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Last updated: Jan, 2021

Infinities Do Not Exist?

The illusion of infinity confirms that if we knew our limitations and where we were, we would be unable to proceed, says psychologist and author A R Graham.

Time's Paradigm: PART THREE – Infinity

Incomprehensible contrivances that stretch the imagination to extremes of large and small: Infinities. Yes, to some degree they are unreal, being of no breadth because they are unable to reach a conclusion. But by the same token, such vagueness offers us freedom from borders, boundaries, ceilings, endings and much more. With infinities there are no limits... or so the illusion begs us to believe.

A meme captioned: Because we cannot relate our exact whereabouts to an infinite horizon we are presented with the illusion of progress.

To put it bluntly, we create infinities, they do not exist. They are born out of the consequence of having to take measurements in order to make sense of our lives. As the last chapter explained, points impede progress; nothing can move towards, through or away from such identified markers. Numerical points we impose on space, like, minutes, kilometers or degrees would do the same damage. Only, they don't really exist; so neither do infinities.

Infinities know this. It is why they appear in the first place, then glee to reconcile with a point in time or space that shouldn't really be there.

Because everything is connected, there should be no distinction or boundary between things, so that fluid progress can keep right on going. However, if you demand that a point be established – such as on a piece of paper – then an infinite progression is created to bog everything down, heading for the end of emptiness where it meets the edge of your point.

For example, a brief list of points might look something like this: The beginning or end of time; the edge of space; the present moment; a stationary point in the universe; your back door; a car on the highway. Yup, infinity will approach them all, fractioning up the space left and recurring until the cows come home. Or it will multiply away from them, seemingly forever.

((((((((((((((( O )))))))))))))))

Existence is a strange beast. All of time exists all at once (the Block Universe model), but we can't see it all. We need to place yardsticks in the ground in order to visualize the space between things – with our minds. The present moment suddenly appears, like the release of tension when a drop of detergent hits the surface of oily water. Indeed, perception's struggles are largely due to infinities and their habit of identifying erroneous points.

Actual infinities only occur in linear time and space, in cyclical or spherical models where there are no ends and no points extrapolated within, infinities are nowhere to be seen. The reason? Because we put something out there in empty space and time for infinity to fixate on. It's called, nothing! Nada, naught, zip. Whereas, inside a solid, cyclical universe, time and space can circuit in perpetuity. (See previous chapter).

Though infinities do not exist, they are intricately involved in the illusion of progress. If we knew our limitations we would be unable to proceed.

otherwise it would all be over at once.
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Quantum physics with its Uncertainty Principle and Relativity with its inertial Frames of Reference, both propose a universe where the extrapolation of real points in time and space are not allowed, as we are all in motion. But such idealism is not just the realm of mathematical equations, it affects our senses, too, in how we perceive the passage of time (a topic Einstein and Carl Jung discussed at length together at the beginning of the 20th Century).

The present moment is conjured by our minds to separate the past from the future, creating a flow of time. Conscious creatures like humans slow down that flow to a manageable pace, otherwise it would all be over at once. Magically, we sense a passing of time in this manner, freedom in a solid state universe where in reality flow does not occur... How?

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Revised edition, 2020.
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Time's Paradigm book cover.

The Kalahari Effect

As we wander across the Kalahari salt pans, we see only the horizon in front of us. We look around and back and we are presented with the same vision. In our 360 degree panorama nothing exists, not a tree, not even a blade of grass. We stand in the middle of this flat and bleached landscape and decide, rationally, that we are a certain size; in fact, we make an assumption that we are somewhere in the middle of time and space: Some things are bigger than us and some are smaller; some things are in front of us and some behind; some things have happened and some things are going to happen.

Paradoxically, we cannot relate our position or size to anything out there in the Kalahari Desert because there is no beginning nor end in sight, so we can only use infinity to affirm that we are somewhere in the middle... of everything. Our position is undefined and incalculable, leading us to complete freedom.

Over recent centuries the Universe has been explained to us as being huge, and not just a few miles up there emblazoned with little pin holes. So too, we have been obliged to understand that infinitesimally small objects are spinning around inside atoms. Logically, we reach out in all directions from our central position, it's what we do, and unsurprisingly find ourselves in the middle of things, and we are comfortable with that notion.

