Science – Page 3 – Me on the net

Shadows of Reality

Plato’s Allegory of the Cave has people chained in chairs facing a blank wall. All that they can see are the shadows cast on the wall of the cave. When they break free from their chains they discover that reality is not what they believed it to be. In particular, they don’t know what the sun is, having never seen it before. The implication is that we cannot know reality and that we only see shadows of it and must make do with that.

It’s a nice analogy, and presages Kant’s noumenon and phenomenon, where phenomenon is what we sense or perceive and noumenon is what gives rise to phenomenon. Noumenon is fundamentally unknowable through human sensation, and perhaps corresponds to Kant’s “Ding an sich” (thing-in-itself), which I think of as the thing that gives rise to perceived phenomena, but is not and cannot be experienced through the senses or by other means (if such exist).

The nice thing about allegories and analogies is that you can play around with them. Of course, if you push them too far they fall apart, but that is part of the fun. I’m going to push the Cave Allegory a little bit.

You see, the people in the chairs are not entirely without information about the outside world, aka reality. If the shadows move across the cave wall and they are not moving, then something else is! They won’t know what is causing this phenomenon, but they will notice that it changes in a fixed cycle. The shadows sweep across the wall, only for everything to go dark, and then everything repeats. Let’s call it a day.

If the people in chairs watch for long enough they may determine that there longer cycles. Sometimes the shadows reach higher up the walls, and sometimes they are lower. Let’s call these longer cycles years.

When one raises his hand one of the shadows changes. Some of the shadows are apparently related to the people in the chairs! The person in the chair will most likely come to associate one of the shadows with him/her self, and by extension would assume that some of the other shadows are people also.

He or she might not realise that his/her body is actually seated in a chair, and that the shadow which he/she associates with his/her self are merely outlines. This is a scary thought – if the analogy holds, is it not possible that the same is true of us? We may be seeing shadows and concluding that we are the shadows. Maybe there is a wider reality outside of our perceptual cave and we only need to turn around to see it.

However, just like the people in the cave, if we did wake to a wider reality, we probably would not understand what we are seeing – the people in the cave, when they freed themselves, found the sun to be incomprehensible.

I just realised that in Plato’s original allegory, the light that threw the shadows was not the sun but a fire. I’m going to acknowledge my mistake but let it stand, as it makes my point that the people in the chairs are not completely without clues about the wider world, even if their interpretations are wide of the mark.

Science and what was previously known as ‘natural philosophy’ are attempts to describe the shadows that we see. One of our shadows is the rising and setting of the sun. I’ve described elsewhere that the extreme doubter, the ultimate sceptic, doubts that we will see another sunrise, or rather, cannot see any way that we can know absolutely that we will see another sunrise (leaving aside for arguments sake the possibility that we drop dead – that is not what the issue is).

I don’t actually believe that we are sitting in any conceptual chairs, so we can’t leap out of them to get a wider view of reality in the sense of the allegory, but we do describe the world in terms of what we see, just as those in the cave do. We have no better access to reality than they do. We just have a better class of shadows as it were.

That’s why I find it amusing when the headlines read that scientists have found the Higgs Boson, or that they have detected gravity waves. Oh really? I do not suggest that the Higgs Boson has not been “found” or that gravity waves have not been detected, of course, but no one have ever seen the Boson or watched a gravity wave passing by.

One possible way the Higgs boson might be prod... — One possible way the Higgs boson might be produced at the Large Hadron Collider. Similar images at: http://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/Conferences/2003/aspen-03_dam.ppt (Photo credit: Wikipedia)

No, what they have in fact done is theorised about these things, designed experiments that should show a blip in a graph or find an anomalous number in the printout of their experiments, and this is what they see. They see the predicted blip or the anomalous number.

These results however based on existing theories. Starting from theories about matter and what it is made of. Atoms, you say? Oh OK, we have experiments (from long ago) which show that matter is made up of atoms. We know a lot about atoms from experiments and theories, but no one has ever seen one or held one in his/her hands. We are sure, though, that matter is basically made up of atoms.

However, certain results of these experiments lead to the question of what atoms are made of. So we end up with a (very accurate) theory and experiments which show the existence of sub atomic particles. Some of these theories lead to the theory of the existence of the Higg’s Boson. It is required if some of the theories are correct.

I don’t know the details, but experiments have been done which reportedly appear to show the existence of the Higg’s Boson. What they show is results which are consistent with the stack of theories the top one of which predicts the existence of the Higg’s Boson, and the lower theories predict various behaviours down to the lowest level, those that theorise that matter is fundamentally atomic.

English: Crystal structure of vanadinite. Gray... — English: Crystal structure of vanadinite. Gray: lead atoms, orange: vanadium atoms, green: chlorine atoms, blue: oxygen atoms. (Photo credit: Wikipedia)

Those are our shadows on the wall. We describe what exists by using theories based on what we can see. We see the blip in the graph, and celebrate our theory which is underpinned by other theories down to the lowest and most general theories. However, we can’t get out of our allegorical chairs and turn to actually look at what exists. That’s where the analogy breaks down – there are no chairs and there is no wall. However what we are looking at are shadows.



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What is philosophy for?

English: A cropped version of Antonio Ciseri's... — English: A cropped version of Antonio Ciseri’s depiction of Pontius Pilate presenting a scourged Christ to the people. See: Eccehomo1.jpg for full version. (Photo credit: Wikipedia)

“What is truth?” Pilate asked of Jesus. Jesus had just asserted that he had come into the world to testify to the truth. Pilate used this to close off the conversation, as he knew that truth is exceedingly difficult to define, and that one man’s truth is another man’s falsehood.

We live in a world where politicians cite “alternative facts” to defend themselves when their statements are questioned. Hmm. This seems like a step on the road to fluid “truth” of the authorities in the book “1984”, but is more likely to be a scrambling attempt of the establishment to defend itself.

Philosophy is a means of addressing Pilate’s question and many many others that do not fall into the realm of science or of mathematics. What is real and can we know it? Can we know anything? Is there a God, and if so, why does he permit evil into His universe?

These are questions which fall into the realm of philosophy, as do others about the meaning of science and mathematics, and questions of ethics and morals.

Almost by definition, philosophical questions cannot be answered. The “What is truth?” one is a prime example. Will the sun rise tomorrow morning? Did the sun rise this morning? Is the sun risen at the moment? All of these questions can be pragmatically answered “Yes!” but probe a little deeper and the answer can appear less definite.

