Nothing Matters

To disabuse ourselves of this vision let's look a little more closely at these atoms, to see what they are really made of.

By the time you reach the end of this chapter you'll have discovered that atoms are more bizarre than we can possibly imagine; that they exist in a place where what seems to be solid becomes insubstantial - a place that straddles the borderline between the existent and the nonexistent.

You may rightly be intrigued by this idea that the "stuff" that atoms are made of is bizarre, incomprehensible and mind-boggling - that atoms are weird. However, bear in mind that atoms are the building blocks of everything in the universe. So if atoms have these qualities, so have all of the things that are made of atoms. Any terms that we can apply to atoms, such as "existing on the borderline between the existent and the nonexistent" must also apply to everything else - because after all, everything is nothing more than a large collection of atoms.

This applies to things in the everyday world that we inhabit. And it applies to us.

For all of its seeming robustness, our physical world of mountains and oceans and tables and chairs is in reality a disconcertingly insubstantial place balancing on the edge of existence.

We don't notice this fact because we're right in the midst of it, and we take our world for granted because we see it every day - but that doesn't mean that it's not amongst the most bizarre things imaginable.

To see just how bizarre, let's look deep into the atom.

The idea of atoms has been around since at least the times of the ancient Greeks. They postulated that if a large amount of any substance was repeatedly subdivided an amount would eventually be reached that was so small that it couldn't be divided again. This piece of the substance, incapable of further division, was the smallest possible piece of that substance that could exist. The name of this tiniest speck of substance, an atom, was derived from the Greek term for uncuttable (a-tom: the a means not, as used as a prefix in other negative words such as asymmetrical and atonal; and the tom comes from the verb to cut, which is most familiar nowadays as a suffix to medical surgery that involve cutting, such as tonsillectomy or appendectomy).

All matter is made up of atoms, with the atoms of each element being different to those of the other elements, which is what makes gold different to carbon, carbon different to hydrogen and so on.

For several thousand years the idea of atoms being the smallest, uncuttable level of matter worked extremely well.

However, things started to get more complicated as experiments started to be made into the phenomenon of electricity during the Victorian period.

In 1897 Joseph John Thomson, the son of a Manchester bookseller, was the first person to discover a particle smaller than the "uncuttable" atom. While experimenting with cathode ray tubes he discovered the almost weightless subatomic particle that carries a negative electrical charge - named the electron due to its relationship with electricity. (If you think that cathode ray tubes are old-fashioned contraptions that were only good for outmoded television sets and now-uncool computer monitors, remember that we wouldn't have discovered the electron without them. They were in some ways the Victorian equivalent of the Large Hadron Collider). Thomson won the Nobel Prize for his discovery.

Thomson proposed that the electrons were distributed within the atom in what is sometimes described as "plum pudding" manner, with the negatively charged electrons distributed randomly inside a positively charged cloud (thus making the whole atom electrically neutral).

The discovery of the electron was followed in 1911 by the discovery of the atomic core, or nucleus, by New Zealander Ernest Rutherford. He determined that the nucleus contained positively charged particles, which he christened protons. These particles are much heavier than the almost weightless electrons - around 1,800 times heavier in fact.

Rutherford postulated that the atomic core also contained particles with no electrical charge at all. Some years later, in 1932, his theory was proved correct when the neutron was discovered by Sir James Chadwick at the Cavendish Laboratory in Cambridge University. Yet another Nobel Prize. The neutron was very very slightly heavier than the positively charged proton.

So it was that by the mid 1930s atoms were seen as being made up of three fundamental particles - protons, neutrons and electrons - rather than as being the single, indivisible, uncuttable entities that they had been conceived as previously.

The atoms of different elements had different numbers of these fundamental particles, which was why each element had different properties. Figure 35 shows a typical atom: that of helium..

There are a hundred or so different elements (92 natural ones, rising to 112 when you include man-made ones produced in nuclear physics laboratories under special conditions). It's a nice idea that this large, rather unwieldy number of elements are all composed of the same very small number of basic particles, as this simplifies things no end. It's a good principle in general to assume that complicated things are made up of simpler things.

