# Christian Marks

Ecumenical dispatches from the London Library

## The Official Tea Party Platform?

As difficult as it is to believe, this site ranks second out of 18 million search results (not counting aggregated news at the top) in a Google search on Official Tea Party Platform (without quotation marks). Even more astonishingly, this site ranks first in a Google search of “Official Tea Party Platform” (with quotes). The link to which these searches refer has maintained its search engine supremacy for two years. I have not sought to profit from the fickle finger of fate–I don’t know where the finger has been, or if investigation would be probative.

It’s enough to convert an agnostic to the unswerving mystical belief in a wry, aloof cosmic sense of humor.

UPDATE: Shortly after the Google search rankings were mentioned on this site, the ranking of Official Tea Party Platform dropped below Wikipedia and an August 28 article of the New York Times.

Written by Christian Marks

September 4, 2012 at 12:39 AM

Posted in Uncategorized

with one comment

This had been foreseen. That’s the trouble with being a visionary: you can’t cash in if you are too far ahead of your time.

Algorithmic trading, also known as high frequency trading (HFT), is rapidly replacing human decision making, according to a UK government panel which warned that the right regulations need to be introduced to protect stock markets. Around one third of share trading in the UK is conducted by computers fulfilling commands based on complex algorithms, said the Foresight panel in a working paper published yesterday. Nevertheless, this proportion is significantly lower than in the U.S., where three-quarters of equity dealing is computer generated. The Foresight panel, led by Dame Clara Furse, the former chief executive of the London Stock Exchange, argued that there are both benefits and severe risks to algorithmic trading. There was ‘no direct evidence’ that the computer trading in itself increased volatility, it said, but in specific circumstances it was possible for a series of events with ‘undesired interactions and outcomes’ to occur and cause massive damage.”

Written by Christian Marks

September 12, 2011 at 12:58 AM

Posted in Uncategorized

Ricardo’s concept of comparative advantage was forged in a world where labor and capital were essentially fixed. England could weave cloth more efficiently than Spain, but Spain could make wine more efficiently than England. Therefore, they would both benefit from trade given that each of these countries had a comparative benefit or efficiency to offer. The assumption under comparative advantage is, while the composition of employment would change under trade (more weavers employed in England and more wine makers in Spain), the level of employment would stay virtually the same. Meanwhile the citizens of England would get cheaper wine and the Spanish cheaper cloth.

In today’s world, labor and capital are not fixed. Capital flows wherever the input costs are the cheapest, such as labor and materials. Companies can set up operations in many places around the world. For instance, an American multinational no longer has to produce in the country where it sells, given existing trade treaties that lower tariffs. They can shift production to China or Mexico where the labor costs are a fraction of what it is in the U.S. and not be penalized by tariffs or quotas. In effect workers get fired in the U.S.; this leads to a loss of income for the working and middle classes. The workers in Mexico and China benefit because they have jobs, albeit at low wage rates and substandard conditions in many cases. Contrary to received wisdom, prices for some products might be lower, but not significantly so. The difference in wages (from those in the developed world versus the developing world) goes to investors, or more accurately these days, management. This is trade by absolute advantage, not comparative advantage.

For a while GDP growth seems to be fine. But with production set up abroad, the U.S. runs trade deficits and Americans by definition incur more debt to buy these goods. NAFTA encourages this. As a member of the WTO, China benefits from this trade agreement in that its goods are levied with lower tariffs than would otherwise be the case. Moreover, China manipulates its currency to keep it artificially low. Under a reciprocal trade regimen, the currency of a country that exports more than it imports should rise. A rising currency would act as a braking system to bring trade flows back into equilibrium. But the U.S. and China do not want that. China needs to keep selling goods to the world to continue growing fast enough to generate enough jobs. Despite its protests from time to time, the U.S. government does not
want this because it is captured by the multinationals, which make much more money not employing Americans (or Europeans for that matter). So when media pundits and approved economists say they are puzzled by the lack of employment growth, it is theatre, a necessary piece of kabuki to keep their jobs as propagandists.

