{∅, {∅}, {∅, {∅}}} : Rage Against the Meat Grinder

The geometry proofs are not coming naturally to me.

The psychology is interesting.  I mean, I never felt ashamed studying integral calculus or differential equations no matter how many times I referred to the solution manuals.

And yet, with the geometry, well, I don't know.  It surely has deflated my ego quite a bit.   I know that this was my intention all along, but I am not sure I am all that delighted about how accurate my assessment had been (as far as my need of a total overhaul and re-education) in a rigorous manner.

It has been humbling, but I am not reacting in an emotionally immature manner.  In fact, now I am sure that this has been the right way to proceed for me, that is, to rebuild my skills using the texts I hunted down before becoming too engrossed with physics and advanced mathematics.

I just have to not be too hard on myself.

When I find myself wondering what kind of life I am living, I resist the tendency to become depressed and force myself to look upon these days and years as an unusual opportunity.   I do not trust the suggestions of most people on the Internet as far as using these online courses.  I have my own plan and my own agenda IF THEY DON'T MIND. 

There was another author besides Docliani who may have been even more radical in his axiomatic approach, a certain Frank Allen ... his books are even harder to track down than the Dolciani series (and forget about the solution keys!) ... I found an inexpensive copy of a geometry text by him from 1973 (An Introduction to Proofs) as well as an old copy of a 1970 Algebra with Trigonometry: A Logical Approach. 

You see, I am not just interested in "high school mathematics," but a specific way of presenting the material with set-builder notation and the inclusion of axioms.  Even though I find it difficult, I figure that with continual exposure to it, I will eventually merge with the Weirdness of it all.

from a comment at Amazon left in 2007:

I have an MS in Math from Ohio State, and my wife and I home school our three children. We've been home schooling now for several years and it is approaching time for us to figure out our algebra/geometry/trig (or the equivalent) program. As a former graduate student in math, I know about this thing out there lurking under the surface of college math. It is the proof, of course. Somehow what a "proof" is, what "math" is, and what it is all good for has all gotten extraordinarly lost in a way that goes far beyond even the scope of secondary school education.

This basic problem can be heard reverberating in ancient videos of Feynman lecturing to the public on the role of mathematics in physics (and how rigor is not particularly useful). It can be seen in the mathematics curricula of undergraduate programs all over the nation that pander to other departments' needs, cutting out most of the actual math content and reducing the math major to a generalist in the mathematical sciences rather than a specialist in mathematics. At any rate, it is much, much bigger than even math ed or math ed reform and will stop any meaningful progress in math ed reform, for that matter, since it is a basic disagreement on the necessity and/or intellectual value of rigor (and, in many cases, what "rigor" even is for that matter).

At any rate, it's too bad these books are out of print -- victims of a war far greater in magnitude than even the math wars.  The New Math of the 60s was as close as it gets to mathematics being handed down to society by its mathematicians, and we threw it all away.  Frank Allen's books are not just books written to pay lip service to the movement, but truly written in the spirit of the times by a real advocate of the New Math. In any case, these books are probably the very best algebra books I have ever seen as of this writing. If you put them together with a good geometry program that at the very least proves the Pythagorean Theorem, you will have youself one first class high school education.

Unfortunately, Frank Allen will never receive the vindication he deserved. But, perhaps he imagined that there might be people like me that would happen upon his work and find it immeasurably valuable in an anti-intellectual world so dominated by politics that only the most vulgar displays of superficial mechanical proficiency are ever even noticed while everyone frantically attempts to "Beat the Joneses" with whatever latest gimmick they can get their hands on.



Another comment from 2012 about the Geometry text:

This book is a timepiece that harkens back to the day when it was decided by the mathematics establishment that Mathematics education needed an overhaul in terms of adding additional rigor to various courses. Although it can be argued if this movement was a success, this book is still a very nice rigorous treatment of geometry that lays the foundations for further study in mathematics. The author, Frank Allen, was a champion of the new math movement and was a very influential force. If you have had high school geometry and want to see a watertight logical re-presentation of the material this book is a good choice.

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You know, Holden, in a way, my relationship with mathematics is kind of nightmarish ... if only for the fact that I seem to be doing all this studying in vain ... And, throughout my life, all these "returns to math" may be the result of being shocked by how challenging geometry was for me at age 15/16.  I mean, that was when I was experiencing a kind of identity crisis which has lasted throughout my life.   I still don't really know where I stand with myself. 

The only thing that prevents me from tormenting myself with self-mockery is that I have developed a sense of humor about the whole situation.  It is this sense of humor and being resigned to be a deadbeat loser that differentiates me from the "official" (younger) traditional math students who may suffer great anxiety over this to the point of wanting to commit suicide.

Since I am already ok with my low social status, I have no fear of failure.  I'm already a total failure by society's standards.  This is very liberating for me.

I can finally allow myself to look into the kind of math that left me stumped ...

My humble view of my own mental capacity can sometimes almost drain the nightmare of its ability to torment me.

I can laugh at those who compete for status since my goals are kind of pure and uncontaminated.

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I know my struggles are pathetic in comparison with those with real gut-wrenching issues to deal with.  This is why I have not been writing too much lately about the psychological challenges I am facing while forcing myself to remain devoted to this path I have chosen (as an alternative to alcoholic oblivion).

I will not be detered even if I come to see myself as a madman/freak.

*** On a brighter note, the first Zucchinis have appeared ... the work I put into the garden may bring some wholesome delight into this life (tomatoes, squash, cucumbers, peppers, and zucchini).  It is the highlight of this life of quiet desparation ...

My father is eating again. 

I hope you and Raul (and Mr Maughan) are doing alright.

My nephew and his wife are displaced in South America ... so I am kind of concerned about his well-being.  There is nothing I can do.

I'm just thankful I have a cot and a pillow to lay my head on ... and even a garden.

I am one of the lucky ones, I suppose.

I will not allow the world of competition to rob me of this awareness of my many blessings.