Do you see patterns in Random Walks?
- Thread starter atlTrader666
- Start date
Thanks for the links, I think now I understand more.
According to the first link, a raster is a snapshot of the environment at a certain point in time, then arrange several of those along the time dimension. How could step movements of ticks be an environment at a certain point in time, how many ticks can there be one point in time? I can understand the example of pond depths or a map of rainfall. An extension to markets could be, for example, the end of day heat maps from finviz.
I did a study last year of a random entry strategy, differing only in stop-limit amounts. I suppose this would be a raster, if lined up along a time dimension instead of 6 different pics, to watch as the red (profitable combos) swaps sides with the blue (unprofitable combos). (Yellow = mostly close to breakeven).
SPONTANEOUS SYNCHRONIZATION
The New Yorker © 1947
The Law
By ROBERT M. COATES
THE first intimation that things were getting out of hand came one early fall evening in the late
nineteen-forties. What happened, simply, was that between seven and nine oâclock on that evening
the Triborough Bridge had the heaviest concentration of outbound traffic in its entire history.
This was odd, for it was a weekday evening (to be precise, a Wednesday), and though the
weather was agreeably mild and clear, with a moon that was close enough to being full to lure a
certain number of motorists out of the city, these facts alone were not enough to explain the
phenomenon. No other bridge or main highway was affected, and though the two preceding nights
had been equally balmy and moonlit, on both of these the bridge traffic had run close to normal.
The bridge personnel, at any rate, was caught entirely unprepared. A main artery of traffic, like
the Triborough, operates under fairly predictable conditions. Motor travel, like most other large-scale
human activities, obeys the Law of Averagesâthat great, ancient rule that states that the actions of
people in the mass will always follow consistent patternsâand on the basis of past experience it had
always been possible to foretell almost to the last digit, the number of cars that would cross the bridge
at any given hour of the day or night. In this case, though, all rules were broken.
The hours from seven till nearly midnight are normally quiet ones on the bridge. But on that
night it was as if all the motorists in the city, or at any rate a staggering proportion of them, had
conspired together to upset tradition. Beginning almost exactly at seven oâclock, cars poured onto the
bridge in such numbers and with such rapidity that the staff at the toll booths was overwhelmed
almost from the start. It was soon apparent that this was no momentary congestion, and as it became
more and more obvious that the traffic jam promised to be one of truly monumental proportions,
added details of police were rushed to the scene to help handle it.
Cars streamed in from all directionsâfrom the Bronx approach and the Manhattan one, from
125th Street and the East River Drive. (At the peak of the crush, about eight-fifteen, observers on the
bridge reported that the drive was a solid line of car headlights as far south as the bend at Eighty-ninth
Street, while the congestion crosstown in Manhattan disrupted traffic as far west as Amsterdam
Avenue.) And perhaps the most confusing thing about the whole manifestation was that there seemed
to be no reason for it.
Now and then, as the harried toll-booth attendants made change for the seemingly endless
stream of cars, they would question the occupants, and it soon became clear that the very participants
in the monstrous tieup were as ignorant of its cause as anyone else was. A report made by Sergeant
Alfonse OâToole, who commanded the detail in charge of the Bronx approach, is typical. "I kept askinâ
them," he said, " âIs there night football somewhere that we donât know about? Is it the races youâre
goinâ to?â But the funny thing was half the time theyâd be askinâ me. `Whatâs the crowd for, Mac?â they
would say. And Iâd just look at them. There was one guy I mind, in a Ford convertible with a girl in the
seat beside him, and when he asked me, I said to him, `Hell, youâre in the crowd, ainât you?â I said.
`What brings you here?â And the dummy just looked at me. âMe?â he says. `I just come out for a drive in
the moonlight. But if Iâd known thereâd be a crowd like this . . .â he says. And then he asks me, `Is there
any place I can turn around and get out of this?ââ As the Herald Tribune summed things up in its story
next morning, it "just looked as if everybody in Manhattan who owned a motorcar had decided to
drive out on Long Island that evening."
The New Yorker © 1947
The Law
By ROBERT M. COATES
THE first intimation that things were getting out of hand came one early fall evening in the late
nineteen-forties. What happened, simply, was that between seven and nine oâclock on that evening
the Triborough Bridge had the heaviest concentration of outbound traffic in its entire history.