After all, we might remember the sun coming up this morning, but what if these are false memories. Or maybe what we see is a mere “virtual reality” fed directly to our brains. And just because the sun rose this morning, and the morning before, and so on, doesn’t mean that it will rise tomorrow. Maybe there is some as yet unknown physical event that will cause it not to rise. Maybe cause and effect are illusions and anything can happen.

We nowadays separate science and philosophy, but this was not always so, and science was once termed “natural philosophy“. The ancient Greeks would have been termed philosophers, but they dealt with such questions as what everything is made of. Some of their suggestions would seem quaint today, but they did suggest the concept of atoms.

At the time there was no way that any of their hypotheses, such as the atomic hypothesis, could be tested and some of them even thought that testing them was a bad idea. They meta-hypothesised that everything could be deduced simply by thought. They needed no experiments!

Atomic theory is now definitely in the realm of science. Biology too, and mathematics, though maths now has its own realm, apart from science. Anything that is in the realms of philosophy may find its way to the realm of science or maths.

What about things like ethics and morality? Surely these won’t ever move to the field of science? Well, maybe. I wouldn’t bet on it, though it may be a long time before there is an ethical Newton, a morality Einstein.

Science has made great grabs in recent times for the fields of behaviourism and in studies of human consciousness. These have been until recently the domain of philosophers alone. In a way, it might be better if we did not understand the way that people and societies and human consciousness work, because understanding things is the first step to control things. Let’s hope that the ethical Newton and the morality Einstein arrive before we know how to scientifically control people and societies.

Philosophic pondering on the way things are tend to be wild and diverse. We tend to think of such hypotheses as the multiple worlds theories as new and cutting edge, but Professor Pangloss in Voltaire’s 1759 book “Candide” proclaims that “all is for the best” in this “best of all possible worlds”, which implies that there are, or could be, other worlds where things might be different.

Of course, since there was no real divide between philosophy and science and maths in the early days, we can’t really say that science has taken over these philosophical topics, more that they have been hived off as science split from philosophy. Nevertheless, science is probing topics, such as the nature of reality, which definitely have a philosophical flavour to them. For instance, is the cat alive or dead, or maybe both?

The philosopher Zeno of Elea introduced some paradoxes which even today exercise the minds of philosophers and mathematicians. Basically, Zeno poses the question : How does one (or an arrow for that matter) move from point A to point B? There’s plenty on the Internet about these paradoxes, so I’m not going into them in detail, but essential the core of the problem is how to sum an infinite number of increasingly small intervals of space or time without the result becoming infinite.

Obviously Achilles does overtake the tortoise, the arrow does reach its target and it is possible to travel from A to B, but some people still think that science and maths have not yet solved these paradoxes, and there’s still a sliver of a problem for the philosophers. Arguments these days resolve more around whether the paradoxes have been resolved and therefore we can move from A to B, or are still in the realm of philosophers and therefore we cannot move from A to B!

When the Greek philosophers were thinking about atoms and what things are made of, there was no way to test the various theories out. When they were developing theories about the stars and other astronomical objects they had no way to test the theories out. However, eventually the “natural philosophers” like Newton, laid the basis for astronomical theories, and early chemists like Lavoisier laid the basis for the science of chemistry, which made use of the theory of atoms.

A scan of the first page of John Dalton's &quo... — A scan of the first page of John Dalton’s “A New System of Chemical Philosophy”, published in 1808. Please do not “update” the list with modern spellings. This is a historic list and the old spellings are intentional. Yes, it’s “carbone”, not “carbon”. (Photo credit: Wikipedia)

Philosophy exists because people like to ask questions like “What is beyond the end of the Universe?” or “If God made everything, who or what made God?” Or “How long is the hypotenuse of a right angled triangle with sides on one cm or one inch?” Or “Why is the ratio of the circumference to the diameter of a circle a fixed number and what is it?”

Philosophy exists to postulate parallel Universes, massive balls of fusing gas, and terrestrial planets complete with humans or maybe little green men. Its job is to wonder what lies beyond the bounds of science and what makes humans behave the way that they do, and whether or not God is dead. It is to ask the impossible questions. It is science’s job to prize these issues from the hands of the philosophers and answer them.



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Getting the Wind Up



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A plant disease called “myrtle rust” has appeared in New Zealand, apparently after the spores have been blown across the Tasman sea from Australia. That’s over four thousand miles. The prevailing winds are from Australia to New Zealand and the cyclones and storms that hit New Zealand are formed in or off the coast of Australia, or further north in the Tropics, or further south in the Southern ocean.

In these areas low pressure areas form and consequently winds blow from the surrounding areas of slightly higher pressure into the lower pressure area and start to swirl clockwise. The clockwise movement is the result of the Coriolis effect, which is difficult to explain, but relates to the fact that when an object moves north or south on the rotating Earth, it moves closer to or further from the Earth’s axis of rotation.

A low pressure area sucks in air and it is forced up in the centre where it cools and forms clouds and rain. As this process continues, the pressure at the centre of the low drops and the spiral of winds gets tighter and, if the low is very deep, more destructive. I’m not sure why a low deepens, when one would think that all the in-rushing air would fill the low, and the few explanations that I have read have not convinced me.

On a larger scale, bands of winds circle the Earth, with winds coming from the west in the south and the north of the two hemispheres, with prevailing easterly winds nearer the Equator in both hemispheres. The sometimes destructive cyclones and anticyclones are mere ripples in this larger flow.

Even in quiet wind conditions there is usually a breeze, often stimulated by local conditions, such a large lake or sea. All that is required for a breeze is a small differential in temperature, with local heating expanding the air or local cooling causing it to contract.

The sea will absorb heat from the sun more slowly than the land, and the air over the land is therefore warmer and becomes less dense. Consequently a breeze develops flowing from the sea to the land. The reverse occurs at night, when the land cools more quickly than the sea. Such conditions are however very local and are often unnoticeable and overridden by cyclonic and anticyclonic wind conditions.

Within a large weather system, such as a cyclonic system, local conditions may affect the wind directions and strength. Often the wind direction and strength varies widely locally, giving rise to conditions that are described as “blustery”. While such conditions may be good for drying laundry, they making sailing a difficult pastime. Sailing races can be won or lost depending on whether or not the sailors catch the good air or fall into a pocket of stale air.

