The chain of cause and effect is equally interminable. Every action has a reaction. Chaos theory tells us if a butterfly flutters its wings in Africa today it can create a hurricane in Europe weeks later. The flutter keeps influencing the world even after the butterfly stops fluttering. Its impact continues long after its source has ceased.
The people we were, the impressions we leave and our participation in the world—they outlive us. Children are a way of leaving a legacy—people who share our hopes and beliefs and dreams, in addition to our genetic composition. They continue where we left off, building off what we leave behind.
Wednesday, July 29, 2009
Chaos Theory and Death
An echo is the persistence of a phenomenon after its source has ceased. It reflects that our universe is a closed system of energy. Matter can neither be created or destroyed. Matter can be ground into bits, scattered in the wind or evaporate into the sky but it will never fully disappear; it always go somewhere. Once something has been it can never not be.
Monday, July 20, 2009
The Immutability of Concepts
Abraham Lincoln once commented, "How many legs does a dog have if you call the tail a leg? Four. Calling a tail a leg doesn't make it one." Lincoln was a great President but a lousy linguist. I think most linguists would agree that if all English speakers agreed to change the meaning of the word 'leg' to something more like 'appendage,' a dog's tail could be counted.
But Lincoln was no fool, so perhaps his comment means more than meets the eye (or ear). Although we could change the name for a tail, we cannot turn a tail into a leg. A tail would still lack the defining elements of a leg like a foot and claws or nails. We must be careful to divide the concept of a leg from its name. A name is arbitrary, a concept is timeless.
Of course, some concepts involve arbitrary elements. Consider the case of units of measurement. A 'foot' is an arbitrarily chosen length. In fact, the English and French both used 'feet' for measurement but an English foot was slightly shorter than its French counterpart--leading to a persistently stubborn myth about Napoleon's short stature. Napoleon's height was noted as 5 foot 2 inches. This measurement was in French feet (pieds de roi) and was never correctly converted to standard English measure. In English feet, Napoleon stood 5 foot 6.5 inches tall--slightly above average for his time.
But Lincoln was no fool, so perhaps his comment means more than meets the eye (or ear). Although we could change the name for a tail, we cannot turn a tail into a leg. A tail would still lack the defining elements of a leg like a foot and claws or nails. We must be careful to divide the concept of a leg from its name. A name is arbitrary, a concept is timeless.
Of course, some concepts involve arbitrary elements. Consider the case of units of measurement. A 'foot' is an arbitrarily chosen length. In fact, the English and French both used 'feet' for measurement but an English foot was slightly shorter than its French counterpart--leading to a persistently stubborn myth about Napoleon's short stature. Napoleon's height was noted as 5 foot 2 inches. This measurement was in French feet (pieds de roi) and was never correctly converted to standard English measure. In English feet, Napoleon stood 5 foot 6.5 inches tall--slightly above average for his time.
Monday, July 13, 2009
The Ship of Theseus
"The ship wherein Theseus and the youth of Athens returned [from Crete] had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same."
—Plutarch, Theseus
Plutarch thus questions whether the ship would remain the same if it were entirely replaced, piece by piece. As a corollary, one can question what happens if the replaced parts were used to build a second ship. Which, if either, is the original Ship of Theseus? Consider also, "George Washington's axe" (sometimes "my grandfather's axe") which is the subject of an apocryphal story of unknown origin in which the famous artifact is "still George Washington's axe" despite having had both its head and handle replaced.
One solution to this paradox may come from the concept of four dimensionalism. Ted Sider and others have proposed that these problems can be solved by considering all things as 4-dimensional objects. An object is a spatially extended three-dimensional thing that also extends across the 4th dimension of time. This 4-dimensional object is made up of 3-dimensional time-slices. An object is made up of a series of causally related time-slices. And the whole aggregate of time-slices, namely the 4-dimensional object, is as single object. But the individual time-slices can have qualities that differ from each other.
