Aeon by Antony & the Johnsons

Time to cry, babies.

(Source: http://www.youtube.com/)

Illustration by Andy Gilmore. via thomasbirdblog

What are you doing New Year’s Eve performed by Rufus Wainwright

(Source: http://www.youtube.com/)

Emmett Williams – 09 Duet, 1968

Duet by Emmett Williams

ember of my member, eel of my feel. fort of my effort, flexibility of my inflexibility. hymn of my whim. kin of my skin. licker of my flicker, lapstick of my slapstick. mission of my emission. orpheus of my morpheus. quash of my squash, quiescence of my acquiescence.

Come Softly by Grouper

(Source: http://www.youtube.com/)

The word “Evolution” nowadays suggests “evolution of organisms by natural selection as per Darwin & modern population genetics”.

But what about other kinds of evolution? Any unary endomorphism from a system onto itself, applied over and over to generate “time”, could be considered a kind of “evolution”.

• Crystals and quasicrystals evolve naturally.
• Caves and stalagmites evolve naturally.
• History evolves artificially … although no-one knows the mapping.
• Art evolves artificially … again, no-one knows the mapping. (but we know there is cross-pollination. Could we call it “Art sex”?)
• Proto-biological chemical compounds, like basic amino acids, “evolved” by a method similar to natural selection.
• Businesses (and entrepreneurs) that grow through trial-and-error, evolve their ideas and their business processes by artificial selection.
• Romantic relationships evolve. Any human relationship evolves. Sometimes “a” relationship can evolve with a group of people as-a-unit. But here I’ve found the selection to be more exogenous than endogenous. Friendships seem to pick up exactly where they left off γᵢ(Tᵢ) rather than be pitched to the dustbin of 0. Even romantic relationships seem to hang mostly where they were, even after a breakup. Perhaps the breakup zeroes the romantic part ⌊γᵢ⌋ᵣ, but everything else—sexual chemistry, personality dynamics, humour dynamics, and history—remains stubbornly unbudged by a breakup per se.
• And like I said, any endomorphism, repeatedly applied to a system, could count as “evolution”. (An endomorphism draws both the input and the output from the same domain, i.e. ƒ: X→X.) If there is a throw-away criterion (mapping ↦ 0), we could call that “selection”. Any fixed point of the mapping ƒ(p)↦p is an endpoint of evolution.
   

In this video, John Baez talks about how the inherent interestingness of the number 5 has made itself apparent to us through several processes:

• artists (mosque designers) discovered it. God speaks to us in the language of mathematics, remember?
• crystals and quasicrystals discovered 5 by evolution — but not the biological kind
• soot and space dust found ⬟, also by natural non-bio evolution
• BTW, unrelated but some Scots (perhaps Picts) carved some Platonic solids out of stone centuries before Plato … so perhaps they should be called Scottish solids.
• the Pariacoto virus found ⬟ by biological evolution
• Roger Penrose (a mathematical physicist) discovered & described 5-way symmetry in modern mathematical (group theoretic) terms

In each case, logic is the canvas. Art — nature — mathematicians are the painters.

(Source: http://www.youtube.com/)

[T]he question of what “really” exists pervades the sciences and human thought in general.

The belief that the infinite does not really exist goes back at least to Aristotle. Parrnenides even questioned the reality of plurality and change. (Einstein’s vision has much in common with Parmenides). Towards the end of the nineteenth century an acrimonious exchange took place between Kronecker and Cantor regarding the reality of the actual (as opposed to potential) infinite. Kronecker claimed that only the finite integers really exist and all else is merely the work of man.

Cantor countered that the essence of mathematics was its freedom and that he had attained a larger vision than Kronecker had who could not see the infinite. Most mathematicians have followed Cantor and found his paradise a more beautiful and alluring universe.

…. But this seeing is not explained by modus ponens. In his beautiful book Proofs and Refutations, Lakatos (1976) has shown that the mathematical process itself is dialectical and not Euclidean. At all times our ideas are formally inconsistent. But inconsistency, while still recognized as a pathology, is no longer seen to be a fatal disease. If we come across a contradiction, we localize it, isolate it, and try to cure it. But we have to get over our neurotic phobias concerning this disease and recognize it as inseparable from life itself.

David A Edwards

In the 1930s, almost 10 percent of [American] Christmas spending was financed with money squirreled away into Christmas clubs—bank accounts … helping consumers save for the holiday. Participants promised to contribute weekly, frequently as little as $0.25 at a time. …

Since 1970, by contrast, the explosive growth in consumer credit has had the opposite effect, helping consumers fall prey to their lack of self-control when it comes to borrowing. In recent years, one-third of [American] holiday spending is still not paid off two months after Christmas.

Joel Waldfogel

3-D fly-through of a supernova, seen in the X-ray spectrum

(Source: http://www.youtube.com/)