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TIME EXPLAINED (v2.1)


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#1 Farsight

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Posted 12 December 2006 - 06:33 PM

Time is very simple, once you get it. But “getting it” is very difficult. That’s because your current concept of time is so deeply ingrained. You form a mental map of the world using your senses and your brain. You use this mental map to think, and you are so immersed in it that you can’t see things the way they really are. You are locked into an irrational conviction that clocks run, that days pass, and that journeys take a length of time.

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It takes an open mind, and logic to break out of this conditioning. First of all we need to look at your senses and the things you experience. Let’s start with sight. Look at the picture below:

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The central portions of the two crosses are the same colour. You think the one on the left is grey and the one on the right is yellow. Not true. Tear a small hole in a piece of paper to make a peephole to mask out the context. Hold it up to one image after the other, and you realise that the central portion of the right-hand image really is grey. The yellow was the illusion. What does this tell you? It tells you that something you took for granted is not true. And it should remind you that a photon doesn’t have a colour. It has a wavelength, an oscillation, a motion.

Let’s move on to sound. Imagine a super-evolved alien bat with a large number of ears, like a fly’s eye. This bat would “see” using sound, and if it was sufficiently advanced it might even see in colour. But we know that sound is pressure waves, and when we look beyond this at the air molecules, we know that sound relies on motion.

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Pressure is related to sound, and to touch. You feel it in your ears on a plane, or on your chest if you dive. You can feel it when I shake your hand. But you know you can’t measure the pressure of an atom, because pressure isn’t a fundamental property of the sub-atomic world. It’s a derived effect, and the Kinetic Theory of Gases tells us it’s derived from motion.

How about kinetic energy? A cannonball in space travelling at 1000m/s has kinetic energy. If it impacted your chest you would feel it. But apologies, my mistake. It isn't the cannonball doing 1000m/s. It's you. So where's the kinetic energy now? Can you feel it coursing through your veins? No. Because what’s really there is mass, and relative motion.

You can also feel heat. Touch that pretty stove and sizz, you feel heat. We talk about heat exchangers and heat flow as if there’s some magical mysterious fluid in there. And yet we know there isn’t. We know that heat is another derived effect of motion.

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Taste is chemical in nature, and primitive. Most of your sense of taste is really your sense of smell. Do you know how smell works? Look up olfaction and you’ll learn about molecular shape. But the latest theory from a guy called Luca Turin says it’s all down to molecular vibration, not shape, because isomers smell the same. That’s motion again.

The point of all this is there’s a lot of motion out there, and most of your senses are motion detectors. But it never occurred to you because you’re accustomed to thinking about the world in terms of how you experience it, rather than the scientific, empirical, fundamental, ontological things that are there. And nowhere is this more so than with time.

So, what is time? Let’s start by looking up the definition of a second:

Under the International System of Units, the second is currently defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. This definition refers to a caesium atom at rest at a temperature of 0K…

So, a second is nine billion periods of radiation. Now, what’s a period? We know that radiation is basically light, so let’s have a look at frequency:

Frequency = 1 / T and Frequency = v / λ

So frequency is the reciprocal of the period T, and also velocity v divided by wavelength λ. No problem. Flipping things around, we see that period T is wavelength λ divided by velocity v. We know that a wavelength is a distance, a thing like a metre:

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second...

And we all know that velocity is a distance divided by a time. So a period is a distance divided by a distance divided by a time. The result is another period of time. This definition of time is circular and tells us nothing. How do we define it? Let’s look at frequency again:

Frequency is the measurement of the number of times that a repeated event occurs per unit of time.

So frequency is a number of events per second. And a second is a number of some other events. The interval between events is measured in terms of other events. And the interval between those events is measured in terms of other events. Until there are no events left, only intervals. And intervals are frozen timeless moments. For time is a measure of events, of change, measured by and against some other change. And for things to change, something, somewhere, somehow, has to have motion. You don’t need time to have motion. You need motion to have time.

We measured nine billion oscillation events and defined that as a second. We counted events. We counted motions. One, two, three, four, five… nine billion. Mark that down as a second. But you don’t have to count the motion in an atomic clock. You could count beans in a bucket. Ping, ping, ping, chuck them in, regular as clockwork.

