orthogonality

Problem solving

How do we solve problems? We might say that there we aim to configure some portion of reality from some present state to some desired state.

The achievement of the desired state can in principle be as dumb and brute force as possible. Setting aside practicality, we can assume the totality of the design space at the lowest level is finite and that there exist configurations of reality which produce the desired state. Problem solving is then a brute force search through such a space.

But thanks to combinatorial explosion, this is impractical. In practice we design, which is to say we employ heuristics for breaking down a problem and to search for solutions to the subproblems thus produced.

Decomposition

But on what basis do we perform such decomposition?  Upon encountering a new problem, we are reminded of problems we have already struggled with. Past experience is rich a store of problems encountered and possibly solved.

If the new problem is some variation of the old, then we might assume that we could reuse the solution but with a slight modification. Thus we have decomposed the problem into a reuse and a search for an effective modification.

Or the new problem might not on the whole look like anything we encountered in the past, so we break it down into the subproblem of how to break the problem down and the subproblem of solving the subproblems generated having had broken it down. But before we can finally solve the original problem, we need to have already solved those subproblems we just invented for ourselves!

Decomposition then is about reuse. Nothing comes for free. We productively break down a problem only when we can solve the subproblems we thus inflict upon ourselves.

Atomic problems, definitive solutions

What makes a particular decomposition better or worse? Remember that you need to solve whatever subproblems you divided the original problem into. And so it would definitely be better if the subproblem were similar to something you have already solved. And it would be best if it were exactly the same as some problem you have completely solved.

What then does it take to conclusively solve a problem? Having already solved some problem, we might yet playfully elect to decompose it nonetheless. We may or may not succeed doing so, in such a way that all the subproblems are themselves completely solved. Even if we did not, the recursion would only stop making sense when we cannot further decompose and obtain some problem which could potentially be solved on its own.

We thus arrive at the atomic problems. For example, that of sorting a collection of elements in some total order. From which we might hope we have something we could simply re-employ to solve any other problem involving sorting out there.

Our atomic problems with solutions we have conclusively and definitively solved. It may be the case we cannot divide future problems cleanly into only those within our repertoire of solved atomic problems, but to any extent we can we have made some measure of progress.

A bit of both

Now what about the admittedly more common situation where we do not quite so cleanly decompose the problem into conclusively solved atomic problems? Well we force square pegs into round holds. Or perhaps more charitably we pack spheres into boxes. Or a menagerie of belongings into a suitcase. There is some residual wasted space, but we force-pack what we need into our luggage anyways.

But take two suitcases, does that make things easier? Only if you know that certain things should go into the first and all the others into the second. How could you know this? Perhaps one is cabin luggage and the other is to be check-in, so you might put more important things into the cabin luggage. Or even better: you need to bring your violin along and it can only fit into your violin case, which owing to its fragility you are forced to hand-carry. This latter is a solved atomic problem. It demonstrates orthogonality: it doesn’t matter how you pack anything else, you pack your violin only into your violin case, no debate.

But the problem otherwise of deciding to pack two suitcases and what to pack into each of them; that is a self inflicted problem. That is the problem of modularity.

Modularity is hence a design of design. The contours of the problem itself do not lend themselves into subdividing it naturally and convincingly into subproblems, so you have to impose your own subproblem structure upon it. You design your design in such a way that you perform object-level design only within the boundaries set by your meta-level design.

Modularity versus orthogonality

Which then better lends itself to reuse?

Modularity is something invented, you might hallucinate some decomposition in the problem, but there is no saying if the same hallucination might work for another problem. You may have to adapt your decomposition, and also how you go about solving each self-inflicted subproblem.

Orthogonality is something discovered, you hack away at reality until it does not yield to further attacks. Wherever else the problem occurs you have a definitive solution; if you can recognise it when you see it. It involves no work, only preparation, and a bit of luck.

Why then modularity?

But obviously we cannot rely on orthogonality alone. Not least since rarely do novel problems comprise exactly those already solved. How exactly then are we forced by necessity to modularise?

One reason might be ownership. When we cannot conclusively solve a problem we need to continuously deal with any unexpected complications which do arise. For example, software components have bugs and undependable dependencies and so require upkeep and a maintainer: someone who takes ownership of that component.

