Pythons within Pythons within … By Brian Simpson

     This is interesting; a python vomited up an even bigger python. It raises the question that inside the even bigger python is a larger one, and inside that a larger one yet, so that eventually, in the limit, there is a python so large as to fill the entire universe. So, how did that fit inside the original?

“A gigantic python was recently captured in photos vomiting up another, bigger python. This snake regurgitation happened in East Kimberley, Western Australia, according to local news site The New Daily. Kurt Jongedyk, the manager at Parry Creek Farm Tourist Resort and Caravan Park in the area, reportedly came across a 11.5- to 13-foot (3.5 to 4 meters) python and "relocated" it away from his house. At that point, the python began to "bring up its meal" — "an even fatter python of about the same length." Amanda Jongedyk took the photos, which were posted to the park’s Facebook page. [Photos: Python Chows Down on 3 Deer] Accounts of pythons eating other pythons turn out not to be that rare. Here's a National Geographic video of exactly this sort of snake cannibalism in action. And pythons are more than capable of swallowing larger animals, and even, in some awful cases, humans. Contrary to popular belief, snakes don't unhinge their jaws to swallow bigger critters. "One of the enduring myths about snake feeding mechanisms is the idea that the jaws detach," Patrick T. Gregory, a biology professor at the University of Victoria in Canada, previously told Live Science. "In fact, they stay connected all the time." But the two jaws move independently of one another, without the bony restrictions that you have with human jaw hinges. "The two mandibles are not joined at the front by a rigid [joint], as ours are, but by an elastic ligament that allows them to spread apart," Gregory said. In order to swallow snakes larger than themselves, Live Science previously reported, smaller snakes force their prey's spinal columns to bend in waves. That shrinks the swallowed snake's overall length, "packaging" it to fit in the predator snake's stomach."

     I know readers are going to find this strange, but there could be a mathematical reason for all of this, but I don’t understand it:

“The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in 3 dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball. Indeed, the reassembly process involves only moving the pieces around and rotating them without changing their shape. However, the pieces themselves are not "solids" in the usual sense, but infinite scatterings of points. The reconstruction can work with as few as five pieces. A stronger form of the theorem implies that given any two "reasonable" solid objects (such as a small ball and a huge ball), the cut pieces of either one can be reassembled into the other. This is often stated informally as "a pea can be chopped up and reassembled into the Sun" and called the "pea and the Sun paradox". The reason the Banach–Tarski theorem is called a paradox is that it contradicts basic geometric intuition. "Doubling the ball" by dividing it into parts and moving them around by rotations and translations, without any stretching, bending, or adding new points, seems to be impossible, since all these operations ought, intuitively speaking, to preserve the volume. The intuition that such operations preserve volumes is not mathematically absurd and it is even included in the formal definition of volumes. However, this is not applicable here because in this case it is impossible to define the volumes of the considered subsets. Reassembling them reproduces a volume, which happens to be different from the volume at the start. Unlike most theorems in geometry, the proof of this result depends in a critical way on the choice of axioms for set theory. It can be proven using the axiom of choice, which allows for the construction of non-measurable sets, i.e., collections of points that do not have a volume in the ordinary sense, and whose construction requires an uncountable number of choices. It was shown in 2005 that the pieces in the decomposition can be chosen in such a way that they can be moved continuously into place without running into one another."

     Here are some videos to watch on this, which are best consumed while drinking copious quantums of alcohol, which is well know to increase thinking ability. I think.

     Talk about mathe-magic!


All Blog Posts Authorised by K. W. Grundy
13 Carsten Court, Happy Valley, SA.



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Wednesday, 17 August 2022