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You’re sitting there counting beans into the bucket, ping, ping, ping. Now, what is the direction of time? The only direction that is actually there, is the direction of the beans you’re throwing. “Fuller Bucket” is not the direction of time. “More Beans" is not the direction of time. The direction of your time is the direction of your counting, and I could have asked you to count them out of the bucket. There is no “Arrow of Beans”. There is no “Arrow of Time”. That’s just an illusion, as imaginary as the direction you take when you count along the set of integers.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 →

So why do we say things like Clocks slow down as if a clock is something that moves like a car? It isn't travelling. There's no slow or fast or up or down to it. We say the day went quickly but we know it didn’t go anywhere, and it didn’t go quickly at any speed at all. It isn’t travelling and there is no direction. The only directions that are there, are the directions of the motions that make the events that we use to measure the intervals between the other events. And they’re being counted, incremented, added up. We count regular atomic motion to use as a ratio against some other motion, be it of light, atoms, clocks, or brains. All of these things have motion, both internal motion and travelling motion. And all those motions are real, with real directions in space, ending in the sameness we call entropy. But the time direction isn't real. It's as imaginary as a trip to nine billion.

That's why the past is only in your head and your records. It isn’t a place you can travel to. It’s the places where things moved from. All those places are still here, now. And while the past is the integral of all nows, now lasts for no time at all. Because time needs events, and if there were only intervals and no events, there wouldn’t be any time. When you take away the events and the motion, you take away the time. A second isn’t some slice of spacetime, it’s just nine billion motions of a caesium atom. Accelerate to half the speed of light and a second is still nine billion motions of a caesium atom. But there's only half the local motion there used to be, because the other half is already doing the travelling motion through space. Imagine yourself as a metronome. Each tick is a thought in your head, a beat in your heart, a second of your time. If you’re motionless with respect to me I see you ticking like this |||. If you jet off in a spaceship, you tick like this ///. If you could reach c and we know you can’t, you wouldn’t tick at all. Your time would flatline like this ______ because any transverse motion would cause c to be exceeded. And you wouldn’t tick for anybody else in the universe. That’s the thing that’s out there, the thing we’re trying to learn about. This is what it’s like:

http://upload.wikime...onal_motion.gif

What can you see? What can you measure? Yes you can measure height. And width. And if it wasn't just a picture you could also measure depth. That's three Dimensions, with a capital D because we have freedom of movement in those dimensions. What else can you see? What else can you measure? You can see things moving, but you can’t see a fourth dimension. You might imagine a time dimension, with direction and length. But the picture comes from the wikipedia temperature page. The thing you should measure is temperature, which used to be considered a dimension, before the word changed from “measure” to “Dimension” under your feet. Temperature is an aspect of heat, that derived effect of motion. When you measure the temperature you are measuring motion, because that’s what’s there. You can call it a dimension, but there can be no motion in this dimension, because it’s a measure of motion. If you were one of those dots, immersed in temperature like we are immersed in time, you would not talk of climbing to a “high temperature”, because there is no height. Likewise we cannot travel a length of time, because there is no length, just as there is no height in temperature. So time is a dimension with a small d. It's a measure of change of place rather than a measure of place, and it has no absolute units, because you can only measure one change of place against another. The units are relative, which is what Special Relativity tells us.

Special Relativity tells us that your relative velocity alters your measurement of space and time compared to everybody else. You increase your relative velocity and space contracts while time dilates by a factor of √(1-v2/c2). If you travel at .99c, space contracts to one seventh of its former size. So your trip to a star seven light years away only takes you a year. But physics is about the universe, and in that universe it took you seven years. The space in the universe didn’t contract because you travelled through it. But your time did.

http://content.answe...ion-002.svg.png

Einstein didn’t understand the full meaning of Special Relativity until later in life. In the early days he was influenced by Hermann Minkowski, a father-figure whose forename was the same as Einstein’s actual father. It was Minkowski who turned time into the fourth dimension:

The mathematics of his revolutionary paper on Special Relativity was relatively elementary, and at first he resisted its reformulation in terms of four-dimensional space-time by his former teacher Hermann Minkowski, complaining that “since the mathematicians pounced on relativity theory I no longer understand it myself”.