Unlike library dependencies which owing to them being inconclusive solutions to problems and so yet propagate stressors to our poor maintainer, the orthogonal concerns involved in that piece of software he can take for granted. An efficient sorting algorithm he can decide once to use and subsequently completely forget about.

So modules rot, abstractions don’t. But in this fallen state of the world ownership and maintenance of software is something which cannot be avoided.

But can our software maintainer hope to do better? Why yes. For though he can do nothing about compiled artefacts he does not himself produce, the source code he may compose out of orthogonal parts, so long as his compiled artefacts interact with other artefacts in the same old way.

He can for instance with lenses specify where in a data structure he performs his modifications completely orthogonally to how he performs those modifications.

Modularity may be about ownership but orthogonality is about obliviousness. A particular data transformation only cares about the form of its input and does not care where in some larger piece of data that portion which is its input reside. This isn’t an object oriented fetish about taking ownership of that piece of input. The pure function is total and its output is always well defined, no maintenance is required and so no ownership is necessary.

Your programming “abstraction” may involve hiding. But the real numbers are not hiding no Cauchy sequences or Dedekind cuts.

An orthogonal abstraction is synthetic in the sense of Euclidean geometry where the point is defined axiomatically in relation to other things, and is undefined in itself. In contrast to analytic geometry where it is defined with respect to some coordinate system. Of course in the case of analytic geometry the embedding is clean and there are not “abstraction leaks”, but most software modules don’t fare so well.

Every solitary, I told myself, is suspect: a pure being does not isolate himself. To seek the intimacy of the cell, one must have a heavy conscience; one must be afraid of one’s conscience. — Cioran on encapsulation

Inferior men guilt you into dealing with their problems. Superior men inspire you to adopt their solutions. Once Edward Kmett has written the lens library you will simply use it because he has genuinely put to rest a problem you might not even have had the perspicacity to recognise you were suffering. Not some fashionable UI framework which saves you from some boilerplate which was only ever necessary because of someone else’s confusion in the first place.

But can things get worse? Hell yes. Vertical integration is when orthogonal things get collapsed and sacrificed at the altar of a seamless end user experience. Hacks are made and cracks are plastered over in order to present a usable facade to the consumer. Usable that is, until it breaks. Eventually. Always.

So strive for orthogonality, and make do with some modularity if you must. But remember, in the long run, only the higher things are worthwhile.

But I now leave my cetological System standing thus unfinished, even as the great Cathedral of Cologne was left, with the crane still standing upon the top of the uncompleted tower. For small erections may be finished by their first architects; grand ones, true ones, ever leave the copestone to posterity. God keep me from ever completing anything. This whole book is but a draught—nay, but the draught of a draught. Oh, Time, Strength, Cash, and Patience. — Moby Dick

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boredom

All our life passes in this way: we seek rest by struggling against certain obstacles, and once they are overcome, rest proves intolerable because of the boredom it produces. We must get away from it and crave excitement.

We think either of present or of threatened miseries, and even if we felt quite safe on every side, boredom on its own would not fail to emerge from the depths of our hearts, where it is naturally rooted, and poison our whole mind.

Man is so unhappy that he would be bored even if he had no cause for boredom, by the very nature of his temperament, and he is so vain that, though he has a thousand and one basic reasons for being bored, the slightest thing, like pushing a ball with a billiard cue, will be enough to divert him.

 

–Pascal’s Penseés, quoted in Porcupines: A Philosophical Anthology

what do you care for argument?

Why do we care about arguments? Supposedly it’s because they work. They reliably produce truth or good decisions. Mathematical proof, for example, reliably produces correct mathematical knowledge. And even if a 12-year old might not understand the proof, he can tell you that barring his own mistakes he has not come across a counterexample to the proven statement.

But outside of mathematics, and when the participants do not have a real stake in the literal quality of the output of the argument process, this is not why we actually care about arguments. Nobody cares to plug the abstraction leaks for example, which is what you need to do to make anything work in the real world. Rationalists only care about clever reasons, and the plugging of leaks is a tedious chore and does not evince much intelligence. Your common internet user arguing politics only cares about wireheading norms. A libertarian only cares about arguments of a libertarian style for example, and so he gets a kick out of thinking holy thoughts.

Ultimately, all these heretical criteria for good arguments can be subsumed under “making sense”. It is easy to see our favourite patterns in the clouds.

moral progress

Is there such a thing as moral progress? Yes but it is not as you think it is.

