Friday, March 24, 2017

Hard to say which is worse

I'm not sure which circumstance is the more disturbing, the fact that my health insurance is hanging by the thinnest of threads, or the fact that the only reason I have even that faint hope to cling to is that the freedom caucus doesn't think the AHCA bill is horrible enough.  They want to chip away the requirements that insurance plans provide comprehensive coverage, thereby fragmenting (and hence weakening) the market even further.

Let us be clear: the individual health insurance market cannot be made viable without a government mandate.  This is because there are structural features of health care that make it fundamentally unlike other insurance markets.  When insuring an asset like a house or a car, the size of the potential loss is bounded by the value of the asset.  If your house burns down that doesn't make it significantly more likely that your next house will burn down too.

Health care is different.  The cost centers are much more predictable.  80% of the cost goes to taking care of 20% of the population, mainly the elderly and the chronically ill.  Reducing costs is easy: just cut those high-cost people lose and let them suffer or die.  And that is pretty much the Republican plan, though of course they don't market it in those terms.  But that is the net effect: without mandates, insurers will not -- can not -- cover the old and the sick.  It would be economic suicide.

This is not really about insurance, this is about what kind of country we want to be.  Insurance is just the mechanism that we use to implement policy.  The policy decision we have to make is: do we force the 80% of healthy people to bear the high cost of taking care of the 20% of old and sick people, or do we let those people suffer and die and their families go bankrupt?  Neither one of those is a particularly pleasant prospect.  Unfortunately, those are our choices.  "None of the above" is not an option.  (There are other things we can do to lower the cost of health care, like banning tobacco and refined sugar, forcing people to exercise, etc.  But those are not likely to be very popular options on either side of the aisle.)

The problem is that when you are young and healthy it is hard to see the percentage in allowing the government to take a big chunk of your hard-earned cash to take care of old sick people whom you don't know and likely will never meet.  Why should you care about them?  Well, because some day you will be one of them.  Even if (especially if!) you don't get sick you will definitely get old.  It happens even to the best of us sooner or later.

If you, like me, want to live in a country where we do not throw the old and the sick and their families under the bus, please take a moment to contact one (or more!) of the congresspeople who can actually move the needle on this and urge them to (continue to) oppose the AHCA, especially if you happen to be one of their constituents.  There really is a problem that needs to be solved here, but the AHCA is not the way.

Monday, March 20, 2017

Causality and Quantum Mechanics: a Cosmological Kalamity (Part 2 of 2)

This is the second in a two-part series of posts about the Kalam Cosmological Argument for the existence of God.  If you haven't read the first part you should probably do that first, notwithstanding that I'm going to start with a quick review.

To recap: the KCA is based on the central premise that "whatever begins to exist has a cause."  But quantum mechanics provides us with at least two examples of things that begin to exist without causes: radioactive decay results in the decay products beginning to exist, and vacuum fluctuations result in the virtual particles beginning to exist.  In the latter case, the particles are created literally from nothing, but that's just a detail, a little icing on the cosmological cake.  The KCA premise isn't about whether or not things that begin to exist are fashioned from previously existing materials.  It only speaks of causes.  And quantum events don't have causes — at least not local causes — as shown by Bell's theorem.  Bell's theorem actually does more than rule out local causes, it rules out all local hidden state models, not just causal ones.  So there are only two possibilities: either quantum events are not (locally) caused, or quantum mechanics is wrong.

But Bell's theorem does not rule out non-local hidden state, and so it does not rule out non-local causes.  Indeed, what Bell's theorem shows us is that quantum states are in general non-local: an entangled system is a system with a single quantum state spread out over multiple locations.  So could this be the source of quantum causality?

No, it couldn't.  Non-local causality is ruled out both by relativity and by the no-communication theorem.  For a non-local state to be causal, the causal effect would have to propagate faster than the speed of light, otherwise it would just be an ordinary run-of-the-mill everywhere-local chain of causation.  Some popular accounts of entanglement would have you believe that this (faster-than-light causality) does happen, but it doesn't.  Measuring one member of an entangled pair does not change the state of its partner.  So non-local quantum states cannot be causal.

There is one last possibility: maybe there is some other kind of state in the universe, some non-local non-quantum state.  As I noted at the end of part 1 we can never rule out this possibility on the basis of any experiment.  Indeed, we can even demonstrate a hypothetical non-local state that would account for all possible observational data: a cosmic Turing machine computing the digits of pi from wherever it happens to be that they correspond exactly with the outcomes of all experiments that have ever been done or will ever be done.  Assuming pi is normal, this will always be possible.

This is the fundamental problem with hidden state: it's hidden.  Our universe could be run by a cosmic Turing machine, or it could be a simulation built by intelligent aliens.  We can't eliminate either possibility, nor a myriad others, on the basis of experiment.

When I have pointed this out to Christians their response has been: what difference does it make if we're in a simulation?  The aliens were still created by God.  But in fact this possibility is devastating not just to the KCA, but to all theological arguments.  If the universe is a simulation, then I can accept all of the claims of theologians at face value, and still not get to God.  I can accept that Jesus was a real historical figure, that he really did perform miracles, that he really was crucified and rose from the dead, that he really did claim to be God, that the scriptures are the literal truth, that the Flood really happened, that the earth is 6000 years old.  I can accept all of that and still not believe in God because all of that could have just been built in to our simulation by the aliens who designed it.

I can even accept the cosmological argument and still not believe in any particular god.  I only have to accept the uncaused cause in the abstract.  I cannot possibly know anything about God's true nature because all of the information I have at my disposal is filtered through the intelligent aliens who built this simulated universe that I live in.  The information that I have access to may or may not reflect the actual metaphysical truth.  In fact, the aliens that built our universe may themselves not know the metaphysical truth because they themselves could be living in a simulated universe built by meta-aliens.

There could be an arbitrary number of layers of simulation between us and the uncaused cause.  For us to have accurate information about God, that information would have to somehow percolate down through all of those layers without being altered.  It would be like a cosmic game of Chinese whispers.  The odds of the truth emerging unscathed down here at the very bottom of the hierarchy are indistinguishable from zero.

It is worth noting that we may not be at the bottom of the hierarchy for long.  We are on the verge of being able to create simulated universes of our own.  When that happens, will the artificially intelligent inhabitants of that universe have souls?  Unless we are 100% certain that the answer to that question is yes, how can we be sure that we have souls?

In sum, the KCA is completely untenable.  Its central premise is refuted empirically by quantum mechanics.  Even if this were not the case, the KCA only gets you to some unknown uncaused cause.  The nature of the uncaused cause cannot be determined by any experiment, since no experiment can rule out the cosmic Turing machine.

Furthermore, the possibility of simulated worlds is devastating not just to the cosmological argument but to all religious arguments.  Even if you accept all religious claims at face value, you still have to either show that information about God necessarily propagates reliably into a simulation, or somehow prove that our universe is not a simulation, that we are living in the One True Universe, and that any simulations we create will be the first level down.  Otherwise, even in the face of miracles and revelations we cannot know if they are the work of God or the aliens who programmed our simulation.  Or, what is most likely of course, of our own ancestors' imaginations.