Is it not peculiar that we are nowhere near close to the edge of anything in time nor space?

The macro underwater world of coral spawning focuses our attention on the definition of size.

What would be the difference between us, say, living on a planet, or living on the nucleus of an atom? None. Except that, we humans are forced to exist in an environment composed of molecules of breathable gasses, and that influenced the size to which we have evolved. But if conscious life forms did exist on the nuclei of atoms, they might likely have the same dilemma: "Are we really in the middle?"

So where exactly in the grand scheme of things are we..? Infinities on both ends comfort us, it means we are surrounded and far from the fear associated with finalities, like, the end of time, the edge of the world, doomsday asteroids, etc. We stand in the middle of our perceived whereabouts and know our place; even if we walk a few miles this way or that, we are still in the middle because reality's horizon has moved with us and seems to stretch out before us in all directions into infinity. Nothing has changed. (See the supplement here online: Crossing the Kalahari, from the author's journal).

Indeed, our position in the Kalahari Desert suddenly begins to make sense. It's because of infinities that our predicament is assured.

The ambiguity of 'knowing but not' allows us to pass effortlessly through our perceived existence, moving us consciously in both time and space, through a Block Universe where all of time already exists. Only if we really don't know where we truly are or anything about our relative nature, are we capable of movement. We take a step forwards and feel progress, even though in reality we have gone nowhere.

Meme caption: We are aware because we don't know where we are.

If we knew how far away from our horizons we were, a fixed determination would set in. Ironically, we are aware because we don't know where we are.

In the last chapter it was explained how awareness of time's flow is achieved by our brain registering sequential moments through a solid, immobile panorama of time. Here, The Kalahari Effect gives us the wherewithal to experience that paradoxical flow of time where none actually occurs. In essence: virtual reality.

Being unable to determine the extent or finality of existence in any direction gives our consciousness the unfettered ability to experience movement therein. It denies us the possibility of identifying our spacial or temporal location relative to it, if we have nowhere to measure from or to. We may know where we are locally, and be able to pin point our position, say, between one tree and another, experiencing relative motion, but that is all. We can pass these trees and move on beyond them to a river, but we are no nearer the edge of existence having moved, nor are we further away.

Existence is wrapped up in cyclical time, where there are no ends or edges. It gives us the impression of an infinite journey by containing the can of worms.

Relative movement between frames of reference is a key theme in Special Relativity; if there is no stationary reference point in the universe, then we can never knowingly be at rest, we are all in constant motion. Likewise, a finite edge of existence, a wall beyond which nothing exists, would provide a relative point of reference to determine a finite, stationary point within. It appears the universe does not provide fixed points of any sort, otherwise we would all grind to a halt – another good reason to suggest space-time is a non linear platform.

Infinities do not Exist
The Kalahari Effect
Flat-Earth and Edge of the Universe
The Uncertainty Principle
Circular Speedometers vs Flat Clocks
Zeno's Paradox Solved

Download here THE ABSTRACT in .pdf Format

Different Types Of Infinities

The standard model for any active progression that does not go on forever, is a cycle. It then appears to go on forever, it satisfies the conundrum, while justifying the laws it exhibits. Water flows down river, it reaches the ocean where it evaporates and clouds then return the water in the form of rain to the mountains.

Victoria Falls, Zimbabwe

Our planet Earth is not flat, but it used to be considered as such, and even today appears to be from the surface. If we can accept that the Earth is round and so has no end to its surface dimension, then it is no great leap of faith to assume that existence, itself – The Universe, if that is the extent of it – has also a cyclical nature, thus presenting the illusion of infinite progression.

(PS. A world full of forevers, infinities and linear progressions would render a Flat Earth inevitable!)

Let's suppose that we are approaching a brick wall. When we get to it, we are not in the middle of it, but on one side. The wall has thickness, and if we make a hole in it we can reach the other side. We could scale it and stand on top of the wall, and again we can see the other side, we can reach beyond it.

A conceptual barrier between existence and the edge of the universe creates an impossible Flat World scenario.

However, there is figuratively speaking a fine, middle line in the wall, being the actual separation between one side and the other. If this wall were the end – say, the edge of the universe and there was nothing beyond it – our side of the wall might exist, but the other side of the wall would not. What we have is an odd circumstance: a wall with only thickness on one side. Absurd!

