Forgive me as this is an usually long post (even for me!) It is a passage from a book I've just started reading called "Judgement under uncertainty: Heuristics and biases" by Daniel Kahneman, Paul Slovic and Amos Tversky.
Suppose a large group of children has been examined on two equivalent versions of an aptitude test. If one selects ten children from among those who did best on one of the two versions, he will usually find their performance on the second version to be somewhat disappointing. Conversely, if one selects ten children from among those who did worst on one version, they will be found, on average, to do somewhat better on the other version. More generally, consider two variables X and Y which have the same distribution. If one selects individuals whose average X score deviates from the mean of X by k units, then the average of their Y scores will usually deviate from the mean by Y by less than k units. These observations illustrate a general phenomenon known as regression toward the mean, which was first documented by Galton more than 100 years ago.
In the normal course of life, one encounters many instances of regression toward the mean, in the comparison of the height of fathers and sons, of the intelligence of husbands and wives, or of the performance of individuals on consecutive examinations. Nevertheless, people do not develop correct intuitions about this phenomenon. First, they usually do not expect regression in many contexts where it is bound to occur. Second, when they recognise the occurrence of regression, they often invent spurious causal explanations for it. We suggest that the phenomenon of regression remains elusive because it is incompatible with the belief that the predicted outcome should be maximally representative of the input, and, hence, that the value of the outcome variable should be as extreme as the value of the input variable.
The failure to recognise the import of regression can have pernicious consequences, as illustrated by the following observation. In a discussion of flight training, experienced instructors noted that praise for an exceptionally smooth landing is typically followed by a poorer landing on the next try, while harsh criticism after a rough landing is usually followed by an improvement on the next try. The instructors concluded that verbal rewards are detrimental to learning while verbal punishments are beneficial, contrary to accepted psychological doctrine. This conclusion is unwarranted because of the presence of regression toward the mean. As in other cases of repeated examination, an improvement will generally follow an outstanding performance, even if the instructor does not respond to the trainee's achievement on the first attempt.
Because the instructors had praised their trainees after good landings and admonished them after poor ones, they reached the erroneous and potentially harmful conclusion that punishment is more effective than reward.
Thus, the failure to understand the effect of regression leads one to overestimate the effectiveness of punishment and to underestimate the effectiveness of reward. In social interaction, as well as in training, rewards are typically administered when performance is good, and punishments are typically administered when performance is poor. By regression alone, therefore, behaviour is most likely to improve after punishment and most likely to deteriorate after reward. Consequently, the human condition is such that, by chance alone, one is more often rewarded for punishing others and most often punished for rewarding them. People are generally note aware of this contingency. In fact, the elusive role of regression in determining the apparent consequences of reward and punishment seem to have escaped the notice of students in this area.
Friday, November 6, 2009
Monday, August 24, 2009
Forecast like a politician
I'm still reading a collection of Bertrand Russell's sceptical essays and today came across the quote below.
As I read the words "forecasting opinion" it struck me how closely an analogy might be drawn between democratic political process and the operation of financial markets. As a preference processing system, financial markets are just another voting machine and an obvious manifestation of liberal democratic ideology.
My question is, could the intuitive forecasting processes used by politicians be adapted for prediction of financial market behaviour? How might such an approach overcome the limitations inherent in "expert" approaches that tend narrowly to focus on how participants ought to behave rather than how they are actually behaving?
I was particularly attracted by the line "It is useless to urge that politicians ought to be high-minded enough to advocate what enlightened opinion considers good, because if they do they are swept aside for others." With financial markets, the clear parallel is with making a bet against the prevailing view. Even if the crowd are acting in a way that is unsupported by fundamentals, fading their move may still see you swept aside and your capital much diminished.
