Side-Way Trading

As I mentioned in the "S&P 500 Financial" post on August 20, 2010: "At this moment the majority of technical indicators remain to be bearish by suggesting the higher odds of further decline." - the indexes (S&P 500, Nasdaq 100 and DJI) are lower, yet if you take at the hourly chart (1 bar = 1 hour) you will see that most of the time the indexes were in side-way action.

Side-way characteristics of the current down-trend could be noticed from the beginning (August 9, 2010) of this down-trend. It is difficult to compare the current down-trend to the previous down-trends we had over the last couple of years. Te previous down moves where more consistent and had much less side-way trading sessions. It is already almost a month since the indexes in the bearish move and, so far, during t! he recent decline, we have not seen two strongly negative session in a row. Yet, mainly because of the side-way trading, we still have not seen panic trading which would be characterized by the strong bearish volume to the price down-side and strongly oversold advance/decline issues and volume readings.

The other characteristic of the current down move is the high level of volatility. The volatility is not extremely high, yet it remains steady on the high level.

The same a s a week ago, I would say that the majority of technical indicators remain to be bearish by suggesting the better odds of the further decline. Yes, the Friday's advance has pushed some technical indicators into bullish sentiment and if you take a look at shorter-term technical analysis you may see some bullish signals. However, in order to have a strong up-move, in addition to the bullish signal, the stock market should! be predisposed to the up-move. So far, we may see bullish sig! nals on shorter-term frames, yet, personally, I have not seen any strongly oversold indications. Therefore, I would not place a long bet.

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Supermassive black holes and the entropy of the universe

New Scientist has an article about a recent paper by two Australian researchers (http://www.arxiv.org/abs/0909.3983), which contains detailed estimates of the entropy of various components of the universe (black holes, neutrinos, photons, etc.). This paper is related to some work I did with with Frampton, Kephart and Reeb: What is the entropy of the universe?. (Discussion on Cosmic Variance.)

Our work did not focus on the numerical values of various contributions to the entropy (we made some simple estimates), but rather what the physical meaning is of this entropy -- in particular, that of black holes; see excerpt below.

New Scientist: Mammoth black holes push universe to its doom

30 September 2009 by Rachel Courtland

THE mammoth black holes at the centre of most galaxies may be pushing the universe closer to its final fade-out. And it is all down to the raging disorder within those dark powerhouses.

Disorder is measured by a quantity called entropy, something which has been on the rise ever since the big bang. Chas Egan and Charles Lineweaver of the Australian National University in Canberra used the latest astrophysical data to calculate the total entropy of everything in the universe, from gas to gravitons. It turns out that supermassive black holes are by far the biggest contributors to the universe's entropy. Entropy reflects the number of possible arrangements of matter and energy in an object. The number of different configurations of matter a black hole could contain is staggering because its internal state is completely mysterious.

Egan and Linewe! aver found that everything within the observable universe cont! ains abo ut 10^104 units of entropy (joules per Kelvin), a factor of 10 to 1000 times higher than previous estimates that did not include some of the biggest known black holes (www.arxiv.org/abs/0909.3983, submitted to The Astrophysical Journal).

If entropy were ever to reach a maximum level, that would mean the heat death of the universe. In this scenario no energy can flow, because everything is the same temperature and so life and other processes become impossible. "Our results suggest we're a little further along that road than previously thought," Egan says.

But although black holes do boost the universe's total entropy, it is not clear whether they will hasten its heat death. Supermassive black holes don't contribute much to the flows of heat that even out temperature throughout the universe, says physicist Stephen Hsu at the University of Oregon in Eugene.

It's true that these black holes will slowly evaporate by releasing Hawking radiat! ion, particles created near the boundary of the black hole. And this radiation could move the universe towards heat death.

Black holes may evaporate via Hawking radiation, tipping the universe towards its heat death. However, it will take some 10^102 years for a supermassive black hole to evaporate. "The entropy inside those black holes is effectively locked up in there forever," Hsu says. So we may have reached a state approaching heat death long before, as stars burn out and their matter decays.

The large result obtained by the Egan and Lineweaver for the entropy of the universe is primarily due to supermassive black holes. How do we interpret that entropy? Here is an excerpt from our paper (excuse the latex).

