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Fortifications and Democracy in the Ancient Greek World by Josiah Ober, Barry Weingast :: SSRN
- Joshiah Ober, Barry Weingast

In the modern world, access-limiting fortification walls are not typically regarded as promoting democracy. But in Greek antiquity, increased investment in fortifications was correlated with the prevalence and stability of democracy. This paper sketches the background conditions of the Greek city-state ecology, analyzes a passage in Aristotle’s Politics, and assesses the choices of Hellenistic kings, Greek citizens, and urban elites, as modeled in a simple game. The paper explains how city walls promoted democracy and helps to explain several other puzzles: why Hellenistic kings taxed Greek cities at lower than expected rates; why elites in Greek cities supported democracy; and why elites were not more heavily taxed by democratic majorities. The relationship between walls, democracy, and taxes promoted continued economic growth into the late classical and Hellenistic period (4th-2nd centuries BCE), and ultimately contributed to the survival of Greek culture into the Roman era, and thus modernity. We conclude with a consideration of whether the walls-democracy relationship holds in modernity.

'Rulers Ruled by Women': An Economic Analysis of the Rise and Fall of Women's Rights in Ancient Sparta by Robert K. Fleck, F. Andrew Hanssen: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=788106
Throughout most of history, women as a class have possessed relatively few formal rights. The women of ancient Sparta were a striking exception. Although they could not vote, Spartan women reportedly owned 40 percent of Sparta's agricultural land and enjoyed other rights that were equally extraordinary. We offer a simple economic explanation for the Spartan anomaly. The defining moment for Sparta was its conquest of a neighboring land and people, which fundamentally changed the marginal products of Spartan men's and Spartan women's labor. To exploit the potential gains from a reallocation of labor - specifically, to provide the appropriate incentives and the proper human capital formation - men granted women property (and other) rights. Consistent with our explanation for the rise of women's rights, when Sparta lost the conquered land several centuries later, the rights for women disappeared. Two conclusions emerge that may help explain why women's rights have been so rare for most of history. First, in contrast to the rest of the world, the optimal (from the men's perspective) division of labor among Spartans involved women in work that was not easily monitored by men. Second, the rights held by Spartan women may have been part of an unstable equilibrium, which contained the seeds of its own destruction.
study  broad-econ  economics  polisci  political-econ  institutions  government  north-weingast-like  democracy  walls  correlation  polis  history  mediterranean  iron-age  the-classics  microfoundations  modernity  comparison  architecture  military  public-goodish  elite  civic  taxes  redistribution  canon  literature  big-peeps  conquest-empire  rent-seeking  defense  models  GT-101  incentives  urban  urban-rural  speculation  interdisciplinary  cliometrics  multi  civil-liberty  gender  gender-diff  equilibrium  cycles  branches  labor  interests  property-rights  unintended-consequences  explanation  explanans  analysis  econ-productivity  context  arrows  micro  natural-experiment 
november 2017 by nhaliday
Variance of product of multiple random variables - Cross Validated
prod_i (var[X_i] + (E[X_i])^2) - prod_i (E[X_i])^2

two variable case: var[X] var[Y] + var[X] (E[Y])^2 + (E[X])^2 var[Y]
nibble  q-n-a  overflow  stats  probability  math  identity  moments  arrows  multiplicative  iidness  dependence-independence 
october 2017 by nhaliday
New Theory Cracks Open the Black Box of Deep Learning | Quanta Magazine
A new idea called the “information bottleneck” is helping to explain the puzzling success of today’s artificial-intelligence algorithms — and might also explain how human brains learn.

sounds like he's just talking about autoencoders?
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september 2017 by nhaliday
Is the economy illegible? | askblog
In the model of the economy as a GDP factory, the most fundamental equation is the production function, Y = f(K,L).

This says that total output (Y) is determined by the total amount of capital (K) and the total amount of labor (L).

Let me stipulate that the economy is legible to the extent that this model can be applied usefully to explain economic developments. I want to point out that the economy, while never as legible as economists might have thought, is rapidly becoming less legible.
econotariat  cracker-econ  economics  macro  big-picture  empirical  legibility  let-me-see  metrics  measurement  econ-metrics  volo-avolo  securities  markets  amazon  business-models  business  tech  sv  corporation  inequality  compensation  polarization  econ-productivity  stagnation  monetary-fiscal  models  complex-systems  map-territory  thinking  nationalism-globalism  time-preference  cost-disease  education  healthcare  composition-decomposition  econometrics  methodology  lens  arrows  labor  capital  trends  intricacy  🎩  moments  winner-take-all  efficiency  input-output 
august 2017 by nhaliday
Controversial New Theory Suggests Life Wasn't a Fluke of Biology—It Was Physics | WIRED
First Support for a Physics Theory of Life: https://www.quantamagazine.org/first-support-for-a-physics-theory-of-life-20170726/
Take chemistry, add energy, get life. The first tests of Jeremy England’s provocative origin-of-life hypothesis are in, and they appear to show how order can arise from nothing.
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august 2017 by nhaliday
Is the U.S. Aggregate Production Function Cobb-Douglas? New Estimates of the Elasticity of Substitution∗
world-wide: http://www.socsci.uci.edu/~duffy/papers/jeg2.pdf
We find that IPP capital entirely explains the observed decline of the US labor share, which otherwise is secularly constant over the past 65 years for structures and equipment capital. The labor share decline simply reflects the fact that the US economy is undergoing a transition toward a larger IPP sector.
The Fall of the Labor Share and the Rise of Superstar Firms: http://www.nber.org/papers/w23396
The Decline of the U.S. Labor Share: https://www.brookings.edu/wp-content/uploads/2016/07/2013b_elsby_labor_share.pdf
Table 2 has industry disaggregation
Estimating the U.S. labor share: https://www.bls.gov/opub/mlr/2017/article/estimating-the-us-labor-share.htm

