Sunday, December 02, 2007

Is Information Real?

Last time we explored the nature of information and saw how the concept of information was used in statistical mechanics to solve the paradox of Maxwell’s Demon, and in the process, we took the concept of information from something you knew to something you could measure. But this begs the question, what are we measuring? Is information real, or is information just a useful human contrivance that we made up like the constellations we use for locating stars in the night sky? This is an important question for both physics and softwarephysics because it is where the two overlap the most. It is also an important question for IT professionals because we process information all day long, and as I demonstrated in my last posting, software is also a form of information subject to the mischief of the second law of thermodynamics.

Are You Moving or Standing Still?
Strangely, the answer to the question of the reality of information was resolved by an obscure clerk in the Swiss Patent Office in Bern in 1905 by the name of Albert Einstein, but this story starts out much earlier than that. The story really begins with another more fundamental question – are you currently moving or standing still? My fervent hope is that most of you are reading this posting in a quiet room and not on a Blackberry while driving your car in rush hour traffic as you fidget with an iPod and adjust your GPS navigation unit. So hopefully most of you would maintain that you are comfortably at rest in a room with familiar surroundings. But on second thought, recall that the Earth rotates on its axis at 1,038 miles/hour at the equator. I am writing these words in a suburb of Chicago at a latitude of 42° , so I am currently moving to the east at about 771 miles/hour relative to the center of the Earth. Also, don’t forget that the Earth orbits the Sun at 66,660 miles/hour, and that the Sun orbits the center of our galaxy at 132 miles/second, and that our galaxy is moving about 360 miles/second relative to the cosmic background radiation (CBR). So everything in the Universe, including you and me, is in a constant state of relative motion. And yet I do not feel a thing. The reason I do not feel all this motion is that, for the most part, I am moving in a straight line at a constant speed. For example, the Earth takes 365 days to orbit the Sun and complete a full 360° revolution about it. So that comes to about 1 degree/day. The width of your index finger at arm’s length also subtends an angle of about 1°. Now imagine being able to drive a car all day long in a straight line at 66,660 miles/hour, and find that at the end of the day, you have only deviated from your desired straight line path by the width of your index finger at arm’s length, when you look back at your starting point! Most of us would likely congratulate ourselves on being able to drive in such a straight line. Because the circumference of the Earth’s orbit is over 584 million miles and it takes 365 days to cover that distance, the Earth essentially moves in a straight line over the course of a single day to a very good approximation.

Galileo’s Concept of Relative Motion
In 1543, Copernicus published On the Revolutions of the Heavenly Spheres in which he proposed a new model for the solar system that had the Earth revolve about the Sun, rather than having the Sun orbit about a fixed and stationary Earth located at the center of the Universe. Galileo was an early supporter of the Copernican theory because of his observations of the moons of Jupiter revolving about Jupiter and his observations of the phases of Venus as it orbited the Sun. He made these discoveries in 1610 with the first use of a telescope to perform astronomical observations. But the lack of any readily apparent terrestrial evidence for the motion of the Earth was a significant challenge for Galileo because it was the chief argument against the Copernican theory. If the Earth really was moving, why didn’t we feel it move? Galileo addressed this issue in 1632 in his Dialogue Concerning the Two Chief World Systems, in which he proposed that we do not feel the motion of the Earth because the motion of the Earth is, for all practical purposes, in a straight line as outlined above, and that observers cannot sense straight line motion at a constant speed. In a famous passage of this book, Galileo suggested performing a series of experiments down in the hold of a ship on a calm sea. Galileo proposed that if you throw a ball, watch dripping water, or perform any other experiment in the hold of a ship on a calm sea, you will obtain the same results if the ship is rapidly moving under sail or is standing still at anchor. No experiment you perform will allow you to tell if you are moving or standing still. Anybody who has ever poured one of those little bottles of gin on an airplane traveling at 550 miles/hour in a quiet sky can attest to the validity of Galileo’s observations.