Free trade under a truly Ricardian model of comparative advantage is theoretically beneficial to the world because at its heart lies the assumption of full employment. Instead what is touted as free trade is not Ricardian; it is a model of absolute advantage that ensures that the wages of labor are depressed, thereby enabling the rise in income for the top 1%.

The problem for the elites is that these are not sustainable political or economic policies because eventually unemployment will reach unacceptable levels and the right leader will come along and tell the real story to the American people.

****

As long as the political power of the middle and working classes has been undermined and blunted, U.S. multinationals will not hire Americans if they can offshore production. Therefore, people need to be organized to buy goods and services from small businesses whose interests are more aligned with that of the nation. Also, Wall Street should be boycotted. Do not do business with big banks. (I belong to a credit union.) Invest in regional financial institutions. Wall Street, because of its power over Washington, has been able to push through unfair trade bills in exchange for the right to set up shop in those foreign countries that benefit from access to American markets. But it is a one-sided deal in practice. U.S. access to foreign markets translates to this: multinationals offshore production and export to the U.S. at low or nonexistent tariffs.

If you want access to Chinese markets you must manufacture and hire people in China. Also, you must share your intellectual property with local firms. Multinationals accept this as the cost of doing business in China, although the real cost is being borne by the working and middle classes in this country.

Unless there is a substantial reversal in these policies, expect many years of sub par economic growth and high unemployment in the U.S. So why should anyone be surprised when the U.S. GDP growth rate for the second quarter is dismal? Unless of course, they are paid to be surprised.

Written by Christian Marks

July 31, 2011 at 10:54 PM

Posted in Uncategorized

## Kabuki

The headline  ”Unemployment creeps up to 9.2%” reverberated through the Internet on Friday when the Bureau of Labor Statistics reported that the U.S. economy produced 18,000 jobs in June–fewer than the 25,000 jobs the previous month. In its article on the Labor Department report, “Job Growth Falters Badly, Clouding Hope for Recovery“, a startled New York Times wrote, “Economists were stunned. They had been expecting job growth to strengthen in June as oil prices eased and supply disruptions caused by the Japanese tsunami and earthquakes receded… .”

Either the economists are not very good at their job or they are reading from the same official script. The script being this: say anything as long as the real ills of the economy are not diagnosed properly. The media-designated experts chatter away but say nothing. It is all theatre.

The U.S. economy will not create enough jobs if

1. So-called free trade agreements are not revised to have real reciprocity;
2. Tax breaks continue to go to multinationals that ship jobs overseas;
3. Tariffs are not imposed on countries with which the U.S. has substantial trade deficits through currency manipulation, tax subsidies and other mercantilist policies;
5. A steeply progressive tax system is not enacted;
6. Antitrust prosecutions are not instituted against banking, insurance, pharmaceutical, agricultural, and media conglomerates; and
7. The social contract is not rewritten to provide for decent wages and medical care for all workers.

The list can go on.

Written by Qfwfq

July 10, 2011 at 12:09 AM

Posted in Uncategorized

## A co-topological category

with one comment

This post describes a nearly useless category that reminds me of the topologies associated with categories of coalgebras for a set endofunctor.

Let ${X, Y}$ be topological spaces. A not-necessarily continuous map ${f:X\rightarrow Y}$ is open if for every open set ${U\subset X}$, ${f[U]}$ is open in ${Y}$. The category ${\mathbf{Opt}}$ of topological spaces and open maps has the same isomorphism types as the category ${\mathbf{Top}}$ of topological spaces and continuous maps.

Proof: A map is an isomorphism in ${\mathbf{Opt}}$ if and only if it is a homeomorphism in ${\mathbf{Top}}$. $\Box$

Coproducts exist in ${\mathbf{Opt}}$. In general, products do not exist in ${\mathbf{Opt}}$. However, something analogous to powers of a single space exist.

For a topological space ${X}$, ${\square X}$ (“the square of ${X}$“) denotes the topological space with underlying set ${X\times X}$ and topology generated by the basis

$\displaystyle \{ U\times V, \Delta_X[U] : U,V\,\mathrm{open}\,\mathrm{in}\,X\}$

where ${\Delta_X:X\rightarrow X\times X}$ is the diagonal. This topology is the smallest topology on ${X\times X}$ making the diagonal map open (and continuous).