What is it which undergoes progress? Is morality a collection of imperatives and so moral progress consists in more and more people or more of their behavior satisfying such imperatives? Or is it utilitarian, where people on average live better and better lives?

We should be really careful about this since it is not in our interests at all to give the past a fair comparison, we only want to make ourselves look better than them, or at the very least we judge them by our own modern standards.

One glaring observation though, is that we have simply become more wealthy. This obviously leads to better lives, hence by the utilitarian criterion there certainly has been moral progress. But most of us would balk at this. Morality is something higher than this, something transcendent, not something materialistic like the ease and cheapness with which we can attain cars or cheeseburgers. Most of us want to say that, for example, in the past we had slavery, we had racism, we had the death penalty and now we no longer have such vile things, and that this thus constitutes moral progress.

But human values are complex, slavery or racism or the death penalty cannot hope to even capture a sliver of the concrete considerations a person from the benighted past faced. I do not doubt that they too, like us, regarded such things with distaste, only they have other factors to take into account. I couldn’t tell you what they were because I wasn’t alive then, and even if I did, you would not give it a fair hearing unless you too lived thick in the midst of their dilemma. Which is to say you cannot help but be operating in far mode, taking things out of context, and trying to signal the integrity of your conscience for a present-day audience, as opposed to truly trying to empathize with the day to day moral decisions of someone from the past.

But perhaps we can try. Look at your current situation. Perhaps your government is vile and corrupt and needs to be overthrown. Why aren’t you revolting? What lies do you tell yourself to justify this inaction? How can you manage sleep at night? What is wrong with you? Actually, you’re probably fine, there is nothing wrong with you. Nothing wrong either with someone who did not stand up to slavery in the past. The government is corrupt but things are still in working order, if revolt would contrary to fact improve the concrete day to day lives of your countrymen, as opposed to merely satisfying some disembodied ideal, you would all already be at it.

We like to think our values are universal. In a sense they are, since they should apply naturally to everyone alive who share our culture and our way of living. But they are also concrete and local. They are a response to the concrete needs of our culture and were never designed to lecture the past on their bad behavior. We like to think that the death penalty is wrong, and we would like to think that we can provide the correct reasons as justification for why we think it is wrong, but our rejection of it is mostly a heuristic response to our local circumstance, arrived at with ugly tradeoffs amongst considerations both mundane and transcendent.

So yes, we do also think of our modern day values in the abstract, but the difference with applying it to the present and applying it to the past, is that we cannot apply it to the past! The past is gone. All its glorious complexities and contradictions irretrievable. We have no interest at all in subtlety or nuance, we want to positively rape them with censure, since they cannot talk back, and since that makes our consciences look good in the eyes of our modern moral spectators. Which is all fine for us. It keeps our society running. Only it does not fairly judge the past.

So there really probably is no moral progress in the exalted sense of more and more ideals being brought into the realm mundane practice. It’s a good thing.

it’s all about signaling, but of what exactly?

The first step in understanding human behavior is in realizing that X is not about Y, and is instead about signaling something else, Z. But what is Z?

Human behavior is complex, we should be fortunate that we seem to have a theory of signaling at all. With all the myriad human motivations, how can we ever hope to ever pin Z down? It is all just too complex.

Or is it? In my previous post on construal level theory, I proposed an alternative explanation for the empirical finding of the correlation between psychological distance and construal level, saying that far mode is a mental process meant to optimize for the affirmation of ideals and the telling of stories embodying these ideals, while near mode is for everything else. So it is in a sense true that human behavior is too complex for a theory. But that only applies in near mode. In near mode, proximate values are inextricably entwined with local constraints imposed by reality, so there’s no accounting for the behavior appropriate to such situations, and hence neither the mental operations required for such appropriate behavior.

In far mode though, one is less constrained by reality. Which allows you to wax lyrical about your ideals and all that jazz. For example, the ideal could be “help the poor”. In far mode, you will definitely give money to that street beggar. Hell you would even be Robin Hood and steal from the rich and give to the poor and end wealth inequality once and for all. But in actual practice, you could be late meeting up with a friend. You need to save some change for the bus fare. Or whatever mundanities your life throws at you.

