1.6 Colour: From Source to Perception - Part 1
I hope you can find it in your heart to forgive this seeming tangent from our ongoing discussion of genki. There is a particular, wonderful subtlety of ki-sense that I wish to explain fully, and to do so requires a crash course in… well most of modern science, to be frank. You may be tempted to skip this section as I guess for many readers I'll be tugging on those threadbare, unpleasant memories of high school (or memories yet to be made for you younger readers). In that case I hope you at least skim this section and feel encouraged to return as we progress. Some of the concepts I describe here will appear in modified forms throughout the rest of the textbook, and I would hate for you to miss what I believe are astounding parallels throughout the natural world.
I've been attempting to paint the appearance of genki for a while now to give you the impression of what the world looks like to me. I say attempt, not to appear cloyingly modest about my artwork (I am doing my best!), but to impress that portraying ki is extremely difficult with the limited visual palette alone. The images I've painted are an ugly mess of colour, I admit. In paint Pan appears an orange/brown, although I hope you could make out the colours were in fact red and green (and some yellow). With paint, colours run and mix. If you put every colour of the rainbow on a page the page appears a murky brown. In ki-sense this mixing doesn't occur however, and the colours stay bright and distinct.
There is more than just colour, too. A mix of senses and triggered memories contribute to ki signatures. Laughter, the sensation of spinning when dancing, dark chocolate… these are all images invoked when considering Pan's ki, and yet the sum of these ideas alone can not do her ki justice. These interpretations are subjective, of course. If I had never tasted chocolate I may have described her ki like sweetened coffee - bitter and sweet with great depth - and I would be just as close. The red elements of her ki are very much the "Son" family signature - lively, warm and fun. The green is more Videl's family, the cosy bitter chocolate definitely from her mother.
The question is then, why is there such a difference in perception between the colours as experienced by the eyes and colours through ki-sense? Why can't I differentiate every every colour of the rainbow if they're overlapping with my eyes but can with ki? To explain, we need to begin with light itself and how colour arises in the first place before moving onto the brain.
[ Figure 1a,b ]
[ groundbreakingsci-stuff dot com/post/169361700882/1point6p1#one ]
Colours of objects under different lights. My helmet looks black under blue light. Why is that?
Why is it that the helmet above looks orange in sunlight but black in blue light - why not a orange-blue mix? In a sense, the world does not truly have colour. Colour is subjective and lives in our mind and the mind can be fooled. Although, colour is not completely imaginary, the experience is triggered by something. That something is the energy of light, and so we should begin by understanding the nature and properties of light itself.
Light is a bizarre yet helpful phenomenon. We tend to think of light as a nebulous cloud of colour and brightness (or lack thereof) surrounding us. Like solid objects can be broken down into their smallest building blocks known as atoms (or a group of atoms joined together, a molecule), so can light. These little packets of light energy are known as photons. These photons have an energy, a direction of motion and a speed. The maximum speed light can travel is the "speed of light through a vacuum", that is, the speed light travels through empty space, and is pretty fast - seventeen times around the Earth in one second. Photons travels a little slower though materials like glass, air and water - about a third slower though glass - but still in day to day life photon movement is practically instantaneous. Rarely is a photon by itself; the number of photons passing through a surface within a set period of time is known as the flux. The more photons emitted from (say) a flashlight, the brighter the light beam will be. Each of those photons has an associated energy and this energy the photon has is responsible for the photon's "colour".
[ Figure 2 ]
[ groundbreakingsci-stuff dot com/post/169361700882/1point6p1#two ]
The different types of light given out by the Sun and their brightnesses. We've evolved to see the most abundant light as that's the most useful to humans.
Think of the rainbow and the order of colour contained within. Each of those colours has an associated energy running from low to high; red light has a low energy, violet a higher energy. In the grand scheme these energies are very close - violet light being approximately only double the energy of red light. Contrast that to "colours" of light we can't see, beyond the optical section of the light spectrum, that can be thousands of times more or less energetic than the light we can. Light that's beyond the red part of the rainbow has a lower energy than red and is known as infra-red light. We can't see this light, but we can sometimes feel it as heat. TV remotes work with infrared light. Microwaves and radio waves are other low energy kinds of light. Note - specific microwaves made from a microwave oven are dangerous because they are tuned to cause water to vibrate and therefore cook food, microwave light in general is not dangerous. Light that's beyond the violet part of the spectrum has a higher energy than violet light and is called ultra-violet or UV light. Some birds and insects can see this kind of light. As UV photons have lots of energy, they can be dangerous to life, meaning we have to protect ourselves from the Sun with sunscreen. X-rays and gamma rays are another type of high-energy light that are even more damaging without protection. Every one of these colours has a defined, specific energy of light associated with it.
