creation myths and numbers

Recursion is the first cognitive step in the process of abstraction. It helps us overcome the restrictions imposed by our innately empiricist view of the world. Number systems emerge when one asks the question "What comes right after number N?" Creation myths arise when one asks the question "What comes right before year N?"

One prediction that this makes in Pirahã follows from the suggestions of people who worked on number theory and the nature of number in human speech: that counting systems—numerical systems—are based on recursion, and that this recursion follows from recursion in the language. This predicts in turn that if a language lacked recursion, then that language would also lack a number system and a counting system. I've claimed for years that the Pirahã don't have numbers or accounting, and this has been verified in two recent sets of experiments, one of which was published in Science three years ago by Peter Gordon, arguing that the Pirahã don't count, and then a new set of experiments which was just carried out in January by people from Brain and Cognitive Sciences at MIT, which establishes pretty clearly that the Pirahã have no numbers, and, again, that they don't count at all.

...Peter Gordon and I were colleagues at the University of Pittsburgh, and Peter did his Ph.D. at MIT in psychology, with a strong concern for numerosity. We were talking, and I said, there's a group that doesn't count—I work with a group that doesn't count—and he found that very difficult to believe, so he wanted to go do experiments. He went, and I helped him get going; he did the experiments, but his explanation for the reason that the Pirahã don't count is that they don't have words for numbers. They only have one to many. I claim that in fact they don't have any numbers. His idea is that the absence of counting in Pirahã has a Whorfian explanation—that there's a linguistic determinism: if you lack numbers, you lack counting—that is, that the absence of the words causes the absence of the concepts. But this really doesn't explain a lot of things. There are a lot of groups that have been known not to have more than one to many—as soon as they got into a relationship where they needed it for trade, they borrowed the numbers from Portuguese or Spanish or English or whatever other language.

The crucial thing is that the Pirahã have not borrowed any numbers—and they want to learn to count. They asked me to give them classes in Brazilian numbers, so for eight months I spent an hour every night trying to teach them how to count. And it never got anywhere, except for a few of the children. Some of the children learned to do reasonably well, but as soon as anybody started to perform well, they were sent away from the classes. It was just a fun time to eat popcorn and watch me write things on the board. So I don't think that the fact that they lack numbers is attributable to the linguistic determinism associated with Benjamin Lee Whorf, i.e. that language determines our thought—I don't really think that goes very far. It also doesn't explain their lack of color words, the simplest kinship system that's ever been documented, the lack of recursion, and the lack of quantifiers, and all of these other properties. Gordon has no explanation for the lack of these things, and he will just say, "I have no explanation, that's all a coincidence".

...When I began to tell them the stories from the Bible, they didn't have much of an impact. I wondered, was I telling the story incorrectly? Finally one Pirahã asked me one day, well, what color is Jesus? How tall is he? When did he tell you these things? And I said, well, you know, I've never seen him, I don't know what color he was, I don't know how tall he was. Well, if you have never seen him, why are you telling us this?

...The Pirahã, who in some ways are the ultimate empiricists—they need evidence for every claim you make—helped me realize that I hadn't been thinking very scientifically about my own beliefs.

(Source)
 

Because of their culture's ingrained emphasis on referring only to immediate, personal experiences, the tribesmen do not have words for any abstract concept, from colour to memory and even to numbers. There is no past tense, he says, because everything exists for them in the present. When it can no longer be perceived, it ceases, to all intents, to exist. "In many ways, the Pirahã are the ultimate empiricists," Professor Everett says. "They demand evidence for everything."

Life, for the Pirahã, is about seizing the moment and taking pleasure here and now. "I suddenly noticed how excited they were whenever planes crossed the sky then disappeared. They just love sitting around watching people coming around the bend in the jungle. Whenever I came into the village then left, they were amazed."

The linguistic limitations of this "carpe diem" culture explain why the Pirahã have no desire to remember where they come from and why they tell no stories.

(Source)
 

Over the course of three weeks, Everett wrote what would become his Cultural Anthropology article, twenty-five thousand words in which he advanced a novel explanation for the many mysteries that had bedevilled him. Inspired by Sapir’s cultural approach to language, he hypothesized that the tribe embodies a living-in-the-present ethos so powerful that it has affected every aspect of the people’s lives. Committed to an existence in which only observable experience is real, the Pirahã do not think, or speak, in abstractions—and thus do not use color terms, quantifiers, numbers, or myths. Everett pointed to the word xibipío as a clue to how the Pirahã perceive reality solely according to what exists within the boundaries of their direct experience—which Everett defined as anything that they can see and hear, or that someone living has seen and heard. “When someone walks around a bend in the river, the Pirahã say that the person has not simply gone away but xibipío—‘gone out of experience,’ ” Everett said. “They use the same phrase when a candle flame flickers. The light ‘goes in and out of experience.’ ”

(Source)

Living the moment... Demanding evidence for every claim... Don't these sound like familiar aspirations? I feel like these people are light years ahead of us when it comes to cultural advancement.

Some languages predispose their speakers to leave the present. Although our minds are innately capable of going back and forth in time, our tendency to do so increases immensely once the capability becomes institutionalized through language acquisition.

Here is an interview about a man who learned his first language when he was 27 years old. SS refers to the person who taught him English.

RW: Was Ildefonso able to tell you anything about his life before? I take it he did become ordinarily competent in language.

SS: He did. I'm going to guess that at about six or seven years old he was herding sheep and goats and begging. Think about that. His brain was kept alive with problem solving. He had to be taught somehow that you go to this street and put your hand out, or your cup out, and try to get money even though he didn't know what money was.

