Democracy and Tradition (Part 2)

The reader of Democracy and Tradition Part One is likely to have a long list of objections to the thrust of the argument. Say he agrees to work with the tide gauge analogy, but he does not so easily let go of the fact that the sea levels have risen over the past century. This seems to him to play quite easily into the progressive narrative, at least in a sense, that there is a discernible direction to history. While he doesn’t fancy himself akin to the stumbling modern man, less modern man does not suit him much either.

Firstly, let us build on our understanding of random walks. There are two people I could introduce you to when opening this topic again. The first is Andrey Markov, the Ruskie, and the latter is Karl Pearson, the Limey. The former is the namesake of a mathematical concept called the Markov Process, which is a generalization of a random walk. Essentially, if the current state of a phenomenon is the only useful piece of information in predicting its future state, then it is a Markov Process. But Pearson is going to win out in the competition to be showcased, as his now greater than a century old question in Nature was the genesis of using the phrase random walk to illustrate this concept. There is a rich line on the last page of the link provided, which I’ve snipped bellow:

Pearson was an interesting fellow. Certainly a progressive of his time, he checked the boxes of women’s suffrage, eugenics, and socialism. Of those three ideas, I’ll let slip that the author considers one of them to be mere silliness, another dangerous, and the other misguided altruism; it is up to the reader to work out which is which. To get a good feel for Pearson’s thought, I recommend a piece from the 50s in The British Journal of Sociology called Karl Pearson: Socialist and Darwinist. For now, to give the tl;dr of his thinking during his prime, here’s a quote from the end of his address at Newcastle during the time of the Boer War:

I really like analogies. The more you read this blog, the more you’ll pick up on that. Fundamentally, analogies are just isomorphisms. Or maybe, isomorphisms are just analogies, take your pick. When Karl Pearson was trying to come up with a model for random migration, he called his problem the random walk problem in Nature. One of his answerers, Lord Rayleigh, indicated that the model he was looking for was “identical with a problem in the combination of sound amplitudes in the case of notes in the same period.” So there is a seeming analogy between a problem in acoustics and one in migrations. Pearson joked about the stumblings of a drunken man, indicating an analogy between the drunken man’s gait and the prior two phenomena.

Admittedly, I skimmed the Mathematical Theory of Random Migration paper cited above. I am skeptical of the viability of mathematical proofs in explaining anything but the most controlled of phenomena. I am a simple man, so we’ll make simple adjustments to our random walk model of culture in order to illustrate concepts. We are simply making analogies between mathematical objects and phenomena. Realism, ‘proofs’, both scientific and social scientific, are foolish.

So our first modification to the random walk will be to give it some momentum. When we observe political-social history, trying to argue that it’s completely a Markov Process is tough. No one knows what the future will bring; no one knew what the future would bring. But there are directions which once set upon, more often than not that direction continues to be followed. We do not need to remove the essential randomness to our model, we just need to wonder what happens if the current random process is affected by a prior one as well. There are two ways that I’ll try to illustrate this. The first is with a Moving Average model:

The above lines are generated with a very simple formula. The current term in time t, x(t), is equal to the prior term, x(t-1), plus a random term, e(t), and half of the random term generated in the previous period, e(t-1). So: x(t) = x(t-1) + e(t) + .5(e(t-1)). Easy enough, right? This captures somewhat the idea that if the current term is greater than the prior, or more precisely: the current random element generated a positive number in this period; then the next term is likelier than random chance to be greater than the current. You see this come through in the swoops of the lines above.

The second way to do this may be a bit easier to grasp:

This one generates momentum in a much more literal sense. If the prior term is greater than its prior, then the current is a random number between -.4 and .6; else it is a random number between -.6 and .4. So if the slope is tending up, it will continue to tend up; if it is tending down, it will continue to tend down. Again, you can see this in the swoops of the above graph.

Generalize this concept of time to whatever works for you, I think it works on most any scale. Read a history of the French Revolution, until the Thermidorian Reaction, France’s revolutionary tendencies produced more revolutionary tendencies. The larger time frame version of this is well put by my favorite Son of Abraham:

“If there is any constant phenomenon in the last few hundred years of Western history, it’s that – with occasional reversals – reactionaries tend to lose and progressives tend to win. Whether you call them progressives, liberals, Radicals, Jacobins, republicans, or even revolutionaries, socialists or communists, the left is your winning team.”

There’s been a very large swoop, at least in a certain sense. Moldbug continues on to say what I plan to drive at in much of this blog:

“However, if these changes are indeed arbitrary, a random walk could reverse them. Professor Dawkins’ great-great-grandchildren could then explain to us, just as sincerely, the great moral advance of society, which early in the 21st century still turned a blind eye to rampant sodomy and had no conception of the proper relationship between man and servant.”

