One of the more humorous sides to numbers is mathematicians’ attempts to categorise numbers as “interesting” or “dull”. For example, 1 is interesting because it is the first positive integer. 73 is interesting because it is the 21st prime number and 21 is a multiple of 7 and 3. The number 1729 is a good example of how a number can seem dull but later found to be interesting. When the British mathematician G. H. Hardy visited Indian mathematician Srinivasa Ramanujan, he commented that the number of the taxicab he rode in on was 1729 – a number he found to be rather dull. Ramanujan objected and stated it is very interesting as it is the smallest number expressible as the sum of two cubes in two different ways (1729 = 1³ + 12³ = 9³ + 10³). Such numbers are now referred to as taxicab numbers and 1729 is called the Hardy-Ramanujan number.
A way to discover the smallest most uninteresting number is through the Online Encyclopaedia of Integer Sequences, which documents every integer worth noting as it is in some sort of arithmetic sequence. The smallest integer that does not appear in this encyclopaedia as part of a sequence could be considered as objectively the smallest “uninteresting” number. In 2009, this number was 11630, but has since changed to 12407, then 13794 and now 14228 (22 April 2014).
But paradoxically, the smallest uninteresting number is interesting in itself by being the smallest most uninteresting number. This is known as the interesting number paradox. By this paradox, every natural number is unique and ergo, “interesting”.
(Image source: http://www.xkcd.com/899/, and here’s an explanation of some of the numbers on it)
There are many interesting medical facts regarding sleep, but there are strange pathologies that stand out even more from them.
Sometimes, cases resembling sleepwalking are reported, where the patient unconsciously has sexual intercourse with someone else. After waking up, the patient has no recollection of the event, and thus may face a very awkward situation the following morning.
Sexsomnia, or sleep sex, is a rare sleep disorder; to be more specific, it is a type of NREM parasomnia (performing complex actions while asleep). This disorder is quite different from REM sleep disorder, as no dreaming occurs during NREM sleep. Therefore, the sexual behaviour is not due to the influence of an erotic dream, but rather the primitive brain functions acting on basic instincts, as higher brain functions are shut down during NREM sleep. According to reports, sexsomniacs act almost lucidly during episodes.
As it was discovered quite recently, less than 15 years ago, it is under heavy research. However, due to patients feeling too ashamed of the disease or not remembering the events, the number of reported cases is low.
This disease is not directly harmful to the patient, but it can be very problematic socially. It ruins relationships and may even lead to rape. But as the law defines rape as “a conscious act”, sexsomnia is often used as a defence in trials. It is important to note that it occurs in both men and women. Within relationships, the general complaint is not that of rape, but rather exhaustion.
Interestingly, as the primitive brain is not being controlled during the episodes, sleep sex is known to be more vigorous than normal sex. Due to this, patients and their partners often exhibit carpet burns.