Why Workers Are Losing to Capitalists: https://www.bloomberg.com/view/articles/2017-09-20/why-workers-are-losing-to-capitalists
Automation and offshoring may be conspiring to reduce labor's share of income.
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july 2017 by nhaliday
inequalities - Is the Jaccard distance a distance? - MathOverflow
Steinhaus Transform
the referenced survey: http://kenclarkson.org/nn_survey/p.pdf

It's known that this transformation produces a metric from a metric. Now if you take as the base metric D the symmetric difference between two sets, what you end up with is the Jaccard distance (which actually is known by many other names as well).
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february 2017 by nhaliday
Structure theorem for finitely generated modules over a principal ideal domain - Wikipedia
- finitely generative modules over PID isomorphic to sum of quotients by decreasing sequences of proper ideals
- never really understood the proof of this in Ma5b
math  algebra  characterization  levers  math.AC  wiki  reference  nibble  proofs  additive  arrows 
february 2017 by nhaliday
Covering space - Wikipedia
A covering space of X is a topological space C together with a continuous surjective map p: C -> X such that for every x ∈ X, there exists an open neighborhood U of x, such that p^−1(U) (the inverse image of U under p) is a union of disjoint open sets in C, each of which is mapped homeomorphically onto U by p.
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january 2017 by nhaliday
Shtetl-Optimized » Blog Archive » Why I Am Not An Integrated Information Theorist (or, The Unconscious Expander)
In my opinion, how to construct a theory that tells us which physical systems are conscious and which aren’t—giving answers that agree with “common sense” whenever the latter renders a verdict—is one of the deepest, most fascinating problems in all of science. Since I don’t know a standard name for the problem, I hereby call it the Pretty-Hard Problem of Consciousness. Unlike with the Hard Hard Problem, I don’t know of any philosophical reason why the Pretty-Hard Problem should be inherently unsolvable; but on the other hand, humans seem nowhere close to solving it (if we had solved it, then we could reduce the abortion, animal rights, and strong AI debates to “gentlemen, let us calculate!”).

Now, I regard IIT as a serious, honorable attempt to grapple with the Pretty-Hard Problem of Consciousness: something concrete enough to move the discussion forward. But I also regard IIT as a failed attempt on the problem. And I wish people would recognize its failure, learn from it, and move on.

In my view, IIT fails to solve the Pretty-Hard Problem because it unavoidably predicts vast amounts of consciousness in physical systems that no sane person would regard as particularly “conscious” at all: indeed, systems that do nothing but apply a low-density parity-check code, or other simple transformations of their input data. Moreover, IIT predicts not merely that these systems are “slightly” conscious (which would be fine), but that they can be unboundedly more conscious than humans are.

To justify that claim, I first need to define Φ. Strikingly, despite the large literature about Φ, I had a hard time finding a clear mathematical definition of it—one that not only listed formulas but fully defined the structures that the formulas were talking about. Complicating matters further, there are several competing definitions of Φ in the literature, including ΦDM (discrete memoryless), ΦE (empirical), and ΦAR (autoregressive), which apply in different contexts (e.g., some take time evolution into account and others don’t). Nevertheless, I think I can define Φ in a way that will make sense to theoretical computer scientists. And crucially, the broad point I want to make about Φ won’t depend much on the details of its formalization anyway.

We consider a discrete system in a state x=(x1,…,xn)∈Sn, where S is a finite alphabet (the simplest case is S={0,1}). We imagine that the system evolves via an “updating function” f:Sn→Sn. Then the question that interests us is whether the xi‘s can be partitioned into two sets A and B, of roughly comparable size, such that the updates to the variables in A don’t depend very much on the variables in B and vice versa. If such a partition exists, then we say that the computation of f does not involve “global integration of information,” which on Tononi’s theory is a defining aspect of consciousness.
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january 2017 by nhaliday
soft question - Why does Fourier analysis of Boolean functions "work"? - Theoretical Computer Science Stack Exchange
Here is my point of view, which I learned from Guy Kindler, though someone more experienced can probably give a better answer: Consider the linear space of functions f: {0,1}^n -> R and consider a linear operator of the form σ_w (for w in {0,1}^n), that maps a function f(x) as above to the function f(x+w). In many of the questions of TCS, there is an underlying need to analyze the effects that such operators have on certain functions.

