One of the principles often suggested as an axiom of probability is that of additivity. The additivity here is a generalization of arithmetic addivity — which generalization, with other assumptions, will imply the arithmetic case.

The classic formulation of this principle came from Bruno di Finetti. Di Finetti was a subjectivist. A typical subjectivist is amongst those who prefer to think in terms of the probability of events, rather than in terms of the probability of propositions. And subjectivists like to found their theory of probability in terms of unconditional probabilities. Using somewhat different notation from that here, the classic formulation of the principle of additivity is in which X, Y, and Z are sets of events. The underscored arrowhead is again my notation for weak supraprobability, the union of strict supraprobability with equiprobability.

One of the things that I noticed when considering this proposition is that the condition that Y∩Z be empty is superfluous. I tried to get a note published on that issue, but journals were not receptive. I had bigger fish to fry other than that one, so I threw-up my hands and moved onward.

When it comes to probability, I'm a logicist. I see probability as primarily about relations amongst propositions (though every event corresponds to a proposition that the event happen and every proposition corresponds to the event that the proposition is true), and I see each thing about which we state a probability as a compound proposition of the form X given c in which X and c are themselves propositions (though if c is a tautology, then the proposition operationalizes as unconditional). I've long pondered what would be a proper generalized restatement of the principle of additivity. If you've looked at the set of axiomata on which I've been working, then you've seen one or more of my efforts. Last night, I clearly saw what I think to be the proper statement: To get di Finetti's principle from it, set c₂ = c₁ and make it a tautology, and set X₂ = Z = Y₂. Note that the condition of (X₂ | c₁) being weakly supraprobable to (Y₂ | c₂) is automatically met when the two are the same thing. By itself, this generalization implies my previous generalization and part of another principle that I was treating as an axiom; the remainder of that other principle can be got by applying basic properties of equiprobability and the principle that strict supraprobability and equiprobability are mutually exclusive to this generalization. The principle that is thus demoted was awkward; the axiom that was recast as acceptable as it was, but the new version is elegant.

This evening, I was looking at a record of recent failed attempts to log into this 'blog. I found that relatively few attempts tried to do so with the popular username of admin, whereäs by far the majority were with the username oeconomist (that it to say with the second-level domain name). There is not and never has been an account here with username oeconomist; the would-be intruder was guessing mistakenly — but not unreasonably. If my logs are representative, then having an account name match a second-level domain name is less secure than having it be admin. With people avoiding admin, it is natural for crackers to try other likely candidates, including candidates whose probabilities are conditional upon the domain names.

Mind you that the reasoning of my earlier explanation of why the avoidance of admin doesn't add a discernible amount of security if passcodes are properly selected can be applied to avoiding a username that matches a domain name. An account with a known username and a well-chosen password of m+n characters is more secure than an account with a secret m-character username and an n-character password.

Choose a username that pleases you. Choose a password that is long and that looks like chaos, and make occasional changes to it.

84 Lumber bought airtime within the broadcast of the 2017 Superbowl, and presented a video of a Latina mother and daughter travelling through what seems to be Mexico, plainly in hopes of entering America. Inter-spliced with the scenes of their travel are scenes of Americans, clearly constructing something. When the mother and daughter reach the border, they are confronted by a grey and terrible wall. But, as they seek for some hope, they find it — sunlight somehow shining through a section of that wall. Running to it, they find a door. In the awful wall, it was a great door that the Americans in the other scenes were building.

84 Lumber is being attacked for their video, on a theory that its purpose were to defend illegal immigration. Naturally, 84 Lumber denies that their message were any such defense; they now claim that the door were a metaphor for the institutions of legal entry.

I don't encounter a lot of people who will honestly speak in favor of illegal immigration. They ought to do so. There is nothing wrong with illegal immigration. Nothing.

The vast majority of people who oppose illegal immigration or want greater legal restriction on immigration do not do so from racism, and I am very sorry that they have been slandered and libelled; but recognizing the inappropriateness of that accusation doesn't serve to support a case for denying people entry.

