(Was chapter 22 in Version 1)
Some will think that the previous logical considerations are of no concern for them, and that the concrete world exists, anyway, since it is material, that we can see it, that we can touch it, and even modify it. To observe, in scientific terms. To live in, in more common terms, but quite as valid and much more pleasant.
See. Your peace could end soon. Attention, in this chapter we begin with serious business. All that was before was only warming-up, preliminary development of intelligence. It is still time to close this book, what will follow is disturbing. If you read it, you will not be any more the same person after!
Good, you are warned: you accept all the upheavals which this reading will bring into your life. So we are a little further in the future, in the large international university of Zambu Shedrup Ling which I plan to found in Tibet when the ugly invaders will be thrown out. (See my science fiction novels on the «Dumria» series)
On a vast campus adorned with trees, flowery gardens and fountains, hinds run freely between lovely small cottages where the students live. A gentle pipe music and laughters emanate from a near arbour. At the end of a shaded alley, an elegant ultra modern buildings of purest Tibetan style exhibits above its entrance door the curious following panel:
We penetrate into the building, along a broad corridor with many doors. There are plenty of people and enthusiastic students of every countries, dressed with their various national costumes or religious suits, or with beautiful clothes of their invention. A smiling teacher guides us, he stops us in front of a gate:
«Please apologise, with the season of examinations, plus the great projects of the government and the orders of the UNO, it was very difficult to retain a room, and they gave us only this small one. Good, if you wish, please get in...»
Will you dare? The door opens, the teacher smiles at us and invites us kindly...
Be careful, there is a step. Ooops, and even a rather big one. It is careful to rope up.
It is that there is nothing in this laboratory. But nothing of nothing. Not a piece of furniture, not a seat, no working table, no sinks, not the smallest chemical, not the tiniest flask or boiler.
No computers with shimmering screens, no piles of large books, no mysterious cupboards, no pipes with bubbling coloured fluids, no tumble of large black cables, no impressive machines humming in the back, even not the fridge for the aperitifs.
No windows, no walls, no ceiling, no floor. No light, no darkness. No air, no vacuum, no top nor bottom, no space, no time.
No prejudices, no dogmas, no beliefs, no conventions, no opinions, no projections.
Giddiness!!! The new participants have funny faces, some are livid, one of them even flees, screaming with terror. Only a young Mongolian monk laugh cheerfully. He sings like to himself: «No eye, no nose, no ear...» and some laugh by recognising this old Buddhist pun.
And you are warned: all these materials are strongly prohibited in the examinations. In spite of the smiling and poetic ambience of the place, I tell you that peoples here do not play: the offenders are immediately excluded from the school. At Zambu Shedrup Ling the spontaneous joy and the most strict discipline are non-dual.
It is what we should expect: if we want to build a really ultimate metaphysical theory, or even a theory on physics, which claims to explain why the world exists, we should not start from something which already exists, otherwise arises immediately the question: and your thingie, there, from which you claim to explain everything, how did it appeared, at the beginning? Again a blunder like that and it is zero at the examination.
Good, we thus start from nothing. Founding nothingness, like with the i of the imaginary calculation.
We shall imagine something which does not exist. Like that, at least, nobody will ask us how it appeared at the beginning: it quite simply never appeared.
Not the schmolls, that does not look serious. Not the glops©, still worse. Not the smurfs, there is already a copyright on them. Not the broutchemolles©, it is too long (it is a word which I invented, which would fit perfectly, since it has for interesting property of not having any definition.) Not the quarks, it is too late for them, since their existence was proven. When my daughter was small, she adored the gliglis©, perhaps an hybrid of slug (limace in French) and grimace. Not the gornynx©, everyone knows that these are the odd gurglings that we hear in some musics of Jean Michel Jarre. Not the horrible stroubignolons© and racagnasses© which live in rococo furniture. Not the X nor the Y, there are already plenty of them in the labs. Hey, I find a funny one: UIOs, Unidentified Inexistent objects. The Zen koans would fit also; they exist, but they are conceived so that their very existence leads inevitably to a paradox, very interesting to dynamite all our erroneous mental structures.
Good, let us start with the nibs©, (nothing in familiar French), they do not exist, they do not have a form, nor a colour, no definition, and nobody can say what it is nor where we can find some, we can find them nowhere, and worse of all they are even not in the stock exchange. The only property which we shall recognise to them is that they are made in such a way that they will be perfect to use for our demonstration. We shall have no other basis than this founder paradox!
