January 2, 2006

BAD ENOUGH THAT ENTROPY IS BOGUS....:

Quantum Trickery: Testing Einstein's Strangest Theory (DENNIS OVERBYE, 12/27/05, NY Times)

This fall scientists announced that they had put a half dozen beryllium atoms into a "cat state."

No, they were not sprawled along a sunny windowsill. To a physicist, a "cat state" is the condition of being two diametrically opposed conditions at once, like black and white, up and down, or dead and alive.

These atoms were each spinning clockwise and counterclockwise at the same time. Moreover, like miniature Rockettes they were all doing whatever it was they were doing together, in perfect synchrony. Should one of them realize, like the cartoon character who runs off a cliff and doesn't fall until he looks down, that it is in a metaphysically untenable situation and decide to spin only one way, the rest would instantly fall in line, whether they were across a test tube or across the galaxy.

The idea that measuring the properties of one particle could instantaneously change the properties of another one (or a whole bunch) far away is strange to say the least - almost as strange as the notion of particles spinning in two directions at once. The team that pulled off the beryllium feat, led by Dietrich Leibfried at the National Institute of Standards and Technology, in Boulder, Colo., hailed it as another step toward computers that would use quantum magic to perform calculations.

But it also served as another demonstration of how weird the world really is according to the rules, known as quantum mechanics. [...]

"The more success the quantum theory has, the sillier it seems," Einstein once wrote to friend.

The full extent of its silliness came in the 1920's when quantum theory became quantum mechanics.

In this new view of the world, as encapsulated in a famous equation by the Austrian Erwin Schrödinger, objects are represented by waves that extend throughout space, containing all the possible outcomes of an observation - here, there, up or down, dead or alive. The amplitude of this wave is a measure of the probability that the object will actually be found to be in one state or another, a suggestion that led Einstein to grumble famously that God doesn't throw dice.

Worst of all from Einstein's point of view was the uncertainty principle, enunciated by Werner Heisenberg in 1927.

Certain types of knowledge, of a particle's position and velocity, for example, are incompatible: the more precisely you measure one property, the blurrier and more uncertain the other becomes.

In the 1935 paper, Einstein and his colleagues, usually referred to as E.P.R., argued that the uncertainty principle could not be the final word about nature. There must be a deeper theory that looked behind the quantum veil.

Imagine that a pair of electrons are shot out from the disintegration of some other particle, like fragments from an explosion. By law certain properties of these two fragments should be correlated. If one goes left, the other goes right; if one spins clockwise, the other spins counterclockwise.

That means, Einstein said, that by measuring the velocity of, say, the left hand electron, we would know the velocity of the right hand electron without ever touching it.

Conversely, by measuring the position of the left electron, we would know the position of the right hand one.

Since neither of these operations would have involved touching or disturbing the right hand electron in any way, Einstein, Podolsky and Rosen argued that the right hand electron must have had those properties of both velocity and position all along. That left only two possibilities, they concluded. Either quantum mechanics was "incomplete," or measuring the left hand particle somehow disturbed the right hand one.

But the latter alternative violated common sense. Such an influence, or disturbance, would have to travel faster than the speed of light. "My physical instincts bristle at that suggestion," Einstein later wrote.

Bohr responded with a six-page essay in Physical Review that contained but one simple equation, Heisenberg's uncertainty relation. In essence, he said, it all depends on what you mean by "reality." [...]

Another debate, closely related to the issues of entanglement and reality, concerns what happens at the magic moment when a particle is measured or observed.

Before a measurement is made, so the traditional story goes, the electron exists in a superposition of all possible answers, which can combine, adding and interfering with one another.

Then, upon measurement, the wave function "collapses" to one particular value. Schrödinger himself thought this was so absurd that he dreamed up a counterexample. What is true for electrons, he said, should be true as well for cats.

In his famous thought experiment, a cat is locked in a box where the decay of a radioactive particle will cause the release of poison that will kill it. If the particle has a 50-50 chance of decaying, then according to quantum mechanics the cat is both alive and dead before we look in the box, something the cat itself, not to mention cat lovers, might take issue with.

But cats are always dead or alive, as Dr. Leggett of Illinois said in his Berkeley talk.


No one actually believes that reality sometimes doesn't exist, so the obvious answer is that it is always Observed. So Intelligence imposes order from jump street.