[ Figure 3 ]
[ groundbreakingsci-stuff dot com/post/169361700882/1point6p1#three ]
The photon and wave analogy of light are equivalent. The number of wavelengths that pass per second is known as the frequency.
Thinking of light travelling as little balls called photons is a helpful way to map how light moves in straight lines and bounces off surfaces. But light can be thought of as a wave, too (and honestly, many of the particle-like behaviours of photons can be rewritten like waves, but we're not taking an undergraduate class in physics here). The kind of wave I'm describing is an oscillation, an up and down movement, like a ripple on a pond. The wave moves through a space and has peaks and troughs, and a height. What was previously modelled as a collection of photons can now be thought of as waves travelling through a space. The energy of the photon we had previously is now translated to the energy of the wave. Now, rather than hand-wavingly assigning an energy to a photon, we can describe this as a physical property of the wave. A high energy wave oscillates (moves up-and-down) faster than a low energy wave. As a light wave travels passed start a stopwatch - more peaks per second will pass you by with a high energy wave than a low energy wave. The number of peaks per second passing you is known as the frequency of light. As light travels at a fixed speed (through a defined medium) the logic follows that a high energy wave must have a shorter distance between peaks than a low energy wave. This distance between peaks is known as the wavelength. Energy, wavelength and frequency then, are all interchangeable concepts for light waves. Note: that the energy of the wave has nothing to do with the height of the wave (which you might expect), only the wavelength does. The height of a light wave - the amplitude - is a measure of intensity and is a little like talking about the photon flux leaving the end of the flashlight.
Science disciplines will commonly use the word describing light energy that is most appropriate for their work. In astronomy for example this is relative to the way the telescope works. Radio waves from space are picked up with tuned arrays of radio masts, so radio astronomers speak of the wave frequency. Infrared, visible and UV astronomers use telescopes with mirrors acting as lenses and talk about waves and wavelengths. X-ray astronomers need to capture their very rare high energy X-rays, so they speak in terms of the electron-Volts (a measure of energy) of individual photons. Just like astronomers using the most appropriate word for the context, I'll be doing the same with the words photon and light wave, and wavelength, frequency and energy. Just remember that they're interchangeable concepts - give or take some math.
A key point to note here. Two beams of light can exist where the individual photons (or light waves) have different energies and therefore colour, but each have a photon flux such that the total energy leaving both flashlights is the same. So the power, the energy leaving the flashlight per second, can be exactly the same, but the properties of the light completely different. Please store that information for later.
Light from the Sun looks white, or neutral to our eyes. However, white is not a colour with one corresponding wavelength. Instead we have evolved to see a combination of light waves matching daylight as neutral. As every child with a crayon set knows, the Sun's light is actually a rainbow of colours; we evolved to see what we call visible light as these are the most abundant wavelengths emitted from the Sun across its spectrum, and therefore the most useful light to be able to see. Unless something is very hot (like the old-style light-bulb filaments or glowing fire embers) or light is created from a chemical process within an object (like fireflies) it will not give off visible light, only reflect or scatter photons. The next question to ask then is how do we move from an entire rainbow of light in the environment to objects having individual colours in the world around us? What about an object chooses the colour it has?
To understand exactly how an object gets its colour we need to understand quantum mechanics and atoms. Not the entirety of quantum mechanics I hasten to add, but just enough of the 'what's without the rigorous mathematical 'why's (though you're welcome to do further reading).
The world around is made of matter, "stuff", atoms. These building blocks come in different types: hydrogen and helium are the two lightest types of atoms, we breathe in and use oxygen, our bodies contain lots of carbon. The number of particles called protons in the centre of the atom determines its type. Each proton has a positive electric charge of 1, and so the atom's centre has an overall positive electric charge. There are also neutrons, neutral particles in the centre that can vary by a few in number that help keep the atom's centre stable. Together, these particles make the atom's nucleus. To balance out the charge there are negatively charged particles called electrons surrounding the nucleus, an equal number of electrons and protons make a neutral atom.
In school textbooks you've probably seen cartoon pictures of electrons orbiting the nucleus much like the Moon orbits the Earth. This isn't strictly true. Electrons can be thought of like little ball particles, yes, but also as a wave (sound familiar?). If you recall waves, like ripples, have peaks and troughs. In particular, electrons bound to atoms are most easily thought of as a type of wave known as a standing wave. Standing waves happen when a wave has only a finite space to move backwards and forwards in. A string on a guitar is tied at both ends and so plucking it forces the ripple of the pluck to move left and right along the string, bouncing off the bridge and nut and sets up a standing wave. Around an atom an electron can be thought of as being stuck moving in a circle and so only particular shapes of wave are permissible.
