Once I was in an education class where the teacher was telling us when you teach you are wiring the students brain. I asked him: isn’t learning also losing a connection in the brain? Say you want to learn to stop drinking. You have to lose the pathways that lead you you drink. So he said “yes” and I got a lot of “ahas” from the other students. But the teacher wasn’t going to mention that part.

For me, teaching and learning is asking a question, and then answering it. Yes, that is everything, its almost boring to say that. Maybe you like the learning stages “learning is synthesis and analysis” but actually, that is just as boring and unhelpful. I think the question answer model can be helpful. Education is coming up with a problem you see or that you want to shed light on; or seeing an opportunity for how you want to help with problems in the world. The next part is having the capacity, the energy, and the resources to answer the question or shed light on the problem. All human development comes from that process.

So we are told from on high that education happens in the brain. Well, if learning is wiring and unwiring the brain, both, it might as well be neither. Whats the difference? Learning could have nothing to do with the brain. At all. And all the arguments about learning-as-brain come down to the same basic problem that you know things that aren’t wires or connections or brain pathways. There are non-connections that are not just good, but necessary for a good life, like learning not to go down negative rumination pathways.

Just give your self a moment, where you ask a question. A free moment. And you are free to answer with your energy, capacity and resources, and you can see that learning is not the brain.

There is a lot of ugliness in America. I’ll admit that I have personally seen and been the victim of some terrible, horrible, no-good-very-bad ugliness, and watched people close to me basically consent to it. Trump is a symptom of the illnesses of America, not the cause. Biden is closer to the people who caused our illnesses. So we have a choice between the symptom or the cause. If this were a disease, I’d say inflicting more of the cause, just to alleviate symptoms for a short while, is the opposite of a cure. In the case where democracy is close to death; should we choose the symptoms over the cause? Well, the election isn’t a disease, and I don’t know what the cure is. What about culling people and hating based on whether you vote/speak for the symptom, or the cause? Is that behavior of someone who is ill? Bernie expected a surge of young voters to carry him through the primary, but as Chomsky mentions, young people don’t believe voting does anything (except rob them of energy and brain cells). And weren’t they disenfranchised in the last primary when Bernie was winning? As proved by the journalism wikileaks did? Its a perfectly reasonable thing for a young person to think voting is worse than useless. Are we going to hate them for it? What happens after Biden wins? More, potentially worse symptoms than Trump? There is no bottom to the scum that can be dredged up to the top office if we pick the cause over the symptom. I ask these questions to show that the decisions Americans face in this election, and in general, are not black and white. Even if we do decide on one person to vote on, it is a necessity to taste the bitter nuances of such a decision.

When I was doing my dissertation proposal defense my teachers were trying to tease out what makes me tick; what I am working for, and for what purpose. They eventually figured out, and I with them, that what I was really after was freedom of thought for students, and in general. I was not interested in breaking or debunking mathematical structures for no reason. I am specifically interested in improving the quality of discussion by allowing patterns of thought other than mathematical. So much that was not mathematical has become mathematical. Probability was opposed to mathematics by Aristotle and for millennia in the West. Now probability is considered a part of mathematics, and with it “social sciences” now have a shiny veneer of mathematical structures governing what gets published and what research is “significant”. Even poetry, as Borges comments, is better if it is filled with “fire and algebra.” Mathematizing things has the effect of making people feel they really know something is good or bad.

Wouldn’t it be nice if there was a decision that was either pure good or depraved evil? If Trump were the devil, or the savior, we could all go to heaven with a simple, if inconvenient, political act of voting. Trump wont end the world; he could have already started a war. Will Biden keep us from war? Trump is a dumb brute that has served his purpose of scaring us into voting Hillary’s camp back in. Is that what it is to vote? Is voting an untrammeled good, even under the bullying we’re experiencing? Will Biden be finished punishing us when he wins, or will his camp still be vengeful?

Biden’s victory is not a victory. We voted Trump in to vote Biden’s camp out, then we bled for that decision. There will be much more pain too keep Biden in line, more than there was while Trump was president. The working class know that, and the backlash from Biden will be worse than Trump if we do not take those pains. This election shows that we have not given up the fight for the soul of America, that is all.

An interesting empirical example of the axiom of completeness is the night sky with a telescope of ever-increasing magnifying power. Take any space of darkness in the night sky and assume you can magnify as much as you want. The axiom of completeness asserts that you will eventually find a star in that space. Take another, smaller space within (not containing a star) and magnify more, you will find another star in that smaller space, or any space, no matter how small*.This, of course, is impossible under the standard physics mandate that there is an edge of the universe and it is not unlimited. In any case the idea of a limited universe is in direct tension with an elementary empirical (if we could inductively continue to magnify) example of the axiom of completeness. The use of stars instead of points gives an alternative to formulating analysis with 0-dimensional objects such as points. They appear like points only at certain levels of magnification.

Another iteration of the axiom of completeness is one in two or three dimensional space. The usual axiom expressed in two dimensions uses objects of 0-dimension: points, and asserts that a bounded increasing sequence (of points) has a least upper bound. Using more realistic objects of the sequence— instead of points, three dimensional shapes such as spheres or cubes—The cubes have to get smaller and smaller, and be contained in the previous cubes of the sequence (after cube N). The problem is that this sequence always contains some space, and asserts that the sequence converges to a point instead of a cube. This is not the inductive inference. The inductive inference requires that all cases that can be reasonably checked by hand resemble the cases beyond, approaching infinity. If the cases known resemble the cases beyond, there would always be some space inside the cube, and the axiom of completeness fails. All this is related to the unrealistic belief in 0-dimensional objects.

• just for fun lets be precise and say the next smaller circle has 1/4 the radius of the current circle. It is easy to see that this circle can always be found so that it does not include the star you found. Oh, and what if you find two (or more) stars at the same time? leave as an exercise!