Posted by Orrin Judd at January 2, 2006 2:20 PM
Comments

What must Schrödinger think of the lightbulb in my refrigerator?

Posted by: Brian McKim at January 2, 2006 3:05 PM

entropy is bogus

If so, you won't mind conducting a little experiment for us. Light a candle, or the burner on your stove, and stick your finger in the flame. Let us know how it feels. I'm going to predict that the hot flame raises the temperature in your finger, thereby cooling the flame ever so slightly, and as a result increasing the entropy of the flame-finger system as a whole, thereby proving the non-bogosity of entropy, meanwhile giving you a nice blister and me a good laugh.

Posted by: joe shropshire at January 2, 2006 3:44 PM

Entropy isn't what it used to be.

Posted by: Bruno at January 2, 2006 4:08 PM

Schrödinger cut the wave equation down to psis

Posted by: Bruno at January 2, 2006 4:16 PM

joe:

Do you believe that if you shut your eyes the flame disappears?

The elaborate experiment is, of course, just another example of intelligence creating greater order.

Posted by: oj at January 2, 2006 4:25 PM

This whole muddle results from a defective interpretation of the theory leading to the mysterious "collapse of the wave function". Since any measurement is the result of an interaction with a particle (generally a photon), and such interactions occur continuously, how is it that the particle "knows" a particular interaction is a "measurement" causing the collapse of its wave function?

If, instead, you regard quantum mechanics as a statistical ensemble theory, then the mixed wave function does not represent the system's physical state, but our imperfect knowledge of it. A particular interaction becomes a "measurement" because it determines the state for the observer, removing his uncertainty -- it is the observer who gives it privileged status, and the collapse is not physical but epistemic.

Thus, entangled particles, created by a single event, have rigidly correlated properties, but we are ignorant of their state, knowing only the probabilities represented by the wave function. When this uncertainty is removed by a measurement on one particle, we then immediately know the corresponding property of the other. There is no need for some mysterious, instantaneous quantum signal from one particle to the other.

Posted by: jd watson [TypeKey Profile Page] at January 2, 2006 5:16 PM

jd:

Yes, existence requires the interaction, but it exists.

Posted by: oj at January 2, 2006 5:37 PM

Let's see now. Supposedly Science has been a process of removing Man from a position of privilge, not being at the center of the universe, of nature, etc. (I forget the list, starting with Copernicus (or maybe even earlier), that's an exercise for the student...) It would seem that if what JD Watson describes above is a proper explanation, then what we are seeing another case, where "the Observer" needs to be dethroned from his place of privilege in subatomic interactions. It's its insistence on keeping Jerusalem at the center of the Universe is what is causing Quantum Mechanics all its troubles.

Posted by: Raoul Ortega at January 2, 2006 5:58 PM

The current cutting-edge, state-of-the-art, avante-garde, fashion-forward interpretation of QM, which all the cool kids like, is "quantum decoherence." (Wikipedia: http://en.wikipedia.org/wiki/Quantum_decoherence )

In this interpretation, it isn't observation that "collapses the wavefunction." Rather, it's an interaction that introduces randomness to part of the wavefunction -- the part that seems to disappear in the "collapse." It doesn't quite disappear but, because it is now random, it doesn't look like anything, just part of the noise level.

In this view, the universe we know is like the old joke, "How do you make a sculpture of a rhinoceros? Start with a big rock and chip away everything that doesn't look like a rhinoceros." How do you make a universe that contains Aishwarya Rai? Start with the Big Bang and randomize everything that isn't consistent with Aishwarya Rai.

Posted by: Bob Hawkins at January 2, 2006 6:10 PM

what i want to know, is when i can get a quantum ipod.

Posted by: toe's toys at January 2, 2006 6:26 PM

And I've always felt that the whole "Cat" example is bogus, and not peculiar to quantum mechanics. You can easily simulate it here in the real world—

I am handed a piece of paper on which is written "Even" or "Odd". It's sealed in an envelope so I can't know the what it says. If the first number in tonight's Lottery drawing matches the word, the paper is worth $100. If not, it's worth $0. The drawing takes place, and the number is 37. I don't open the envelope. How much is the paper worth? Probablility theory says $50 (.5 * $100 + .5 * $0). But we know that when I open the envelope, I will not get $50, because that's not a "valid quantum state". The "function collapses" to either $0 or $100 when I finally "observe" the paper.

