Zero

19 December 2016

0 the circle, theAbyss, the Shape of Time

I was re-reading notes on Spengler’s Decline of the West, and found it as opaque this time around as the first time (maybe two times) I’d read it. Nevertheless, what I seem to recall is a progression, quite complex (Spengler was a philosopher after all), which I’ve taken in the following direction: the course of cultural events can be seen as following a sin wave. I always pictured them as waves as seen in profile, and circles as seen from the end. Here:

Although instead of the spiral progressing in a straight line, it would follow a sine-wave path, which in turn would follow sine-wave path and so on – spirals within spirals all the way down, as if they were turtles or something.

Read the rest of this entry »


theAbysmal Shape of Time

18 December 2016

If only I knew how to CGI.

I imagine, if I were able to animate theAbysmal Calendar as a visualization, I would begin with a string of days. Each day would be represented by a sphere, and they would stretch off ahead and backwards indefinitely. If you chose to look at the lunar cycles, then the days would form loops of 29 or 30 days out of the line. If we tie those to the year, the there are 12 or 13 of those loops for every year. If we measure the Metonic Cycle, then there’s another loop every 19 years.

That’s one example.  theAbysmal would be highly variable within the year, however, if we organize our year as the Maya by orders of 20, we get 20 day loop, 18 of those in a year (minus 5 leap days), then 20 years, 400 years, 8000, 160000, etc. It would be a similar effect to DNA supercoiling. A coil made up of coils made up of coils made up of…

And if theAbysmal behaves like DNA in this respect, in what other ways can they be linked?

mycelium - theAbysmal Color


Counting from Now

8 August 2014

How to think of time as relative to this particular moment.

Although the idea had passed through my thoughts some time ago, I never gave it much thought, until a friend and I were immersed in a discussion about our relative time-related projects (and for the record, the man is a genius, with some interest projects on the go – but that’s for him to share).

theAbysmal Calendar begins counting measures of time with the numeral 0 (this is how the Maya counted, which is where I learned of it). This allows us to count the time periods, like we do with seconds, minutes, and hours. The day begins at midnight (for some), which on the clock is 00:00:00 – or 0 hour, 0 minute, 0 second.

this is followed by 00:00:01, which indicates that one second has elapsed. It is a way of counting a measure of time AFTER it has run its full course.

This is not how we mark longer measures of time. We begin the numbering with 1 (as in the years 1-2014), or in the case of the days of the month, we use the ordinal system of 1st, 2nd, 3rd, which is an indication of the sequence of the days.

theAbysmal applies the system of counting from 0 (as we saw with clock time) to every measure of time, from the second (and by extension, its subdivisions) to the year (and by extension, all its groupings). So, in this sense, time can be indicated from second (on the right) to the year (on the right)

The moment I finish this sentence would be noted as
01:08:05:13:14:49
Year 1, Month 8, Day 5, Hour 13 (1pm), Minute 14, second 39

or in Gregorian terms
1:16 pm and 39 seconds, August 8th, 2014

That’s the way to have an absolute count of days. Any given day is a fixed reference point on the calendar (and every other calendar).

However, if we apply the 0 to the current moment, as in this year, this month, today, this hour, this minute, this second. As we experience the progression of time, the current moment remains the same, but the numbers assigned to every past and future day change. This is a very different method of thinking about time. We do this to some extent, refering to next year, this month, yesterday.

Having this system overlap with theAbysmal requires some kind of programming knowledge to do anything with, and I abandoned any hope of acquiring such knowledge as I scribbled pencil marks in tiny boxes on punchcards.

At any rate, it’s something I haven’t seen applied to any other calendar system, and it would provide yet another function that this tool could perform, if needed. Here’s a comparison. Not sure I’ve quite figured out how to do this.