Here's the passage in full with emphasis added:
"There are at present two very different kinds of specialists in political questions. One the one hand there are the practical politicians of all parties; on the other hand there are the experts, mainly civil servants, but also economists, financiers, scientific medical men, etc. Each of these two classes has a special kind of skill. The skill of the politician consists in guessing what people can be brought to think advantageous to themselves; the skill of the expert consists in calculating what really is advantageous, provided people can be brought to think so. (The proviso is essential, because measures which arouse serious resentment are seldom advantageous, whatever merits they may have otherwise.) The power of the politician, in a democracy, depends upon his adopting the opinion which seem right to the average man. It is useless to urge that politicians ought to be high-minded enough to advocate what enlightened opinion considers good, because if they do they are swept aside for others. Moreover, the intuitive skill that they require in forecasting opinion does not imply any skill whatever in forming their own opinions, so that many of the ablest (from a party-political point of view) will be in a position to advocate, quite honestly, measures which the majority thing good, but which experts know to be bad. There is therefore no point in moral exhortations to politicians be disinterested, except in the crude sense of not taking bribes."
As I read the words "forecasting opinion" it struck me how closely an analogy might be drawn between democratic political process and the operation of financial markets. As a preference processing system, financial markets are just another voting machine and an obvious manifestation of liberal democratic ideology.
My question is, could the intuitive forecasting processes used by politicians be adapted for prediction of financial market behaviour? How might such an approach overcome the limitations inherent in "expert" approaches that tend narrowly to focus on how participants ought to behave rather than how they are actually behaving?
I was particularly attracted by the line "It is useless to urge that politicians ought to be high-minded enough to advocate what enlightened opinion considers good, because if they do they are swept aside for others." With financial markets, the clear parallel is with making a bet against the prevailing view. Even if the crowd are acting in a way that is unsupported by fundamentals, fading their move may still see you swept aside and your capital much diminished.
Here's the passage in full with emphasis added:
"There are at present two very different kinds of specialists in political questions. One the one hand there are the practical politicians of all parties; on the other hand there are the experts, mainly civil servants, but also economists, financiers, scientific medical men, etc. Each of these two classes has a special kind of skill. The skill of the politician consists in guessing what people can be brought to think advantageous to themselves; the skill of the expert consists in calculating what really is advantageous, provided people can be brought to think so. (The proviso is essential, because measures which arouse serious resentment are seldom advantageous, whatever merits they may have otherwise.) The power of the politician, in a democracy, depends upon his adopting the opinion which seem right to the average man. It is useless to urge that politicians ought to be high-minded enough to advocate what enlightened opinion considers good, because if they do they are swept aside for others. Moreover, the intuitive skill that they require in forecasting opinion does not imply any skill whatever in forming their own opinions, so that many of the ablest (from a party-political point of view) will be in a position to advocate, quite honestly, measures which the majority thing good, but which experts know to be bad. There is therefore no point in moral exhortations to politicians be disinterested, except in the crude sense of not taking bribes."
Friday, August 21, 2009
On philosophical pragmatism...
Some thoughts on philosophical pragmatism from one of Bertrand Russell's "Sceptical Essays":
"Although pragmatism may not contain ultimate philosophical truth, it has certain important merits. First, it realises that the truth that we can attain is merely human truth, fallible and changeable like everything human. What lies outside the cycle of human occurrences is not truth, but fact (of certain kinds).
Truth is a property of beliefs, and beliefs are psychical events. Moreover their relation to facts does not have the schematic simplicity which logic assumes; to have pointed this out is a second merit in pragmatism.
Beliefs are vague and complex, pointing not to one precise fact, but to several vague regions of fact. Beliefs, therefore, unlike the schematic propositions of logic, are not sharply opposed as true or false, but are a blur of truth and falsehood; they are of varying shades of grey, never white or black.
People who speak with reverence of the 'Truth' would do better to speak about Fact, and to realise that the reverend qualities to which they pay homage are not to be found in human beliefs. There are practical as well as theoretical advantages in this, since people persecute each other because they believe the know the 'Truth'. Speaking psycho-analytically, it may be laid down that any 'great ideal' which people mention with awe is really an excuse for inflicting pain on their enemies. Good wine needs no bush, and good morals need no bated breath."
The sinister side to this philosophy is the idea that "Truth ... is what pays in the way of beliefs. Now a belief may be made to pay through the operation the criminal law. In the seventeenth century, Catholicism paid in Catholic countries and Protestantism in Protestant countries. Energetic people can manufacture 'truth' by getting hold of Government and persecuting opinions other than their own."