This was odd, for it was a weekday evening (to be precise, a Wednesday), and though the
weather was agreeably mild and clear, with a moon that was close enough to being full to lure a
certain number of motorists out of the city, these facts alone were not enough to explain the
phenomenon. No other bridge or main highway was affected, and though the two preceding nights
had been equally balmy and moonlit, on both of these the bridge traffic had run close to normal.
The bridge personnel, at any rate, was caught entirely unprepared. A main artery of traffic, like
the Triborough, operates under fairly predictable conditions. Motor travel, like most other large-scale
human activities, obeys the Law of Averagesâthat great, ancient rule that states that the actions of
people in the mass will always follow consistent patternsâand on the basis of past experience it had
always been possible to foretell almost to the last digit, the number of cars that would cross the bridge
at any given hour of the day or night. In this case, though, all rules were broken.
The hours from seven till nearly midnight are normally quiet ones on the bridge. But on that
night it was as if all the motorists in the city, or at any rate a staggering proportion of them, had
conspired together to upset tradition. Beginning almost exactly at seven oâclock, cars poured onto the
bridge in such numbers and with such rapidity that the staff at the toll booths was overwhelmed
almost from the start. It was soon apparent that this was no momentary congestion, and as it became
more and more obvious that the traffic jam promised to be one of truly monumental proportions,
added details of police were rushed to the scene to help handle it.
Cars streamed in from all directionsâfrom the Bronx approach and the Manhattan one, from
125th Street and the East River Drive. (At the peak of the crush, about eight-fifteen, observers on the
bridge reported that the drive was a solid line of car headlights as far south as the bend at Eighty-ninth
Street, while the congestion crosstown in Manhattan disrupted traffic as far west as Amsterdam
Avenue.) And perhaps the most confusing thing about the whole manifestation was that there seemed
to be no reason for it.
Now and then, as the harried toll-booth attendants made change for the seemingly endless
stream of cars, they would question the occupants, and it soon became clear that the very participants
in the monstrous tieup were as ignorant of its cause as anyone else was. A report made by Sergeant
Alfonse OâToole, who commanded the detail in charge of the Bronx approach, is typical. "I kept askinâ
them," he said, " âIs there night football somewhere that we donât know about? Is it the races youâre
goinâ to?â But the funny thing was half the time theyâd be askinâ me. `Whatâs the crowd for, Mac?â they
would say. And Iâd just look at them. There was one guy I mind, in a Ford convertible with a girl in the
seat beside him, and when he asked me, I said to him, `Hell, youâre in the crowd, ainât you?â I said.
`What brings you here?â And the dummy just looked at me. âMe?â he says. `I just come out for a drive in
the moonlight. But if Iâd known thereâd be a crowd like this . . .â he says. And then he asks me, `Is there
any place I can turn around and get out of this?ââ As the Herald Tribune summed things up in its story
next morning, it "just looked as if everybody in Manhattan who owned a motorcar had decided to
drive out on Long Island that evening."
2
The incident was unusual enough to make all the front pages next morning, and because of
this, many similar events, which might otherwise have gone unnoticed, received attention. The
proprietor of the Aramis Theatre, on Eighth Avenue, reported that on several nights in the recent past
his auditorium had been practically empty, while on others it had been jammed to suffocation.
Luncheon owners noted that increasingly their patrons were developing a habit of making runs on
specific items; one day it would be the roast shoulder of veal with pan gravy that was ordered almost
exclusively, while the next everyone would be taking the Vienna loaf, and the roast veal went begging.
A man who ran a small notions store in Bayside revealed that over a period of four days two hundred
and seventy-four successive customers had entered his shop and asked for a spool of pink thread.
These were news items that would ordinarily have gone into the papers as fillers or in the
sections reserved for oddities. Now, however, they seemed to have a more serious significance. It was
apparent at last that something decidedly strange was happening to peopleâs habits, and it was as
unsettling as those occasional moments on excursion boats when the passengers are moved, all at
once, to rush to one side or the other of the vessel. It was not till one day in December when, almost
incredibly, the Twentieth Century Limited left New York for Chicago with just three passengers aboard
that business leaders discovered how disastrous the new trend could be, too.