Three basic subatomic particles is simpler than a hundred or so basic elements, I think you'll agree, but there's something slightly odd about there being three subatomic particles.

Things could be simpler. Two subatomic particles would be simpler for instance, with one of them being positively charged and the other negatively charged. There's a nice symmetry to that.

This simplicity could be achieved if the neutrally charged neutron turned out to be nothing more than a proton and an electron stuck together.

That's nice and simple.

Now, what if those two subatomic particles, the positive and the negative one, were simply the same particle, but in different configurations (such as different ways up)? Looking at the particle one way up you would see a positive particle, while looking at it the other way up you'd see a negative one.

That would give just one subatomic particle.

You can't get much simpler than that. It sounds right.

There seems to be something odd going on though: one way up the particle has a different mass to the other way up. How can one particle have two different masses? This seeming paradox may possibly be explained by the following analogy.

Imagine that the single subatomic particle is cone shaped, as shown in Figure 36. (Remember, this is an analogy purely for visualisation purposes - I'm not implying that such a particle actually is cone shaped.) Imagine that the cone is resting on a soft and giving surface (such as rubber).

Depending on which way up the cone is orientated it manifests itself as either a positively charged heavy particle or a negatively charged light particle.

One way up the cone stands on its point (exhibiting its positive charge), while the other way up it rests on its base (when it exhibits its negative charge). When resting on its base the cone makes a relatively shallow impression in the surface on which it rests, due to the large area that's in contact with the surface (in a similar manner to that of a snow shoe on snow). In contrast, when standing on its point the cone sinks deep into the surface, as its entire force is concentrated on a small area (in a similar manner to that of a high-heeled shoe on snow).

The depth of the impression in the surface is the thing that we experience as mass. Thus the same object can exhibit different masses depending on its orientation.

That's quite neat as far as it goes, but there's a problem.

This way of looking at subatomic particles would be fine if there were only three fundamental particles, protons, neutrons and electrons, as was once thought. But it turns out that there are more. Many more. By the end of the 1930s other, more elusive, subatomic particles were being discovered as a result of improved technology.

These particles were harder to detect than the proton, neutron and electron for a variety of reasons.

For instance, one of these subatomic particles, the neutrino, is very much like the electron in that it is almost weightless, but it differs in that it has no electrical charge. The combination of weightlessness and lack of charge means that neutrinos don't interact much with other particles, making them extremely tricky indeed to detect. As a consequence they remained undiscovered until 1959. Although they are extremely elusive they are surprisingly common. In the time it takes you to read this sentence untold billions of them will have flowed through your body, while numbers of them beyond all imagination will have passed through the entire earth completely unhindered and unnoticed.

By the 1960s the number of subatomic particles that had been discovered was in danger of becoming ridiculous. So much for simplicity. Most of these particles were only observable in special conditions such as in the atom-smashing apparatus in nuclear physics laboratories and didn't seem to be stable components of the atom in the way that the proton, neutron and electron were. They frequently existed for only a fraction of a second before disappearing in a puff of energy, but they were there all the same.

All of these subatomic particles vary wildly in how heavy they are. For instance the proton is 1,836 times heavier than an electron, while another particle, the pion, is 273 times heavier, and another, the muon, is 207 times heavier.

Although their masses vary so greatly all of the particles have a restricted choice of electric charge: either plus or minus one, or no charge at all. Charges of plus or minus one are essentially the same charge in opposite directions, so in some ways they can be thought of as being the same as each other - so in reality the particles either have the same charge or no charge.

This implies that charge is something very basic, because of the fact that when it exists it seems to only exist at one value. Mass however isn't quite so basic- as its value varies far too much from particle to particle for that to be the case. This problem of the large number of disparate masses, or the mass of masses mystery, may be explainable by using an analogy that's not too dissimilar to the one I used a page or two ago, in which a single object (a cone) exhibited different weights in different configurations.