Today
Calendar Year Month Day Hour Minute
Gregorian 2014 8 8 1 28 pm
theAbysmal 1 8 5 13 28
Relative 0 0 0 0 0

 

Past Date
Calendar Year Month Day Hour Minute
Gregorian 1945 8 6 8 15 am
theAbysmal N/A 08 03 8 15
Relative -69 0 -2 -5 -13

 

Future Date
Calendar Year Month Day Hour Minute
Gregorian 2050 1 1 1 01 am
theAbysmal 38 0 10 01 01
Relative +37 -8 +5 -12 -27

A Paradise Built in Hell – Carnival and Disaster

8 July 2013

A Paradise Built in Hell – the extraordinary communities that arise in disaster by Rebecca Solnit

III Carnival and Revolution – Mexico City’s Earthquake

Standing on Top of Golden Hours

The True Feast of Time

Falling in love is easy. The experience carries us along effortlessly for a while, everything is harmonious, and the possibilities seem endless. Then one day you wake up in the same room as another human being with his or her own needs and views and the interesting process of actually finding common ground and forming a resilient and lasting bond begins… or fails. A disaster is as far from falling in love as can be imagined, but disaster utopias are also a spell when engagement, improvisation, and empathy happen as if by themselves. Then comes the hard business of producing a good society by determination and dedication Civil society has moments when it falls in love with itself or celebrates its anniversaries, when those ties again become enchantments rather than obligations. The era when the connections were made, the possibilities were exciting, and joy came readily matters afterward. Memory of such moments becomes a resource to tap into through recollection and invocation, and celebrating those moments revives and reaffirms the emotions. Thus it is that we celebrate birthdays, the dates on which couples met or were married, on which revolutions began, battles were won, on which a god, saint, or hero was born, performed a miracle, left the earth, and more. Then enchanted time can be reclaimed and renewed by memory and celebration, and most cultures have a calendar of such occasions, when the linear time of production pauses and the cyclical time of celebration appears.

Disaster and revolution both create in some sense a carnival – an upheaval and a meeting ground, and there are carnivalesque aspects to disaster. We could think f revolutions as carnivals, for whatever good they create in the long term it is only in the moment that they create the sense of openness to each other and to possibility that is so exhilarating. That is, imagined as moments of renewal and reinvention rather than attempts to secure some good permanently, we could see the ephemeral utopia they create with new eyes. And certainly carnival and revolution have long been linked. (Though the word is used more generally in the English-speaking world, Carnival is most specifically the festivities that occur before Lent – in other words, a series of celebrations in the span of time between Christmas and Easter.)

Carnival makes sense as a revolution too: an overthrow of the established order under which we are alienated from each other, too shy to act, divided along familiar lines. Those lines vanish and we merge exuberantly.. Carnival is a hectic, short-lived, raucous version of utopia, one that matters because it is widely available, though just as carnival is scheduled and disaster is not, so carnival has known limits and consequences and disaster does not. Still, the resemblances are significant – carnival, for example, often features grotesque images, motifs of death, role inversion and transformation, and much chaos, as well as the basic ingredient of people living together in a shared space and going beyond their usual bounds. Carnival is in some sense a formalized disaster, a ritual to reap disaster’s benefits with a minimum of disaster’s tragic consequences. You could call it disaster made predictable, both in when it happens and what it wreaks. Fritz spoke of “the failure of modern societies to fulfill an individual’s basic human needs for community identity” and concluded that “disasters provide a temporary liberation from the worries, inhibitions, and anxieties associated with the past and future because they force people to concentrate their full attention on immediate moment-to-moment, day-to-day needs within the context of the present realities.” He could have also been describing what carnival provides in the more safe and structured break from ordinary time.

Some ancient calendars had three hundred sixty days; the five at the end of the year were categorically outside time, so that the ordinary rules did not apply (similarly, Halloween was initially a Celtic year’s-end festival when the dead could travel through the gap between the old year and the new). A sense of being outside ordinary time, of disorder and inversion, governs saturnalias and carnivals. They are liminal in an almost literal sense, since that word means crossing lintels or thresholds. The Roman Saturnalia was a year-end winter festival of freedom: gambling was permitted in public, everyone wore the wool caps of freedmen, slaves were relieved of their duties and masters sometimes waited on slaves, a lord of misrule was chosen (and in some accounts, this holiday of Saturn was assimilated into that of Kronos, the god of time and the Golden Age). The festival lasted a few days and then several days, but long after it was over it must have left a lingering sense that the everyday order of things was not the inevitable one; it must have, like disaster and revolution, opened up the possibilities.