Sunday, March 19, 2017

Causality and Quantum Mechanics: a Cosmological Kalamity (Part 1 of 2)

I'm a little burned out on politics, so let's talk about religion instead.

I often lurk on religious debate forums, and one of the things I've noticed over the years is that various arguments presented by Christian apologists seem to go in and out of fashion, not unlike bell bottoms and baggy pants.  At the moment, something called the Kalam Cosmological Argument (KCA) seems to be in vogue.  KCA is a modern riff on the classical cosmological argument, which goes back to antiquity.  The Kalam variation goes like this:
Whatever begins to exist has a cause; 
The universe began to exist; 
The universe has a cause. 
If the universe has a cause, then an uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful; 
An uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless and enormously powerful.
I've never understood how you get from "uncaused cause" to "personal creator", and I've particularly never understood how you get from "personal creator" in general to Jesus in particular.  I have yet to find an apologist willing to even try to explain that one to me.  I think I scare them.

But it turns out that the cosmological argument in general, and the KCA variation in particular, can be debunked before you even get to that question because it is simply not true that whatever begins to exist has a cause.  There are at least two examples in nature of things that begin to exist without causes.  Vacuum fluctuations are the spontaneous creation of particles and their associated anti-particles.  Normally these just annihilate each other almost immediately after their creation, but in some circumstances they can create observable effects, so there is no question that they really do happen.  The second example is radioactive decay, in which an atom of one element emits a particle and in the process becomes an atom of a different element.  Both vacuum fluctuations and radioactive decay are random events.  They have no cause.  And yet they result in things beginning to exist.

If you believe all that then you can stop reading now.  The rest of this post is for those of you who don't believe my bald assertions and demand proof (which is perfectly fine, BTW.  You should never accept anything as true simply because someone says so.)  In particular, my claim that quantum randomness is truly random is often met with legitimate skepticism, so I thought it would be worthwhile writing down why this is (extremely likely to be) true.  In the process of formulating this argument I came up with a completely different and much more powerful (IMHO) refutation of the cosmological argument, which I will write about in the second part of this series.


Because the issues are subtle I'm going to have to go into some excruciating detail, starting with what it means for something to be caused.

Let's start with a simple example: I flip a light switch and the light comes on.  We would say that my flipping the switch caused the light to come on.  Actually, my flipping of the switch was the beginning of a chain of "causal events", each one of which was caused by the previous event in the chain: My flipping of the switch caused the completion of a circuit, which caused electricity to flow, which caused the filament of a light bulb to heat up (or, nowadays, the electrons in the atoms of a PN-junction in an LED to become excited) which caused some photons to begin to exist.  If I hook my light switch up to an Alexa, I can literally say, "Let there be light" and cause light to begin to exist.

Why do we say that I caused the the light to come on and not the other way around?  It's because causes must precede effects.  They cannot reach back in time.  A consequence of this is that causes cannot propagate faster than the speed of light because moving faster than light means going backwards in time in some reference frames.  Causes must precede effects in all reference frames.

Note that temporal precedence is necessary but not sufficient for one event to be considered the cause of another.  Suppose I turn on one light, and then a minute later I turn on a second light.  The first light coming on preceded the second (in all reference frames) but it is not the case that the first light coming on caused the second to come on.  So causality involves something more than mere temporal precedence.

Figuring out exactly what that "something more" is turns out to be quite tricky.  For example, we might hypothesize that the reason I cause both lights to come on and not that the first light causes the second is because I am an agent with free will and the light bulbs aren't.  But this is easily disproven: suppose that I am in a room with two lights.  One is on, the other is off.  The bulb in the first light burns out and I am left in the dark.  I fumble around for the switch to the second light and turn it on.  Now I am in the middle of a causal chain that resulted in the second light coming on.  In this case it is fair to say that the failure of the first light caused the illumination of the second, with me as an intermediate cause.  And, of course, we can eliminate me as an intermediate cause by designing an automatic mechanism that turns on the second light when the first one fails.

Another possibility is that effects are "necessary consequences" of causes.  In the situation where I turn on one light and then another, the activation of the second light is not a necessary consequence of the activation of the first.  I could decide after turning on one light not to turn on the second one.  On the other hand, having been turned on, a light cannot just "decide" stay off.

The situation gets a bit fuzzy in the case of the burned-out bulb because I could have decided to not turn on the backup light and just sit in the dark.  Nonetheless, if I do decide to turn on the backup light, the fact that the first light burned out surely had a hand in that.  It's not mere coincidence that I turned on the second light right after the first one failed.  I turned it on at least in part because the first one failed, notwithstanding that I am (or at least feel like) an agent with free will.

Now let us consider a third scenario: suppose I am a puppet master controlling a marionette in a scene where the marionette activates a light switch.  Consider two scenarios, one in which the switch that the marionette activates actually controls the light, and the second in which the switch that the marionette activates is a prop, and the real switch is located off-stage but is still activated by me.  In both cases I'm the one who is controlling the light, either indirectly by pulling the marionette's strings, or directly by activating the off-stage switch.  In the first case, the marionette is part of the causal chain that activates the light.  In the second, it is not.

Now imagine that the marionette is not just a puppet, but is equipped with a sophisticated artificial brain capable of doing scientific reasoning.  We have programmed the marionette to not be aware of the fact that we are pulling its strings.  It might suspect this to be the case, but it has no access to any direct evidence.  The marionette is effectively a Calvinist, and we are playing the role of God.

Now we walk the marionette through a series of experiments where it turns the light switch (the one on the stage) on and off.  It observes a 100% correlation between the state of the switch and the state of the light, and also a time delay sufficient for the propagate of a causal effect from the switch to the light.  Now we ask it: are you living in a world where your switch actually causes the light to come on, or are you living in a world where your switch is just a prop, and the light is actually controlled by a switch hidden off stage where you can never see it?


Let's leave our marionette to ponder this question while we consider a second question: what does it mean for something to be "truly random"?  Let me illustrate this with another familiar example: suppose we flip a coin.  While the coin is spinning in the air the outcome (heads of tails) is unknown to us.  Now we catch the coin and flip it over onto our wrist in the traditional manner.  At this point the outcome is still unknown to us.  Nevertheless, the coin is now in a fundamentally different kind of state than it was while it was spinning.  Its state is still unknown to us, but it is determined.  We may not know whether it is heads or tails, but we do know that either it is heads or it is tails.  This was not the case while it was spinning.  While it was spinning it was neither heads nor tails.  It was spinning.

Now, it is possible that there are two kinds of spinning states, one of which inevitably leads to the coin landing heads and the other of which inevitably leads to the coin landing tails.  If this is the case, then it would be fair to say that the outcome was determined even before the coin actually landed, and so the spinning states are not fundamentally different from the landed-but-covered states.  There is a spinning-but-going-to-land-heads state and a spinning-but-going-to-land-tails state.  We may not be able to tell them apart, but that doesn't change the (hypothetical) fact that these two states exist.  Our inability to tell them apart may simply be a technological limitation.  If we had x-ray vision we would be able to distinguish the land-heads (but still covered) state from the landed-tails (but still covered state).  Maybe if we had just the right kind of high speed camera and trajectory analysis software we could distinguish spinning-and-going-to-land-heads from spinning-and-going-to-land-tails.