Russell goes on to critique what he believes are the the exaggerations latent in this view. Let me know if you'd like me to post more on the topic. Otherwise, the book is called "Sceptical Essays" and it is Routeledge Classic.
"Although pragmatism may not contain ultimate philosophical truth, it has certain important merits. First, it realises that the truth that we can attain is merely human truth, fallible and changeable like everything human. What lies outside the cycle of human occurrences is not truth, but fact (of certain kinds).
Truth is a property of beliefs, and beliefs are psychical events. Moreover their relation to facts does not have the schematic simplicity which logic assumes; to have pointed this out is a second merit in pragmatism.
Beliefs are vague and complex, pointing not to one precise fact, but to several vague regions of fact. Beliefs, therefore, unlike the schematic propositions of logic, are not sharply opposed as true or false, but are a blur of truth and falsehood; they are of varying shades of grey, never white or black.
People who speak with reverence of the 'Truth' would do better to speak about Fact, and to realise that the reverend qualities to which they pay homage are not to be found in human beliefs. There are practical as well as theoretical advantages in this, since people persecute each other because they believe the know the 'Truth'. Speaking psycho-analytically, it may be laid down that any 'great ideal' which people mention with awe is really an excuse for inflicting pain on their enemies. Good wine needs no bush, and good morals need no bated breath."
The sinister side to this philosophy is the idea that "Truth ... is what pays in the way of beliefs. Now a belief may be made to pay through the operation the criminal law. In the seventeenth century, Catholicism paid in Catholic countries and Protestantism in Protestant countries. Energetic people can manufacture 'truth' by getting hold of Government and persecuting opinions other than their own."
Russell goes on to critique what he believes are the the exaggerations latent in this view. Let me know if you'd like me to post more on the topic. Otherwise, the book is called "Sceptical Essays" and it is Routeledge Classic.
Wednesday, August 19, 2009
Derren Brown explains the art of "Cold Reading" to Richard Dawkins
From Dawkin's two-part documentary "The Enemies of Reason"
Part 1
Part 2
Part 3
Part 4
Part 5
Part 6
Part 1
Part 2
Part 3
Part 4
Part 5
Part 6
Some interesting videos on the falliability of our perceptions
Two part series by Derren Brown: "Can NLP be weaponised?"
http://www.youtube.com/watch?v=dU10LTfF9UQ
http://www.youtube.com/watch?v=eyl22X2v6zg
Reponse to The Falcon on the matter of independent betting markets. Also, how Warren Buffet unwittingly changed the world.
You know Falcon, you've brought us full circle and back to the crux of the market conundrum.
I know we've talked of this before, but the mispricing in the horse racing situation does not influence the outcome because it is independent of the bettors expectations. This means that if you know the real factors that influence the outcome of the race you can take advantage of that mispricing, much like the quantitative horse racing model Thor sent a while back that used an algorithm that balanced approximately 120 weighted factors.
(quantitative horse model: http://www.contingenciesonline.com/contingenciesonline/20090506/?sub_id=qxyLfphSqUiJ)
As we know that is not the case with financial markets owing to feedback between expectations and outcomes. Those feedback loops are deep, varied and I'd imagine nearly impossible to quantify in a non-stationary way.
For example, the present sharp rally in equities might reflect the most optimistic recovery themes. Without an objective metric we'll never actually know. But what we can strongly suggest is that the rise has allowed many firms to raise additional capital where they would have otherwise been unable. This has undoubtedly changed the future path of their businesses in an unknowable and unalterable way. In addition there will have resulted certain less tangible elements that stem from prices acting a signal, e.g. of broader sentiment and the perceived wealth effects. In other words, do the higher equity prices encourage consumers to spend, employers to hire, etc?
This isn't just abstract Kantianism. This is a fact.
Warren Buffet once remarked that in the short run markets were a "voting machine" but in the long run a "weighing machine". But I doubt strongly whether the market machine serves two masters. Instead, I suspect that Buffet has been unusually lucky in the sense that the voting machine has always tended to eventually validate his weighing process.