We can whittle this paradox down to atomic particles if we wish. We can say that the end of a worm's nose is the end of the worm and the beginning of earth in front of it, but we would be wrong to suggest there was a finite point at which one began and one ended. The interaction between atomic particles of one and the other are indeterminate, complex and uncertain at any given moment; there is no finite line between them. The worm is the earth and the earth is the worm. If it were not so, then there would be some finite separation between them and the worm would not be going anywhere.

Everything is connected. Infinities do not exist, we just want them to.

Space can be assumed in this way without too much fuss. But what about the expansive platform we call time? Is it also constrained by the same principle? After all, Space-Time is one and the same thing. If there are no walls and infinity stretches out in all dimensions in either time or space we are free, we are not shackled, we can progress. This is the illusion provided by infinity, and it is devilishly so!

Big or small, long or short? The subtleties of perception through time and space are numerous, common-place and, more often than not, illusory.

When we are young we perceive time to crawl along from one year to the next; our teenage life seems to drag on forever. But when we get into our 50s, suddenly five years goes by in a flash. Five years, when we are ten years old, is fifty per cent of our entire existence; but only ten per cent of our life experience at age 50. It's just a matter of time.

There is no end to small; the smallest small cannot be defined. Is the smallest small a tiny quantum particle whizzing in and out of existence in the blink of an eye? Could there not be things much smaller than that, that live for less time? Why not? Infinity says there must be, otherwise, like the aforementioned wall, those tiny quantum particles would not exist.

Is the biggest big the edge of our universe? How come there is nothing beyond? Surely there is no edge of The Universe and it is infinitely large – or cyclical.

Fractal images show repeated structures scaling up and down, with no mathematical evidence to suggest there is an end to big or small. And we, somewhere in the middle of this vast illusion called existence, can therefore be forgiven for categorising our state, at will. The Kalahari Effect.

Everything you ever wanted to know... About Time!

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The Uncertainty Principle

Physics is full of infinities. In the 1960s, Wheeler and DeWitt finally came up with an equation which did away with the baffling infinities that kept on popping up when trying to unify Relativity with Quantum mechanics. Infinity was tamed... a bit. But, unfortunately this ugly beast has been perpetuated in myth for so long we can't seem to rid ourselves of it.

Infinities breed like rabbits; where do they come from? Infinities lead to and away from physical points. Without points there would be no infinities. We are, we believe, in an identified location in both time and space and for this reason it is we that are unwittingly creating infinities – that aren't actually there.

On the one hand, infinite extension of existence without boundaries does allow us to maneuver somewhere in the middle of our perceived whereabouts because our position cannot be determined relative to any edges, but then there is the curse of infinities that do lead to so called 'determined' points in our midst crashing our prospects of progress.

We can name these two brothers:

infinite increments, as fractions head away from us
infinite decrements where fractions head toward us

The problem with the first one is that of stretching out the unknown into a ludicrous prospect of forever, and the problem with the second is trying to stuff never ending bits into a finite space. The first, mathematicians recognised as useful and tamed by formulaic manipulation, the second they found disastrous but as yet have failed miserably to tame.

These two infinities are demonic twins; so if we live in a world with one the other will surely be lurking nearby.

We cannot pin-point where we are, as quantum physics has explained perfectly: "Either the position of an object or its velocity can be determined, but not both at the same time." The Uncertainty Principle. So, if we are moving, our position is not certain. And, as all things in the Universe are always moving, no position can be known.

If a point is defined in space 'infinite decrements' will get to work and terminate existence – it's that horrendous. A single, defined point is as influential and deadly as a defined edge of existence. It's Game Over.

We can experience motion but we don't know the truth of it, because there is no fixed point that does not move that we can point at and say: "That is not moving, so I know what I'm doing!" Moreover, as just explained, if there were such a stationary point in the Universe, then up would pop infinity and we would all screech to a halt.

Illustration of a city landscape and the impossibility of motion.

Fluid progress is only possible under never ending conditions. Cyclical models of progression provide such a scenario, where no points along the way are isolated and so identifiable as individual entities. This resolves Zeno's Paradox of motion (see below). If all considered points are unrealistic, then flow is possible. Otherwise, 11.59 would never become midnight.