There are two other possibilities: one is that the coin flip is truly random, which is to say, that there really is only one spinning state.  Our inability to predict the outcome is not a technological limitation.  Even if we had arbitrary super powers — indeed, even if we were God — we would not be able to predict the outcome of the experiment.  The second possibility is that the outcome is not truly random, but the mechanism that determines the outcome is hidden from us.  In this case we can't predict the outcome with any amount of technology, but God can.

Where all this matters is not flipping coins, but quantum mechanics.  The outcomes of quantum mechanics experiments appear to be random, like coin flips.  The question is: Is our inability to predict the outcome a technological limitation?  Or is there hidden state that we can't access?  Or is this really true randomness?

We can quickly dispense with the first possibility.  The randomness of outcomes is a fundamental part of the quantum mechanical formalism, a direct logical consequence of the theory's mathematical structure, just as the constancy of the speed of light is a fundamental part of the mathematical structure of relativity.  If a way were ever discovered to predict the outcome of a quantum experiment that would mean that quantum mechanics was completely, totally, utterly wrong.  And quantum mechanics is one of the best confirmed scientific theories ever.  No experiment has ever disagreed with its predictions.  (Indeed, theoretical physicists consider this to be a serious problem because it leaves them with no guidance on how to make further progress!)

The fact that quantum outcomes really cannot be predicted is directly confirmed by experiment: the phenomenon of interference depends crucially on the unpredictability of quantum experiments.  The presence or absence of interference is a direct reflection of whether or not the particle is in a predictable or unpredictable state.

So that leaves two possibilities: one is that there is hidden state.  The second is that quantum randomness is really, truly random, and that quantum events are really truly "uncaused", and so quantum mechanics is a direct experimental refutation of the central premise of the Kalam cosmological argument.

For decades it was believed by physicists that this question could not possibly be resolved.  Indeed, Einstein famously cited this apparent impossibility as evidence that there must be something wrong with quantum mechanics.  The mere possibility that there could be true randomness (or even hidden state) bothered him to the point where he quipped that God does not play dice (to which Neils Bohr replied that Einstein should not tell God what He can and cannot do).

But it turns out that this question can be resolved.  Not only that, but it can be resolved experimentally.  The way to resolve the question was discovered by John Bell in 1964.  The first experiment was conducted in 1972.  The results have since been reproduced many, many times, and they are absolutely clear: quantum randomness is true randomness.  There is no hidden state.  If you want to know the details, I recommend David Mermin's excellent exposition (also available in this splendid book).

Non-local hidden state

Now, I have to give one caveat to this result.  The Bell inequalities don't rule out all hidden state, they only rule out local hidden state, that is, hidden state that is physically located at the place where and time when the experiment is conducted.  The results do not rule out the possibility of non-local hidden state, that is, state which not only do we not have access to, but which is located someplace other than where-and/or-when the experiment happens.

Does this rescue the Cosmological argument?  No, it doesn't.  Why?  Because eliminating the possibility of non-local hidden state is a logical impossibility.  Why?  Because the universe is finite.  There are a finite number of particles, and there is only a finite amount of time between the Big Bang and the heat death of the universe.  Therefore, in the entire lifetime of the universe we can only ever do a finite number of experiments.  The outcomes of all those experiments can be written down as a finite string of bits, and those bits can be found somewhere in the expansion of (say) pi.  So we cannot ever on the basis of any experiment rule out the possibility that the outcome of that experiment has been pre-determined by some cosmic Turing machine computing the digits of pi.  So even if God exists and is pulling the quantum strings, we can never tell, at least not on the basis of the outcome of any experiment, not even an experiment that violates the predictions of QM!

I've pointed all this out to a number of Christians.  They all responded (essentially) that if you cannot rule out the possibility of non-local hidden state, then you cannot rule out the possibility that it exists and is in fact God.  Well, that's true.  But it turns out that this apparent concession doesn't help the cause of theology at all, and in fact only makes things much, much worse.  Explaining why will be the subject of the second post in this series.

Thursday, March 09, 2017

A theory of Trump's wiretap tweets

The MSM has been busily parsing Donald Trump's latest unfounded (and some might say unhinged) allegations about Barack Obama spying on him during the election.  The analysis seems to shift between bewilderment and a resigned there-he-goes-again: still more buffoonery from the buffoon-in-chief.  What did you expect?
Of course, a more economical explanation is also available: It could be that the president of the United States was making bizarre counterfactual assertions based on whatever half-baked conspiracy theories he just read on right-wing media.
(We interrupt this missive to bring you an important aside: it's worth watching the video clip linked above of Ronald Reagan delivering his famous, "There you go again" line.  The clip includes the context in which that line was delivered, which no one seems to remember.  It's particular noteworthy in the light of what has happened in the subsequent 37 years, and indeed what is happening today.  We now return to our regularly scheduled blog post.)

But what if, as Scott Adams has pointed out 1000 times, Trump is not a buffoon?  What if there is method to this apparent madness?  To what end could all this chaos possibly be in service of?

Well, here's a theory.

First, let us catalog what I think are some relevant facts:

1.  On December 29 of last year, then-still-President Obama, in a standard response to reports of Russia attempting (perhaps successfully) to influence the U.S. election through computer hacking, expelled 35 Russian diplomats from the U.S.  The next day, Vladimir Putin, to everyone's surprise, announced that he would not invoke the standard retaliatory response to Obama's response to Russia's hacking, a departure from the script that left everyone at the time scratching their heads.

2.  Not even two months in, one Trump administration official has already resigned and another is under a dark cloud of suspicion for having attempted to conceal the fact that they met with Russian officials during the campaign.

3.  Donald Trump really really really doesn't want anyone to see his tax returns.

Next we have to ask just how un-bufoonish do we want to believe that Trump is.  I see three possible answers to this.  One possible answer is that he is a true Master of the Game, on a par with Vladimir Putin or Kim Jong Un.  (Say what you will about North Korea, the fact that the regime has not fallen and Kim's power faces no serious challenges -- when by all rights both of these things should have happened long ago -- is testimony to his political skill.)  But this is not consistent with the evidence.  There are a lot of things happening that Trump is apparently unhappy about.  He does not give the appearance of a man who is entirely in control of the situation.

So that leaves two other possibilities: one is that Trump is better than Putin, and all the chaos and confusion is all part of the plan.  This again is inconsistent with the evidence.  Yes, Trump is the President of the United States of America, which is no mean feat.  But he got there on the slimmest of margins, losing the popular vote, and running against the second most unpopular candidate in the history of presidential politics (he himself being the first).  If he were Putin's master I would expect him to do better.

His prior history also doesn't square with the master-of-masters theory.  Yes, he's rich, but he's a piker compared to Putin.  Even Trump's own inflated estimates put his net worth around only a few percent of Putin's.  Donald Trump seems to be particularly skilled at only one thing: screwing people over and getting away with it.