Scholarship nowadays denies a direct relationship between the Roman Saturnalia and Christian Carnival, but there are many similarities, including a lord of misrule and acts of inversion of ordinary power relations. In his book Carnival and Other Christian Festivals, Max Harris recounts the theological basis for the inversion of hierarchies, the passage in the Magnificat where Mary says (in Luke 1:22), in celebration of the impending birth of her son, “He hath put down the mighty from their seat and hath exalted the humble.” And he quotes Peter burke, who wrote that the whole Christmas season was “treated as carnivalesque, appropriately enough from a Christian point of view, since the birth of the Son of God in a manger was a spectacular example of the world turned upside down.” Carnival, which was originally part of the Christmas season rather than the prelude to Lent, could include impersonations of the clergy; cross-dressing actual members of the clergy; comic blasphemies, including parodies of the Mass and risqué humor; ritual enactments of historic battles (particularly in the New World) in which the losers were no longer necessarily the losers; masks; dances; fireworks; spectacles; uproar; and chaos. The Russian critic Mikhail Bakhtin goes further in his famous description of carnival: “Carnival celebrated temporary liberation from the prevailing truth and from the established order; it marked the suspension of all hierarchical rank, privileges, norms, and prohibitions. Carnival was the true feast of time, the feast of becoming, change, and renewal. It was hostile to all that was immortalized and completed. … People were, so to speak, reborn for new, purely human relations. These truly human relations were not only a fruit of imagination or abstract thought; they were experienced.”

Looking back from the perspective of disaster and revolution, carnival seems not merely to punctuate the calendar of ordinary time but to puncture it as well, as if with air holes to breathe through, or to let pressure off, or to let outside possibilities in. Carnival is often spoken of as liminal, as a moment of suspension between two states, of openness to transformation and difference, a moment when the rules are no longer in effect (though the disorder that Carnival creates and celebrates has its own strict parameters). Europe’s Protestant Reformation, in eliminating so many festivals and celebrations, did not merely increase work time but also undid the dialogue between ordinary time and its festive interruption, an interruption that is also an assertion of civil society, of memory, of collective liberation. And so one way to regard uprisings and maybe even disasters is as unseasonal outbreaks of carnival, assertions of civil society, community, and the breakdown of categories and boundaries. Covert new erotic unions are a staple of old stories about masked Carnival, but the public union of each to each is its point.

Many traditional carnivals feature subversive and mocking elements: parodies of the church and religion, status reversals, re-enactments of historical moments – such as the conquest of Latin America – in ways that reclaim power and voice. There is a permanent debate over whether carnival is truly subversive or the way an unjust society lets off pressure that allows the status quo to stand, but the only possible answer is that it varies, as do carnivals. The only great carnival rites in the United States include segregated balls and the public parade of New Orleans’s most powerful people in masks and hats that vaguely resemble the pointed caps of the Ku Klux Klan. When the City of New Orleans mandated in the early 1990s that the parades no longer be racially exclusive, some of the old elite white krewes canceled their public events rather than integrate.

The last surviving oligarchical public parade, Rex, still follows Zulu, the blackface African American parade that was founded as a parody of both Rex and African American stereotypes a century ago. Each year Rex and Zulu acknowledge each other in an uneasy truce while all the rest of the city revels, dresses up, dons masks, promenades, and drinks a lot. Mardi Gras is a strange festival, balanced between asserting the status quo and letting loose, between hierarchy and subversion. After all, the great majority excluded from the elite carnival balls have their own balls, parades, street revels, and parties, some of which include biting social commentary. Traditional carnivals continue throughout Europe, India, and the Americas, notably in Brazil, the Caribbean, and Bolivia, while the feast days and festivals of Mexico and indigenous New Mexico continue another version of the rite

Disaster belongs to the sociologists, but carnival to the anthropologists, who talk of its liminality. That is, like initiation rites, carnival takes place in a space betwixt and between familiar, settled states; it is a place of becoming in which differences diminish and commonalities matter, a separation from what came before. The anthropologist Victor Tune noted that liminal moments open up the possibility of communitas, the ties that are made when ordinary structures and the divides they enforce cease to matter or exist. The celebration that is carnival often resembles disaster in being made of turbulence and destruction: of people throwing colored powders in India or candies and meringues in Spain or beads in New Orleans; of creating huge messes in the streets and leaving piles of debris behind; of shouting, rushing, dancing, spinning; of mingling with strangers who are for the moment less strange; of images of the grotesque, the morbid, and the unsettling.