The strength of the wind obviously varies tremendously. At the one end of the scale a breeze may cause a flag to limply stir, while at the other end of the scale, a really large storm may uproot trees and destroy houses. In some parts of the world tornadoes may form when weather conditions are right and may sweep destructively over the land, ripping apart anything that stands in their way.

There is energy in the wind, and efforts are being made to economically harvest this energy to reduce our reliance on fossil fuels. Such fuels are not infinite, and we will sometime or other run out of them. It may be that we have enough fossil fuels to last centuries, but getting at them involves the disruption of mining, and as they are used up, mining will become even more disruptive than it is now. Mining even small amounts will become very expensive.

It makes sense to develop machines to harvest wind power, and the signs are that this is becoming economically more competitive. At one time, before petrol engines became common, the only ways to power transport were wind and steam, and it may be that petrol and other fossil fuelled engines may only have a relatively short time span of usefulness, maybe only a century or so.

We also use fossil fuels for our plastics. Almost everything in our modern world has a large proportion of plastics in it, sourced almost entirely from oil. It remains to be seen if we could replace our need for fossil resources from renewable resources.

Hay fever suffers may curse the wind as it blows pollen up their noses and into their respiratory systems, but many plants rely on the wind to propagate themselves. A case in point is the myrtle rust I mentioned at the start of this post. Plant pollen can travel thousands of kilometres and fall all I know can circle the Earth. It’s an efficient way of spreading the reproductive material, but its a really inefficient way of getting the reproductive material to a member of the species of the opposite gender.

Obviously it works best where the plants are grouped together, and it works even better if the plants are hermaphrodites, but it does work (occasionally) when the plants are far apart. This mechanism for reproduction probably arose a long time ago before plants invaded the land. plants growing in the sea, and many animals too, just broadcast their gametes into the sea and trust in at least some of them finding other gametes so that they can grow into mature individuals. (Caution: It’s complicated!)

We often hear the sound of wind. It can be caused by wind blowing through trees or other plants. It can be caused by wind blowing through gaps in our houses, mainly doors and windows. We build our houses to protect us from the wind and other aspects of the weather, as a sort of synthetic cave, I guess.

We can even make music (well, musical sounds) using the wind. Many people have “wind chimes” which are metallic objects strung on wires arranged so that the wind can bash them together, making a chiming noise. Some people like them, and others dislike them (I fall into the second camp).

Strings can be placed on a sounding board and used to produce musical sounds, and such “Aeolian Harps” were once as common as wind chimes. An accidental Aeolian harp can be heard in the sound that power and telephone lines make when a strong wind blows.

Time for this post about wind to wind down now, if you will excuse the pun.

A Sum of All the Parts

Cover of the Book Conscious Robots (Photo credit: Wikipedia)

Consciousness is fascinating and I keep coming back to it. It is personally verifiable in that a person knows that he or she is conscious, but it is difficult if not impossible to tell if a person is conscious from the outside.

When you talk to someone, you and that person exchange words. You say something, and they respond. Their response is to what you say, and it appears to show that the person is a conscious being.



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It’s not as easy as that, however, because it is conceivable that the person is a zombie (in the philosophical sense) and his or her responses are merely programmed reactions based on your words. In other words he or she is not a conscious being.

It seems to me that the best counter to this suggestion is that I am a conscious being and I am no different in all discernible ways from others. It is unreasonable to suggest I am the only conscious being anywhere and that all others are zombies.



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Of course this leaves open the suggestion that some people may be philosophical zombies, but that then raises the question of what the difference is, and how can one detect it. William of Occam would probably wield his razor and conclude that, if one can’t tell, one might as well assume that there are no zombies, as assuming that there are zombies adds a (probably) unnecessary assumption to the simple theory that all humans are conscious beings.

It follows that consciousness is probably an emergent phenomenon related to the complexity and functioning of the brain. It also follows that lower animals, such as dogs, cats and apes are also probably conscious entities, though maybe to a lesser extent that we are.

The only way we can directly study consciousness is by introspection, which is more than a bit dubious as it is consciousness studying itself. We can indirectly study consciousness by studying others who we assume to be conscious, maybe when they have been rendered unconscious by anaesthetics and are “coming round” from them.

In addition, consciousness can be indirectly studied using mind altering drugs or meditation. However we are mainly dependant on verbal reports from those studied this way, and such reports are, naturally, subjective.

Chemical Structure of LSD (Lysergic acid dieth... — Chemical Structure of LSD (Lysergic acid diethylamide) (Photo credit: Wikipedia)

When we introspect, we are looking inwards, consciously studying our own consciousness. There are therefore limits on what we can find out, as the question arises “How much about itself can a system find out?”

A system that studies itself is limited. It can find out some things, but not all. It’s like a subroutine in a bigger program, in that it knows what to do with inputs and it creates appropriate output for those inputs. Its sphere of influence is limited to those processes written into it, and there is no way for it to know anything about the program that calls it.

A subroutine of a larger program uses the lexical, syntactical and logical rules that apply to the program as a whole, though it may have its own rules too. It shares the concept of strings, number, and other objects with the whole program, but it can add its own rules too.

The Universe is like the subroutine in many ways. The subroutine has inputs and outputs and processes the one into the other. In this Universe we are born and we die. In between we spend our lives.



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An aware or conscious subroutine would know that it processes input and creates outputs, but it would have no idea why. We know that we are born, we live and we die. Apart from that we have no idea why.

This sort of implies that while we may use introspection to investigate some aspects of consciousness we will always fall short of understanding it completely. We may be able to approach an understanding asymptotically however – we might get to understand consciousness to the 90% level, so it would not be a total waste of time to study it.

Consciousness seems to be more than a single state, and the states seem to merge and divert without any actions on our part. For instance, when I am driving there is a part of me that is driving the car and a part of me that is route planning, and maybe a part of me that is musing on the shopping that I intend to do.

The part of me that is driving is definitely aware of what is happening around me. I don’t consciously make the decision to slow down when other traffic gets in the way, but the part of me that is driving does so.

Similarly the part that is route finding is also semi-autonomous – I don’t have to have a map constantly in my mind, and don’t consciously make a decision to turn right, but the navigator part of my consciousness handle that by itself.

Those parts of my mind are definitely conscious of the areas in which they are functioning, because if they were not conscious, they would not be able to do their job alone and would frequently need to move to the front of my consciousness disrupting my musing about my shopping.

It’s like part of my consciousness are carved off and allowed to perform their functions autonomously. However if an emergency should arise, then these parts are quickly jolted back into one.

