Tim Golden BandTech.com

2020-08-31 12:50:10 UTC

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PermalinkAbstract Algebra Broken

So this issue I can only repeat myself on so many times. Still I'll try another variation.

Possibly eventually you will be able to at least regurgitate my own position to yourself since my position is completely unchanged.

https://en.wikipedia.org/wiki/Closure_(mathematics)

https://en.wikipedia.org/wiki/Ring_(mathematics)

https://en.wikipedia.org/wiki/Binary_operation

These links all fit together. The ring construction is at the base of the curriculum of abstract algebra. It is treating the operators with extreme care. They are so carefully defined that they don't even require the usage of the terms 'multiply' and 'add' though that is exactly what these operators do in the real numbers.

After the careful construction of the ring from two groups, both operators obeying the closure principle, the polynomial is introduced with an 'X' that is not real, and then those polynomials are simply assigned real coefficients, but this operation has not been defined, for the multiplication of a real by a non-real value X is undefined within their own operator theory that was just so carefully constructed. The term

a1 X

is not a binary operation. It distinctly disobeys the closure requirement. Thus abstract algebra has only managed to rebuild a conundrum that even DesCartes trailed off on in his book Rules For The Direction Of The Mind. The sad part is that the weakness of the construction cannot be challenged. Your own impedance is a fine instance of a subconscious power that doctrine holds over us. We are en mass hypnotized. This obvious blunder within Abstract Algebra is a fine instance. It has nothing to do with polysign. Well, at least this argument holds with or without polysign. I just happen to have seen it through polysign, which brought me to Abstract Algebra. Still it is true that the ultimate behavior of the polynomial that they are after is the modulo effect, which is painfully constructed though the 'quotient' and the 'ideal' which to this day do not make sense to me. I suspect that the cause of the contaminated language is the flaws which they dodge. I have bumped into an online AA book that alludes to it but it has been some time.

To formalize this argument we should really take the acclaimed ring behaved

a0 + a1 X + a2 XX + ...

then assign an = 0 when n not equal to one. This then leaves us the ring behaved

a1 X

which is not ring behaved because it offends the closure principle. Now likewise each term in the polynomial can be attacked and after all they are a sum which in the ring definition requires that they all be in one set together. The entire polynomials fails under their own formalities.

Your own denial of this is fine, for this is also true of anyone else who has bumped into this falsification. Clearly the extent of the problem if I am correct does develop a philosophical statement on the modern human and its culture. The burden of credibility; particularly in a subject such as mathematics; the main burden of the modern student is of mimicry; something which humans excel at. Mimic the complexities of this subject and you can achieve an A grade and a future within academia. Deny the credibility of this subject and you will be shunned out of the system. Even within our own heads this bad dog relation is playing out as we are social animals and so the biblical nature of academia is established not only from without but from within. The developments of academia are more a method of fitting more and more PhDs than it is a pursuit of the truth. Such a branch as abstract algebra with its imperfections goes unchallenged in this arena for good reason. As one PhD steps on another PhDs subject as false the whole system will collapse its extraordinary accumulation. Should it collapse down to truth? I doubt it. I think we are more like monkeys in the tree still trying to figure out fundamental principles. We are only part way and we've landed ourselves in this morass.

We need to maintain these subjects as alive rather than as dead and pickled to perfection. Our past leaders should not be placed up on a mantle as unapproachable. The burden of their work is on us.