To make fellowship, joy, and freedom work for a day or a week is far more doable than the permanent transformation of society, and it can inspire people to return to that society in its everyday incarnation with renewed powers and ties. The anarchist theorist Hakim Bey famously coined the term temporary autonomous zones to describe these phenomena, neither revolution nor festival, in which people liberate themselves for pleasure and social reinvention. He saw their ephemerality as a survival technique, a way of arising, affecting, and vanishing before any move to repress arose: “The TAZ is like an uprising which does not engage directly with the State, a guerilla operation which liberates an area (of land, of time, of imagination) and then dissolves itself to re-form elsewhere/elsewhen, before the state can crush it.” The goal is not permanence or confrontation, and the moment of liberation can be re-created, so that its lapse is not necessarily a defeat.


More on 10th Dimensional Space

19 August 2012

I still don’t quite get it.

While I explored the tenth dimension and multiverses in the previous post Multiverse, Multidimensions, and Dark Matters of the Mind, I can’t say that I’m any closer to wrapping my head around it (and I imagine that the multiverse is okay with that). Nevertheless, I just wanted to add to this subject a website for Imagining the Tenth Dimension.

Here’s the summary:

0. A point (no dimension)

We start with a point. Like the “point” we know from geometry, it has no size, no dimension. It’s just an imaginary idea that indicates a position in a system.

1. The first dimension – a line

A second point, then, can be used to indicate a different position, but it, too, is of indeterminate size. To create the first dimension, all we need is a line joining any two points. A first dimensional object has length only, no width or depth.

2. The Second Dimension – A Split

If we now take our first dimensional line and draw a second line crossing the first, we’ve entered the second dimension. The object we’re representing now has a length and a width, but no depth. To help us with imagining the higher dimensions, we’re going to represent our second dimensional object as being created using a second line which branches off from the first.

Now, let’s imagine a race of two-dimensional creatures called “Flatlanders”. What would it be like to be a Flatlander living in their two-dimensional world? A two-dimensional creature would have only length and width, as if they were the royalty on an impossibly flat playing card. Picture this: a Flatlander couldn’t possibly have a digestive tract, because the pipe from their mouth to their bottom would divide them into two pieces! And a Flatlander trying to view our three-dimensional world would only be able to perceive shapes in two-dimensional cross-sections. A balloon passing through the Flatlander’s world, for instance, would start as a tiny dot, become a hollow circle which inexplicably grows to a certain size, then shrinks back to a dot before popping out of existence. And we three-dimensional human beings would seem very strange indeed to a Flatlander.

A 3D projection of an tesseract performing an ...

3. The Third Dimension – A Fold

Imagining the third dimension is the easiest for us because every moment of our lives that is what we’re in. A three dimensional object has length, width, and height. But here’s another way to describe the third dimension: if we imagine an ant walking across a newspaper which is lying on a table, we can pretend that the ant is a Flatlander, walking along on a flat two-dimensional newspaper world. If that paper is now folded in the middle, we create a way for our Flatlander Ant to “magically” disappear from one position in his two-dimensional world and be instantly transported to another. We can imagine that we did this by taking a two-dimensional object and folding it through the dimension above, which is our third dimension. Once again, it’ll be more convenient for us as we imagine the higher dimensions if we can think of the third dimension in this way: the third dimension is what you “fold through” to jump from one point to another in the dimension below.

4. The Fourth Dimension – A Line

Okay. The first three dimensions can be described with these words: “length, width, and depth”. What word can we assign to the fourth dimension? One answer would be, “duration”. If we think of ourselves as we were one minute ago, and then imagine ourselves as we are at this moment, the line we could draw from the “one-minute-ago version” to the “right now” version would be a line in the fourth dimension. If you were to see your body in the fourth dimension, you would be like a long undulating snake, with your embryonic self at one end and your deceased self at the other. But because we live from moment to moment in the third dimension, we are like our second dimensional Flatlanders. Just like that Flatlander who could only see two-dimensional cross-sections of objects from the dimension above, we as three-dimensional creatures can only see three-dimensional cross-sections of our fourth-dimensional self.