This time compare the subatomic particles with the Moon rather than with a cone.

The Moon is an object that looks different at different phases, even though it is just one object that simply seems to be different depending on the direction of the light that's illuminating it. If you were to imagine the Moon to be a giant fundamental particle the mass of which was for some reason dependant solely on how much of it was visible, the thin crescent Moon would exhibit a very low mass while the full Moon would be very massive. The new Moon, when the Moon is invisible, would have no mass at all. The same Moon would exhibit a different mass at each phase: one subatomic particle would seem to be many.

Appealing as this metaphor is, it turns out to be unnecessary (at this stage - but I'll come back to something similar later), as it's now generally assumed that the reason there are such a large number of different fundamental subatomic particles is because these particles aren't actually fundamental at all, but are made up of a deeper level of even more fundamental particles.

These even-more-fundamental sub-subatomic particles were given the name quarks when their existence was first postulated in the 1960s.

It was proposed that protons and neutrons were composed of two types of quark, these quarks being essentially the same except for their electrical charges. They were named up quarks and down quarks - names chosen simply to infer difference rather than any intrinsic up-ness or down-ness. The up quarks had a positive charge, while the down quarks had a negative charge - however, the up quarks' positive charge was twice the strength of the down quarks' negative one.

The proton and the neutron are each composed of three quarks (Figure 37). The neutron is composed of one up quark and two down quarks (with the result that, because positive up quarks have twice the charge of negative down ones, the combined charges neutralize each other). The proton is composed of two up quarks and one down quark, giving it an overall positive charge.

By the way, the component parts of the atom aren't tightly packed billiard balls as shown in these (and most other) diagrams of atoms. The individual components are tiny, if indeed they can be said to have any size at all, but they define a volume because they take up a certain amount of "personal space". You could try imagining them by thinking of the way that when you wave a torch around on a dark night you see an after-image of where the torch's light traces out a shape: the shape isn't solid, but it defines a region in space. The components are only shown as being large balls because if they were represented more realistically there'd be nothing to show. Not only that, the scale of these diagrams is completely unrepresentative of the true scales involved: in Figure 35 for instance (a representation of a helium atom), at the scale at which the atom's nucleus is represented the electrons would actually be whizzing around several miles away. To say that there's a lot of empty space inside an atom would be an understatement.

So, let's see where we've got to now in our quest to find the simplest, most fundamental level of matter.

An atom is essentially composed of electrons, protons and neutrons, while a whole menagerie of other subatomic particles exist in supporting roles. The protons and neutrons are composed of two types of quark. The electron is so small and simple that it's assumed to be indivisible, a bit like a quark itself - the quarks however are about 600 times heavier than the electron, with the electron having three times the charge of the negative quark.

Things don't seem to be getting that much simpler, do they? In fact, things seem to actually be getting a touch more complicated.

And they get even more complicated still. It turns out that in order to account for all of the different types of subatomic particles other than protons and neutrons there aren't two types of quark needed, but six.

Added to this, it transpires that there are also six types of electron-like particle - almost weightless subatomic particles that are thought to be fundamental in their own right, a little like quarks.

That's twelve types of fundamental particle.

It gets worse still.

Each type of subatomic particle, from protons and electrons to quarks, has a twin that's opposite in all of its characteristics (of which opposite charge is only one). For instance the negatively charged electron has a positively charged twin, the positron, and each of the quarks has a corresponding doppelganger, called an antiquark (from which such particles as antiprotons and antineutrons are made). These "equal though opposite" particles are known as antimatter..

So, the twelve fundamental particles - electrons, quarks etc - have suddenly broadened to twenty-four. Surely that's too many particles to be fundamental? We're getting back to the earlier, confusing level where atoms seemed to be the smallest particles - even though there were a hundred or so different ones.

There are (at least) two possible answers to the question of why there seem to be so many different "fundamental" particles.