Plutarch thus questions whether the ship would remain the same if it were entirely replaced, piece by piece. As a corollary, one can question what happens if the replaced parts were used to build a second ship. Which, if either, is the original Ship of Theseus? Consider also, "George Washington's axe" (sometimes "my grandfather's axe") which is the subject of an apocryphal story of unknown origin in which the famous artifact is "still George Washington's axe" despite having had both its head and handle replaced.
One solution to this paradox may come from the concept of four dimensionalism. Ted Sider and others have proposed that these problems can be solved by considering all things as 4-dimensional objects. An object is a spatially extended three-dimensional thing that also extends across the 4th dimension of time. This 4-dimensional object is made up of 3-dimensional time-slices. An object is made up of a series of causally related time-slices. And the whole aggregate of time-slices, namely the 4-dimensional object, is as single object. But the individual time-slices can have qualities that differ from each other.
Wednesday, July 8, 2009
Raises
Marilyn vos Savant posed this question: Say you're making $10,000 a year. Your boss offers you a choice between a $1,000 raise once a year and a $300 raise every six months. Which do you choose? Marilyn says you should choose the $300 raise. I disagree but I'll lay out Marilyn's math and explanation for you.
Say Marilyn vos Savant and you each makes $10000 a year. Starting Jan. 1, 2001, Marilyn takes the $300 raise every six months and you take the $1000 raise once a year. In the first six months you both make $5000. In the next six months, Marilyn makes $5300 and you make $5000 for a total on the year of $10300 and $10000, respectively.
On Jan. 1, 2002, you both get raises - $300 for her, $1000 for you. Her pay for the next six months is $5600, yours is $5500. On July 1, she gets a raise and you don't; for the next six months, her pay is $5900 and yours is $5500. After two years she's made $21800 and You've made $21000. In the first six months of 1993, Savant makes $6200 and you make $6000, for a grand total of $34000 for her and only $33000 for you.
Marilyn vos Savant YouYou'll notice that as time goes on, the earnings gap only increases. Can anyone deduce what's wrong with all this?
Pay for Running Pay for Running
Period period total period total
-------------- ------- ------- ------- -------
2001, 1st half $5000 $5000 $5000 $5000
2nd half $5300 $10300 $5000 $10000
2002, 1st half $5600 $15900 $5500 $15500
2nd half $5900 $21800 $5500 $21000
2003, 1st half $6200 $28000 $6000 $27000
2nd half $6500 $34500 $6000 $33000
2004, 1st half $6800 $41300 $6500 $39500
2nd half $7100 $48400 $6500 $46000
Answer:
Given the question as stated, most people would interpret a $300 raise to mean a $300 increase in annual salary--that is, after six months your salary would rise from $10,000 to $10,300 per year. In your first year you'd make $10,150--$5,000 the first six months, $5,150 the second--not the $10,300 Marilyn claims. Under Marilyn's math she's giving herself two $600/year a raises--as reflected in her starting salary for 2002 which is $11,200 (5,600 x 2)--thus her modest $300 raise somehow bolstered her salary by $1200 in a single year. Applying the raise to the yearly salary, there's no way a semiannual $300 raise would beat out an annual $1,000 raise.
Sunday, July 5, 2009
Wormholes
In physics, a wormhole is a hypothetical topological feature of spacetime that is fundamentally a 'shortcut' through space and time. Wormholes allow faster-than-light travel by ensuring that the speed of light is not exceeded locally at any time. If two points are connected by a wormhole, the time taken to traverse it would be less than the time it would take a light beam to make the journey if it took a path through the space outside the wormhole. However, a light beam traveling through the wormhole would always beat the traveler. As an analogy, running around to the opposite side of a mountain at maximum speed may take longer than walking through a tunnel crossing it. You can walk slowly while reaching your destination more quickly because the distance is smaller.