The second possibility, the much more likely one, is that Trump is out of his league.  He was able to navigate the waters of real estate development, reality TV, and New York City politics, but the presidency is a whole new ballgame, one for which he is utterly unprepared.  In particular, I don't think he reckoned on the power of the Deep State, and now he is scrambling to figure out how to deal with it.

Whether or not there really is a deep state in the U.S. is not the point.  My theory is simply that Trump did in fact make a deal with the Russians.  He made this deal because he has been doing business with Russia for years.  He probably thought (maybe even still thinks) that there is nothing at all wrong with it.  He may even be right about that.  But when he extended that deal-making as a private citizen to deal-making as president-elect but not as president, he crossed a very serious line.  He probably didn't realize it at the time, but he almost certainly does now.

Somewhere in the deep labyrinth of the intelligence agencies (it is surely that even if it is not a deep state) I'm pretty sure there is a Nixonian smoking gun, a recording of Trump that proves that he knew about and authorized a deal with the Russians on or around December 29.  Someone knows.  And Trump knows that they know.

So why hasn't this evidence been released?  Well, obviously because whoever has it (let's call him/her/them Deep Sam as a gender-neutral homage to both Mark Felt and the Deep State) thinks that it is more advantageous to them or to the nation to keep it secret for now.  Maybe Deep Sam is a patriot who believes that releasing the smoking gun would be bad for the country.  After all, if we get rid of President Trump we just end up with President Pence, who is vastly worse than Trump, in no small measure because Pence is actually a competent politician.  Trump's incompetence, and the resulting chaos and delays, somewhat limit the damage that he and the Republicans will be able to do.  (It is a sad, sad commentary on the state of our nation that the fact that our president is incompetent is actually a feature and not a bug.)  It is also possible that Deep Sam is an opportunist who wants to hang on for as long as possible to the considerable power provided by having dirt on the POTUS.

A more difficult question to answer is why Putin pulled back on retaliation when that provides such clear evidence that a deal was struck before the inauguration.  That seems like a rookie mistake, the sort of blunder Trump would make but not Putin.  I must confess I don't have a good answer for this.  Maybe Putin himself didn't realize that striking a deal with Trump before the inauguration would be viewed unfavorably in the U.S.  Maybe he was just having a bad day.  I don't know.  But it's clear that something unusual happened that day.  So it's not completely unreasonable to suspect that two unusual things happened.

This theory is the only one I can think of that accounts for Trump's publicly accusing Obama of wiretapping him but does not require Trump to just be a total loon.  Think about it: someone breaks the news to Trump that 1) dealing with the Russians before the inauguration was a serious no-no and 2) someone (Deep Sam) has proof that he did it.  Trump is pwned, so he plays the only move he has left: blame Obama.

The reason Trump accused Obama of wiretapping him is because Trump thinks it's true.  How else could anyone have that smoking gun?  It must have been Obama.  He even has evidence this time, God damn it!  But he can't reveal that evidence because the evidence is the smoking gun, and revealing that would be his own undoing.

I have no idea if this theory is correct, but it does seem to be a pretty good fit to the available facts.  Also, it's a hell of a lot of fun to contemplate.

Sunday, March 05, 2017

A climate change counterpoint

In the interests of maintaining the moral high ground with respect to relying on evidence, experiment and reason as the best guides to Truth I feel honor bound to point out an answer to a question on Quora posted recently by Richard Muller:

What are some widely cited studies in the news that are false?
That 97% of all climate scientists accept that climate change is real, large, and a threat to the future of humanity. That 97% basically concur with the vast majority of claims made by Vice President Al Gore in his Nobel Peace Prize winning film, An Inconvenient Truth. 
The question asked in typical surveys is neither of those. It is this: “Do you believe that humans are affecting climate?” My answer would be yes. Humans are responsible for about a 1 degree C rise in the average temperature in the last 100 years. So I would be included as one of the 97% who believe. 
Yet the observed changes that are scientifically established, in my vast survey of the science, are confined to temperature rise and the resulting small (4-inch) rise in sea level. (The huge “sea level rise” seen in Florida is actually subsidence of the land mass, and is not related to global warming.) There is no significant change in the rate of storms, or of violent storms, including hurricanes and volcanoes. The temperature variability is not increasing. There is no scientifically significant increase in floods or droughts. Even the widely reported warming of Alaska (“the canary in the mine”) doesn’t match the pattern of carbon dioxide increase; and it may have an explanation in terms of changes in the northern Pacific and Atlantic currents. Moreover, the standard climate models have done a very poor job of predicting the temperature rise in Antarctica, so we must be cautious about the danger of confirmation bias.
But under no circumstances should you interpret this as being synonymous with, "The climate alarmists are wrong and there's nothing to worry about."  To put this answer in the proper context, go to Muller's Berkeley Earth project page and read the summary of findings.  There you will find the following:
...the average temperature of the Earth’s land has risen by 1.5 °C over the past 250 years. The good match between the new temperature record and historical carbon dioxide records suggests that the most straightforward explanation for this warming is human greenhouse gas emissions.
A previous Berkeley Earth study, released in October 2011, found that the land-surface temperature had risen by about 0.9 °C over the past 50 years (which was consistent with previous analyses) and directly addressed scientific concerns raised by skeptics, including the urban heat island effect, poor station quality, and the risk of data selection bias.
In other words, the rate of increase is itself increasing.  Dramatically.  This is one of the many things that make this process so insidious.  There are huge time lags (by human standards) and multiple integrals involved.  If we wait for it to become apparent that climate change is causing serious problems it will be much too late to prevent catastrophe.

Also worth noting:
...the Berkeley Earth team was able to conclude that over 250 years, the contribution of solar activity to global warming is negligible. 
Some of the scientists on the Berkeley Earth team admit surprise that the new analysis has shown such clear agreement between global land-temperature rise and human-caused greenhouse gases. “I was not expecting this,” says Richard Muller, “but as a scientist, I feel it is my duty to let the evidence change my mind.”

Sunday, February 05, 2017

How Donald Trump Could Build an Autocracy in the U.S.

David Frum in the Atlantic has a long-form piece describing a frighteningly plausible scenario of how Donald Trump can lead the U.S. into an autocracy.  The TL;DR is that it won't be obvious that it's happening.  It's a splendidly written piece, worth reading all the way through despite its length.  I can't even find an excerpt that does it justice.  Just set aside some time and read it.  I don't assign homework that often.

Also, this cartoon came through on my feed today, noteworthy not just for its content but also for its (historical) context.

Thursday, February 02, 2017

Autocracy: Rules for Survival by Masha Gessen

Commenter Tony pointed me to this piece by Masha Gessen.  I'm not entire certain yet whether Trump is actually planning a Machtergreifung or if it just seems that way, but the warnings and portents are all looking quite ominous to me.  Worth reading.

I'll just leave this here

To which I would add:

Countries where Donald Trump does business: Saudi Arabia, UAE, Egypt and Lebanon.  (Oh, and Turkey, which is also excluded from the ban.)

Filling in the Countries where Donald Trump does not do business is left as an exercise.