Back to your question. Of course, you and I are interested in learning what was it like? It's another frustration that Ildefonso doesn't want to talk about it. For him, that was the dark time. Whenever I ask him, and I've asked him many, many times over the years, he always starts out with the visual representation of an imbecile: his mouth drops, his lower lip drops, and he looks stupid. He does something nonsensical with his hands like, "I don't know what's going on." He always goes back to "I was stupid."

It doesn't matter how many times I tell him, no, you weren't exposed to language and... The closest I've ever gotten is he'll say, "Why does anyone want to know about this? This is the bad time." What he wants to talk about is learning language.

RW: What does he say about that?

SS: He uses "dark" and "light." That's when everything "became light." That's when he understood that he could ask questions and get answers. He learned that there were explanations. Before, he'd had to figure out everything on his own. He could get macho behavior. You could see that. But if he couldn't see it, like history... He had no clue why he was picked up by people wearing green and put back in brown-skin land. So he wanted to talk about what you could do with language. Did you know that you could talk to anyone in the world! Did you know that you could read!

The only thing he said, which I think is fascinating and raises more questions than answers, is that he used to be able to talk to his other languageless friends. They found each other over the years. He said to me, "I think differently. I can't remember how I thought." I think that's phenomenal!

RW: It is. It's quite... well, I don't know what it is.

SS: As far as the critical language learning period goes, of course, his adult brain couldn't learn language as well as a child's brain. But he's got a lot of language! Where he gets lost is especially with too many references to time in one sentence. He can't handle too many tenses in one sentence. But he can handle more than one reference and he can handle any amount of information. He did learn language. The few problems he has are nothing compared to not having language.

But the second thing is the psychological slash philosophical things with language. He says he thinks differently. However, there are a few things he doesn't think differently about. I try to meet him once a year and I always ask him, "When was the last time we saw each other?" I ask him a "when" question because it tickles me. Time was the hardest thing for him to learn. And he always prefers to say "the winter season" or "the Christmas time." He wants to point to a season or to a holiday. It's not a cognitive problem. To this day, he thinks it's weird that we count time the way we do. He can do it, but he doesn't like it. Think about it. For twenty-seven years, he followed the sun. He followed cows. He followed the seasons. It's that rain-time of the year.

RW: And this is how people have done it in more traditional societies.

SS: There's some sanity in it. We care too much about counting time. Every single religion and spiritual practice that I've ever seen has something in it about living in the present. So there's some sanity in it.

(Source)

codifiable knowledge

While a practitioner over-emphasizes the importance and the share of non-codifiable knowledge in his field, an academician does the exact opposite. The latter's behaviour is understandable since

1) Only what is codifiable can be transferred to students inside a classroom environment, in a short duration of time.

2) Due to its higher level of generality and explicitness the codifiable knowledge has greater scientific value.

Practitioners, on the other hand, ignore the successful academic codifications at their own peril. Since most can not help making their own attempts at codification, they often end up reinventing the wheel or coining some awkward terminology.

Here are two examples from the finance world. I am sure one can find plenty of examples from other fields as well:

- McComish coins the term "anti-cash" in his book Anti-Logic

- Soros invents the term "reflexivity" in his book Alchemy of Finance

The former concept is awkward and unenlightening. The latter was codified in academia a long time ago. It was sad to hear Soros describing his finding as a major philosophical discovery.

alphabet and philosophy

Some of our biases are so engrained that it took us literally a few thousands years to unearth them.

Acquisition of a language involves a high dose of cognitive indoctrination. This indoctrination starts at a very early stage: During the internalization of the alphabet, our perception of reality becomes altered in subtle ways.

Writing creates an artificial memory, whereby humans can enlarge their experience beyond the limits of one generation or one way of life. At the same time it has allowed them to invent a world of abstract entities and mistake them for reality. The development of writing has enabled them to construct philosophies in which they no longer belong in the natural world.

The earliest forms of writing preserved many links with the natural world. The pictographs of Sumer were metaphors of sensuous realities. With the evolution of phonetic writing those links were severed. Writing no longer pointed outwards to a world human shared with other animals. Henceforth its signs pointed backwards to the human mouth, which soon became the source of all sense.

When twentieth-century philosophers such as Fritz Mauthner and Wittgenstein attacked the superstitious reverence for words they found in philosophers such as Plato they were criticising a by-product of phonetic writing. It is scarcely possible to imagine a philosophy such as Platonism emerging in an oral culture. It is equally difficult to imagine it in Sumeria. How could a world of bodiless Forms be represented in pictograms? How could abstract entities be represented as the ultimate realities in a mode of writing that still recalled the realm of the senses?

It is significant that nothing resembling Platonism arose in China. Classical Chinese script is not ideographic, as used to be thought; but because of what A.C. Graham terms its 'combination of graphic wealth with phonetic poverty' it did not encourage the kind of abstract thinking that produced Plato's philosophy. Plato was what historians of philosophy call a realist- he believed that abstract terms designated spiritual or intellectual entities. In contrast, throughout its long history, Chinese thought has been nominalist- it has understood that even the most abstract terms are only labels, names for the diversity of things in the world. As a result, Chinese thinkers have rarely mistaken ideas for facts.

John Gray - Straw Dogs (Pages 56-57)

- The core of Wittgenstein's picture theory of meaning rests on the trivial discovery that Latin alphabet is non-pictographic.

- As the Chinese characters have lost touch with their pictographical origins, has the Chinese people become more susceptible to Platonism?

See for instance the evolution of the character for "horse":

- Both Arabic and Chinese scriptures admit beautiful calligraphical representations. However the Arabic alphabet is not pictorial. It is phonetic, just as Latin alphabet is. No wonder why the early Islamic philosophers were very fond of Aristotle and Plato...

cay bardagi

Ne zaman, kim buldu bilmiyorum ama inanılmaz bir dizayn! Batılılar neden bu dizaynı benimseyememiş gerçekten anlayamıyorum.

