Weezer

Weezer died.

He was the neighborhood cat, and was very friendly. I'd gotten to know him fairly well in my time here in Erwin, TN, mostly on account of him introducing himself to me when I first moved in. I fed him occasionally and spent more than a few afternoons talking and playing with him.

Born with the name Oliver, he led a long and happy life, growing up as a part of my neighbor's family. In late 2010, he had a tough battle with cancer, but survived. The tumor removed from his throat gave him the chance to enjoy another year of life, but at the cost of a need to constantly wheeze, earning him his nickname in old age.

I'll miss seeing him during my daily outings. I'd grown rather accustomed to seeing him whenever I'd go out for the day. I'll miss him.

Good-bye, Weezer. We had fun.

My Favorite Poems

I am not generally fond of poetry, but there are a few poems that really stand out in my mind. Seeing as how a friend decided she would celebrate Poem in the Pocket Day, I thought it might be appropriate for me to create a list of a few of my favorite poems to share with whomever it is that reads this blog.

The Tuft of Flowers

I'll start with Robert Frost's The Tuft of Flowers. It's about an afternoon groundskeeper who is going about his job mowing a large lawn with a scythe. He mulls over how his work keeps him alone, separated from contact with others, concluding that this is how all men work, even if they happen to have coworkers around them. Yet then he he notices a small tuft of flowers beside the brook that the morning mower had not cut. As he, too, decides to not cut these flowers, he realizes that he has made a connection with his coworker closer than most will ever achieve, even though his coworker works in the morning, and he never sees him face-to-face.

To me, the poem represents the wonders of the internet, where I can find and enjoy friendships that are rare to find "in real life".

Dover Beach

Matthew Arnold's Dover Beach is also quite moving to me, but not for the same reason most who like it cite. It is about the spiritual doubts of a believer who has his faith shaken by the realization that all he previously believed was false. It is a description of the pain one undergoes when they move from a belief in solid values to the seemingly obvious conclusion that the basis for all values are invalid.

As a rationalist skeptic, I no longer believe in "value" of the sort described in fairy tales or religion, so in a way, I identify strongly with the ending lines of Dover Beach. Yet I also have come to believe in the worthwhile nature of creating one's own value from the sea of valuelessness, sort of how J. L. Mackie describes his worldview on this issue.

Jabberwocky

My favorite nonsense verse is definitely Lewis Carroll (Charles Dodgson)'s Jabberwocky, from Through the Looking Glass. Carroll is a wonderful writer, especially when it comes to logical word play.

The poem is complete nonsense, yet it is a peculiar sort of nonsense that nevertheless makes sense. Even though every other word is made up entirely by the author, you can sort of make out from context what the poem is saying, which is a really strange thing in and of itself, if you think about it. Carroll has taken the idea of discerning a word through context and pushed it to its utter limits, by writing an entire poem that can only be understood through context. Yet even with no reference point to clue you in on what the poem is about, readers can nevertheless find themselves following the story as it is told.

Jabberwocky is an amazing construction to behold, and earns its spot on my list of favorites by virtue of its form rather than any of its contents, unlike most other poems on this list.

l(a

e. e. cummings' l(a is another poem whose form I cannot help but to admire. The structure of the poem is meant to represent a leaf falling -- the letters themselves represent the leaf graphically -- and the text reads "loneliness", with "a leaf falls" inserted between the first "l" and the next three letters: "one". The font used in the poem makes the "l" look a lot like the numeral "1". There is a lot going on in this poem, even though it consists of very few characters, and much of the meaning comes from the common trope among poems of his era representing loneliness by a single falling leaf. There is something about the way the typeface seems to show the leaf drifting from side to side as it falls that never ceases to get to me. l(a is definitely one of my favorite poems.