Until then, the New York Central, for instance, could operate confidently on the assumption
that although there might he several thousand men in New York who had business relations in
Chicago, on any single day no moreâand no lessâthan some hundreds of them would have occasion
to go there. The play producer could be sure that his patronage would sort itself out and that roughly
as many persons would want to see the performance on Thursday as there had been on Tuesday or
Wednesday. Now they couldnât be sure of anything. The Law of Averages had gone by the board, and if
the effect on business promised to be catastrophic, it was also singularly unnerving for the general
customer.
The lady starting downtown for a day of shopping, for example, could never be sure whether
she would find Macyâs department store a seething mob of other shoppers or a wilderness of empty,
echoing aisles and unoccupied salesgirls. And the uncertainty produced a strange sort of jitteriness in
the individual when faced with any impulse to action. "Shall we do it or shanât we?" people kept asking
themselves, knowing that if they did it, it might turn out that thousands of other individuals had
decided similarly; knowing, too, that if they didnât, they might miss the one glorious chance of all
chances to have Jones Beach, say, practically to themselves. Business languished, and a sort of
desperate uncertainty rode everyone.
At this juncture, it was inevitable that Congress should be called on for action. In fact, Congress
called on itself, and it must be said that it rose nobly to the occasion. A committee was appointed,
drawn from both Houses and headed by Senator J. Wing Slooper (R.), of Indiana, and though after
considerable investigation the committee was forced reluctantly to conclude that there was no
evidence of Communist instigation, the unconscious subversiveness of the peopleâs present conduct
was obvious at a glance. The problem was what to do about it. You canât indict a whole nation,
particularly on such vague grounds as these were. But, as Senator Slooper boldly pointed out, "You can
control it," and in the end a system of reëducation and reform was decided upon, designed to lead
people back toâagain we quote Senator Slooperâ"the basic regularities, the homely averageness of
the American way of life."
In the course of the committeeâs investigations, it had been discovered, to everyoneâs dismay,
that the Law of Averages had never been incorporated into the body of federal jurisprudence, and
though the upholders of Statesâ Rights rebelled violently, the oversight was at once corrected, both by
Constitutional amendment and by a lawâthe Hills-Slooper Actâimplementing it. According to the Act,
people were required to be average, and, as the simplest way of assuring it, they were divided
The incident was unusual enough to make all the front pages next morning, and because of
this, many similar events, which might otherwise have gone unnoticed, received attention. The
proprietor of the Aramis Theatre, on Eighth Avenue, reported that on several nights in the recent past
his auditorium had been practically empty, while on others it had been jammed to suffocation.
Luncheon owners noted that increasingly their patrons were developing a habit of making runs on
specific items; one day it would be the roast shoulder of veal with pan gravy that was ordered almost
exclusively, while the next everyone would be taking the Vienna loaf, and the roast veal went begging.
A man who ran a small notions store in Bayside revealed that over a period of four days two hundred
and seventy-four successive customers had entered his shop and asked for a spool of pink thread.
These were news items that would ordinarily have gone into the papers as fillers or in the
sections reserved for oddities. Now, however, they seemed to have a more serious significance. It was
apparent at last that something decidedly strange was happening to peopleâs habits, and it was as
unsettling as those occasional moments on excursion boats when the passengers are moved, all at
once, to rush to one side or the other of the vessel. It was not till one day in December when, almost
incredibly, the Twentieth Century Limited left New York for Chicago with just three passengers aboard
that business leaders discovered how disastrous the new trend could be, too.
Until then, the New York Central, for instance, could operate confidently on the assumption
that although there might he several thousand men in New York who had business relations in
Chicago, on any single day no moreâand no lessâthan some hundreds of them would have occasion
to go there. The play producer could be sure that his patronage would sort itself out and that roughly
as many persons would want to see the performance on Thursday as there had been on Tuesday or
Wednesday. Now they couldnât be sure of anything. The Law of Averages had gone by the board, and if
the effect on business promised to be catastrophic, it was also singularly unnerving for the general
customer.
The lady starting downtown for a day of shopping, for example, could never be sure whether
she would find Macyâs department store a seething mob of other shoppers or a wilderness of empty,
echoing aisles and unoccupied salesgirls. And the uncertainty produced a strange sort of jitteriness in
the individual when faced with any impulse to action. "Shall we do it or shanât we?" people kept asking
themselves, knowing that if they did it, it might turn out that thousands of other individuals had
decided similarly; knowing, too, that if they didnât, they might miss the one glorious chance of all
chances to have Jones Beach, say, practically to themselves. Business languished, and a sort of
desperate uncertainty rode everyone.
