I need literary analysis every time I read a technical paper
I was going to mod you funny, but since you have a +5 Insightful I'm starting to think nobody here actually knows what literary analysis is...
It's not reading comprehension! No, it's about interpreting symbolism, etc. Usually it's sort of a game you play, where you either try to find a particular political message (Marxist, feminist schools of criticism) in a work, or just create a contradiction between the work and itself (deconstructionism)...
We could use, at least, a basic understanding of probability..
I don't know. All the math gives you is measure theory and some operations on sets. What you're talking about is getting outside the purview of mathematics. Now you're talking about philosophy, almost metaphysics...
Me, I "get" Kolmogorov's axioms, but I still don't truly understand how they map to reality -- or why we should believe that they do. And among people who do believe that probability theory describes reality, there isn't even really agreement; you've got Bayesians (and isn't this point of view anthropocentric?) and frequentists (is "statistical significance" or lack thereof actually significant?) and nobody really seems to have a handle on what all this stuff means.
I think the way to look at it is this (linear algebra): Your input to the four wires, at each time, is a 4-vector. The common mode is another 4-vector, (1,1,1,1); that picks up a lot of noise. Nevertheless, you have the whole orthogonal complement to (1,1,1,1) to work with. The vectors (1-1,0,0), (0,0,1,-1), and (1,1,-1,1) -- the two pairs and the "virtual pair," respectively -- form an orthogonal basis for this subspace. So you represent all data as linear combinations of those three vectors.
You might notice, though, that there's nothing really special about this basis; any isometry (rotation/reflection) and/or scaling of these three vectors would also work. For instance, the vectors (1,-1,1,-1), (1,-1,-1,1), (1,1,-1,-1) (which, together with the common mode (1,1,1,1), is the Hadamard basis in R^4), or a DCT basis, both work.
You just CONFIRMED what he said, not contradicted it. Diesel DOES have more energy per volume - more than 10% more.
I mean... yes, I read the numbers; I did post them after all. Still, it's the higher compression ratio that's the dominant factor, which is what my point had been.
Here, look at the 2010 Volkswagon Jetta. Here are the numbers for more-or-less identical vehicles, one with a diesel engine, one with a gasoline one (and a fairly high-compression one at that):
To drive one mile, it takes the gasoline-engined car 32% more fuel. By comparison, the diesel fuel itself has only 14% more energy per gallon. Energy density of the fuel alone is not sufficient to explain the difference. The difference comes from the efficiency of the engine.
I should note that this is in spite of the fact that the Otto cycle (which approximates gasoline engine operation) is more efficient than the Diesel cycle (which approximates the operation of real diesel engines) at the same compression ratio. Diesels, in practice, simply have compression ratios that are high enough to overwhelm that advantage.
Diesel contains significantly more energy per gallon than gasoline
Nah, the fuels have roughly the same energy; the difference is that diesel engines typically operate at much higher compression ratios and so are more efficient.
Some numbers:
Gasoline has a heating value of 32 MJ/L, neglecting condensation of exhaust (which I'll assume doesn't happen).
It's PD but EVERY row violates the diagonal dominance property.
Basically, PD matrices are Grammians -- there exist vectors such that the elements of the matrix are the inner products of those vectors -- and, if you pick a bunch of vectors that are linearly-independent-but-not-too-much-so, then the inner products between them (the off-diagonal elements) can overwhelm their squared norms (the diagonal elements).
Here, all the columns of C are within 35 degrees of a line along the vector (0.8588, -0.4937, 0.1368); you see that they're close enough to being linearly dependent to allow large inner products, but not so much that the matrix loses rank.
So, picking a bunch of random vectors that lie in a somewhat tight cone and computing their Grammian is a constructive way to produce PD, non-diagonally-dominant matrices, with high probability.
If the condition number is very high, all this means is that the matrix is semi-definite, which tells you that some of your random variables are actually linear combinations of others. A conjugate gradient solver should be able to compute the minimum-norm solution for you easily. Or do PCA; this'll directly tell you what the independent variables are (all the components corresponding to nonzero eigenvalues), and you can just use those coordinates and work with a smaller, full-rank matrix.