Dulce et Decorum est

Wilfred Owen's Dulce et Decorum est is a poem of war. It describes soldiers in the first world war dying from poison gas. Owens stringently denies Horace's famous line that "it is sweet and right to die for your country"by describing the true horror of war. I cannot help but to envision the scene vividly every time I read this poem, and the thought of people drowning where they stand turns my stomach every single one of those times. Patriotism is indeed one of the worst traits I can imagine that some people actually seem to think is laudable.

The Hollow Men

Perhaps my favorite poet of all is T. S. Eliot, and while The Wasteland is a masterpiece when it comes to literary appreciation, I nevertheless find myself always returning to The Hollow Men whenever I want to reread Eliot. If you have not read Dante, much of the poem will be lost on you, but assuming you are familiar with the works he alludes to, the message Eliot gives in this poem is both dramatic and powerful. There are even references to ancient Greek philosophy in there at the key turning point of the poem, so the only real way to read Eliot is with notes close at hand.

At its heart, the poem is about morality, focusing clearly on what the most immoral thing to do is. Although he does not reference it in the poem, the real issue here is that of Buridan's ass as it applies to choosing an ethical action. Inaction, Eliot attempts to point out, is the worst state of all when it comes to matters of ethics.

I'm sure that my personal interpretation is not shared by all readers of Eliot, but I like to look at it from a consequentialist point of view, instead of the religious view Eliot himself probably meant when he composed the poem. Even if your action results in worse consequences, one must at least attempt to do good in the moment. I look at the issue from the point of view of Bayesian probability with regard to consequentialistic choices; we are not all-knowledgeable, but we can calculate Bayesian probabilities, and we should undertake actions which Bayes would agree with, even if they result in worse consequences.

I fully realize that the last paragraph is not a standard interpretation of The Hollow Men, but it is nevertheless what I see every time I reread the poem. Eliot is trying to ensure we realize the true horror of inaction when we have reason to believe action should be taken. Being sinless is not enough -- we must also do in order to be rightly called good.

Paradise Lost

I will end with a poem too long to summarize in a few short sentences: John Milton's Paradise Lost. This epic poem is a retelling of the beginning of Genesis, describing the fall of Satan and the events of Adam and Eve in the Garden of Eden. Strangely, the author says himself in Book One that the purpose of the poem is to justify God's actions, but my reading of the text is that Milton is doing the exact opposite. Satan's portrayal is dreadfully convincing. His argument that God's nature is tyrannical despite its benevolence is extremely powerful, and resonates even to this day.

My interpretation here is reminiscent of Henrik Ibsen's A Doll's House. Torvald is a wonderful husband in the sense that he is doting and kind. He takes care of his wife dutifully and kindly. Yet, nevertheless, their relationship is utterly horrid. As the man, he is in charge, so no matter how kind or good he tries to be with his wife, he can never interact with her on anything like an equal level. This power differential underlies every action he takes, even if he has no ill intent whatsoever. Despite his benevolence, the very fact of his position over her is what makes living under him so terrible. Even if he tries to connect with her on an equal level, it cannot work, because the fact remains that if he wanted to be mean, he could, and she would have no recourse.

Similarly, Satan argues that God, despite his benevolence, is nevertheless tyrannical. Following him is unjustified, even if he has nothing but good intentions at heart. Milton does not say this explicitly, but I understand the situation like this: The only way God would be justified in being a ruler over others is if the power of that rule comes from the ruled in addition to benevolence; benevolence is not enough. Imagine Ulysses in the scene of Homer's Odyssey where he must sail past the sirens. Ulysses is captain, and justly retains power over the sailors because the boat must have a captain in order to sail. Yet he voluntarily relinquishes this power to the sailors while they go past the sirens, since their calls will make him mad. Homer describes Ulysses tied to the masthead barking orders that the sailors justly ignore. In this moment, the sailors rule over Ulysses benevolently, but not in the same way Torvald or God does. The sailors do not rule over Ulysses because they are better than him, but because they were given the power to do so by Ulysses in advance. It is a combination of voluntary rule and benevolence that justify the sailors' domination over Ulysses. Meanwhile, both Torvald and God have only the benevolence part -- they do not have any voluntary rule, as Satan rightly points out.