A wormhole could allow time travel. This could be accomplished by accelerating one end of the wormhole to a high velocity relative to the other, and then sometime later bringing it back; relativistic time dilation would result in the accelerated wormhole mouth aging less than the stationary one as seen by an external observer, similar to what is seen in the twin paradox, in which a twin who makes a journey into space in a high-speed rocket will return home to find he has aged less than his identical twin who stayed on Earth.
For example, consider two clocks at both mouths both showing the date as 2000. After being taken on a trip at relativistic velocities, the accelerated mouth is brought back to the same region as the stationary mouth with the accelerated mouth's clock reading 2005 while the stationary mouth's clock read 2010. A traveler who entered the accelerated mouth at this moment would exit the stationary mouth when its clock also read 2005, in the same region but now five years in the past. Such a configuration of wormholes would form a closed loop in spacetime, known as a closed timelike curve.
Time connects differently through the wormhole than outside it, so that synchronized clocks at each mouth will remain synchronized to someone traveling through the wormhole itself, no matter how the mouths move around. This means that anything which entered the accelerated wormhole mouth would exit the stationary one at a point in time prior to its entry. There is a catch though: a time traversing wormhole cannot take you back to before it was made--which might explain why there's no time travelers popping into your local McDonald's.
A wormhole could allow time travel. This could be accomplished by accelerating one end of the wormhole to a high velocity relative to the other, and then sometime later bringing it back; relativistic time dilation would result in the accelerated wormhole mouth aging less than the stationary one as seen by an external observer, similar to what is seen in the twin paradox, in which a twin who makes a journey into space in a high-speed rocket will return home to find he has aged less than his identical twin who stayed on Earth.
For example, consider two clocks at both mouths both showing the date as 2000. After being taken on a trip at relativistic velocities, the accelerated mouth is brought back to the same region as the stationary mouth with the accelerated mouth's clock reading 2005 while the stationary mouth's clock read 2010. A traveler who entered the accelerated mouth at this moment would exit the stationary mouth when its clock also read 2005, in the same region but now five years in the past. Such a configuration of wormholes would form a closed loop in spacetime, known as a closed timelike curve.
Time connects differently through the wormhole than outside it, so that synchronized clocks at each mouth will remain synchronized to someone traveling through the wormhole itself, no matter how the mouths move around. This means that anything which entered the accelerated wormhole mouth would exit the stationary one at a point in time prior to its entry. There is a catch though: a time traversing wormhole cannot take you back to before it was made--which might explain why there's no time travelers popping into your local McDonald's.
Friday, July 3, 2009
Back to the Future Time Travel
As Marty McFly explores the world of 1955, he is confronted with the fact that the history of his parent's life is changing before his eyes, and his own existence is in jeopardy. He has interfered with the meeting of his parents, and must correct the situation before it's too late, or he will cease to exist. Back to the Future is essentially the classic grandfather paradox: a man goes back in time and undoes his own birth. However, Back to the Future's theory of time travel suggests a different resolution than a never-ending loop.
Like the Terminator series, Back to the Future insists there can only be one timeline and rejects a many worlds interpretation. Both series also allow 'temporal refugees,' visitors from possible future timelines who by virtue of their presence in the past, nullify their own creations. In T2 we have the T800 that comes from a world where Cyberdyne created Skynet, In BttF we have Marty. The difference between the two theories of time travel, however, is that Marty immeadiately feels the consequnces of his temporal mischief and begins to dissappear whereas the terminator persists even after destroying Cyberdyne.
Unlike the traditional grandfather paradox solution, where a time traveler who undoes their own existence thereby nullifies their own trip, in Back to the Future, the consequences of Marty's time travel aren't felt until after he meddles with his parents meeting. Marty exists long enough to mess up the past, but its not until the moment of divergence between his past and the new past that his continued existence is put in jeopardy. Of course, Marty is given a chance to redeem his timeline by getting his parents back together before he blinks out of existance (imagine his increasingly vanishing presence as representing the diminishing probability of his conception). This is what allows for the suspense in the Back to the Future movies, Marty could concievably nullfy his own existance without nullifying his trip altogether--the universe will only reconcile his anarchorismic presence after the point he meddled with his parent's meeting.