A vicarious deep dive into climate change

I've had an item on my todo list for months to take a deep dive into the question of anthropogenic climate change.  Alas, with everything going on right now I just don't have the time.  Happily, it turns out that a Berkeley physics professor named Richard Muller has done it for me.  Muller was a climate-change skeptic who did an exhaustive study of the literature in 2012 and changed his mind.  He now runs an organization dedicated to sober, objective, open, and reproducible analysis of climate data.  It's a model of how science ought to be done.  They've done a much, much better and more thorough job of cutting through the gordian knot than I could ever hope to.  So thanks, Prof. Muller!

Welcome to your new theocracy

Donald Trump vowed today to 'totally destroy' the wall of separation between church and state.

Of course, in Trump's America, not all religions are created equal.
We've seen unimaginable violence carried out in the name of religion. Acts of wanton slaughter against religious minorities. Terrorism is a fundamental threat to religious freedom.
I'm pretty sure he was not referring to Christian terrorists, of which there have been many.  (So many, in fact, that I ran out of words before I ran out of links.)

Let's hope this doesn't become a self-fulfilling prophecy

Donald Trump's closest advisor Steve Bannon thinks there will be war with China in the next few years.  And he probably has the power to make it happen.

Tuesday, January 31, 2017

So many scandals, so little time

The Trump administration is mass-producing outrages on such an industrial scale I can barely keep up.

Yesterday Trump fired the acting attorney general who refused to defend his unconstitutional travel ban.  The last time something like that happened was in the Nixon administration.  Less than a year later, Nixon was forced to resign in disgrace.

Ben Mathis-Lilley at Slate has some useful perspective on the theory that the immigration order was a trial balloon for a coup.  (For the record, despite linking to this story yesterday, I never endorsed the use of the word "coup".  To me, the events of the last few days have "merely" been chipping away at the rule of law, the foundations of which have been crumbling for some time now.  Not that anyone should take much comfort in that.

My wife, Nancy, turned me on to two interesting pieces at The Week (a really excellent publication, by the way.  Everyone should subscribe.)  The first, by Ryan Cooper, soberly describes how Trump is imperiling the Constitution.
Donald Trump's executive branch is defying the judiciary, even with the personal, in-person assistance of national legislators. He is attempting, in part at least, to overturn constitutional government in the United States. 
This is not an exaggeration. In a republic, a professional legal corps gets to interpret the law as written by the elected representatives of the people, and the agents of state violence must obey their commands. In a tyranny, the leader does whatever he wants. That is what Trump, with the close counsel of his advisers Stephen Bannon and Stephen Miller, is trying to create.

The second explains the obvious truth (often the most difficult to describe without getting hyperbolic, because, geez, how can anyone with even half a brain not see this?) that the reason Trump's immigration order is outrageous has nothing to do with discrimination or the rule of law and everything to do with the fact that not a single terrorist has ever come into the U.S. from the countries from which immigration is being blocked.  Of course, this is far from the first time that Trump has made policy based on falsehoods, nor, sadly, is it likely to be the last.

Finally, but perhaps most importantly in the long run, there is a first-person account from Kieryn Darkwater about what it's like to be indoctrinated as a right-wing culture warrior as a home-schooled child.  This should be required reading for every aspiring liberal leader.  It describes exactly how the right won (and continues to win) the culture war, in short, by breeding, blocking out opposing views, and taking over the government from the bottom up, starting with local school boards.  It is a terrifyingly effective strategy, and if the left doesn't wake up to the realization that we are in fact at war and that the enemy is both amongst us and formidable, we are probably doomed.  One symptom of the fact that the left has not woken up is that we're all focused on how horrible Trump is and fantasizing over getting him impeached (or otherwise removed from office), apparently oblivious to the fact that Mike Pence is actually much, much worse.
I watched the Tea Party takeover and was surprised no one saw it coming. After all, this was part of the plan. Trump being elected is also part of the plan, although not Trump specifically; the true goal is Pence. 
Christofascists have been wanting someone like Pence in the White House and, until now, didn’t have a way to get one in. They know Trump is easily manipulated and will change his mind with the wind if it makes him feel more powerful and famous. Trump couldn’t care less about policy, a fact he’s made quite obvious. The Right has given a tyrant power and fame; he will do whatever they want him to do in order to keep it. This way they can sneak Pence in on a piggyback while filling Congress with even more evangelical conservative Republicans. Compared to Trump’s abrasive and terrifying behavior, Pence seems much less threatening. This is not the case. Pence has a proven track record of legalizing discrimination and acting against women and marginalized people. Those of us who didn’t leave the far Right are being elected to federal positions or are taking over states and cities. With Pence in office, even the reasonable-seeming incumbents – who have been and are still at the mercy of the Tea Party – are growing more bold in their attempts to further the Christofascist agenda: To Take Back The Country For Christ.
We need to wake up and smell the theocracy.  ISIS is not the imminent threat.  Quiverfull and the Promise Keepers are.

Monday, January 30, 2017

Getting really scary really fast

I had a truly frightening realization today.  I have been wrong about Donald Trump nearly every step of the way.  At first I thought there was no way he could win the nomination.  Then I thought there was no way he could win the general election.  Then I thought there's no way he can keep from imploding because he's an incompetent entitled narcissistic con man.

But what if he's not.  What if all of this success is not accidental.  What if he actually knows what he's doing, and all of this chaos is actually part of his plan.  Yonatan Zunger, a principal engineer (and former theoretical physicist) at Google, has written a thorough, sober and well-researched essay exploring that question, and the conclusion he reaches is really scary.
I see a few key patterns here. First, the decision to first block, and then allow, green card holders was meant to create chaos and pull out opposition; they never intended to hold it for too long. It wouldn’t surprise me if the goal is to create “resistance fatigue,” to get Americans to the point where they’re more likely to say “Oh, another protest? Don’t you guys ever stop?” relatively quickly.
Note also the most frightening escalation last night was that the DHS made it fairly clear that they did not feel bound to obey any court orders. CBP continued to deny all access to counsel, detain people, and deport them in direct contravention to the court’s order, citing “upper management,” and the DHS made a formal (but confusing) statement that they would continue to follow the President’s orders. (See my updates from yesterday, and the various links there, for details) Significant in today’s updates is any lack of suggestion that the courts’ authority played a role in the decision.
That is to say, the administration is testing the extent to which the DHS (and other executive agencies) can act and ignore orders from the other branches of government. This is as serious as it can possibly get: all of the arguments about whether order X or Y is unconstitutional mean nothing if elements of the government are executing them and the courts are being ignored. 
Worth reading the whole thing.

There are at least two more ominous developments today.  The first is the deliberate failure to mention Jews or anti-semitism in Trump's statement for International Holocaust Remembrance Day.
Reince Priebus, the White House chief of staff, defended the language in a Sunday interview on NBC’s “Meet the Press,” telling the host, Chuck Todd, “I don’t regret the words.” 
Mr. Priebus continued, “I mean, everyone’s suffering in the Holocaust including obviously, all of the Jewish people affected and the miserable genocide that occurred — it’s something that we consider to be extraordinarily sad.”
This is the same ploy that the right used to defuse the Black Lives Matter movement by deploying the aphorism, "All lives matter."  Yes, that's true, but it misses the point rather badly.