Note the entropy used in this paper describes the uncertainty in the precise quantum state of a system. If the system is macroscopic the full quantum state is only accessible to a kind of ``super-obser! ver'' who is unaffected by decoherence \cite{decoherence}. Ind! ividual observers within the system who have limited experimental capabilities can only detect particular decoherent outcomes. These outcomes arise, e.g., from an effective density matrix that results from tracing over degrees of freedom which are out of the experimenter's control (i.e., which form the ``environment''). In \cite{BID} the experimental capabilities necessary to distinguish decoherent branches of the wavefunction, or, equivalently, the precise quantum state of Hawking radiation from a black hole, are discussed. It is shown that a super-observer would either need (at minimum) the capability of making very precise measurements of accuracy $\exp(- M^2 )$ (see also the proposal of Maldacena \cite{eternal} for a specific measurement to determine whether black hole evaporation is unitary), or alternatively the capability of engineering very precise non-local operators, which measure a large fraction of the Hawking radiation at once, including correlations (i.e., as opposed t! o ordinary particle detectors, which only measure Fock state occupation numbers and are not sensitive to phase information).

An observer who lacks the capabilities described in the previous paragraph would be unable to distinguish the states in the $S = M^{3/2}$ subspace in Fig.~\ref{figure1} from those in the larger $S = M^2$ subspace, assuming the unitary evaporation resembles, in gross terms, Hawking evaporation, with the information hidden in correlations among the emitted quanta. In that case, the future uncertainty for ordinary (non-super) observers might be better characterized by the larger $S = M^2$ entropy. Putting it another way, an ordinary (non-super) observer is forced (due to experimental limitations) into a coarse grained description of the radiation; they cannot distinguish between most of the radiation states, and for them the $S = M^2$ entropy is appropriate. For a super-observer, however, due to unitary evolution, the uncertainty in the quantu! m state does not increase. For them, black holes do not have g! reater e ntropy than the precursor states from which they formed.

For the super-observers described above, the large black hole entropies in Table I do not reflect the actual uncertainties in the (current and future) state of the universe and are in that sense misleading. A black hole of mass $M$ whose formation history is typical for our universe (e.g., it originated from gravitational collapse of a star or galactic core) satisfies the bound S [less than] M^{3/2} \cite{MI}. Thus, re-evaluating the numbers in Table I, the total entropy of all black holes in our universe is not bigger than the total matter entropy: the dominant uncertainty in the precise state of the universe, at least as far as arises from known physics, is, in fact, due to CMB photons or neutrinos.

Figure 3 caption: Ordinary matter (star, galactic core, etc.) collapses to form an astrophysical black hole. Under unitary evolution, the number of final Hawking radiation states that are actually accessible from this collapse is $\sim \exp M^{3/2}$, i.e.~precisely the number of ordinary astrophysical precursors (\ref{th1}). It is therefore much smaller than the the number of $\sim \exp M^2$ states a black hole, and its eventual Hawking radiation, could possibly occupy if nothing about its formation process were known.

Final mysterious comment, maximally compressed for the cognoscenti: assuming unitarity, black holes do not push us closer to heat death (equilibrium) in the multiverse! , but can contribute (albeit very slowly) to the (coarse g! rained) heat death experienced by a non-super observer (i.e., an observer subject to decoherence). See here for more on equilibrium in the multiverse.

standard entropy table

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Krugman: Greece Could "Solve" Its Problems if it Could Print More Money

In his best-seller, The Return of Depression Economics (which I am having my MBA students read this spring), Paul Krugman declared that most economic problems can be "solved" rather easily: the government prints more money. I am not making up that declaration, nor am I embellishing it or putting it out of context. That is what he said, and, like Sgt. Friday, just the facts, ma'am.

Today, he looks once again at the crisis in Greece, which has spread to Spain and where Austrians see fiscal folly and wages and work policies that are totally out of line with the structures of production in those country, a situation that must be put back into balance to end the crisis, Krugman sees the lack of inflation being at fault. Don't take my word for it. Read on:

The fact is that three years ago none of the countries now in or near crisis seemed to be in deep fiscal trouble. Even Greece’s 2007 budget deficit was no higher, as a share of G.D.P., than the deficits the United States ran in the mid-1980s (morning in America!), while Spain actually ran a surplus. And all of the countries were attracting large inflows of foreign capital, largely because markets believed that membership in the euro zone made Greek, Portuguese and Spanish bonds safe investments.

Then came the global financial crisis. Those inflows of capital dried up; revenues plunged and deficits soared; and membership in the euro, which had encouraged markets to love the crisis countries not wisely but too well, turned into a trap.

What’s the nature of the trap? During the years of easy money, wages and prices in the crisis countries rose much faster than in the rest of Europe. Now that the money is no longer rolling in, those countries need to get costs back in line.

