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.

That sounds more like (philosophical) skepticism to me. ;-)

I don't know, or care, whether atheism "is a religion." In fact, I don't even know what that sentence means.

What I do know is that, like the religions, it is becoming a group identity -- an "-ism" -- as evidenced by the extremely defensive posts being made here. If it were just a collection of ideas relating to abstractions, if people didn't identify with those ideas, if people didn't see attacks on those ideas as attacks on themselves, then nobody would care enough to get angry.

Maybe that's ok. Maybe it's useful. Maybe, most atheists grew up in staunchly religious communities, and the politics of group identity, of belonging to an oppressed minority, are helpful to resist a more generally destructive culture of religious bigotry.

But for those of us who were lucky enough to grow up in a secular environment, it gets annoying. Me? I don't need to "fight back." I'm not so afraid of the concept of God that I need to destroy it. It's an abstraction. Asking whether it exists is meaningless. Do the integers exist? Mu. I like Spinoza. I'm cool with panpsychism (what makes your unfalsifiable worldview better than mine? Maybe contemplating my part in Infinity alters my outlook.). We can flirt with ideas without marrying them. Unitarian Universalists? Sometimes too New-Agey for my tastes (For me, "energy" is measured in Joules), but I think the basic idea is the right one. Jesus of Nazareth? He did say things worth hearing. The Beatitudes? The Golden Rule? I don't need to accept Old-Testament jingoism, or Paul's sexual issues, or the dogma of a politicized medieval Church, or the divinity of Christ, to recognize that they stand on their own merits (and probably predate Jesus, which is OK).

The other day, I saw a car, with two bumper stickers. One was the common "CoEXiSt" sticker. The other was a shot at Christians. They're at odds, no? Get along, I say.

Yeah... It seems reasonable to guess that the effective power of an army grows quadratically for small numbers of units, but more-or-less linearly after that -- and terrain advantages like chokepoints can shift when that transition between quadratic and linear growth happens (E.g., if three units can get through a chokepoint at a time, then the transition probably happens around three).

I suppose that if you really want an answer, you need to do some experiments, and compile some statistics! Custom maps seem like a good way do this... I'd be surprised if hardcore Starcraft players hadn't already done these kinds of studies...

Ok, let's see... In your model, a group of n units has fighting power proportional to n*sqrt(n). Good! As expected, it's slower-than-quadratic, but faster-than-linear. Sounds like what I read people measure empirically.

Specifically, say

dx/dt = -a y^q

dy/dt = -b x^q

for some a,b,q>0; for you, q=1/2. Then the quantity

D = a y^(q+1) - b x^(q+1)

is conserved.

More generally, if

dx/dt = -f(y)

dy/dt = -g(x)

then, letting F and G be antiderivatives of f and g respectively, the quantity

D = G(x) - F(y)

is conserved.

You say "employment simulation?" I say "crowdsourcing!" What's a better simulation than the real thing?

In fact, let's get rid of the whole "we might hire them" thing entirely (but don't remove that text from the website).

Best. Post.

I hadn't seen that '08 study.

Sounds like you travel in defense circles, so you've probably seen this, but I'll also point out the 2002 Millennium Challenge, where, also, technologically-superior "American" forces lost out to numbers and swarming tactics.

Indeed! There are (admittedly very simplified) models of combat that indicate that the power of a fighting force is proportional to the square of its number of members.

This is something that I stumbled across when developing simple ODE models of Starcraft combat, and later discovered is known as Lanchester's Square Law. The idea is simple: Suppose you have two opposing groups of identical combat units, with x and y members, respectively. If you assume that all units concentrate fire on the weakest enemy, then the rate at which enemy units is depleted is proportional to the number of units you have, and vice versa. In symbols,

dx/dt = -y

dy/dt = -x

It turns out that the quantity D = x^2 - y^2 is conserved by this system (to verify this, just differentiate D with respect to time, use the product rule, and substitute in from the ODEs). What this means is that the fighting power of a fighting force is proportional to its square, and when the smaller force is eliminated, the larger force will have lost as much fighting power as the smaller force had, in order to defeat it.

You can modify the equations to include constants that reflect unequal kill rates, but you will find that the equivalent conserved quantities still depend quadratically on the number of units, but only linearly on the kill rate coefficients. The conclusion to be drawn is that, given a choice between a unit that's twice as effective, and twice as many units, you should choose to have twice as many units.

All this is predicated on the accuracy of the mathematical model, of course, and that model, I freely admit, is a rather drastic simplification. However, its aesthetics are appealing, and I think it may have a grain of truth. If it does, than Rafales or Super Hornets may indeed be the better choice than F-35s.

Hmm... I do guess that's true.

Me, I'd been comparing engineering education in the US to engineering education abroad -- but that's mostly in college. The American students consistently have more practical experience, have done more projects, and have been more frequently required to invent creative solutions to problems, than many of their Indian and Chinese peers. Not because the Americans are "inherently" better -- whatever that means -- but because engineering school just works differently here.

But elementary school? I think I agree. I think it's highly variable (e.g., there are good public schools in high-property-tax areas, and private schools like Montessori Schools), but I think I agree that, even when they are good, it's only by overcoming a tradition of rote learning which still dominates -- in practice if not necessarily in theory. I am also under the impression that, until 'No Child Left Behind' emerged, elementary education had improved significantly over that of two or three generations ago. Nevertheless, yes, elementary education is definitely as much about socialization as it is about academic learning -- for both good and ill.

Finally, there is an element of tracking in education. If you were a "smart kid," if you got into honors classes, you probably were able to have a high school experience that avoided some of the rote learning that other kids were subjected to. That was my experience, at least. But, again, it doesn't happen until high school.