These nibs have the same existential statute as the i of the imaginary numbers: they do not exist, but doing as if they existed will allow us for very interesting things. In more, as they do not exist, they cannot impose us their properties, qualities or defect, and we can rid them with any arbitrary quantity of properties useful for our purposes.
I take profit of this to introduce a symbol of the nib: ¤ a circle which centre is empty (of the same colour than the background). This symbolises the non-duality between the fact that the nib appears to a suitably placed observer, while having no existence by itself. The four branches in a cross will be justified in chapter IV-5.
Happily this symbol exists, it is called «currency sign» and it is code ASCII 164 (ISO/IEC 8859-1), alt-207 on a PC keyboard, unicode U+00A4 , HTML ¤ or ¤ It is not used often, as a general place holder for any currency symbol (or in some soviet software, in place of the $ !).
(Some readers will think that this is only a game, a gratuitous joke. But we shall however see in part 4 on physics, that the nibs play a fundamental role in today physics. Simply, physicists do not see things in the same way).
No nib makes objection; thus let us continue.
Good, we shall take two of them, of nibs. Easy to transport, these things which do not exist. We shall say that these two have a relation X. No mater which relation: that they are equal, or different, that there is one larger than the other, or more dumb, as you like.
Hey, but this relation exists, on its side. The mathematicians cannot contradict me: starting from that i which does not exist, we have surprised them red-handed building a whole world of calculations which exist, and which has even very significant technical applications. Yes, i does not exist, but the equality i+i=2i exists, and it is even true. The materialists cannot contradict me: Tintin and the Professor Calculus (one of my masters, who unfortunately never understood me) do not exist, but their friendly relation exists. Yes it does. Their friendship exists, their hatred does not exist. And all the accounts of their imaginary adventures exist. This even has a concrete implication, for example the number of albums of the adventures of Tintin, which is materially observable and measurable. Not either the politicians nor the ideologists of any kind cannot contradict me, especially not them who are so clever to take us at war for their phoney dreams.
Right, of course, this relation X exists only as a relation, it does not exist materially, concretely. But this will be enough for us.
We shall say that a small group of nibs and their relations with each other are made in such a way that their descriptions form the axioms of a logical system. Perhaps it is possible to make the same reasoning with the Sets Theory, by supposing that somewhere in this theory is a group of logical statements which could be used as axioms to generate some other statements.
Logical deductions starting from the first group of nibs form a second group of it: each nib of the first group generates 2 nibs of a second group. Then according to the same process, both nibs of the second group generate three in a third group of them, then these three generate four in a fourth group, and so on. We could represent this relations of filiation according to a graphic, in a tree structure:
The founder nibs, for example the 3 in the centre, generated a second group, then a third, then a fourth... which are represented as concentric layers, as growth rings in a tree. For the figure to be understandable, each layer is represented with a curve in dotted line. That also resembles the Penrose network, but here the founding paradox is that the nibs do not exist. (There was a very beautiful statue of nib on the campus of Zambu Shedrup Ling; it was not expensive, since there was nothing on the pedestal) After a very great number of stages, millions or billions, the individual layers are indistinguishable, and, if we take the precaution of putting the successive layers the ones at the top of the others, the diagram takes the shape of a bowl, where the successive layers are parallel with the edge. With the number of layers, the bowl grows accordingly, by addition of successive layers along the edge. To show this growth, we represented in dotted line a layer to be added after a number of steps approximately 5% larger.
Here is typically a mathematical construction really obscure and devoid of any practical use, you may think. How do these nibs of nothing behaves is hardly a concern for us, we who exist, and that the diagram has the shape of a bowl, a potato or a wrench, it does not matter.
But you may perhaps wonder what are these two long arrows «space» and the short one «time», what does this mean?
It is that, if you take again the first diagram, you notice that the layers follow each other in a given order. For example the layer numbers ending with zero will proceed regularly, whereas the squares become increasingly rare. That can be compared with a «time» which passes, where events occur regularly or according to different intervals. This «flow of time» is done according to the arrow, in the drawing of the bowl. In the same way, within a given layer, the nibs have a relation of more or less vicinity, which allows to say that some are close and other are far, in the meaning for instance of two words being close or distant in the alphabetical order. That can be compared to a «distance». In the two figures, this «distance» was represented along a line, which corresponds to a «space» with one dimension (the curved line where the two large arrows are). We could as well have chosen the properties of the nibs in such a way that this «space» may be with two, even three dimensions, or any other value, but if so, I would be unable to draw the diagram, because it would be in four dimensions. So only one dimension of «space» was shown, but it is much more interesting to suppose three of them, as in our own universe, or any other number. This «space» with three dimensions already curiously resembles ours, and the bowl diagram is commonly used in cosmology: the origin point corresponds to the Big-bang, and the progressive growth in diameter with the expansion of the universe.
