Ah… Equilibrium.  Awesome sci-fi movie.  Starring Batman.

The setting: It is the future.  War, murder and crime have been eliminated from society.  How?  By eliminating all emotion.  Twice a day, every man, woman and child in the world is required to inject themselves with a drug that will numb them, eliminating all emotion.  Bingo.  No more crime.

All art and music have also been purged from society, because these things elicit emotion.

But there is an underground resistance.  Those who are secretly refusing to take the drug, feeling in secret, and creating underground chambers filled with “contraband”: Paintings, photographs, radios, and books.

Without emotion, life would be much simpler, and certainly less dangerous.  But at what cost?

No, I don’t think that the purpose of life is to feel.  But I do think that without feelings, life would not be worth living.

How do you view your emotions?  Do you see them as a nuisance?  Something you’d rather not deal with?  Or are they sometimes a frightening monster, dwelling in the dark closets of your soul?

Consider: Your emotions are a treasure: a gift from God, and a reflection of his own character.  We feel because He feels!  He feels joy, sadness, anger, jealousy, and even (I think, in his own way) fear.

If Spock was real, I think he would be elected president. I also think it would be a bad idea.

And also consider: In our society, we spend countless hours being trained how to think rationally.  Because we are a society that values rationality and logic.  I think this is wonderful.  Rationality and truth: These are important and beautiful aspects of God’s creation.

But we spend comparatively little time being trained to deal with and appreciate our emotional selves – a part of ourselves that, I would argue, is as important as our rationality.  The consequence is that we tend to do a decent job of thinking cohesively in America, but we are plagued by disordered emotions.  We are, arguably, the most depressed and anxious society in the history of the world.  Our messed up emotions do indeed cause lots of problems in society, from war, crime and violence, to affairs, broken families and damaged relationships.

Isn't this cheesy? But I like it.

I believe passionately that this shows us not that our emotions are bad, but that it is of grave importance that we learn how to value them more highly and deal with them appropriately.

In fact, I love emotions.  I love that God created our hearts to not just see and understand the world around us, but also to respond to it.  If I am paying attention, I see that for everything that I see around me, there is an internal response, a voice that says, “This is right!” or “This is wrong!”, or “How wonderful!”, or “How awful!”.  And even, “I want to celebrate!”, or “I want to share this with somebody!”

I so enjoy getting to the end of a day and knowing that I have been alive, that I have really let myself feel the full range of emotions of which my heart is capable.  When this happens, I feel closer to God, and as if I am being who he made me to be.

Click to follow me on twitter.

A previous post briefly reviewed convex analysis. Here I’ll review the application of convexity in basic thermodynamics.

Equilibrium states

The concept of thermodynamic equilibrium is a generalization of mechanical equilibrium, where all forces and torques cancel each other. Informally, the idea is that a system in thermodynamic equilibrium has stable, unchanging macroscopic properties, which may be characterized by an n-tuple of extensive variables. How many and which variables depends on the system at hand and is, as far as I know, an empirical matter. For simple fluids, which consists of only one kind of particles, the extensive variables are the internal energy, the volume, and the number of particles. More complicated systems require additional variables. In general, the extensive variables may be collected in a vector , with the first variable being the internal energy . Some of the extensive variables may be fixed by external constraints, while others are free to vary.

Identifying the n-tuple with an equilibrium state, the first assumption is:

Postulate 1: The manifold of equilibrium states is a convex set.

For simplicity, this convex set will be taken to have the form .

Postulate 2: There is a function , called entropy, of the extensive variables of a system. At thermodynamic equilibrium, the extensive variables take values that maximize the entropy subject to the external constraints.

Before the entropy function can play a useful role in the theory, it is necessary to know some of its properties:

Postulate 3: The entropy is (i) additive over subsystems, (ii) homogenuous in the sense that (with ), and (iii) a strictly monotonically increasing function of the internal energy .

When two systems with equilibrium states are considered subsystems of a larger system the equilibrium states of the joint system can be taken to be the convex set . For convenience, the manifolds and are assumed to be equal. This can always be achieved by adding to the to the manifold fictional coordinates that are considered subject to constraints . These constraints are lifted when the two subsystems are able to interact by exchanging the quantity represented by . Consider, for example, two rigid vessels containing hydrogen molecules and oxygen molecules, respectively. When isolated, the systems are characterized by their internal energies, volumes and number of particles (hydrogen molecules and oxygen molecules, respectively). Thus the extensive variables of the first system could be taken to be , but it is convenient to let and consider as an additional external constraint on the system since no oxygen or water molecules can enter the isolated system. Since the system is isolated and the vessel is rigid the variables are also subject to the constraints . The variables for the vessel containing oxygen molecules are chosen and constrained analogously. When the two vessels are brought into contact and their volumes are connected, the joint system is characterized by . Letting denote the sum of extensive variables for the subsystems, the relevant constraints are now:

• (constant total energy),
• (constant total volume),
• (constant number of hydrogen atoms), and
• (constant number of oxygen atoms).

Notice that the joint system has a new macroscopic degree of freedom, , that is not a real degree of freedom in either of the subsystems before they are brought into contact.

Keeping the above discussion in mind, the meaning of Postulate 3(i) is that the entropy of the joint system can be decomposed into entropies of the subsystems,

,

where the entropy of a subsystem is a function of only the extensive parameters of that subsystem. Here, and are defined on the same domain and are the same function.