And why wouldn't it? In the same way Smith's work cemented our belief in the "laws" of supply and demand, Graham's Security Analysis has had a profound influence on beliefs about valuation. As just another belief, this is liable to change with time. However, at the present time it appears that while price might deviate substantially from "value" in the Graham/Dodd sense, eventually price and value converge and reward those with the time, liquidity and patience to wait for it to do so.
And this is where Buffet has been genius. He has always ensured that any acquisition has provided him with "float". These invaluable free cash flows have funded his speculation while waiting for the voting machine to catch up. Stripped of all the narrative it is just another convergence bet, not too dissimilar to the ones made by Long Term, with the exception that Buffet due to his fear of leverage and use of "float" has always been in a position to withstand the liquidity risks associated with convergence bets.
I also think it is interesting to ponder how Buffet has played a hand in spreading the Graham and Dodd gospel upon which he relies to make a profit. What would the world now be like without Security Analysis, and without Warren Buffet?
So finance guru's, the question is how then to create a model which can account quantitatively for exogenous and endogenous factors?
Finally, one thing to note with that quantitative horse betting model is that their experience working solely off the 120 factors was relatively mixed. Their performance didn't' really improve until they incorporated market generated prices into the model.
I know we've talked of this before, but the mispricing in the horse racing situation does not influence the outcome because it is independent of the bettors expectations. This means that if you know the real factors that influence the outcome of the race you can take advantage of that mispricing, much like the quantitative horse racing model Thor sent a while back that used an algorithm that balanced approximately 120 weighted factors.
(quantitative horse model: http://www.contingenciesonline.com/contingenciesonline/20090506/?sub_id=qxyLfphSqUiJ)
As we know that is not the case with financial markets owing to feedback between expectations and outcomes. Those feedback loops are deep, varied and I'd imagine nearly impossible to quantify in a non-stationary way.
For example, the present sharp rally in equities might reflect the most optimistic recovery themes. Without an objective metric we'll never actually know. But what we can strongly suggest is that the rise has allowed many firms to raise additional capital where they would have otherwise been unable. This has undoubtedly changed the future path of their businesses in an unknowable and unalterable way. In addition there will have resulted certain less tangible elements that stem from prices acting a signal, e.g. of broader sentiment and the perceived wealth effects. In other words, do the higher equity prices encourage consumers to spend, employers to hire, etc?
This isn't just abstract Kantianism. This is a fact.
Warren Buffet once remarked that in the short run markets were a "voting machine" but in the long run a "weighing machine". But I doubt strongly whether the market machine serves two masters. Instead, I suspect that Buffet has been unusually lucky in the sense that the voting machine has always tended to eventually validate his weighing process.
And why wouldn't it? In the same way Smith's work cemented our belief in the "laws" of supply and demand, Graham's Security Analysis has had a profound influence on beliefs about valuation. As just another belief, this is liable to change with time. However, at the present time it appears that while price might deviate substantially from "value" in the Graham/Dodd sense, eventually price and value converge and reward those with the time, liquidity and patience to wait for it to do so.
And this is where Buffet has been genius. He has always ensured that any acquisition has provided him with "float". These invaluable free cash flows have funded his speculation while waiting for the voting machine to catch up. Stripped of all the narrative it is just another convergence bet, not too dissimilar to the ones made by Long Term, with the exception that Buffet due to his fear of leverage and use of "float" has always been in a position to withstand the liquidity risks associated with convergence bets.
I also think it is interesting to ponder how Buffet has played a hand in spreading the Graham and Dodd gospel upon which he relies to make a profit. What would the world now be like without Security Analysis, and without Warren Buffet?
So finance guru's, the question is how then to create a model which can account quantitatively for exogenous and endogenous factors?
Finally, one thing to note with that quantitative horse betting model is that their experience working solely off the 120 factors was relatively mixed. Their performance didn't' really improve until they incorporated market generated prices into the model.
Copy and Paste : The Falcon's response to my post on the role of belief's in markets
In response to the prior musing, my friend "The Falcon" added
The Melbourne Cup reference is an interesting one - and for this reason:
" Imagine if every single punter at the Melbourne Cup this year placed
their bet on the apparently irrefutable communal belief that only even
numbered horses win races... it would considerably alter the market's
pricing dynamics. "
The result would be mis-pricing in betting markets - however, the result
of the race itself would remain unaffected.