Of course, from what I understand of history, John Milton did not share the interpretation I give in the above paragraphs when he wrote Paradise Lost. But I nevertheless see the above when I think of Satan's arguments against God's rule.

Conclusion

While these are just a few of my favorite poems, I have to admit that there really aren't that many more that speak to me at the same level that these do. My problem with ancient Greek poetry is that I know just enough koine to stumble through them in the original, making it extremely difficult for me to simultaneously follow complex literary themes. And I know no Latin at all, so most Latin poems based on wordplay do absolutely nothing for me. Meanwhile, more recent classics are hit or miss with me, and really depend on my mood. The above listed poems really and truly are the best of the best that I've run into so far in my life -- although admittedly I don't exactly read new poetry often, so I'm likely missing a number of gems out there.

If you take issue with any of my interpretations, feel free to let me know in the comments. I'd love to hear just how wrong I am about this stuff.

Thanks to Elizabeth Herboso for spurring me to compose this blog entry.

Why Many Worlds is Correct

I recently read a four year old article by Eliezer Yudkowsky on why Many Worlds survives Occam's razor. The argument was persuasive enough to cause me to change my mind on a stance I've held for nearly two decades.

The way he explains the issue is a little roundabout, so I thought I'd try my hand at reproducing the basic argument in a more succinct manner. Note that this post assumes some prior knowledge of the Many Worlds Interpretation (MWI) of quantum physics and how it differs from interpretations that involve collapsing wavefunctions. Basically, if you understood the last sentence, you'll be good to go; otherwise the following might be a little jargon heavy. Nevertheless, I'll try to give background where appropriate. (If you're really lost, the best book to pick up is Feynman's QED, but if you're in a hurry, the Everett FAQ can answer basic questions with plain English. It's no substitute for reading Feynman, though.)

Some Background

There are several possible interpretations of quantum theory. MWI explains just as well as any other, but it is often called out as violating Occam's razor. "Stipulating all these extra worlds", proponents of wavefunction collapse theories argue, "certainly counts as extra assumptions." Of course, there's no reason why nature must respect parsimony, just as there's no reason nature must respect induction. Nevertheless, both have proven effective at making correct predictions over time (pun intended), so a good response is needed.

Occam's Razor

The law of parsimony does not refer to complexity in the same way that we use the word in common usage. Most of the time, things are called "complex" if they have a bunch of stuff in them, and "simple" if they have relatively less stuff. But this cannot possibly be what Occam's razor is referring to, since we all gladly admit that Occam's Razor does not imply that the existence of multiple galaxies is less likely to be true than just the existence of the Milky Way alone.

Instead, the complexity referred to in Occam's razor has to do with the number of independent rules in the system. Once Hubble measured the distance to cepheid variables in other galaxies, physicists had to choose between a model where the laws of physics continue as before and a model where they added a new law saying Hubble's cepheid variables measurements don't apply. Obviously, the model with the fewer number of physical laws was preferable, given that both models fit the data.

Just because a theory introduces more objects says nothing about its complexity. All that matters is its ruleset. Occam's razor has two widely accepted formulations, neither of which care about how many objects a model posits.

Solomonoff inductive inference does it by defining a "possible program space" and giving preference to the shortest program that predicts observed data. Minimum message length improves the formalism by including both the data and the code in a message, and preferring the shortest message. Either way, what matters is the number of rules in the system, not the the number of objects those rules imply.

Quantum Mechanics

So when we apply Occam's razor to competing interpretations, we need to be parsimonious with laws, not objects. How then, does MWI stack up?

Theory-wise, MWI is nearly equivalent to other interpretations. MWI will predict what the Copenhagen interpretation will predict, so in terms of accurate predictions, they seem about on par. But while MWI stops there, most other interpretations start tacking on extra assumptions. (Except instrumentalism, of course, but it always wins the parsimony battle, and doesn't really count.)