Later Einstein struggled with the Twins Paradox in 1918. He used acceleration from General Relativity as the explanation, but this explanation was erroneous and didn’t account for passing clocks. Look it up on wikipedia. A couple of years on in 1920 he gave an address at the University of Leyden about the dreaded ether:

..according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable inedia, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it.

When you read the history you can see a slow evolution from the postulate that says the laws of physics are the same in all inertial frames of reference. The problem with reference frames is that all our observer velocities are zero, and if you don’t take care the sun goes round the earth. They don’t explain why the speed of light is always the same. It wasn’t until Einstein met Godel in Princeton that he realised the full impact of what Special Relativity really meant:

In his response to Godel's paper in the Schilpp volume, Einstein acknowledged that "the problem here disturbed me at the time of the building up of the general theory of relativity." This problem he described as follows: "Is what remains of temporal connection between world-points in the theory of relativity an asymmetrical relation (like time, intuitively understood, and unlike space), or would one be just as much justified to assert A is before B as to assert that A is after B? The issue could also be put this way: is relativistic space-time in essence a space or a time."

Godel didn’t “find a way to time travel” with his rotating universe. He merely used this conjecture to demonstrate that time could not have passed if you could visit the past. Einstein was with Godel on this, and understood full well the implications:

It is a widely known but insufficiently appreciated fact that Albert Einstein and Kurt Godel were best friends for the last decade and a half of Einstein's life. They walked home together from Princeton's Institute for Advanced Study every day; they shared ideas about physics, philosophy, politics, and the lost world of German-Austrian science in which they had grown up. What is not widely known is that in 1949 Godel made a remarkable discovery: there exist possible worlds described by the theory of relativity in which time, as we ordinarily understand it, does not exist. He added a philosophical argument that demonstrates, by Godel's lights, that as a consequence, time does not exist in our world either. If Godel is right, Einstein has not just explained time; he has explained it away...

That’s the true meaning of Special Relativity. The “speed of light” was always the problem. And it was always the problem because time was always the problem. Because at the speed of light there’s no time left for anything else to happen. It’s why c isn’t really a speed, because you run out of time trying to get there, and if there’s no time, there’s no speed because speed is distance over time. Velocity is prime. It defines your metres and your seconds. We should talk of it as a fraction of c like in the equations, or by degrees, but not by the things it itself defines. Because like temperature time is derived from motion, which is what is there. And c is the total motion, the rapidity of inductance from which we slice our immersive time, the inescapable property of oscillating photons and those electromagnetic things from which we’re made. From which the universe is made.

http://content.answe...-Light-wave.png

The universe is not a block universe, it is a world in motion. The worldlines are only in mathematical space, and in your head. There is no future, there is no past, only the now that is always now, the now of Presentism. We don’t travel in time at one second per second. We don't travel in time at all. Relativistic clocks don’t travel in time at different rates, they travel in space at different degrees of c, and when they collide, they collide at the same location and at the same time whatever their faces say is local time. Local time.

To travel backwards in time we'd need to unevent events, we’d need negative motion. But motion is motion whichever way it goes. You can’t have negative motion. So you can’t travel backwards in time. There are no time travel paradoxes, because there is no time travel, and there is no time travel because there is no travelling in time. And there never was. Time didn’t start fifteen billion years ago. Because time didn’t start in the first place. It was motion that started in the first place. And it was fifteen billion light years away by every light path you can track through timeless space. That’s how far we’ve come.

And now we can move on.

http://www.human-evo...lock_silver.jpg

Acknowledgements:

Thanks to echalk and R Beau Lotto re colour perception, to Palle Yourgrau for “A World Without Time” re Einstein history, and to Julian Barbour (“The End of Time), Paul Davies (“About Time”) and Carlo Rovelli (various) for background reading. And thanks to all the forum fellas for all the feedback, wiki contributors, anybody who put up an image I’ve borrowed, and anybody else I’ve missed. And Albert Einstein

Thanks guys.


#2 Farsight

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Posted 12 December 2006 - 06:36 PM

I thought a new version was in order to take on board some of the feedback I've had. Any comments and views will be gratefully received.