At this juncture, it was inevitable that Congress should be called on for action. In fact, Congress
called on itself, and it must be said that it rose nobly to the occasion. A committee was appointed,
drawn from both Houses and headed by Senator J. Wing Slooper (R.), of Indiana, and though after
considerable investigation the committee was forced reluctantly to conclude that there was no
evidence of Communist instigation, the unconscious subversiveness of the peopleâs present conduct
was obvious at a glance. The problem was what to do about it. You canât indict a whole nation,
particularly on such vague grounds as these were. But, as Senator Slooper boldly pointed out, "You can
control it," and in the end a system of reëducation and reform was decided upon, designed to lead
people back toâagain we quote Senator Slooperâ"the basic regularities, the homely averageness of
the American way of life."
In the course of the committeeâs investigations, it had been discovered, to everyoneâs dismay,
that the Law of Averages had never been incorporated into the body of federal jurisprudence, and
though the upholders of Statesâ Rights rebelled violently, the oversight was at once corrected, both by
Constitutional amendment and by a lawâthe Hills-Slooper Actâimplementing it. According to the Act,
people were required to be average, and, as the simplest way of assuring it, they were divided
3
alphabetically and their permissible activities catalogued accordingly. Thus, by the plan, a person
whose name began with "G," "N," or "U," for example, could attend the theatre only on Tuesdays, and
he could go to baseball games only on Thursdays, whereas his visits to a haberdashery were confined
to the hours between ten oâclock and noon on Mondays.
The law, of course, had its disadvantages. It had a crippling effect on theatre parties, among
other social functions, and the cost of enforcing it was unbelievably heavy. In the end, too, so many
amendments had to be added to itâsuch as the one permitting gentlemen to take their fiancées (if
accredited) along with them to various events and functions no matter what letter the said fiancéesâ
names began withâthat the courts were frequently at a loss to interpret it when confronted with
violations.
In its way, though, the law did serve its purpose, for it did induceârather mechanically, it is
true, but still adequatelyâa return to that average existence that Senator Slooper desired. All, indeed,
would have been well if a year or so later disquieting reports had not begun to seep in from the
backwoods. It seemed that there, in what had hitherto been considered to be marginal areas, a strange
wave of prosperity was making itself felt. Tennessee mountaineers were buying Packard convertibles,
and Sears, Roebuck reported that in the Ozarks their sales of luxury items had gone up nine hundred
per cent. In the scrub sections of Vermont, men who formerly had barely been able to scratch a living
from their rock-strewn acres were now sending their daughters to Europe and ordering expensive
cigars from New York. It appeared that the Law of Diminishing Returns was going haywire, too.
alphabetically and their permissible activities catalogued accordingly. Thus, by the plan, a person
whose name began with "G," "N," or "U," for example, could attend the theatre only on Tuesdays, and
he could go to baseball games only on Thursdays, whereas his visits to a haberdashery were confined
to the hours between ten oâclock and noon on Mondays.
The law, of course, had its disadvantages. It had a crippling effect on theatre parties, among
other social functions, and the cost of enforcing it was unbelievably heavy. In the end, too, so many
amendments had to be added to itâsuch as the one permitting gentlemen to take their fiancées (if
accredited) along with them to various events and functions no matter what letter the said fiancéesâ
names began withâthat the courts were frequently at a loss to interpret it when confronted with
violations.
In its way, though, the law did serve its purpose, for it did induceârather mechanically, it is
true, but still adequatelyâa return to that average existence that Senator Slooper desired. All, indeed,
would have been well if a year or so later disquieting reports had not begun to seep in from the
backwoods. It seemed that there, in what had hitherto been considered to be marginal areas, a strange
wave of prosperity was making itself felt. Tennessee mountaineers were buying Packard convertibles,
and Sears, Roebuck reported that in the Ozarks their sales of luxury items had gone up nine hundred
per cent. In the scrub sections of Vermont, men who formerly had barely been able to scratch a living
from their rock-strewn acres were now sending their daughters to Europe and ordering expensive
cigars from New York. It appeared that the Law of Diminishing Returns was going haywire, too.
Interesting, Asimov founded a concept called psychohistory that basically used math to predict the trajectory of large groups of people under certain situations. Is this what you do?