One is that there aren't that many, and that the ones that there are simply exhibit different properties in different circum-stances, as described in the analogies of the cone and the phases of the Moon a few pages ago.

The other possibility is that the fundamental particles aren't fundamental at all. They are constructed of something that's even more fundamental.

What could that "something" be? Well, whatever it is, to use the word "particles" is probably stretching it a bit.

The word particle implies something that has some semblance of solidity. Solid things are objects like bricks and billiard balls. The tiniest object that can meaningfully be labelled solid is probably the atom. But when you get smaller than an atom everything becomes a bit fuzzy and the use of words like particle becomes rather imprecise and misleading, even though the things are usually depicted as being rather billiard-ball-like. Instead, think of something closer to that torch that I mentioned a few pages ago, tracing out a region in space as it's waved around.

Just as the light from the torch is a form of energy, think of the component parts of atoms as tiny bundles of energy too (Exactly what "energy" is is open to debate needless to say, but at least it's a suitably nebulous term for whatever's going on at the subatomic level). The fact that the components of an atom are actually composed of energy is why they have electric charge - electric charge being one of the ways that energy manifests itself.

If subatomic particles are actually nothing more than energy this means that as a result solid objects can be thought of as quite literally being made up of nothing more than energy too.

The main difference between the energy as we experience it when we touch a live electric wire and the energy in solid matter is that in solid matter the energy has a stable configuration, tied up within its atoms. So when you sit in a chair the energy in the atoms of the chair stops you falling through it, while when you sit in an electric chair the consequences don't bear thinking about.

We're so used to the idea of the energy of electricity that we tend to forget that we don't really know what it actually is, only what it does. You have to go back to the nineteenth century, when the humble electric light bulb was a cutting-edge invention, in order to relive the feeling of wonder that the phenomenon of electricity evoked.

Think of the solidity of matter as being the result of the electric forces acting within each atom - that each atom is in essence nothing more than a stable force field that stops other atoms entering the particular volume of space that it occupies (a little like mini versions of the force fields or deflector screens that are generated by spacecraft in many science fiction stories - the main difference being that while science fiction force fields are used to stop photon torpedoes or other advanced and improbable weaponry from reaching a spaceship, atomic force fields are more commonly associated with stopping coffee cups falling through table tops, at least in philosophical discussions).

So, if atoms are made up of bundles of energy that are in a configuration that forms a stable entity, what form does the energy take at a truly fundamental level? The currently favoured theory is that at the most fundamental level everything is composed of vibrating strands of energy called strings.

The idea that the stuff of the universe is composed of vibrating strings gives the impression that even at this fundamental level the "stuff" is "solid" in some way: the idea of strings sounds very much like the idea of particles after all. However, the string involved is only one-dimensional, with no thickness, like an infinitely thin line (although they have other dimensions "wrapped up" inside them, for mathematical reasons).

These strings are thought of as vibrating at different frequencies, with each frequency making the string manifest itself as a different subatomic particle - a little like the way that the strings on musical instruments give rise to different notes or that different wavelengths of light give rise to different colours.

String theory isn't the only game in town however. Other theories propose that everything is composed of point-like entities rather than extended string-like ones, while others invoke sheets or membranes of some fundamental "medium".

Points, strings, sheets: take your pick.

Whether string theory is correct or not, the idea that the fundamental "stuff of existence" is essentially something that vibrates does possess a quality that seems to be essential for a theory of the fundamental nature of everything: the essential stuff of existence must be very simple, yet be able to manifest itself in more complex ways. In other words, if the "stuff" is a vibration, then the same sort of vibration can give rise to all of the different manifestations of matter and energy, simply by vibrating at different rates.

Let's by-pass the issue of whether the fundamental nature of the stuff of the universe is closer to strings, membranes or whatever, and instead just concentrate on the concept that it is a disturbance of some kind, or an irregularity of some sort, in the empty nothingness of the "primordial void".

