I really like this post. I have been playing with (or -- threatening to play with) a nearly identical model myself. There are a number of things to prove about this Markov chain, including what the stationary distribution is.

One additional effect to consider would be something like a "blur kernel," which could describe the flow of wealth within the economy to "nearby" individuals (e.g., the coffee shops in the finance district might be able to charge more, and so wealth will tend to diffuse to them). I think that effects like this are, at least in theory, what are supposed to prevent the excessive concentration of capital. Modeled on a graph, one could ask questions like, "How does income inequality (e.g., Gini coefficient) change as a function of graph connectivity (e.g., Fiedler number)?" The obvious story then would be that, as the economy becomes increasingly centralized in a topological sense (with some appropriate graph-theoretic measure of centralization), or as people become less dependent on commerce with their peers, distributions sharpen and inequality grows.

Finally, I'll add that there are other models of social phenomena, like armed conflict, with similar "inequality exacerbating" properties; see e.g. Lanchester's square law of combat. In fact, I think RTS games like Starcraft are an interesting model for this kind of thing -- they're really-abstracted models of violent societies -- and, between Lanchester's square law, and the exponential growth of the economy (the rate at which you can build SCVs is the rate at which you can mine minerals is the rate at which you can build SCVs...), you see the same kind of positive feedback there. Of course, I don't think you need a full-on video game to demonstrate this; the old board game Monopoly was invented by a Quaker woman to exhibit the same property and so demonstrate the evils of capitalism (...and everyone missed the point). In short, I think it's easy, and interesting, to construct mathematical systems that broadly have these properties.

Of course, to turn this kind of mathematical play into something with actual predictive power -- to do science -- would be a whole 'nother undertaking.

If people's net worths were iid Gaussians, all those "amount of wealth in the bracket vs. center of bracket" plots you see floating around to demonstrate wealth inequality (e.g., this one) would be erfinv curves. But you see, they're not.

Now, I get that we can take some liberties with the language and call various distributions besides Gaussians "bell curves." One model, which arises from reasonable-enough assumptions, would be a Boltzmann distribution -- and, indeed, for incomes under about $250k in the US, the distribution does match the Boltzmann pretty well. So, within that broad swathe of incomes, maybe you can make an argument that there's just always going to be a certain amount of random variability.

But those aren't the income ranges people are talking about. People are talking about a systematic movement of wealth, which requires more explanation.

Everyone talks like this: "You spend too much on little luxuries; you should not be enjoying these things; there is a moral value to going without them; and you will be rewarded in the economy for your asceticism."

But here's the thing: Those little luxuries are absolutely negligible expenses. You could buy a $5 latte every day for under $2k a year.

For comparison:
- College for one child (4 yrs) can be expected to cost $250k.
- A one-bedroom condo costs $500k.
- A 20-year retirement at $50k/yr costs $1M

Those numbers may sound large, but they really are accurate for desirable metro areas. And you will have to work for each one of those dollars, because at this point, any assumption that investment appreciation will outpace inflation is just wishful thinking (outside of property, whose very appreciation is placing it increasingly out-of-reach).

Next to the sheer magnitude of those costs, what's $5?

The case for the humanities is easy:

1. Science is about how the physical world works.
2. Engineering is about how to get the physical world to do what you want.
3. The humanities are about deciding what you want in the first place.

A metaphor

Say life is about finding the shortest path through a graph. Science tells you what the edges of the graph are -- what nodes are connected to what other nodes. Engineering gives you a shortest-path algorithm (say, Dijkstra's). The humanities tell you what node to find the shortest path to

. A control-theoretic perspective:

More generally, the world has a state x(t), and science gives us the transition model -- the function f such that,

dx/dt = f(x,u)

where u(t) is our control input to the world at time t. This is Newton's Theory of Universal Gravitation, or Einstein's Theory of General Relativity, or whatever.

Engineering is about the following problem: Given a functional V that takes a state trajectory and returns a cost for that trajectory (this summarizes our opinion about what we want and what we do not want), solve (or approximately solve) the following optimization problem:

minu V(x) s.t. dx/dt = f(x,u) x(0) = x0

In other words: Having decided what I want (V), and having figured out how the universe will react to my actions (f), figure out how to make the universe do what I want.

The humanities are about deciding what functional V to use. Science can't give it to you: It's an input to this whole thing.

The above formulation can be tweaked a little -- for instance, there is no uncertainty involved -- but it captures the gist of things.

Agreed.