The parts of my mind are definitely conscious as, at a low level, I am aware of them. I’m aware of the fact that I’m following that blue car, and I’m aware that I have to turn left in 200m or so. I’m also aware of my shopping plans, while I’m aware of the music on the radio.

Deutsch: Servicemenü des Blaupunkt Bremen MP74... — Deutsch: Servicemenü des Blaupunkt Bremen MP74 (Aktivierung: Gerät mit gedrückter “Programm1”- und “Menü”-Taste einschalten). Aktuelle Frequenz: 89,70 MHz (France Musique, Sender Luttange (Metz), PI-Code F203); aktuelle Suchlauffrequenz: 96,80 MHz (bigFM Saarland, Sender Friedrichsthal/Hoferkopf, PI-Code 10B2) (Photo credit: Wikipedia)

While it sounds scary that I’m not totally concentrated on my driving, I believe that this sort of has to happen. If I was totally concentrated on my driving, I would need to stop at every intersection so that I could decide which way to turn.

I would need have my shopping list completely sorted out, to the point of knowing which stores I am going to before even getting the car, and I would have to plan my route precisely. This would not allow for those occasions when passing by something or some shop reminds you that you need something that is not on your shopping list.

This splitting of consciousness allows us to perform efficiently. The only downside is that splitting things too much can result in us becoming distracted. And that is the reason we shouldn’t fiddle with the radio or use cellphones when driving.

Heaven and Hell



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What if there is an afterlife? Personally I don’t believe in one, but still. What would it be like? The Christian version is that you get judged on your behaviour in this life then go to either heaven or hell. Some versions of Christianity require that you are at the very least baptised, or that you experience being “saved” or that you have taken part in certain rituals before your worldly behaviour is considered.

These lead to awkward questions about, for instance, babies who die before they have a chance to be baptised or whatever. Will they be condemned for ever? I hardly seems fair and various versions of Christianity have ways of getting around this issue. Some suggest that such babies go to a third type of afterlife where they experience neither heaven nor hell – a sort of post life waiting room, which to me seems to be a particularly cruel version of hell!

What is heaven like, though? It must be a pleasant place, as it is a given that it is a reward for a good life, and it has been suggested that it is a place where, the Deity, God, is glorified and worshipped, where all is light, and all the “souls” there experience the joy of being in the presence of the Deity.

Since no one who has died has reported back, the sources for these ideas come from speculation presented as fact, or, as some claim, divine inspiration, an actual message from the Deity. There’s a world of difference between these two options. In other words, it’s either a complete fiction, or absolute fact.

What could we logically deduce, given, for the sake of argument, the existence of an afterlife? It could be that we are reborn in this world, as either a new human or an animal. However, no human can remember any previous existence on this earth, or even on a planet circling a star somewhere across the Universe.



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Of course some people claim to remember previous lives, but strangely, these remembered lives are frequently people who were famous when they were alive, like Anne Boleyn or Shakespeare, and the people who claim to be such reincarnated people often get well documented details of their lives wrong. Of course, history may be wrong, completely wrong, but it is more likely that people who claim to remember previous lives are mistaken or even purposefully deceitful.

If we dismiss the idea of reincarnation, what then? Certainly we can throw away all we know of physics. The only thing that we can be sure of is that things will be different. It may well be that there would be something analogous to our usual physics in play but we have no way of knowing what that would be.

English: Stylized light cone based on the logo for the World Year of Physics 2005. (Photo credit: Wikipedia)

It may be that personality as such would not exist. No meeting with a previously expired spouse in the afterlife would occur, as the personality of the spouse would not exist, and nor would the personality of the recently expired person.

If personalities of the dead did exist in the afterlife, then this could cause issues. What if the recently expired person had remarried after a spouse had previously died. Which of the two spouses would be matched up with the recently expired person? Maybe the physics would be similar to our current physics, but different enough that one person could spend eternity with two or more people?



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I get the impression that there are many more versions or varieties of hell postulated than there are heavens. Visions of hell are often detailed and gruesome. One only needs to look at the right most panel of “The_Garden_of_Earthly_Delights” by Hieronymous Bosch” to see some extreme examples.

Hell is punishment for transgressions in this world. Punishment extends “for all time” which would seem harsh as, surely any sin would be expiated eventually, just as any punishment with the exception of capital punishment in this world is time limited. However this assumes that time in this world is the same as time in the next world, and this may not be so.

Eternity may pass in a different way in the next world – maybe how eternity feels to the sufferer may depend on the seriousness of the transgressions. That may be fairer than for a minor transgressor to suffer through an endless time, judged by the standards of this world.

In accounts of heaven and hell both have inhabitants who have never (so far as I understand it) ever been mortal or human. Angels inhabit heaven and devils and demons live in hell. In both realms the job of the inhabitants appears to be to provide direction for the souls or entities from this world. Angels presumably assist in providing the dead souls with their appropriate rewards and devils and demons punish the transgressors.



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Over the centuries people have imagined or vouchsafed a vision of heaven and hell. It seems that both heaven and hell have a hierarchy of inhabitants. The hierarchies are power hierarchies with the Deity at the top of the one, and the anti-Deity at the top of the other one. This is either a reflection of the prejudices of the person who is imagining these realms, or an interesting structural characteristic or heaven and hell.

Naturally hell is nasty and heaven is nice. I don’t know if it is some cultural bias as a result of my background and upbringing, but it seems to me that the stories and legends of hell are much more detailed than the stories and legends of heaven. My thought is that people are more interested in the gruesomeness of hell than the niceness of heaven.

Certainly the Wikipedia articles on heaven and hell support this theory, as the section on the Christian hell is much longer than the corresponding article on the Christian heaven. The Christian heaven merely has “many mansions“, while the Christian hell is more complex. In fiction especially as exemplified by Milton’s Paradise Lost, and in myth as in Egyptian beliefs hell can be envisaged as complex hierarchies.

But basically, we have no way of knowing for sure if heaven and hell are real and separate realms from our standard world. There can be no physical contact between such realms and our own, since physics describes only the behaviour of things within a single realm and it has no purview outside of that.

We can’t know for sure, so while we may think that they exist and believe in heaven and hell, we should look for our ethics only in this world. Any other course is illogical.

The Space Between the Stars

Space is big. The Voyager spacecraft (Voyager I and II) were launched in 1977 and are, forty years later, only just entering interstellar space. Though the exact point at which space becomes “interstellar” is debatable.