Indeed, immigrants might come to our nation and do a variety of things that are violations of the rights of the people who are here now, or that are otherwise undesirable; but every genuine right that might violated by an immigrant could also be violated by someone born and raised here; more generally, every socially corrosive act that might be perpetrated by an immigrant could also be perpetrated by a native. A man or woman who was born here can violate the property and person of someone else; a man or woman who was born here can demand that his or her religion or language be give a privileged legal status; a man or woman who was born here can live at the expense of the taxpayers. None of these behaviors is made better or worse by virtue of where the person were born, nor by whether he or she were allowed to immigrate by the law. I will grant that groups coming from some foreign cultures have a greater share of members likely to do undesirable things of some sorts; but some groups native to America have a greater share of members likely to do undesirable things of some sorts.

There is a dire confusion of the legal with the moral, both on the part of those who insist that illegal immigrants are already in the wrong by virtue of having broken laws that are ostensibly ours in coming here, and by those who insist that there is no such thing as an illegal immigrant. Law can be wrong, and when it is wrong then it may be ignored without doing wrong. Those immigrants here in violation of law are neither wrong simply for being illegal, nor legal because they are not wrong to be here.

America is not a club nor a corporation. The persons and properties within the area occupied by America are not ipso facto in any way the property of all Americans. The right to trade, the right to give without condition, and the right to take that which is freely offered are not rights that in any way reflect nationality. Those who would do business with newcomers are within their rights; newcomers who would do business with those Americans are within their rights.

It's offensively absurd to claim an entitlement to exclude people by pointing to state-managed infrastructure and programmes. They weren't brought into existence through some sort of social contract; ultimately, they were effected through threats of violence; and generally they crowded-out alternative institutions that would have been created by free people. Of course, the welfare state cannot survive in a world of such freedom; it could not survive even if the progressives were allowed to pursue their wildest dreams of taxation, nationally or globally. But so much the worse for the false generosity and false security of the welfare state, which cannot avoid bankruptcy in this century, regardless of whether it keeps all of us trapped on one side or another of its jurisdictional boundaries.

Many people who are going or went through the process of legal immigration may feel that it is unfair for others now to jump the queue; but the queue should never have existed in the first place, and one only compounds the injustice by imposing it upon others.

There should be no queue, no wall, no need for doors.

I returned home on foot this evening, carrying various things. As I got back to the apartment complex and was going to enter by way of the vehicular gate, I saw and smelled what appeared to be a fire outside of the central front pedestrian gate, so I investigated.

Yup, there was a small fire inside of what appeared to be a pylon or one of those tall butt receptacles, which was within an inch or so of the building, if not up against it.

So I first got my phone to call emergency services. The first dispatcher switched me to a fire department dispatcher, who was a fool following a flowchart. I started to tell him There's a small fire outside of 4050— at which point he interrupted me to tell me that he needed my location. So I told him my location exactly as I'd begun doing when he interrupted me — I didn't note to him that I'd been doing just that — and I told him what was on fire. At this point, I wanted to put down what I was carrying, and go get a fire extinguisher, which meant getting off the phone. Of course, the fire was worsening and the burning object was collapsing in a way that could further fuel the flames. But the dispatcher was demanding my phone number in case we get cut off. I shouted at him that I'd told him what he needed to know, and wasn't going to stay on the phone with him. My phone set resisted my attempt to hang-up, so I turned it off. I got-out my keys, got through the gate, was interrupted by someone who told me that there were a fire, put my packages down, went (barking about stupidity) to a case near the elevator, retrieved a fire extinguisher, then returned to put-out the damn'd fire.

I thought that I heard a fire truck, so I waited, and one indeed arrived. They decided that the fire were extinguished, and so went on their way. The complex manager showed-up, so I explained the situation to her. Then a cop showed-up so I explained the situation to him. Satisfied, he too went on his way. The manager stayed to deal with the clean-up. I grabbed my things, went on to my apartment, and grumbled sub-vocally about inhaling things that I didn't want to inhale.

When I restarted my phone, I found that I had a message waiting. The dispatcher said that they needed me to call back to tell them what were on fire.

Thinking about there already being an effort to persuade voters that they must support whomever the Democratic Party nominates in 2018 and in 2020, I was naturally led to wonder what sort of candidates those would be; and thence, more generally, what politics would be like in about three years.

What politics will be is something within the context of what they can be, so I try to imagine the plausible scenarii. To me, these look very grim.

I expect the Republican Party to continue to reshape itself around Donald Joseph Trump, to be more informed by his poison. I don't expect the dissenters within the Republican Party to enjoy much success, especially as I don't expect them to find any help either from main-stream of the media or from the alternative led by Fox. Some of the better people in that tribe whom we call the political right will leave it, and even some people who were enthusiastic about Trump will see or sense where things are leading, and turn away; however, it will continue to recruit people who were not previously its members but are attracted to Trump or to Trumpism. And a very large share of those who were already members of that tribe will reshape their ostensible beliefs to fit the pronouncements and actions of Donald Trump.

