Sunday, December 14, 2014

What is Entropy?

Anyone who thinks they know is going to absolutely hate this answer.

Entropy is a measurement of how much work, with current human knowledge, can be extracted from a system.  It is a measurement of all potential energy that is yet untapped, combined with a theoretical maximum of "useful" work that can be extracted from this energy.  It is a useful fiction, but it is still a fiction.  So is the second law of thermodynamics.

In truth, entropy has the potential to change with every change in human knowledge.

If we discover a new force - say, a subtle attractive force far weaker than gravity, but attenuating far less quickly - the entropic values of all systems change.  You can use this information to extract slightly more energy from the system by building an engine that somehow takes advantage of this new source of potential energy.

In more down-to-earth terms, suppose we just discovered fire today.  Suddenly the potential energy that can be extracted from coal increases enormously - previously, we could just extract whatever energy we could get from its falling, much as we extract enormous energy from the gravitational potential energy in water.  We have to rewrite all of our entropy tables, which previously just concerned themselves with height relative to, say, sea level.

Fortunately for the industrial revolution, we already discovered fire, so we already had enormous amounts of potential energy to extract - although never as much as we would have liked, which produced our obsession with calculating exactly how much energy we -could- extract.  Entropy is an engineer's concept which arose from that obsession.

Entropy is really just an elaborately-dressed up way of saying that time flows in one direction - that the physical processes flow in one direction.  Coal burns; carbon dioxide doesn't draw heat in and convert itself into coal, raining down upon us.  If the reverse were true - carbon dioxide drew heat in and converted itself into coal, it would be an endothermic, instead of exothermic, reaction - these kinds of processes do in fact exist in real life.  If it did -both-, we couldn't extract any useful energy from the process, because as we "burned" coal it would re-consume the energy and re-precipitate carbon - these kinds of processes -also- exist in real life, they're called reversible reactions.

Now, it sounds like a compound like this would be really useful, and you'd be right.  It's exactly what water does - absorbs heat to evaporate, then gives off heat to re-precipitate.  If coal behaved as I described, you'd require a heat source to re-precipitate the carbon dioxide after you've extracted work - and thus heat - from the system, since it would require that energy to re-bond.  (Actually, coal -sort of- works as I described - exposed to the right sort of energy and conditions, it -does- re-precipitate, which is part of what plants do when they convert carbon dioxide into carbon.)  The difficulty is that managing the boundary conditions to make the process cyclic requires something -else- be providing useful work.

Entropy, as a concept, is made much more mysterious than it really is.  In its shortest form, the second law of thermodynamics is just stating that all the laws of physics -continuously- apply.  Time flows in only one direction.

The fiction is in the implication - that a given amount of energy can ever only do some finite amount of work before it is spent for good.  There's nothing we have yet discovered in the laws of physics that says you can't have a perpetual motion machine, or that you can't extract an infinite amount of usable work in a closed system.  There's just nothing in the laws of physics we have yet discovered which -permits- an infinite amount of usable work to be performed in a closed system.

It's an important distinction, because there's a -lot- we haven't yet discovered.

Lossy Transformations and Mathematics

I'll lead with a question:  What is X divided by X?

The immediate and obvious answer is "1", but this is, in fact, incorrect.  The answer is, roughly, "1 except where X equals 0".  This is both pedantic and important - 0 divided by 0 isn't 1, it's "Undefined".  5 times 0 is -also- 0.  "Undefined" in this case really means something like "Every answer simultaneously."

Division, as it is typically defined, is a lossy transformation - you have the potential to lose information in performing the operation.  So is multiplication - the equation "5 = 3" can be "made correct" by multiplying by zero, a conceptually valid operation.

Squaring numbers is too.  5^2 is 25 - but once you've done this, you can no longer determine, from the current properties of whatever it is you're working with, whether you started with five or negative five.  You've lost information about your starting configuration by performing what we usually consider a perfectly valid operation.  Reversing the operation doesn't give you what you started with.

The issue is one of simplification.  There isn't one single zero.  There are an -infinite- number of 0's.  Zero apples isn't the same as zero oranges - they're different zeros.

Squares are similar; a rectangle five feet long and four feet wide has twenty square feet, but it's not the same square feet as from a rectangle ten feet long and two feet wide.  A square value doesn't maintain information about its constituent parts - this information is simplified away.

Division, again, is similar; 5 / 5 equals 1.  Is it the -same- 1 as provided by 4 / 4?  No.  They're different 1's, but once we've reduced to a single number, that information is lost to us.

This simplification is great, if you don't need that information, and terrible, if you do.

Every mathematical operation results in a loss of information.  Again, this is helpful, if you're looking for a simple result, and worthless, if you end up needing that information.  Knowing that the combined length of two walls is 10 doesn't tell you anything about the individual length of the individual walls - you lost that information when you added the two numbers together.