A simple, cyclical measuring device, like a clock or compass, has no ends and, therefore, all points around it are uncertain. If we don't know exactly where we are on it, we can pass through it from one moment or angle to the next. They accomplish this by offering infinite progression in a controlled environment. Cyclical processes thus ensure continuity and immeasurable flow; whereas, linear models with finite ends impede progress.

Even just one end would do the trick. The Big Bang, if considered the beginning of time and space, would be a serious impediment to progress. Quantum Correctional Theories for General Relativity also point to the 'singularity' before a Big Bang, and are asking if there really was a beginning of existence – in other words, time.

A road with one end leads nowhere.

Linear Models Of Space-Time

A linear model having defined ends means that any point along its length can be precisely extrapolated – leading to the impossibility of motion therein.

... Unless it is conceived, as it has been by mathematicians, that the two ends of such a linear model are not relative to anything in between. In this rather dubious model, progress throughout is perceived to exist while the two ends are understandably unattainable. Et voila!

In physics, velocities are described on a linear scale, like a speedometer, from zero to the speed of light. At the beginning of the last century, in order to explain certain cosmological conundrums, light speed was established as being invariant, the other end was deemed irrelevant. Light was then seen to travel at a constant speed regardless of any observer's inertial frame of reference, and the conundrum was resolved – the luminiferous ether could be put to bed.

What do we have? Velocity measured on a flat, plastic ruler from zero to the speed of light... laying on a table that apparently does not exist. And what if there were a formula that took into consideration the fact that a ruler could be bent? I guess we'll find out one day when NASA finally gets around to building a spaceship capable of relativistic speeds.

We could in fact describe time's passage in the same way by cutting the circumference of a clock at midnight and stretching it out like a flat ruler on a table. We would then, in order to progress from one minute to the next, have to conclude that neither end of the day was relative. Movement throughout the day would seem to flow smoothly, but as we approached the evening things would get decidedly tense as midnight would seem forever to regress and tomorrow would never arrive. However, for creatures such as mayflies that only live for a few hours... no problem.

On the flip side... Imagine what would happen if we took velocity's linear ruler and bent it around so that zero and the speed of light were one and the same place... like an acceleration clock? That is what Chapter 6. Travel is all about.

Linear models of progression with defined ends cannot support passage between designations along the way because the mere fact that a point has been established provides infinity with potential. Cyclical models can. Because infinities are only created by our consciousness, not by reality.

While it is perfectly understandable that mathematicians need points to establish fact and express our understanding of spatial awareness in any reasonable fashion, such reference should only extend so far. Points have no width, no substance, they are for all intents and purposes, invented non-entities. (See the author's supplementary article Prime Numbers Busted for more infinite conundrums). Mathematicians realised early on that points on a linear scale of velocity would render their models useless, so they invented calculus -– avoiding another pothole rather than filling it in.

The assumption we have that acceleration is a linear progression is analogous with our ancient belief that the World was flat. It is clearly not. It curves around on its self as does time and, also, space. A linear model with invariant ends is merely a pseudo-cyclical phenomenon that works well up until the moment when somebody calls its bluff.

Brighton Pier, England. Lights at night from a seaside town reflect of the water.

The Curiosities of Light

A top speed, at which no mass can travel and beyond which is out of bounds. Light travels at the same speed, regardless of any observers' motion or the platform from which the light was beamed, says Special Relativity. Unlike us mortals, all floating about without a clue. By keeping every point or reference frame moving, none can be identified as true points. Thus, progress is deemed possible and we are aware of it.

However, this is only because variable speeds of motion are measured on a linear scale, and invariant light speed is regarded as being at the end. If time and distance are cyclical, then acceleration must also be. In which case, there would be no ends of relative significance on a cyclical speedometer, lightspeed and nospeed being the same. Added to which, no identifiable points within the cycle to impede progress.

Photons of light are not without paradoxes; for one thing, we are told they do not accelerate.

They depart their launch platforms at full speed, 300,000 km per second (c). If we just measure the distance a pulse of light takes to pass between two mid points on its journey –- which is the classical experiment –- then, we don't know how much time it took to accelerate from its point of departure (which is of no great concern to physics). Never mind, that's the way light behaves, and it works.

