Finite or Infinite Number of Possible Images on an LCD Display?

This question is adapted from another forum, which had nothing like what I would consider a definitive answer to this question. I've been discussing the idea with a graphic artist who seemed depressed at the idea that, as he claims Brian Greene among others have suggested, that the number of works of art possible are finite and also predetermined from the instant of the Big Bang.

Suppose that a typical LCD display of 2,000,0000 pixels or so is limited only to display black and white images. So n^2 = 2,000,0000, and a data word (ones and zeros; binary) length of 2^(n^2) is therefore sufficient to display every black and white image of which the display is capable (rendered without any shades of grey also), and the question is: is this number of images really, truly, uncountably infinite or not?

I maintain that the number of images displayable is infinite, but for a reason that is different from this rather simplistic discrete math calculation. Think of the act of displaying a frame of the display as an element of a mosaic that gets larger each time a new image is displayed.

Imagine you could display every frame of every motion picture ever produced on 100 trillion different worlds for all time on this display. Now imagine you could also show all of the outakes and even all of the frames between frames, or that could be filmed from different angles, or watch each such movie 1,000,000 time or more and that the film deteriorates as you watch them each time, including films like Dorian Grey.

My claim is that time adds an element not contemplated by discrete math and that this display would be capable of displaying every observable (black/white/visible) event in the known universe for all time, or even juxtapose arbitrary numbers of them on any scale, and with the right instruments and special camera equipment, even at wavelengths not normally visible to us. So, is this not sufficiently 'infinite' even without tossing in the element of colored pixels? Is it countably finite or uncountably infinite?

 

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Still countably finite. Every effect you list can be expressed as a range of discrete options. You'd get some quibbles about brightness or frequency, but light is a quantizable effect as well - especially the light that a human eye can perceive.

 

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This is what I initially thought. But the mosaic effect of time that I mentioned means the the NUMBER OF PIXELS actually increases with each new image of an event produced by the display.

The display is no more or less finite than the number of discrete events in the universe from its beginning to forever is (finite). I've established a 1 to 1 correspondence here, and moreover, if a single image is not sufficient to make each image of an event unique, it can be aggregated with four or five angles with other images (of a clock, for instance) to make certain the event recorded and the image that accompanies it is actually unique. The cardinality of infinity that results will not be reduced by such a procedure.

The digits of the constant pi NEVER repeat, except for relatively small frames. Imagine each pixel of the display is generated by means of separate, infinitely long strings representing a digital representation of the digits of the number pi. The strings or threads, if you prefer, extend to infinity in four directions and they can be moved in the frame to produce discrete images. The number of combinations is infinite, just like the number of digits before pi repeats.

I don't care what the discrete math shows. Moreover, there exists a website that indicates with an exponent you can input for 2^(2,000,000 pixels), and the answer to that input is infinity.

Discrete math does not deal any better with infinity than other mathematical disciplines because infinity is not a number to begin with. The scenario you are suggesting could just as well prove that 1=2. It's not, and the number of combinations in this case is uncountably infinite.

If the display only had a single pixel, you could use that single pixel to record/generate a mosaic of the 2,000,000 pixel display and keep doing that in the same manner to record events and it would still be infinite. In black and white.

Infinity is not a number, but could be defined simply as a magnitude sufficiently large so that any finite numerically represented exponent may be subtracted from it without noticeably diminishing the amount that remains. This discrete problem more than qualifies for that description.

 

Here's how I see it: there is a finite matrix of pixels, akin to a finite length string of abstract characters. Each pixel can be lit in one of three ways (or, there are three different colored lcds per pixel). Each pixel also has an intensity level. which is how many times that pixel is lit per unit time.

So the 'language' of images is generated by a finite-length set of pixels, in a rectangular arrangement, There is a finite number of colors, and a finite number of intensity levels per pixel.
There must therefore be a finite number of images generated. Unless I missed something.

How big does the matrix need to be? You can watch the same movie on two different sized digital screens, so that has to be a function of human ability to resolve images, far enough from the, um, emitting surface.

What about randomly generated images, from some computer program? Would you expect to see any patterns over time, like say a test pattern? Or the Mona Lisa?