The purity, the cleanness, of mathematics is an illusion, produced by rules which encourage you not to notice the information that goes missing with every step.  Mathematics, in truth, is a very messy process, the process of crossing out information until you're left only with the information you think you need.  The erasure is intellectually satisfying, but it is wholly the act of hiding complexity to make the complex -seem- simple.  The complexity is still there, and knowing the square footage of a room you're tiling tells you next to nothing about the number of tiles you need to cut, and how.

Saturday, December 6, 2014

Obvious Things Part 3: Entitlement

I don't think anybody -likes- an entitlement mentality, it's just that none of us can agree on exactly what this means.  Loosely speaking, entitlements are just expectations to things we personally don't agree should be expected.  Remember, however, that your position in society is dependent entirely upon your conformance to others' expectations - entitlements, therefore, are most injurious to the upper classes, which is exactly why entitlements are fomented by those who oppose the stratification of society.

Entitlements are fomented as a form of political brinkmanship, by either those who have power and intend to make power to difficult to aspire to, or by those who don't have power and seek to push those in power out.  This is obvious if you think about it for a moment - that's exactly what political promises -are-, the setting of expectations, of entitlements.

The difficulty, however, is that this is a ratchet, a one-way process that keeps going until everything destabilizes, until the promises exceed the ability of those in power to fulfill them.  I can point to several eras in history where exactly this happened - the result is never pretty, although it does generally do a pretty good job of resetting everybody's expectations.

Because there is always a benefit to some party of creating expectations - of creating entitlements - I suspect this process is inevitable, and social stability cyclical.  Of course, as time has gone on, the ability of powerful people to meet promises has increased, producing longer and longer periods of stability - and with technology, it's possible the cycle may be broken already, as ever-increasing productivity ensures the ever-increasing promises of the powerful can perpetually be met.

There's thus an incentive for those seeking power to destroy the advance of technology.  The question, of course, is whether they realize it.  I suspect some have, given the degree of effort taken towards precisely that goal.

Consider that in a Democracy, the public is ultimately in charge.  The Party Leaders are jealous of this.  Consider what this means in the long term.

Tuesday, November 18, 2014

Obvious Things Part 2: Hats

I've encountered a -lot- of people who comment on the funny hats in religion.

Y'know the weird thing?  Nobody comments on the fact that hats play a role in -every- religion.  They also play huge roles in official government positions.

"Well, yeah," you might say, "they're part of the costume, part of the uniform; it helps define people's expectations of who you are and what you represent."

That's true, of course; that is part of the role of a hat.  But see, you're underestimating the cleverness of some people who lived a very long time ago.

Why, pray tell, are non-clergy men traditionally forbidden from wearing hats in religious gatherings - and why are women frequently permitted them?  Why are hats traditionally forbidden in schools, government buildings, and the home?  Why do clergical hats typically lack a brim?

Do you think your personality is different on a sunny versus a cloudy day?  Outdoors, versus indoors?

Hats - brimmed hats in particular - have a -huge- impact on your mood and personality.  I don't say this because I've read a study - I don't have to.  A hat doesn't just darken your face - it darkens your mood.  It makes you less empathetic, less vulnerable, more insular.  You know the person who refuses to ever take off their hat?  It's because removing it leaves them exposed and vulnerable; it's probably the only thing that lets them comfortably interact in public.

A brimmed hat can easily turn 10-20% of your field of vision into utter darkness.  What do you think that does to a police officer wearing a hat?

What do you think it's done to our society that hats have vanished from common dress over the past sixty years?

And trust me, this isn't a unique insight.  Social engineering can be as simple as popular figures no longer wearing a hat, setting fashion, and thus social, trends for decades to come.

Obvious Things Part 1: Social Freedoms and Class

This is the first part of a sequence I'll contribute to irregularly, discussing things most people grok without ever actually knowing.  Everything I intend to write in this sequence is something which is so obvious we never even notice it - although, trust me, many of our historical elites -have- noticed these things, which has granted them subtle power over our lives we never even notice.

Do you know the difference between our upper classes and our lower classes?  It's not, as one might immediately think, power, or money.  These things don't change your station in life.  Your station in life is determined by one thing and one thing only: The expectations of other people.  This is well-understood in the East, and formed the explicit principles by which Imperial China was governed, in the written teachings of Confucius, but here in the West we tend to try to ignore it.  We tend to see things like ritual suicide as honorable but ultimately barbaric practices, not seeing the way these practices tie into civilization itself.

