Symbols

Discussion in 'Physics & Math' started by arfa brane, Nov 9, 2016.

1. arfa branecall me arfValued Senior Member

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What's the difference between a number and a colour?

What's the difference between colouring a number and numbering a colour?

These questions have been plaguing me. I don't care who won the bloody election.

3. Fednis48Registered Senior Member

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Tripping balls, eh? I guess that's as good a coping mechanism as any.

If you're really serious, though, I would say that numbers and colors are disjoint, uncountably infinite sets of abstract concepts. Neither set is ordered, although some subsets of the set of numbers (for example, real numbers) are ordered. At the highest level, "coloring a number" and "numbering a color" describe the same thing: associating a particular member of the set of numbers with another particular member of the set of colors.

5. arfa branecall me arfValued Senior Member

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I can go with that. Except that if you introduce the concept of frequency and say a colour has a fixed frequency, that should also introduce an order, or is it just numbering a colour?

I also recall from somewhere that colour is a Hilbert space. You take a pair of colours (equivalently, fixed frequencies) and define a continuous space between, or something like that.

7. DaveC426913Valued Senior Member

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Numbers are objectively identifiable entities.
Colours are an artifact of perception; they are subjective, possibly compound, and any order applied to them is arbitrary.

The "colour" purple might actualy contain no purple at all. Your TV screen is a good example.

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8. Fednis48Registered Senior Member

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If we were really looking for an objective definition of the set of colors, we could maybe define an "averaging time" T representing the shortest time over which a typical human eye can see temporal variations, then define a "color" as a particular electromagnetic waveform that's periodic with period T or less. Interestingly, such a set would not form a Hilbert space, because it would not be closed under addition. As a simple example, the sum of two sine waves whose frequencies are irrational multiples of each other is itself aperiodic. In principle, this non-closure under addition should be directly observable: the intersection of two stable lasers with slightly different colors should appear to "flicker" at either the difference of their frequencies or half that (I forget which). Since visible light is in the THz range and a flicker couldn't be much faster than 10 Hz to be visible, I don't know if the technology exists to actually perform this experiment.

9. DaveC426913Valued Senior Member

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Except that a colour very rarely correlates to a single EMR frequency.
Virtually all colours in the natural world, and most in the artifiical world are comprised of multiple frequencies. The actual percieved colour need not even be one of them.
Again, the purple in your TV - or on the wings of a butterfly in your garden - may have no actual purple in it at all.

And I'm not sure how periodicity or any temopoal element has to factor in.

10. Write4UValued Senior Member

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First of all colors have wave lengths with specific values, not numbers per se, which are human symbolic approximations....

All colors other than primary colors are a mixture of two or three primary colors, a set of wavelengths made up from a mixture of wavelengths which have assigned *values*, which we have numbered (quantification of a value)

This can be seen when pixilating a photograph, where each pixel has three numbers (values)which gives the pixel its specific color.

Last edited: Nov 10, 2016
11. Confused2Registered Senior Member

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12. DaveC426913Valued Senior Member

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You are describing one - of many - arbitrary colour definitions.

There are no primary colours in nature.

We chose three colours to be primary based on our three biological colour detectors.

Even the primary colours are arbitrary. Ask a painter or graphic designer. Their primary colours are cyan, magenta, yellow and black.

Last edited: Nov 10, 2016
13. Fraggle RockerStaff Member

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Many mammals, especially those who are active primarily at night, have only two.

It was recently discovered that many birds have four receptors. The fourth one is higher in the spectrum and senses ultraviolet. This explains how so many species of birds can distinguish between the males and the females, when we can't. Their feathers have ultraviolet pigmentation!

Some insects have even more receptors further up in the ultraviolet range--bees, for example. It allows them to tell which flowers are mature enough to be full of pollen.

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14. arfa branecall me arfValued Senior Member

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My take is, numbers are symbols, colours can also be symbols. If you use numbers as labels (say, of the vertices of a graph) you can use colours in an entirely equivalent way.

The difference being a set of distinct colours can be ordered arbitrarily whereas numbers, particularly natural numbers, already have a natural order because of the "less than, greater than, or equal" relation. It doesn't really make sense to say red is greater than green, say, unless you're talking about the difference in frequency.