In the Back to the Future theory of time travel, a grandfather paradox would be resolved like this: one day, Papy Joe would be walking home, when someone who sorta looks like him pops out of thin air, murders him and then proceeds to fade out of existance. In a Terminator universe, the assailiant wouldn't dissappear but could linger around the timeline indefinetly, even though his origin had been nullified. If Terminator gives refugees a passport, Back to the Future only gives them a travel visa.
Like the Terminator series, Back to the Future insists there can only be one timeline and rejects a many worlds interpretation. Both series also allow 'temporal refugees,' visitors from possible future timelines who by virtue of their presence in the past, nullify their own creations. In T2 we have the T800 that comes from a world where Cyberdyne created Skynet, In BttF we have Marty. The difference between the two theories of time travel, however, is that Marty immeadiately feels the consequnces of his temporal mischief and begins to dissappear whereas the terminator persists even after destroying Cyberdyne.
Unlike the traditional grandfather paradox solution, where a time traveler who undoes their own existence thereby nullifies their own trip, in Back to the Future, the consequences of Marty's time travel aren't felt until after he meddles with his parents meeting. Marty exists long enough to mess up the past, but its not until the moment of divergence between his past and the new past that his continued existence is put in jeopardy. Of course, Marty is given a chance to redeem his timeline by getting his parents back together before he blinks out of existance (imagine his increasingly vanishing presence as representing the diminishing probability of his conception). This is what allows for the suspense in the Back to the Future movies, Marty could concievably nullfy his own existance without nullifying his trip altogether--the universe will only reconcile his anarchorismic presence after the point he meddled with his parent's meeting.
In the Back to the Future theory of time travel, a grandfather paradox would be resolved like this: one day, Papy Joe would be walking home, when someone who sorta looks like him pops out of thin air, murders him and then proceeds to fade out of existance. In a Terminator universe, the assailiant wouldn't dissappear but could linger around the timeline indefinetly, even though his origin had been nullified. If Terminator gives refugees a passport, Back to the Future only gives them a travel visa.
Thursday, July 2, 2009
Eternalism
Eternalism is a philosophical explanation of the nature of time. It builds on the standard method of modeling time as a dimension in physics, to give time similar properties to that of space. This would mean that time is just another dimension, that future events are "already there", and that there is no objective flow of time. In the view suggested by Eternalism, there is no passage of time; the ticking of a clock measures durations no differently than the marks on a measuring tape measures distances between places.
Consider the relationship the primary three dimensions bear to each other. It helps to imagine our three dimensional world is composed like a pile of paper with infinite discrete two dimensional slices. For instance, a two dimensional slice of a ball would be shaped like a circle. If that two dimensional slice was taken at the exact center of the ball, and it would have lots of increasingly smaller circles above and beneath it. Each slice would be very similar to the one next to it except it would be slightly smaller until eventually they got so small the circle vanished. Every two dimensional slice next to it would be imperceptibly different from the one.
Likewise, every moment in time is another piece of paper in a time stack, the fourth dimension. Every moment is inextricably "next to" every snapshot before of after it. Much like the ball example, every snapshot closely resembles the ones adjacent to it but is slightly different. Conceptually, it's hard for us to imagine a spacial fourth dimension because we 'run out of place' to put things, but by using time as the fourth axis we can store more information. So how is time different than space? time seems to move in only one direction.
Eternalists say time marching forward at a constant pace is merely an illusion because our minds cannot comprehend all things at once. In an eternalist model, time travel is as easy as turning around and walking backwards. One interesting implication of eternalism is that everyone consciousness need not have the same idea of the "present," so although my consciousness exists right now, your conscious could be perceiving the present as twenty years from now. The role the observer plays in a eternalist universe is unfixed.