The ${\square}$ construction defines an endofunctor ${\square}$ on ${\mathbf{Opt}}$ together with a natural transformation ${\delta_X:X\rightarrow\square X}$ (the same underlying map as ${\Delta_X}$) from the identity functor ${1_\mathbf{Opt}}$ to ${\square}$. There is a one-to-one correspondence between maps ${f:X\rightarrow Y}$ and maps ${g:X\rightarrow\square Y}$ such that ${\pi_1 g= \pi_2 g}$ for ${i=1,2}$, where ${\pi_i:\square Y\rightarrow Y}$ is the projection (projections are open).

Proof: Given a open map ${f:X \rightarrow Y}$, the open map ${\delta_Y f}$ satisfies ${\pi_1\delta_Y f = f = \pi_2 \delta_Y f}$. Conversely, a map ${g:X\rightarrow \square Y}$ with ${\pi_1 g= \pi_2 g}$ for ${i=1,2}$, defines ${f=\pi_1 g}$. Then

$\displaystyle \delta_Y f = (\pi_1 g \times \pi_1 g) \delta_Y = (\pi_1 g \times \pi_2 g) \delta_Y = (\pi_1 \times \pi_2) \delta_Y g = g$

$\Box$

Written by Christian Marks

July 6, 2011 at 3:37 AM

Posted in Bagatelle

## Ham Radio expeditions with two goats

WG0AT, the goat man of ham radio, has produced a series of videos that go well beyond logs of Field Day and Summits On The Air expeditions. The videos convey the addictive allure of QRP (low-power) DX (distance) ionospheric propagation; the older-male demographic of amateur radio and the relative absence of women; the rarefied club of CW (morse code) operators; the association of ham radio with the military and civil defense; and off-the-grid consumerism, which combines American rugged individualism with an inextricable dependence on miniaturized high-tech electronics, geo-positioning satellites, chemical engineering, and cellular telephony. WG0AT has a knack for translating into English the Capridese irony of his two rescued goats Rooster and Peanut, who provide running commentary and comic relief.

Written by Christian Marks

July 3, 2011 at 6:46 PM

Posted in Uncategorized

## The tyranny of the majority function

The majority function ${m_3:2^3\rightarrow 2}$ of three variables is

$\displaystyle m_3(a, b, c)= (a \land b) \lor (a \land c) \lor (b \land c)$

The majority function ${m_5}$ of five variables is definable in terms of ${m_3}$:

$\displaystyle m_5(a,b,c,d,e)= m_3(m_3(m_3(a,b,c),d,e), m_3(a,m_3(b,c,d),e), m_3(a,b,m_3(c,d,e)))$

In two variables, the only functions derivable in the term algebra generated by ${m_3}$ are the projections. We clearly have ${m_3(x,x,y)=x}$; the rest is an induction. It follows that neither ${x\lor y}$ nor ${x\land y}$ is definable in the term algebra of ${m_3}$ over two variables. Likewise for negation.

The following function is the majority function for four voters ${(a,b,c,d)}$, where the first will break a tie.

$\displaystyle m_5(a,a,b,c,d)=m_3(m_3(a,c,d),m_3(a,m_3(a,b,c),d),a)$

Some facts. The ${n}$-fold cartesian product ${2^n}$ of ${2=\{0,1\}}$ is a poset with ${v\le w}$ iff ${v_i\le w_i}$ for ${1\le i\le n}$. For a term ${t}$ in the term algebra of ${m_3}$ over the variables ${x_1,x_2,\ldots}$, we borrow a notation from type theory and write ${v:t\triangleright x}$ to assert that term ${t}$ evaluates to ${x\in 2}$ on argument ${v\in 2^n}$. We have the following properties.

If ${v:t\triangleright 1}$ and ${v\le w}$ then ${w:t\triangleright 1}$.

If ${v:\triangleright\, 0}$ and ${w\le v}$ then ${w:\triangleright\, 0}$.

