William M. Briggs

Statistician to the Stars!

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Quantum Mechanics & Free Will: Guest Post by Bob Kurland

Quantum mechanics and duplicate bridge share the same idea of randomness

This post originally appeared in longer form at Bob’s place. There’s a lot of meat here; I recommend biting it off in small chunks.

“Of course I believe in free will. I have no choice.” —The Salon Interview, 1987, Isaac Balshevis Singer

“There is no evidence for determinism.” —Princeton Lectures, John H. Conway

“Philosophy is too important to be left to philosophers” —Unification beyond the Core, Frank Wilczek (also attributed to John Wheeler)

“Does it even matter if God plays dice?” —Rachel Thomas’ Plus-math Interview of John Conway

“…[D]early beloved…be not disturbed by the obscurity of this question; I counsel you first to thank God for such things as you do understand; but for all which is beyond the reach of your mind, pray for understanding from the Lord, observing at the same time peace and love among yourselves…” —On Free Will and Grace, St. Augustine of Hippo

In one of the later Foundation novels, Isaac Asimov envisages a world, Gaia, in which a super-conscious mind pervades the world, from the smallest virus or rock to the humans (and robots). In such a world it would be natural that quantum entities have free will, and there would be nothing remarkable in the Conway-Kochen Free Will Theorem:

It asserts, roughly, that if indeed we humans have free will, then elementary particles already have their own small share of this valuable commodity. More precisely, if the experimenter can freely choose the directions in which to orient his apparatus in a certain measurement, then the particle’s response (to be pedantic—the universe’s response near the particle) is not determined by the entire previous history of the universe. (The Strong Free Will Theorem, John Conway and Simon Kochen.)

See Rachel Thomas for a rigorous proof. Or read John Conway’s six Princeton lectures on his Free Will Theorem. I should note that Conway does not claim his Free Will Theorem disproves determinism; indeed, he says there is no way to disprove determinism, despite the fact that there is no evidence for it.

Here I use the Free Will Theorem (abbreviated as FWT) as a springboard to discuss several issues in interpreting quantum mechanics, namely how randomness and consciousness might enter into interpretations of quantum mechanics. (Fear not, gentle reader–this will not be a “What the Bleep” presentation, or a jump into Eastern mysticism.)

What do Conway/Kochen mean by “free will”? Both for the investigator and for particle system they mean that the choice–what is done–does not depend on previous history. A more conventional interpretation might be that free will is the ability to freely choose amongst several options. The term “freely” is susceptible to a number of definitions. (As with Justice Potter Stewart’s definition of pornography, “I know it when I see it”.) In his Princeton lectures and interviews for Rachel Thomas, Conway is quite emphatic that this freedom is not just “randomness”.


To show how randomness might enter, he sets a backgammon tournament as an example. The tournament director casts all the throws of the dice the night before the tournament, and then calls them out sequentially as each game is played, so that there is a level playing field for each contestant.

An example more familiar to me is that of a duplicate bridge tournament. At each table, four hands are dealt out randomly and teams rotate from table to table, so that (eventually) each team has played at each table with the same dealt hands. There is a predetermined initial lay of the cards, but the players are free to deal with the sets of hands as they will. (Is this an example of what philosophers call “compatibilism” in free will?)

Conway strongly argues that the FWT forbids randomness as an agency, whether occurring at the event or predetermined:

That’s why it doesn’t matter if God plays dice with the Universe, or not. Even if we allowed random numbers into the Universe, which I’ll think of as God’s dice, that’s not sufficient to explain the lack of pre-determinism in quantum physics.

I have a problem understanding this assertion. Granting that the FWT shows that the particle response cannot be predicted by a function involving past history, how exactly does this dispense with pseudo-randomness, predetermined before the world began? What can we learn from physics, in general, and quantum mechanics, in particular, to understand Conway’s argument?

Let’s consider first “random noise” in electronic devices, my old friend from nmr spectroscopy and MRI. Such noise can be characterized by mean square amplitude and correlation times, which in turn can be related to physical parameters. Molecular motion candidates for randomness also obey functional relationships. I’ve cited these as examples that don’t contradict Conroy’s argument about predetermined randomness. Can the reader cite others that might? I can’t.

Quantum Measurement

If we turn to quantum mechanics, the state function, which most generally can be put as a superposition of basis states (e.g. “Schrodinger’s Cat“), evolves deterministically. The randomness comes at measurement, when the state function collapses, except for that basis state which gives the measured result. Chance/randomness for the measured result comes from the component nature of basis states, and should be distinguished from weighting in a mixture of states (also see Quantum divine intervention). Quantum Mechanics does not include this state function collapse on measurement as part of the general theory, and thus results the so-called Measurement Problem.