The scary thing is - if the same latent human desires create misguided
human beliefes in the market place then the result is a grave
misallocation of so called scarce resources.
Then again - maybe my desire to have resources optimally allocated is
feeding some evolutionary drive that has been with me since I first
climbed out of the slime millions and millions of years ago....
The Melbourne Cup reference is an interesting one - and for this reason:
" Imagine if every single punter at the Melbourne Cup this year placed
their bet on the apparently irrefutable communal belief that only even
numbered horses win races... it would considerably alter the market's
pricing dynamics. "
The result would be mis-pricing in betting markets - however, the result
of the race itself would remain unaffected.
The scary thing is - if the same latent human desires create misguided
human beliefes in the market place then the result is a grave
misallocation of so called scarce resources.
Then again - maybe my desire to have resources optimally allocated is
feeding some evolutionary drive that has been with me since I first
climbed out of the slime millions and millions of years ago....
The role of beliefs in markets
The other day i used the idea of a living science as an example of how objective reason is an illusion, and the rather central importance of beliefs.
In the same way that we can't have science without the pre-scientific belief that there is a discoverable order of things, isn't the belief markets reflect supply and demand similarly the result of the underlying belief that resources ought to be valued in proportion to their scarcity?
When he made his inquiry into the nature and causes of the wealth of nations, Adam Smith didn't uncover the mystical natural order of the market place. Instead he issued a prescription, which just so happened to be intellectually satisfactory to his contemporaries.
A widespread political doctrine has, as a rule, two very different kinds of causes. On the one hand, there are intellectual antecedents: men who have advanced theories which have grown, by development or reaction, from previous theories. On the other hand, there are economic and political circumstances which predispose people to accept views that minister to certain moods.
I'm sure beliefs and actions based on supply and demand long preceded Adam Smith, but like the case with science, such beliefs in turn probably cater to latent human desires. In any case I think we would be severely misguided to continue seeking to establish either the truth or falsity of the concept, not least because like all illusions it misdirects our attention from the real action.
Vis-a-vie supply and demand, all that matters is that it is a widely held belief, and insomuch as it is consequently an operative cause of action for those who participate in markets we must accept that the belief is self-perpetuating. By believing in it, people unwittingly create a perception of reality that is largely self-supporting, and further it conditions them to actively search for evidence of those self-fulfilling expectations!
Were every market participant to believe so ardently in the "truth" of fibonacci retracements on a daily candle I'm almost certain the effect would be identical.
The problem we face is that these types of belief are probably the rule rather than the exception. And unfortunately that means their circuitous assumptions enable otherwise intelligent people to unwittingly perpetuate an illusion of rational debate.
In view of our failure to find an answer to Hume, "reason" cannot be regarded as something absolute, with any departure being condemned on theoretical grounds. Consequently we ought to be realistic and accept that any reliance upon reason must assume a certain community of interest and outlook between oneself and one's audience.
It is true that Mrs Bond tried on her ducks, when she cried, "come and be killed for you must be stuffed and my customers filled"; but in general the appeal to reason is thought ineffective with those whom we mean to devour. Those who would believe in eating meat do not attempt to find arguments which would seem valid to a sheep, and Nietzche does not attempt to persuade the mass of the population, whom he calls, "the bungled and botched". Indeed, nor does Marx try to enlist the support of capitalists.
When communal assumptions cannot be found, men are driven to rely on their own intuition. Thankfully this is not the case with markets, since without large scale bias' I would imagine they'd be practically unpredictable.
The punch-line to this rant is that with markets, the apparent regularities we see in pricing are no more than the complex result of the many operating beliefs of the market's participants. This is reality. From this not even the so-called laws of supply cannot escape.
Imagine if every single punter at the Melbourne Cup this year placed their bet on the apparently irrefutable communal belief that only even numbered horses win races... it would considerably alter the market's pricing dynamics.
And so it is with beliefs and all markets.
In the same way that we can't have science without the pre-scientific belief that there is a discoverable order of things, isn't the belief markets reflect supply and demand similarly the result of the underlying belief that resources ought to be valued in proportion to their scarcity?