İnce belin yarattığı eğim bir taşla üç kuş vuruyor:

1) Ağız kısmındaki dışa açılan kıvrımı sayesinde, ince belli bardağı hiç bir enerji harcamadan (bardağın kendi ağırlığını kullanarak) kaldırabilirsiniz. Böylece parmaklarınızı yakmadan çayınızı rahatça içebilirsiniz. Sıcak bardağı ortasından sıkarak kavramanın ne kadar zor olduğunu farkeden Batılı ise kulp denen garip şeyi icat etmiş.

Sizce hangisi daha zekice? Olanı hafif eğmek mi, yoksa olana bambaşka bir parça eklemek mi? (İlkinin üretim sürecinin daha basit ve ekonomik olduğu kesin.)

2) Dibe çöken minik çay tanecikleri, çayınız bitinceye kadar sizi rahatsız etmez. Bardak yatay haldeyken bile ağzınıza girmezler çünkü ince belin yarattığı kaviste sıkışıp kalırlar. Batılı ise minik çay taneciklerin yarattığı problemi ancak “poşet çay” teknolojisiyle çözebilmiştir.

3) Havaya kaldırdığınızda ince belli bardak tam anlamıyla özgürlüğünü kaybedip kolunuzun bir uzantısı haline gelmez. Tutuş yönünüze dik açıdaki eksende sallanma özgürlüğünü korur. Böylece, bu eksen doğrultusunda (mesela yürürken) yaptığınız hareketler çayınızın dökümesine sebep olmaz. Oysa kulplu bardakla hareket ederken çok dikkatli olmanız gerekir.

abstract valuation theory

Let M be a DCF (Discounted Cash Flow) valuation model. M could, for instance, be an Excel spreadsheet model constructed by an investment bank analyst for the purpose of determining the enterprise value of a company. More generally, M can be regarded as a function from S to R^∞ where S is the space of all possible configurations of assumptions and R^∞ is the infinite dimensional real vector space. Each point s∈S encodes all the assumptions needed for the valuation of the company, and each v∈R^∞ is an infinite vector of future cash flows where v_t is the cash flow at time t.

We will assume that S is large but nevertheless finite.

For an illustration of the new terminology, note the following two observations:

- The technique of scenario analysis can be broken down into two simple steps. First select a small subset S' of S, and then present the value of M at each s∈S'.

- The technique of sensitivity analysis consists of a depiction of what happens to M(s) as s∈S varies.

Analysts try hard to come up with the right discount rate for the company being valued. This calculation is important since the NPV (Net Present Value) of a company is determined uniquely by the discount rate d (a positive real number) and the projected stream of cash flows v.

Let R^e stand for the extended real number line and R^+ stand for the positive real numbers. Then NPV can be viewed as a function from (R^∞)x(R^+) to R^e. It maps a pair (v,d) to Σ(v_t/((1+d)^t)) where the infinite summation is taken from t=1 to ∞. (Note that this infinite series does not necessarily converge for a given (v,d). That is why we set the range of NPV as the extended real number line.)

For the determination of the appropriate discount rate, analysts either rely on garden-variety asset pricing models (such as CAPM) or create their own models. Each such model D can be viewed as a function whose domain is S and whose range is R^+. This makes sense since the calculation of the discount rate depends on the set of assumptions relevant to the valuation of the company.

Remark Both M and D are defined in such a generality that even intuition-based guesses qualify to be considered as "models".

Let P be a probability measure on S. Think of P as a function from S to the closed line segment [0,1], assigning probability P(s) to scenario s∈S. Moreover, P is chosen in such a way that the sum of all P(s) is 1. (i.e. It is believed that at least one of the scenarios in S will be realized.) Introduction of a probability measure into the picture allows us to utilize analyst's beliefs about the likelihood of each set of assumptions in S. Some scenarios, for instance, will be so nonsensical that they will be assigned zero probability.

Let's see what sorts of meaningful definitions we can make about the space of all valuation models M.



For the first five definitions, fix some arbitrary D.

Definition 1 We say that s∈S is M-equivalent to s'∈S if NPV(M(s),D(s)) = NPV(M(s'),D(s')). In other words M gives the same valuation under both scenarios.

Definition 2 We say that model M is more (s,s')-sensitive than model N if |NPV(M(s),D(s))-NPV(M(s'),D(s'))| is greater than |NPV(N(s),D(s))-NPV(N(s'),D(s'))|.

Definition 3 Expected-P-NPV of M, denoted by ∫(P,M), is Σ(NPV(M(s),D(s))*P(s)) where the finite sum ranges over s∈S. This quantity gives you the NPV expected by the analyst who assigns probability P(s) to scenario s∈S. Even if two analysts have wildly different probability measures P and P', they may end up agreeing on the expected NPV of M. In other words, ∫(P,M) may be equal to ∫(P',M) even if P≠P'. Although the sum involved in the definition is finite, ∫(P,M) may nevertheless be infinite because each NPV(M(s),D(s)) is an infinite sum. Of course, for reasonable M and P, either NPV(M(s),D(s)) will be finite or P(s) will be zero.

Definition 4 P-Covariance between M and N, denoted by Cov(P,M,N), is Σ((NPV(M(s),D(s))-∫(P,M))*(NPV(N(s),D(s))-∫(P,N)) where the finite sum ranges over s∈S. This definition corresponds exactly to what is called covariance in statistics.

Definition 5 P-Correlation between M and N, denoted by Corr(P,M,N), is Cov(P,M,N)/((√Cov(P,M,M))*(√Cov(P,N,N))). This quantity reflects the strength of a linear relationship between valuations given by M and N.