The next step I want to take on our journey into random walks is to open up our concept of them into another dimension. There have only been two dimensions thus far, a time and a magnitude. But we need a second magnitude, another axis, so that we can visualize this spatially.

For this one I needed to switch over to R, there’s no good way to graph this as nicely in Excel. So above we have two random walks (with momentum of the second kind discussed (though it would work just as fine with pure random walks)), and they are plotted against each other, one for the x axis and the other for the y. We now have the drunken man’s stumble. One could easily draw a map behind the plot above, showing the drunken man’s path from bar to bar, sometimes revisiting one for a second or third time. He’s definitely moved far from his starting point, but assuming he is indeed drunk (aka the process generating the numbers (the error term) has a mean of 0), he will find his way home eventually. Here are a few more:

Above are 42 momentum random walks in 2 dimensions, each with 1000 data points. I promise I didn’t just make that in Microsoft Paint.  They are a bit hard to look at, but see how they blob around the middle? Try and abstract here with me a bit, say we throw different cultural traits/tendencies around the graph. Similar ones are closer together. Now let’s define a culture on our graph as some subset of these points, for now we’ll stick to circles to define our culture subsets. The following illustrates this idea:

Now put these two graphs together. Say cultures migrate over time, in a random walk-ish fashion. We’ll start them all at the point above, centered around (0,0). Now let’s see where they have gone after 100 random movements:

After 500:

After 1000:

You see the variation of these cultures increasing with time, but you can still pick out a center, even after 1000 points in. Imagine not only the same 42 circles spanning in, out, and around; but also circles spawning off other circles, as cultures have split and drifted apart. You will always have some outliers, but you will also be able to pick out that center.

In part three, we will tie this idea back around to the constants idea defined in part one.

 

Democracy and Tradition (Part 1)

A following is quote from G.K. Chesterton’s Orthodoxy. It floats around blogs and intellectual circles that I follow, even popping up in my Facebook feed from some of the edgier pages one could dare to follow. It has been a while since I’ve read the book, and the context of the quote isn’t fresh on my mind, however it is a great starting place for this post, so here it is:

“Tradition means giving votes to the most obscure of all classes, our ancestors. It is the democracy of the dead. Tradition refuses to submit to the small and arrogant oligarchy of those who merely happen to be walking about.”

Reactions to this quote depend heavily upon your politics. It is likely to rub you the wrong way unless you share a peculiarly Anglo and Catholic world view. It’s a rough world view, full of cognitive dissonance over 19^th century encyclicals. Though to be fair they can’t have nearly as difficult a time as a well-read American Catholic, who has to worry about accusations of treason over owning anything written before the Second Vatican Council.

The reaction to Chesterton of the contemporary man is discomfort. He likes democracy, the more the better. His room is full of Democracy Now posters, he volunteered at the polls on Election Day, and now he is troubled by the notion of denied suffrage to anyone. Yet the world progresses, meaning those of the past were ignorant of future affairs. Not only do they know as little about him as he does of them, it seems unfair that the dead should influence his world while his world does not influence them. Reflecting, but only briefly, contemporary man shuts down the incoming thoughts of how so many of today’s voters lack skin in the game. How regressive it would be of him to question the validity of their participation in the democratic process.

Fortunately for the reader, the author of this blog is rather regressive. For the reader’s enjoyment, he will not only question the validity of certain voters’ participation in the democratic process, he will question the validity of all voters. The path will be very round about, and the skimming reader may even take the arguments as being pro-democracy if he is not careful. But we will get there.

Before the political realm, take a trip down epistemology lane. Asking yourself ‘how can I know I am not crazy’ is the first step towards a solid epistemology. You could do the Descartes thing and come out realizing that you are, in fact, crazy. Another route is to construct a sort of web of coherent ideas, you will feel less mentally fragile, but like the greatest minds of the field which is coherency itself, you will succumb to the lunacy in the end. Another route, which I will advocate here, is that which asks: ‘how many people would have to be crazy for me to believe such a thing?’ This is not an argument which seeks certainty, but one which builds confidence. When an idea fosters a competition between you and the rest of the world, and only one of you can emerge sane, lean towards yourself coming out on bottom. The alternative is to prefer to think of most people, the living and those who lived in the past, as detached from reality; at which point your options are to despair at your loneliness in sanity, or submit.