(If Trump should leave office early, then the Party will presumably work to reshape itself around Michael Richard Pence, who will attempt to segue from whatever Trumpism then is, to a frightening social conservatism. But I don't expect Trump to be removed.)

Meanwhile, the aforementioned Democrats are in a dark political death-pit. Their most recent nomination was decided as a struggle between what progressivism has become (and was always destined to be) and crony capitalism posturing opportunistically as that progressivism. The leadership ensured that the crony capitalist got the nomination, but the subsequent result was, if anything, to intensify the need of the leadership to pander to the progressive urges of the Party's base. And the response of the base to Trump's election has been to move still further left and to become more overtly violent.

That base is about 25% of the nation and of the voters. It likes to imagine itself as a plurality, as a majority, or sometimes even as the other 98% or as the 99%. But the political left has inflated its apparent size by taking disproportionate control of the commanding heights of our social institutions, and by implicitly coöperating with the political right (also only about a quarter of the population) to marginalize those with views that do not conform to the left-right framework; remarkably, the political right has kept the political left viable, and vice versa. (These days, about a third of the American population wants the state to be less involved both in matters of sex and of religion and in matters ordinarily classified as economic. That makes them a larger group than either the left or the right, but not larger than the two combined.) Given how small they actually are, the left (like the right) cannot take political power without getting votes from those outside their tribe. If the Democratic Party cannot free itself from the influence of those who continue down the path of progressivism, then it cannot return to power based upon a positive appeal; its hopes would lie only in Republican over-reach.

Which over-reach would certainly have recent precedence. In 2006 and 2008, the Republican Party was in its own death-pit. They'd stumbled into it under the influence of neo-conservatism. The neo-conservatives pursued two wars, guided by a theory that the people in Afghanistan and in Iraq were aching for liberal democracy and prepared to fight for it. And they pursued fiscal and regulatory policies that triggered a major financial crisis. The Republicans lost control of both chambers of Congress, and then of the White House.

What pulled them from that death-pit was the Tea Party, which began coälescing with rallies, and then organized itself well enough to displace candidates of the Republican establishment in primary races. Those in the Republican establishment who held onto their positions fought vigorously with the Tea Party, which served to burnish the credentials of the Tea Party candidates and office-holders. Attempts by the left to treat the Tea Party Republicans as responsible for the prior actions of the neo-conservative Republicans were unsuccessful in persuading those outside the Democratic base. Ultimately, it seems that the Tea Party failed in its objectives; they did not succeed in capturing the leadership of the Republican Party, and some office-holders who had cultivated the support of the Tea Party betrayed their trust. The Tea Party appears now itself displaced by an uglier and angrier populism. But the Tea Party had the effect of allowing the Republican Party largely to free itself from association with the awful policies of the Administration of George Walker Bush.

That brings me to the Women's March on Washington, and to its sister Marches in other cities. It is not impossible that these rallies could be the beginning of a process that could reälign the Democratic Party, pulling it from its death-pit as the Tea Party pulled the Republican Party from its own. The odds, however, are very much against that reälignment.

First, though a great many of the women who participated wanted to be heard, rather that to be told what to say by celebrities and by icons — definitely shouting No! to goddamn'd Donald Joseph Trump, but not all saying Yes! to what the Democratic Party or its progressive base have been offering — the objective of most of those who called and led these marches in the first place was not to reälign the Party, but to reälign women. A new leadership of reformers would have to be found.

Second, while the Tea Party did not much have to fight the Republican base, that is exactly what anyone seeking fundamentally to reälign the Democratic Party would have to do.

Those without much hope for the Republican or Democratic Parties as instruments of positive change sometimes turn to third parties. Some exist, others could be creäted. We've already seen a collapse of the institutionalized myth that third parties must always be formed either around one issue or around one candidate. The left and the right will join together, through the media that they control and through bi-partisan commissions, to fight the emergence of a real alternative; but, if the left continues to get ever more repulsive to those voters outside of the left and right, then the right will have a greatly weakened partner in their unholy alliance to exclude rival views. I don't imagine that I myself will find a party or Presidential candidate whom I can, in good conscience, support; but perhaps 2020 will be made less awful by the emergence of a better major party.