When he made his inquiry into the nature and causes of the wealth of nations, Adam Smith didn't uncover the mystical natural order of the market place. Instead he issued a prescription, which just so happened to be intellectually satisfactory to his contemporaries.
A widespread political doctrine has, as a rule, two very different kinds of causes. On the one hand, there are intellectual antecedents: men who have advanced theories which have grown, by development or reaction, from previous theories. On the other hand, there are economic and political circumstances which predispose people to accept views that minister to certain moods.
I'm sure beliefs and actions based on supply and demand long preceded Adam Smith, but like the case with science, such beliefs in turn probably cater to latent human desires. In any case I think we would be severely misguided to continue seeking to establish either the truth or falsity of the concept, not least because like all illusions it misdirects our attention from the real action.
Vis-a-vie supply and demand, all that matters is that it is a widely held belief, and insomuch as it is consequently an operative cause of action for those who participate in markets we must accept that the belief is self-perpetuating. By believing in it, people unwittingly create a perception of reality that is largely self-supporting, and further it conditions them to actively search for evidence of those self-fulfilling expectations!
Were every market participant to believe so ardently in the "truth" of fibonacci retracements on a daily candle I'm almost certain the effect would be identical.
The problem we face is that these types of belief are probably the rule rather than the exception. And unfortunately that means their circuitous assumptions enable otherwise intelligent people to unwittingly perpetuate an illusion of rational debate.
In view of our failure to find an answer to Hume, "reason" cannot be regarded as something absolute, with any departure being condemned on theoretical grounds. Consequently we ought to be realistic and accept that any reliance upon reason must assume a certain community of interest and outlook between oneself and one's audience.
It is true that Mrs Bond tried on her ducks, when she cried, "come and be killed for you must be stuffed and my customers filled"; but in general the appeal to reason is thought ineffective with those whom we mean to devour. Those who would believe in eating meat do not attempt to find arguments which would seem valid to a sheep, and Nietzche does not attempt to persuade the mass of the population, whom he calls, "the bungled and botched". Indeed, nor does Marx try to enlist the support of capitalists.
When communal assumptions cannot be found, men are driven to rely on their own intuition. Thankfully this is not the case with markets, since without large scale bias' I would imagine they'd be practically unpredictable.
The punch-line to this rant is that with markets, the apparent regularities we see in pricing are no more than the complex result of the many operating beliefs of the market's participants. This is reality. From this not even the so-called laws of supply cannot escape.
Imagine if every single punter at the Melbourne Cup this year placed their bet on the apparently irrefutable communal belief that only even numbered horses win races... it would considerably alter the market's pricing dynamics.
And so it is with beliefs and all markets.
Does reality really look like our visual impression? A little maths/physics to bend your mind
Clouds are not spheres, mountains are not cones and lightening does not travel in a straight line. The complexity of nature's shapes differs from the shapes of ordinary geometry. To describe the shapes that populate the real world, famed mathematician Bonoit Mandlebrot conceived and developed a new geometry - the geometry of fractal shapes, which has been described as the attempt to understand quantitatively the notion of roughness.
Below is a little extract from Mandlebrot's "The Fractal Geometry of Nature".
Although closer observation of an object generally leads to the discovery of of a highly irregular structure, we often can approximate its properties by continuous functions. Although wood may be infinitely porous, it is useful to speak of a beam that has been sawed and planed as having a finite area. In other words, at certain scales and for certain methods of investigation, many phenomena may be represented by regular continuous functions, somewhat in the same way that a sheet of tinfoil may be wrapped round a sponge without following accurately the latter's complicated contour.
However, if we were to go further and we attribute to matter the infinitely granular structure that is in the spirit of atomic theory, our power to apply to reality the rigorous mathematical of continuity will greatly decrease.
Consider, for instance, the way in which we define the density of air at a given point and at a given moment. We picture a sphere of volume "v" centered at that point and including the mass "m". The quotient "m / v" is the mean density within the sphere, and by true density we denote some limiting value of this quotient. This notion, however, implies that at the given moment the mean density is practically constant for spheres below a certain volume. This mean density may be notably different for spheres containing 1,000 cubic meters and 1 cubic centimeter respectively, but but it is expected to vary only by 1 in 1,000,000 when comparing 1 cubic centimeter to one-thousandth of a cubic centimeter.