All theories that posit a wavefunction collapse, for example, are positing something on top of the needed rules that agree with observations (pun intended). Why posit a wavefunction collapse whose only purpose seems to be a method of denying the reality of the wavefunction? Of course, maybe reality is such that the wavefunction does collapse. But Occam's razor would clearly prefer the option asserting fewer assumptions.

"But wait!", say the wavefunction collapsers. "MWI asserts way more stuff than any other theory ever made! Don't you see that the addition of a single simple law of wavefunction collapse does away with having to admit the existence of all the excess crap MWI forces us to believe in?"

Yet they are missing the point. If something is a deductive consequence of the rules of a system, then you get that extra thing for free without having to refer to Occam's razor. As Yudkowski puts it, if P(Y|X) ≈ 1, then P(X∧Y) ≈ P(X). All the "excess crap" that gets posited into existence with MWI is just the deductive consequence of the quantum theory all interpretations agree upon. Even in wavefunction collapse theories, many worlds exist until the collapse occurs. The extra rule positing a collapse is the real "excess crap".

Parable of the Invisible Spaceship

If you're still not convinced, consider Yudkowski's implied invisible spaceship.

"Suppose you're going to launch a spaceship, at nearly the speed of light, toward a faraway supercluster.  By the time the spaceship gets there and sets up a colony, the universe's expansion will have accelerated too much for them to ever send a message back." They will be unable to interact with us even in principle, as they can never intercept our world-line. "Do you deem it worth the purely altruistic effort to set up this colony, for the sake of all the people who will live there and be happy?  Or do you think the spaceship blips out of existence before it gets there?"

If you're like me, you'll find it intuitive to believe the spaceship and its colonists continue existing, even after they reach the point of no return, because claiming they cease to exist requires extra laws that wink them out of existence when they get too far away. Parsimony demands that we accept implied invisibles.

A Personal Note

Although I only just recently was convinced of this stance by Yudkowsky, the basic argument is quite old, and I really should have run into it before now.  I guess the main reason I never did is because quantum physics was something I spent a lot of time on while I was still young, and I just haven't kept up with the field since I was a teenager. Since I didn't encounter Bayesian probabilities until studying philosophy of science at Spring Hill College, I just never put two and two together. Let this be a lesson to myself to never stop learning, and always update old beliefs with newly acquired information. (c:

Oh, and by the way, if you're wondering why I called this write-up succinct, you should see how much Yudkowsky writes on the topic.

A Working Quantum Computer

The diamond in the center measures 1mm by 1mm.

If you've been following news on the quantum computing front, you'll know that a major stumbling block so far has been the issue of decoherence. Every time we get a proto-quantum computer to start computing, it quickly breaks down from an inability to store data for calculation.

This problem has now been resolved.

A paper just published in Nature claims that they have found a way to protect multiple qubits from decoherence over an extended period of time, and built a quantum computer into a diamond to prove it. Since I realize most of my readers don't keep up with this field as much as I do, I'll try my best to explain.

How it works.

Classical computers use bits (binary digits) to store information in memory. These are the binary digits (1s and 0s) that get stored in between calculation steps in any non-trivial program. If a 1 were to turn into 0 randomly in the middle of an operation, a program might still be able to recover if it has good error detection, but if huge numbers of bits were to switch from one to the other while a program was running, there's just no way it could continue to function as desired.

Quantum computers use qubits instead of bits. This is what makes quantum computing as a concept so very powerful. Rather than use 1s and 0s that are either one or the other, the qubits of quantum computing utilize a superposition of states where a single qubit might be partly a 1 and partly a 0. Yet this reliance upon qubits has been a fundamental problem in quantum computing so far. It is just too easy for qubits to decohere and lose whatever information you try to store in it.