But that’s a much harder thing to do now than it was when each European nation had its own currency. Back then, costs could be brought in line by adjusting exchange rates — e.g., Greece could cut its wages relative to German wages simply by reducing the value of the drachma in terms of Deutsche marks. Now that Greece and Germany share the same currency, however, the only way to reduce Greek relative costs is through some combination of German inflation and Greek deflation. And since Germany won’t accept inflation, deflation it is.

Krugman, of course, supports Germany having a round of inflation. We have been down this road before, people, and it ends in disaster. In the late 1920s, Great Britain did not want to devalue the Pound, which at that time should have been trading at about $3.50 instead of the $4.86 "official" rate.

To keep the $4.86 rate intact, Benjamin Strong, who then was the chairman of the New York Federal Reserve Bank, cut a deal with Montagu Norman, Britain's equivalent of the Secretary of the Treasury, to inflate the U.S. Dollar. This led to the infamous stock market bubble that burst in October, 1929, and President Hoover's response to that crash (to try to prop up failing firms, as well as prop up high prices and wages) led to the Great Depression.

The Germans have their own history with inflation (1923 anyone?) and are not about to go the Benjamin Strong route, as to do so would create a series of troubles down the road. Unfortunately, inflation ultimately distorts an economy's structure of production, leads to unsustainable booms, and then to disaster. However, Keynesians like Krugman hold that the Very Worst Thing that can happen to an economy is deflation, and that prosperity is possible only through inflation.

Here is the problem with Krugman's prescription (Germany inflate, Greece continue as is): It does nothing to get the Greek fundamentals back into order and it distorts the economic fundamentals in Germany. In other words, it does nothing to solve the real, underlying problems in Greece, but it lays the foundation for a future crisis in Germany, as inflation will create its own problems.

If you wish to see an important difference between Austrians and Keynesians, here it is. Keynesians really don't see economic fundamentals, nor do they see any issues with factors of production. Instead, in their view, the economy is a homogeneous mix that works when government throws lots of money into the recipe. If there are imbalances (and the theory does not allow for that to happen, although Krugman himself recognizes that imbalances could be an issue), then inflation can solve everything. Unfortunately, what happens when governments engage in policies of inflation is that the seeming good effects come first, but then when the factor prices get out of balance with what is being produced, the economy moves toward an inevitable bust, and any attempts to "fix" things through another round of inflation only make things worse.

Austrians, on the other hand, look first at the factors of production for the distortions in the entire structure of the economy. Deflation, far from being the enemy of the economy, allows those factors to get back into balance with the overall structure of production, and direct production to consumer desires. It is the opposite of inflation: the bad effects come first (unemployment and initial dislocation), but the "good" effects come later (a recovery).

There is no way to bridge the gap between Keynesians and Austrians. Today, it is the Keynesians that rule, and it is economy that ultimately will suffer because their "theories" ultimately lead to disaster.

No, Greece cannot "solve" anything by going back to the Drachma and printing out the wazoo. Instead, it is up to that country to get its house back in order by letting the factors, including labor, get back into balance. That means, in the initial stages, that Greeks will find their wages being cut and their standard of living will fall. Yet, that initial stage is absolutely necessary if, in the long run, Greeks want to enjoy a higher standard of living in the future with an economy that is sustainable.

[Note]: It is good to be posting here again. I have been following the Tonya Craft trial in Ringgold, Georgia, and it is a fiasco. The prosecutors are running the show, and they are acting like typical high school bullies. It is a tragedy and a train wreck in progress.

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Help!

Here's the deal:  I'm working on curriculum for my school and Algebra 2 is making my eyes cross.  I think the major problem is the state of Virginia is in a transition year between "old" Standards of Learning (SOLs), and "new" ones.  This year is supposed to be the year that we're still teaching and assessing the old SOLs, but we're supposed to teach the new ones, too.  Those of you that teach Algebra 2 already know that there's an enormous amount of information to cover in a short period of time.  To give you context, our school teaches it as a semester-long block course.  There's only so much a brain can handle in one day, though! 

Here's the first draft of my skills list and structure...I'm not sure what to do about the old vs. new SOLs (my skills list is based on the old SOLs because that is what will be assessed).