To give some examples of places where this does matter... Anything that "feels" like heat flow or diffusion.
The computer graphics problem of radiosity rendering (where light makes multiple bounces.)
Solving for voltages in a resistor network with various sources in it.
Computing the pressure induced in an incompressible fluid by a force field (a key step in fluid simulation).
In all of the above examples, you're inverting a matrix known, depending on the field, as either the graph Laplacian, or the admittance matrix. Basically any time you have a PDE where the Laplacian operator shows up, the discretization will be diagonally dominant.
In image processing, this can even appear; e.g., various diffusion processes are often used to blur an image.
In terms of random variables... It's possible for a covariance matrix to be only positive semidefinite. E.g., consider a zero-mean random variable x, with E(x^2)=1, and another one y = cx, with c a constant. Then the covariance matrix is [[1 c][c c^2]], which is not full rank (the second column is just 'c' times the first). More generally, this happens because the random variables are not linearly independent.
What do you need actual chemicals and stuff for, not to mention rulers and paper clips? Why not just a "My Science Kit" app, and do virtual experiments? Although I guess you could drop the PC on your foot or something, which could also be dangerous.
In a way, this is a metaphor for what I fear is happening at all levels. I worry that we are placing too much faith in mathematical models of reality, and spending too little time working with physical reality itself, not just at the grade-school level but throughout academic society. Math may be undervalued in some ways, but it has too much social prestige in other circles.
The smartest people I know spent their childhoods on farms doing stuff dangerous enough that they have scars to show for it.
Hahaha, you're a funny guy! Public schools focusing on education, that's hilarious!
In the U.S., public schools are funded by property taxes. So in rich towns with high property taxes, the public schools can be good. Vast inequalities exist within the public system.
There are various kinds of strong and weak atheism and agnosticism, some of which meet your description and some of which don't. It sounds like you ascribe to some kind of weak atheism. That's totally fair, but strong atheisms also do exist.
This is an income tax for individuals making over 200k. It is not a corporate tax. It only affects the ability of a company to hire workers to the extent that, maybe, upper management would demand commensurately higher salaries at the expense of hiring.
This also is not so much about Bezos vs Gates as about Bezos vs a tax that will affect him personally. The Bill Gates angle is really that Gates' father believes strongly that individuals who become wealthy are indebted to the society that enabled them to do so -- something he wrote extensively about in a book he authored. Presumably, despite his shady business practices, this is a belief that Bill himself ascribes to. His advocacy of this tax, and his considerable charitable giving, would both tend to support this idea.
I thought he had been diagnosed with early-onset Alzheimer's, but that it had not yet advanced very far yet. I had the impression of a man aware of the impending gradual loss of his cognition who was trying to make the best of what he had left.
as long as it doesn't pollute the water (I don't see why it should, if it's just the mechanical removal of stuff).
On land, mining often causes significant pollution of groundwater. Stuff like arsenic and heavy metals are freed from the earth in the process, and they end up in the water supply. I'm no geologist, but I'd guess you'd have similar problems with sea-floor mining.
That's simply not true in all cases. I have neither of those addons installed, and Flash never crashes on this machine. Win7 64bit, Firefox.
Ditto. Flash is a resource hog but I never remember it crashing. This is on various 32-bit XP and Vista machines, and a Kubuntu install (though Flash performance was so abysmal on this last one that I said "to hell with it" and put XP back on it).
That's really cool. Robot navigation is always a problem, so it's interesting how they've dealt with it.
If that thing had an LCD on it to make the link two-way, it'd be basically perfect. Well, that and if the camera and LCD were mounted at normal eye level.
Slashdot Mirror
I need literary analysis every time I read a technical paper
I was going to mod you funny, but since you have a +5 Insightful I'm starting to think nobody here actually knows what literary analysis is...
It's not reading comprehension! No, it's about interpreting symbolism, etc. Usually it's sort of a game you play, where you either try to find a particular political message (Marxist, feminist schools of criticism) in a work, or just create a contradiction between the work and itself (deconstructionism)...
We could use, at least, a basic understanding of probability..