It wasn't until 2008 that a group first figured out how to keep a qubit from losing its information for a grand total of 1.75 seconds. Not only is this amount of time too short to do anything with, but the process could not handle multiple qubits, making this type of quantum computer incapable of using more than one qubit at a time.

Today's news marks the first time anyone has figured out how to shield multiple qubits from decohering for an extended period of time. I won't get into details of how they accomplish this; you can read the paper yourself for that. (Suffice it to say that they used microwave pulses to delay decoherence continuously.) But the point is that they were able to construct a working quantum computer and run a simple program on it to verify the qubits are not decohering.

The fun part of the story.

Quantum circuit representation of Grover's algorithm.

In order to prove their method worked, they used the quantum computer to run through Grover's algorithm, a function-inverting quantum algorithm.

The usual explanation of Grover's algorithm starts by imagining a phone book organized in alphabetical order. (We'll need a new mental example soon; I can't remember the last time I actually saw a phone book in person.) If we have a specific phone number we're looking for, our only real recourse is to search through the book one entry at a time. We might get lucky and find it as soon as we open phone book, but we also might be unlucky and not find it until the very last entry. (Technically the second to last, since we assume the number exists in the book, but please ignore this sentence for clarity.) In general, it turns out that, on average, we will find the number we seek on our N/2nd try, where N is the total number of entries in the phone book. For a book with four entries, we'll find it on our second try on average; if the book has a hundred entries, we'll find it on the fiftieth try on average. A phone book listing everyone in New York City would have ~8,000,000 entries; we'd find a particular entry on the four millionth try on average.

Grover's algorithm, on the other hand, will find it, on average, on our O(N^1/2) try. For a book of four entries, we'll basically find it on the first try every time. With a hundred entries, we'll find it on the tenth try on average. With 8,000,000 entries, on average, we'll find it on the 2,829 try. That's not a typo; it really is less than three thousand tries for an eight million entry database. This speed increase is enormous. The applications for such sheer speed has drastic repercussions in the real world.

The team used Grover's algorithm on their quantum computer and found the correct entry on their first try 95% of the time. This puts the question of whether their computer works or not entirely to rest. Their quantum computer not only works, but works well enough to actually be capable of quantum calculation at a 5% error rate. Sure, that's not perfect, but it's already enough accuracy that, if one desired, error-correcting could be done. Just redo the calculation ten times; with a 95% accuracy rate, that is more than enough to determine the correct output. The insane speed increase quantum computers have over classical computers is enough to make it more than worthwhile to repeat the same calculation ten times in a row each time.

Of course, the quantum computer they built held only two qubits, and so can only store so much information at a time. Doing Grover's algorithm on an 8,000,000 entry database, for example, would require seven qubits. (In general, O(log(N)) qubits would be required for a database of N entries.) But there is nothing stopping someone from creating such a quantum computer in principle, so long as they have enough microwave pulses to keep them all from decohering. The future, it appears, is now.

So what does this all mean?

First of all, it means that somebody has a working two qubit quantum computer right now. Realistically, this is not enough to cause much of a ruckus. To put it in context, this is only enough storage to solve Grover's algorithm for databases of seven entries or less. (Although Grover's original paper points out that his algorithm requires only that the processing be done with qubits; the memory can be saved in a classical bits.) However, quantum computers do not scale linearly like classical computers do. As mentioned previously, a mere seven qubits would be enough memory to store steps for Grover's algorithm on a database of 8,000,000 entries. It takes very few qubits to handle very large problems.

Now that the conceptual hurdle has been passed, someone could, right this very moment, build a quantum computer with a dozen qubits. There is nothing preventing us from accomplishing such a feat now, save sheer expense. But if you can afford the dozen microwave lasers and have an appropriately flawed diamond to work with, it is certainly doable. What could one do with such a machine?

To put it bluntly, nearly everything.

All bounded error, quantum, polynomial time (BQP)
problems are efficiently solved by quantum computers.