The Voyagers will take 40,000 years or so to reach one of the stars in the “local” group. That’s about one fifth of the time that humans have existed as a separate species. Or 400 times as long as the length of time that a human is able to live. If a generation is around 20 years long, that is about 2,000 generations. It is a long, long time, and we may well be extinct as a species by then, for one reason or another.

The “local group” of stars is an arbitrary group of stars which are (relatively) close to the Sun. I’m unsure whether they really constitute a group of bodies bound by gravity or whether they are close to the sun by chance. Of course if any of the stars in the local group are bound by gravity, then the stars would form a binary or multiple star system.

Of course, our star and all the others in the local group are part of our galaxy, the Milky Way. Specifically we are part of one of the arms of the Milky Way, which is a spiral galaxy. All stars in the Milky Way are bound by gravity, with the possible exception of stars which are merely passing through the Milky Way at this time.

Just like stars, galaxies seem to form groups, which then form super-groups and so on. All these structures are several orders of magnitude larger than the prior smaller ones, are more complex and contain more matter.

The majority of space however is just space. The gaps between the bits of matter, stars, systems, galaxies, groups and so on contain almost nothing, or a seething sea of virtual particles depending on how you look at it.

The “almost nothing” consists of a very small number of particles (usually hydrogen atoms or nuclei, protons) in a cubic metre. For comparison the best vacuum that can be created on Earth may contain several million atoms in that volume. This of the same order of magnitude as molecular clouds as observed by astronomers. Molecular clouds are among the densest clouds observed in space.

The stars, planets, asteroids and similar bodies comprise only a very small part of the Universe and the average density of the Universe is much the same as the density of empty space. In other words, the Voyagers are heading into areas where the conditions are more typical of the Universe than those around our star.

Voyager 1 is currently within the heliosheath ... — Voyager 1 is currently within the heliosheath and approaching interstellar space. (Photo credit: Wikipedia)

I mentioned virtual particles earlier. While virtual particles show up as short-lived particles that briefly come into existence in some particle interactions, the virtual particles that I refer to come into existence in a vacuum as pairs and almost immediately mutually annihilate. Though they do not interact with other matter, they do have an effect which can be measured.

Mathematicians have a different concept of space. In mathematics space is a (usually) three dimensional construct that serves merely to separate and give structure to such things as points, lines, planes, volumes and shapes. Point A is distinguished from point B by the distance between them and also the orientation of a line joining them.



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In a simple case every point has (usually) three coordinates which define its position relative to some fixed point or origin and fixed coordinate system. The coordinate system can be any system that locates the point.

For instance, you can describe the point A’s position as “Face along a given axis, rise up until you are level with point A. The distance moved up is one coordinate. Rotate left through an angle until a line parallel to the plane you rose up from passes from you through the point A. The angle you turned through is the second coordinate. The third coordinate is the distance along the line from you to the point.

I’ve described a cylindrical coordinate system, but the coordinate system may be any system that gives three unique (in that system) coordinates for point A. A common system is the Cartesian system of three mutual perpendicular axes. Another is the spherical system, defined by two angles and a distance.

Of course, such systems can be generalised to more dimensions or fewer, depending on the needs of the mathematician. Most people can understand simple two dimensional graphs which are usually drawn using a two dimensional Cartesian coordinate system.

Of course scientists use mathematical models for various purposes. For instance the scientist may wish to know the probability of one hydrogen atom in the interstellar space meeting another such molecule. Since we have only about one such atom in every cubic metre, the probability is going to be small, but, of course, we can assume as lone a time period as we wish.

Gravity has to be figured in, to be sure, but a long time will be required for such atoms to collide. If the atoms are by chance moving slowly relative to each other, they may stick together and form the basis of a particle of matter. Such a clump might attract other atoms and before long (well actually after literally an astronomical length of time) a star will form.

It must have happened otherwise we would not be here. We are the result of matter aggregating and then exploding. All the atoms in our bodies that are not hydrogen were made in the centres of stars. The stars have to have exploded to allow these atoms to end up in our bodies.

A long time has passed since the birth of the Universe. In that time matter has crept together hydrogen atom by hydrogen atom until great collections of atoms have compressed in the centre to the point where nuclear reactions have occurred. Hydrogen fused to helium, then to heavier elements all the way up to Uranium.

Ball-and-stick model of the haem a molecule as... — Ball-and-stick model of the haem a molecule as found in the crystal structure of bovine heart cytochrome c oxidase. Histidine residues coordinating the iron atom are coloured pink to distinguish them from haem a. Colour code: Carbon, C: grey-black Hydrogen, H: white Nitrogen, N: blue Oxygen, O: red Iron, Fe: blue-grey Structure by X-ray crystallography from PDB 1OCR, Science (1998) 280, 1723-1729. Image generated in Accelrys DS Visualizer. (Photo credit: Wikipedia)

At which point the stars have exploded throwing all the elements out into the Universe. These elements then crept together again to produce new stars like our sun and gaseous and rocky planets orbiting them. Prior to this there were no rocky planets and no life. We live in the Universe Mark II.

Let’s be Rational – Realer Numbers

Leopold Kronecker said “God made the integers, all else is the work of man”. (“Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk”). However man was supposedly made by God, so the distinction is logically irrelevant.

I don’t know whether or not he was serious about the integers, but there is something about them that seems to be fundamental, while rational numbers (fractions) and real numbers (measurement numbers) seem to be derivative.

English: Note: The irrational and rational num... — English: Note: The irrational and rational numbers make the set of real numbers. (Photo credit: Wikipedia)

That may be due to the way that we are taught maths in school. First we are taught to count, then we are taught to subtract, then we are taught to multiply. All this uses integers only, and in most of it we use only the positive integers, the natural numbers.

Then we are taught division, and so we break out of the world of integers and into the much wider world of the rational numbers. We have our attention drawn to one of the important aspects of rational numbers, and that is our ability to express them as decimal fractional numbers, so 3/4 becomes 0.75, and 11/9 becomes 1.2222…

The jump from there to the real numbers is obvious, but I don’t recall this jump being emphasised. It barely (from my memories of decades ago) was hardly mentioned. We were introduced to such numbers as the square root of 2 or pi and ever the exponential number e, but I don’t recall any particular mention that these were irrational numbers and with the rational numbers comprised the real numbers.

Why do I not remember being taught about the real numbers? Maybe it was taught but I don’t remember. Maybe it isn’t taught because most people would not get it. There are large numbers of rational accountants, but not many real mathematicians. (Pun intended).