Note this isn’t to say that ideals have no sway in near mode. Quite the contrary. It is in fact in near mode where such ideals are meant to have their effect. Given that you are not pressed for time and are not taking the bus, you might actually give the poor bugger some money. (Note that the constraints don’t have to be anti-moral either, just tradeoffs between various uninteresting (to a far mode mind that is) considerations.) In the absence of the ideal of helping the poor, you might not even bother donating the money. (But then again you might, coz there might be this girl you’re dating standing beside you you hope to impress with your altruism; you get I hope by now a sense of the vicissitudes of near mode operation).

But ideals are by their nature devoid of concrete information. Simple laws are effective laws. The complexity should be present not in the courtroom, but in the decision whether or not to break the law. But unfortunately, as with laws the same with ideals. One has to constantly argue for one’s adherence to them, while at the same time pragmatically breaking them because it would be silly not to.

Which is why we have this thing called a conscience. As a substitute for justifying our actions individually. Rather we have this thing in our brains which exhorts us to behave according to the norms we claim we adhere to. One’s outward affirmation of the ideals then serves as a signal for the integrity of one’s conscience. So now we argue norms in the abstract without reference to the concrete actions they are supposed to inspire. And the mechanism which enforces the norms in our behavior is our conscience. Hence I posit that far mode is basically this process which deals with signaling the integrity of one’s conscience, by telling and responding to stories (fictional) and narratives (non-fictional, e.g. the news) embodying the ideals we subscribe to.

So there you go. X is not Y, but about Z = signaling the integrity of one’s conscience. Hence far mode is about talk of ideals.

But wait, what of near mode?

Near mode is not even about about, baby. Near mode is a bunch of non-propositional heuristics and rules-of-thumb which tells you only what to do in various situations. There is no need for justification or explanation in near mode, only action. In other words, near mode is anything which is not talk about ideals. Anything else. This is why we can say stuff like “everything is about signaling” or “X is not about Y”. Because those cases where stuff isn’t about signaling isn’t even about about.

construal level theory my way

Many seem to be confused by my use of construal level theory, the concepts of near and far. So this post is meant to clear things up. I see near mode and far mode as summarizing the psychological adaptations for navigating various domains of reality. Far mode is meant for human ideals, near mode for everything else.

This is not how the construal level theory researchers see it. To them it is about something called “psychological distance” and something called “construal level”. Quoting Trope and Liberman:

The fact that something happened long ago does not necessarily mean that it took place far away, that it occurred to a stranger, or that it is improbable. Nevertheless, as the research reviewed here demonstrates, there is marked commonality in the way people respond to the different distance dimensions.

…

the various distances are cognitively related to each other, such that thinking of an event as distant on one dimension leads one to thinking about it as distant on other dimensions

…

remote locations should bring to mind the distant rather than the near future, other people rather than oneself, and unlikely rather than likely events.

…

“having fun,” compared with “playing basketball outside,” may bring to mind activities in the more distant future and past, in more remote locations, in hypothetical situations, and with more socially distant others.

…

construing another person’s behavior in terms of a personality trait (a high-level construct) involves considering that person’s behavior in the past and future, in other places, and in hypothetical situations.

…

More generally, forming and comprehending abstract concepts enable people to mentally transcend the currently experienced object in time and space, integrating other social perspectives, and considering novel and hypothetical examples.

Note that the quote describes the empirical phenomenon whereas the concepts of “psychological distance” and “construal level” are their explanations for that observation.

Now in psychology there are all sorts of process-based theories and they are almost all bullshit. So I highly suspect “psychological distance” or “construal level” is bullshit as well. The most productive psychological theories I find focus on what humans are trying to achieve when they behave in a certain away, as opposed to those theories which focus on psychological processes.

So I honestly don’t care about much of the content of construal level theory. I am more interested in the phenomena they are trying to explain. And I explain it not with a theory of process but a theory of purpose.

Far mode is meant to deal with ideals. Near mode deals with everything else.

To take an example among the ones in the quote above.

“having fun,” compared with “playing basketball outside,” may bring to mind activities in the more distant future and past, in more remote locations, in hypothetical situations, and with more socially distant others.