For the next three definitions, fix some arbitrary D and P.

Definition 6 We say that model M is equivalent to model N if NPV(M(s),D(s))=NPV(N(s),D(s)) for s∈S. If this is the case, we write M≅N. Since our goal is to value a company, it makes sense to not distinguish models that output the same NPV under every scenario.

Definition 7 We say that model M is probabilistically equivalent to model N if P({s|NPV(M(s),D(s))=NPV(N(s),D(s))})=1. If this is the case, we write M≈N. While deciding whether M and N are equivalent, we should not care about a valuation difference under an impossible scenario s where P(s)=0.

Definition 8 We say that model M is expectationally equivalent to model N, if ∫(P,M)=∫(P,N). If this is the case, we write M∼N. While comparing M and N, we should only look at the average NPV predicted by each model.

Proposition 1 M=N implies M≅N implies M≈N implies M∼N. The proof is obvious. Also, note that the reverse implications may not hold.



For the rest of the definitions, fix only an arbitrary P.

Definition 9 We say that model M is P-viable if, for all s∈S such that P(s)≠0, there exists a positive real number d such that NPV(M(s),d) is finite. This condition ensures that M(s)_t does not grow in a crazy fashion as t goes to infinity. Of course, there may still be an impossible scenario s such that there is no positive real number d rendering NPV(M(s),d) finite.

Definition 10 We say that model M is viable if, for all s∈S, there exists a positive real number d such that NPV(M(s),d) is finite. A viable M is necessarily P-viable.

Definition 11 We say that the pairs (M,D) and (N,D') are in P-agreement if NPV(M(s),D(s)) = NPV(N(s),D'(s)) for all for all s∈S such that P(s)≠0.

Proposition 2 Given a pair (M,D) and a P-viable N, there always exists a D' such that (M,D) and (N,D') are in P-agreement. For a proof, pick an arbitrary s∈S such that P(s)≠0. Then there exists a positive real number d such that NPV(N(s),d) is finite. This implies that the function f(x)=NPV(N(s),x) is surjective. In particular, there exists a positive real number d' such that f(d') = NPV(M(s),D(s)). Let D'(s) be this d'. The resulting function D' from S to R^+ may look nonsensical as a "discount rate model", but nevertheless it exists.

Definition 12 Generalized NPV function is the map from (R^∞)x((R^+)^∞) to R^e, which takes a pair (v,d) to Σ(v_t/((1+d_t)^t)) where the infinite summation is taken from t=1 to ∞. We denote this function NPV in bold. Here each d∈(R^+)^∞ is an infinite vector of discount rates where d_t is the discount rate that NPV applies to the cash flow coming at time t.

Proposition 3 Let M be viable model. Then, for each s∈S and d∈(R^+)^∞, there exists a positive real number d' such that NPV(M(s),d) = NPV(M(s),d'). In other words, introduction of generalized NPV function does not seem to yield any additional insight in the space of viable models. As in Proposition 2, the proof follows from the surjectivity of the function f(x)=NPV(M(s),x).



The above theoretical musings have no practical value. Nevertheless they do point out some of the intricacies involved in the art of discounted cash flow valuation.

irrelevance of constancy

A steady sound, with constant frequency, intensity, and spectrum is annoying. Moreover, after a while, our conscious present would not register it any more. Only when that sound is turned off, may we suddenly realize that it had been there.

Roederer - The Physics and Psychophysics of Music (Page 6)

Auditory constancy is filtered out by the brain. Unchanging aspects of an ambience are not deemed important because they contain no information with regards to the dynamics unfolding in the ambience. Here is a simple mathematical formulation of this idea. Interpret X as a constant feature of the setting, and Y as an ongoing arbitrary event that can assume numerous different trajectories with non-trivial probabilities:

(Here X may have values other than "a" as well, but this region of inconstancy is assumed to be probabilistically insignificant. The lemma is copied from this book.)

The same idea also governs the way the brain treats visual inputs. Retina receptors can detect only fluctuations in illumination. However, there is an ingenious mechanism that allows us to detect visually steady objects as well. We have jittery eyeballs that artificially introduce the necessary fluctuations. Even if the book in front of you is staying still, since your eyeballs are active the image of the book on the retina is moving around.

We live in a constantly changing world, so nervous systems have evolved to detect changes in our environment. Motion in our visual field might indicate that a predator is approaching or that prey is escaping. Stationary objects generally pose less of a threat and so tend to be studiously ignored owing to neuronal adaptation mechanisms. Some nervous systems are specialized to detect only motion signals; for example, a frog might not see a resting fly, but will react rapidly as soon as the fly takes off. In a sense, this ability to see only moving objects might be true of all visual systems. Even our own visual system can detect stationary objects only because the images projected onto our retinas are never stationary for long. Involuntary fixational eye movements prevent the adaptation of our neurons to an unchanging environment. The movement of the retinal images is what keeps stationary objects of interest from fading perceptually. (Source)

(The last sentence here may be misleading. Not just the stationary objects of interest, but all stationary objects are kept from fading. In other words we can not consciously bring stationary objects in and out of our perception.)

Evolution has come up with a patch to compensate for a previous neural adaptation that ignored visual constancy. Now the brain is able to register steady images even while we are not moving our heads.

A similar counter-adaptation has not occurred in the auditory realm. Nevertheless we are able to overrun the brain's tendency to stop registering steady sounds. For instance, because of its underlying meaning, we will continue to register a civil defence siren despite its steady character.