Amongst the various interpretations and alternative theories which attempt to resolve the measurement problem, I’d like to focus on two: 1) the relation between the observer, consciousness and measurement in quantum mechanics; 2) many worlds/many minds (relative state theory). From the earliest days of quantum mechanics, the great thinkers–Von Neumann, Wigner, Schrodinger–have posited that the final step in the measurement process was observation by a mind, a consciousness, and thus the mind and quantum mechanics were entwined. The delayed choice experiment adds weight to this belief, I believe.

Enter Minds

There are many physicists (not abashed by the popularization of this notion in quantum leap science fiction) who subscribe to the Many Worlds interpretation of quantum mechanics that at each measurement one option is made apparent and the rest branch (into alternative universes; or alternative minds?).

With John Wheeler, I believe there is a participatory universe created by the observer, by conscious minds (ours? God’s? both?). The free will of the quantum entity is our own free will. There is an infinitude of possible universes and our ego, our consciousness traverses these as it makes choices. If there is a universe where we measure the particle going through one slit, there is another (with other conscious minds) where it goes through both. Such a view resolves a conflict between free will and God’s omniscience and omnipotence–if God knows what our future actions will be, how can our will be free? And the answer would be a type of Molinism, God is aware of all possible counterfactuals, but they are only counterfactuals for our mind, our ego, not for God.

Malthus’ Proof That Welfare Leads To Increasing Need For Welfare

First person that giggles at my hand drawings gets a mean look. My computing facilities are somewhat lacking…

It' all here.

It’ all here.

This of course is only a cartoon, but a helpful one of one of the proofs the Reverend Thomas Malthus used in his An Essay on Population to show government handouts beget increasing government handouts. Malthus believed, and history thus far vindicates, there were only two possible forms of human community: one in which most are comparatively (or relatively) poor and one in which everyone is absolutely poor. Laws designed under the influence of Benevolence must lead to the latter.

I was reminded of this proof in David Stove’s what?-you-haven’t-read-it-yet What’s Wrong With Benevolence?.

We start at [1] with a small class of Poor who are to be fed, clothed, sheltered, cell-phoned, cable-TVed, and so forth by Government with funds provided by the Taxed. Government extracts wealth, keeps a portion for itself (this step is oft forgotten), and dispenses the rest to the Poor. At this level, the portion the Government keeps is small and the disparity in wealth between Poor and Taxed, while it exists, is small and feels natural: there are rich, mostly middle class, and a few poor.

But since some of the Taxed are not rich, are just above the Poor threshold, and that these At Risk receive some of their wealth from those richer than themselves, who are now surrendering that wealth to Government, and they themselves are unable to afford the tax burdens, some fall into Poverty.

By [2] the class of Poor has grown. This necessitates Government asking the Taxed to “pay their fair share”, i.e. politicians take a larger bite. By this point, the disparity in wealth which once seemed natural and almost invisible has grown noticeable; people wonder how to “correct” it. The Government swells in size and power as more wealth comes under its control: a smaller proportion of taxes are given to the Poor, but this is masked by “borrowing from the future.” Those At Risk struggle harder than before, and more fall into Poverty.

After a while [n], the class of Poor is large and its maintenance becomes painful. The Taxed are excessively burdened; many make devils’ bargains with Government to forestall the inevitable, which has the effect of increasing Government power. The wealth disparity is now glaring, with loud calls for it to be eliminated, by force if necessary. Government, fattened by the many iterations of Taxes, becomes powerful enough to insist on this. It deduces the only way to remove the disparity is by resorting to community of property, where all share equally in the wealth (except the class of necessary leaders). This happy phrase convinces the majority, and away we go into communism once again.

Now this feedback cycle is exactly what happened when England first created its Poor Laws. From Benevolence (emphasis original):

[T]o the immense puzzlement of almost everyone, it was found that the proportion of the population receiving money under the laws (and consequently, of course, the burden of those who paid the tax) always increased. [p. 46]

[For this proof all] that Malthus actually assumed were certain elements of human psychology, as past experience has disclosed them to be. Namely, he assumed an instinct of hunger in all; a sexual instinct in virtually all; a plentiful supply of laziness in the vast majority; and no shortage anywhere of selfishness, stupidity, or short-sightedness. There is, indeed, no rational way to proceed, as Malthus himself says, except on the assumption that human beings will be what past experience has uniformly shown them to have been.

The history of the Twentieth Century is known well enough. But why haven’t we yet (again) “spun down” into the depths? Because new forms of wealth created by advancing technology have propped up the system, enriching many and forestalling outright decline. Stove credits gasoline and electricity. Our age has its own amazements, but just think how long it took the Government to reach in and grab (i.e. “regulate”) the Internet, a process still unfolding. Technology can also hurt: machines are slowly replacing workers at the bottom of the scale, and now some in the middle. It is only a matter of faith, and a hope against the evidence of human history, that “progress” leads only to improvement. Change is not always that which we can believe in.