Western media has increasingly tended to portray the enforcement of social rules as a bullying behavior, and we have in recent years begun to strongly discourage this enforcement.  I'm a staunch individualist - but I'm also a rationalist, and I recognize a self-destructive attitude when I see one.  I also recognize a particularly insidious form of social engineering - a re-stratification of society.  Because, you see, classes have always, and everywhere, been divided first and foremost by adherence to social law.  The upper classes have -far- more expectations heaped upon them; expectations of dress, behavior, accent and verbal tics, dinner manners, how to stand, how to walk, how to address people - the upper classes have etiquette drilled into them from birth.  You think this is an accident of fate?  More, you think it is an accident of fate that our upper classes are telling the lower classes that none of these things matter?

Clothing, to pick one example, is -always- a uniform.  It -always- tells other people who you are.  Who do you think gets the job in an interview - the lower-class person who shows up in jeans and a t-shirt because they think the people who insist that a suit and tie are important are just bullies, or the upper-class child who wears a suit and tie because they've been taught the important of a good uniform since birth?  It's not money, nor connections, that guide children from birth to remain in the social standing they began it in - it's knowledge, knowledge that is being carefully and deliberately sabotaged by those -claiming- to be standing up for the disadvantaged even as they make their disadvantage permanent.

The upper classes don't have more freedom - this is an illusion.  They have far, far less freedom, because while their station in life theoretically grants them greater privilege, they only enjoy that privilege so long as they do not actually exercise it.  Quite a lot like money, actually - the rich man is only rich so long as he doesn't spend his money, after all.

Li is the path to power.  Appear the fool, and be treated as one.  Appear to be a person to be taken seriously, however, and you will be.

Not that I advise anyone to pursue this course, any more than I would advise others to become misers so that they might become rich, and for precisely the same reasons.  However, while I would not advise miserliness, I -would- advise careful consideration of purchases and the establishment of a financial reserve - and likewise I would advise the careful evaluation of social expectations.

Bullies, as anybody who tries to teach social rules is now being labeled, are teachers of a lesson which needs teaching - gone are the days when "bully" referred to the teenager who picked on the elementary school student, now the "bully" is the teen who makes fun of the one teen who doesn't wear deodorant, or who dyes their hair an unnatural color.  The question, of course, is which social class is hosting the backlash against "bullies", and why.

Tuesday, July 8, 2014

Game Theory and Naivety

Game theory can teach some very curious lessons.

Perhaps the most important is that the obvious solution is frequently the wrong solution.  In order to create an environment where cooperation is possible, you have to create an environment where profitable defection isn't.

The naive solution is always "Let's cooperate".  In an environment of people who -always- cooperate, defecting is a -very- powerful tool, and very attractive.  "Always cooperate" as a strategy rewards defection.

In order to foster a truly cooperative environment, you have to be willing to defect, and most specifically against those who have first defected.

Naive anarchism or communism is the belief that "Let's just work together" is a viable strategy, that you can rely upon goodwill.  Even I'd defect in that system, if for no other reason than resentment of a system that doesn't punish defection.

We can't reward cooperation enough to make defection unattractive - we have finite resources, and defection is, in any system, the gaming of the system to get disproportionate reward.  The only real option is to make defection less attractive.

Government is one mechanism of punishing defection; it is a universal agent, with whom cooperation is paramount, and whose defection is lethal.  There's just one issue with the use of government in this manner: It permits a grander scale of defection, that of false accusation.  Government becomes the arbiter of grudge, rather than law.  Coyote Blog comments on one example.  It's hardly the only.

Belief in government as a reliable arbiter isn't -quite- as naive as "Let's just work together", but still makes the same mistake: Assuming cooperation and defection can be made infallible.  They can't.  That's the metagame.  Then there's the third level of naivety - the belief in a solution to this mess.  There is no end solution - whatever rules you use, there's a metagame that will defeat them.

The Cure... surprisingly simple: It's a sledgehammer.

Our existing government is made up of masons; the legislative branch exists to build new walls, the Supreme Court -at best- exists to make sure the walls are in the right places, and the Executive branch mans the walls.

We need a branch whose purpose is to knock walls down.  Our government is fundamentally constructivist - it needs a deconstructivist element.  A branch devoted to knocking down the things the legislature builds.

The courts have kind-of sort-of fulfilled this role in the past, but only for the most egregious cases.  The legislative branch has this power, but rarely if ever uses it; they're elected to fix problems in society.  Knocking down parts of the government just makes it harder for them to do their job.

So break the legislative branch's powers up.  One branch to construct, one branch to destroy.  Hell, even give them the power to send the bills back to the legislation with notes on what needs to be adjusted and why - they can't propose new legislation, but they can remove legislation and suggest changes.

And give them a reason.  Put a cap on the total pages of law in the government.  Is a single person's life even long enough to -read- all the laws on the books right now, after all?