P.S. Car alarms are extremely annoying because they are designed to be so. The manufacturers make sure that there is enough non-steadiness built into these sounds so that our brains can not filter them out. At this very moment I am being subject to one of these sounds, and I feel like I am going nuts. I wish I had the capacity to ignore any sound at will... All I can do now is to massage my forehead in a rhythmic fashion and fully subjugate myself to the pulse of the alarm.

distaste for uncertainty

Since the elevator was broken, we had no choice but to use the stairs to go to the roof. The theme of the party was "Michael Jackson" and each of us was looking forward to this retro night. At some point while we were still climbing the stairs, a friend paused and asked "How many more floors to go?" I said "Three!" Then I thought whether knowing the answer made her any better off. Our pace was slow and there was no need to take a break. So what compelled her to ask that question?

Uncertainty can get irritating sometimes and its resolution can cause great relief. I think this is what happened in the above story.

Here are some quite unrelated examples that demonstrate the universality of this distaste for uncertainty:

• The whole insurance industry is based on the desire to eliminate risk.
• Uncertainty prolongs economic crises. Companies hate it when the future becomes blurry.
• Terminal cancer patients feel better-off when they know how much time they have left.
• Countdown traffic lights relieves the stress caused by the uncertainty of go-time.
• "The Discovery Channel series MythBusters investigated Chinese water torture in the season 3 episode Brown Note, Water Torture, and found that dripping water on the forehead, by itself, was not particularly stressful. Immobilizing the subject along with a variable water drop schedule proved the most stressful of the methods they tried, and cold water intensified the effect. The key part of this is that the water drop was made to be randomly timed. Thus, the victim would not know when the next drop would come. This was meant, in turn, to drive the victim insane." (Source)
• Job insecurity causes greater stress than unemployment.
• "Religious believers have less anxiety because religion reduces uncertainty-related distress." (Source)
• For a long time physicists resisted the idea of absolute uncertainty. Einstein claimed "God does not play dice." Eventually the Copenhagen interpretation of quantum mechanics caused a paradigm shift in the understanding of nature.
• We have a tendency to see patterns, even in complete randomness. (e.g. clustering illusion) Such cognitive biases help us create order and meaning out of uncertainty.
• We like confident people who speak as if everything is certain and under their total control. "Financial advisors who insist they know whether stocks will go up or down in the future are seen as more credible and trustworthy than advisors who express modest confidence, even when both predict which way the stock’s price goes with equal accuracy (Price & Stone, 2004). Political experts who claim more certainty and make more extreme predictions are in more demand by the media (Tetlock, 2005). Sniezek and Van Swol (2001) found that advisors who expressed more confidence earned greater trust, were more likely to have their advice followed, and engendered more confidence in those receiving their advice." (Source)

Of course the perceived uncertainty may not be in line with actual uncertainty. In other words our distaste may be misguided:

We pride ourselves on being the only species that understands the concept of risk, yet we have a confounding habit of worrying about mere possibilities while ignoring probabilities, building barricades against perceived dangers while leaving ourselves exposed to real ones. Six Muslims traveling from a religious conference were thrown off a plane last week in Minneapolis, Minn., even as unscreened cargo continues to stream into ports on both coasts. Shoppers still look askance at a bag of spinach for fear of E. coli bacteria while filling their carts with fat-sodden French fries and salt-crusted nachos. We put filters on faucets, install air ionizers in our homes and lather ourselves with antibacterial soap. "We used to measure contaminants down to the parts per million," says Dan McGinn, a former Capitol Hill staff member and now a private risk consultant. "Now it's parts per billion."

At the same time, 20% of all adults still smoke; nearly 20% of drivers and more than 30% of backseat passengers don't use seat belts; two-thirds of us are overweight or obese. We dash across the street against the light and build our homes in hurricane prone areas--and when they're demolished by a storm, we rebuild in the same spot. Sensible calculation of real-world risks is a multidimensional math problem that sometimes seems entirely beyond us. And while it may be true that it's something we'll never do exceptionally well, it's almost certainly something we can learn to do better. (Source)

If we hate uncertainty so much, why do some people enjoy gambling? Here are possible reasons:

• Such people are more delusional and overconfident than the rest. They may also have a greater capacity to bear risk.
• In a casino the source of uncertainty is under your control. In principle you can always "leave the table". This makes you feel more secure.
• People prefer structured uncertainties over unstructured ones. Gambling games have a structured quantitative character. (See Ambiguity Aversion)
• The time of resolution of uncertainty in a gambling game is often known in advance. This is not the case for most real-life uncertainties.

formal semantics

Once we scribble down the mathematical formulation of an intuitive idea, an essential part of it may get lost in translation. I had touched upon this theme in an old post where I wrote about the mathematical formulation of randomness. Now I would like to give another example.

Model Theory does not use the word "semantics" in the usual sense.

Everything in mathematics is syntactical. There can be no semantics confined within mathematics. Symbols can not donate meanings to other symbols. Meaning is an interpretor-dependent concept. Although formal semantics does not completely banish the interpretor from the picture, it certainly pushes him as far away as possible. For instance, axiomatic formulations of Set Theory effectively reduce all semantic questions to one big semantic question: What does the symbol ∈ mean? If you are asked to teach this subject, you will have to tell your students that "a∈A means that a belongs A." At that moment you will be doing real semantics, namely asking your interpretors to interpret a symbol in the way you intend it to be interpreted. Since the notion of "belonging" is so primitive and intuitive, you will probably have no difficulties in conveying the correct interpretation.

sustainability of government debt

The following discussion took place between Onur Ozgode and myself. (Please keep in mind that he did not have time to write out full responses.)

Onur quotes a WSJ article and comments: "An interesting perspective on how much of government debt is sustainable in the aftermath of shocks to the national economies."