Marquis de Condorcet is the brain behind every political science freshman’s favorite proof, the Jury Theorem. The idea is that people tend to be correct, at least more often than they are wrong. A very low bar, any fraction above 50% will do. If that is true, then as you increase the number of people involved in deliberation, you will increase the likelihood that the group will reach a correct conclusion. You can find this theorem in various forms in different justifications for democracy. There are obvious limitations, making Condorcet is less like the epistemological messiah, and more like the guard who provided the wine. Most obviously, it can be doubted that the typical individual is more often than not correct. Beyond basic knowledge of the world, collective opinion varies drastically in short periods of time, making it difficult to argue these opinions correspond to any underlying truth.

Rapidly varying opinions are an especially damning blow to democracy. The waves of public opinion crash violently against the shorelines of the political realm, making it difficult for those interested to get an accurate read on the levels of public sentiments. Even worse, every four years we kick up a hurricane in the ocean of the people, wherein at the most dangerous moment, the height of the highest wave is measured, and it is called the sea level. There is a sea level, but there are better ways to measure it.

If you read this blog’s prior post, you may have good reason to be suspicious of the following graph:

What do you think? How confident are you that the above graph is/is not a computer generated random walk? In this case the graph is from a blog which looks to be about climate change skepticism. I snipped out the edges to remove the labels. This particular graph comes from a post about Long Term Tide Gauge Data, it is the average of the mean of sea levels for a couple hundred years’ worth of data from different tide gauge sources. I am not trying to sell you on climate change or climate change denial, I have a different motive. Take a look at the graph below:

These are the raw data of which the prior graph is the mean of. At any particular time, even if you believe you see an underlying trend in the data, the difference between the low measures and the high ones is very large. Imagine if I requested you to find me today’s sea level, and dutifully you collected the average of a few of the day’s tide gauge levels and reported them back to me. Then when I wrote a blog post using it, it went viral. Now there are info graphics about the rising sea level, textbooks cite my blog, and during the next four years the sea level is assumed by everyone to be the one you reported on that fateful day. See the parallels yet?

Tide gauges, when their data are understood properly, really solve our temporal problems for measuring the sea level. They beat bringing rulers to the beach. The epistemological/political analogue to tide gauges, if you have slept through this short piece and have not figured it out yet, is tradition.

Up perks the ears of the less modern man. He enjoyed the spirit of Chesterton’s quote, even if he cringed at the use of oligarchy as a negative descriptor, and democracy as an ideal. He can look at the data from the tide gauge and know that while the tide is high, and waves crash against it, this momentary uptick in the gauge’s measure will fall, and oscillate around a mean. He can think of some ideas which not only have been accepted in the West, until recently, but also by the bulk of the rest of the contemporary world. He does not give an endorsement of all ideas accepted over periods of time by large groups; many of them are lunacy. But as the number of years and people claimed by an idea increases, he thinks it may be wise (even epistemologically savvy) to pay that idea more heed.

Let’s do some tidying up: what is the analogue to sea level? We need a term which is the Jeopardy answer to “some sort of underlying truth.” Be it for practical purposes, the political, or the philosophical, there are ideas which have been thought true by most within a culture group(s), most of the time. Even when groups diverge, they still will be within walking distance of each other. Further, these ideas, especially on the practical/political level, tend to throw things into disarray when there is too much deviation. They also tend to reset themselves once the conditions which caused the deviation cease. Traditions log these things, in their various manifestations. Since it is too hard to invent new words, and we can’t just mash a bunch of words together like the Germans, we’ll stick to the mathy theme of this blog and call these ‘underlying truths’ constants. So tide gauges are to the sea level as traditions are to these constants.

Culture Walk

There’s a tendency for man to see patterns in the world, why shouldn’t he? Each morning of his life, the Sun has risen, why should it not rise the next? Each time he drops a stone, it falls to the ground, why ought it to be different next time? Each time he blinks, the world is as it was a moment prior to closing his eyes. Patterns are not only noticeable, they are useful. Man sees the fresh tracks of deer overlaying older tracks, he concludes that his game traverses here often, and it would be a good place to hunt. Man notices brave men do not flee in battle, are revered by fellow tribesmen, and that cowardly men turn their backs and are cut down; man resolves to be brave. Men who are revered also have more access to the women, he notes.

There are other, more abstract patterns that the contemporary man is aware of. He has seen the march of technology to greater and greater heights, why should it stop? Each group which has fought for more rights has gained them, why should he doubt the progress of society will continue? He is more liberal than his father, who is more liberal than his father; this is true for all his friends, and so he is sure he is on the correct side of the history.