Concavity of the entropy function

Postulate 2 asserts that the joint equilibrium state of two interacting subsystems is the solution to the optimization problem

Here the matrix defines which linear combinations of variables are constrained. Often, but not always, the constraint is simply that is constant. Note that there were two constraints of a more general form in the above example with the vessels of hydrogen molecules and oxygen molecules. Defining the function

it is now possible to reexpress the optimization problem as

Now temporarily assume that is invertible so that is uniquely determined from the constraints on the joint system. In that case may be considered the entropy of a joint system formed by bringing into contact two isolated systems, initially in states and , respectively. Furthermore, the function may be identified with the subsystem entropy functions , because it is defined on the same domain and it represents the same physical quantity. Writing , it now follows that when two systems are brought into contact, with resulting changes of states from to , , the entropy of joint system is

where the inequality follows from the expression for in terms of a supremum and the expression as a whole holds for all . The last inequality holds in full generality and together with extensivity (Postulate 3(ii)), it follows that entropy is a concave function, i.e.

,

for all .

Turning to the somewhat artificial case when is not invertible and the joint system is therefore not constrained to the states of constant , but can relax its state further (perhaps by being able to exchange particles with its environment), the above discussion remains valid with the following modification

The last inequality remains unchanged and concavity follows as before.

Conclusion: The entropy is a concave function of the extensive variables.

From concavity it follows that the entropy has no minima (except at the boundary of the manifold of equilibrium states), no saddle points, and all local minima are also global minima. When the entropy function is differentiable, the state of maximum entropy may therefore be determined by seeking stationary points of the entropy (or, more precisely, of a Lagrangian taking the constraints into account).

Energy representation

At this point it is useful to change the notation slightly. In order to clearly distinguish functions from function arguments, the entropy function and the internal energy function will in this section be denoted by the calligraphic symbols and , respectively. The fact that is a strictly increasing function of the internal energy (see Postulate 3(iii)) enables the internal energy function to be defined implicity through the equation

.

Strict monotonicity of the entropy function guarantees that this equation has a unique solution. From the concavity of it now follows that for the convex combinations and , with ,

.

Using the monotonicity of the entropy function to “invert” this relation now yields

.

Thus, the internal energy is a convex function. Instead of maximizing the entropy subject to the constraint that the sum of all subsystem energies is constant (and other constraints not involving energy), one may equivalently minimize the internal energy subject to the constraint that the sum of all subsystem entropies is constant (and other constraints unchanged).

Conclusion: Energy-constrained maximization of entropy is equivalent to entropy-constrained minimization of internal energy. Both methods yields the equilibrium state of a thermodynamic system.

From this principle one recovers as a special the mechanical condition for equilibrium. Mechanical equilibrium is attained when the potential energy is minimized. At zero temperature the internal energy coincides with the potential energy and the thermodynamical and mechanical equilibrium conditions are equivalent.

Intensive variables

When the internal energy is differentiable one may define an intensive variable for each extensive variable,

,
.

The derivative w.r.t. volume yields the (negative) pressure, the derivative w.r.t. a particle number yields the corresponding chemical potential, the derivative w.r.t. an external electric field yields the polarization, the derivative w.r.t. an external magnetic field yields the magnetization, derivatives w.r.t. strain deformations yield the stress tensor, and so on. Most intensive quantities are familiar from other branches of physics. The temperature (derivative w.r.t. entropy) is special in that it has no analogue in other branches of physics. Intensive variables provide a convenient way to express equilibrium conditions. For example, two fully interacting subsystems are in equilibrium when all their intensive variables are equal.

If the internal energy is not differentiable, one may introduce intensive variables as the new variables that are introduced when the internal energy is Legendre-Fenchel transformed (see the previous post on convex analysis).

Thermodynamic potentials and Massieu functions

Thermodynamic potentials are partial Legendre-Fenchel transforms of the internal energy. Transforming the internal energy w.r.t. entropy yields

.

The new variable can be identified with the temperature and for a differentiable internal energy function it will coincide with the definition in terms of a derivative. A partial Legendre-Fenchel transform flips the convexity/concavity property of a function. The internal energy is convex in all extensive variables), while the transformed function is concave in the temperature and convex in the remaining (extensive) variable. In general, the Legendre-Fenchel transforms are concave in the intensive variables and convex in the extensive variables.

The Legendre-Fenchel transformed functions, called thermodynamic potentials, are primarily useful in situations when the thermodynamic system of interest is in equilibrium with an environment with known intensive parameters. For example, if the system is in equilibrium with an environment with known temperature and pressure, it is very useful to perform two Legendre-Fenchel transforms that replace entropy and volume by temperature and pressure. The resulting thermodynamic potential is called the free energy and the equilibrium properties of the system follow from holding temperature and pressure fixed while minimizing the free energy w.r.t. the remaining variables.

Massieu functions are analogous to thermodynamic potentials, but they arise from Legendre-Fenchel transforms of the (negative) entropy rather than of the internal energy.

When postulates fail: monotonicity and spin chains

Spin chains in external magnetic fields provide a simple example of how the postulates above can fail. Consider a spin chain consisting of spins that interact with an external magnetic field . Readers not familiar with the quantum mechanical concept of spin may think of microscopic magnets having the peculiar property that they are either parallel or anti-parallel to the magnetic field. Letting and , denote the number of spins that are parallel and anti-parallel to the magnetic, respectively, the internal energy of the system is given by

where is a constant. In statistical mechanics, the Boltzmann entropy is defined as the logarithm of the number of microstates consistent with a given thermodynamic equilibrium state. The number of microstates consistent with a magnetization $\mu (N_1-N_0)$ is given by

and the Boltzmann entropy is

.