Salviatis:
Shut yourself up with some friend in the main cabin below decks on some large ship, and have with you there some flies, butterflies, and other small flying animals. Have a large bowl of water with some fish in it; hang up a bottle that empties drop by drop into a wide vessel beneath it. With the ship standing still, observe carefully how the little animals fly with equal speed to all sides of the cabin. The fish swim indifferently in all directions; the drops fall into the vessel beneath; and, in throwing something to your friend, you need throw it no more strongly in one direction than another, the distances being equal; jumping with your feet together, you pass equal spaces in every direction. When you have observed all these things carefully (though doubtless when the ship is standing still everything must happen in this way), have the ship proceed with any speed you like, so long as the motion is uniform and not fluctuating this way and that. You will discover not the least change in all the effects named, nor could you tell from any of them whether the ship was moving or standing still. In jumping, you will pass on the floor the same spaces as before, nor will you make larger jumps toward the stern than toward the prow even though the ship is moving quite rapidly, despite the fact that during the time that you are in the air the floor under you will be going in a direction opposite to your jump. In throwing something to your companion, you will need no more force to get it to him whether he is in the direction of the bow or the stern, with yourself situated opposite. The droplets will fall as before into the vessel beneath without dropping toward the stern, although while the drops are in the air the ship runs many spans. The fish in their water will swim toward the front of their bowl with no more effort than toward the back, and will go with equal ease to bait placed anywhere around the edges of the bowl. Finally the butterflies and flies will continue their flights indifferently toward every side, nor will it ever happen that they are concentrated toward the stern, as if tired out from keeping up with the course of the ship, from which they will have been separated during long intervals by keeping themselves in the air. And if smoke is made by burning some incense, it will be seen going up in the form of a little cloud, remaining still and moving no more toward one side than the other. The cause of all these correspondences of effects is the fact that the ship's motion is common to all the things contained in it, and to the air also. That is why I said you should be below decks; for if this took place above in the open air, which would not follow the course of the ship, more or less noticeable differences would be seen in some of the effects noted.

Sagredus:
Although it did not occur to me to put these observations to the test when I was voyaging, I am sure that they would take place in the way you describe. In confirmation of this I remember having often found myself in my cabin wondering whether the ship was moving or standing still; and sometimes at a whim which I have supposed it going one way when its motion was the opposite....


This is a key point. Galileo proposed that all motion is relative, meaning that you can only define motion as a change in the distance between objects. There is no such thing as absolute motion relative to some absolute and fixed space. Galileo’s concept of relative motion was carried forward further by Gottfried Leibniz, a contemporary and strident rival of Newton, who fervently claimed that there was no such thing as absolute space; there only was relative motion between objects – absolute space was a fantasy of our common sense. So when you tell a police officer that you really did come to a full and complete stop at a stop sign, you really mean a full and complete stop relative to the stop sign and not some fixed and absolute space filling up the entire Universe. This flies in the face of our common sense notions about space and motion, and there were many objections to this idea of relative motion and an Earth moving about the Sun. Galileo was tried for heresy in 1633 by the Inquisition and was sentenced to life imprisonment under house arrest. The uncensored version of the Dialogue Concerning the Two Chief World Systems was banned until 1835.

Newton’s Concept of Absolute Space and Time
In the first few pages of Newton’s Principia, published in 1687, Newton proposed that there really was an absolute and fixed space filling the entire Universe that all objects existed in and moved through. This absolute fixed space was like a stage or background upon which the motions of all the objects in the Universe were played out upon. Newton admitted that, as Galileo had proposed, you could not measure this fixed and absolute space directly, but just the same, it still existed. Newton also proposed that there was a fixed and absolute universal time that all observers agreed upon. All observers agreed on the number of seconds it took the police officer to write out your ticket. The ideas of a fixed and absolute space and time are such common sense self-evident concepts that Newton almost dismissed dealing with them outright in the first few pages of the Principia because they seemed so obvious to him, but this turned out to ultimately lead to his undoing. It would take more than 200 years to reveal the flaws in his reasoning.