I don't know. All the math gives you is measure theory and some operations on sets. What you're talking about is getting outside the purview of mathematics. Now you're talking about philosophy, almost metaphysics...
Me, I "get" Kolmogorov's axioms, but I still don't truly understand how they map to reality -- or why we should believe that they do. And among people who do believe that probability theory describes reality, there isn't even really agreement; you've got Bayesians (and isn't this point of view anthropocentric?) and frequentists (is "statistical significance" or lack thereof actually significant?) and nobody really seems to have a handle on what all this stuff means.
At least I don't.
Thanks; that was interesting.
I think the way to look at it is this (linear algebra): Your input to the four wires, at each time, is a 4-vector. The common mode is another 4-vector, (1,1,1,1); that picks up a lot of noise. Nevertheless, you have the whole orthogonal complement to (1,1,1,1) to work with. The vectors (1-1,0,0), (0,0,1,-1), and (1,1,-1,1) -- the two pairs and the "virtual pair," respectively -- form an orthogonal basis for this subspace. So you represent all data as linear combinations of those three vectors.
You might notice, though, that there's nothing really special about this basis; any isometry (rotation/reflection) and/or scaling of these three vectors would also work. For instance, the vectors (1,-1,1,-1), (1,-1,-1,1), (1,1,-1,-1) (which, together with the common mode (1,1,1,1), is the Hadamard basis in R^4), or a DCT basis, both work.
You just CONFIRMED what he said, not contradicted it. Diesel DOES have more energy per volume - more than 10% more.
I mean... yes, I read the numbers; I did post them after all. Still, it's the higher compression ratio that's the dominant factor, which is what my point had been.
Here, look at the 2010 Volkswagon Jetta. Here are the numbers for more-or-less identical vehicles, one with a diesel engine, one with a gasoline one (and a fairly high-compression one at that):
4 cyl, 2.0 L, Manual 6-spd, Diesel......41 mpg hwy
4 cyl, 2.0 L, Manual 6-spd, Premium.....31 mpg hwy
To drive one mile, it takes the gasoline-engined car 32% more fuel. By comparison, the diesel fuel itself has only 14% more energy per gallon. Energy density of the fuel alone is not sufficient to explain the difference. The difference comes from the efficiency of the engine.
I should note that this is in spite of the fact that the Otto cycle (which approximates gasoline engine operation) is more efficient than the Diesel cycle (which approximates the operation of real diesel engines) at the same compression ratio. Diesels, in practice, simply have compression ratios that are high enough to overwhelm that advantage.
Diesel contains significantly more energy per gallon than gasoline
Nah, the fuels have roughly the same energy; the difference is that diesel engines typically operate at much higher compression ratios and so are more efficient.
Some numbers:
Source.
What do you mean? There are no positivity constraints on 'x' either, no inequalities anywhere.
Yeah, the converse is not true in general.
.
E.g.,
[ 4 -2 5 ]
M = [ -2 5 -5 ]
[ 5 -5 9 ]
It's PD but EVERY row violates the diagonal dominance property.
Basically, PD matrices are Grammians -- there exist vectors such that the elements of the matrix are the inner products of those vectors -- and, if you pick a bunch of vectors that are linearly-independent-but-not-too-much-so, then the inner products between them (the off-diagonal elements) can overwhelm their squared norms (the diagonal elements).
For the above example, one such factorization is
M = C'*C
with
[ 2 -1 2.5 ]
C = [ 0 2 -1.25 ]
[ 0 0 sqrt(19)/4 ]
Here, all the columns of C are within 35 degrees of a line along the vector (0.8588, -0.4937, 0.1368); you see that they're close enough to being linearly dependent to allow large inner products, but not so much that the matrix loses rank.
So, picking a bunch of random vectors that lie in a somewhat tight cone and computing their Grammian is a constructive way to produce PD, non-diagonally-dominant matrices, with high probability.
No, this is just Ax=b, without inequality constraints.
If the condition number is very high, all this means is that the matrix is semi-definite, which tells you that some of your random variables are actually linear combinations of others. A conjugate gradient solver should be able to compute the minimum-norm solution for you easily. Or do PCA; this'll directly tell you what the independent variables are (all the components corresponding to nonzero eigenvalues), and you can just use those coordinates and work with a smaller, full-rank matrix.
