Adrian's Science Blog

a darkened tinge of orange the screen dots dance so soft eyes relaxed and backs untaxed we lay here, on the bedspread forgot the world beyond the glass tap tap, tap tap, it loves me do I love it? I guess I did. It's in my hands, regardless ---------------------- there's tension in my shoulder blades as I type the text you read here you feel the tingle down my spine when I tell you how it feels. oh dear, i fear you've come to near a poet with his people. I swear the day we come to bear you'll know me more than i do ---------------------------- I see the sea so near to me horizontal lines soon broken mondrian v. adrian the sage man's songs forgotten The pier of madness  picasso's one floodlights caught me fishing I wish the day would come to bear where I caught it and it liked me ------------------------------ a decent day it's one to play I tried to and I didn't a sun so bright it saps the light right out me and I hate it --------------------------- ...

An Isomorphism is the mathematical concept that generalizes ‘equality’.   ‘Equality’ is just as it was presented in middle school, there is an equal sign and an expression on each side. Like so: 3x = y This means that 3x is precisely equal to y. Anywhere you see 3x you can substitute y, and vice versa.  But this type of equality, while intuitive, is constraining. In reality, we see things that are the ‘same’, but not precisely. You might really want to say that these things are equal, but they don’t satisfy our intuitive definition, ie. you can’t switch one out for the other willy-nilly. For example, the Golden Gate Bridge in San Francisco and the George Washington Bridge in New York. These are both clearly bridges, so they are the ‘same’ in some sense, but not exactly. You can’t magically change the Golden Gate Bridge to the George Washington Bridge, they were specifically designed to be built in one place.  So can we capture this equivalence? What does it actual...