Onur - Wow that's crazy! I had no clue their debt/gdp ratio was so high! but then again the key is the fact that 95% of their debt is held by domestic investors, so it seems as long as they can preserve domestic balance, they are fine... The question is whether the US can do the same in the international scene.

Me - It should not matter whether the debt is held by domestic investors or not. The credit worthiness of the debtor is usually independent of the credit worthiness of the creditor. (Of course there are always some closed loops in this vastly complex network of who-owes-who.)

It does matter whether the debt is denominated in domestic currency or not. This is where your reference to "preservation of domestic balance" comes into play. Countries tend to default more often on their "external" debt for the obvious reasons. On the other hand, internal debt can always be "implicitly" defaulted on via inflation.

I do not understand what is meant by "unstable" in the WSJ article quoted above: "Also working in Japan's favor is the fact that nearly 95% of its outstanding government debt is held by domestic investors, a group who has few other investment options. In the U.S., foreigners hold roughly a quarter of the outstanding Treasury notes, making the market inherently more unstable."

1) Efficient pricing entails volatility. That is normal.

2) Having more customers is always a good thing.

3) If more bonds are changing hands more often, that means the market is more liquid. People prefer to pay more for things that they can get rid of efficiently in case the need arises.

4) In every securities market, there are long-term "passive" investors and short-term "active" investors. The article seems to suggest that the US and Japanese bond markets differ with respect to this composition. It also seems to imply that the greater the percentage of bonds that is being actively traded, the more unstable is the underlying market. This may or may not be true. Here is a reason for believing the opposite: Lesser the number of bonds trading, the more likely that the market price will be affected by erratic factors. Here I am referring to factors which are not "fundamentally" related to the valuation of the security that is being traded. For example, an investor may feel the need to dumb your bonds for liquidity purposes. (He may need cash for some reason.) If the market is "thin", his action may create a downward pressure on the prices. Meanwhile practically nothing has changed about your creditworthiness. Of course this downward pressure may not be long-lasting, but it nevertheless "destabilizes" the market price.

Onur - Merhaba Tarik, nice to hear from you after so many years!

And thanks a lot for this nuanced and technically rich response. we, the ppl who live in the earthn, need these explanations as to why we actually need efficient and deep markets especially in these times where it has become a virtue to bash markets for all the ills of collective life.

Nevertheless I have to respectfully disagree with your intervention, not b/c it is irrelevant or wrong, but because it is an incomplete account of the reality in the ontological sense. The problem is not whether you are simply right or wrong, or whether neo-classical theory of markets is a good theory of how markets function or not. Neither is it the simply the case that whether the inefficiencies due to the materiality upon which markets are constructed are an enough of a source of error to make efficient markets hypothesis invalid or not. We all know that the theory of markets do not match perfectly well onto the way in which markets work in reality on the ground in everyday basis. This divergence from the theory of markets due to the inefficiencies and frictions inherent into the world is not my real concern.

For me the real issue in both the case of Japan and the US seems to be not about the technicality of how to make markets work efficiently, but about the institutional configurations upon which markets are inserted to reach a certain goal by the state. To put it more simply, it is a question of political economy and not simply good economics or financial theory.

I would not want to pretend that political economy is a force that is in direct opposition to the market, at the end of the day which is a techno-political technology of government anyways. I think what matters is how markets are integrated into an institutional configurations, be it the international monetary system or the national state-private sector structure.

So, what I mean by "domestic balance" in the case of Japan's state-private sector structure which to my knowledge is very corporatist to this day. I am not an expert on this but as far as i understand the liberal set up of strict state-capital differentiation does not apply to way in which the japanese capital is organized and how that organization relates to the state. that is probably why japan can keep carrying such high levels of debt-gdp ratio to begin with. in a way it might be interesting to compare it to the war economies in liberal western countries such as UK and US during and in the aftermath of world war II where capital has vested interest in supporting the deficits of governments for an extended period of time without much hesitation.

In the case of the US, on the other hand, we have to not forget much of the creditworthiness of the US is derived from its position within the political economy of the international monetary system. Not only the dollar is the most dominant reserve currency, but also it is the only currency through which oil can be traded. Furthermore, this structure is enhanced further by a US-China tacit agreement over financing the ever-growing american deficit. So, in my mind the question of stability drives at a much deeper level than that of the market stability. In other words, it is a matter of structural stability of the global political economy as opposed to the market stability. We are already seeing movements that try to even out these imbalances in the structure of the international monetary system. afterall you should not forget that markets are integrated into the system only after the system is constituted in a particular configuration and as that configuration changes the markets will have to adapt too.

Logan - I won't pretend to have the same understanding of finance and economics as you two, but isn't the WSJ article simply suggesting that when sovereign debt is held domestically, the creditors have a greater interest in the stability of the bond market, since they live and work in -- and rely on the economic stability of - the country they are lending to? Whereas the US bond market is dominated by foreign investors who may have less of an interest in that stability -- or might even use it as a tool of foreign policy?

Is this a point you've already made, Onur? I am sorry if I missed it.

In any case, I find this debate very interesting and don't mean to interrupt it.

Me - I did not mean to get in to the technical details. But unfortunately the devil usually resides in the details.

My thinking may have resembled the neoclassicists'. However the resemblence is only at a superficial level. I did not make any ideological claim. I did not refer to any complex phenomenon that admit more than one coherent interpretation.

All I did was to point out some almost-tautologically-true facts. (e.g. Holding everthing else constant, having a more liquid bond market and having more demand for your bonds are good things.) Yes, my use of the word "efficient" was referring to the Efficient Markets Hypothesis of the Neoclassical School. But again the reference was rather superficial. I do not need to convince you that values of goods naturally fluctuate. Even if you do not believe in the existence of a fundamental value and even if you do not believe in the capability of free markets to reveal this value, you will still admit that prices in healthy markets fluctuate. In some sense even wild fluctuations are more natural then no-fluctuation-at-all. There is something inherently unstable about values of goods. The source of this instability probably goes beyond economics and politics.