The second ominous development was Trump's unprecedented appointment of far-right-wing (and well-known anti-semite) Steve Bannon to head the national security council.
President Donald Trump has reorganized the National Security Council—elevating his chief political strategist, Steve Bannon, and demoting the director of national intelligence and the chairman of the Joint Chiefs of Staff. 
Bannon will join the NSC’s principals committee, the top inter-agency group advising the president on national security. 
Meanwhile, the director of national intelligence and the chairman of the Joint Chiefs of Staff will now attend meetings only when “issues pertaining to their responsibilities and expertise are to be discussed,” according to the presidential memorandum issued Saturday.
If you were pinning your hopes on the possibility that cooler heads would prevail, you should be very afraid now.  All of the cooler heads are being systematically and expeditiously dispatched.

Sunday, January 29, 2017


Donald Trump has been in office less than two weeks and already he has managed to plunge the United States of America into utter chaos.  I knew Trump was going to be a terrible president, but even in my most pessimistic moments did I ever imagine that things would get this bad this fast.

Let us survey today's headlines:

Mitch McConnell says we have no religious tests in the U.S. while at the same time supporting Trump, who says that the U.S. will prefer Christian immigrants over non-Christian immigrants, a position widely denounced by Christian leaders around the world.  Giving preference to Christians sure sounds like a religious test to me, but in the era of alternative facts I guess a religious test can be whatever you say it is as long as you're the person in power.

Trump chief of staff Reince Priebus said that the executive order barring entry into the U.S. from seven Muslim countries does not apply to green card holders.  While he was saying this, green card holders were being denied entry into the U.S. all over the world contrary to court orders.

A twelve year old girl who is one plane trip away from being a U.S. citizen is stuck in Djibouti:
The 12-year-old is now in the worst possible limbo. That immigrant visa grants her lawful permanent resident status the instant she’s admitted to the U.S. by Customs and Border Protection. And once she reaches the United States, Section 320 of the Immigration and Nationality Act stipulates that, as a minor living with her U.S. citizen parents, she automatically becomes a U.S. citizen. But on Saturday, hours after Trump signed that executive order, Ali and his daughter were pulled out of line by airline personnel and prevented from boarding their Ethiopian Airlines flight. Until she’s admitted to the United States, she will not have green card status. The girl and her father are trapped in East Africa, where they have no friends or family, as they wait for a resolution to an ordeal they had thought was over
At least two people were actually forced to surrender their green cards:
The Aziz brothers’ story is particularly stunning because, says Sandoval-Moshenberg, not only were they handcuffed while they were detained by CBP at Dulles, and not only were they turned away and sent to Ethiopia, but they were also made to sign a form, known as the I-407. In doing so, they surrendered their green cards, under the threat of being barred from the U.S. for the next five years if they did not. 
This is particularly chilling.  If people can be forced to surrender their green cards, what is to stop Trump from forcing Muslim American citizens from surrendering their passports?  Think it can't happen?  It already has.  If Barak Obama can revoke Ed Snowden's passport, you'd better believe that Donald Trump can revoke yours.

It goes on and on  and on and on and on and on.

Oh, this might be a good time to remind everyone that Steve Job's father was an immigrant from Syria.  If Donald Trump's immigration policy had been in place in the 1950s there would be no Apple Computer today.

If there is any doubt in your mind about the human toll of Donald Trump's reckless executive order, you should read this:
Hamid Kargaran ... is a U.S. citizen, and a successful one at that. He owns a Bay-area marketing company that works with Google, another that consults with medical practices and teaches at two local universities. His wife of two years, Elaheh Iranfard, 28, is a painter studying at the San Francisco Academy of Art. They both embrace California and U.S. culture with gusto. 
She had been back home for a short visit with her family, a trip she’d planned after her parents were unable to get a visa for the United States. But in the hours after President Trump signed the executive order banning entrants from seven Muslim countries, including Iran, the door slammed shut. Agents at multiple airlines told her she couldn’t board, legal U.S. resident or not. 
For two sleepless days, he has desperately tried to get information from airlines, government officials, friends and family. At one point, he staked out a part of San Francisco International Airport where Customs and Border Protection officers take their break. Three of them gave him different answers to the same questions; one of them told him: “Iranians are not our friends.” 
It’s been a shock to a man who joined pro-American demonstrations in Tehran after terrorists struck the United States on September 11, 2001. What he was hearing now, as friends advised him to scrub from his phone any social media posts that suggested he disagreed with Trump, reminded him of the Iranian repression that drove him from the country
“I never thought when I moved here and made this country my home that this would happen,” he said. “I employ people, I pay taxes. We love this country. But I feel like the hard work has been meaningless. We’re second-class citizens.” 
Now he was waiting, and he knew there would be no relief until his wife actually walked into the sun in San Francisco. In three hours, she would find out if Lufthansa agents in Tehran would let her on the plane. In Germany, she would learn if officials there would let transit on to California. At home, she still had to pass through U.S. passport control. 
“I don’t know,” Kargaran said. “We’ve tried to do everything right. Doesn’t that matter?

Saturday, January 28, 2017

Texas mosque destroyed in early-morning blaze, cause unknown

A mosque in Victoria, Texas was destroyed by fire this morning.  The cause is being reported as "unknown" but I'll give you long odds against it being an accident.

What did Donald say to Melania?

When he crushed her soul?

It's not just the change in Melania's expression that is striking; the smug self-satisfied look on Donald's face is downright chilling.  It's clear that he intended to say something to devastate her, and that he knew he had succeeded, and that he was happy about it.  That is one of the marks of a psychopath.

So much for playing by the rules

It's easy to miss just how far off the deep end Trump has gone with his  executive order to bar entry into the U.S. from seven Muslim countries.  Many people seem to think the order applies only to refugees and migrants, but it doesn't.  It applies to everyone, including legal immigrants, even permanent residents with green cards.  If you happened to be out of the country when the order was issued, you now can't get back in without a waiver from DHS.  And if you are in the country, now you can't leave because you might not be able to get back in.

With this order Donald Trump reveals beyond any doubt that he cannot be trusted.  His rhetoric all during the campaign was that he wanted to exclude and deport illegal immigrants.  But this executive order draws no such distinctions.  Legal or not, if you're from one of the Muslim countries targeted by the whims of the dear leader (Saudi Arabia, tellingly, is not on the list) you are no longer free to cross the border.

The litany of outrage here is so long it's hard to know where to begin.  Let's start with the obvious: banning people because of their religion or ethnicity is shameful at best, unconstitutional and un-American at worst.  The U.S. turned away Jewish refugees and interned Japanese residents (including U.S. citizens) during WWII, to our everlasting ignominy.  That this policy is being supported by a vice president who (rightfully) called it "offensive" during the campaign is hypocrisy of the highest order.  And of course there's the fact that two of the countries most likely to actually send terrorists to the U.S. -- Pakistan and Saudi Arabia -- are not on the list.

But the worst part of this is the fact that no exception was made for legal residents.  That is not only so far beyond stupid that you can't even see stupid from there, it's bad business.  We made a deal with those people: work hard, pay your taxes, don't blow shit up, and we'll let you stay.  They held up their end of the bargain, but we have now reneged on ours.