Both are in the set of finite images that can be generated, but a random generator could take a while to get to the Mona Lisa, or even a cartoon version. The number of possible images is very large but countable, since you can start with the set of images of 1 pixel; there are more of these for larger numbers of pixels, but they're the same image up to intensity (from detectable to fully illuminated). Intensity is a function of the on/off rate per pixel, and must be a finite range.

As you go to 2-pixel, 3-pixel and so on "images", there are more combinations, but still a finite number of possible images.

And bear in mind that we view only a small subset of this finite (but very large) set of images, the ones we "recognise", like the Mona Lisa, movies, computer games, etc, all of which have low randomness.

 

Adding a time component only means that a finite number is multiplied by another finite number. A painting, however, has an infinite number of possible images, since the position of each molecule of paint can vary to an infinitely fine degree.

Perhaps an analog CRT screen can show an infinite number of images.

 

Can you elaborate on "analog CRT screen"?

 

An analog TV screen utilizes tricolor dots (can be a continuous range of intensities each) to produce a single pixel. An LCD pixel changes color based on modulating its thickness, which changes the phase angle before the linearly polarized decoder in order to display a range of colors. This is also complicated, but when I attempted to simplify the problem, I noticed there definitely was a one to one correspondence between 1) whatever the display was able to render and 2) any visible (or made visible) event taking place in the known universe since the Big Bang, (including the Big Bang itself), to present day and well beyond, and on any scale from atoms to galaxies, and at any frame speed or camera angle. These images are just as capable of being rendered in black and white as they are in color, and there are infinitely many of them. If you say that many will be duplicates, OK, but I stipulate that a time and location code is provided within each frame. I also stipulate that with every frame generated, there become more images possible by rendering the previous display as an element of a mosaic or if you prefer, a scrolling banner effect. There is no doubt, the number of images thus produced is infinite.

Discrete math be damned with all of the other kinds of math that has no tractable, much less practical method to discern what infinity really means.

The argument I had with the graphic artist on this subject started out talking about a continuous range of frequencies (colors) also, but I quickly found this is unnecessary to make absolutely certain it was infinite.

A data word combinatoric calculation in discrete math is assumed static. It's not something you can make movies with like frames of pictures. It's not something that takes into account everything that a computer might be able to do with a random sequence of such data words given enough time to compute a meaningful result in a memory space that is even larger than the data word itself (analogous to a picture viewed in unlimited space in unlimited time). If you are not viewing each frame, it is countably finite, though extremely large. If you view each frame, it becomes uncountably infinite. Time is what makes the real difference.

 

No, each pixel is given an intensity by the scanning electron beam, I don't think this is possible on a per-pixel basis but is spread over several pixels. With a continuous range of intensities though, you would think any image would also have an infinite set of intensity maps.

 

This problem has nothing to do with the limitations of discrete math and everything to do with the importance of framing a well-posed question. The question originally posed can perhaps be summarized as: "How many different pictures can an array of N black and white pixels display?" Since time gets brought into the discussion, maybe we can refine it to: "How many different pictures can an array of N black and white pixels display in time T?" where T may or may not be infinite.

Now before we can answer this question, we have to narrow down a definition: what exactly do we mean by "display a picture"? The most common-sense definition, I think, is that an array of LCDs form an image in the formal optics sense; that is, they define a boundary condition to which we can apply ray tracing and find out what an observer at any location relative to the array will see. By this definition, the spacetime location of the array has no bearing on the image it produces, so the number of displayable pictures is just 2^N.

Alternatively, maybe we will allow the array to display a picture in parts, such that every part of the picture must eventually be shown but the whole thing is never visible at any one time. I think this is what danshawen's "mosaic effect" is describing. But this raises another important question: how long will the array spend displaying each tile in the mosaic? Say we look at the array to get the first tile (according to whatever ordering we've chosen), and one second later, the array is the same. Is that because the second tile is identical to the first, or because it hasn't finished displaying the first tile yet? In order to know, we have to choose some "refresh time" dt and check the array at intervals of dt to get consecutive tiles in the mosaic. If T is finite, the number of dts we can squeeze in will also be finite, and the number of displayable pictures is 2^(N*T/dt). If T is infinite, then there is time enough to display any mosaic, no matter how large. However, the chain of dts will still be a well-ordered sequence, so this actually leads to a countably infinite set of displayable pictures.

