Saturday, July 6, 2013
thought for the day/ ancient knowledge mathematically defined
Image Credit & Copyright: Adam Block, Mt. Lemmon SkyCenter, U. Arizona
I defined ancient knowledge in the previous incarnation of my blog. I had said how three hundred years defines ancient knowledge. A full human lifetime appears to be about a hundred years. So, two hundred years is certainly a previous human generation, but to go beyond human memory, we should go to three hundred years. This is not a very mathematical definition of ancient knowledge, but it's interesting. Recently, I was rereading John D. Barrow's "Pi in the Sky" to review once again the origin of mathematical knowledge and compare to Jacob Bronowski's ideas in his "Origins of Knowledge and Imagination."
I've always said that chapter two, "The Counter Culture", is worth the price of the book. It's about seventy pages about tally bones found thirty thousand years ago to base two and five and all the number linguistics. Reading it, you appreciate that the primitive numbers of the Egyptians and Mesopotamians(who went much further algebraically than the Egyptians) were a sophisticated development that required a long period of development. In rereading that chapter, I found some interesting stuff about the number three.
Three meant beyond. In latin, there's trans and tres. Tres is three, and trans is beyond. In French, we have trois and tres. Trois is three, and tres is "very". The anthropologists of the eighteen hundreds and early nineteen hundreds(just like the Golden Bough, you can't even do some of this research anymore. The education of peoples throughout the world is kindof erasing this knowledge) found tribes in Islands, Africa and the like who had words for one, two, and then many, or beyond.
Well, I find it kind of interesting that my idea for defining ancient knowledge corresponds numberwise with the significance of the number three at one time tens of thousands of years ago.
So, if three hundred years is the standard for ancient knowledge, how much knowledge is ancient today? Well, due to our young species, very little is ancient knowledge! Three hundred years ago was of course around early 1700. Right now that's 1713. At that time, differential equations were still exercising the best efforts of mathematicians. This is all the mathematics past a first and maybe a second semester calculus class. Basically, the mathematics and Physics of Isaac Newton is now ancient knowledge, and almost nothing afterwards! The seventeen hundreds was dominated by Euler but had some other underrated mathematicians like Lagrange. The seventeen hundreds closed with the publication of Laplaces vast generalization of Newton's "Principia." Basically, after Isaac Newton, mathematians created a vast amount of differential equations, calculus of variations, some beginnings of complex analyses, number theory beyond Fermat. Laplaces "Celestial Mechanics" generalizes Newton's "Principia" with all that mathematics. It goes to five thousand page each volumes; it was obsolete the day it was published. William Hamilton, discoverer of quaternions, made an early name for himself by finding a single mistake in it all. The majority of all that knowledge is not quite ancient knowledge.
In the eighteen hundreds. A Cantor, not the George Cantor of transfinite numbers fame in the same century, published a technical history of mathematics up to the eighteen hundreds. It went to four thick volumes. The eighteen hundreds of course saw mathematics go abstract - abstract or alternative algebras, abstract geometries, or non-Euclidean geometries and projective geometry to unify them all. The eighteen hundreds had mathematicians breaking free of all the rules and making them on their own. Analyses of course continued to develop as it does so today. Technical histories of eighteen hundreds mathematics are still coming out today. The collective works of Leondard Euler are still not quite complete. The point is of course the vast majority of mathematical knowledge is not ancient knowledge.
-------------------------------------------science/tech goodie extras
When Eric Drexler first started thinking about nanomanufacturing, he innovated artificial proteins. He knew the idea of making smaller machines to make smaller machines all the way down to single atoms is a long road. Nobody then seemed to be able to make complete characterization of ribosomes(natural nanomachines that make nanotechnologies - proteins). Proteins that could self-assemble into nanomachines seemed a bit far fetched as well. But, he thought of a way to maybe make that more practical than ribosomes. Today, making artificial proteins has become reliable enough, but nanotechnologists are not so excited about them as they are about peptides . Still, this breakthrough in Ribosomes is kind of exciting.
SpaceX has done a pretty good job bringing down the price of space rocketry. But others have made even more breakthroughs. One other space company has innovated pistons instead of turbopumps for rocketry. Here, nasa has created composite cryogenic fuel tanks. My only problem with all this is everyone is keeping their innovations to themselves. Imagine combining everyone's ideas where possible! England has these jet engine/rocket engine hypbrid innovations. I recall they use superconductors to cool incoming air.