To give some examples of places where this does matter... Anything that "feels" like heat flow or diffusion.
In all of the above examples, you're inverting a matrix known, depending on the field, as either the graph Laplacian, or the admittance matrix. Basically any time you have a PDE where the Laplacian operator shows up, the discretization will be diagonally dominant.
In image processing, this can even appear; e.g., various diffusion processes are often used to blur an image.
Really close.
Diagonally dominant ==> positive semidefinite
Strictly diagonally dominant ==> positive definite
For understanding these things, I really like Gershgorin's circles.
In terms of random variables... It's possible for a covariance matrix to be only positive semidefinite. E.g., consider a zero-mean random variable x, with E(x^2)=1, and another one y = cx, with c a constant. Then the covariance matrix is [[1 c][c c^2]], which is not full rank (the second column is just 'c' times the first). More generally, this happens because the random variables are not linearly independent.
Hope that helps!
Is that you, William Gibson?
What do you need actual chemicals and stuff for, not to mention rulers and paper clips? Why not just a "My Science Kit" app, and do virtual experiments? Although I guess you could drop the PC on your foot or something, which could also be dangerous.
In a way, this is a metaphor for what I fear is happening at all levels. I worry that we are placing too much faith in mathematical models of reality, and spending too little time working with physical reality itself, not just at the grade-school level but throughout academic society. Math may be undervalued in some ways, but it has too much social prestige in other circles.
The smartest people I know spent their childhoods on farms doing stuff dangerous enough that they have scars to show for it.
Hahaha, you're a funny guy! Public schools focusing on education, that's hilarious!
In the U.S., public schools are funded by property taxes. So in rich towns with high property taxes, the public schools can be good. Vast inequalities exist within the public system.
Also, alkaline batteries, cigarettes, and gasoline.
Not all atheism is weak atheism.
There are various kinds of strong and weak atheism and agnosticism, some of which meet your description and some of which don't. It sounds like you ascribe to some kind of weak atheism. That's totally fair, but strong atheisms also do exist.
This is an income tax for individuals making over 200k. It is not a corporate tax. It only affects the ability of a company to hire workers to the extent that, maybe, upper management would demand commensurately higher salaries at the expense of hiring.
This also is not so much about Bezos vs Gates as about Bezos vs a tax that will affect him personally. The Bill Gates angle is really that Gates' father believes strongly that individuals who become wealthy are indebted to the society that enabled them to do so -- something he wrote extensively about in a book he authored. Presumably, despite his shady business practices, this is a belief that Bill himself ascribes to. His advocacy of this tax, and his considerable charitable giving, would both tend to support this idea.
I thought he had been diagnosed with early-onset Alzheimer's, but that it had not yet advanced very far yet. I had the impression of a man aware of the impending gradual loss of his cognition who was trying to make the best of what he had left.
Perhaps I'm mistaken.
This might be useful for Starcraft. On Windows 7, the palette used for 256-color mode is all messed up. Strangely, it does work on Vista.
as long as it doesn't pollute the water (I don't see why it should, if it's just the mechanical removal of stuff).
On land, mining often causes significant pollution of groundwater. Stuff like arsenic and heavy metals are freed from the earth in the process, and they end up in the water supply. I'm no geologist, but I'd guess you'd have similar problems with sea-floor mining.
Roughly twice the volume of Mount Everest!
Iowa and Kansas are a little flat...
That's simply not true in all cases. I have neither of those addons installed, and Flash never crashes on this machine. Win7 64bit, Firefox.
Ditto. Flash is a resource hog but I never remember it crashing. This is on various 32-bit XP and Vista machines, and a Kubuntu install (though Flash performance was so abysmal on this last one that I said "to hell with it" and put XP back on it).
That's really cool. Robot navigation is always a problem, so it's interesting how they've dealt with it.
If that thing had an LCD on it to make the link two-way, it'd be basically perfect. Well, that and if the camera and LCD were mounted at normal eye level.