Here is a list of responses/observations/suggestions. (There is no natural flow to it. Sorry.)

1) I am not expert on this issue. But I bet that all government bond markets today enjoy similar legal frameworks. These frameworks cater to the big participants. If you want money, the easiest way to obtain it is to create an institutional framework that caters the investors. Of course, you can also print money, but then you will have to face the consequences.

2) You can start with the same configuration and end with two different market structures. the composition of the participants with respect to active vs passive investor types is one of the parameters that the two structures can different among. These differences are simply due to the fact that you can not configure everything if you also want to give participants some degrees of freedom.

3) You tend to used the word "organised" for both the framework and the activity that is being frameworked. (e.g. "...the japanese capital is organized...") Once you set the framework, the capital flows freely among the participants. To call the resulting total structure organized can be misleading.

4) Here is a point you may find interesting. Institutional frameworks rest on laws. Due to the extremely large spectrum of possible events, laws can never totally specify the courses of action to be taken should any of these events arise. In other words, institutional frameworks are by definition "incomplete." Hence even if you have the perfect execution system, there will be smart people who will be able to game the framework. That is essentially the job of many tax experts in investment banks. It would not be wrong to say that, on average, those who try to cheat the system are smarter than those who build/revise/run the system. (In fact, this was the opinion of a tax expert who spent some time on the government side. I am willing to take his word. The mentioned asymmetry is essentially due to salary differences.)

5) When you make a cross-country analysis of economic organizations, you have to be really careful. When you make a cross-country and cross-time analysis, you have to be even more careful. Two illustrations:

5a) If people want to save, you can not force them to spend money. If companies do not want to invest no matter how low the interest rates are, you can not force them to invest. (Of course you can order the government-owned companies to invest. But at the end of the day, you can not force the end-consumers to buy the goods that these investments will produce. In other words, if you make a decision against the market today, you will suffer the financial consequences sooner or later.) This is partly the case in Japan where there has been a "savings-glut" for years. Hence country-specific, non-organizational issues are extremely important. You can have the exact institutional framework as Japan's, but an entirely different Debt-GDP ratio.

5b) Of course you have to bring "time" into your analysis at some point. For example, high public debt that Japan has accumulated today is partly due to the political decisions that were taken in the past for the sake of stimulating the domestic economy.

5c) During times (e.g. war) when there are great uncertainties and unstabilites, capital flows to the safest places. People will not desire to invest, because there are too many unknowns and it is impossible to make calculated guesses. People will not want to consume because they are worried about future. They will simply convert their wealth into extremely liquid and safe items such cash, gold or government bonds. All these dynamics are behavioral. They have nothing to do with the organizational aspects of the economy. (Of course we take into granted the freedom to make decisions about one's own money. You could count that freedom as part of the economic framework. But I doubt whether that would be of any use. The frameworks that do not grant individuals this freedom would be very uninteresting indeed.)

6) "The credit worthiness of the US is derived from its position within the political economy of the international monetary system." This sentence unfortunately does not explain anything. It is almost tautological. You could have said the reverse too: "The position of US within the political economy of the international monetary system is derived from its creditworthiness." Perhaps we differ on how we define credit worthiness. I take it as a very general notion, almost equivalent to the word "trust".

7) "Not only the dollar is the most dominant reserve currency, but also it is the only currency through which oil can be traded." Two points:

7a) I think you are getting the causal arrows in the wrong direction here. US is not creditworthy because US Dollar is the dominant reserve currency. It is exactly the opposite. US Dollar is the dominant reserve currency because US is the most creditworthy. For example, Central Banks of the developing countries (with floating currencies) are not coerced to accumulate dollar reserves. They make free decisions based on past experiences. If their own citizens view USA as the most creditworthy country and switch their holdings to US dollars during times of domestic crises, then the Central Banks have no choice but to accumulate US dollar reserves for the bad times. If they do not, then they will face the prospect of a potential run on their currency by their own people.

7b) Dollar is not the only currency that oil can be traded in. You can trade oil in any currency you want. Iron is also priced in the world markets, in US Dollars. When people locally trade iron in Turkey, they take these the world price as a benchmark, but they conduct the actual transaction in Turkish Liras. You do not need US Dollars to trade anything. However you cannot escape from the fact that most commodity prices are determined in world markets which by definition need to be denominated in some currency. There are some restrictions here of course. You do not want the denomination to be in the currency of a country which is run by a money-printing maniac. If you do, then the commodity prices will be destabilized by the monetary choice made there. The price signals will be fuzzy. It will be very painful to distinguish which fluctuation is due to the underlying supply/demand situation of the commodity, and which fluctuation is due to concerns about the value of the currency that the commodity is being traded in.

8) "Furthermore, this structure is enhanced further by a US-China tacit agreement over financing the ever-growing american deficit." You seem to believe that history proceeds in a very calculated fashion. Unfortunately things are not that simple. Nobody made such an agreement behind closed doors. There was probably time in the history when the dynamics could have taken a different direction. However after a certain threshold, things get locked into a trajectory. Call it an equilibrium, a tacit agreement, whatever you want. (People usually tend to choose words that reflect their ideological leanings.)

9) "We are already seeing movements that try to even out these imbalances in the structure of the international monetary system." Who is trying to do this? How credible are their efforts? I do not think you gave enough thought to this. It is extremely tough to re-orient an export-dependent, investment-driven economy to a domestic-demand-dependent, consumer-driven one. You can not expect China to perform such a trick over night. Even over a decade! It would be a wild social experiment to try to achieve this. Things can unravel in very unpredictable ways.