Construal level theory says that “having fun” is “psychologically distant” and evokes a more abstract/higher “construal level” than does “playing basketball outside” and this is why it leads to people thinking of more remote locations, hypothetical situations, socially distant others, etc. Well, that might or might not be true, and I don’t care which. “Fun” is not something you pursue in the abstract, not at all (Trope & Liberman would spin here some story about how one has one’s life goal of “having fun” and satisfies this abstract goal with the concrete action of “playing basketball outside”, which is bullshit). “Fun” is a story you tell about yourself playing basketball. As a fun loving person, you like to travel to exotic locations, and you have an active imagination, and are eager to meet new people, etc. etc. And what is playing basketball? Anything else other than all that storytelling of ideals. Anything else.

intellectual norms as wireheading

Here’s another related bunch of ideas. Let’s see where this goes.

Why do humans tell stories? I think it is because stories reinforce social and moral norms. The modern idea of a theory, as in theory of relativity, theory of evolution, etc., is based off of that psychological hardware. What?!

Yes. In stories, you hear of a brave man saving a drowning child. This is to exhort readers to be brave men who save drowning children. But what about intellectual norms? For example, one must use Bayes rule. But what is the story? The use of Bayes rule? Yes. With science there is feedback in the form of empiricism. So for example, the Ptolemic model exhorts the circleness of orbits, but such circles must be corroborated in reality. In the case of philosophy though, it is quite different.

In philosophy, there is a tendency to go as meta as possible. This is so that one can short-circuit that feedback loop of norms and bahavior, such that norms become behavior and behavior become norms. It’s really just a form of wireheading. You see, with morality governing human bahavior for instance, one gets a kick out of affirming moral norms, but that cannot compare to the sheer ecstasy of actually behaving like an upstanding citizen. With intellectual norms with high dose of meta however, object and meta levels blur. So that simply by doing meta one gets high on the satisfaction of norms. The philosopher is basically a norm-addict.

We all know what happens with addicts. They are escapists who want nothing to do with the real world. So philosophy gets ever more detached from reality. More philosophy for philosophy’s sake. This happens even in the case of philosophies which purportedly try to engage directly with the practical world. For example, science has recently been sold as the prime driver of technological progress. But that is just plain untrue. Technological progress happens mostly by trial and error, based not on scientific theories but on highly domain-specific heuristics and rules of thumb. It is scientists which retroactively steal credit for certain high profile inventions as they spin out a yarn of applied science.

But science is supposed to produce technological progress. So we keep throwing in more government funding and founding new fake fields of supposedly-practical enquiry, corrupting real science in the process. But what is real science and why is it worthwhile? Well science is basically art, art should be beautiful and should not be required to be functional. Insisting that art be functional only leads to the spiritually barren practice of ‘design’. I want my toaster to work. I want my Rembrandt to be beautiful. I don’t want a Rembrandt toaster.

I think democracy is another related form of wireheading. In democracy everybody gets to advocate some policy or another without at all being exposed to the consequences of such policies when put in practice. Brave men actually have to save drowning children, but pro-immigration folks do not have to live in immigrant-majority places. I’m sure pre-democratic folks do also have political opinions, but politics was never an obsession of the common man. Neither does the common man derive much satisfaction from politics, for he does not have that all-powerful-symbol of the vote. With democracy, the story is that you matter, nevermind the fact that your importance is mere story. The norm is the behavior which is the norm.

All this leads (I hope) to another idea I call monuments and technology. Art is harmless. Art does not affect the mundane but important workings of a society. The painter does not ruin the furniture the carpenter makes. Alas this is not the case with a society with an advanced case of rent-seeking parasitism. The industrial revolution was not a product of scientific knowledge. But rather science is a monument built on top of the success of the industrial revolution. Another example would be GDP and educational spending. The narrative is always that educational spending is investment in human capital which leads to our nation’s wealth. That narrative is as narratives tend to be, backwards. Nation’s celebrate their wealth in the form of educational expenditure. The absurd amounts of money an American students spends for college and the wholesale import of Anglophone universities into Abu Dhabi are cases in point.

Both are necessary. We need monuments and we need technology. The finer things in life and the substrate which provide for those finer things. Trouble is when we confuse to the two. In democracy, political ideals and practical governance. In industry, science and technology. In universities, education and vocational training. More generally, and the main thrust of this article, theory and practice.

the event is not the exposure

So I should really be writing down my ideas in some systematic form. But I never know where to start. So I’ll start here, which is to say, at a random place. We’ll see where this goes.

Today’s idea is the distinction between event and exposure. Event is whatever happens “out there in the world”, and exposure is your payoffs in relation to that event. So for example the event might be “tsunami” and your exposure would be “loss of property”.