Here we start running into serious conceptual difficulties, as this primordial void or expanse of nothingness is a tricky thing to get your head round, to say the least.

How to imagine nothingness? Of course it's impossible, partly because our brains just aren't wired to conceive of such a thing (for everyday purposes it's a pretty pointless and needless exercise after all), but also because nothingness simply isn't like anything. Mainly because it isn't anything.

It's probably best to not even try to imagine it, and to just accept that it's there, if "there" is a word that can be used in this situation. However, if we do want to have a go at imagining it we have to resort to slightly unreliable and inadequate metaphors.

A suitable metaphor for nothingness may be to think of it as being like a flat, perfectly still surface of water extending endlessly, with the flatness of the water representing the total featurelessness of nothingness. To differentiate between this profound ultimate nothingness and other more day-to-day nothingnesses let's call it Nothingness - with a capital N. In fact let's call this endless flat expanse the Sea of Nothingness. In this infinite, shoreless Sea of Nothingness any disturbances in the form of ripples on the surface could be likened to the vibrations that give rise to "stuff".

These particular ripples or vibrations aren't to be confused with the vibrating strings of string theory. The vibrations I'm describing here are metaphorical vibrations or ripples in a metaphorical medium - the Sea of Nothingness. (If anything, think of these metaphorical vibrations as giving rise to the vibrations of the strings in string theory - imagine that the strings of string theory are floating on the surface of the Sea of Nothingness and that the undulations in the sea are causing the undulations of the strings - because the strings are riding the sea's undulations.) The idea that everything in the universe, all matter and energy, is the manifestation of ripples in Nothingness, and that these ripples are the simplest "things" that exist, is quite appealing because of one important factor. A ripple, in essence, is a form of wave that has only one fundamental characteristic or property: it goes up and down. If you're thinking that this up-and-down-ness gives the wave two characteristics rather than one, think of the crest and the trough of the wave as being inseparable parts of the same single characteristic - that a single wave automatically has both parts in very much the same way that a single coin automatically has a heads and a tails, and in fact can't exist without having both.

The ripple's possession of only one characteristic is important because whatever it is that exists at the most fundamental level, it can only have one property. This is because, working on the assumption that only one property can arise at a time, having two properties makes something more complex than absolute fundamentality allows.

Grafted onto this one property are other characteristics such as its wavelength and amplitude as secondary features.

Not only is the simplicity of the concept of a wave-like disturbance being the fundamental phenomenon that manifests itself as matter and energy appealing, but the concept has yet another appealing feature.

Look at the wave in Figure 38. This represents a ripple on the surface of the Sea of Nothingness (Notice the flat, featureless nothingness extending endlessly on either side of the ripple).

As you can see, the wave goes up and down, as waves do: it has a crest and a trough. Imagine the crest of the wave as being "positive" energy, and the trough of the wave as being "negative" energy, as depicted in the graph in Figure 39.

You can see that the positive energy and the negative energy (the shaded areas in the figure) are the same, but are in opposite directions. This means that when the energy of the crest and the energy of the trough are added together to give the wave's total energy they add up to nothing.

This is very pleasing philosophically, as it means that although the wave exists, the sum of its parts is zero, so in some ways its existence adds up to nothing.

Because this ripple is a disturbance in Nothingness, it can be said that Nothingness actually becomes Something - and that because the up and down parts of the ripple cancel out energy-wise and don't add anything to the overall status of Nothingness, you can still say that Nothingness nevertheless contains nothing.

Because the ripple straddles either side of the flat line in the graph - the line that represents Nothingness - the universe can be thought of as hanging on either side of Nothingness.

I expect that you've been asking yourself "These ripples in Nothingness are all very well, but what caused them?" Here we run slap-bang into the infinite regression problem - what made the thing that made the thing? Bear in mind that my ripples in Nothingness aren't real ripples, they are metaphorical ripples. And metaphors, after all, are by their nature imprecise comparisons of the things that they are standing in for - if they weren't imprecise they'd actually be exactly the same as the thing they represented, and thus wouldn't be metaphors at all. Due to this imprecision you could say that if metaphors were elastic bands you could stretch any metaphor until it snapped.