Now suppose the volume of our sphere becomes continually smaller. Instead of becoming less and less important these fluctuations in fact begin to increase. For scales at which Brownian motion shows great activity, fluctuations may attain 1 part in 1,000, and they become of the order of 1 part in 5 when the radius of the hypothetical spherule becomes of the order of a hundredth of a micron.
One step further and our spherule becomes of the order of a molecule radius. In a gas, it will generally lie in intermolecular space, where its mean density will henceforth vanish. At our point the true density will also vanish. But about once in a thousand times that mean point will lie within a molecule, and the mean density will be a thousand times higher than the value we usually take to be the true density of the gas.
Let our spherule grow steadily smaller. Soon, except under exceptional circumstances, it will become empty and remain so henceforth owing to the emptiness of of intra-atomic space; the true density vanishes almost every where, except at an infinite number of isolated points, where it reaches an infinite value.
Below is a little extract from Mandlebrot's "The Fractal Geometry of Nature".
Although closer observation of an object generally leads to the discovery of of a highly irregular structure, we often can approximate its properties by continuous functions. Although wood may be infinitely porous, it is useful to speak of a beam that has been sawed and planed as having a finite area. In other words, at certain scales and for certain methods of investigation, many phenomena may be represented by regular continuous functions, somewhat in the same way that a sheet of tinfoil may be wrapped round a sponge without following accurately the latter's complicated contour.
However, if we were to go further and we attribute to matter the infinitely granular structure that is in the spirit of atomic theory, our power to apply to reality the rigorous mathematical of continuity will greatly decrease.
Consider, for instance, the way in which we define the density of air at a given point and at a given moment. We picture a sphere of volume "v" centered at that point and including the mass "m". The quotient "m / v" is the mean density within the sphere, and by true density we denote some limiting value of this quotient. This notion, however, implies that at the given moment the mean density is practically constant for spheres below a certain volume. This mean density may be notably different for spheres containing 1,000 cubic meters and 1 cubic centimeter respectively, but but it is expected to vary only by 1 in 1,000,000 when comparing 1 cubic centimeter to one-thousandth of a cubic centimeter.
Now suppose the volume of our sphere becomes continually smaller. Instead of becoming less and less important these fluctuations in fact begin to increase. For scales at which Brownian motion shows great activity, fluctuations may attain 1 part in 1,000, and they become of the order of 1 part in 5 when the radius of the hypothetical spherule becomes of the order of a hundredth of a micron.
One step further and our spherule becomes of the order of a molecule radius. In a gas, it will generally lie in intermolecular space, where its mean density will henceforth vanish. At our point the true density will also vanish. But about once in a thousand times that mean point will lie within a molecule, and the mean density will be a thousand times higher than the value we usually take to be the true density of the gas.
Let our spherule grow steadily smaller. Soon, except under exceptional circumstances, it will become empty and remain so henceforth owing to the emptiness of of intra-atomic space; the true density vanishes almost every where, except at an infinite number of isolated points, where it reaches an infinite value.
Is absolute reason just a superstition?
The influence of our wishes upon our beliefs is a matter of common knowledge and observation, yet the nature of this influence is very generally misconceived. It is customary to suppose that the bulk of our beliefs are derived from some rational ground, and that desire is only an occasional disturbing force. The exact opposite of this would be nearer the truth: the great mass of beliefs by which we are supported in our daily life is merely the bodying forth of desire, corrected here and there, at isolated points, by the rude shock of fact.
Man is essentially a dreamer, wakened sometimes for a moment by some peculiarly obtrusive element in the outer world, but lapsing again quickly into the happy somnolence of imagination. Freud claimed that our dreams at night are the pictured fulfillment of our wishes. But might he not equally included the day-dreams which we call beliefs?
We have a hierarchy of comforting beliefs: those private to the individual, those which we share with our family, those common to our class or nation, and finally those that are equally delightful to all mankind.
Neo-classical economists pioneered their creed on the "rational" acting man. And many disputes over the fallibility of the economic method of reasoning typically decay into facile disputes between economists and social-psychology types over whether we think or act rationally.
