How many images is it possible to see?

[Asbo Zaprudder]

For a distraction, I'll estimate many possible images it is possible for an average human eye to see in the visible light spectrum (about 380 to 720 nanometres). It's thought that the foveal region covers only 2 degrees of our vision in each eye and contains approximately 7 million red, green and blue cone cells (omitting those rare tetrochromats - people who have four types), coincidentally sensitive to approximately 7 million colours with higher sensitivity to shades of green around 555 nanometres than red and blue (in that order). I'll average the colours perceivable by an average cone cell to about 3 million. The brain stitches together larger images from what the foveal region records as the eye moves about. The total effective pixel count per eye is probably a lot larger than 7 million because of peripheral vision but let's consider only the foveal region with which we perceive with acuity. Finally, the eye is estimated to to have a dynamic range of 1,000:1 (10 stops in log base 10) contrast levels for any given scene. Let's say a thousand contrast levels.

So putting those numbers together, 1000 contrast levels times 3 million colours per cone cell raised to the power of 7 million cone cells is (3x10^9)^(7x10^6) or about 6.068×10^66,339,848 different possible images. That's a huge number - roughly 6 followed by 66,398,482 zeroes - there are something of the order of 10^82 atoms in the visible universe for comparison - however, it's not an infinite number. It's equivalent to 10^(10^7.821774477241238), so it's a lot smaller than a googolplex (10^(10^100), but at 10^66,339,848.78303748, it's also a lot larger than a googol (10^100).

That's the approximate upper limit on the number of possible images that an average human brain can perceive in the foveal area of one eye (the other eye will usually see only a slightly different image). It includes every image that a human eye could possibly capture - all images whether real or fantastical - all written texts in any script or alphabet, all photos of whatever nature, all faces of beings real or imaginary, all vistas or landscapes on earth or elsewhere, all mappings of images from other wavelengths to the visible light range - everything. It is an upper limit on what we can perceive about the Universe through sight as humans.

 

[marsh8472]

For a distraction, I'll estimate many possible images it is possible for an average human eye to see in the visible light spectrum (about 380 to 720 nanometres). It's thought that the foveal region covers only 2 degrees of our vision in each eye and contains approximately 7 million red, green and blue cone cells (omitting those rare tetrochromats - people who have four types), coincidentally sensitive to approximately 7 million colours with higher sensitivity to shades of green around 555 nanometres than red and blue (in that order). I'll average the colours perceivable by an average cone cell to about 3 million. The brain stitches together larger images from what the foveal region records as the eye moves about. The total effective pixel count per eye is probably a lot larger than 7 million because of peripheral vision but let's consider only the foveal region with which we perceive with acuity. Finally, the eye is estimated to to have a dynamic range of 1,000:1 (10 stops in log base 10) contrast levels for any given scene. Let's say a thousand contrast levels.

So putting those numbers together, 1000 contrast levels times 3 million colours per cone cell raised to the power of 7 million cone cells is (3x10^9)^(7x10^6) or about 6.068×10^66,339,848 different possible images. That's a huge number - roughly 6 followed by 66,398,482 zeroes - there are something of the order of 10^82 atoms in the visible universe for comparison - however, it's not an infinite number. It's equivalent to 10^(10^7.821774477241238), so it's a lot smaller than a googolplex (10^(10^100), but at 10^66,339,848.78303748, it's also a lot larger than a googol (10^100).

That's the approximate upper limit on the number of possible images that an average human brain can perceive in the foveal area of one eye (the other eye will usually see only a slightly different image). It includes every image that a human eye could possibly capture - all images whether real or fantastical - all written texts in any script or alphabet, all photos of whatever nature, all faces of beings real or imaginary, all vistas or landscapes on earth or elsewhere, all mappings of images from other wavelengths to the visible light range - everything. It is an upper limit on what we can perceive about the Universe through sight as humans.

If we treated an eyeball like a camera that number could represent an estimate for how many possible discrete light data inputs can be sent into an eyeball for the average human. But most people have 2 eyeballs and the brain does all sorts of manipulation, reconstruction of the data like flipping the image back right-side up, combining data from both eyeballs to make a single sight we see, and adding or removing things that aren't actually there before having experience of seeing it.

 

[Asbo Zaprudder]

If we treated an eyeball like a camera that number could represent an estimate for how many possible discrete light data inputs can be sent into an eyeball for the average human. But most people have 2 eyeballs and the brain does all sorts of manipulation, reconstruction of the data like flipping the image back right-side up, combining data from both eyeballs to make a single sight we see, and adding or removing things that aren't actually there before having experience of seeing it.

...which I mentioned in my assumptions. My estimate was for the foveal region, which the brain uses as raw data and is the region that we concentrate on. If we restrict the calculation to the mass and volume of the visual cortex, we could use the Bekenstein bound to put an upper limit on the number of possible quantum states, which, of course, would be a gross overestimate, although it would not take into account other parts of the brain, which might be involved in vision. The Bekenstein bound for an average human brain is about 10^(7.8x10^41) possible quantum states. However, I'm sticking to my estimate until someone else comes up with better numbers.