Electromagnetism Creates Problems
In the 19th century, great advances were made in the area of electrodynamics, the dynamical study of charged particles in the presence of electrical and magnetic fields. It began in 1820 when Hans Christian Oersted discovered that an electrical current in a wire produced a magnetic field. You can repeat this famous discovery by simply connecting a wire to a standard 9-volt battery, like the ones used in many toys, and watch the current deflect a compass needle. Shortly thereafter, Andre-Marie Ampere came up with a mathematical model which explained this phenomenon. When electrical charges move, they create a magnetic field, and when charged particles move in a magnetic field, they feel a magnetic force perpendicular to their motion that deflects them. Before you connect the wire to the 9-volt battery, there are many free electrons in the copper wire moving about in random directions creating magnetic fields that all cancel each other out. When you connect the battery, an electric field is created in the wire, and the free electrons in the wire begin to drift slowly towards the positive pole of the battery. Contrary to what many people believe, the electrons do not flow at the speed of light. In fact, they drift at the stupendous rate of about one foot per hour in the wire. It is the driving electrical field that travels at nearly the speed of light and which makes rapid telecommunications possible. So now we had a handy way of telling if something was standing still or moving. All you had to do was observe an electrically charged object. If it gave off a magnetic field, then you knew it was moving; if it did not give off a magnetic field, then you knew it was standing still. So Newton was “right” and Galileo was “wrong”, an observer could use electromagnetic experiments to tell if he was standing still or moving relative to absolute space. There was just one problem, the idea did not work. In 1901, Trouton and Noble conducted just such an experiment using a suspended charged capacitor. They tried to observe the magnetic field that should have been given off by the suspended charged capacitor as it moved through absolute space on board the Earth, as the Earth orbited the Sun. But they did not find any! Also, in 1887, Michelson and Morley conducted an experiment in which they measured the speed of light, an electromagnetic wave, in two perpendicular directions separated by an angle of 90°. The expected result was that a difference in the speed of light in the two directions would be observed because of the Earth’s motion about the Sun, but again, none was detected. The speed of light was always found to be the same even as the experimental rig was rotated in different directions while the Earth orbited the Sun at 66,660 miles/hour.

Einstein’s Concept of Relative Space and Time
Albert Einstein graduated from college with a degree in physics in 1900, but could not find a job in academic physics, and instead, settled for a job as a patent clerk in the Swiss Patent Office in Bern from 1902 – 1908. In 1905, Einstein published On the Electrodynamics of Moving Bodies in which he proposed that Galileo was right after all. In this paper, Einstein proposed that you really could not conduct any experiment, including electromagnetic experiments, that would reveal if you were moving or standing still relative to an absolute space, because there was no such thing as an absolute space. All motion was relative to other objects just as Galileo had proposed from the start. In order for this to be true, Einstein had to raise two conjectures to the level of postulates:

1. The laws of physics are the same for all observers, even for observers moving relative to each other at constant speeds in straight lines.

2. The speed of light is the same for all observers, even for observers moving relative to each other at constant speeds in straight lines.

If the above two postulates were not true, you could easily tell if you were moving or standing still relative to an absolute space. All you would have to do is measure the speed of light in different directions, and if it were not the same in all directions, then you would know that you were moving relative to an absolute space.

You can read an English translation of On the Electrodynamics of Moving Bodies at

http://www.fourmilab.ch/etexts/einstein/specrel/www/

The first few sections are very enlightening and not that difficult.

In an earlier posting, I covered the steps in the scientific method. The above two postulates in On the Electrodynamics of Moving Bodies comprised the first step of the scientific method - inspiration/revelation. In the remainder of the paper, Einstein uses deductive rationalism to expand the postulates into a self-consistent theory by deducing the implications of the postulates. So let’s do the same. Imagine that you have a friend on a spaceship far from all the stars in our galaxy and that he has a special clock that we shall call a LightClock. The engine on his spaceship is turned off, and he is just coasting along in the vacuum of space. As far as your friend can tell, he is not moving because he does not feel any motion in the pit of his stomach, just as you do not feel any motion sitting in your quiet room reading this posting. The LightClock consists of a flash unit, a mirror, and a camera and works like this. The flash unit emits a burst of light that reflects off the mirror back into the camera. Every time the camera detects a reflected flash of light, the flash unit triggers again and sends out another burst of light. Each burst of light from the flash unit is considered a tick of the LightClock, and the time interval between ticks is used to tell time on your friend’s spaceship.