Now at no time after the drawing occurred did that envelope contain a paper with shimmering text that said something like "Ovdn". Its state never changed, but the surrounding universe did, in the form of the drawing going from the future to the past.

I realize that unmathematical analogies like this are almost useless, but, really, if the experts can't come up with "thought experiments" that are peculiar to Quantum Mechanics, then, to follow my previous comments, maybe the problem lies with the expert "observers" and what they are actually measuring (and where).

(And there's something about the idea of a Wikipedia article on Quantum Mechanics that would seem to embody "random noise.")

Posted by: Raoul Ortega at January 2, 2006 6:28 PM

Yeah. Well, either way, I still hate cats.

Posted by: John Resnick at January 2, 2006 7:13 PM

Could be, Orrin. Why don't you try that experiment with your eyes closed. It might not even hurt that way.

Posted by: joe shropshire at January 2, 2006 8:16 PM

joe:

I believe in the Observer and thus the flame. It's you who pretend not to.

Posted by: oj at January 2, 2006 8:42 PM

Reality is always observed, but not by the same observer, thus there are alternate realities.
And I would hardly call God starting a snowball effect exactly in line with the arguments of intelligent design. It actually could be some kind of reconciliation between your idea of God and the much-maligned Darwin; that natural selection and design are not necessarily mutually exclusive?

Posted by: Grog at January 3, 2006 4:13 AM

No, there aren't. Reality exists because God determines it.

Darwinism depends on no intelligence guiding evolution.

Posted by: oj at January 3, 2006 4:17 AM

Aside from the points made by jd and Raoul, there's also this:
1. Science is careful observation.
2. The Schrodinger's Cat parable is all about what state the cat is in before it is observed.
3. Therefore the Schrodinger's Cat example is not science.

In fact, it is metaphysics of precisely the kind that early 20th century physicists like Shrodinger said they were going to eliminate.

Posted by: Tom at January 3, 2006 12:21 PM

Tom:

Science is merely a product of the scientist's metaphysics.

Posted by: oj at January 3, 2006 12:24 PM

I don't understand what you said.

Posted by: Tom at January 3, 2006 12:30 PM

Your point (1) is false. "Scientific" observations are a function of ideology.

Posted by: oj at January 3, 2006 12:42 PM

There was a young man who said "God,
I find it exceedingly odd
That this very tree
Should continue to be
When there is no one about in the quad."

"Young man, your question is odd.
I am always about in the quad.
And that's why this tree
Continues to be"
Signed by, yours faithfully, God.

Posted by: Jim in Chicago at January 3, 2006 1:12 PM

Mr. Judd;

So the observations of Brownian motion and the photo-electric effect (which lead to quantum theory and computers) were just functions of the observers ideology? If only those observers had been more conservative we would have computers built on purely classical properties?

Posted by: Annoying Old Guy at January 3, 2006 1:19 PM

AOG:

Yes, no one believes they're anything more than mathematical models.

Posted by: oj at January 3, 2006 2:30 PM

So, math is an ideology?

Posted by: joe shropshire at January 3, 2006 2:55 PM

Joe - OJ's in one of his epistemological relativist "there's no such thing as truth (except Revealed)" moods. Just make sure he stays warm and gets plenty of fluids until it dies down again. And give him some Foucoult and Derrida; it will comfort him until it passes.

Posted by: Tom at January 3, 2006 3:57 PM

joe:

Yes, mathematics is naught but ideal constructs.

Posted by: oj at January 3, 2006 4:11 PM

Tom:

Ah, but Foucault and the rest of the French make a key mistake. They contend that just because nothing is true in purely rational terms therefore nothing is true. Hume and the other Anglo-Americans long ago differentiated us from the French by accepting that Revelation suffices.

http://www.brothersjudd.com/index.cfm/fuseaction/reviews.detail/book_id/1344/

Posted by: oj at January 3, 2006 4:13 PM

This was Hume's attitude toward anything not mathenatical or empirically observed:

"If we take in our hand any volume of divinity or school metaphysics, for instance, let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames, for it can contain nothing but sophistry and illusion."

This is why David Hume rocks ass.