Consider the relationship the primary three dimensions bear to each other. It helps to imagine our three dimensional world is composed like a pile of paper with infinite discrete two dimensional slices. For instance, a two dimensional slice of a ball would be shaped like a circle. If that two dimensional slice was taken at the exact center of the ball, and it would have lots of increasingly smaller circles above and beneath it. Each slice would be very similar to the one next to it except it would be slightly smaller until eventually they got so small the circle vanished. Every two dimensional slice next to it would be imperceptibly different from the one.
Likewise, every moment in time is another piece of paper in a time stack, the fourth dimension. Every moment is inextricably "next to" every snapshot before of after it. Much like the ball example, every snapshot closely resembles the ones adjacent to it but is slightly different. Conceptually, it's hard for us to imagine a spacial fourth dimension because we 'run out of place' to put things, but by using time as the fourth axis we can store more information. So how is time different than space? time seems to move in only one direction.
Eternalists say time marching forward at a constant pace is merely an illusion because our minds cannot comprehend all things at once. In an eternalist model, time travel is as easy as turning around and walking backwards. One interesting implication of eternalism is that everyone consciousness need not have the same idea of the "present," so although my consciousness exists right now, your conscious could be perceiving the present as twenty years from now. The role the observer plays in a eternalist universe is unfixed.
Eternalism has implications for the concept of free will, in that it proposes that future events are as immutably fixed and impossible to change as past events. Augustine of Hippo wrote that God is outside of time—that time exists only within the created universe. Many theologians agree. On this view, God would perceive something like a block universe, while time might appear differently to us finite beings.
Wednesday, July 1, 2009
Multiple Universes
In 1972, Hugh Everett formulated the many-worlds interpretation of quantum mechanics. In layman's terms, this means that there is a very large, perhaps infinite, number of universes since everything that could possibly have happened in our past (but didn't) has occurred in the past of some other universe(s). Parallel universes might provide a way out of paradoxes because all possible quantum events can occur in mutually exclusive histories. These alternate, or parallel, histories would form a branching tree symbolizing all possible outcomes of any interaction. If all possibilities exist, any paradoxes could be explained by having the paradoxical events happening in a different universe. Thus time travel then involves not moving forward and backwards through a single universe, but moving horizontally between similar universes.
A curious consequence of many-worlds is an experiment known as the quantum suicide machine has been proposed by cosmologist Max Tegmark. It examines the Schrödinger's Cat experiment from the point of view of the cat.
For example, a man sits down before a gun, which is pointed at his head. This is no ordinary gun; it's rigged to a machine that measures the spin of a quantum particle. Each time the trigger is pulled, the spin of the quantum particle is measured. Depending on the measurement, the gun will either fire, or it won't. If the quantum particle is measured as spinning in a clockwise motion, the gun will fire. If the particle is spinning counterclockwise, the gun won't go off. There'll only be a click.Nervously, the man takes a breath and pulls the trigger. The gun clicks. He pulls the trigger again. Click. And again: click. The man will continue to pull the trigger again and again with the same result: The gun won't fire. Although it's functioning properly and loaded with bullets, no matter how many times he pulls the trigger, the gun will never fire. He'll continue this process for eternity, becoming immortal.
Go back in time to the beginning of the experiment. The man pulls the trigger for the very first time, and the particle is now measured as spinning clockwise. The gun fires. The man is dead.
But, wait. The man already pulled the trigger the first time -- and an infinite amount of times following that -- and we already know the gun didn't fire. How can the man be dead? The man is unaware, but he's both alive and dead. Each time he pulls the trigger, the universe is split in two. It will continue to split, again and again, each time the trigger is pulled, and become quantum immortal.The idea behind quantum immortality is that the experimenter will remain alive in, and thus remain able to experience, at least one of the universes in this set, even though these universes form a tiny subset of all possible universes. Over time, the experimenter would therefore never perceive his or her own death.
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