Figure 1

Now imagine that you are on an identical spaceship also far from all the stars of our galaxy with the engine turned off just coasting along. You have an identical LightClock on board your spaceship to keep time, and you also do not think that you are moving because you do not feel any motion in the pit of your stomach either. All of a sudden, you see your friend’s spaceship fly by at a high rate of speed relative to your spaceship. As your friend’s spaceship flies by, you see his LightClock ticking away with light flashes. Because your friend’s spaceship is moving relative to yours, you do not see the light rays moving straight up and down between the flash unit, mirror, and camera as he does. Instead, it appears to you that in order for the light flashes from the flash unit to reflect off the mirror and hit the camera, they have to move at an angle like a billiard ball in a bank shot because the camera will have moved to the right as the spaceship speeds by. The faster your friend’s spaceship speeds by, the greater the angle that is required for the bank shot.

Figure 2

From your perspective, the identical LightClock on your spaceship behaves just like Figure 1 above with the light rays going straight up and down from the flash unit to the mirror and back into the camera.

Now here comes the strange part when we start to apply Einstein’s two postulates. From your perspective, the bank shot path taken by the light rays in your friend’s LightClock, going up from the flash unit to the mirror at an angle, and finally coming back down to the camera at an angle, is clearly longer than the straight up and down path taken by the light rays in your identical LightClock. Since Einstein’s second postulate states that the speed of light is the same for all observers, from your perspective, the apparent time between light flashes in your friend’s LightClock must be greater than in your identical LightClock. Your conclusion must be that time is running slower for your friend than it is for you! Now you might object that this is all nonsense. Yes, these strange LightClocks might have a problem keeping proper time when they move relative to each other, but nobody uses such strange time pieces, and “real” clocks would certainly not have a problem keeping in sync with each other on the two spaceships. This is where Einstein’s first postulate comes into play. If “real” clocks on board your friend’s spaceship did not behave just like his LightClock, then he would have a way to tell if he was moving relative to absolute space or standing still. All he would have to do is compare his LightClock to a “real” clock, and if the two clocks did not keep the same time, then he would know that he was “moving”. If the LightClock and “real” clock stayed in synch, then he would know that he was “standing still”. So the “real” clocks on your friend’s spaceship must slow down too, just like his LightClock. It goes further than that. Everything on your friend’s spaceship must slow down too to keep in sync with the LightClock, including the biochemical aging reactions in your friend’s body. From your perspective, everything would have to move in slow motion on your friend’s spaceship. Some further analysis also reveals that the length of objects on your friend’s spaceship would also have to shrink relative to the same objects on your identical spaceship. In fact, his whole spaceship would shrink in length from your perspective as it flew past your spaceship. The faster his spaceship flew past you, the greater would be the slowing down of his time and the greater the shrinking of his spaceship. As his spaceship approached the speed of light, time on board would come nearly to a stop and his spaceship would shrink to the thickness of a piece of paper! Now for the strangest part of all. Since all we know is that the two spaceships are in relative motion with each other, your friend would see the very same thing when he looked at your LightClock and your spaceship! He would say that your LightClock was running slow, that time on board your spaceship had slowed down, and that your spaceship had shrunk too. And you would both be right!

The above implications of Einstein’s two postulates do some serious damage to our common sense notions of space and time, so we need to do some investigative work to check things out. To complete the final step of the scientific method, we need to use inductive empiricism to conduct experiments to test the deduced implications of Einstein’s postulates. Surprisingly, all known laboratory results confirm Einstein’s strange predictions. For example, when high energy cosmic rays (mainly fast moving protons) strike the upper atmosphere of the Earth, they create particles called muons at an altitude of about 30,000 feet. A muon is a fundamental particle very much like a very heavy electron, but unlike electrons, muons decay into other particles in 2.2 x 10-6 seconds. In order to conserve the momentum of the incoming high energy cosmic rays, the muons created by the collision of cosmic rays with atoms in the Earth’s upper atmosphere end up moving at about 99.8% of the speed of light. But with a lifetime of only 2.2 x 10-6 seconds, the muons should only travel about 2165 feet before decaying, so none of the muons should reach the Earth’s surface. Yet we do observer a large number of muons striking the Earth’s surface. The reason we observe muons at the surface of the Earth is that at a relative speed of 99.8% of the speed of light, the time on board the muons slows down considerably, and the lifetime of the muons increases to 34.8 x 10-6 seconds from our perspective. This allows plenty of time for the muons to reach the Earth’s surface before decaying.