#3 HydrogenBond

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Posted 12 December 2006 - 07:30 PM

A much easier explanation of time is that it is a potential quanta; time potential. Things move to the future because time potential is decreasing over measured time.

The easiest way to quantize time potential is to look at energy. For EM energy, energy is wavelength and frequency multiplied by a constant. The time potential is contained in the frequency aspect of energy, with higher frequency containing more time potential. For example, if one inputted a quanta of gamma into a system, it would take longer to reach steady state than a quanta of IR. More time potential inputted takes more measured time to dissipate.

The conservation of energy implies that energy is conserved. This implies that all forms of energy contain time potential. Time potential can spread out into different energy forms but the total will be conserved. For example, if a nuclei absorbed the gamma quanta into mass, the atom will reach thermal steady state quicker. This is because the time potential is now stored in the nucleus and the time potential can be released at a later time. Hydrogen fusion does this, releasing time potential that has been stored in the hydrogen atoms since 100K years after the BB. This time potential is converted back to heat that now takes much more time to linger and dissipate.

If one looks at time as only a reference variable the physics of time gets very complicated and hairly. It time is looked at as a potential quanta that we measure with clocks, it is extremely simple.

If one looks at time dilation, time will slow down, relative to a stationary reference. For example, 1 sec in the time dilated reference may take one hour in the stationary reference. Using special relativity, what cause this is velocity. Velocity means kinetic energy. This, in turn, means the time dilated reference contains more time potential. Basically, it accumulated time potential and can only trickle out and be used up at the slower pace of stationary reference. Everything appear to take more time because it has more time (potential).

Garvity can also cause time dilation due to gravitational potential energy being stored, ie., accumulates time potential.

#4 Farsight

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Posted 13 December 2006 - 08:47 AM

Things move to the future because time potential is decreasing over measured time... Time potential can spread out into different energy forms but the total will be conserved.


Do you want to run that by me again?

#5 niin

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Posted 13 December 2006 - 06:51 PM

Popular, you wrote a long text.
You said you wanted feedback, well after reading i still finds a few things...unclear.
Could you answer the following questions.

1) time doesn't physically exist?
2) spacetime doesn't exist?
3) Einstein did not believe in spacetime?
4) Einstein believed in the ether?
5) Special Relativity can be used to prove that time doesn't exist?

#6 Farsight

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Posted 13 December 2006 - 07:25 PM

niin:

1) time doesn't physically exist?

There's some subtlety to this. I was reminded the other day when I read an article about Hogfather see Sky One where Terry Pratchett was talking about justice. He said you could grind the Universe down to a powder and you wouldn't find a single atom of justice. It's the same with lots of things that we talk about. Like weather, entropy, colour, sound. These are things that we experience, and as such we can say they exist. But whether they really physically exist becomes a matter of language and definition. I'd say time is like heat, and is a derived effect of motion, and cop out by saying it isn't fundamental because it isn't what you think it is.

2) spacetime doesn't exist?

I think here I'd say no, it doesn't. Spacetime comes with some "fundamental" baggage, and if time isn't fundamental, I've got to say that space exists, but not spacetime.

3) Einstein did not believe in spacetime?

The quotes I found say he had issues with Minkowski, doubts when he was formulating general relativity, and more when he was hanging out with Godel. I think he wavered, and ended up thinking spacetime was space. But I can't prove this.

4) Einstein believed in the ether?

Maybe not "the" aether. Definitely not the aether Michelson and Morley were looking for. But see the Leyden address of 1920. He definitely believed in "an" aether. Basically he was saying that space is a kind of aether.

5) Special Relativity can be used to prove that time doesn't exist?

That's a bit black and white. It's more like Special Relativity can be "interpreted" in terms of space rather than spacetime. Here's a paper that goes some way to illustrate what I mean:

A New Interpretation of Special Relativity

Note the following excerpts:

Let us consider what relativity principal would hold in general if distances were always measured by wave propagation times (or conversely if time were defined in terms of wave propagation distance).

With this definition of distance, the constant c is simply a scaling factor which relates the units of distance to the units of time.

Let us take this as an alternative postulate for special relativity: matter consists of waves which propagate at the speed of light.

it makes little difference whether we assume that Lorentz invariance is truly a property of time and space or whether it is merely the result of using matter waves to make measurements.