Finally, we might merely demand that the array convey enough information for us to reconstruct the picture, and not even require that all parts of the picture be directly visible. In this case, the array can have an arbitrary state as a function of time, and there are uncountably infinite such functions even for finite T. If we choose some mapping between this function and pictures, then, the array can in some sense display uncountably infinite pictures. But in my opinion, this gets too far from the original spirit of the question, because this argument no longer depends on the definitions of "LED" or "picture"! We may as well ask how many songs can be played by a dial with N settings. The fact that the answer is "uncountably infinitely many" is an important result in signalling theory, but nothing more.

 

I think the only way to get infinitely many images is to have either a screen which is infinite in size, or a finite size screen with infinitely small pixels.
Since we can't construct either, we have finite size screen with finite size pixels. Pixels are fixed elements, but intensities vary; a countably infinite set of images implies there is a "smallest" image, perhaps this is an image of one pixel.

And then you would need to be able to vary intensity levels continuously and be able to distinguish the different levels which would be difficult for the human eye. It seems there are some details which complicate things. For example, is an image of the Mona Lisa at 'normal' intensity a different image than the Mona Lisa at half that intensity, and so on.

 

I'm suggesting that an external device or devices are recording the images produced by the supposedly 'finite' display device as it displays images one by one. This would be the observer. I further stipulate that the observer of the display is capable of observing and remembering every event in the universe viewed through this display for all time. The display is an artificial retina of sorts. This would work even if it only displayed a single pixel, and even though it would take much longer to determine what was being observed, the same degree of infinity could yet be achieved. It's a thought experiment, but belongs in math because of its tie-in to discrete math.

Even if such a display is not equipped with software to smoothly rotate its image, the entire display may be reoriented (rotated by vanishingly small increments) adding yet another layer of infinite variety to the image.

I maintain that the supposedly finite device is nothing of the sort when the dimension of time (and an observer) are added. As far as I am aware, this is new, and may find application both in physics and our understanding of consciousness.

The equivalent analysis by notable scientists using only discrete math has been abused to come to nonsensical ideas about free will vs predestination, block universes and multi verses, as well as misleading ideas about the nature of infinity. These might indeed be conceivable in a static analysis with neither time nor observers, but not in this universe. One or more bindings are missing from their versions of reality. It's time those were put back into the picture.

 

Even a finite time interval delta T may be subdivided into an arbitrary number of additional frames.

The motion picture of a light pulse traversing a Coke bottle in another thread is an example of this. Shown at a normal rate of frame speed, the femtosecond movie produced would take more than a year to view from start to finish. And finer temporal resolution movies are obviously possible. Simply install a second femtosecond camera next to the first one and delay the shutter of the second one so that it photographs frames between the ones taken by the original one. Each shutter frame is a recording of a discrete event. In fact, I believe this was part of the technique used to produce the first movie, by means of a beam splitter, if memory serves.

The original n x n display device can also be induced to operate like this, and this is one way to get shades of grey out of such a display (because a pixel need not be all the way on or all the way off; it could be induced to "flicker" at a rate determined by the intensity of the image being viewed.

You see how the absolutes inherent in discrete mathematics calculations can mislead us into making simple assumptions that aren't necessarily a limitation in terms of resolution or capability of a display device in this case? Tbe timing of "pixel on" and/or "pixel off" is just one easy way to make certain the number of possible images displayed is uncountably infinite, as my cardinality exercise aptly demonstrates.

Stop teaching absolutes. Stop teaching them in math and science. Stop teaching them in religious tradition. Great harm comes from this. Teach the truth about absolutes (like truth) in philosophy. Teach this first, and teach it right. Forget Aristotle. Teach philosophy someone can really use and make their lives and the world a better place in which to live.

 

If there are 2,000,000 pixels in a fixed LCD that are binary in operation (I.e. On or off) then there is a finite number of images that could be displayed, as already stated. The maths is irrefutable on that score, without repeating itself.

What you seem to be proposing is that an "image" is a series of stills displayed on the LCD. And that with the addition of each still or frame you effectively create a new "image" than the one without that additional frame. I.e. A film.
Given an infinite time then there are indeed an infinite number of distinct "films" that could be produced, all finite in length, merely by adding an additional "frame" onto the end of an existing film.

Much like pi is merely 10 digits in a never ending string.