Forget other programs. Let's just focus on Grover's algorithm, which has already been shown to work on this quantum computer. All symmetric-key algorithms could be broken by sheer brute force in half the time. This includes all Advanced Encyption Standard (AES) codes, the standard block cipher ratified by the National Institute of Standards and Technology. All NP-complete problems could be solved with a quadratic speed-up over current brute force methods. Not to mention exponentially faster database search in general, which I already pointed out earlier in the article. And all this is just from Grover's algorithm alone. Other algorithms can reduce password cracking time on certain types of passwords from years of processing to mere seconds. These algorithms already exist; they just never had a quantum computer to run them before. Now they do.

This effectively breaks most commercial-grade encryption now in use on the internet. Some encryption does survive; notably lattice-based and McEliece cryptosystems.

Practicability.

Although the last section makes it seem like quantum computers have now arrived, there are still problems that need to be addresses. David DiVincenzo points out that a practical quantum computer must have:

• scalable physically to increase the number of qubits;
• qubits can be initialized to arbitrary values;
• quantum gates faster than decoherence time;
• universal gate set;
• easily read qubits.

This new discovery solves the first (albeit expensively) and third issues completely. The second issue is still problematic, but is something that can be programmed around. The fifth issue is a matter of convenience; expense and repeatability makes this solvable with money alone. This leaves only the fourth issue: a universal gate set. As this is not yet solved, we will not yet be able to program whatever we want on a quantum computer. But we can still run Grover's algorithm, and a few other programs to which we know the necessary gates, and I've already shown how this affects society directly.

A note on how the press is covering this.

As a skeptic, I was very disappointed in a quote by Daniel Lidar on their method of delaying decoherence. He told press "it’s a little like time travel", because the microwave pulses that made the electron qubit switch their direction of rotation did so in a way that makes the decoherence disappear by moving back in the direction it came from. But, quite frankly, this is bullshit. That has no more to do with time travel than moving left does when you want to take back a move to the right. However, now that the quote is out there in a story that headlines with the word "quantum", you can be sure lots of quacks will completely misunderstand, as they so often do.

A few credits.

Although credit for stuff like this gets cited in journals, blogs rarely take the time to actually link out to the individual scientists' blogs/social media in articles like this. So I thought I'd buck the trend by giving a shout out to the authors of the study, including Daniel Lidar, Zhihui Wang, Toeno van der Sar, Machiel Blok, Hannes Bernien, Tim Taminiau, David Toyli, David Awschalom, & Ronald Hanson. Well done.

Also, thanks to Wikipedia for its help in understanding basic principles and the University of South California for their press release summarizing the findings of the paper. And a tip of the hat to the Skeptic's Guide to the Universe for letting me know about this recent development in the first place. Your podcast is awesome. (c:

Supreme Court Party Time

The other day, a friend and I decided to go through all 5.5 hours of Supreme Court oral argument on the Affordable Care Act together, plus background materials to familiarize ourselves with the case.

Oyez' awesome player.

It was a fun experiment, and resulted in much great discussion. I'd highly recommend it, as I'd definitely consider it the kind of party that I'd try again. Oyez.org also makes it especially easy to go through. Not only do they provide great background material and audio, but they also provide text to make it easy to read along. I'm very impressed with the quality of features Oyez makes available to the public for free.

If you're interested in trying it yourself, here are a couple of pointers to help get you started.