By varying the number of parallel spins over the interval one obtains a discrete set of points that define the Boltzmann entropy as a function of the internal energy. A complication arises here since the notions of convexity and concavity used above are only defined for functions of continuous domains, while the entropy is only defined for a discrete domain of energy values. However, extending the Boltmann entropy function through interpolation circumvents this problem. (Alternatively, a fully quantum mechanical treatment using the von Neumann entropy also circumvents this problem, without resolving the underlying failure of the thermodynamic postulates.) The underlying problem is instead that the Boltzmann entropy $S_{\text{B}}(U)$ is not an increasing function of the internal energy, in contradiction with Postulate 3(iii). Plotting the points , as done on the left in the figure below for the case , reveals that the Boltzmann entropy reaches a maximum at zero internal energy, and decreases as the internal energy is increased further.

Plots of Boltzmann entropy (left), coldness (middle), and temperature (right) as functions of the spin chain internal energy. Arbitrary units.

The slope at different points on the entropy curve is the coldness of the system, defined as the inverse temperature. At the maximum of the entropy, the coldness passes zero, and the temperature tends to infinity. When the maximum is approach from the left, the temperature tends towards and the spin chain becomes infinitely hot! For positive values of the internal energy the temperature is negative and as the maximum is approached from the left the temperature tends towards . It is easier to think of this in terms of coldness, which decreases monotonically with increasing internal energy. Thus, a higher internal energy also corresponds to a lower coldness, i.e. a hotter system. In a sense, is the hottest of all temperature limits, is a colder limit that nevertheless is hotter than any positive temperature. Heat spontaneously flows from a system with negative temperature to any system with positive temperature and the negative temperature states that occur for are perhaps best thought of as some kind of pseudo-equilibrium states, rather than true equilibrium states.

The non-monotonicity of the Boltmann entropy for the spin chain also means that the maximum entropy principle cannot be equivalently reexpressed as a minimum internal energy principle.

http://www.youtube.com/watch?v=DIzKduK3_Dc
http://www.youtube.com/watch?v=fL_95Ujj-Ac
http://www.youtube.com/watch?v=q10Mkt20unw
http://www.youtube.com/watch?v=2Yxo24gEWeY
http://www.youtube.com/watch?v=33raBOHNK8I
http://www.youtube.com/watch?v=jsyFV7zjPgA
http://www.youtube.com/watch?v=X_Zow969shI
http://www.youtube.com/watch?v=nArpPTr9SG4
http://www.youtube.com/watch?v=hx4YeHFT_Y8
http://www.youtube.com/watch?v=FzCCuNH2wQI

In my upcoming book Proving God I touch on the topic of a most perplexing problem facing physicists concerning how quantum indeterminacy (potentialities) take on irreversible measurable results. In other words, what is the mechanism whereby a quantum wave function, which consists of tendencies to exist, finally “chooses” where it really is and what it is really doing.

This is called the measurement problem in quantum physics. What is really being asked here is how do “propensities” settle into stable forms of matter with real velocities seeking equilibrium in real space and in real time?

Current thinking involves some kind of outside influence (even human consciousness), which causes the wave function to “collapse” into an actual measurable result.  If quantum potentials actually collapse then this implies that none of the wave-potentialities associated with a quantum cloud disappear, but they all somehow take part in the event.

Scientists know that energy coheres into matter and that matter coheres into stable units like atoms—which cohere into galaxies and solar systems. What modern science does not yet know is that quantum potentials cohere as well. Quantum potentials seek equilibrium (balance) among themselves according to both active and passive principles. These active and passive forces effect cooperation among propensities to produce dynamical magnitudes (the change and renewal of equilibrium).

A single quantum potential contains the active force relative to all the others. All other potentials within a quantum “cloud” represent the passive force (parameters and constraints) relative to each single potential. In other words, the quantum potentials cohere (collapse) because they enter into a cooperation whereby they all act to determine and influence a type of mass (“dressed mass”) that takes physical form and becomes kinetic. (No active force or potential is realized or given form without a passive or restraining principle that quantifies and qualifies the event—and no passive principle would have existed in the early universe unless potentials could provide this force.)

All existence is through subsistence. Every entity in the created universe exists continuously from that which gives it its existence. Quantum potentials could not bring anything into formal existence unless they were the means by which a measured result subsists.

Why would such a principle of coherence and order point to the work of a Designer-God? Theology tells us that God is Infinite Love. The essence of love is to unite. It is God’s Love that drives nature to self-organize through the change and renewal of equilibriums.

Happy holidays! (I didn’t want you all to just stuff your stomachs!)

http://www.provinggod.com

Auziţi, bate vîntul, şi stropi de ploaie cad acolo în depărtare. Tot ce am crezut a fost o iluzie, da ştiu că nu vă pasă, mie nu’mi pasă, and I mean it. Dar auziţi, bate vîntul acolo departe, mă cheamă să’l liniştesc, să’i dau o îmbrăţişare, dar lui de ce îi pasă, sau nu’i pasă.. Da! uiziţi cum şuieră? îi este frică, că e singur, ei şi ce, azi sunt şi eu singură şi nu mă plîng, doresc un Muller, dar cred că las dulcele, ehh sure.. cum şi ieri am spus… Şi ca de fiecare dată mă înec în pustiu, mă ard în apă, mi’e foame mîncîd, mă doare fericirea, şi mă bucură durerea, cine ar fi crezut că va fi aşa? ceva nu e bine, poate eu nu sunt bine? nuuu.. eu sunt bine, sunt liberă să visez şi asta e ce contează, ceea ce mereu a contat, iuuupi!

Why do economies fail to coordinate levels of activity consistent with labor market clearing? Any theory that claims to answer this question must account for the main stylized facts of unemployment.