Note:  Gray items are not included in old or new SOLs but might be necessary for student understanding
          Blue items are being taken out of the SOLs starting next year
          Red items are new to the SOLs starting this year

Unit 1 Algebra 1 Review/Solving Equations


1 Solve multi-step equations and inequalities
2 Matrix +/-
3 Solve compound inequalities
4 Solve absolute value equations
5 Solve absolute value inequalities

Unit 2 Polynomial Review/Add Depth

6 Factor trinomial a = 1
7 Factor trinomial a > 1
8 Factor special cases (sum/diff of cubes, diff of squares, perfect square trinomials)
9 Factor out GCF first (factor completely)
10 Exponent rules
11 +/- polynomials
12 Multiply polynomials
13 Divide polynomials

Unit 3 Rational Expressions

14 Identify undefined values
15 Simplify rational expressions by factoring and canceling out common factors
16 Multiply and divide fractions
17 Multiply and divide rational expressions
18 Add and subtract fractions
19 Add and subtract rational expressions
20 Simplify complex fractions
21 Solve rational equations

Unit 4 Radicals, Radical Equations and Complex Numbers

22 Simplify numbers under radical
23 Simplify monomials under radical
24 Multiply and divide radicals
25 Add and subtract radicals
26 Nth roots to rational exponents and vice versa
27 Simplify expressions with nth roots and rational exponents
28 Solve radical equations
29 Simplify square roots with negative terms inside radical using i
30 Add and subtract complex numbers
31 Powers of i
32 Multiply complex numbers

Unit 5 Functions (intro)

33 Domain and range of relations (from ordered pairs, mapping, graph, table)
34 Identify relations that are functions and one-to-one
35 Given graph and a value k, find f(k)
36 Given graph, find zeros
37 Given graph and a value k, find where f(x)=k

Unit 6 Linear Functions


38 Slope from graph, equation, points
39 Graph from equation
40 Equation from graph
41 x- and y- intercepts
42 Determine whether lines are parallel, perpendicular, or neither from equation or graph
43 Write equations for parallel and perpendicular lines given line and point off the line
44 Graph linear inequalities

Unit 7 Systems


45 Solve systems of equations by graphing
46 Multiply Matrices using a graphing calculator
47 Inverse matrix method of systems
48 Systems of equations word problems
49 Graph systems of linear inequalities
50 Linear programming max/min problems

Unit 8 Functions (reprise)

51 Function math (addition, subtraction, multiplication, division)
52 Function composition, find a value i.e. f(g(3))
53 Function composition, find the function i.e. f(g(x))
54 Find an inverse function by switching variables

Unit 9 Quadratics

55 Graph from vertex form, identify max/min and zeros
56 Solve by factoring
57 Solve by Quadratic Formula (including complex solutions)
58 Determine roots using the discriminant
59 Write equation for quadratic given roots
60 Quadratic systems
61 Polynomials: relating x-intercept, zeroes and factors
62 End behavior for polynomials

Unit 10 Exponential/Logarithmic functions

63 Exponential growth or decay from function
64 Sketch base graph of exponential/log functions
65 Exponential to log and vice versa
66 Data analysis/curve of best fit for linear, quadratic, exponential and log

Unit 11 Transformations and Parent Functions

67 Graph absolute value functions
68 Horizontal and vertical translations of linear, quadratic, cubic, abs value, exponential and log
69 Reflections and stretching of linear, quadratic, cubic, abs value, exponential and log
70 Combinations of transformations on parent functions
71 Identify parent graphs of parent functions
72 Identify equations of parent functions

Unit 12 Conics

73 Identify a conic from graph
74 Identify a conic from equation

Unit 13 Variations

75 Write equation for direct, inverse and joint variation problems
76 Find the constant of variation

Unit 14 Sequences/Series

77 Write n terms of an arithmetic sequence
78 Find the sum of a finite arithmetic series
79 Write n terms of geometric sequence
80 Find sum of geometric series
81 Use formulas to find nth term
82 Identify sequence/series as arithmetic, geometric or neither

Unit 15  Statistics

83 Determine probabilities associated with areas under the normal crve
84  Compute permutations and combinations

 
If you made it this far, here's my call for help:  Anyone have advice/suggestions for how to make this work and/or a better way to organize the information into cohesive units that seem to occur in a somewhat logical order?  There is and will continue to be an emphasis on function families and transformations (as there should be).  I find it difficult to express on paper how each function category needs to be a resting place, but they are all connected in the ways that transformations apply.  Any ideas?
 
...oh...and I'm going to be teaching one section of deaf students and one section of blind students...in case that makes a difference

**edit:  I've added links to the old and new Virgina SOLs for Algebra 2 if anyone's interested**

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properties of quadrilaterals

Trapezoids:A pair of opposite sides is equal in trapezoid.If non-parallel pairs of opposite sides are equal then it is called as isosceles trapezium.The angles on the both sides of the base are equalThe sum of the adjacent angles are equal to 180oA trapezoid is nota parallelogramKite:The adjacent sides are equal, so it kites two pairs of equal sides. The diagonal angles is equal to 90oOne pair of opposite angle is equalThe diagonal is bisected by a longer diagonal

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