Now, the point is that the Fourier basis is the basis that diagonalizes all those operators at the same time, which makes the analysis of those operators much simpler. More generally, the Fourier basis diagonalizes the convolution operator, which also underlies many of those questions. Thus, Fourier analysis is likely to be effective whenever one needs to analyze those operators.
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december 2016 by nhaliday
gt.geometric topology - Intuitive crutches for higher dimensional thinking - MathOverflow
Terry Tao:
I can't help you much with high-dimensional topology - it's not my field, and I've not picked up the various tricks topologists use to get a grip on the subject - but when dealing with the geometry of high-dimensional (or infinite-dimensional) vector spaces such as R^n, there are plenty of ways to conceptualise these spaces that do not require visualising more than three dimensions directly.

For instance, one can view a high-dimensional vector space as a state space for a system with many degrees of freedom. A megapixel image, for instance, is a point in a million-dimensional vector space; by varying the image, one can explore the space, and various subsets of this space correspond to various classes of images.

One can similarly interpret sound waves, a box of gases, an ecosystem, a voting population, a stream of digital data, trials of random variables, the results of a statistical survey, a probabilistic strategy in a two-player game, and many other concrete objects as states in a high-dimensional vector space, and various basic concepts such as convexity, distance, linearity, change of variables, orthogonality, or inner product can have very natural meanings in some of these models (though not in all).

It can take a bit of both theory and practice to merge one's intuition for these things with one's spatial intuition for vectors and vector spaces, but it can be done eventually (much as after one has enough exposure to measure theory, one can start merging one's intuition regarding cardinality, mass, length, volume, probability, cost, charge, and any number of other "real-life" measures).

For instance, the fact that most of the mass of a unit ball in high dimensions lurks near the boundary of the ball can be interpreted as a manifestation of the law of large numbers, using the interpretation of a high-dimensional vector space as the state space for a large number of trials of a random variable.

More generally, many facts about low-dimensional projections or slices of high-dimensional objects can be viewed from a probabilistic, statistical, or signal processing perspective.

Scott Aaronson:
Here are some of the crutches I've relied on. (Admittedly, my crutches are probably much more useful for theoretical computer science, combinatorics, and probability than they are for geometry, topology, or physics. On a related note, I personally have a much easier time thinking about R^n than about, say, R^4 or R^5!)

1. If you're trying to visualize some 4D phenomenon P, first think of a related 3D phenomenon P', and then imagine yourself as a 2D being who's trying to visualize P'. The advantage is that, unlike with the 4D vs. 3D case, you yourself can easily switch between the 3D and 2D perspectives, and can therefore get a sense of exactly what information is being lost when you drop a dimension. (You could call this the "Flatland trick," after the most famous literary work to rely on it.)
2. As someone else mentioned, discretize! Instead of thinking about R^n, think about the Boolean hypercube {0,1}^n, which is finite and usually easier to get intuition about. (When working on problems, I often find myself drawing {0,1}^4 on a sheet of paper by drawing two copies of {0,1}^3 and then connecting the corresponding vertices.)
3. Instead of thinking about a subset S⊆R^n, think about its characteristic function f:R^n→{0,1}. I don't know why that trivial perspective switch makes such a big difference, but it does ... maybe because it shifts your attention to the process of computing f, and makes you forget about the hopeless task of visualizing S!
4. One of the central facts about R^n is that, while it has "room" for only n orthogonal vectors, it has room for exp⁡(n) almost-orthogonal vectors. Internalize that one fact, and so many other properties of R^n (for example, that the n-sphere resembles a "ball with spikes sticking out," as someone mentioned before) will suddenly seem non-mysterious. In turn, one way to internalize the fact that R^n has so many almost-orthogonal vectors is to internalize Shannon's theorem that there exist good error-correcting codes.
5. To get a feel for some high-dimensional object, ask questions about the behavior of a process that takes place on that object. For example: if I drop a ball here, which local minimum will it settle into? How long does this random walk on {0,1}^n take to mix?

Gil Kalai:
This is a slightly different point, but Vitali Milman, who works in high-dimensional convexity, likes to draw high-dimensional convex bodies in a non-convex way. This is to convey the point that if you take the convex hull of a few points on the unit sphere of R^n, then for large n very little of the measure of the convex body is anywhere near the corners, so in a certain sense the body is a bit like a small sphere with long thin "spikes".
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december 2016 by nhaliday
Quarter-Turns | The n-Category Café
In other words, call an operator T a quarter-turn if ⟨Tx,x⟩=0 for all x. Then the real quarter-turns correspond to the skew symmetric matrices — but apart from the zero operator, there are no complex quarter turns at all.
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december 2016 by nhaliday

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