In any case I don’t believe that it was taught as a big thing, and a big thing it is, mathematically and philosophically. It the divide between the discrete, the things which can be counted, and the continuous, things which can’t be counted but are measured.

The way the divide is usually presented is that the rational numbers (the fractions and the integers) plus the irrational numbers make up the real numbers. Another way to put it, as in the Wikipedia article on real numbers, is that “real numbers can be thought of as points on an infinitely long line called the number line or real line”.

Collatz map fractal in a neighbourhood of the ... — Collatz map fractal in a neighbourhood of the real line (Photo credit: Wikipedia)

Another way to think of it is to consider numbers as labels. When we count we label discrete things with the integers, which also do for the rational numbers. However, to label the points on a line, which is continuous, we need something more, hence the real numbers.

Real numbers contain the transcendental numbers, such as pi and e. These numbers are not algebraic numbers, which are solutions of algebraic equations, so are defined by exclusion from the real numbers. Within the transcendental numbers pi and e and a quite large numbers of other numbers have been shown to be transcendental by construction or argument. I sometimes wonder if there are real numbers which are transcendental, but not algebraic or constructible.

A rather sexy image of Pi from the german wiki... — A rather sexy image of Pi from the german wikipedia. (Photo credit: Wikipedia)

The sort of thing that I am talking about is mentioned in the article on definable real numbers. It seems that the answer is probably, yes, there are real numbers that are not constructible or computable.

Of course, we could list all the constructible real numbers, mapped to the real numbers between 0 and 1. Then we could construct a number which has a different first digit to the first number, a different second digit to the second number and so on, in a similar manner to Cantor’s diagonal proof, and we would end up with a number that is constructed from the constructible real numbers but which is different to all of them.

I’m not sure that the argument holds water but there seems to be a paradox here – the number is not the same as any constructible number, but we just constructed it! This reminds of the “proof” that there are no boring numbers.

So, are numbers, real or rational, just labels that we apply to things and things that we, or mankind as Kronecker says, have invented? Are all the proofs of theorems just inventions of our minds? Well, they are that, but they are much more. They are descriptions of the world as we see it.

Whether or not we invented them, numbers are very good descriptions of the things that we see. The integers describe things which are identifiably separate from other things. Of course, some things are not always obviously separate from other things, but once we have decided that they are separate things we can count them. Is that a separate peak on the mountain, or is it merely a spur, for example.

Other things can be measured. Weights, distances, times, even the intensity of earthquakes can be measured. For that we of course use rational numbers, while conceding that the measurement is an approximation to a real number.

A theorem represents something that we have found out about numbers. That there is no biggest prime number, for example. Or that the ratio of the circumference to the diameter is pi, and is the same for all circles.

We certainly didn’t invent these facts – no one decided that there should be no limit to the primes, or that the ratio of the circumference to the diameter of a circle is pi. We discovered these facts. We also discovered the Mandlebrot Set and fractals, the billionth digit of pi, the bifurcation diagram, and many other mathematical esoteric facts.

It’s like when we say that the sky is blue. To a scientist, the colour of sunlight refracted and filtered by the atmosphere, peaks at the blue wavelength. The scientist uses maths to describe and define the blueness of the sky, and the description doesn’t make the sky any the less blue.

The mathematician uses his tools to analyse the shape of the world. He tries to extract as much of the physical from his description, but when he uses pi it doesn’t make the world any the less round as a result. Mathematics is a description of the world and how it works at the most fundamental level.

English: Adobe photoshop artwork illustrating ... — English: Adobe photoshop artwork illustrating a complex number in mathematics. (Photo credit: Wikipedia)

[I’m aware that I have posted stuff on much the same topic as last time. I will endeavour to address something different next week].

Rational versus real

(My last post was very late because I had taken part in a 10km walk on the Sunday and spent the week recovering.)

There’s a fundamental dichotomy at the heart of our Universe which I believe throws some light on why we see it the way we do. It’s the dichotomy between the discrete and the continuous.

A rock is single distinct thing, but if you look closely, it appears to be made of a smooth continuous material. We know of course that it is not really continuous but is constructed of a mesh of atoms each of which is so small that we cannot distinguish them individually, and which are connected to each other with strong chemical and physical bods.

An early, outdated representation of an atom, ... — An early, outdated representation of an atom, with nucleus and electrons described as well-localized particles on well-localized orbits. (Photo credit: Wikipedia)

If we restrict ourselves to the usual chemical and physical processes we can determine to a large extent determine what the atoms are which comprise the rock, and we can make a fair stab at how they are connected and in what proportions.

We can explain its colour and its weight, strength, and maybe its magnetic properties, even its value to us. (“It’s just a rock!” or “It’s a gold nugget!”) We have a grab bag of atoms and their properties, which come together to form the rock.

English: Gold :: Locality: Alaska, USA (Locali... — English: Gold :: Locality: Alaska, USA (Locality at mindat.org) :: A hefty 63.8-gram gold nugget, shaped like a pancake. Very beautiful and classic locality nugget. 4.5 x 3 x 0.6 cm Deutsch: Gold :: Fundort: Alaska, Vereinigte Staaten (Fundort bei mindat.org) (Photo credit: Wikipedia)

The first view of atoms was that they were indivisible chunks with various geometric shapes. This view quickly gave way to a picture of atoms as being small balls, like very tiny billiard balls. Then the idea of the billiard balls was replaced by the concept of the atom as a very tiny solid nucleus surrounded by a cloud of even tinier electrons.

Of course the nucleus turned out not to be solid, but to be composed of neutrons and protons, and even they have been shown to be made up of smaller particles. Is this the end of the story? Are these smaller particles fundamental, or are they made up of even smaller particles and so on, “ad infinitum”?

It appears that in Quantum Physics that we have at least reached a plateau, if not the bottom of this series of even smaller things. As we descend from the classical rock, through the smaller but still classical atoms, to the very, very small “fundamental” particles, things start to get blurry.

The electron, probably the hardest particle that we know of, in the sense that it is not known to be made up of smaller particles, behaves some of the time as if it was a wave, and sometimes appear more particle like. The double slit experiment shows this facet of its properties.

Diagram of the double-slit experiment (Photo credit: Wikipedia)

The electron is not unique in this respect, and in fact the original experiments were performed with photons, and scientists have performed the experiment even with small molecules, showing that everything has some wave aspects, though the effect can be very small, and is for all normal purposes unnoticeable.