This seems obvious enough. Why do we need a mantra? Well, it’s because of this other mantra “the map is not the territory”. That one is basically an epistemic rationalist’s slogan. The map, which is to say your model of reality, is not reality itself. Again, as a propositional statement it should be obvious. The problem is in what it emphasizes. The assumed epistemology there is that we have this model of reality, and we have our intention of how we want reality to be, and based on our model of how reality works, we do certain things in order to bring about our vision of reality.

That is wrong. Wrong as a description of how human beings actually behave. Wrong also as a prescription for how human beings should behave. We go about our daily lives mostly depending on heuristics and rules of thumb, not theories. To a mind brainwashed by the dominant enlightenment ideology of our times this can seem like a bizarre assertion. I don’t pretend I can convince the skeptic here. It is something you have to be on the lookout for and something you must train yourself to notice in your daily life. The narratives are certainly there, only they merely adorn behavior and do not govern it.

Taleb would call those who believe theories drive human behavior “fools”. But I know better than to be so insufficiently cynical. Hanson would say theory-talk is simply far mode story-telling. Homo hypocritus is never stupid enough to walk the talk, but hypocritically and sanely chooses to rely on his trustworthy heuristics when it comes to the mundane practice of day to day living.

So since we do not after all rely on maps to get around in the territory, the mantra of “the map is not the territory” is at best irrelevant and quite often actually harmful. Homo hypocritus’s hypocrisy performs best at the level of the individual when he is in charge of his own stories and behavior. He knows precisely when not to take his stories too seriously if he cares at all about the life he actually lives, as opposed to the fairy-tale life his stories describe. But it all goes painfully astray in modern democracies. (Oh shit, here comes another idea I thought was meant to be in another post; you see the problem here; I will try not to get carried away). With democracy, it is veritable orgy of far mode idealization with virtually no near mode accountability. You can tell stories and even when they get disastrously implemented in policy you will not be at all personally punished by the consequences. But like I said in the parentheses a detailed analysis of this phenomenon deserves another blog post.

Theoretically (ha! caveat emptor), it is not model error per se which is pernicious but a function of that model error, viz. your payoffs. Sure, you say, the map is not the territory, we are well aware of the presence of error. But mathematically speaking the model error is but one cost function among many. A person guided by the map-territory mantra will try to minimize the cost function which is the model error, when he should in fact be minimizing the cost function which is true penalty, i.e. that which does violence to his values, of getting the model wrong.

All very technical, but perhaps I tossed that in there to perhaps convince a rationalist to be willing to consider that other mantra, the event-exposure one.

So should we just build models in observation of the true subjective cost (relative to our values) of getting things wrong? As opposed to some objective measure? Son, if you think that is what human beings have been doing ever since anatomically modern homo sapiens, then I must say you are a supreme specimen of the fool. The whole point of paying attention to your payoffs is that it is what you in fact care about. You don’t care about what the model predicts, you care about whatever shit reality is prepared to dish out to you. That is to say, you should take a non-predictive, as opposed to a predictive stance (oh god, is this yet another blog post?).

Give up on predicting reality. Rather, pay attention to insulating yourself from unacceptable harm, while at the same time allowing yourself the option of seizing on any serendipitous opportunities for great payoffs which come your way. This is what Taleb calls being antifragile. Notice that this does not require a model. For example, you don’t try and predict the weather to plan ahead for what you should do for the weekend. You only make sure that the worse possible weather isn’t going to ruin your weekend, and that you have options for the basic contingencies of rain or shine. And if it snows, great, you can bust your sled and have some fun. The event is not the exposure. You should have fun regardless of the weather.

lessons from mathematics

Those who know math tend to draw the wrong lessons from it. This is because they want to signal their affinity for math more than they want to communicate the wisdom which do in fact transfer. They would tend to champion things like formal precision not because precision will get you anywhere outside of math (and various allied domains) but precisely because precision is largely useless outside of math. If you find precision difficult then it must be because you are doing something wrong, because we mathematicians seem to have no trouble with it. Oh right, I forgot, you aren’t a mathematician. Ha!

it all adds up to normality

The metacontrarian contemplates an insane idea.The magician locks himself up in a tank of water. Breaths are held. The magician breaks free. The metacontrarian renormalizes. Applause all round. Everything adds up to normality!