Shimer uses CPS data to look at the stocks and flows from the households’ point of view:

Reassessing the Ins and Outs of Unemployment [PDF]

This paper uses readily accessible data to measure the probability that an employed worker becomes unemployed and the probability that an unemployed worker finds a job, the ins and outs of unemployment. The job finding probability is strongly procyclical and the separation probability is nearly acyclical, particularly during the last two decades. Using the underlying microeconomic data, the paper shows that these results are not due to compositional changes in the pool of searching workers, nor are they due to movements of workers in and out of the labor force. These results contradict the conventional wisdom that has guided the development of macroeconomic models of the labor market during the last fifteen years.

The BLS’s Job Openings and Labor Turnover Survey (JOLTS) has establishment data on ”Total Employment, Job Openings, Hires, Quits, Layoffs & Discharges, and Other Separations.”

Bewley’s Why Not Cut Pay? [PDF], p.483, reviews and critiques several hypotheses on wage setting behavior and unemployment. Perhaps not surprising, few of these theories have ever been implemented in fully specified DSGE models.

Finally, when and why should we care about unemployment? Is there a labor supply rationing problem in the first place? This vintage Lucas paper has ome controversial thoughts on this: Unemployment Policy [JStor]

Done with Kissinger. Great read.

From early 90s – but highly relevant. Valuable commentary to the current white house and presidency – choices and changing landscapes.

Nach dem Ende des dritten Weltkriegs wurden zur Erschaffung einer sicheren Zukunft sämtliche Gefühle der Menschen mittels Drogen abgetötet. So entstand ein totalitäres System ohne Kriege, aber auch ohne Emotionen. Zur Bekämpfung derer, die die Einnahme der Droge verweigern und weiter an ihren Gefühlen festhalten, wurde ein übermächtiger Kriegerorden gegründet, der in den Ruinen zerstörter Städte Rebellen aufspürt und zur Strecke bringt. Zu diesen “Grammaton-Kleriker” genannten Kriegern gehört auch John Preston (Christian Bale), dessen bedingungsloser Glaube an das System nicht einmal durch den Verrat seines Partners (Sean Bean) erschüttert wird – bis er eines Tages vergisst, die Droge zu nehmen …

Drei Jahre vor dem erfolgreichen Reboot des “Batman”-Franchise qualifizierte sich “American Psycho” Christian Bale hiermit als Actionheld der Zukunft. Dabei ist “Equilibrium” nicht einmal ein reiner Actioner; Schusswechsel und Martial Arts spielen tatsächlich eher eine untergeordnete Rolle, während die Handung deutlich mehr in den Vordergrund tritt als in dem Genrefilm, an dem sich “Equilibrium” Anfang der 2000er natürlich messen lassen musste, “Matrix” nämlich. Offensichtlich, dass “Equilibrim” es nicht leicht hatte, diesen Vergleich zu bestehen. Erstaunlich, dass der Film sich dabei so gut aus der Affäre zieht.

Die negative Utopie, auch Dystopie genannt, ist beinahe so alt wie die Science Fiction selbst – ein untrügliches Anzeichen für den angeborenen Pessimismus des Menschen. Gleichzeitig lassen sich vor diesem Hintergrund immer noch interessante Geschichten erzählen. “Equilibrium” lehnt sich dabei an Klassiker des Genres wie “Brave New World” oder “Fahrenheit 451″ an – letzterem kommt dabei besondere Bedeutung zu, denn in der über alle Maßen regulierten Zukunft ist jede Art von Kunst und Kultur verboten, weil sie bei Menschen eben Gefühle auslöst. So kommt den Klerikern nicht nur die Aufgabe zu, Rebellen auszulöschen, sondern auch deren Besitz zu vernichten, seien es Musik, Gemälde oder Literatur. Geschickt stellt “Equilibrium” dabei die Bedeutung dieser Dinge für uns heraus, was sich vor allem in der beeindruckendsten Szene des Filmes manifestiert, in der John Preston durch Zufall Beethovens Neunte zu hören bekommt – eine Referenz an Stanley Kubricks “A Clockwork Orange”, vor allem aber eine grandiose Liebeserklärung an die Musik. Die facto eine der berührendsten Filmszenen, die ich je gesehen habe.

Natürlich kann man in eine Handlung wie diese reichlich Gesellschaftskritik hineininterpretieren, gerade im heutigen Piratenzeitalter. Das halte ich aber nicht für die Hautintention des Regisseurs und Drehbuchautors Kurt Wimmer. “Equilibrium” ist vielmehr eine Warnung davor, was geschieht, wenn wir anderen Dingen Priorität über unsere Emotionen einräumen – vor sozialer Kälte also. Letztendlich stellt der Film die Frage, was vom Menschen noch übrig bleibt, wenn er die Fähigkeit zu fühlen verliert. “It’s circular – you exist to continue your existance. What’s the point?“, fragt eine der Rebellen John Preston und ergänzt: “Without love, breathe is just a clock ticking.” Nur zu wahr. Von der Handlung her kann es “Equilibrium” ohne Weiteres mit “Matrix” aufnehmen, selbst wenn das Ende den Bogen dann doch etwas überspannt.

Außerdem wäre da ja noch die Action, die – ich erwähnte es eingangs schon – den Film nicht alleine trägt, aber mehr als ansehnlich ist. Highlight: Nahkampf mit Pistolen; geiler geht’s einfach nicht mehr. Überhaupt ist “Equilibrium” optisch absolut gelungen, sieht deutlich teurer aus als die 20 Mio. $, die tatsächlich als Budget verbucht wurden, allerdings bei weitem nicht wieder eingespielt werden konnten: An den Kinokassen ist “Equilibrium” ebenso dramatisch wie unverdient gefloppt, was ohne Zweifel an der erwähnten Konkurrenz in Form der “Matrix”-Trilogie lag. Schade, denn “Equilibrium” ist ein überzeugender Film und kann es zumindest mit den “Matrix”-Fortsetzungen locker aufnehmen.

