Ever complained about the academic daily routine having become a quest for the best journal that would nevertheless accept one's half-cooked manuscript? Ever felt that citations and impact factors were way too overrated, and that selectivity should prevail? Look no further, as it is my pleasure to share my recent discovery of (arguably) the best journal ever!
With an acceptance rate way lower than 1%, the journal of universal rejection may rightfully pride itself of enforcing the strictest of academic standards (Nature beware!). Created in 2009, the journal solicits submissions in poetry, prose, visual art, and research. Despite such a wide scope, its widely competent editorial board can be trusted to lay an expert eye on your submission, and helpfully motivate its final decision.
Today is the day I almost died laughing while reading Scott Aaronson's Shtetl-Optimized blog dedicated to Complexity Theory. Ok, I know, this sort of humor alone may be regarded as a conclusive diagnostic by future generations of psychopathologists, but I'd still like to share his beautiful, human-centric, argument for why P != NP. Basically, he is asked the question:
He starts by stating the question in four informal ways, one of which is:
and adds
I woke up the following morning at the hospital, and must be clinicaly monitored during any future access to Scott's blog, but I encourage you to check it out for a daily dose of CS wittiness.
Amicable numbers are members of the number theory zoology (See their Wikipedia page), which, like trousers and all sorts of useful stuff, come handy in pairs. Formally, one starts by defining the restricted divisor function s(n) to be the sum of all divisors of n, itself excepted.
For instance for n = 220, one finds
Then, amicable numbers are pairs of natural numbers (p,q) such that s(p) = q and s(q) = p.
To make this notion explicit, we get back to the example above and find
and therefore (220,284) are amicable numbers.
Now there is something about this definition that may sound arbitrarily limited to a computer scientist. Indeed, consider the (infinite) directed graph whose vertices are natural numbers, and whose edges are pairs (n,s(n))): One then easily sees that amicable numbers are in bijection with cycles of length 2 in the graph. This raises the question
Indeed, one can alternatively, yet equivalently, define amicable numbers as pairs
which naturally generalizes into what is called sociable numbers, i.e. k-tuples of numbers
For k=1, sociable numbers are perfect numbers.
For k=2, sociable numbers are amicable numbers.
In general, what are sociable numbers of cycle length k? Do they even exist for large values of k?
Whether there exists a cycle-free infinite sequence of iterations of s is currently open!