The metaphor of ripples is just a way of visualising something that is impossible to comprehend. The ripples in the Sea of Nothingness are, by definition, the most basic disturbance in the uniform, all pervasive state of Nothingness that underlies everything. The phenomenon that these metaphorical ripples are standing in for is not caused by anything (at least in any way that we can meaningfully understand). They are just something in the nature of Nothingness (Again, whatever that means).

In fact, if anything, they are the thing that's at the beginning of the infinitely regressive chain of events that I just mentioned. They are the thing that caused the thing.

The idea of ripples in a (metaphorical) Sea of Nothingness may be seized upon by those amongst us who are of a religious inclination, who may then say "Ah-ha, yes. The ripples are caused by God dipping his fingers in the Sea of Nothingness!" This, unfortunately (or fortunately, depending on your outlook), isn't possible, as the ripples are the simplest thing that there can be, by definition. This means that they can't be caused by something that's more complex than they are themselves, such as an all-knowing entity that happens to have fingers. Even metaphorical fingers.

Talking about complexity, there's one final point that has to be mentioned about these metaphorical ripples. I've been stating that they are the simplest thing in existence: that there is nothing simpler than they are. However, if you look at the shape of the ripple you can see that it itself is not totally simple: it starts to rise up gradually, then rises steeply for a while before flattening off and then dropping down again. That's quite a lot of things to be going on for something that there's nothing simpler than. In "reality" the ripple would be a single blip, with no initial gradual appearance and final decay - it would in fact be more like a digital pulse that's just "there" rather than an analogue wave that rises and decays.

So there you have it. Despite its incredible complexity the universe is little more than the result of disturbances or ripples in the void. And despite the universe's "content-rich" appearance the sum total of its contents (the peaks and troughs of the ripples in the void) adds up to nothing.

You could indeed say that because the crests and the troughs of the ripples cancel out when added together, and they thus in combination add up to nothing, the end result of the ripples is less than the sum of their parts. While of course, just looking at the universe around us shows that at the same time the end result of all of these ripples is definitely greater than the sum of their parts..

The universe is both everything and nothing. It just sounds right (to me, at least).

Nothing becomes Something. But at the same time it all still adds up to nothing, and thus it remains Nothing. You could actually say that the universe is composed of Nothing. That "Nothing exists". As in "Something exists".

This rather disconcerting fact that the universe and all of the matter within it is made out of nothing at all could at first sight seem to imply that the universe is totally meaningless. You can't get more meaningless than nothing, after all.

However, the fact that matter is nothing doesn't in any way imply that nothing matters.

In fact, because the universe is made of Nothing (the capitalised Nothing that exists in the Sea of Nothingness), it can very much be said that Nothing matters.

If only so that people like me can mess about playing with words in this rather silly and irritating way.

I'd better move on.

But before I do so, here are a couple of footnotes to this chapter, held back until now simply so that they didn't interrupt the flow of the chapter as a whole.

You may be wondering how anything as complicated as a universe can manifest itself out of something as simple as ripples. A ripple, after all, has only two components - an up part and a down part.

It's not as far-fetched as it first sounds. Bear in mind, for instance, that the entire contents of a computer, ranging from the calculations that it performs, through to the photos and videos that it displays and the music that it plays, is composed entirely of different sequences of only two states: on and off - or as it is expressed digitally, of zeros and ones. This two digit "language" is known as binary code and is the underlying principle of all digital technology.

It's not only computers that have a very basic code underlying their ultimate complexity. Life itself has such a code too. The genetic code that is carried by the DNA that is the building-block of all living things is essentially created by a sequence of only four separate chemicals, adenine, thymine, cytosine and guanine (known as A, T, C and G for short), spread along the DNA double helix molecule (Figure 40). One side of the helix is from the mother and the other side from the father: the sides fuse together like a long zip, with the A molecules on one side linking with the T molecules on the other, and the C molecules with the G molecules. The order in which these chemical bonds occur along the molecule determines the genetic characteristics of their possessor. Very simple - but just look at the results in the mirror!