Of course, reneging on commitments is nothing new to Donald Trump.  It is, sadly, nothing new to the United States of America either.  But that doesn't make it right.

[UPDATE] I urge you to read Scott Aaronson's excellent post on this topic.

Friday, January 27, 2017

GOP Quietly Admits There Will Be No Obamacare Replacement

What should come as no surprise to anyone, the GOP Quietly Admits There Will Be No Obamacare Replacement:
The history of the development of the Republican alternative to Obamacare since the beginning of the health-care debate, in 2009, has been an endless loop of loud promises that a full plan will be announced soon, followed by quiet admissions that it will not. Seventeen days ago, Donald Trump promised a vote to repeal the law “probably some time next week” with a vote for a replacement “very quickly or simultaneously, very shortly thereafter.” At a meeting in Philadelphia yesterday, Trump and his House Republican allies produced no agreement on a plan. If there is a consensus, it is that there will be no replacement plan at all.
You can't defy the laws of physics or economics.  The free market does not lead to good outcomes when it comes to health care.  If Johnny gets hit by a bus we want him taken to a hospital whether or not he's able to pay the bill.  Letting him bleed out on the sidewalk is not an option anyone is willing to accept.  So the government has to do something, at which point things get complicated and thought is required, something which the Republicans seem to be incapable of.  So much easier to bury your head in the sand and blame everything on the democrats.  Except even that won't work this time around.

The pro-life movement should be taken seriously

Tens of thousands marched for life on the national mall today.  The crowd was large and diverse enough that the pro-life movement cannot be dismissed as a radical fringe movement, notwithstanding its shadowy and ignominious roots.  It must be taken seriously.  Unlike the anti-gay-marriage movement, which is driven entirely by bigotry and the desire to impose religious beliefs on others, the pro-life movement actually advocates some defensible positions.  In particular, they ask the very reasonable question: where do you draw the line between embryo-hood and person-hood?  There are only a few bright lines: conception.  First heartbeat.  Birth.  The pro-choice side rejects the first two, and no one argues for the third one (see below), so what we are left with is the arbitrary trimester lines plucked from a hat by Harry Blackmun in Roe v. Wade.

On the other hand, having a defensible position is not enough.  It is incumbent on the pro-life side to start advancing some serious policy proposals that align with reality.  It doesn't work simply to state as a principle that life begins at conception, and therefore abortion is murder.  It is, alas, much more complex than that.

For example: excess human embryos are routinely produced and frozen during fertility treatments.  Reliable figures of how many such embryos are currently on ice are not available, but estimates put the count at about half a million.  If you are pro-life, what exactly do you propose to do with those?  Are you going to start conscripting women to carry these "innocent babies" to term?

Even without modern technology, the thesis that life begins at conception is deeply at odds with reality: miscarriages in the first trimester are common.  15-20% of known pregnancies end in miscarriage, and many more surely go unreported and possibly even unnoticed.  Even God seems to be OK with killing babies as long as it's early enough.  Then there's the fact that there are certain behaviors that increase the risk of miscarriage.  Are you really going to start investigating every miscarriage as a possible homicide?

Abortion appears to be a clash of absolutes but it's not.  There is quite a lot of common ground between the two sides.  For example, everyone agrees that an hour or a day or a week or even a month before a baby is born that it's a baby, a person, and it's not OK to kill it.  The debate is only over whether to draw the line between embryo-hood and person-hood at conception or somewhere else.  And as I've noted above, drawing the line at conception leads to a lot of difficulties for which the advocates of this position seem to have no answers.

It is for this reason that I believe that being pro-choice is at the moment the only principled stand.   Until those who argue that life begins at conception come up with acceptable answers to these and other questions (What about rape and incest?  What about pregnancies that endanger the life and health of the mother?  What about encephalitic fetuses?) the only principled position is to err on the side of the interests of the party whose personhood is not in doubt: the mother, and let her decide based on the totality of her circumstances.

Note that being pro-choice is absolutely not the same as being pro-abortion.  No one is pro-abortion.  To be pro abortion would mean that you advocate abortion as a good thing in its own right, and no one believes that.  Everyone agrees that all else being equal the world would be a better place if there were fewer abortions.

Unfortunately, there are vested interests on both sides who benefit from the on-going conflict and so refuse to allow the fact that there is agreement to be acknowledged, because this would cost them power.  The path forward is clear: ditch the extreme rhetoric on both sides, acknowledge the the issues are complex, but that there is a consensus that, all else being equal, reducing or even eliminating abortions would be a Good Thing.  Then we can start to talk about how best to achieve that goal rather than vilifying each other as baby-killers or enslavers of women.  It seems pretty clear to me (and I think it's clear to most people) that throwing women and doctors in prison for murder is probably not the most effective strategy.  Providing them with better education and alternatives (like easy access to birth control) would probably work better.

Despite the fact that there exists a path to reconciliation, I prophecize that this war will continue for a good long while.  Sometimes I feel like a voice crying in the wilderness.

(Interesting side note: as I went looking for links for the above I found this story all over today's news: scientists have successfully implanted human stem cells into pig embryos which were then allowed to develop for up to 28 days.  What would be the status of these human-pig chimeras if abortion were made illegal, I wonder.)

Thursday, January 26, 2017

Miami-Dade Is the First Sanctuary Domino to Fall

The nazification of the United States has begun.  Miami-Dade is going to start jailing suspected illegal immigrants without a warrant.

Here's the problem: if I get picked up by the police and they suspect me of being in the country illegally, how am I supposed to prove them wrong?  I'm a citizen, so I don't have a green card.  I happen to have a passport because I do a lot of international travel, but I don't carry it around with me; it's too bulky.  And not all citizens have passports.  The only identification I carry with me regularly is a drivers license, and because I'm from California that does not prove I'm in the country legally.

Of course, I'm pretty sure no one is going to suspect me of being an illegal immigrant, because I'm a white guy and I drive a nice car and I don't go to the disreputable parts of town.  But my civil liberties should not depend on such things.  I should be just as confident of not being deprived of life or liberty without due process of law even if my skin is brown and I speak with an accent and I drive a ratty truck and my name is Juan.  But you can be pretty sure that the detention cells are not going to be full of white people, they're going to be full of brown people.  That is the problem.

Locking people up simply because they can't prove they're in the country legally whenever a cop demands it is a clear violation of the fourteenth amendment, which says in part, "... nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws."  Note well that is says, "person", not "citizen."

Look, I get the frustration that people have with illegal immigration.  It sucks when you follow the rules and you see people cutting in line.  But locking people up without warrants is not the right answer.  A lot of things are easier in a police state.  But the United States is not supposed to be about what is easy, it's supposed to be about what is right.  And this ain't right.

Pondering the pedagogy of the projective plane

[Another geeky break from Trump bashing]

I had an "aha" moment about the project plane that I thought I would share.  For those who don't know, the projective plane is a mathematical construct that arises in algebraic geometry which has a lot of uses, but the one that drew my attention to it has to do with elliptic curves, which are used in cryptography.  An elliptic curve is a curve with an equation of the form y^2 = x^3 + [some other stuff that doesn't matter for this discussion].  The graph of this equation looks like this:

Elliptic curves have this interesting property that a line through any two points on the curve is guaranteed to intersect the curve at a third point.  This property allows you to define an operation called point addition which generates a group which lets you do cryptography.  None of this matters for this post.  I mention it only for context.