A wave as we normally see it is an apparently continuous thing. As we watch waves rolling in to the beach we don’t generally consider it to consist of a bunch of atoms moving up and down in a loosely connected way that we call “liquid”. We see a wave as distributed over a breadth of ocean and changing in a fairly regular way over time.

At the quantum level particles are similarly seen to be distributed over space and not located at a particular point. An electron has wave like properties and it has particle like properties. Interestingly the sea wave also has particle like properties which can be calculated. Both the sea wave and the electron behave like bundles of energy.

You can’t really say that a wave is at this point or that point. A water may be at both, albeit with different values of height. If the wave is measured at a number of locations, then by extension it has a height in between locations. This is true even if there is no molecule of water at that point. The height is in fact the likely height of a molecule if it were to be found at that location.

By analogy, and by the double slit experiment, it appears that the smallest of particles that we know about have wave properties and these wave properties smear out the location of the particle. It appears that fundamental particles are not particularly localised.

It appears from the above that at the quantum level we move from the discrete view of particles as being individual little “atoms” to a view where the particle is a continuous wave. It points to physics being fundamentally continuous and not discrete.

There’s a mathematical argument that argues against this however. Some things seem to be countable. We have two feet and four limbs. We have a certain discrete number of electrons around the nucleus of an atom. We also have a certain number of quarks making up a hadron particle.

Other things don’t appear to be countable, such as the positions a thrown stone can traverse. Such things are measured in terms of real numbers, though any value assigned to the stone at a particular instance in time is only an approximation and is in fact a rational number only.

At first sight it would appear that all we need to do is measure more accurately, but all that does is move the measurement (a rational number) closer to the actual value (a real number). The rational gets closer and closer to the real, but never reaches it. We can keep increasing the accuracy of our measurement, but that just gives us a better approximation.

It can be seen that the set of rational numbers (or the natural numbers, equivalently) maps to an infinite subset of the real numbers. It is usually stated that the set of real numbers contains the rational numbers. I feel that they should be kept apart though as they refer to different domains of numbers – rational numbers are in the domain of the discrete, while the real numbers are in the domain of the continuous.

Numbers are fascinating

Numbers fascinate me. What the heck are they? They seem to have an intimate relationship with the “real world”, but are they part of it? If I heave a rock at you, I heave a physical object at you. If I heave two rocks at you, I heave real objects at you. It’s a different physical experience for you, though.

If I heave a third rock at you, again, it’s a different qualitative experience. It’s also a different qualitative experience from having one rock or two rocks thrown at you.

Numbers come in three “shapes”. There are cardinal numbers, which answer questions like “How many rocks did I throw at you?” There are ordinal numbers, which answer questions like “Which rock hit you on the shoulder?” Finally there are nominal numbers, which merely label things and answer questions like “What’s you phone number?”

As another example, in the recent 10km walk which I took part in, I came sixth (ordinal) in my age division. That sounds good until I admit that there were only seven (cardinal) entrants in that division. Incidentally, my bib number was 20179 (nominal).



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Cardinal numbers include the natural numbers, the integers and the rational numbers and the real numbers (as well as more esoteric numbers). For instance the cardinal real number π is the answer to the question “How many times would the diameter fit around the circumference of a circle?”

It’s a bit more difficult to relate ordinal numbers with real numbers, but the real numbers can definitely be ordered – in other words a real number ‘x’ is either bigger than another real number ‘y’, or vice versa or they are equal. However, there are, loosely speaking, more real numbers than ordinals, so any relationship between ordinal numbers and real numbers must be a relationship between the ordinal numbers and a subset of the real numbers.

English: Example image of rendering of ordinal... — English: Example image of rendering of ordinal indicator º Italiano: Immagine esemplificativa della resa grafica dell’indicatore ordinale º (Photo credit: Wikipedia)

Subsets of the real numbers can have ordinal numbers associated with them in a simple way. If we have a function which generates real numbers from a parameter, and if we feed the function with a series of other numbers, then the series of other numbers is ordered by the way that we feed them to the function, and the resulting set of real numbers is also ordered.

So, we might have a random number generator from which we extract a number and feed it to the function. That becomes the first real number. Then we extract another number from the generator, feed it to the function and that becomes the second real number, and so on.

The random map generator provides a limitless ... — The random map generator provides a limitless supply of colourful terrains of various themes. Open island maps, like this one, allow players to use airstrikes. Cavern maps have an indestructible roof which cannot be passed. (Photo credit: Wikipedia)

What we end up doing is associating a series of integer ordinal numbers with the generated series of real numbers. These ordinal numbers are associated with the ordered set of real numbers that we create, but the real numbers don’t have to be ordered in terms of their size.

Nominal numbers such as my bib number are merely labels. They may be generated in an ordered way, though, as in the case of my bib number. If I had registered a split second earlier or later I would have received a different number. However, once allocated they only serve to show that I have registered, and they also show which event I registered for.



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On the occasion that I took part there were two other events scheduled : a 6.5km walk and a half marathon. My bib number indicated to the marshals and officials which event I was taking in and which way to direct me to go.

I’m not a mathematician, but it seems to me that ordinal numbers are more closely aligned to the natural numbers, the positive integers, than to any other set of numbers. You don’t think of someone coming 37 and a half position in a race. Indeed if two people come in at the same time they are conventionally given the same position in the race and the next position is not given.

There’s a fundamental difference between natural numbers or the integers, or for that matter the rational numbers and the real numbers. The real numbers are not countable : they can’t be mapped to the natural numbers or the integers. The rational numbers can, so can be considered countable. (Once again, I’m simplifying radically!)

Natural numbers and integers are related to discrete objects and other things. The number of dollars and cents in your bank account is a discrete amount, in spite of the fact that it is used as real number in the bank’s calculations of interest on your balance. If I toss two rocks at you that is a discrete amount.

English: Causal loop diagram (CLD) example: Ba... — English: Causal loop diagram (CLD) example: Bank balance and Earned interest, reinforced loop. Diagram created by contributor, with software TRUE (Temporal Reasoning Universal Elaboration) True-World (Photo credit: Wikipedia)

Even I tip a bucket of water over you, I douse you in a discrete number of water molecules (plus an uncertain number of other molecules, depending on how dirty the water is). However the distance that I have to throw the water is not a discrete number of metres. It’s 1.72142… metres, a real number.