It's got aether written all over it, though he doesn't actually use the word. I wonder if there's any rebuttals kicking around? I was reading another more relevant paper, but it's late and I can't find it. Time for bed.

#7 HydrogenBond

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Posted 14 December 2006 - 05:34 PM

If one looks at quanta of EM energy, it is composed of two dynamic factors; wavelength and frequency. The wavelength gives us a measure of distance and the frequency a measure of time. I call these two aspects, distance potential and time potential, the product of which equals the value of the energy quanta. The only other factor in the equation is a constant; Planck's constant. As such, within these distance and time manifestations defines the energy content of that energy quanta.

If we inputted a quanta of EM enegy into a hydrogen atom, the electron will kick up into a higher state and then drop back down to ground state. Notice what happens, the size or distance of the hydrogen atom increases and a certain amount of time lapses to kick up the electron to an excited state. Or in other words, the distance potential within the energy quanta increases the distance characteristic of the hydrogen atom and the time potential aspect induces a change of state that can be used as a standard to measure time.

When we measure distance, for example, energy is always required. One can not see a meter stick unless visable light energy goes through our eyes into our brains. Even measuring atomic distances with x-ray diffraction requires the equipment see x-rays before we can measure these small distancces. Time and distance may be reference tools, but they need energy to be measured. The energy not only allows one to measure distance and time, but energy also contain distance and time potential, which is used to induce distance states and the changes of state equated with time.

If we assume distance and time are potential quanta, then time dilation and distance contraction are explanable without heavy math. Special relativity uses velocity (kinectic energy). This velocity state required an energy input to achieve. This energy input and/or potential energy stores time potential. General Relativity is based on gravity. This stores gravitiaiton potential energy, and also accumulates time potential.

The laws of physics being the same in all reference implies, that the accumulated time potential, due to velocity/kinectic energy, is evenly distributed over the entire moving reference. Everything has changed its time potential state in proportion, allowing the laws of physics to dissipate time potential in charateristic proportions. But relative to stationary reference, the rate of dissipation appear to slow because the base time potential state is lower in stationary reference.

Has anyone ever wondered why electrons and protons last so long, compared to all the parts generated during accelerator experiments? The original particle composites contain a lot of time potential, enough to last for billions of years. The accelerator adds even more as special relativity. The accelerator collisions dissipate the time potential. The change of state output shows up as temporary states that don't last long. In other words, if you could take all the subparticles and add time potential back you could make electrons and protons.

#8 Farsight

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Posted 15 December 2006 - 06:03 AM

HydrogenBond, I'm sorry, IMHO your mental model above is wrong.

Read ENERGY EXPLAINED for why I think why.

http://hypography.co...-explained.html

#9 HydrogenBond

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Posted 19 December 2006 - 06:17 PM

If we look at energy with respect to photons, energy equals Planck's constant, times wavelength, times frequency. The only reason there is a Planck's constant is because of the way we reference energy for measurement. The standard is connected to heating water. Water is widely available and serves as a terrestrial standard.

Theorectically, there should be a universal standard of measure, where Planck's constant becomes 1. I have no idea what that may be, but it would be a good thesis project for anyone interested. Under these universally valid conditions, energy is directly related to wavelength and frequency. These two separate things, meausred separately, acting together, define the value of the energy. One is distance potential and the other is time potential.

Maybe the nomenclature of "potential" is causing confusion since potential is normally equated with energy and not to the two halves that make energy work and give it energy potential. These are sort of half potentials the product of which equals energy potential.

Looking at energy inputted into an atom, lower wavelength or higher frequency cause the most affect in distance and time. This implies that distance potential is the reciprical of wavelength, while time potential is directly related to frequency.

#10 Farsight

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Posted 20 December 2006 - 08:20 AM

HydrogenBond: you need to check up on the above.

Here's an excerpt from another essay I'm writing.

OK, we know from Time Explained that distance is related to time by the thing we call c. It’s a conversion factor. Divide by c and you convert a distance-based view into a time-based view. That’s why the energy of a photon is hf, and the momentum is hf/c. Just as a reminder, h is Planck’s constant, which is 6.63 x 10-34 Joule-seconds. That’s an “action”, which is also a momentum times a distance. The f is the frequency per second. If you divide Joule-seconds by seconds you get Joules, our familiar units of energy. You can also express the momentum as h/λ where λ is the wavelength in metres. Basically c is λ/f, distance over time.

