Geometry does something for me that mathematical notation cannot. It connects me to the world, and makes me feel alive and vibrant, interactive and pungent. the putative part of computation ,and the manhandling part of manipulation are all thrilling and engaging parts of living and breathing and thinking, and apprehension in this form is precursor to comprehension in any form.
Geometry plugs me in, wires me up and sets my senses sizzling, my taste buds popping and my juices flowing, just like the merest frissance of a delectable essence or spice.
that this is as equally valid an experience of "mathematics" in the world is not evident because i was robbed when younger, and some of our children a re being robbed today of the relevance of mathematics, because all they are being given o are getting is dried up, burnt to a crisp overcooked spaghetti of a notation, without any sauce even!
And I am supposed to digest that? No way Jose!
Geometry for me was given the same dessicated treatment, but somehow of all my mathematical mis-education it still shines through as engaging, constructive and intriguing. And this is from what i learned in primary school!
I never rated geometry as i do now,because i was misled into thinking it was old stuff, not relevant to new mathematics, or modern thinking! How absurd that seems to write!
As i grew little snippets filtered through about how some real greats of history read classics and Plato and Euclid's geometry, but i never was shaken from my blinded stupor.
Jakob Steiner railed against the algebraists, and now i know why. The encrusting notation , like barnacles has sunk the noble ship of geometrical mathematics, and the direct proprioceptive link to reality, notFS has been eviscerated from our beings by cotton wool, stringy notational predilections!
Newton Was perhaps the greatest synthetic geometer that most people are unaware of, Thinking, and being taught that his "genius" came out of "nowhere". But as Newton himself observed, he stood on the shoulders of Geometry giants!
Reality and the interactions within our experience of reality are all firmly described and appreciable in geometry. All science in fact is in a very real sense geometry or derivations from geometry.
So wake up with me this morning to a beautiful world view in which geometry explains and makes sense of everything in your experience in a direct and and fundamental way, and do not be fooled by those who would have you think that wisdom is only expressed in words.
Any artisan can make as much or more of a profound statement about reality as any noble scientist or mathematician.
Manipume rule! Let's Rock!