Why don't we put on our Hume hats and look past that debate to the true emptiness of "reason" and "rationality"?"
Kant had to invent the distinction between 'pure' and 'practical' reason to circumvent the causation debate, but really when are we going to wake up?
Even when we do reason deductively we must accept that there is still some underlying assumption from which we choose to work. Take the idea of science for example. We all probably roughly believe that the scientific method is a path to enlightenment about nature and our existence
But the reality is that there could be no living science unless there was first a widespread conviction in the existence of an order of things, and, in particular, an order of Nature. Science could only have been created by mean who already had this belief, and therefore the original sources of the belief must have been pre-scientific.
This same pre-scientific beliefs is probably the reason for our age old deference to theology, and even back to our cave-dwelling forebears who believed that might inherit the strength of a beast by consuming it or adorning themselves in its flesh.
Man is essentially a dreamer, wakened sometimes for a moment by some peculiarly obtrusive element in the outer world, but lapsing again quickly into the happy somnolence of imagination. Freud claimed that our dreams at night are the pictured fulfillment of our wishes. But might he not equally included the day-dreams which we call beliefs?
We have a hierarchy of comforting beliefs: those private to the individual, those which we share with our family, those common to our class or nation, and finally those that are equally delightful to all mankind.
Neo-classical economists pioneered their creed on the "rational" acting man. And many disputes over the fallibility of the economic method of reasoning typically decay into facile disputes between economists and social-psychology types over whether we think or act rationally.
Why don't we put on our Hume hats and look past that debate to the true emptiness of "reason" and "rationality"?"
Kant had to invent the distinction between 'pure' and 'practical' reason to circumvent the causation debate, but really when are we going to wake up?
Even when we do reason deductively we must accept that there is still some underlying assumption from which we choose to work. Take the idea of science for example. We all probably roughly believe that the scientific method is a path to enlightenment about nature and our existence
But the reality is that there could be no living science unless there was first a widespread conviction in the existence of an order of things, and, in particular, an order of Nature. Science could only have been created by mean who already had this belief, and therefore the original sources of the belief must have been pre-scientific.
This same pre-scientific beliefs is probably the reason for our age old deference to theology, and even back to our cave-dwelling forebears who believed that might inherit the strength of a beast by consuming it or adorning themselves in its flesh.
Thursday, July 2, 2009
Welcome to my blog. What it is about and why I am writing it.
In 1895, French author Gustave Le Bon released one of the most influential works on social psychology. "The Crowd" was more rhetoric and narrative than "scientific", but it was nonetheless the milestone in our analysis of mass human behaviour.
As members of a scientific or "information age" we would like to think that we've come along way from our irrational and ignorant origins. This is a fallacy. With the aid of computers and the scientific method our knowledge seems to be growing at an exponential rate, but the way we think and act as membesr of a collective has arguably changed very little at all.
My main interest is in financial markets. Not only are they the most organic and robust source of data on the flights and fancies of the collective human mind, but they also reflect the too infrequently challenged liberal belief that a market is the best way to allocate resources in a society.
Please feel free to comment, critique or in any way help me to augment this stream of consciousness. I'm on a journey of intellectual discovery here, and what better way to develop my developing views than by exposing them to criticism.
Most of my posts will either be personal musings or copies of emails and letters between colleagues in finance, policy and academia.
Enjoy
As members of a scientific or "information age" we would like to think that we've come along way from our irrational and ignorant origins. This is a fallacy. With the aid of computers and the scientific method our knowledge seems to be growing at an exponential rate, but the way we think and act as membesr of a collective has arguably changed very little at all.
My main interest is in financial markets. Not only are they the most organic and robust source of data on the flights and fancies of the collective human mind, but they also reflect the too infrequently challenged liberal belief that a market is the best way to allocate resources in a society.
Please feel free to comment, critique or in any way help me to augment this stream of consciousness. I'm on a journey of intellectual discovery here, and what better way to develop my developing views than by exposing them to criticism.
Most of my posts will either be personal musings or copies of emails and letters between colleagues in finance, policy and academia.
Enjoy
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