[ Figure 4 ]
[ groundbreakingsci-stuff dot com/post/169361700882/1point6p1#four ]
The connection between standing waves and electron energy levels, giving rise to very specific energy requirements for electrons to move between energy levels in an atom.
A standing wave is so-called as for all intents and purposes it appears as though the wave is stuck still. Some parts of the wave move up and down by a huge distance, and at the midpoint (nodes) between these the wave does not move up or down at all. By construction the points where, say, a guitar string is fixed must be a node, too. In the simplest case a node would be at either end and the centre would move up and down. Remembering that one wavelength is the distance between two peaks with a trough between, then the distance between the two end nodes here is half a wavelength. In music this is known as the fundamental frequency and it is the lowest energy wave that will fit in the gap. You can add more nodes in the gap too, each an equal distance from each other to make waves with shorter wavelengths. The possible frequencies allowed for a standing wave in a space then are always going to be multiples of that fundamental frequency. This is why a plucked guitar string has a specific sound, the sound frequencies are related to standing waves and these higher so-called harmonics are multiples of that fundamental frequency (the first harmonic), making music sound in tune and rich.
Like with the guitar string, a similar process happens to an electron. If we treat an electron as a standing wave around an atom (with an equally spaced number of nodes along the electron's orbit) then there are only some specific frequencies and therefore some energies that an electron can have. What the fundamental energy an electron in an atom can have is, and what the subsequence harmonics are, is dependent on the type of atom and what other atoms are nearby (if the atom is combined in a molecule or metal for example). An electron can be in its so-called ground-state at the fundamental frequency, or with an injection of energy can jump to those higher harmonics or energy levels (a process called excitation). Those very specific varying energy levels an electron can have (or more precisely, the difference in energy between the energy levels) gives rise to an object's colour.
To prevent the inevitable letters I'd receive on this topic otherwise - yes, I am aware this is a simplification and that the subtleties of quantum mechanics mean there are more nuanced effects than a simple standing wave analogy can cover (like spin, the shape of the electron orbitals, the effect of filling the electron shells on available energy levels or those not-quite-forbidden states). But this is a fair first approximation and standard, classical harmonics will appear later in a different situation. I trust the interested reader will investigate for further information.
We now have white sunlight hitting an object. We know that objects reflect or scatter light and the light that bounces off an object will have a colour. I've just explained that the set of colours bounced back is governed by the very specific energy levels electrons in different atoms or molecules can have. The electron will interact with light in two ways depending on the light's energy - through either absorption or scattering.
[ Figure 5 ]
[ groundbreakingsci-stuff dot com/post/169361700882/1point6p1#five ]
Absorption and scattering, the two processes that happen to light dependent on the light's energy.
First, absorption. Look at the clothes you're wearing. There are probably one or more dyes on them. A dye is a complicated molecule that, crucially, has differences in electron energy levels corresponding to many different energies of visible light. An electron can move up an energy level if given energy to do so. That energy comes from photons. To be absorbed the photon must have precisely the correct energy to cover the energy gap between the levels (all of the photon must be absorbed) so the photon must be the right colour to cause the electron to jump up. This colour of light is then removed from the spectrum.
What about those colours that aren't quite right? Well, this light will probably still hit an electron as it passes through your clothes. But instead of being absorbed by the electron, the photon bounces off - the light is scattered. The maths of exactly how the light bounces depends on the shape of the fabric surface, how the electron is moving relative to the light and the chemistry of the dye. As clothing is really rough (it's no smooth sheet of glass), the light can be scattered in any number of directions. If your clothes were really smooth (say, a helmet) the light would bounce off in a similar direction allowing you to see a reflection. It is the scattered colours that we see.
Those remembering the laws of energy conservation may wonder what happens to the absorbed light. The jumped-up electrons now exist at a higher energy level, and to accept a photon of the same colour they need to drop down again. To do so they can lose that energy spontaneously, emitting energy in the form of another photon. The emitted photon won't necessarily be of the same energy, the same colour as the one absorbed (otherwise everything would still look white). Visible light is fairly high energy, so when an electron absorbs visible light, the electron jumps up a few levels in one step. When the electron loses energy again through emitting packets of light, the electron will take smaller steps on the way down the energy level ladder. As these are smaller and therefore lower energy steps, the light emitted will probably be in the infrared instead. We can't see infrared, but we can feel this type of light on our skin as heat. This is why black clothes, absorbing all the light and reradiating in the infrared, feel hotter coming inside from sunlight than white clothes that scatter most of the light.
This also explains our puzzle with my helmet at the start. Why does the orange turn black in blue light, rather than brown? Well, only the red part of the spectrum would be scattered by the helmet, the blue absorbed, so under blue light no visible light is scattered back for us to see.
We now have light of a particular set of wavelengths reflected in our direction. How do we go from wavelengths to a colour we understand?