Wertung: 8 / 10

(Der Film ist übrigens besser als der Trailer. Wobei mir einfällt: Wenn irgend möglich, nicht synchronisiert anschauen …)

It’s not your grandfather’s Ramsey rule!

Kocherlakota has a draft of a book on the NDPF literature on his U. of Minnesota webpage: The New Dynamic Public Finance [PDF]

Comprehensive work on optimal policy should account for general equilibrium interactions, growth/dynamics and the incentives-insurance trade-off.

Optimal monetary policy results are highly sensitive to the assumptions made on the distortions that money helps mitigate, i.e. why and when agents choose to hold money and what role does it play in implementing better allocations. Lagos and Wright have a summing-up paper on recent work on these questions.

A unified framework for monetary theory and policy analysis [IDEAS]

Search-theoretic models of monetary exchange are based on explicit descriptions of the frictions that make money essential. However, tractable versions of these models typically need strong assumptions that make them ill-suited for studying monetary policy. We propose a framework based on explicit micro foundations within which macro policy can be analyzed. The model is both analytically tractable and amenable to quantitative analysis. We demonstrate this by using it to estimate the welfare cost of inflation. We find much higher costs than the previous literature: our model predicts that going from 10% to 0% inflation can be worth between 3% and 5% of consumption.

This cannot be the entire story. For most transactions, even those with cash, there’s little if any searching going on.

my dissertation, due jan 20-something, is going to be on intuitions.

i say ‘going to be’ with full knowledge of what this entails regarding my progress thus far.

i’m using david lewis for my starting point, which is to define intuitions.

he thinks they are opinions, but goes on to give them the power to decide between which theory to accept if we reach an impasse where rival theories are methodologically equal to each other.

so say smith says that because we have no criteria for individuation when it comes to personhood beyond the identification of a person’s body, we should be materialists.

but then his girlfriend, jones, says now hold on, that doesn’t sit well with my intuitions, this implies after all that i do not have a soul and that i am inextricably tied to my body, but i think thoughts that go well beyond my physical surroundings (and i do like the idea of going to heaven). and seeing that we have these two rival hypotheses, namely dualism and materialism, which both account for the facts equally well but in different ways, and i prefer one over the other because it fits better with my intuitions, i may legitimately hold dualism to be true.

now edith comes along and flirts with smith just to piss jones off. the way i hope to get into smith’s pants is by saying

now jones, even if i were to assume that dualism and materialism are methodologically equal

(which i contest, and in fact i believe that if this were the case that would be reason in itself to suspend judgement and develop each position and perhaps an alternative more fully before making any kind of decision)

i take smith’s reasoning to be more sound than your intuitions concerning having an identity beyond your physical body.

this is what (david) lewis refers to as measuring the price, which he expands in a really fun way in his piece “holes”, which he wrote with stephanie lewis. am trying my darndest to find a free copy online, may just have to upload onto scribd next time i feel like breaking the law…

i’ve oversimplified the problem but i will get back to it

let me say for now that my eventual aim is to put intuitions in their place, so that people don’t get to say something like what jones says above. i don’t think lewis thinks she would be right either, he has a whole nother idea about equilibrium which ties in to holism about beliefs and i guess a certain anti-realism about truth…

but as i said i’m just using the man for my starting point. so back to my definition of intuitions, this is what i came up with after some considered thought (it’s been about 9 months of thinking):

intuitions are beliefs (lewis calls them opinions, i equate the two) which we use to assess our other beliefs. the other beliefs we assess are our theories. the way in which we assess them is to measure their coherence with our other beliefs which — this is the important bit — do not depend on holding the theory being assessed as true.

i know, nine months and this is what i come up with, don’t take up parenting, i get it.

but i have a whole nother idea about simplicity and modesty in philosophy, which maybe i’ll write a paper about.

once this is done, of course/

How to find approximate Nash equilibrium for sparse games

Constantinos Daskalakis is one of the experts in modern game theory, especially the structure of Nash Equilibrium for non-zero sum games. He has written a wonderful paper with Christos Papadimitriou On oblivious PTAS’s for nash equilibrium. Also see his nice survey for more information.

Today I want to talk about Costis and Christos’ paper as it relates to sparse games. This is another example of the Iceberg Effect: their paper has a beautiful result on game theory, but I missed another of their results.

Constantinos, Costis, was kind enough to point out two things about sparse games after my earlier discussion on games. First, that in his paper with Christos at STOC 2009, they stated a theorem that solves the sparse case of symmetric games. He went on to sketch the proof, which they did not include in their paper: I will give their proof in a moment.

Second, he points out that Shanghua Teng has observed that the uniform distribution is trivially a -Nash equilibrium of a -sparse game—the expected payoff from any row is at most for the row player and similarly for the column player.

His second point is one that I would like to discuss, since it raises an issue by what we mean to approximate a Nash Equilibrium (NE).

Let’s turn to discuss first NE and then their theorem.

Nash Equilibrium: Exact and Approximate

What does it mean to find an approximate NE? I think it will be easier to first explain the main issue involved by an analogy. Anyway I love analogies.

Suppose that you have a polynomial and want to find an so that

of course, we call a root. Usually is not a rational number, so we cannot write it down exactly. Thus, what we do is try to find a so that

where is the required precision and are integers.

