New Definition

The 9 pseudoline counterexample means my prior definition of linear space is inadequate for constructibility. A sufficient condition for constructibility is that the space has a cospace. Then the proof of constructibility is perhaps possible as follows.

If pseudolinear space S with m boundaries has cospace C then S is constructible as hyperplanes.

Assume the conclusion for spaces with only m-1 boundaries. Construct the hyperplanes for the subspace S' of S with one boundary b removed. The subspace C' of C with vertex b removed is a cospace of S'. C' is constructible, so choose a point in the superregion. That is a consruction of b, as required.

 The cospace condition is also necessary because a constructible space has a constrctible cospace.

This is still not complete, because the cospace is not unique. My technique for constructing a cospace produces a particular cospace which may be different from the subspace of the cospace obtained by removing a vertex. I guess I could patch this by requiring the space to have one of the cospaces that my cospace construction would produce, but I have to express that without reference to construction. Another option that might exist is to prove that every cospace of a constructible space is constructible.

Counterexample

identify

 Among the most satisfying for me interactions on social media such as Bluesky could be described as codependent. We argue incessantly without convincing each other. One such climate denier was fooled by anti-doomists into believing the keeling curve is exponential when it is obviously parabolic. The climate denier prefers for it to be exponential because anti-doomists falsely believe worse is less motivating than less than worse. Anyway, after trouncing the climate denier with the rolling average of the derivative of the keeling curve, I suggested taking me down with a counter example to my proof of the constructibility of linear spaces, and the climate denier took me up on the challenge. By then, I was arguing with copy pasted images of professionally formatted text from AI. After some undefined insistence from the AI, I got a reference out of it, and it turns out there is a counter example buried in the literature that I never could have found on my own. One thing that nagged me about my proof was that it did not depend on my definition of linear. Now I believe my proof is still good, and contains a better definition of linear. I just need to state precisely what that is.

Reality Changes

Corporations are persons, so they have character. We vote for president based on character, so we should vote against corporations based on character. If we don't like a corporation, because it pays its CEO too much, for example, the electorate should choose to put it out of business. But you don't trust the electorate, so we are doomed.

"Corporations are not persons, they are an instrument for avoiding risk, like insurance."

If an individual tried to do what corporations get away with, they would not be allowed to use money. I'm saying if a corporation has externalities or products we don't like, the only recourse is to vote it out of business. We can't trust representatives to micro manage which companies get to exist, so we need to vote the most notorious out of business on a regular schedule. Then, much like persons would, corporations would take responsibility to preserve their existence.

"That's not how voting, money or businesses work. I think you might be asking for better regulation of corporations, but it is obvious that you're confused."

Yes, I'm confused by economic conservatives. Why are you that way? Regulation, nationalization, and restrictions are fine, but to make corporations responsible, we have to eliminate some stocks, not just restrict some flows.

"I would regulate corporations by making them illegal, which most people wouldn't consider conservative economically. Maybe try to understand the meanings of the buzzwords you are tossing about, preferably before you offend someone less forgiving than myself."

Yes, make one of them illegal, but why use the regulate buzzword? Be forgiving of yourself, accept that reality changes, and allow one of your sacred cow corporations to be sacrificed. It has to be an executive order or initiative, not a law, because laws apply to all corporations equally, which means they don't put any of them out of business. Once voters realize how beneficial to the economy eliminating an irresponsible company is, we will have to put it up to the voters directly with online voting or something.

YouTube

 YouTube is different from other social media. One had 50000 comments after 3 days? I'm not convinced the algorithm is being honest about that, but it's true, back and forth is less common, not only because of the number of responses, but also because YouTube limits number of response to 3. Anyway, putting thoughts into words in a context is as important as argument. The post in question was an argument, 20 MAGAts vs 1 student younger than any of the MAGAts. It was respectful because of the 1 debater's discipline. The last interchange was about abortion, and these are my thoughts.

I like the idea of consciousness, but I like breathing more. Everyone likes different things, but to define life, mothers rule. Fine if the evoluture is breathing, the mother can't stop that, but before that, it is up to the mother as to when life begins. Probably, the poor will define it later than the rich, unless they are ElonTrump level of anti-life, but fix that with better unemployment benefits. I value motherhood, but I also value other things people do when they are unemployed, as much as art and science.

Economic Conservatives

 Economic conservatives are the worst. Even they admit social conservatives are bad. Why should we let the hide behind the economy? Conservatives are that way because of their biological imperative to hurt others. By hurting others, they believe they are advantaging their selfish genes. I believe the genome is more complex than that. Genocide hurts us all. Economy conservatives defend weapons manufacturers that propagandize entire populations such as Israel into genocidal paranoia. Am I to believe the economic conservative’s self delusion that consumer demand washes all blame from companies whose primary contribution to the economy is the Keeling curve? No, the economy is what it produces, and preventing it from changing is the most harmful thing we could do. Economic conservatives are the worst.