Good Ship Names:

• U.S.S. Dauntless
• U.S.S. Enterprise
• H.M.S. Indefatigable
• H.M.S. Indomitable
• H.M.S. Implacable
• U.S.S. Intrepid

Bad Ship Names:

1. U.S.S. Freedom
2. U.S.S. George H. W. Bush
3. H.M.S. Unicorn

Ship Names Too Excellent to Use:

1. G.S.V. Eschatologist

I would agree that "GMO" is too broad a label -- but if anything, this is an argument for more labeling, rather than less.

Let's look at established food technology. It would not be helpful to simply list "WARNING: Contains synthetic ingredients" on packaging. Nevertheless, this does not stop us from requiring producers to clearly label what is in the food, in the form of an ingredients list. We do this despite the possible "public confusion" that could be caused by the fact that most people do not know what, e.g., "sodium benzoate" is.

If we are now putting other new ingredients in our food -- at the genetic level -- then it would seem that these changes should also simply be listed, with a little more specificity than, "WARNING: GMO," in the ingredients list. E.g., don't just list "corn;" list "corn (Monsanto RoundupReady (TM) strain 2.09387)."

There is also a suspicion now that sublethal effects of glyphosate (Roundup) are making bee colonies susceptible to infection by other pathogens, and that this "one-two punch" is what's causing colony collapse. I wouldn't want to risk something essential -- pollinators -- just to get marginal boosts to yield.

I can't generalize, but I believe that my own writing was better in high school and early college than it is now. Whenever I stumble across one of my old essays I am amazed.

After nine years of engineering school, those skills rust over.

I am also frequently amazed by books from a generation or two ago. Compared to the stream of articles I typically read, they're a breath of fresh air.

On the other hand, when I pick up old video games that I remember being hard, I beat them easily, even though I haven't touched them -- for whatever that's worth.

The mind changes.

The world? I don't know. Their boss will ask for Powerpoint slides.

At first, instead of "billion," I read "bitcoin."

I was surprised, to say the least.

My understanding is that a need for gold (to use as currency) was a major reason for the Roman invasions first of Gaul (recent finds show pre-Roman Celts had significant gold-mining operations) and then of Dacia (now Romania). We can say with more certainty that gold was a major motive of the Spanish conquest of the New World.

The mechanism by which commodity-backed currencies motivate wars looks pretty straightforward: If your economy grinds to a screeching halt and you want to do "quantitative easing," you need to physically go out and grab more of the commodity. Fiat currencies avoid at least this issue -- and your argument about them being useful for funding wars seems to apply just as well to funding any other activity.

(It's also worth noting that, if you do have a gold or a gold-backed currency, and you do succeed in grabbing a bunch of coin from your neighbors, then, despite being commodity-backed, you will still have inflation. Apparently this is what happened in the Spanish empire as a result of all that New World gold.)

Ah, good. Thanks.

I just ran these numbers to see what they would say. I assumed the upper bound would be absurdly high. If I have not made a mistake, the bound is actually disturbingly close:

A bit of googling tells me that, in a year, the sun puts out 150 EJ.

It is said that people should consume 2000 kCal/day = 3.05 GJ

To get an upper bound on the number of people that can be supported, we take the ratio, to get 4.92e10.

The current world population is 7e9. This is 1/7-th the upper bound.

The doubling time for the world's population, at current growth rates, is (after some more googling), 54 years. That means that it will increase by a factor of 8 -- more than can be supported -- in just 162 years. More precisely, it will increase by a factor of 7 in 152 years.

That's about two human lifetimes.

Either (1) my numbers are wrong, (2) I made an arithmetic mistake, (3) growth will level off very soon, (4) we will learn to practice space agricuture at a massive scale in an implausibly-short timeframe, or (5) we're in for some pain.

A number of northern European countries -- Sweden, Denmark, Norway, Finland -- provide state health care and pensions, but also respect individual liberties to an extent sometimes even beyond in the United States.

Denmark is #3 in the World Audit Civil Liberties rankings.
Finland is #1
Sweden is #2
Norway is #5
The United States is #15.
See here.

These are the classic "Third Way" democracies -- and they outnumber the Stalinist states (USSR, North Korea, Cuba) that are always put up as straw men. In short: Your argument sounds compelling, but, like Aristotle's reasonable-sounding assertion that heaver objects accelerate faster in freefall, it is not supported by empiricism.

One of my labmates did exactly this, on Android, for a project involving (IIRC) the Air Force (He flew the resulting drone at a nearby airbase, at least). The thing worked; he controlled it by sending text messages.

Along the same lines: Why give 100 people each tiny yards, when they can have nice apartments next to a large park instead? I think the New Urbanists have it right.