Posted by: Tom at January 3, 2006 5:36 PM

He's even better than that:

When I turn my eye inward, I find nothing but doubt and ignorance. All the world conspires to oppose and contradict me; tho' such is my weakness, that I feel all my opinions loosen and fall of themselves, when unsupported by the approbation of others. Every step I take is with hesitation, and every new reflection makes me dread an error and absurdity in my reasoning.

For with what confidence can I venture upon such bold enterprises, when beside those numberless infirmities peculiar to myself, I find so many which are common to human nature? Can I be sure, that in leaving all established opinions I am following truth; and by what criterion shall I distinguish her, even if fortune shou'd at last guide me on her foot-steps? After the most accurate and exact of my reasonings, I can give no reason why I shou'd assent to it; and feel nothing but a strong propensity to consider objects strongly in that view, under which they appear to me. Experience is a principle, which instructs me in the several conjunctions of objects for the past. Habit is another principle, which determines me to expect the same for the future; and both of them conspiring to operate upon the imagination, make me form certain ideas in a more intense and lively manner, than others, which are not attended with the same advantages. Without this quality, by which the mind enlivens some ideas beyond others (which seemingly is so trivial, and so little founded on reason) we cou'd never assent to any argument, nor carry our view beyond those few objects, which are present to our senses. Nay, even to these objects we cou'd never attribute any existence, but what was dependent on the senses; and must comprehend them entirely in that succession of perceptions, which constitutes our self or person. Nay farther, even with relation to that succession, we cou'd only admit of those perceptions, which are immediately present to our consciousness, nor cou'd those lively images, with which the memory presents us, be ever receiv'd as true pictures of past perceptions. The memory, senses, and understanding are, therefore, all of them founded on the imagination, or the vivacity of our ideas.

No wonder a principle so inconstant and fallacious shou'd lead us into errors, when implicitly follow'd (as it must be) in all its variations. 'Tis this principle, which makes us reason from causes and effects; and 'tis the same principle, which convinces us of the continu'd existence of external objects, when absent from the senses. But tho' these two operations be equally natural and necessary in the human mind, yet in some circumstances they are directly contrary, nor is it possible for us to reason justly and regularly from causes and effects, and at the same time believe the continu'd existence of matter. How then shall we adjust those principles together? Which of them shall we prefer? Or in case we prefer neither of them, but successively assent to both, as is usual among philosophers, with what confidence can we afterwards usurp that glorious title, when we thus knowingly embrace a manifest contradiction?

This contradiction wou'd be more excusable, were it compensated by any degree of solidity and satisfaction in the other parts of our reasoning. But the case is quite contrary. When we trace up the human understanding to its first principles, we find it to lead us into such sentiments, as seem to turn into ridicule all our past pains and industry, and to discourage us from future enquiries. Nothing is more curiously enquir'd after by the mind of man, than the causes of every phenomenon; nor are we content with knowing the immediate causes, but push on our enquiries, till we arrive at the original and ultimate principle. We wou'd not willingly stop before we are acquainted with that energy in the cause, by which it operates on its effect; that tie, which connects them together; and that efficacious quality, on which the tie depends. This is our aim in all our studies and reflections: And how must we be disappointed, when we learn, that this connexion, tie, or energy lies merely in ourselves, and is nothing but that determination of the mind, which is acquir'd by custom, and causes us to make a transition from an object to its usual attendant, and from the impression of one to the lively idea of the other? Such a discovery not only cuts off all hope of ever attaining satisfaction, but even prevents our very wishes; since it appears, that when we say we desire to know the ultimate and operating principle, as something, which resides in the external object, we either contradict ourselves, or talk without a meaning.

This deficiency in our ideas is not, indeed, perceived in common life, nor are we sensible, that in the most usual conjunctions of cause and effect we are as ignorant of the ultimate principle, which binds them together, as in the most unusual and extraordinary. But this proceeds merely from an illusion of the imagination; and the question is, how far we ought to yield to these illusions. This question is very difficult, and reduces us to a very dangerous dilemma, whichever way we answer it. For if we assent to every trivial suggestion of the fancy; beside that these suggestions are often contrary to each other; they lead us into such errors, absurdities, and obscurities, that we must at last become asham'd of our credulity. Nothing is more dangerous to reason than the flights of the imagination, and nothing has been the occasion of more mistakes among philosophers. Men of bright fancies may in this respect be compar'd to those angels, whom the scripture represents as covering their eyes with their wings. This has already appear'd in so many instances, that we may spare ourselves the trouble of enlarging upon it any farther.