What this post is about is the claim that I just made, that a line through any two points on the curve will intersect the curve at a third point, because it looks like there is an obvious counter-example: two points that have the same X coordinate will produce a vertical line, which looks like it cannot possibly intersect the curve again.  In fact, we can easily prove that this is true, because we can take the square root of both sides of the elliptic curve equation and get y=sqrt(x^3 + [other stuff]).  So for a given value of X, Y will only have two solutions.

What you will find if you dig into the elliptic curve literature is that the third point of intersection is something called the "point at infinity", and that this point can be mathematically justified (i.e. it's not just a random hack thrown in to make things work out) using something called the projective plane.  But then if you try to find out what the projective plane is and how it works you end up in a horrible mathematical mess, none of which seems to have anything to do with elliptic curves, or how we can possibly justify the point at infinity.  In particular you will learn that the projective plane involves mapping every point of the plane onto a line, but very few explanations about why mapping points to lines is a good idea.

Here is what finally made it click for me:

There are two ways you can imagine looking at an infinite plane.  The first is to take a “God’s eye view” where you are looking straight down at the plane as though from an infinite distance through an infinitely powerful telescope.  Like this:

From this point of view, grid lines (lines parallel to the x and y axes) always appear to intersect at right angles. Parallel lines always appear to be separated by the same distance.  And you can’t see the line at infinity because, even though your telescope is infinitely powerful, it only has a finite field of view.  You can look at any point by positioning yourself over that point, but you can’t go out an infinite distance.

The second way to look at an infinite plane is the “mortal’s-eye view”, where you are standing on the plane at some particular point looking at it from some finite distance (your own height), like so:

The only point you can look straight down on is the point you are standing on.  To see other locations you have to tilt your head, so you are looking at all other points from some oblique angle.  Like this:

From this point of view, grid lines generally do not appear to intersect at right angles.  The distance between parallel lines does not appear constant, and indeed parallel lines will appear to meet at the horizon.  The point on the horizon where parallel lines meet is determined entirely by the slope of the lines, completely independent of the distance between them.  And, most importantly, you can see the horizon, which looks like a circle surrounding you.  But this "circle" is infinitely far away.  A circle with infinite radius has zero curvature, so this “circle” is in fact a line: the line at infinity.

The reason that the projective plane is constructed by mapping points in 2-space to lines in 3-space is that from the mortal’s-eye view you can’t actually tell how far away a point is (we’re assuming no stereoscopic vision here).  All you can tell is the azimuth and elevation relative to your vantage point.  So all of the points along a given line of sight form an equivalence class from the mortal’s-eye view.

In the figure above, if we imagine that we are looking "up" along the Y axis, all vertical lines meet at the point O, which is a point at infinity.  Lines going up and to the left at 45 degrees to the vertical meet at Z, and lines going up to the right at 45 degrees meet at N.  Z, O and N are all points at infinity.

The reason vertical lines and elliptic curves meet is because as X increases, the slope of the curve also increases, approaching infinity as X approaches infinity.  (As a little elementary calculus will reveal, the slope of the curve is proportional to the square root of X.)  So "at infinity" the curve is vertical, and so intersects the horizon (the "line at infinity") at O, which is the same point where all vertical lines intersect the line at infinity.  So the point O is "the point at infinity" for any elliptic curve.

The projective plane is cool because it unifies a lot of things that would otherwise have to be treated as special cases.  For example, on the projective plane there is no distinction between circles, parabolas, and hyperbolas.  All conic sections are the same.

Vulgar, vile and evil

The utter cluelessness of Donald Trump's supporters is beyond mind-boggling.  In Franklin, Tennessee, the owner of a knitting store put up a Facebook post saying:
With the recent women's march on Washington, I ask that you if you want yarn for any project for the women's movement that you please shop for yarn elsewhere. The vulgarity, vile and evilness of this movement is absolutely despicable. That kind of behavior is unacceptable and is not welcomed at The Joy of Knitting. I will never need that kind of business to remain open. Two wrongs will never ever make it right. 
As the owner of this business and a Christian, I have a duty to my customers and my community to promote values of mutual respect, love, compassion, understanding, and integrity. The women's movement is counterproductive to unity of family, friends, community, and nation. 
I do pray for these women. May the God work out His love in their hearts and continue to heal and unite Americans.
Say what??? "Vulgarity, vile [sic], and evilness?"  What exactly is it that is vulgar, vile and evil about the Women's movement?  To the contrary, the marches last week were 100% peaceful.  No violence, no arrests.  What could possibly be wrong with that?

Well, the Washington Post has a clue:
“This is starting to undermine their efforts,” Poe said. “I think if you want to get your point across you need to do it the right way and I just think that walking around dressed as a vulva is gross. Hatred is not acceptable speech.”  [Emphasis added]
Say what???  I presume that she is referring to the so-called "pussy hats", but seriously, has this woman ever even seen a vulva?  Pussy hats look nothing like vulvas, they look like cat ears, which is what they are intended to look like.  They are called "pussy hats" to rhyme with "pussy cat", not the kind of pussy that Donald Trump like to brag he grabs women by.

Here, let me show you:

Pussy Hat

Pussy Cat

I was tempted to post a picture of a vulva for comparison but ultimately decided that I want to keep this blog family-friendly.  If you don't know what a vulva looks like, enlightenment is just a Google search away.

Even if these women were dressed as vulvas (which they weren't) where in the world do you get from there to hatred?  Dressing up like a pussy (of either sort) isn't hatred.  This is hatred.

[UPDATE] Apparently there were a few people actually dressed up in vulva costumes at some of the marches, though I didn't see any at the one I attended, and I didn't see any coverage of this in any of the news reports I saw.  I had to go looking to find them.  You know what?  I actually agree that these costumes are vulgar (though I wouldn't go as far as "vile" and they certainly aren't "evil").  I guess the Trump camp does not have a monopoly on cluelessness.  Honestly, people, how on earth do you imagine that dressing up like genitalia is going to move the needle in a positive direction?

But I still don't understand how refusing to sell yarn to women's movement members is supposed to help.  None of the vulva costumes I was able to find pictures of looked like they were made out of yarn.  Elizabeth Poe's facebook post didn't ask for people to not buy construction materials for vulva costumes, it specifically asks for women's movement members to shop elsewhere for yarn:
I ask that you if you want yarn for any project for the women's movement that you please shop for yarn elsewhere.  [Emphasis added -- obviously.]
The most charitable interpretation I can come up with is that because there were a few tasteless apples out of millions who attended the marches, Elizabeth Poe wants to refuse to sell yarn to anyone if they want to use it for making "any project for the women's movement."  Seriously, can there be any doubt that she had pussy hats in mind when she wrote that?

The irony here (it has been a long, long time since I have been able to make any observation about the political right without using the word "irony") is that but for the advances made by people like the ones Elizabeth Poe wants to exclude from her business she wouldn't even have a business to exclude them from.