ETA: On a similar theme, the number of possible sounds that it is possible to hear must also be limited. The bit rate for a Red Book audio CD is 44,100 samples per second per channel times 16 bits per sample, which is about the limit of an average people can distinguish sounds. So the number of possible waveforms that can be encoded per second per channel is (2^16)^44,100 or about 6.31x10^212,696, although that also includes many identical waveforms at different sound levels. For an N-second sample, the number of possible waveforms goes as (6.31x10^212,696)^N. So generating waveforms at random, it'd be a long time before Beethoven's Fifth turned up.

 

[marsh8472]

...which I mentioned in my assumptions. My estimate was for the foveal region, which the brain uses as raw data and is the region that we concentrate on. If we restrict the calculation to the mass and volume of the visual cortex, we could use the Bekenstein bound to put an upper limit on the number of possible quantum states, which, of course, would be a gross overestimate, although it would not take into account other parts of the brain, which might be involved in vision. The Bekenstein bound for an average human brain is about 10^(7.8x10^41) possible quantum states. However, I'm sticking to my estimate until someone else comes up with better numbers.

K more peer review from me. I don't know about calling that Bekenstein bound an overestimate. What if something exists smaller than sub-atomic particles or Planck lengths are not the smallest possible valid lengths in space-time?

The number of possible images is also proportional to that lowest unit of measurement on the scale that you would consider as "the same color" like where you said a cone can only react to 3 million possible colors. So if your eye gets hit with light frequency of 700nm compared to 700.00001nm they would both appear to be the same color of red and the same image at a conscious level if you have someone inspect the image and make a judgement call about whether they're the same image or not. But maybe that little bit of difference causes some neuron to fire alittle sooner or later or flickers at a slightly different speed. Then the butterfly effect from that causes the brain to react to it in a different way. Since the brain would react to these "same images" in different ways you could say that would make the images not the same image afterall.

Like asking this question: How many possible paths from point A to point B here:

Then say it's 210 but it's counting all "up, up, up, up, right, right, right, right, right, right" as a same path. But maybe one version of "up, up, up, up, right, right, right, right, right, right" is where I take the sidewalk on the left side of the street instead of the right side to avoid the dog there or take the fast lane instead of the slow lane. It's quite a few more possible paths depending on your smallest unit of measurement there.

 

[Asbo Zaprudder]

That there is a smaller unit of length than the Planck length is a possibility but perhaps it would only alter the scaling and therefore not the number of possible states. I'm sticking with Physics as we know it, for now. The main point is that the possibilities are finite, although enormous, but they are probably not infinite. If one could use a quantum computer to simulate a human brain, only a finite (yet huge) number of qubits would be required to represent all possible sensorial brain states of anyone who has ever lived or who will live or, indeed, any living creature with a smaller brain, not to mention all matter/energy configurations with the same mass and volume.

Is there any underlying profundity in these musings? Perhaps not - but it does seem to me that we are fundamentally limited to less than infinite potential in how we can perceive and interact with the cosmos.

 

[marsh8472]

That there is a smaller unit of length than the Planck length is a possibility but perhaps it would only alter the scaling and therefore not the number of possible states. I'm sticking with Physics as we know it, for now. The main point is that the possibilities are finite, although enormous, but they are probably not infinite. If one could use a quantum computer to simulate a human brain, only a finite (yet huge) number of qubits would be required to represent all possible sensorial brain states of anyone who has ever lived or who will live or, indeed, any living creature with a smaller brain, not to mention all matter/energy configurations with the same mass and volume.

Is there any underlying profundity in these musings? Perhaps not - but it does seem to me that we are fundamentally limited to less than infinite potential in how we can perceive and interact with the cosmos.

To prove it's possible to have an infinite number of possible brain states we would either need to prove it's possible to have an infinite sized brain or infinitely small scale where the infinitesimal differences make the brain state different. The physics applies only in our universe when using the Bekenstein bound. What if in a different possible world where the physics is different and allows for smaller scales. It probably wouldn't be what we call carbon based life or light particles at that point but the qualia in the consciousness of the entity could be like what we consider seeing. Or maybe if there exists a possible world where a lifeform exists of infinite size with an infinitely sized brain.

Theoretical brain states that don't or can't actually physically exist could make it possible to have infinitely possible brain states. Even if those brain states don't exist in nature if we could figure out how qualia works on paper and maybe generate infinite qualia versions of images from that.

 

[Asbo Zaprudder]

I doubt we'll ever be able to tell for certain whether qualia are equivalent in how they are perceived by two different human brains. My red is not necessarily quite the same as your red etc. The nerve signals might look very similar but that establishes nothing. However, does swapping red for green, for example, change the ability to perceive the world and survive in it? I'm not certain introducing even subtle variations in qualia perception necessarily leads to infinite potential images but I can't think of a logical argument against it.

ETA: If the number of possible human being states is also limited by a larger, yet still finite, Bekenstein bound, I assume that the spectra of qualia available to the various senses are also limited.

I don't like infinities of whatever variety. They're useful for calculations but accepting them as real can lead to nonsensical results. Some mathematicians eschew infinity altogether.