There is no Absolute Now
Let’s look into another problem caused by the relative motion between the spaceships. Imagine the two spaceships are outfitted with some new timing equipment. This time two flash units are installed, one at each end of the spaceship and a camera is installed exactly in the middle of each spaceship. Suppose your friend observes that two bursts of light from the flash units on his spaceship arrive exactly at the same time at his camera. Since the camera is exactly midway between the two flash units, your friend must conclude that both flash units fired off simultaneously.

Figure 3

Suppose you observer the same two events as your friend’s spaceship flies past at a great speed relative to you. You also observe that the two flashes arrive at the camera at the same time. However, because his spaceship is moving relative to yours, you know that flash A had to happen before flash B. The light from flash A has to chase after the camera, while the camera runs into the oncoming light from flash B, so the light from flash A had to travel a greater distance to reach the camera than the light from flash B. Consequently, flash A happened before flash B from your perspective.

Figure 4

If there was a third spaceship going even faster to your right than your friend’s spaceship, observers on that spaceship would see just the opposite. They would contend that flash B happened before flash A!

Now we have a problem. We have three observers; one says that A and B happened at the same time; one says that A happened first and then B happened; and the last says that B happened first and then A happened. These are all true statements. Do not think that these observations are optical illusions caused by the observers not taking into account time lags due to the time it takes for light to reach them from different objects on the other spaceships. When all such adjustments are made, the conclusions of all three observers are found to be true.

In the Newtonian concept of space and time, such problems do not arise because everybody agrees on a common universal “now”. But in Einstein’s concept of space and time, there is no universal “now”. Each observer has his own “now”, and if I am moving relative to you, then my “now” has to be different than your “now”. This creates a problem for the concept of causality. Consider the situation where we think that flash A “causes” flash B to occur. Suppose we rig up a detector at B waiting for a signal from A along an ethernet cable. When an IP packet from A arrives at B, B fires off a flash of light. We set up A so that it sends the IP packet after it flashes. So in this arrangement we think that flash A causes flash B to happen, so we had better not get into a situation where B happens before A! The only way we can manage that is to conclude that the IP packet cannot travel faster than the speed of light, since we are already using light beams for all of the timings in our example. If the IP packet or any other form of information does not travel faster than the speed of light, all observers will agree that A happens before B and we will not have a problem with causality.

In another supplemental paper on relativity published by Einstein in 1905 he put forward an “Oh, by the way, I nearly forgot to tell you” additional concept:

E=mc²

Matter is a form of energy! Now watch the coming together of ideas. The concept of energy as formulated by Rudolph Clausius in the first law of thermodynamics is found to be equivalent to matter in Einstein’s reformulation of space and time, and the concept of information which grew out of the second law of thermodynamics, Maxwell’s Demon, and the concept of entropy in statistical mechanics, is found to preserve the idea of causality in Einstein’s Universe of relative motion. And the conservation of energy outlined in the first law of thermodynamics matches up nicely with Lavoisier’s earlier discovery of the conservation of matter. Matter can turn into energy and energy can turn into matter, but the total amount of energy and matter in the Universe remains constant.

In this second paper on relativity, Einstein also showed that material objects could not move faster than the speed of light because it takes more and more energy to accelerate objects as they approach the speed of light, and it would take an infinite amount of energy for an object to surpass the speed of light. So now we have a very an interesting finding. Matter, energy, and information cannot move faster than the speed of light. Based upon this finding, we can consider information to be just as real as energy and matter! So the answer to the question posed by this posting is yes, information is truly as “real” as matter and energy!

Resistance to Outside Ideas
Einstein had great expectations for his two papers on relativity published in 1905. He had also published two other papers in 1905, one which helped launch the quantum mechanical revolution by proposing that light waves were quantized into particles we now call photons, and the other, which used Brownian motion to prove that atoms and molecules actually did exist after all, despite the misgivings of the physicists who gave Ludwig Boltzmann such grief over the idea. Einstein hoped that these papers would be his ticket out of the patent office. But to Einstein’s great surprise, there was a deafening silence. Again, Einstein was an outsider and not taken seriously by the physics community of the day. Luckily for Einstein, Max Planck read his work and thought that it was significant. With Planck’s endorsement, other physicists began to take a look too, and a grudging acceptance of Einstein’s ideas began to develop over the years. Einstein was not freed from his patent office until 1908, when he became a teaching assistant at the University of Bern. In 1911, he finally became an associate professor at the University of Zurich, and finally became a full professor at the Eidgenössische Technische Hochschule in Zurich in 1912. Relativity remained controversial for many years, and Einstein never received the Nobel Prize for this work, but he was awarded the Nobel Prize in Physics in 1921 for his work on light and photons.