• First, get a friend. Seriously, this kind of thing is much better when discussion occurs than it ever would be alone. I've listened to oral arguments via podcast for years, but as interesting as it may have been, it's never approached the level of interaction you get when multiple people are around to give differing viewpoints in realtime.
• Second, set aside enough time. The oral arguments come in four sections, so you could theoretically do this over four days. The first two, 11-398, are 1.5 hours for the Anti-Injunction Act and 2 hours for the Individual Mandate. The last two, Severability (11-393) & the Medicaid Expansion (11-400) are each 1.5 hours. Remember to allow a minimal five to ten minutes beforehand to go over background, and another half hour afterward to discuss the case in depth. I strongly recommend taking the time to go into more background than just five minutes, but if you're rushed for time, it'll have to do. Just don't be surprised if discussion continues well after the event ends.
• Third, learn the players. Sure, we all know the styles and leanings of the Justices by now, but you also need to know the lawyers speaking before the court, and whom they each represent. It also might be interesting to bring up background on key players, like the fact that Paul Clement clerked for Scalia and served as Solicitor General under Bush for four years.
• Fourth, enjoy the show! Oyez does an excellent job of integrating the audio of the oral arguments along with highlighted text to read along. The free experience they provide to the public is great not just for policy makers and those with a need to know, but also to people like you and me who just want to experience Supreme Court oral arguments for ourselves for fun.
• Finally, don't forget to discuss. There's a lot to talk about in these oral arguments. No matter where you stand on the issue, both sides have plenty of interesting things to say. I know that I was certainly surprised when I first went through them.

If you haven't listened to the oral arguments yet, I encourage you to stop reading here and go set up your own Supreme Court party. It's definitely worth the effort of setting up.

However, if you've already heard the oral arguments, or if you want some extra pointers on discussion points that might be appropriate, I'll give some of my thoughts on each section of the cases.

• Anti-Injunction Act: Do they even have standing to sue?
  We're forbidden from bringing suit against a disputed tax until after we pay the tax. If the penalties described in the Affordable care Act are indeed taxes, then the Anti-Injunction Act applies, and this entire suit must be thrown out. While both sides argue it is a tax here, a friend of the court was appointed to argue that it isn't. Absurdity gets highlighted when one realizes that the very next day the states will be forced to argue that it is not a tax after all. Is it ethical for lawyers to take up opposing stances on specific issues each day in order to promote their greater goals?
• The Individual Mandate: Does Congress have the power to force citizens to buy insurance?
  The commerce clause has been construed to have broad power over the years, but is it really this broad? If you are not buying insurance, are you part of the insurance market? If government can not only regulate commerce, but also force purchase of insurance, why can't they also force us to buy broccoli? Compare the styles of Verrilli to Clement to Carvin. Notice any substantial differences in how well they argued their case? (I certainly did.)
• Severability: If the individual mandate gets struck down, what happens to the rest of the law?
  The Affordable care Act is huge, so even if the mandate is determined unconstitutional there are still plenty of clauses that can stand on their own. But would Congress have passed these smaller laws separately? How far should we look to Congress' intent? What about the fact that the mandate is a necessary provision for other parts of the bill to work properly? And what does necessary really mean, exactly?
• The Medicaid Expansion: The final constitutional issue is that of coercion.
  Is it blackmail to threaten to remove all Medicaid funding from states if they don't accept the new Medicaid expansion? What about the fact that it is all-upside for the states? What about if the threat would be illegal to carry out? What about the fact that the states and the Secretary of Health and Human Services have common goals and so the threat doesn't even make sense? And how can it be coercion if Congress is fully capable of dismantling all of Medicaid and retooling it from scratch? What makes the states think they have the right to continue receiving federal aid no matter what Congress decides? Note Verrilli's closing remarks where he turns to arguments of ethics rather than law to urge Justices to uphold the Affordable Care Act, and Clement's casual dismissal of them.

Surprisingly, I found myself extremely impressed with Mr. Clement's arguments. Of course, I believe healthcare is dreadfully important to have for all, and I desperately want the court to uphold the Affordable Care Act. But I want this from a moral standpoint, which is different than a legal standpoint. I have to admit that Clement's arguments in the Individual Mandate section were quite persuasive. To be honest, it just further irritates me that Congress did not just pass a single payer system, which would have been perfectly constitutional no matter how you look at it. As it stands now, I'm honestly not sure what the correct legal thing to do is, and that's a disheartening admission to make.