Social Media

 I do think social media has different emergent properties from other forms of communication. Of course, being booted off of it prejudices me against it. But I think a completely different approach might make it constructive. In that way it is the same as everything else; change is not only the only constant; change is the only hope; growth has sufficed til now, but now we are doomed without change. The change I propose for social media is to make it more contextual, and less like call and response. My experience was that any departure from conformity elicited insults. Call and response in real life can be fine, especially when it is spontaneous. I imagine religious call and response is bad, because of pedagogy, or whatever. I think protest call and response is fine in a protest march, since it is just for fun. But call and response in social media isolates users into bubbles, and subjects those that cannot be classified into bubbles to insults. It is the rules of social media that make it toxic. Open source social media imitates the rules of corporate social media, so it is equally toxic. There simply hasn't been time for new rules to be invented by those working on it in their spare time, and those doing it professionally are too busy refining the existing rules to make any new ones. My obsession with an as yet non-mathematical abstraction, forces me to imagine what I suspect would be different rules. Instead of calls for conformist responses by those with lots of followers, how about facet decorations hidden except in specific context. Ideally, context would be the point; taking a decoration out of context would be meaningless, because the new context it was put into would overwhelm the context it was taken from. Whether someone invites discussion in a context, or rejects disagreement in a context, would be as important as the decoration that elicited the discussion or disagreement. It is not possible to lie if the mode of expression is permission or rejection of response. It is only through the rules of communication that people can lie. Written and spoken words can be untrue, because of syntax. Social media calls for response, are even easier to use for disinformation, because the rules of social media are presently geared that way. I think shifting from call and response rules to context rules would decrease disinformation. At any rate, anything would be better than growth of social media without changing its rules, same as anything would be better than growth of the economy without changing what it produces.

Nothing New

My opposition to reactionaries and socialists is perhaps a love of being different. Perhaps that is also one reason I thought of the solution to climate change without reading it in a book or on a protest sign. True, my idea, to delicense an oil major, follows logically from environmentalism, but no one comes out and says it like me. Everyone else beats around the bush, trying to phase out fossil fuel with subsidies and taxes. Subsidies will not work for the same reason taxes will not work. My reasoning there is perhaps a distortion of other mainstream ideas. Both subsidies and taxes increase GDP, and increased GDP increases fossil fuel production, and every drop produced is burnt, no matter its price. According to MMT, taxes are what gives money value, and I interpret giving money value as a boost to GDP. It's telling that MMTers want guaranteed employment; they don't want us to work less. Leftists may have given us weekends, but they still want us to identify as workers. Work and consumption are two sides of the same Orwellian coin. The problem with degrowthers is that they are invariably undemocratic. They oppose democracy by proposing to use it in corporations; that would destroy democracy as certainly as reactionaries do. Workers are habitual; they would toe the company line, just like share holders do. I even disagree with other new econonomists that I have studied even less. The idea that government causes innovation is only half true. In fact neither government nor economy causes innovation. Innovation is wasted time, plain and simple. There is zero incentive for scientific experiments, or hobbies, that all innovation comes from. If you want more innovation, you need more unemployment. Full employment is business as usual. Corporations grow because their employees, from CEO all the way down, are compassionate and want to spread the wealth that their company affords them. Corporations cannot change because they are hierarchical; if an employee changes, peers, managers, and underlings will oppose the change; it's only external threats against the existence of their company that can change every employee at once. A company's financials statement is like its skin, and like animals, their existence does not end at skin; it extends out into the environment or the economy. Oil companies, more than others, depend on the entire economy to exist. CEOs are the employees most dependent on their company, and oil companies are the companies most dependent on the economy. I don't know if eliminating a CEO would be good for a company, but I suspect eliminating an oil company would be good for the economy. It would be good because, not in spite, of increasing unemployment. Allowing a few powerful companies to exist goes hand in hand with fascism; noting is new. Fighting against fascism just makes it stronger. Instead, destroy one of its puppet masters; delicense an oil major. Why do I call Trump a fascist, and not an authoritarian? I guess fascist has fewer syllables, but also there are authoritarians that are qualitatively different from Trump. Other authoritarians were created by the USofGenocide; they exist to serve weapons corporations in the USG, not in their own country. Even petrostate authoritarians just serve the top dog oil companies, that all call USG home. Oil companies don't compete; they prop each other up in the economy, just like employees prop each other up in a company. Like Hitler, Trump serves corporations in his own country. Killing Nazis did not end the war; destroying the top dog corporations ended the war.