Nonetheless, given a finite set of colours, you can always put them in one to one correspondence with natural numbers.

15. Write4UValued Senior Member

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That is an interesting comment. Is there really a finite set of colors or are we just unable to see All wavelengths as colors.

16. DaveC426913Valued Senior Member

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Colour happens in the brain, and is dependent on our biochemistry. That means there is a limit at both ends, and there are a finite number of gradations between.

17. Fednis48Registered Senior Member

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I wasn't just talking about single frequencies; one can have spectrally broad waveforms that are still periodic. And because EM waves obey the superposition principle, any color can be expressed as some EM waveform, however complex.

When I said that we could put an upper limit on the cycle period, I was thinking that any variations on a time scale slower than human perception don't really count as new colors so much as time-varying colors. (For example, putting a 1 Hz modulating envelope on a blue light wouldn't change the hue of blue. It would just make the blue brighten and darken in alternation.) Of course, that's still setting aside the question of whether it's really fair to treat every waveform as a unique color. Red and green light together give yellow - can we make a different hue of yellow just by shifting the phase of the red light relative to the green? It certainly wouldn't look any different, but then again, any sufficiently small frequency shift wouldn't be visible either, and different frequencies definitely count as different colors.

I think when arfa brane said "given a finite set of colors," he meant "if we restrict ourselves to looking at only some finite subset of the full set of colors." As I said above, I'm pretty sure the set of colors is uncountably infinite.

18. DaveC426913Valued Senior Member

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The biochemistry of our vision, from which stems our perception of colours, has a lower bound of resolution.
At some point, two adjacent but distinct colours will excite the same number of nerves in the retina.

19. Fednis48Registered Senior Member

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Good point. I guess when you get right down to it, colors probably don't even form a set, because when we bring subjective perception into the mix, the question "Is color A different from color B?" isn't well-posed.

20. Write4UValued Senior Member

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There is at least one exception to this rule, the Cuttlefish. It is able to blend into its environment both in shape and color.
The amazing thng is that a cuttlefish is color blind.
There must be another way to perceive colors in the Cuttlefish. It seems that it can perceive and react to the wavelengths physically, even as it cannot *experience* the wavelength(s) itself as a color.

21. arfa branecall me arfValued Senior Member

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Well, we know it's more or less impossible to produce a colour with a pure frequency, and we know that humans aren't equipped to distinguish colours with close enough frequencies--we can't tell if say, 600nm wavelengths are distinct from 601nm wavelengths.
Albeit we have instruments that can do this.

So we're obliged to choose some neighbourhood of a fixed frequency/wavelength as a distinct colour, say red. This is what laser diodes do, in a sense, because they emit a narrow band of frequencies in a resonance curve. So finding a correspondence between natural numbers which have an exact value, and a colour which is not a single exact frequency must involve something slightly more complex. Whatever that is, it is well-posed to label a colour "red" and say it isn't the colour "yellow".

You can choose a set of colours which are all perceived as different, just like how different number symbols are perceived. That is to say, the numbers are far enough apart (despite their exact values) to be perceived as different or distinct from each other even if you use say, a unary number system, likewise a set of distinct colours has this property of "apartness".
So are symbols just down to how we perceive?

Last edited: Nov 11, 2016
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22. danshawenValued Senior Member

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A color is just one aspect of EM radiation, in the same way that order is just one aspect of the set of natural numbers. Symbols are like that; they can't capture the entire truth of anything.

The problem with a finite mind is that it always falls short of a grasp of infinity, and this is principally the reason why that is the case and they must resort to the use of symbols for expression of ideas.

So, why are holy scripture written in symbols? What kind of proof of infinite comprehension is this? Not even a shadow, that's what. Idols are not G-d. Neither are any set of symbols worthy of idolatry.

Last edited: Nov 17, 2016
23. DaveC426913Valued Senior Member

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Except that, for humans, the superposition of 550 nm and 650 nm is the same "red".
Though that does not mean it is for other animals - who might well see two distinct colours, or not see one of them at all.