5. The Fifth Dimension – A Split

One of the most intriguing aspects of there being one dimension stacked on another is that down here in the dimensions below we can be unaware of our motion in the dimensions above. Here’s a simple example: if we make a Möbius strip (take a long strip of paper, add one twist to it and tape the ends together) and draw a line down the length of it, our line will eventually be on both sides of the paper before it meets back with itself. It appears, somewhat amazingly, that the strip has only one side, so it must be a representation of a two-dimensional object. And this means that a two-dimensional Flatlander traveling down the line we just drew would end up back where they started without ever feeling like they had left the second dimension. In reality, they would be looping and twisting in the third dimension, even though to them it felt like they were traveling in a straight line.

The fourth dimension, time, feels like a straight line to us, moving from the past to the future. But that straight line in the fourth dimension is, like the Möbius strip, actually twisting and turning in the dimension above. So, the long undulating snake that is us at any particular moment will feel like it is moving in a straight line in time, the fourth dimension, but there will actually be, in the fifth dimension, a multitude of paths that we could branch to at any given moment. Those branches will be influenced by our own choice, chance, and the actions of others.

Quantum physics tells us that the subatomic particles that make up our world are collapsed from waves of probability simply by the act of observation. In the picture we are drawing for ourselves here, we can now start to see how each of us are collapsing the indeterminate wave of probable futures contained in the fifth dimension into the fourth dimensional line that we are experiencing as “time”.

6. The Sixth Dimension – A Fold

What if you wanted to go back into your own childhood and visit yourself? We can imagine folding the fourth dimension through the fifth, jumping back through time and space to get there. But what if you wanted to get to the world where, for example, you had created a great invention as a child that by now had made you famous and rich? We can imagine our fourth-dimensional selves branching out from our current moment into the fifth dimension, but no matter where you go from here the “great child inventor” timeline is not one of the available options in your current version of time — “you can’t get there from here” — no matter how much choice, chance, and the actions of others become involved.

There are only two ways you could get to that world – one would be to travel back in time, somehow trigger the key events that caused you to come up with your invention, then travel forward in the fifth dimension to see one of the possible new worlds that might have resulted. But that would be taking the long way. The shortcut we could take would involve us folding the fifth dimension through the sixth dimension, which allows us to instantly jump from our current position to a different fifth dimensional line.

7. The Seventh Dimension – A Line

In our description of the fourth dimension, we imagined taking the dimension below and conceiving of it as a single point. The fourth dimension is a line which can join the universe as it was one minute ago to the universe as it is right now. Or in the biggest picture possible, we could say that the fourth dimension is a line which joins the big bang to one of the possible endings of our universe.

Now, as we enter the seventh dimension, we are about to imagine a line which treats the entire sixth dimension as if it were a single point. To do that, we have to imagine all of the possible timelines which could have started from our big bang joined to all of the possible endings for our universe (a concept which we often refer to as infinity), and treat them all as a single point. So, for us, a point in the seventh dimension would be infinity – all possible timelines which could have or will have occurred from our big bang.

8. The Eighth Dimension – A Split

When we describe infinity as being a “point” in the seventh dimension, we are only imagining part of the picture. If we’re drawing a seventh dimensional line, we need to be able to imagine what a different “point” in the seventh dimension is going to be, because that’s what our line is going to be joined to. But how can there be anything more than infinity? The answer is, there can be other completely different infinities created through initial conditions which are different from our own big bang. Different initial conditions will create different universes where the basic physical laws such as gravity or the speed of light are not the same as ours, and the resulting branching timelines from that universe’s beginning to all of its possible endings will create an infinity which is completely separate from the one which is associated with our own universe. So the line we draw in the seventh dimension will join one of these infinities to another. And, as boggling as the magnitude of what we are exploring here might be, if we were to branch off from that seventh dimensional line to draw a line to yet another infinity, we would then be entering the eighth dimension.