Our contemporary man comes across the above graph while reading a blog, and it lacks labels or context. He sees that it is about flat, with some bumps here and there, until around the halfway point when it starts to trend up. Being a pattern recognizing man, he recalls that this is sort of like how he thinks of American history, largely uneventful until about halfway through when we start to make social progress. Perhaps it’s a graph of human rights, with the beginning of the upward trend being the end of the civil war, the slight down slope for a moment having to do with Jim Crow, or something, which he vaguely remembers from history class. Then MLK gets progress back on track, until Bush ruins it as rights seem to slide backwards a bit at the end. Maybe this graph only goes until around 2008.

Another graph? This one is mostly downward trending, with a couple of peaks here and there. What’s gone down over the years? Ignorance, perhaps? Or, similarly, religiosity and church attendance? It starts high, those in the past were pretty ignorant, he can forgive the people of those days for their churchiness. It spikes, wasn’t there a great awakening? Then it gradually falls until again it spikes, the First World War was probably around there, people like God more when it’s war time. Then it falls, the twenties were a prosperous time, who needs God when you’re well off? More church during the Great depression, then it spikes for World War Two. After that it gradually falls thanks to a secularizing public education, dispelling those old superstitions.

Reading further into the article, he is surprised to learn that the graphs do not represent anything at all. They are just the first two random walks the author generated on Excel while pondering writing his post. Not used to being tricked as such, modern man doesn’t believe the author, after all his explanations of the graphs fit so well. It couldn’t be that graphs, with such obvious trends and corresponding so well to real world events, could just be randomly generated.

For readers who aren’t familiar with random walks, the La Wik does little to alleviate your anguish unless you took a couple of statistics courses in college. The idea is simple: each point is only dependent upon the previous point, and some random process which is as likely to point up as it is down. In this case, for both graphs, point 1 (p1) is equal to 0, and point 2 (p2) is equal to p1 plus a random number between .5 and -.5 (e2). So p2 = p1 + e2. Each point follows this pattern, so p3 = p2 + e3, and so on. This produces a random pattern, but sometimes they veer off in one direction or the other, especially after enough points have passed. If you want to try it, open Excel, put 0 into the A1 cell, and into the A2 cell put: {A1+RAND() – 0.5}, don’t include the braces. Then drag the lower right hand corner down a bunch of cells until you have as many values as you want. You’ve now made a random walk, where each point is plus or minus .5 the prior.

You can make a bunch of them, and you can see how the same formula generates a bunch of different lines, many of which you might think have trends. However, you know they don’t. You know that the underlying process is random, the graph is no more likely to move up or down, yet your brain sees a pattern in the graph, and it’s natural to think that there ought to be a discoverable force pushing it up or down. But there’s not. Below is a graph of a hundred random walks, with 500 points each:

Each of these random walks start at the same point, 0, yet they fan out over time. In spite of the increasing variation of the lines as they move forward, the mean stays about the same, 0, the point where they started. Point 1 for all is 0, and the mean (average) of all ‘Points n’ are 0. Let’s play a bit less modern man than contemporary man for a moment.

Less modern man takes a look around and notices the variation of cultures and people around the world. Whereas contemporary man might think of these people as backwards, and he may be right, less modern man sees that many cultures have common traits. Some cultures have women at equal social stature to men, some treat them as slaves, but most are somewhere between the two. Some cultures are quite hostile to outsiders, others are suicidally friendly, but most are somewhere around cautious. There’s a mean, perhaps, to most cultural traits. Histories often trace the movements of these traits, calling the succession of a few positive random terms progress. Yet the mean, when cultures are examined together, remains fairly constant. With Western hegemony, perhaps it could be argued that the other cultures skew West. But in the long run, does the hegemony have significant enough pull to parse it out of the random (error) term?

Less modern man has an idea. The mean of the random walks is equal to their shared starting point. Humans, too, had a shared beginning, a last common ancestor. Might they have a last common culture? If there is a discernible mean of cultures and cultural traits now, might that be equal the last common culture, or p1 of the culture trait random walks? Rather unprogressively, Less modern man thinks this could be evidence of an underlying human nature. (Extremely unmodern man might argue that the nature of humans change, and that these culture walks could also be nature walks, but that’s for another post.)

The arc of the moral universe is random, sayeth Excel. There are patterns in society and nature which are useful to notice. But not every pattern, every trend, has a gleanable cause. Further, the simplest explanation, the most intuitive, is not always correct. Early man is easily convinced the Sun orbits the Earth, your grandmother is convinced that water won’t boil when you watch it, and the contemporary man is convinced that morals progress in a discernible direction.