We must therefore assume: Because we cannot add vectors of speed (such as a moving platform) to the speed of a photon of light -– otherwise it could be travelling faster than (c) –- a photon's point of departure, such as the bulb in a flash-light, must be static.

Zero velocity has just become invariant, also.

Indeed, any body in the universe that reflects or produces light must be observed in this manner –- an invariant platform that appears to be at rest.

It may be acceptable to a tiny quantum particle, in as much as suggesting that it is quite likely to be at rest and moving at the same time (that cat cat emoji again, and a superposition of states). But this is a macro scenario we are discussing, concerning tangible items like flash-lights, and filaments in a bulb. If we accept that we cannot have ends or beginnings, starts and stops, finalities and edges, otherwise things cease to move, both ends of a speeding photon of light are the same.

Consider: light has no need for time; clocks stop at such speeds. So, if we accept that there are two ends to motion, zero velocity and the speed of light, neither being affiliated with time or space, we can thus propose that these two designations are equals -– and a cycle is created.

Our current formulas cannot take such transitions into account because we are not looking beyond the speed of light or, for that matter, zero velocity. In the wider sense, our cycle of motion can not have points verifying zero or light speed, anywhere in the cycle they are both equally valid, and a constant energy value of zero is, therefore, established throughout.

The energy, required to create a photon of light, was in motion before impact. The photon then came into contact with an object in its path and energy was again given off. The fact that we only consider the passage of a beam of light in linear models, rather than what was going on before and after, is paramount to this paper's postulate: Universal Contraction.

Conscious consideration of progress is due to the illusion of an infinite horizon, being as how there are no finite points in time or space. Here's what happens when you put a finite point in your way.

TIME'S PARADIGM, the ebook
now available free to view
or download from this site
Revised edition, 2020.
for desktops, Kindles, readers.

Time's Paradigm book cover.

Solving Zeno's Paradox of Motion.

A slow moving terrapin pushing through tall grass.

They say, "You can never reach the door, because you have to go half way first, then half of what's left, then half of that, and so on.., ad-infinitum." That was the conundrum Achilles would have been faced with when trying to catch up with the tortoise, philosopher Zeno amusingly proposed.

... And the infinity of decrements rears its ugly head.

First of all, the tortoise is moving, so there is no fixed point toward which infinity can approach. If that weren't the case Achilles could not catch up with the tortoise because he would not be able even to depart from his own rest point, as all identified points have an infinity paradox leading towards and away from them.

Back to the door. Infinity in this case is between you and it. Under the constraints of perception, you consider yourself at a point in time and space. This is a fallacy, as explained by the worm above. Moreover, you make the assumption that there are an infinite number of halves of halves between you and reaching the door, none of which actually exist as true identities.

Some mathematicians refute this. To resolve Zeno's paradox of motion they have formulated a convergent trick with infinities, stating that an infinite number of reductions towards a whole number, actually adds up to that whole number. So, a half plus a quarter plus an eighth and so on, adds up to one – and so you reach the door.

Hmm... [sounds of hammer bashing square pegs into round holes]. On the other hand, what if you could call those halves of halves and bits and pieces something else?

Consider a table on the other side of the door. A point half way to your door immediately has more than one possible identity because it can instead be called one third of the way to the table. Well, does it really exist? I see an apple, but actually it could be an orange. It may remind you somewhat of the argument quantum theorists had with that cat! While they say particles may have all their states on offer in time, we might also say that points have all their identities on offer in space.

Now you can proceed to the table, presumably passing through the door on your way out.

Quantum physics repeatedly offers solutions to the bizarre nature of time, existence and progress, while routine physics is constrained and limiting due to stubborn practicalities. Achilles catches up with and passes the tortoise because there is existence beyond the tortoise... Just as infinity runs up to the tortoise, discovers it to be a non-entity and runs right on by, heading for the horizon.

A brown hare running in the English countryside.

Crucially, an end is finite, and if the door were the end of everything then motion would cease. Space only exists between things, so neither would space continue.