At least that is what I have garnered from your explanations.
But this is a very different matter to your original question of how many possible images can an LCD display, when the LCDs are binary in operation.

 

Yes, that's what I'm saying.

And also that a block universe or a multiverse makes no sense at all, yet those are the things that are built up by "frames" INSTEAD OF extending the idea of infinite variation that results from the dimension of time alone in a SINGLE universe without anything like time travel or wormholes. The former ideas are simply not the way it works.

When the Standard Model threw out considerations of time in order to eliminate the singularities, and replaced it with probabilities (something else that derives of discrete mathematics), THAT is where something was lost in translation. The infinities they thought they had eliminated are still there; just in a different form they don't even recognize as infinities because they believe they have numerical expressions for them. Just like this display we are analyzing.

A 2,000,000 pixel display can, for all intents and purposes, display an infinite number of images that are all different from each other.

 

I think that depends on how you define difference between images.

I also think that Brian Greene's idea is correct, mostly because there are a finite number of particles in the universe (the ultimate "screen") and the history of the universe contains a finite set of "images", i.e. it has one history.

Then again, we might be creating a particular history (from a possibly infinite set of histories) by observing the past, or at least I think that's what Stephen Hawking was saying.

 

This is a very important problem right now, and especially for particle and quantum physics.

If you toss out the infinity that is associated with time, you wind up with space that can be both finite and static and that behaves exactly as Brian Greene described, including, as you say, very large numbers that are for all intents and purposes infinite, but for which we have serviceable discrete math expressions, like the one we derived from a rectilinear display of n x n pixels, for instance. Quantization can be imposed on such a structure at any level without a loss of generality. Believe it or not, this is a problem because this universe doesn't deal in absolutes, and the continuous dimension of time is the reason. Probability can be substituted for time, but this is a mathematical cheat. Sooner or later, this approach must be reconsidered.

But what folks like Greene leave out of the equation is the fact that even atoms are dynamic with respect to time. This was not understood before the discovery of the Higgs boson (the force carrier for the Higgs mechanism), which imparts inertia to electrons, quarks, W and Z bosons and their antiparticles. This is what makes atomic structure a sort of kinetic sculpture. Without the dimension of time, atomic structure itself would not even be possible. Without time and also time dilation, a unified field theory that covers physics at all ranges of scale will not be possible. Matter continuously interacts with energy at all scales (even vacuum energy) and this is what makes an n x n picture as dynamic as the atoms in the elements of which it is composed. We are all dynamic mosaics in time. Not part of a block universe or a multiverse, but an eternal present influenced by the dynamics of past interactions and also by the element of a free will crafted by the experiences we can remember having in our corner of a dynamic mosaic universe. Expecting such dynamics ever to repeat as if they were somehow predestined is fantasy. If your math shows this is possible, then your method is as static as it is eternally wrong. Most likely, you have omitted an infinity or three.

Time was the missing infinity in this puzzle, just as it is in physics. On a quantum physics level, time was replaced with probabilities to replace the infinities that resulted from using time over 50 years or so ago. If it cannot be put back, the math associated with physics will no doubt continue to diverge from describing the nature of a physical reality that has time extending to infinity in both directions of scale. Only time and energy exist. It is space that has always been the illusion.

 

I forgot to mention, when (delta T)=0, as Peter Lynds has pointed out, conservation of energy / momentum doesn't work either, because all motion and forward momentum stops cold. This is one reason why block universes and multiverses suddenly become possible (from a quantum / probabilistic point of view), but this is no replacement for time. The atoms supposedly still have sufficient cohesive energy, but in an instant of time shrunken to zero they are robbed of any semblance of inertia. We know this cannot possibly be the case, in any universe that resembles reality.

In a static universe with no element of time (delta T = 0), an n x n pixel display by definition can never change its display. The number of possible displays therefore shrinks from more than 2^(n^2) possible displays to a single display with n^2 pixels and only a numerical possibility that it might have ever displayed anything different from what it displays in the current instant. This makes sense only in a universe that is very young and with no prospect for any future events of any kind. This might have been the case once, a very long time ago, but we have come a very long way since then. A very large number of events have occurred, and many more will continue to occur, no doubt. Has an infinite number of events yet occurred? That point is arguable, but I would tend to support the idea.