9. The Ninth Dimension – A Fold

As we’ve explored already, we can jump from one point in any dimension to another simply by folding it through the dimension above. If our ant on the newspaper were a two-dimensional Flatlander, then folding his two-dimensional world through the third dimension would allow him to magically disappear from one location and appear in a different one. As we’re now imagining the ninth dimension, the same rules would apply – if we were to be able to instantaneously jump from one eighth dimensional line to another, it would be because we were able to fold through the ninth dimension.

10. The Tenth Dimension – A Point?

Before we discussed the first dimension, we could say that we first started out with dimension zero, which is the geometrical concept of the “point”. A point indicates a location in a system, and each point is of indeterminate size. The first dimension then, takes two of these “points” and joins them with a line.

When we imagined the fourth dimension, it was as if we were treating the entirety of three-dimensional space in a particular state as a single point, and drawing a fourth-dimensional line to another point representing space as it is in a different state. We often refer to the line we have just drawn as “time”.

Then in the seventh dimension, we treated all of the possible timelines which could be generated from our big bang as if this were a single point, and imagined drawing a line to a point representing all of the possible timelines for a completely different universe.

Now, as we enter the tenth dimension, we have to imagine all of the possible branches for all the possible timelines of all the possible universes and treat that as a single point in the tenth dimension. Whew! So far, so good. But this is where we hit a roadblock: if we’re going to imagine the tenth dimension as continuing the cycle, and being a line, then we’re going to have to imagine a different point that we can draw that line to.  But there’s no place left to go! By the time we have imagined all possible timelines for all possible universes as being a single point in the tenth dimension, it appears that our journey is done.

In String theory, physicists tell us that Superstrings vibrating in the tenth dimension are what create the subatomic particles which make up our universe, and all of the other possible universes as well. In other words, all possibilities are contained within the tenth dimension, which would appear to be the concept we have just built for ourselves as we imagined the ten dimensions, built one upon another.

Makes my head hurt to just to cut and paste that stuff.

Hope you have better luck than I did. =)

124 Days to Dec 21st 2012


Quantum never Crashed

18 May 2012

Time keeps on slipping every which way but loose.

I’m a little behind in posting this (which is appropriate in its own twistedly way). I understand some of the characteristics of quantum, but can’t fathom the reasons (it depends on more math and Greek letters than I am capable of grasping). Nevertheless, it continues to fascinate me, to the point where it all might click, like I’m a cat in a box someone’s just opened.

Quantum decision affects results of measurements taken earlier in time

Quantum entanglement is a state where two particles have correlated properties: when you make a measurement on one, it constrains the outcome of the measurement on the second, even if the two particles are widely separated. It’s also possible to entangle more than two particles, and even to spread out the entanglements over time, so that a system that was only partly entangled at the start is made fully entangled later on.

This sequential process goes under the clunky name of “delayed-choice entanglement swapping.” And, as described in a Nature Physics article by Xiao-song Ma et al., it has a rather counterintuitive consequence. You can take a measurement before the final entanglement takes place, but the measurement’s results depend on whether or not you subsequently perform the entanglement.

Delayed-choice entanglement swapping consists of the following steps. (I use the same names for the fictional experimenters as in the paper for convenience, but note that they represent acts of measurement, not literal people.)

  1. Two independent sources (labeled I and II) produce pairs photons such that their polarization states are entangled. One photon from I goes to Alice, while one photon from II is sent to Bob. The second photon from each source goes to Victor. (I’m not sure why the third party is named “Victor”.)
  2. Alice and Bob independently perform polarization measurements; no communication passes between them during the experiment—they set the orientation of their polarization filters without knowing what the other is doing.
  3. At some time after Alice and Bob perform their measurements, Victor makes a choice (the “delayed choice” in the name). He either allows his two photons from I and II to travel on without doing anything, or he combines them so that their polarization states are entangled. A final measurement determines the polarization state of those two photons.

The results of all four measurements are then compared. If Victor did not entangle his two photons, the photons received by Alice and Bob are uncorrelated with each other: the outcome of their measurements are consistent with random chance. (This is the “entanglement swapping” portion of the name.) If Victor entangled the photons, then Alice and Bob’s photons have correlated polarizations—even though they were not part of the same system and never interacted.