But on the other hand, if the consideration of these instances makes us take a resolution to reject all the trivial suggestions of the fancy, and adhere to the understanding, that is, to the general and more established properties of the imagination; even this resolution, if steadily executed, wou'd be dangerous, and attended with the most fatal consequences. For I have already shewn, that the understanding, when it acts alone, and according to its most general principles, entirely subverts itself, and leaves not the lowest degree of evidence in any proposition, either in philosophy or common life. We save ourselves from this total scepticism only by means of that singular and seemingly trivial property of the fancy, by which we enter with difficulty into remote views of things, and are not able to accompany them with so sensible an impression, as we do those, which are more easy and natural. Shall we, then, establish it for a general maxim, that no refin'd or elaborate reasoning is ever to be receiv'd? Consider well the consequences of such a principle. By this means you cut off entirely all science and philosophy: You proceed upon one singular quality of the imagination, and by a parity of reason must embrace all of them: And you expressly contradict yourself; since this maxim must be built on the preceding reasoning, which will be allow'd to be sufficiently refin'd and metaphysical. What party, then, shall we choose among these difficulties? If we embrace this principle, and condemn all refin'd reasoning, we run into the most manifest absurdities. If we reject it in favour of these reasonings, we subvert entirely the, human understanding. We have, therefore, no choice left but betwixt a false reason and none at all. For my part, know not what ought to be done in the present case. I can only observe what is commonly done; which is, that this difficulty is seldom or never thought of; and even where it has once been present to the mind, is quickly forgot, and leaves but a small impression behind it. Very refin'd reflections have little or no influence upon us; and yet we do not, and cannot establish it for a rule, that they ought not to have any influence; which implies a manifest contradiction.

But what have I here said, that reflections very refin'd and metaphysical have little or no influence upon us? This opinion I can scarce forbear retracting, and condemning from my present feeling and experience. The intense view of these manifold contradictions and imperfections in human reason has so wrought upon me, and heated my brain, that I am ready to reject all belief and reasoning, and can look upon no opinion even as more probable or likely than another. Where am I, or what? From what causes do I derive my existence, and to what condition shall I return? Whose favour shall I court, and whose anger must I dread? What beings surround me? and on whom have, I any influence, or who have any influence on me? I am confounded with all these questions, and begin to fancy myself in the most deplorable condition imaginable, inviron'd with the deepest darkness, and utterly depriv'd of the use of every member and faculty.

Most fortunately it happens, that since reason is incapable of dispelling these clouds, nature herself suffices to that purpose, and cures me of this philosophical melancholy and delirium, either by relaxing this bent of mind, or by some avocation, and lively impression of my senses, which obliterate all these chimeras. I dine, I play a game of backgammon, I converse, and am merry with my friends; and when after three or four hours' amusement, I wou'd return to these speculations, they appear so cold, and strain'd, and ridiculous, that I cannot find in my heart to enter into them any farther.

Here then I find myself absolutely and necessarily determin'd to live, and talk, and act like other people in the common affairs of life. But notwithstanding that my natural propensity, and the course of my animal spirits and passions reduce me to this indolent belief in the general maxims of the world, I still feel such remains of my former disposition, that I am ready to throw all my books and papers into the fire, and resolve never more to renounce the pleasures of life for the sake of reasoning and philosophy. For those are my sentiments in that splenetic humour, which governs me at present. I may, nay I must yield to the current of nature, in submitting to my senses and understanding; and in this blind submission I shew most perfectly my sceptical disposition and principles. But does it follow, that I must strive against the current of nature, which leads me to indolence and pleasure; that I must seclude myself, in some measure, from the commerce and society of men, which is so agreeable; and that I must torture my brains with subtilities and sophistries, at the very time that I cannot satisfy myself concerning the reasonableness of so painful an application, nor have any tolerable prospect of arriving by its means at truth and certainty. Under what obligation do I lie of making such an abuse of time? And to what end can it serve either for the service of mankind, or for my own private interest?