Illustrated next is a nice graphic example of how easy it is to generate complexity from very simple beginnings.

To start, take a couple of black dots (Figure 41). Move them so that they overlap slightly. Then make the regions where the black of the dots overlap "cancel out", leaving white.

Not a particularly complicated outcome, you may quite rightly be thinking. But now, instead of using a couple of single dots, do the same thing with two simple grids of dots such as the one shown in Figure 42.

Place the grids one above the other, with one at an angle, as here in Figure 43.

Just look at all of those flowers! Or are they snowflakes? Or mini-eruptions of some sort? All simply the result of overlapping areas of black cancelling each other out on very basic grids of dots. It couldn't be much simpler.

You can see an animated version of this phenomenon, where the grids rotate relative to each other in spectacular fashion at the bottom of this page.

Another point that I mentioned earlier in this chapter was the enigma concerning the fact that the electrical charges of subatomic particles are always either plus or minus one (or zero), while their masses vary incredibly. A model that accommodates this relationship between charge and mass can be built into the metaphor of vibrating waves, such as those in the Sea of Nothingness. Imagining that a subatomic particle is not an actual particle at all but is the manifestation of a wave, the electrical charge of the particle may be thought of as a manifestation of the amplitude, or height, of the wave (Figure 44). If all waves had the same amplitude for some fundamental reason, then all electrical charges would be the same (though positive or negative depending on whether they went up or down).

Meanwhile, the mass of the particle may be thought of as a manifestation of the frequency, or wavelength, of the wave. The wavelength may be capable of varying greatly, hence the large variety of masses that subatomic particles manifest.

If you have trouble with the idea of a wave's frequency somehow manifesting itself as something that's as "solid" as mass, look at it this way. Think of the mass of an object not in the way that we normally experience it - as something that has the feel of kilograms or pounds about it - but as the magnitude of the effect or impression that the object has on its surroundings. A massive or heavy object has a greater effect than a light one.

Figure 45 shows an analogy that demonstrates what I mean.

The figure shows a number of circles of varying shades. As you can see, the impact that each circle has on the page is different, depending on its shade. If the shade of the circles were to manifest themselves as weight rather than tone, the black circle on the left would be the heaviest, as this circle has the greatest effect on the page. The two gray circles would weigh less, with the lighter gray circle being the lighter in weight.

What you probably didn't notice when you looked at the series of circles in Figure 45 is that at the right hand end of the row there's a circle that's almost white. This fourth circle is for all intents and purposes invisible, and thus it has no effect on the page at all. If its tone were translated into mass, this circle would be practically weightless. It's the metaphorical equivalent of one of the almost massless subatomic particles such as an electron or a neutrino.

So in this analogy the black circle represents a particle that is analogous to a wave that has a frequency or wavelength that makes a great impression, while the white circle represents one that makes practically no impression at all. Yet, despite the difference in their impacts, the only real difference between the different circles is the frequency of the waves that form their contents.

Finally, one last note on the subject of nothingness.

If you find the notion of "nothing" being "something" a bit of a tricky concept to hold in your head, you're not alone. Neither can I. Our brains just aren't meant to work with such concepts (As I mentioned earlier, why would they need to?).

In a similar way, only one and a half thousand years ago people didn't have the concept of the number that denotes nothing - zero.

This number is something that we now take for granted, but back then the concept of giving "the absence of a quantity of something" a numerical value just seemed bizarre. If your friend had five oranges, while you had no oranges, and you had to write down how many oranges you each had, you'd be able to write 5 for your friend but you'd be at a total loss to know how to express your own quantity. It wasn't until around 500AD, in India, that our current understanding of the concept of the number zero began to be developed.

Today we think nothing of it.