Also check out these wikipedia links.

Photon - Wikipedia, the free encyclopedia
Energy - Wikipedia, the free encyclopedia
Momentum - Wikipedia, the free encyclopedia
Planck's Constant - Wikipedia, the free encyclopedia

With respect, I think you're going off at a tangent here, perhaps you should start a new thread.

#11 Qfwfq

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Posted 28 December 2006 - 09:02 AM

Popular, you should try to be a bit more tactful when talking about someone's mistake. :D

energy equals Planck's constant, times wavelength, times frequency.

Wavelength times frequency is equal to phase velocity. Energy is Planck's constant times frequency.

Textbooks often use so-called natural units, h = 1 is just that, a choice of units, but it's a separate matter from that of Joule's constant.

#12 cwes99_03

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Posted 28 December 2006 - 01:50 PM

The central portions of the two crosses are the same colour. You think the one on the left is grey and the one on the right is yellow. Not true. Tear a small hole in a piece of paper to make a peephole to mask out the context. Hold it up to one image after the other, and you realise that the central portion of the right-hand image really is grey.


Umm,care to try that again? The right hand image has a yellow center piece, measureable with a photometer.

To test it out on your computer, take the picture into a graphical editing software and use the program to copy the color. Then write down the hue saturation etc. Compare that to the color gray and the color yellow and you'll see the numbers fall inbetween.

#13 cwes99_03

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Posted 28 December 2006 - 02:00 PM

Pop, might I make a suggestion.

It seems you are writing several essays at once, all of which depend upon the others. The essay you cite here cites this essay, which is still unfinished. While I realize you want to keep moving on, and responses can be slow, you must also realize that by moving on, your new theories may be completely debunked by a mistake in an earlier theory. Try to solidify one before moving on. Additionally don't cite a theory here that depends on the theory already in question, it turns into cyclical reasoning which you will be stuck in like a whirlpool while everyone else tries to throw you a line.

#14 InfiniteNow

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Posted 28 December 2006 - 11:02 PM

Cwes,

Please send members a PM if you wish to coach them on their style. Threads are for topics, and your post above is :hyper:.

#15 Farsight

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Posted 29 December 2006 - 05:53 AM

cewes: sometimes the local image reproduction isn't quite right. Try it here on the original website.

eChalk: optical illusions

Re style, the later MASS EXPLAINED essay is now finished, and doesn't mention the TIME EXPLAINED essay. I do expect to have to revisit essays in the light of feedback and revealed insight - hopefully not for any radical corrections, but if that's how it turns out, so be it. I need the feedback to be able to move forward.

#16 cwes99_03

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Posted 29 December 2006 - 09:54 AM

I visited the site. The matter is that the light being transmitted through the mask is fundamentally different due to the filter. Thus until you move the filter the light being transmitted is actually a different wavelength. Thus it is not just some perception as your initial post suggested.
I can't copy and test the flash based example to test whether or not they are physically changing the colors, but I would just about garauntee they are. If you could get unedited video in which the same basic effect is occuring then you would have nothing more than the first part of this post. It is not a matter of how your brain perceives the color because of surrounding colors, but a matter of what wavelength is being transmitted through the filter.

#17 Farsight

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Posted 31 December 2006 - 11:21 AM

I visited the site. The matter is that the light being transmitted through the mask is fundamentally different due to the filter. Thus until you move the filter the light being transmitted is actually a different wavelength. Thus it is not just some perception as your initial post suggested. I can't copy and test the flash based example to test whether or not they are physically changing the colors, but I would just about garauntee they are. If you could get unedited video in which the same basic effect is occuring then you would have nothing more than the first part of this post. It is not a matter of how your brain perceives the color because of surrounding colors, but a matter of what wavelength is being transmitted through the filter.


Sorry cewes, I think you're kidding yourself. Make a small hole in a piece of paper and hold it up to each central area in turn. Then you see that they're both grey.

Here's another one that's more dramatic.

Posted Image