There is a fundamental problem: simply because is small does that mean that it is near an actual root of ? It does not, in general. What we want are the stronger statements:

1. The value of is near ;
2. There is a so that and is also small.

In this case we can say that is an approximate root of the polynomial. If there is no such , then is an interesting point, but it is not correct to call it an approximate zero.

This behavior is analogous to what happens with “approximate NE’s.” There are two types of interpretations of what an approximate NE is:

An -near NE: This is a pair of strategies that are within an of an exact NE.

An -NE: This is a pair of strategies such that a player who defects from their strategy can gain at most an .

Costis, in his survey, points out that the first notion is reasonable, but the latter is the one that we usually use: Note also that it is easy for a player to check the approximate optimality of the actions used by her mixed strategy. So the notion of an approximate Nash equilibrium is much more appealing and, in fact, this is the notion most commonly used.

Note, the analogy to the root problem: in the first we are near a root, and in the second we are at a small value. As Costis points out the latter can be checked easily, while checking that a point is near an exact root is not as easy.

Sparse Games

I will now state their theorem:

Theorem: Suppose that is an matrix with entries in , such that each row and column in has at most ’s. Then, for the symmetric game defined by , we can find an -NE in time bounded by

Here is a sketch of their proof:

Proof:

The key insight is that it is enough to consider strategies for the row and column player where the probabilities are integer multiples of . The number of such strategies for either player is at most

This follows since the number of strategies are bounded by the number of ways to place objects into “bins.”

We now have a “small” set of strategies, the following argument will show that one of these strategies contains a pair that is an -near NE. Consider an exact NE say . Notice that there exist strategies such that the following are satisfied:

1. For all : and .
2. For all : if then , and if then .

Consider . If , then set to . Otherwise, set to the nearest multiple of . This almost works: the small issue is that if is not a exact multiple of , then do we round up or down? Either rule will make satisfy the needed conditions above. However, we also need to be a probability vector: it is easy to see that by rounding some up or down we can adjust to satisfy

which will make it a probability vector. The same method works for . Now we need to prove that this strategy pair is an -near NE. The payoff for the row player is and for the column player is . Let denote a unit vector with at -th coordinate. For notational convenience, we omit the transform symbols on the vectors. The usage should be clear from the context.

Notice that the pair of strategies and the NE satisfy:

1. , for all .
2. , for all .

The first claim follows from the fact that

The second claim is analogous. This is where we use that has at most ’s in each row/column. Therefore, the total error from the NE is at most

It follows from the above that is an -near NE of the game.

The above proof shows the existence of an -near NE in the search space formed by the strategies that are multiples of . This strategy pair is near the exact NE . However, because of the difficulty of searching for an -near NE, an exhaustive search in this space can only guarantee that we would find an -NE, and not an -near NE.

Open Problems

An interesting open problem is to try to found an -near NE. The above proof shows that it is in a relatively “small” list of strategies. Is it possible to discriminate and determine which are near exact NE’s?

The above proof gives us a PTAS for games with a bounded number of 1’s in each row and column. However, for matrices with 1’s in all, the problem of finding a PTAS is still, I believe, open.

In a previous post titled “Spiritual Gravity” I talked about the well-known law of physics that states that once something is set into motion it seeks out its equilibrium—the condition whereby it finds stability.

Since the universe exists as a dynamical process, everything finds its stability in motion.  Planets “fall” towards the sun while the sun is itself falling towards its equilibrium within a galaxy of stars—also seeking their common equilibrium through space.  So as one cosmic concentration falls, others have to constantly try to keep up.

God is the prime mover.

So ultimately, everything in the created world must try to “catch up” and find stability in God’s Holy activity. But the physical universe tries to catch up with God’s perpetual influence not only by being constantly on the move, but through finding stability within new units of complexity and self-organization.

If there were no Creator-God, all things would simply fall to the “bottom” (entropy). But since everything is being moved by God and is trying to keep up with God, the so-called “bottom” must keep rising to a higher plane of order and thermodynamics. This creates new orders of organization in the universe (reverse entropy).

The evolution of bio-complexity on earth is the continued endeavor of things in dynamical process to catch up and more perfectly mirror God’s Holy qualities. These qualities become more apparent as nature brings forth higher-levels of organic structure. For instance, the higher the degree of complexity we see in evolving living structure the more we see a perfection of reciprocal cooperation. Every cell lives for the welfare of the entire body and the compound body lives for the welfare of all its cells.

How is the evolution of bio-structure representative of Nature’s incessant striving to catch up to God? God is Infinite Love. The essence of love is to unite and share. Increased organic complexity is the result of increased unified sharing. Nothing new comes together without perfecting reciprocation. In this way evolution attempts to catch up to God by perfecting an image and likeness of LOVE.

This physical analog of love becomes even more God-like as it evolves into the psychical realm—that is, through the evolution of increased intelligence and consciousness. Human subjective experience allows creation to find its equilibrium in acts of kindness and goodness. Reverse entropy now moves from increased thermodynamics to its equivalent psycho-spiritual dynamics.

Religion is God’s strategy to offer guidance for the human heart and mind to find stability in spiritual love. This will allow the human spirit to ultimately find its proper equilibrium in God’s eternal kingdom of mutual love, called heaven.

http://www.provinggod.com

( scroll down for German Text )

Rocktower Festival Lübeck – The Easter Metalfestival 3. April 2010

On the 3rd April 2010, at 11 am, the Lübecker Musik- und Kongreßhalle and Treibsand will open their gates for the second Rocktower Festival Lübeck. The buzz starts on Friday with the metalmarket in the „Muk“ and warm-up Shows in Treibsand and Sounds.