The Introduction of the Concept of Effective Theories
Since Newtonian mechanics was built upon a foundation of absolute space and time, it had to be modified when Einstein’s concepts of relative space and time were introduced. Everything got a little cockeyed at that point because the foundation of physics had shifted. Because of the shift in the underlying foundation, strange things like E=mc² began to pop up. But for the most part, if you kept your speeds down below 10% of the speed of light, the relativistic adjustments to Newtonian mechanics were so small that they could be ignored. So Newtonian mechanics worked very well over the velocity range of 0% - 10% of the speed of light. That defined the velocity range over which Newtonian mechanics worked as an effective theory. Recall that an effective theory is an approximation of reality that only holds true over a certain restricted range of conditions and only provides a certain depth of understanding of the problem at hand.

Einstein’s ideas were quite a shock to the early 20th century physicists because they were not used to the concept of effective theories. Physicists in the 18th and 19th centuries did not think that they were discovering effective theories that were only approximations of reality; they thought that they were discovering the true fundamental laws of the Universe that defined actual reality. It soon got worse. About the same time that relativity was struggling for acceptance, it became evident that Newtonian mechanics did not work very well for small things like atoms either. Again it was the interplay of Newtonian mechanics and classical electromagnetism that caused the problem. In an earlier posting, I discussed the Ultraviolet Catastrophe in which classical electromagnetism predicted that the walls of the room you are sitting in should be at a temperature of absolute zero, having converted all of their available energy into ultraviolet light and x-rays. Newtonian mechanics and classical electromagnetism also predicted that the electrons surrounding the nuclei of all the atoms in the Universe should rapidly convert all of their orbital energy into electromagnetic radiation and collapse in the blink of an eye. What was happening here was that the effective theories of Newtonian mechanics and classical electromagnetism were bumping up against the limits of their effective range of applicability. Beyond a limited range of velocities and sizes, the approximations of Newtonian mechanics and classical electrodynamics simply did not work and had to be supplemented by additional effective theories that covered these new ranges of conditions – relativity and quantum mechanics.

Implications From an IT Perspective
What lessons can we draw from all of this from an IT perspective? First of all, we can see that information plays a very significant role in the physical Universe, just as it does in the Software Universe that we live in as IT professionals. Secondly, it highlights the pitfalls of common sense. Since traditional computer science currently relies heavily on common sense for predicting the behavior of software, we need to be very wary of the “obvious” assumptions that IT common sense is built upon. Remember, IT common sense is just an unwritten effective theory of software behavior based upon our common sense experiences with software and certainly is subject to the constraints of all effective theories. IT common sense only works for a limited range of IT conditions, and it only provides a limited depth of understanding.

We should also take note of Einstein’s strong adherence to a positivist approach to a relative space and time versus Newton’s concept of an absolute space and time. In Einstein’s original conceptualization of relativity, we only deal with observable phenomena like the ticking of light clocks, the paths and timings of light beams, and the lengths of objects measured directly with yard sticks. Einstein does not make any reference to an absolute space or time that we presume exists, but which we cannot directly measure as Newton did in his Principia. In softwarephysics we also take a positivist point of view of software behavior. We do not care what software “really is”, we only care about how software is observed to behave.

The above material published in 1905 has become known as Einstein’s special theory of relativity because it covers the special case in which all of the observers are in relative motion with each other at constant speeds in straight lines. In 1915, Einstein generalized his theory by allowing observers to accelerate, and this has become known as Einstein’s general theory of relativity. Next time we will explore the general theory of relativity, spacetime, and extend these ideas to the concept of cyberspacetime.

As a supplemental reading, you can find an excellent treatment of the above material with very little math, at professor John D. Norton’s course HPS 0410 Einstein for Everyone at:

http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_rel_sim/index.html

Be sure to investigate the animated graphic on the Relativity of Simultaneity towards the middle of the webpage.

Comments are welcome at scj333@sbcglobal.net

To see all posts on softwarephysics in reverse order go to:
http://softwarephysics.blogspot.com/

Regards,
Steve Johnston

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