Posted by: oj at January 3, 2006 6:09 PM

Mr. Judd;

Neither of those (Brownian motion, photoelectric effect) is a mathematical model. Both are "scientific observations", which you claim are "functions of ideology". Therefore I ask if these observations would have been different and have not lead to quantum mechanics if the observers had had a different ideology.

Posted by: Annoying Old Guy at January 3, 2006 11:28 PM

Of course, they would have. And they'll change when the paradigm shifts again. Science isn't about reality but about modelling.

Posted by: oj at January 4, 2006 8:48 AM

"Science isn't about reality but about modelling." But any models which work are observationally equivalent, at least regarding the particular phenomena they're intended to explain. I might say all objects are attracted to each other and you might say there's a little gravity demon who's constantly pushing objects toward each other, but insofar as our descriptions of this are similar - e.g., the strength of the attraction varies inversely with the square of the distance between them - they're just two ways of saying the same thing. That is very important; it means (workable) theories are NOT different insofar as they're workable; they're just expressed differently, like writing 2 vs. writing 6/3.

Regarding the Hume quote, there's no mention of Revelation.

Posted by: Tom at January 4, 2006 10:13 AM

Tom:

Exactly. We have no idea what gravity is, just mathematical models we can make work. The math matters, not the reality.

Posted by: oj at January 4, 2006 10:32 AM

in this blind submission I shew most perfectly my sceptical disposition and principles

All of us live by blind submission.

Posted by: oj at January 4, 2006 10:33 AM

No; reality doew matter, which is why some models don't work. If reality were irrelevant, all models would work just as well.

Posted by: Tom at January 4, 2006 10:48 AM

Tell a mathematician what reality you want to believe in and he'll be glad to give you the formulas to fit it.

Posted by: oj at January 4, 2006 10:57 AM

Mr. Judd;

Ah. I see now what NASA's mistake is. Instead of trying to build more complex rockets or other exotic launch technologies, NASA should instead hire some mathematicians to develop a model of gravity that makes orbital insertion cheap and easy.

Even better, since scientific observations are a function of ideology, NASA should set up some re-education camps to create observers whose ideology will cause them to observe that certain materials fall up instead of down, and then NASA can build their spacecraft out of that material. That would definitely save on the budget.

Why do you think NASA hasn't already done this? A vast, secular conspiracy?

Posted by: Annoying Old Guy at January 4, 2006 11:19 AM

Because our model works well enough to do the job. When we start exploring further afield we'll come up with new models and completely change how we travel to other worlds. It'll be cheap and easy.

Posted by: oj at January 4, 2006 11:22 AM

Mr. Judd;

You keep talking models, but I am talking about observations. Observations such as "objects fall toward Earth" or "Only light of a certain frequency or higher causes a voltage to be induced on a photo-receiver". Allow me to quote you once again:

"Scientific" observations are a function of ideology [emphasis added]
So why can't NASA get observers with the proper ideology to observe objects falling away from Earth instead of toward it?

This is a bit of a hobby horse of mine, because I discussed it in depth in my doctoral thesis. You are correct that current theories / model are kept because they are either sufficiently accurate (e.g., Newtonian mechanics) or the best we know (e.g., hydrodynamics). However, to go from that to considering them to be "functions of ideology" is a completely unjustified leap (and the idea that observations are arbitrary is truly bizarre).

The use of accuracy as the criteria used to judge these models means that the models must satisfy very severe constraints which can not be surmounted by some ideological or rhetorical flourish*. Having spent my career building such models under such constraints, I can tell you that there is generally not a lot of freedom of choice in how to structure the model and still have it work. The idea that ideology is determinitive, rather than just a weak influence, is not supportable.

P.S. One need only look at the progress of string theory to see this in action. The various models get rejected not because of ideology or viewpoint, but because the models are demonstrated to not work (i.e. are internally inconsistent or predict non-observed outcomes). Certainly the worldviews of the physicists greatly affects what types of models they try, but in the end it has little effect on what models succeed.

* The fact that you bring up accuracy shows that you don't really believe your own quote about scientific observations, which if true would make the very concept of accuracy meaningless.

Posted by: Annoying Old Guy at January 4, 2006 8:41 PM

There's nothing scintific about the observation that objects fall to the earth.

Posted by: oj at January 5, 2006 7:35 AM
« PRIVATIZED WELFARE FOR THE LEFT: | Main | THE SHAPE OF THE REFORMATION: »