At the level at which we normally measure distances distances don’t appear to be broken down into tiny bits. To cover a distance one first has to cover half the distance. To cover half the distance one must first cover one quarter of the distance. It is evident that this halving process can be continued indefinitely, although the times involved are also halved at each step.



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This seems a little odd to me. Numbers are at the basis of things, and while numbers are not all that there is, as some Greek philosophers held, they are important, and, I think, show the shape of the Universe. If the Universe did not have real numbers, for example, then it would be unchanging or perhaps motion would be a discrete process, like movements on a chess board.

If the Universe did not have any integers, the concept of individual objects would not be possible, since if you could point at an object you would have effectively counted “one”. In other words we need the natural numbers so that we can identify objects and distinguish one from one another, and we need the real numbers so that we can ensure that the objects don’t all exists at the same spot and are, in fact separated from one another.

Visualisation of the (countable) field of alge... — Visualisation of the (countable) field of algebraic numbers in the complex plane. Colours indicate degree of the polynomial the number is a root of (red = linear, i.e. the rationals, green = quadratic, blue = cubic, yellow = quartic…). Points becomes smaller as the integer polynomial coefficients become larger. View shows integers 0,1 and 2 at bottom right, +i near top. (Photo credit: Wikipedia)

The Search for the Fundamental

Motion of gas molecules Español: Animación mos... — Motion of gas molecules Español: Animación mostrando la agitación térmica de un gas. Cinco partículas han sido coloreadas de rojo para facilitar el seguimiento de sus movimientos. Русский: Хаотическое тепловое движение на плоскости частиц газа таких как атомы и молекулы (Photo credit: Wikipedia)

When does it stop? This screen that I am looking at, the keyboard that I am typing on, the invisible air between my eyes and the screen, even my body, all are composed of atoms, I told and believe. Apart from atoms, all there is is radiation, of various sorts.

The ancient Greek philosophers didn’t know about atoms so proposed various theories, which today seem quaint, but eventually they came around to atomism, and abandoned the other theories. In particular the theory of the four classical elements, earth, fire, water and air was dropped.

As I said, the theory now sounds quaint, but, given that the ancient Greek philosophers were not of an experimental frame of mind, the four classical elements could explain much of what could be observed. Everything could have been a mixture of these elements in various proportions.

After all, it appeared to work for colours – all colours that can be displayed on a computer screen can be specified in terms of the amount of the three primary colours of red, green and blue that a single pixel or dot on the screen emits. Why shouldn’t this scheme work for other things than light?

However Greek philosophers (and of course, philosophers in other cultures) noticed that, while some things could be broken down into component parts – sugar could be melted and burned, water could be driven off to leave the salts behind, and more importantly alcohol could be evaporated off and collected to make spirits, some things could not be broken down.

Gold, sulphur and phosphorus stubbornly refused to separate into earth, air, water or fire. Of course such stubbornness could be explained by the classical element theory – after all some things are easier to break down than others, but the Greeks eventually dropped the theory in favour of atomism. (This and what follows is highly simplified and condensed).

(Click here for rotating model) (Photo credit: Wikipedia)

This is the belief that everything is made up of small indivisible particles which differ from element to element. The lump of gold contains billions of gold atoms, while the sulphur block contains sulphur atoms.

From about the start of the scientific revolution, people started to work out the rules of chemistry, and the ‘why’ of chemical reactions. Why did carbon in coal burn away and leave an ash? We know that the carbon in the coal burns using the oxygen in the air and creates oxides of carbon which are gasses and not easily detectable, but the experiments which led to this knowledge were preformed in the era of the scientific revolution.



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So, matter is composed of atoms. That seemed to be the end of the story, as the vast majority of chemical experiments could be explained in terms of atoms, but exactly why atom A reacts in fixed proportions with atom B, but won’t have a bar of atom C. These relationships were noted but not really explained.

By the middle of the 19th century scientists began to detect problems with the “atoms as billiard balls” model. Electrons were discovered and soon related to chemistry, answering the above question. The new model, “atoms as small planetary-like systems”, had a small positively charged, and solid nucleus surrounded by a swarm of negatively charged electrons, with the electrons taking a major role in determining the chemistry of the atom.



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It was discovered that many elements behaved as if each atoms of the element weighed the same, but some elements broke this rule. The gas Chlorine for example has an atomic weight of 35.45. In other words each atom weighed about 35 and half times as much as a Hydrogen atom.

It was eventually discovered that not all Chlorine atoms weighed the same. Most had an atomic weight of 35 but some (about half) had a weight of 36. To cut a long story short it was discovered that the supposedly solid nucleus was composed of a collection of other particles called protons and neutrons.

While the number of protons and electrons determine the chemistry of an atom almost completely, the number of neutrons contribute mass to the atom and barely affect the chemistry.

While electrons appear to be truly fundamental particles and cannot be broken down further, the protons and neutrons are composed of particles called quarks. For reasons mentioned in the Wikipedia article quarks cannot be found in isolation, but are only found in other particles.

In addition to protons and neutrons, quarks make up other sub-atomic particles such as mesons. Scientists have discovered or postulated bosons which are particles that bind quarks and other fundamental particles together. From then on, things get complicated!

I haven’t mentioned the photon, which is bosonic, or the neutrino which is a fermion. All fundamental particles fit into one of these two families, and all sub-atomic interactions are the result of the rather incestuous exchange of these particles in their various groups and a strict set of rules. So far so good.

English: Enrico Fermi (Photo credit: Wikipedia)

However, there are still questions to be answered. Are these particles truly fundamental or do they have components, which may or may not be particles in the classical sense? What are the sizes of these particles, if such a concept is appropriate at this level? Have we found them all? What about dark matter?

Scientists have abandoned the first question. They don’t generally refer to particles as fundamental. They have seen a long list of fundamental particles turn out to be not so fundamental after all.



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Sizes of the particles may not make sense at the particle level, but the various theories may indicate sizes for some of them. There are difficulties over the size of the electron for instance. If it were a point object rather than having something that equates to size, then that causes difficulties with some theories.

As for the third and fourth questions, it appears that scientists may have found all the particles that explain ordinary matter, but naturally cautious, they don’t rule out other forms of matter such as the so called “dark matter” and “dark energy“. Dark matter and dark energy apparently interact with gravity and (from the Wikipedia article) and the Weak Nuclear Interaction.

My original question was “When does it stop?” By this I meant, which particles are truly fundamental and which have components that determine their properties? This question remains open, but if you have followed through my exposition, you will probably see that this is a question without an easy answer.



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