I have previously explored the logical absurdity of insisting that those who don't vote for one of the two foremost candidates in an election are effectively voting for the other of these two candidates. That analysis could easily be generalized to include ballot measures; where abstaining from voting has sometimes been claimed to be the same as opposing a measure, and sometimes been claimed to be the same as supporting the measure.

The primary purpose of claims of these forms is to pressure someone into voting for a candidate whom — or measure which — the potential voter finds unappealing. We especially see these claims when there are actual candidates, or formulated ballot measures. But we also see that purpose at play when an election has been held and candidates and proposal for the next election are not yet identified. Some of those declaring You are now to blame for X because you did not vote for Y! are hoping to motivate the audience to tolerate whatever is demanded by the claimant's faction in that next election. An alternative would be to promise to offer something better than Y in that next election; but they are engaged in brinksmanship, threatening to take the community off a cliff if a plurality don't agree to their demands.

Other motivations for such claims in the wake of an election are simple ventilation and blame-shifting. It is frustrating to lose an election, and a blow to the ego to acknowledge that one's own faction may be largely responsible for that loss.[1]

There's another, unrecognized motivation for these claims. Although there is a very great logical distance between refusing to support one of the two major political tribes and thinking as do members of the other major tribe, it is easy enough for tribal members to disregard that distinction almost perfectly. Thus, these absurd claims that refusal to support Y is operationally the same thing as supporting X implicitly become part of a more general psychological device of treating politics as all falling along a left-right spectrum, and thereby avoiding any challenge to one's thought or behavior that cannot be dismissed from the left by pointing to the right or from the right by pointing to the left, and saying You guys are worse!, even if the challenger is not one of those guys. The challenge may even be spuriously taken as proof that, after all, the challenger were really a member of the other tribe, as he or she is not challenging them, and them alone.

[1] For example, James Henry (Jim) Webb could have beaten any of the Republican candidates for President in 2016, and it is at least plausible that Bernard (Bernie) Sanders could have beaten Donald J[oseph] Trump; but the Democratic Party chose its weakest or second-weakest candidate. (Martin Joseph O'Malley might have been a still worse choice, as his mythology of Baltimore collapsed in the face of the police murder of Freddie Carlos Gray jr.)

The word problem is used for multiple concepts:

• a challenge, especially a mental challenge
• an unhappy state of affairs that exercises the mind
• a seemingly insurmountable difficulty

These may actually be very different things, because some states-of-affairs may be changed, and some may not; but it is often hard to distinguish the former from the latter. Thence we use the same word for all three concepts, and thence we get the famous Serenity Prayer of Reinhold Niebuhr:

God, grant me the serenity to accept the things I cannot change, courage to change the things I can, and wisdom to know the difference.

A good economist is going to note that sometimes the costs of changing what we can would be higher than the benefit. Properly understood, that greater costs would mean that we were trading some greater problem for a solution to the problem under immediate consideration. The Serenity Prayer might lead one to mistake sensible calculation for cowardice, though poetry might have to be sacrificed to provide better guidance.

Still, the distinction between that which we can change and that which we cannot is most fundamental, and confusion between the two is a source of frustration and of anguish. That which displeases us and which we can change is a challenge about which we can usefully exercise the mind, until such time as either we develop a reasonable method of changing things or we recognize that it's not worth the cost. That which displeases us and which we cannot change is an unhappy condition of existence; and — ideally — we ought to come to terms with that condition, to accept it, so that it no longer exercises our minds. (And we ought, similarly, to accept those states the changing of which, though possible, truly would be too costly.)

One seldom-noted root of some of the confusion is a failure to distinguish between what the person in question may change and what someone else may change. The state-of-affairs might be a problem for a person who could change it, or it might not be a problem for that person; but, either way, by someone who cannot change it, it is best treated as a condition of existence.

It may be especially hard to see the distinction when the other person might indeed act to change things and, if that other person did, the first person would want to undertake quickly some course of action. But, likewise, there might be some potential event which would have to be impersonally caused (if at all) and which would call for a prompt response. One should not try to cause that which no person can cause, and one should not try to cause that which only another person can cause, even if there would be things to do should it happen.

It may be too much to hope for serenity from such realizations. It is certainly too much to demand that others be serene in the face of indifference, indecision, or madness on the part of those around them. Sometimes grim acceptance is the best that one can manage.