The practicalities of delayed-choice entanglement swapping bears many similarities to other entanglement experiments. Ma et al. sent pulsed light from an ultraviolet laser through two separate beta-barium borate (BBO) crystals, which respond by emitting two photons with entangled polarizations, but equal wavelength. The BBO crystals acted as the sources labeled I and II above; the oppositely polarized photons they produced were sent down separate paths. One path for each BBO crystal led to a polarization detector (“Alice” and “Bob”), while the other passed through a fiber-optic cable 104 meters long before arriving at the “Victor” apparatus.

That little bit of cabling was enough to ensure that anything that happened at Victor occurred after Alice and Bob had done their measurements.

The choice about entangling the photons at the Victor apparatus was made by a random-number generator, and passed through a tunable bipartite state analyzer (BiSA). The BiSA contained two beam-splitters that select photons’ paths depending on their polarization, along with a device that rotated the polarization of the photons. Depending on the “choice” to entangle or not, the polarization of the photons from I and II were made to correlate or left alone. Finally, the polarization of both photons at Victor were measured, and compared with the results from Alice and Bob.

Due to the 104-meter fiber-optic cable, Victor’s measurements occurred at least 14 billionths of a second after those of Alice and Bob, precluding the idea that the setting of the BiSA caused the polarization results to change. While comparatively few photons made it all the way through every step of the experiment, this is due to the difficulty of measurements with so few photons, rather than a problem with the results.

Ma et al. found to a high degree of confidence that when Victor selected entanglement, Alice and Bob found correlated photon polarizations. This didn’t happen when Victor left the photons alone.

Suffice it to say that facile explanations about information passing between Alice’s and Bob’s photons lead to violations of causality, since Alice and Bob perform their polarization measurement before Victor makes his choice about whether to entangle his photons or not. (Similarly, if you think that all the photons come from a single laser source, they must be correlated from the start, and you must answer how they “know” what Victor is going to do before he does it.)

The picture certainly looks like future events influence the past, a view any right-minded physicist would reject. The authors conclude with some strong statements about the nature of physical reality that I’m not willing to delve into (the nature of physical reality is a bit above my pay grade).

As always with entanglement, it’s important to note that no information is passing between Alice, Bob, and Victor: the settings on the detectors and the BiSA are set independently, and there’s no way to communicate faster than the speed of light. Nevertheless, this experiment provides a realization of one of the fundamental paradoxes of quantum mechanics: that measurements taken at different points in space and time appear to affect each other, even though there is no mechanism that allows information to travel between them.

217 Days to Dec 21st 2012


the Imposing Number Line

6 May 2012

not so much natured as nurtured numbers.

see previous posts

[Quoting the article in its entirety]

Study Finds Twist to the Story of the Number Line

Yupno of Papua New Guinea provide clues to the concept’s origins – and suggest familiar notion of time may not be straightforward, either

Tape measures. Rulers. Graphs. The gas gauge in your car, and the icon on your favorite digital device showing battery power. The number line and its cousins – notations that map numbers onto space and often represent magnitude – are everywhere. Most adults in industrialized societies are so fluent at using the concept, we hardly think about it. We don’t stop to wonder: Is it “natural”? Is it cultural?

Now, challenging a mainstream scholarly position that the number-line concept is innate, a study suggests it is learned.

The study, published in PLoS ONE April 25, is based on experiments with an indigenous group in Papua New Guinea. It was led by Rafael Nunez, director of the Embodied Cognition Lab and associate professor of cognitive science in the UC San Diego Division of Social Sciences.

“Influential scholars have advanced the thesis that many of the building blocks of mathematics are ‘hard-wired’ in the human mind through millions of years of evolution. And a number of different sources of evidence do suggest that humans naturally associate numbers with space,” said Nunez, coauthor of “Where Mathematics Comes From” and co-director of the newly established Fields Cognitive Science Network at the Fields Institute for Research in Mathematical Sciences.

“Our study shows, for the first time, that the number-line concept is not a ‘universal intuition’ but a particular cultural tool that requires training and education to master,” Nunez said. “Also, we document that precise number concepts can exist independently of linear or other metric-driven spatial representations.”