MUK rocks. And this time it’s gonna be heavy! Now in it’s second year, the Easter Metalfestival will be raising the roof of the white house at the River Trave on Easter Saturday. Get ready for Hard Rock and Heavy-Metal fever. Thanks to the cooperation of „Treibsand”, this year we are able to present 19 national and international bands performing live. Two stages – two worlds: MuK meets Treibsand. Perfect conditions for the 14 hours concert marathon with top-class bands showcasing different styles of Metal and Hard Rock.

Appearing live are: Kalmah, Endstille, Finntroll, Powerwolf, Van Canto, Blitzkrieg, Raven, Cursed Anguish, Nastrandir, Entombed, Thunderbolt, Omen, Equilibrium, Asmodis, RAM, Roxxcalibur, Ruffians, The Devils Blood, The Rods.

The buzz starts on Friday in Lübeck with the Metalmarket in the MuK and warm-up shows in the „Sounds“ and in „Treibsand“. (More information to follow)

Festival starts: Saturday 03. April 2010 – 11:30 a.m. (Doors open: 11 a.m.)

Festival Tickets: www.metaltix.com . Advance booking: 42.90 € incl. all fees; Available from all known ticket agencies. Box office: 46.00€ incl. all fees.

Tickets for the warm-up show: 12 € direct from the box office or advance booking also available online.

For more information on travel possibilities, location and tickets: www.muk.de / www.metaltix.com / www.myspace.com/rocktower / www.rocktower.de

RUNNING ORDER 2010 :

Stage one:
 
11:15 – 12:00 Uhr Nastrandir
12:20 – 13:05 Uhr RAM
13:25 – 14:10 Uhr Ruffians
14:30 – 15:30 Uhr Kalmah
15:50 – 16:50 Uhr Blitzkrieg
17:10 – 18:10 Uhr Endstille
18:30 – 19:30 Uhr The Rods
19:50 – 20:50 Uhr Raven
21:10 – 22:10 Uhr Entombed
22:30 – 23:45 Uhr Equilibrium
00:00 – 01:15 Uhr Finntroll
 
Stage two:
 
13:50 – 14:35 Uhr Cursed Anguish
14:55 – 15:40 Uhr Asmodis
16:00 – 17:00 Uhr Thunderbolt
17:20 – 18:20 Uhr Omen
18:40 – 19:40 Uhr Van Canto
20:00 – 21:00 Uhr Powerwolf
21:20 – 22:20 Uhr The Devil´s Blood
22:40 – open End Roxxcalibur

Rocktower Festival Lübeck – The Easter Metalfestival 3. April 2010

Am 3. April 2010 um 11.00 Uhr öffnen die Lübecker Musik- und Kongresshalle (MuK) und das“ Treibsand“ ihre Tore für das zweite Rocktower Festival Lübeck. Und bereits am Freitag beginnt in Lübeck, mit der Metal-Börse in der „Muk“ und warm-up Shows im „Treibsand“ und im „Sounds“, der Ausnahmezustand.

Die „MuK“ rockt. Und dieses Mal wird’s richtig hart. Im zweiten Jahr erbebt das weiße Haus an der Trave am Ostersamstag im Hardrock- und Heavy-Metall-Fieber. 19 nationale und internationale Bands haben sich angekündigt. Sie spielen parallel auf zwei Bühnen: in der „MuK“ und im „Treibsand“, dem Veranstaltungsraum der „Alternative e.V.. Zwischen beiden Veranstaltungsorten liegen Welten aber nur wenige Schritte zu Fuß

Der vierzehnstündige Konzertmarathon mit hochkarätigen Bands aus verschiedenen Richtungen des Metal- und Hardrock beginnt am Sonnabend, dem 3. April 2010, um 11.30 Uhr. Tickets gibt es im Vorverkauf für 42,90 Euro, an der Abendkasse für 46 Euro.

Am Freitagabend stimmen warm-up-Shows im „Treibsand“ und im „Sounds“, An der Untertrave 81-83, auf das Marathonfestival ein. In der „MuK“ beginnt am Freitag die Metal-Börse mit Fan-Artikel-Verkaufsständen. (Weitere Infos folgen)

Kurzinfos:
2. Rocktower Festival Lübeck – The Easter Metalfestival
Sonnabend, 3. April 2010
Musik- und Kongreßhalle Lübeck und „Treibsand”, Willy-Brandt-Allee 9
Einlass 11 Uhr, Konzertbeginn 11.30 Uhr
Karten: www.metaltix.com . 42,90 Euro im Vorverkauf, 46 Euro an der Abendkasse

Weitere Informationen und Eintrittskarten:

www.muk.de / www.metaltix.com / www.myspace.com/rocktower / www.rocktower.de

 RUNNING ORDER 2010 :

Stage one:
 
11:15 – 12:00 Uhr Nastrandir
12:20 – 13:05 Uhr RAM
13:25 – 14:10 Uhr Ruffians
14:30 – 15:30 Uhr Kalmah
15:50 – 16:50 Uhr Blitzkrieg
17:10 – 18:10 Uhr Endstille
18:30 – 19:30 Uhr The Rods
19:50 – 20:50 Uhr Raven
21:10 – 22:10 Uhr Entombed
22:30 – 23:45 Uhr Equilibrium
00:00 – 01:15 Uhr Finntroll
 
Stage two:
 
13:50 – 14:35 Uhr Cursed Anguish
14:55 – 15:40 Uhr Asmodis
16:00 – 17:00 Uhr Thunderbolt
17:20 – 18:20 Uhr Omen
18:40 – 19:40 Uhr Van Canto
20:00 – 21:00 Uhr Powerwolf
21:20 – 22:20 Uhr The Devil´s Blood
22:40 – open End Roxxcalibur

3303533    ดุลยภาพของอิออน    Ionic Equilibrium

การคำนวณหาความเข้มข้นของสารต่างๆ ในสารละลายมัลติเพิลบัฟเฟอร์ และการตกตะกอนของสารที่เป็นกรด และเบสออกมา โดยการเปลี่ยนพีเอชของสารละลาย

(Calculation of chemical concentrations in solution of multiple buffers and precipitation of acidic and basic substances as a function of pH.)