The poor must not and cannot be ignored. So what is the Solution? Well, the (old) Christian one, which is to say, private, preferably local, charity. Individuals (or groups of them) undirected by Government can choose how much and when to give. They know better than Government just how much charity they can bear and where it is best placed, and when they give they are unlikely to sink into poverty.

This approach strengthens rather than weakens families, and families are a strong defense against poverty. Forcing somebody to “donate” is not charity, a logical fact socialist clergy members should recall. Yet with the disappearance of the family and retreat of religion, all people see is Government.

Just a sketch, just a sketch…

Update Real-life current example: Conservatives don’t want to face reality of inequality.

Update CBO shows latest welfare effort, Obamacare, to kill a few million jobs. White House says this is a good thing. No, really.

In other words, it’s not that employers will be offering 2.5 million fewer jobs. It’s that ObamaCare, by subsidizing low earners and expanding Medicaid for the very poor, will incentivize 2.5 million people not to work.

About That Lefties-Drink-More-Than-Conservatives Study

Makes sense to me!

Makes sense to me!

“Honey? Did you meet our new neighbors?”

“Not yet. Why?”

“I’m a little worried about them. They have an ‘I heart NPR’ sticker on their Prius.”

“Oh, God. Pass me the bottle.”

This is only one scenario, and a plausible one, of how the migration patterns of progressives can change the drinking habits of normal citizens.

This isn’t Yours Truly speaking. Science itself says so.

Or so claim Pavel Yakovlev and Walter Guessford in their peer-reviewed “Alcohol Consumption and Political Ideology: What’s
Party Got to Do with It?” (pdf) You’d be inclined to answer “Not much”, but then you haven’t taken the almost-desperate need of sociologist to research questions like this. And research they have, compiling statistic after statistic which prove, beyond all doubt, that a person’s mood and circumstance has something to do with whether they’ll take a tipple. Who knew?

News organizations are breathless over the pair’s “findings.” The Week leads with “Study: Liberals drink more alcohol than conservatives: Apparently, being liberal is thirsty work” and UPI chimed “Study: When a state becomes more liberal drinking increases” (via this site).

And just what are these “findings”? Foremost—and economists will want to take note—“Alcohol shipments are highly collinear with alcohol consumption”. The more alcohol bought, the more that is drunk. Counterintuitive? However, this is independent of politics, our main interest, so let’s push on.

A fellow named Berry allowed our duo to measure the political attitude of each State of the union. How States can have political attitudes is a vexing question better left unexamined. How Berry did it is, however, easily answered. Through equations like the one pictured above. Each State is awarded (via equations) its own unique number per year, which is labeled more or less liberal.

How does Berry handle States like New York, which in surface area is largely conservative except for the dangling carbuncle which is New York City? How dare you ask is the answer. Science, he says. So Science.

Anyway, our researchers calculated Berry’s Number for each State for each year between 1967 and 2003 and then averaged over the years. Yes, because not much has changed politically from 1967 to 2003. Result: one number per State. Then our pair took the amount of beer, wine, and booze flowing into each State for the same years; they took the population of each State for each of those years, then calculated the per capita average consumption of each type of alcohol. Then, in a step of statistical boldness, they averaged this average across the same time period. Result: one number per State of each of beer, wine, and booze per capita consumption. Yes, because drinking patterns (especially type) have not changed over this period.

You still following? Point is, all that manipulation allowed our guys to make plots like this (I left out wine, which looks like beer).

Something to do with beer.

Fig. 4. Something to do with beer.

Something to do with booze.

Fig. 6. Something to do with booze.

Now my dad would call this, and call it rightly, a “German Airplane”, i.e. a Messerschmitt. But then my old man isn’t a scientist. No, a scientist would say something like this, “The scatter plots shown in Figure 4, 5, and 6 suggest that average U.S. beer and wine consumption rises and spirits consumption falls as states become more liberal over time.”

It suggests nothing of the kind, because these plots are part silliness (the political leanings measure) and part unjustified averaging of heterogeneous data (both axes). And even if this weren’t a problem, the weird patterns in the scatter proves the futility and fallacy of using regression as causal explanation. Those lines are nowhere neat the dots. (Yes, of course, wee p-values were discovered.)

The authors do go on from these pictures to create a statistical model so freaky that it made my eyes tear, so I’ll skip discussing it. I can tell you it’s typical in its arbitrary, piece-meal construction and in the wildly speculative conclusions drawn from it.

How they take all this and conclude “that when a state becomes more liberal politically, its consumption of beer and spirits rises” says more about the authors’ preconceptions than it does about the drinking habits of citizens.

On the other hand, I’m perfectly willing to accept that the more progressive a person becomes they more they are driven to drink. These sad people have to cope somehow.

Will Someone Please Laugh At These Jokes?

Well, I think these are funny.

Update And then for something not as funny.

Update This is for my number-two son.

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