They tend to be oil-producing countries with otherwise-weak economies.
Prices determine resource allocation. If you increase gasoline taxes, you discourage gasoline use. This has a variety of ripple effects, including to increase the value of urban relative to suburban real estate (and increase urban rents), and encourage investment in wind, solar, etc. There are winners and losers.
(I believe we should increase fossil fuel taxes; it's the textbook way to price in externalities. It is exactly what a free-market approach to the environment looks like.)
I can't tell if these are arbitrarily chosen symbols meant to be a joke ("everybody is looking for an easy algorithm to get rich and there is none"), or an esoteric reference ("there is a standard formula used in finance, called..."), or maybe an idea you began to play with on your own... Are you being serious?
I ask because it looks almost like a dynamic programming solution to some problem -- like your "F" is a Q-table or Bellman Value Function, and "d" is some instantaneous cost.... although I'd expect inequalities, not equalities... unless S(Ai,Bj) and d are slack variables(?).... and S even suggests "slack" -- but what are Ai, Bi?
Your symbols are on the verge of making sense to me... Is this just pareidolia? Have I just had too much coffee? Or is there actually some (optimal control?) problem you're hinting at?
But you can always trade contracts, outside that market (and unclocked/asynchronously), for shares in it, at which point it's the price of those contracts that you need to look at, I would think. Or in other words, if you make certain kinds of financial transactions "illegal" (i.e., asynchronous/"unclocked" ones), the demand for those transactions is filled by another, "black" market (i.e., the one where contracts are bought and sold). Or in yet other language, you can build the old, asynchronous, abstraction, on top of the new, synchronous one, by adding a "side channel" of asynchronous information.
(I assume "real" econ./finance people have words for all of this.)
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.
At the end of a year, there's going to be a bell curve of results.
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?
Engineering is about how to get the physical world to do what you want.
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.
Wait, did they [write well]? Do you have metrics to show it?
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.
Does the world really need [good writing] from them?
The world? I don't know. Their boss will ask for Powerpoint slides.
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.
If I'm not mistaken, your basic iPhone has most of this built in. It's aware of its orientation and location, and it has a camera. Speed could be dealt with in a variety of simple ways, and avoidance problems minimized.
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.
It makes more sense to put more people on smaller land (do away with yards altogether) for energy efficiency/cost reasons than to have millions of sub-acre semiproductive farms.
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.
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.
If you consider that there is a modest practical limit imposed on the number of units that can fire on one another at a given time, isn't there an inherent advantage for the army that's twice as effective that engages the army that is half as effective but twice as large?
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
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.
It's not just premed that is taught in this fashion, it's everything up to and including premed.
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.
The American method of 'learning' is mostly rote learning
Overall? No. I'd say the US has been much better in this respect than many other countries. (Though "No Child Left Behind" has done its damndest to screw that up by encouraging teachers to teach-to-the-test.) However, it is like this for premeds, and that's what matters!
Why? The stakes are too high. Push up the stakes high enough, and people don't think; they memorize. Indeed, when faced with very high incentives in psychological studies, people bomb IQ tests. You can't think when something as important as a career as a doctor is on the line. (That's why classes need to be exactly as hard as necessary -- and no easier -- but also no harder!!)
It's also how biology is taught in college. "Go memorize this arbitrary chemical pathway. No, we won't talk about 'why.' Yes, you can forget it later. We all know this class is just for weeding, anyway." Partly because it's all premeds. (And partly because there's no helping the fact that, compared to physics, biology is much more about facts than principles. It's messier. Such is life.)
Slashdot Mirror
Here is a map of the countries that subsidize fossil fuels:
http://www.iea.org/subsidy/index.html
They tend to be oil-producing countries with otherwise-weak economies.
Prices determine resource allocation. If you increase gasoline taxes, you discourage gasoline use. This has a variety of ripple effects, including to increase the value of urban relative to suburban real estate (and increase urban rents), and encourage investment in wind, solar, etc. There are winners and losers.
(I believe we should increase fossil fuel taxes; it's the textbook way to price in externalities. It is exactly what a free-market approach to the environment looks like.)
It could even work... (For some other authors, perhaps it already has...)
(Oh -- and, off topic; I saw your signature -- respect for finishing a novel. That's cool.)
I can't tell if these are arbitrarily chosen symbols meant to be a joke ("everybody is looking for an easy algorithm to get rich and there is none"), or an esoteric reference ("there is a standard formula used in finance, called..."), or maybe an idea you began to play with on your own... Are you being serious?
I ask because it looks almost like a dynamic programming solution to some problem -- like your "F" is a Q-table or Bellman Value Function, and "d" is some instantaneous cost.... although I'd expect inequalities, not equalities... unless S(Ai,Bj) and d are slack variables(?).... and S even suggests "slack" -- but what are Ai, Bi?
Your symbols are on the verge of making sense to me... Is this just pareidolia? Have I just had too much coffee? Or is there actually some (optimal control?) problem you're hinting at?
But you can always trade contracts, outside that market (and unclocked/asynchronously), for shares in it, at which point it's the price of those contracts that you need to look at, I would think. Or in other words, if you make certain kinds of financial transactions "illegal" (i.e., asynchronous/"unclocked" ones), the demand for those transactions is filled by another, "black" market (i.e., the one where contracts are bought and sold). Or in yet other language, you can build the old, asynchronous, abstraction, on top of the new, synchronous one, by adding a "side channel" of asynchronous information.
(I assume "real" econ./finance people have words for all of this.)
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.
At the end of a year, there's going to be a bell curve of results.
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:
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:
Bad Ship Names:
Ship Names Too Excellent to Use:
Wait, did they [write well]? Do you have metrics to show it?
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.
Does the world really need [good writing] from them?
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.
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.
If I'm not mistaken, your basic iPhone has most of this built in. It's aware of its orientation and location, and it has a camera. Speed could be dealt with in a variety of simple ways, and avoidance problems minimized.
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.
It makes more sense to put more people on smaller land (do away with yards altogether) for energy efficiency/cost reasons than to have millions of sub-acre semiproductive farms.
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.
It's a lack of belief system.
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.
If you consider that there is a modest practical limit imposed on the number of units that can fire on one another at a given time, isn't there an inherent advantage for the army that's twice as effective that engages the army that is half as effective but twice as large?
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.
It's not just premed that is taught in this fashion, it's everything up to and including premed.
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.
The American method of 'learning' is mostly rote learning
Overall? No. I'd say the US has been much better in this respect than many other countries. (Though "No Child Left Behind" has done its damndest to screw that up by encouraging teachers to teach-to-the-test.) However, it is like this for premeds, and that's what matters!
Why? The stakes are too high. Push up the stakes high enough, and people don't think; they memorize. Indeed, when faced with very high incentives in psychological studies, people bomb IQ tests. You can't think when something as important as a career as a doctor is on the line. (That's why classes need to be exactly as hard as necessary -- and no easier -- but also no harder!!)
It's also how biology is taught in college. "Go memorize this arbitrary chemical pathway. No, we won't talk about 'why.' Yes, you can forget it later. We all know this class is just for weeding, anyway." Partly because it's all premeds. (And partly because there's no helping the fact that, compared to physics, biology is much more about facts than principles. It's messier. Such is life.)