{'fraction_non_alphanumeric': 0.026752767527675275, 'fraction_numerical': 0.0018450184501845018, 'mean_word_length': 4.961538461538462, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
The tangled web of self-tying knots

Mathematician Leopold Kronecker stated “God created the integers, all else is the work of man,” alluding to the fact that the natural numbers most likely arose from physical counting, as in one's fingers or goats in the pasture. Topology, however, is arguably a different creature altogether and may have had its own independent origins from the physical world in the ubiquitous knot—something that cannot be undone without using the free ends because the individual strands cannot move through each other (1). One imagines a primordial knot getting tied accidentally in Cro-Magnon times and then tugged at to no avail … perhaps eventually cut. Of course, knots went on to have their uses in early societies, still far from any theoretical considerations but very much related to their ability to bind or secure things such as animals, sails, hair, etc. Knotted strings were also used by the Inca civilization for record-keeping and possibly even communication (2), still a few centuries before Euler began counting bridge-crossings in Konigsberg.