Brandymore Castle

The heart of OCD is a feeling of "not being right" or repeating a ritual until it "feels right." A creative mathematician experiences intuition as a feeling there is "something going on here but I don't know what it is" according to William Byers in How Mathematicians Think. You were probably taught in high school that mathematics is a rigorous and logical endeavor and that for every mathematical principle there is a proof. It was implied to you that mathematicians seek out new principles by following threads of logic from an existing proof to a new proof. You were taught a myth. Most mathematical breakthroughs began with an intuition. Only later, after the instruction was explored well enough to believe it was true, to believe it was worth proving, perhaps even after it was proved to the satisfaction of the mathematician was an "official" proof created for the record. Proof comes after the fact, not before it. An interesting relationship bet...

I have a suspicion the near 4:3 ratios of the traditional photographic print sizes (probably based on traditional canvas sizes, but I am unsure of this...it seems likely) emerged due to a concentration of photography on portraiture in its early days and that photography adapted the canvas sizes used in painting, which very likely emerged out of portraiture. I am not entirely sure of this, but it seems reasonable to assume the majority of traditional paintings, as painting emerged in the Renaissance as an important feature of Western art, were portraits at first. The landscape I assume is a later invention as nature began to be seen less of a threat to life and more as an enjoyable extension of human space. We have to remember that nature, i.e. the forest, was a terrifying place for our ancestors and only in the 19th century did the modern conceit of the 'pastoral' emerge. So I hazard that most paintings were portraits. I doubt many of the first patrons wanted paintings of the l...