Nunez and the research team, which includes UC San Diego cognitive science doctoral alumnus Kensy Cooperrider, now at Case Western Reserve University, and Jurg Wassmann, an anthropologist at the University of Heidelberg who has studied the indigenous group for 25 years, traveled to a remote area of the Finisterre Range of Papua New Guinea to conduct the study.

The upper Yupno valley, like much of Papua New Guinea, has no roads. The research team flew in on a four-seat plane and hiked in the rest of the way, armed with solar-powered equipment, since the valley has no electricity.

The indigenous Yupno in this area number some 5,000, spread over many small villages. They are subsistence farmers. Most have little formal schooling, if any at all. While there is no native writing system, there is a native counting system, with precise number concepts and specific words for numbers greater than 20. But there doesn’t seem to be any evidence of measurement of any sort, Nunez said, “not with numbers, or feet or elbows.”

Neither Hard-Wired nor “Out There”

Nunez and colleagues asked Yupno adults of the village of Gua to complete a task that has been used widely by researchers interested in basic mathematical intuitions and where they come from. In the original task, people are shown a line and are asked to place numbers onto the line according to their size, with “1” going on the left endpoint and “10” (or sometimes “100” or “1000”) going on the right endpoint. Since many in the study group were illiterate, Nunez and colleagues followed previous studies and adapted the task using groups of one to 10 dots, tones and the spoken words instead of written numbers.

After confirming the Yupno participants’ understanding of numbers with piles of oranges, the researchers gave the number-line task to 14 adults with no schooling and six adults with some degree of formal schooling. There was also a control group of participants in California.

The researchers found that unschooled Yupno adults placed numbers on the line (or mapped numbers onto space), but they did it in a categorical manner, using systematically only the endpoints: putting small numbers on the left endpoint and the mid-size and large numbers on the right, ignoring the extension of the line — an essential component of the number-line concept. Schooled Yupno adults used the line’s extension but not quite as evenly as adults in California.

“Mathematics all over the world – from Europe to Asia to the Americas – is largely taught dogmatically, as objective fact, black and white, right/wrong,” Nunez said. “But our work shows that there are meaningful human ideas in math, ingenious solutions and designs that have been mediated by writing and notational devices, like the number line. Perhaps we should think about bringing the human saga to the subject – instead of continuing to treat it romantically, as the ‘universal language’ it’s not. Mathematics is neither hardwired, nor ‘out there.'”

Out-of-Body Time

The researchers ran several experiments while in Gua, Papua New Guinea, including those that examine another fundamental concept: time.

When talking about past, present and future, people all over the world show a tendency to conceive of these notions spatially, Nunez said. The most common spatial pattern is the one found in the English-speaking world, in which people talk about the future as being in front of them and the past behind, encapsulated, for example, in expressions such as the “week ahead” and “way back when.” (In earlier research, Nunez found that the Aymara of the Andes seem to do the reverse, placing the past in front and the future behind.)

In their time study with the Yupno, now in press at the journal Cognition, Nunez and colleagues find that the Yupno don’t use their bodies as reference points for time – but rather their valley’s slope and terrain. Analysis of their gestures suggests they co-locate the present with themselves, as do all previously studied groups. (Picture for a moment how you probably point down at the ground when you talk about “now.”) But, regardless of which way they are facing at the moment, the Yupno point uphill when talking about the future and downhill when talking about the past.

Interestingly and also very unusually, Nunez said, the Yupno seem to think of past and future not as being arranged on a line, such as the familiar “time line” we have in many Western cultures, but as having a three-dimensional bent shape that reflects the valley’s terrain.

“These findings suggest that how we think about abstract concepts is even more flexible than previously thought and is profoundly affected by language, culture and environment,” said Nunez.

“Our familiar notions on ‘fundamental’ concepts such as time and number are so deeply ingrained that they feel natural to us, as though they couldn’t be any other way,” added former graduate student Cooperrider. “When confronted with radically different ways of construing experience, we can no longer take for granted our own. Ultimately, no way is more or less ‘natural’ than the Yupno way.”

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229 Days to Dec 21st 2012