Still, January ?

Mathematics as, " the subject in which we never know what we are talking about, nor whether what we are saying is true". , quote from Bertrand Russell .which I associate with group theory.

This is all about why do ground hogs, really care about their shadows, from a slightly different angle, and inspired by what seemed like a Penrose talk on Paul Dirac, and what a physicist , might mean by " Sea " ?


So, during a " stint ", in college I worked on a paper, " Groups of Order, Less Than 100 " .


Apparently , to my knowledge , there are no groups of order less than zero.  But, right now, I would like to concentrate .  by which I mean focus on groups of order 4, like the Beatles, but from a slightly more mathematical way, than Beatles are generally thought of.

I am going out on a limb , but I doubt there is a good way to count all the groups of order 4, either , mathematically or musically.. but one thing about them , all is that they have an identity, all they all contained 4 members, or elements.   This is connected to an idea, which is called Isomorphism.

Now, in the mathematical context, well , let me say this:

For some reason, maybe sanity, we never talk about groups with a negative number of elements. or zero, but  , for obvious reasons a group of order 4 can never have more than , 4 elements.  ?????

And so the big difference between the Beatles , and a mathematical group of order 4, is mostly, the interactions with in the group, don't really affect anything outside themselves, which is like " closure ", not to be confused with " clojure " ?

And , the point to this is that inherent in all this is the essence of the why the idea of " structure ", specifically as in the form of rules, can be somewhat misleading and  confusing, because it has to do with how generally we are able to " sort " things out, on a pretty fundamental level, which includes various activities in our lives, like religion,  politics, building things, walking or even drinking water,

The point is that unlike a group of order 1,2, or 3, there must always be, two distinctly different groups of order 4, a rather disturbing notion , to be sure.


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