If the table were not there beyond the door then the door – like that wall – would only be half a door. Having a table on the other side of the door provides distance with a dilemma – it must go on. You can now reach the door because all those halfway points have been re-classified. Equally, if a point you wish to reach does not actually exist then it does not impede your progress.

By considering the elimination of definable points the 'key' to progress, a cyclical function for time is the process by which the door is unlocked. No longer are we limited by ends, as in a linear model of progress. A cyclical progression, by nature, has no points with certain identities, and thus infinity is fooled.

Infinity is not just an unfathomable distance, it is also the scourge of individuality. Infinity gives us the pretense of motion, while denying it. Continuity and the lack of individual points allows motion. Infinities are created by mathematicians in their desire to utilize points to describe our life; points that do not in fact, exist; points which demand something as ridiculous as infinity exist, because those points are, themselves, unreal.

If points did exist then theoreticians would have every right to say you could never reach the door. Reason dictates otherwise.

Mathematicians are not unaware of the horror they have created in infinities. The likes of Leibniz, Newton and others realised many centuries ago that movement was impractical if individual points existed. So they created another horror to vanquish the demon: Calculus! In part, this monster is defined as: the summation of infinitesimal differences.

In order to make sense of a body progressing through a distance it would clearly be impossible to accurately determine things like acceleration by dividing the distance up into tiny points and saying that from one point to the next it was going at 'this' velocity, and to the next point it was going at 'another' velocity. There would be no continuous flow. So, to eliminate this bumpy road, mathematicians devised an alternative strategy; they conceived: time divided by itself – or seconds per second – to dispense with all those points.

It worked. Infinities were avoided and progress was possible. Time's Paradigm arrives at the same conclusion by the use of logical deduction rather than mathematics.

Setting Limits on Existence.

In chapter one, Destiny, a lake in Idaho was used to illustrate the concept that there has to be something beyond "Now". In order for Achilles to progress, here we are considering that he must deny a point existence by aiming beyond it. This is relevant to many avenues of research.

An example that has been alluding scientists for a while: Reaching the temperature considered for the universe to be absolute zero (-273.15C), or zero Kelvin. Physicists have got to within thousandths of a degree, but they just can't quite reach what could equally be described as Zero Energy or, for that matter, Zero Velocity. However, in light of the discussions above on the limits of linear progression perhaps it is understandable; there must be something beyond absolute zero in order to reach it. Unfortunately, a wall was erected, beyond which nothing was set to register, and in so doing the goal was deprived them.

Never up, never in. A golf ball will not sink if it is not aimed beyond the hole.

If we approached that invisible wall we were discussing earlier denoting the edge of our Universe, with the physical laws we assume today, it seems likely we would not reach it. No amount of energy would suffice to allow us to even come close, just as Special Relativity says of bodies approaching the speed of light. Reality would cease to make sense, norms would buckle as we tried to force our way towards it. Laws and principles would fail in all aspects.

Somewhat like approaching a black hole, one might imagine. So could there be such a barrier that demands absolute finality and refuses to allow us through? Or have we simply made these barriers ourselves in an attempt to understand with laws of physics that actually restrict us?

To reach a goal we must aim beyond it. Such goals include Zero Kelvin, Light Speed and the Big Bang... And holes in the greens of golf courses.

The theory that the Big Bang was the beginning of our Universe is the best we can do at present, but it is unrealistic. Nothing begins or ends. Of course, it is such a gigantic unknown that it will take many decades and many thousands of minds to finally fathom. In so doing, many exotic particles will give up their secrets and the universe may begin to appear that much smaller to us.

It will be immensely satisfying to discover what occurred in that instant... and then find clues as to what happened before.

But that can only be achieved by looking beyond the horizon. Because nothing by itself exists. The Divas of Destiny we discussed earlier did not shoot for the stars: They aimed well beyond them.

There will in the future be no halves of halves, segments of value between moments or velocities of bodies in space. Paradoxical infinities will be abandoned by science because they do not in fact exist.

Light and infinity, two curious components of perceived existence, both dressed up to accommodate our necessary relative meanderings. Such concepts will be discussed in more depth in the following chapters. First job, in part 4. Dimensions, will be to consider the physical nature of time's progresses from the past to the future.

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For further reading, Crossing the Kalahari, from the author's journal.

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