speculation and puffery -- will be rightly skeptical, as to how in heaven’s name  paleontologists could deduce that some crumpled heap of fossil bones corresponded to a creature with superior intelligence -- after all, none of the soft cerebral material has survived, let alone its noetic capabilities.   Even the sheer size of the brain cavity -- a highly imperfect indicator -- can hardly be in play here, since the creature, Timurlengia euotica,  was far smaller than its T. rex descendents, with a cranium to scale.

The answer -- not surprising once you think of it -- lies not in the conformation of the bones themselves, which tell us virtually nothing about intellectual capacity, but rather in what was found with those bones -- just as Cro-magnon or Neanderthal skeletons buried with particular styles of flint tools, provide a window into their industry.

In the case of Timurlengia,  the bones are rather ill-preserved, except for the right forepaw, which, holding a fragment of carbon, is stretched towards a stone tablet, on which is sketched the outline of a proof of the Urysohn Metrization Theorem.  Tragically, the creature never lived to the Q.E.D.
(Additionally, some tefillin found near the body  indicate the creature may have been Jewish.)

Scientists point out that this achievement, which will doubtless impress the peanut gallery, is not quite as impressive as it looks:  since, in the case of Timurlengia, the form of the proposed theorem ran:  “Every space that is regular and first-countable  is metrizable.”   We ourselves, better instructed, sadly shake our heads.  In that guise, the theorem does not go through:  second-countability is required.
Nice try, though, Tim.

At all events, this intellectual career, however impressive or otherwise, was destined to be short-lived.  The hormones kicked in, the youngster shot up, and quickly evolved into that massive Jurassic bully we all know and loathe, the aptly named Tyrannosaur.  From then on, intellectual endeavors fell by the wayside, as T. rex was able to make a living much more simply  by stealing lunch-money from the other dinosaurs.

~  The World of Dr Justice ~
~~  Science U Can Trust  ™ ~~

For additional, extraordinarily reliable paleontological reporting, try this:

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