(3303533 จุฬาลงกรณ์มหาวิทยาลัย)

Diese Woche gab es gleich zwei große Hightlights im Bereich der großen Multihulls. Die zwischendurch das ein oder andere Mal gekenterte Hydroptère hat einen neuen Rekord mit 50,17 Knoten (92,91 km/h) über eine nautische Meile aufgestellt und sieht von vorne nur leicht gefährlich aus:

In den USA hat derweil das Team BMW/Oracle nach Verlust des alten Mastes einen sogenannten Wingmast montiert, der alles bisher dagewesene in den Schatten stellt. Es gab zwar noch Probleme bei den ersten Tests, die sich aber schnell beheben lassen sollen.

Auch hier wieder geht man Dank an Sailing Anarchy.

Mein aktuelles Projekt ist ein Zeitfresser, deshalb ging es mit meiner equilibrium auch lange Zeit nicht weiter. Jetzt laufen die Planungen für die nächsten Umbauten in Vorbereitung auf die 2010-Version an.

It is a well-known law of physics that once something is set into motion it seeks out its equilibrium. This is what occurs to all dynamical things that come under the universal force of gravity.

Physicists are still trying to grasp the concepts of gravitational order (the spontaneous self-organization of gravitational systems like galaxies and solar systems) as well as quantum gravity.

Gravity is seen as something continuous – getting stronger or weaker but never representing a discrete unit (as quantum physics would require). Thus gravity and quantum physics are at odds with each other and the best brains in the world have yet to find a satisfactory means of unifying the two.

Perhaps the answer has already been given in the discoveries put forth by scientist/theologian Emanuel Swedenborg. He believed that action could find its equilibrium not only within units of distinct quantities but also units operating within distinct QUALITIES of space!!! Action could be physical, mental and spiritual according to the type and number of inertial constraints ruling their trajectories.

It is beyond the scope of this blog post to provide all the details of Swedenborg’s multidimensional theory but it spans everything from inert physical matter to the ontological reality of spiritual substances. (Today’s 11-dimensional string or membrane theories only provide a physical account of the universe and leave out transcendental principles.)

My main point is, Swedenborg showed that the activity of the human mind also seeks out its proper equilibrium. The mind finds its “trajectory” and equilibrium in reaching goals. Human goals are based on values (which are derivatives of love).

Many serious physicists believe (as Swedenborg did) that the human mind operates outside of time and space—and quantum physics informs us that dynamical things can indeed be non-local and non-temporal. Therefore, if the human mind finds its equilibrium in reaching its chosen values, then spiritual gravity is LOVE.

If this were not so, then it would be hard to imagine how angelic activities could find coherence and order in the non-physical spiritual world. Those who adopt God’s principles of mutual love find their equilibrium in heaven. While those who have contempt for others have their equilibrium in another, opposing realm. One’s love determines one’s “place” in the spiritual world. Put into scientific language, one’s love adapts and bends the fabric of reality into its own disposition.

That is why religion offers a value system. Religion is God’s lawful strategy to help the human race find their ultimate equilibrium in eternal blessedness and peace.

I have written a new book Proving God that attempts to put all Swedenborg’s pioneering ideas into a scientifically plausible model. It will be available in Spring 2010.

Feel free to browse http://www.provinggod.com for more info.

Sooooo

get that? its an interpretation of Hal Foster’s views on art, which I kinda agree with.

The (postmodern) artist becomes a manipulator of signs more than a producer ofart objects, and the viewer and active reader of messages rather than a passive contemplator of the aesthetic.

From that drawing I could go in a number of directions, which is why I went back to the smaller drawings.

I started combining disney and artworks, and artworks and other artworks to create art that was a culmination of efforts by me (the sign-manipulator) and the artists of yore.

Apologies for the photographs as I had already linked my camera to the computer and could not be bothered to unlink it so its done with photobooth.

From these I began to make different products:

With these drawings I’d taken a different step into both the commercialism of art, and the success of contemporary artists.

In the top one, “mickey koons” I morphed mickey into a work which although was a found-object piece before, had more symbolism to the Jeff Koons piece. Thus showing the power of contemporary painters compared to a great like walt disney whose company has become a major company of commercial success. Also brings back to the fact that artists are modern day heroes, in comparison with heroes I had when I was younger.

In the latter, “Minnie Hirst” I feel the success is even greater. Its all about success in this one. The famous business artist Hirst is draped over an unsuspecting Minnie Mouse. The tres chic polka dot dress is but one of Hirst’s most recognisable paintings. It is painted onto acetate in the same way my other cel objects where made. This represents the collector’s value of the artwork as well as the value of Hirst and Disney’s work. It raises questions of success and if the value of an art should be based entirely around its price-tag. I feel this second piece is more successful, mainly due to the simplicity and the cryptic nature. Even though the dots represent the over-success of Hirst, they can also be seen as what his work originally meant, faith in medicine (something that is completely unindulgent), and juxtaposed next to something that has become so much of an indulgence (disneyland) it becomes a battle for what is more important in life, indulgence of necessities. Tis also quite nice due to the fact that Minnie Mouse wears a polka dot dress already and its just a slight modification of a well-known image.

Am gonna start working with 3D things possibly next time, so stay tuned.

Till next time.