To those concerned that this post might delve into esoteric areas of Physics let me say, I put in all those fancy words in the title just for effects. However let me also admit that I am not above a bit of posing, posturing and showboating when it comes to that. So some references to Physics and Mathematics will be presented so as to impress the reader. Today you can find anything by googling. You must, however, know what to look for though.
We were taught in school that there is a Law of Conservation of Energy. Who has not memorized the words, "energy can be transformed from one form to another, but cannot be destroyed" without even understanding what it really meant or how it really worked. We were told that chemical energy from coal can be transformed into heat energy of steam which then can be transformed into kinetic energy by driving a great big engine. We accepted all that without questioning, despite also learning that these transformations were not 100% efficient and that there were always losses. Ah, those were the good days when you could accept something uncritically on the say so of teachers and elders. The problem is, today we are the elders and I am not sure what to say..
We were also told that the Law of Conservation of Momentum made billiard balls fall into different pockets or that in a line of suspended steel balls it made only the balls at the end move, or, in a macabre twist, prevented motor cars from stopping before travelling a certain distance when brakes were applied. The most mysterious of all was how Physicists divined the existence of unseen and unseeable particles and their properties based just on this Law.
We were told that there existed a whole menagerie of particles with all sorts of exotic names and possessed of weird properties. These were thought to exist based almost entirely on the conservation of something or the other. In the 1960s mankind's understanding of the universe was held together by gossamer threads linking weird particles, fields, forces, and suchlike, most of which one could not hear, see, feel or touch, only talk about. But we accepted their existence nevertheless, and the universe they represented.
At the centre of our knowledge was conservation of something or the other, which came about because of the "invariance" of some properties under certain "transformations". A very smart young lady, a rare female mathematician in a field overrun with men, came up with an original thought in the second decade of the twentieth century. Emmy Noether's work stated that if any system remained invariant under certain transformations, some property of it was conserved. The words are mine and admittedly imprecise.
For example if a system remained invariant under linear transformation in space or time, its linear momentum is conserved. If a system remained invariant under rotation then its angular momentum is conserved. And so on and so forth. Using mathematics Noether proved that Laws of Conservation were the result of invariance under transformation. The important thing to remember is that Conservation of something resulted from invariance under transformation.
Nearly a hundred years after Emmy Noether propounded her eponymous theorem, and many many particles, properties and universes later we have another type of Law of Conservation. This one is propounded and maintained by another female, albeit one of considerably inferior academic achievements, so inferior that you don't speak of this person and academic achievements in the same breath. Whereas Emmy was born to a mathematician father her modern-day equivalent was born to a bricklayer of shady credentials. Emmy was invited to University of Gottingen by luminaries such as David Hilbert and Felix Klein. Her modern day equivalent paid her way through a language school in Cambridge. The contrast couldn't be starker.
Both Emmy and her modern-day equivalent posited their own theories of conservation. For Emmy Conservation resulted from Invariance under Transformation.
For Sonia, conservation of family power is central to any transformation. Only transformations that ensure invariance of family power and which conserve family dynasty are allowed.
We were taught in school that there is a Law of Conservation of Energy. Who has not memorized the words, "energy can be transformed from one form to another, but cannot be destroyed" without even understanding what it really meant or how it really worked. We were told that chemical energy from coal can be transformed into heat energy of steam which then can be transformed into kinetic energy by driving a great big engine. We accepted all that without questioning, despite also learning that these transformations were not 100% efficient and that there were always losses. Ah, those were the good days when you could accept something uncritically on the say so of teachers and elders. The problem is, today we are the elders and I am not sure what to say..
We were also told that the Law of Conservation of Momentum made billiard balls fall into different pockets or that in a line of suspended steel balls it made only the balls at the end move, or, in a macabre twist, prevented motor cars from stopping before travelling a certain distance when brakes were applied. The most mysterious of all was how Physicists divined the existence of unseen and unseeable particles and their properties based just on this Law.
We were told that there existed a whole menagerie of particles with all sorts of exotic names and possessed of weird properties. These were thought to exist based almost entirely on the conservation of something or the other. In the 1960s mankind's understanding of the universe was held together by gossamer threads linking weird particles, fields, forces, and suchlike, most of which one could not hear, see, feel or touch, only talk about. But we accepted their existence nevertheless, and the universe they represented.
At the centre of our knowledge was conservation of something or the other, which came about because of the "invariance" of some properties under certain "transformations". A very smart young lady, a rare female mathematician in a field overrun with men, came up with an original thought in the second decade of the twentieth century. Emmy Noether's work stated that if any system remained invariant under certain transformations, some property of it was conserved. The words are mine and admittedly imprecise.
For example if a system remained invariant under linear transformation in space or time, its linear momentum is conserved. If a system remained invariant under rotation then its angular momentum is conserved. And so on and so forth. Using mathematics Noether proved that Laws of Conservation were the result of invariance under transformation. The important thing to remember is that Conservation of something resulted from invariance under transformation.
Nearly a hundred years after Emmy Noether propounded her eponymous theorem, and many many particles, properties and universes later we have another type of Law of Conservation. This one is propounded and maintained by another female, albeit one of considerably inferior academic achievements, so inferior that you don't speak of this person and academic achievements in the same breath. Whereas Emmy was born to a mathematician father her modern-day equivalent was born to a bricklayer of shady credentials. Emmy was invited to University of Gottingen by luminaries such as David Hilbert and Felix Klein. Her modern day equivalent paid her way through a language school in Cambridge. The contrast couldn't be starker.
Both Emmy and her modern-day equivalent posited their own theories of conservation. For Emmy Conservation resulted from Invariance under Transformation.
For Sonia, conservation of family power is central to any transformation. Only transformations that ensure invariance of family power and which conserve family dynasty are allowed.
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