We’ll prove the first by induction. This is true for a variable. If ${t}$ is ${m_3(t_1,t_2,t_3)}$ and ${v:t\triangleright 1}$, then there exist ${i\ne j\in\{1,2,3\}}$ such that ${v:t_i\triangleright 1}$ and ${v:t_j\triangleright 1}$. By induction, ${w:t_i\triangleright 1}$ and ${w:t_j\triangleright 1}$. Hence ${w:m_3(t_1,t_2,t_3)\triangleright 1}$.

Once consequence of this that negation cannot be represented in the term algebra generated by ${m_3}$.

The median algebra

I wimped out and checked the Wikipedia, according to which the majority function ${m_3}$ is a median algebra; i.e., a set with a ternary function ${m_3}$ satisfying the following four axioms.

1. ${m_3(x,x,y)=x}$
2. ${m_3(x,y,z)=m_3(z,x,y)}$
3. ${m_3(x,y,z)=m_3(x,z,y)}$
4. ${m_3(m_3(x,w,y),w,z)=m_3(x,w,m_3(y,w,z))}$

Equations before rhetoric

The conventions of tensor notation state that free upper (lower) indices must occur once on each side of an equation in the same position, upper or lower. Bound (or dummy) indices must occur in the upper and lower indices of a term; the terms are summed according to the Einstein summation convention. Tensor notation barely distinguishes vectors from covectors: vector coordinates have upper indices; covector coordinates have lower indices. In a doubly indexed array ${A_{r, \ell}}$ the first index ${r}$ is the row number and the second index ${\ell}$ is the column number; in a doubly indexed array with an upper and lower index, we would write ${A^r_\ell}$: the Row index is the uppeR index and the Lower index is the coLumn index (I need mnemonics: uppeR Row, Lower coL).

Consider two bases ${(e_1,e_2,e_3)}$ (the “old” basis) and ${(\overline{e}_1,\overline{e}_2,\overline{e}_3)}$ (the “new” basis). A vector v in the old and new coordinates is ${v=x^i e_i=\overline{x}^i\,\overline{e}_i}$. The transition matrix from the old basis to the new basis is given by ${\overline{e}_j=S^i_j e_i}$ by the conventions of tensor notation. The inverse transition matrix is ${e_j=T^i_j\overline{e}_i}$, where ${S^i_k T^k_j=T^i_k S^k_j=\delta^i_j}$. But then, ${v=x^j e_j = x^j T^i_j\overline{e}_i = (T^i_j x^j)\overline{e}_i=\overline{x}^i\,\overline{e}_i}$. Equating coordinates, we have that ${\overline{x}^i = T^i_j x^j}$.

This says that the coordinates of a vector in the new basis transform from the coordinates in the old basis under the inverse of the transition matrix from the old basis to the new basis. Well, it beats writing ${\Sigma}$.

Covariant vectors (covectors) have lower-indexed coordinates, which transform under rules dual to those for (contravariant) vectors, i.e., ${\overline{a}_j = S^i_j a_i}$ and ${a_j = S^i_j \overline{a}_i}$, where ${\overline{e}_j=S^i_j e_i}$ defines the transition matrix from the old basis, and where ${T^i_j}$ is the inverse. We have assumed that covectors can be defined with respect to the basis for which we defined vectors under a one-to-one correspondence that respects linear operations. Note that the direction of coordinate dependence has reversed: the coordinates of a covector in the new (corresponding dual) basis transform from the coordinates in the old (corresponding dual) basis under the transition matrix from the old basis to the new basis.

The transformation rules defined show ${\overline{a}_i \overline{x}^i=a_i x^i}$: ${\overline{a}_j \overline{x}^j = S^i_j a_i T^j_k x^k = a_i S^i_j T^j_k x^k = a_i \delta^i_k x^k = a_i x^i}$.

My relationships are none of my business

My uncle and I drove past the elevated train. He pointed to the grizzled bums on the street. “They’ve given up.” One of them came over, and leaned into the windshield. His teeth were missing. “What are you going to do when your looks fade?” my uncle said. The bum backed away.

Written by Christian Marks

June 30, 2011 at 11:46 PM

Posted in Uncategorized