10) Imbalances are not bad. They are bad only in the sense that they introduce fragilities into the system, and fragilities tend to create problems during times of stress. I tend to think of US-China as separate political entities but as interwined economic entities. They both need each other.

11) "When sovereign debt is held domestically, the creditors have a greater interest in the stability of the bond market, since they live and work in -- and rely on the economic stability of - the country they are lending to?" I have a simple question for you Logan. Let's say you are holding a Turkish government bond, and you hear from a very reliable source that tomorrow there will be a coup d'etat. Will you dump your bond today or not? Bond markets do not create instabilities. Usually it is the other way around. Bond prices reflect realized or potential instabilities.

11a) A subtle point: Collectively rational outcomes may be impossible to achieve since decision-making actually takes place at the individual level. Let's assume that the economy is in a crisis, and it is in the interest of the nation as a whole to increase consumption and investment levels. Will you be the first stupid guy stepping ahead and spending your savings? Of course not! Why? Because the others may not follow you. If they don't, the general economic distress will linger on, and by the time there is a recovery you will be bankrupt. Even if you care about your country, you may not be able personally to shoulder the risks associated with the consequences you may face if others do not act as patriotic as you do.

11b) Another subtle point: It is never in the interest of the current holders of a security to introduce new sources of unstability into the market where that security is being traded. (Here you can take security to mean a piece of paper of some value.) Once that happens the price will go down. Why? Because now it is more risky to hold that piece of paper.

11c) Combining the two subtle points: Sometimes you will see crowd-behavior in securities markets. Instability breeds itself. This is really a human phenomenon that is not restricted to domestic nor international investors. People panic because they can. (This includes everybody, especially the regulators who create the "framework".)

12) My interpretation of the concept of economic value probably differs from yours. I should have used a less contaminated word (like utility) instead. You can control prices but you can not control how much people value things. That is essentially why command economies face extremely tough problems while trying to eliminate shortages and surpluses. (Here I use the word shortage in a very general sense. There may a shortage of X even if X does not exist. This is essentially why innovation is important for economic growth.)

Onur - Tarik your points are very interesting, but unfortunately I don't have the time to respond to them seriously. I will just say this: 1) My initial point is still there, despite all you say about the markets, there are different ways in which you can organize these technologies depending on political environment and desire-this is not to say this is desirable or good, but it is just to acknowledge that markets dont exist in a vacuum. 2) I think it is rather presumptuous to think that I have a particular ideological leaning, whether it is marxist or keynesian, just because I used the term "political economy" and referred to a domain outside of the market. I think you are reading too much into differences in the mode of registry due to disciplinary differences and forget that different disciplines carry with them different modes of inquiry. So, for me the question is not so much what I believe in, but analyze what exists out there; and to me for good or bad does not matter, what exists out there is not simply markets, whether they are really as you characterize them or not, but markets along with other mechanisms deliberately created by the states to manipulate the outcome of the markets toward their own interests. This does not mean I believe it is a good thing to do that, I actually think it is a dangerous thing as we see in the Greek case right now... In short, you would be surprised how much we agree than we disagree.

Me - I myself have used the term `political` in reference to Japan`s past macroeconomic policies. That issue about `the ideology-based choice of vocabulary`was referring to something else. Nevertheless you are right. It was an offensive and unrelated comment on my part. (I think I was just too absorbed and got carried on.)

Yes. States do set the rules. Often they directly manipulate characteristics of their economy. In some sense this is their job. Markets can not achieve efficient outcomes without the proper framework. (An obvious example would be the perpetual poverty of corrupt states.) But even more importantly, macroeconomic policies have wealth redistributionary consequences. Hence politics and economics inevitably get intermingled.

My desire was to solely focus on the issue of macroeconomic stability. I do not know how much I managed to do this in my previous post...

Except for a few parties, it is in the interest of everyone to make sure that economies growth takes place without its sudden and painful swings. However for some reason, the history just keeps repeating itself. No matter what changes are introduced into the framework, economic shocks can not be avoided. In my personal studes, I was shocked to realize how stupifyingly hard it is to achieve stability without making other sacrifices. (Hence my skeptical attitude.)

In your previous post, you had mentioned the following: `So, in my mind the question of stability drives at a much deeper level than that of the market stability. In other words, it is a matter of structural stability of the global political economy as opposed to the market stability.` This is probably the main point of our disagreement. There are many complicated dimensions to this topic of stability. But the `abyss` moment really comes at the level of psychology. Most of the puzzles boil down to bizarre questions about human psyche. You can build better organizational structures, but the real sources of instability will stay there.

That is all I wanted to say. Hopefully we can continue our discussion in the future. These topics interest me greatly and I have good reasons to believe that we have a lot to learn from each other.

sources of comfort

Back in high school, I developed a marvellous way of calming my anxieties. With this method, burdensome and insurmountable problems seemed to acquire minimalistic dimensions.

Say I was stressed out during an examination, squeezed under the weight of my own perfectionism, felt insufficient because of societal expectations or sad because of an emotional event... I took a deep breath, and imagined my position on earth, earth's position in the solar system, solar system's position in the spiral arm Orion, Orion's position in the Milky Way, and so on...

Today I find refugee in the ignorances of the past generations. I do not go back too far. I imagine the people of 19th century. They did not know about DNA, black holes, computers etc. Today even the average guy on the street knows more about how nature operates than the most educated man of 18th century. The depth of our ignorance about nature is and will always be beyond astronomical scales. If you find the realization of the "insignificance of human condition" as comforting as I do, try meditating on that.