Let us explain to the non-mathematician reader that mathematics usually evokes such diagrams with a notion of «space», it is even an important part of algebra and structures, dealing with vectorial spaces with one, two, three dimensions or more, which geometrical properties can be completely identical to those of our usual material space, or to those of our intuitive notion of space. We even find perfect mathematical counterparts of our space-time, having exactly the same properties. There is thus nothing new in this space of nibs which we propose, except to give it the bowl shape of an universe diagram.
Until now, we only obtained a mathematical analogy of our space-time, curious but without real interest. We can however go a little further in this concept of «space» and «time», if we assume that the nibs possess properties which are transmitted from a layer to the following according to specified rules. For instance, in a layer, the majority of the nibs bear the property 0 (black dot) and some bear the property M (white dot), which is mandatorily transmitted to only one nib in the following layer. But with each new layer, the property is shifted of a constant distance, regarding the previous layer. Moreover, if another nib of the M type is in the vicinity, the reappearance place is moved in such a way that M type nibs flee each other. We are perfectly free to consider things in this way, without supposing that the whole layers pattern is subjected to a time which passes by, since causes of all what occurs in a given layer are entirely contained in the previous layer, and each layer contains the causes of all what occurs in the following layer. And remember that we are still in an immaterial axiomatic system, without any kind of relation with our space and time. Let us see what it looks like on a figure (There is only one dimension of space represented, but there can be three)
In this figure, the relation of cause and effect works from left to the right, and the idea of «space» is vertical. We see a «particle» (in top on the left) moving quickly downwards. It meets another motionless «particle» (medium on the left). The two «particles» «run up» (or more exactly they repel each other by a «force» which gets stronger when they get closer). The one of the top is stopped, and it communicated all its «speed» to the one of the bottom.
This strangely resembles the following figure, which represents the collision of two electrons in our own physical universe:
According to our laws of mechanics, this is called an elastic diffusion (collision without loss of energy nor change of the particles). A fast moving particle (high left) strikes another motionless (middle left), and transmits to it all its kinetic energy, exactly as with billiard balls hitting each other. In the case of electrons, the contact does not take place, since the energy exchange is done by the remote influence of the electric field (undulated arrow). In the diagram of nibs, the «speed» is represented by the constant shift from a layer to another of the nib M, (here by the slope), and the «electric field» by the way in which this shift is modified by the presence of another M nib close by.
It seems that we now created a far more realistic mathematical equivalent of our universe, which too appears following a «big-bang», which consists of a «space» where flows a «time». If we consider only the successive layers of nibs, our «time» was no more that a simple numbering of the layers, following their creation order. But now what occurs in a layer is the direct cause from what will occur in the following one. Each layer determines the following one. And we have particles behaving and phenomenon happening. Exactly as in physics, since all the mechanics science can be reduced to the study of the motion of particles, for which what occurs at a given moment is the direct and only cause of what happens at the following moment. We can thus legitimately speak about a «time», even if we cannot remove the quotation marks for now, because it obeys the same laws and functions in the same way than our physical time. We shall speak again of this astonishing definition of time in chapter IV-3.
And our mathematical «universe», with its «time», begins with a phase of expansion, contains «particles» which will behave the same way as our material particles. We can complicate the arbitrary properties which we gave to the nibs: it can appear several kinds of «particles», which behaviour will be that of the quarks, electrons, photons, neutrinos... of our universe, or any other set of new particles for different universes with three dimensions or more... And into there, it will also form «gases», «stars», «galaxies», «planets», and, the same causes producing the same effects, we shall also find in there an «evolution», which will also give «living beings» and even the mathematical equivalent of «scientists», who will undoubtedly have very real questions to ask us.
We can legitimately wonder how far can go the comparison between our «physical» universe, «real», «material», and this «universe» of nibs, «abstract», «imaginary», formed only of logical relations between elements, the nibs, which do not exist, but that we rigged with an arbitrary quantity of ad hoc properties.
Certainly we can easily imagine an universe of nibs reproducing exactly the physics of our material universe, its life, and even any ideal civilisation we can wish for. This is what we shall do in all the continuation: assume a perfect imitation of the physics of our material universe, to the point that a nibs physicist would be unable to tell any difference between his universe of nibs and our physical universe. We shall discuss more precisely in the fourth part on physics in which extend this is possible, and see that, not only it is possible, but that it is precisely the way it happens in our material universe!
(An important point to keep in mind all along this book is that I always refer to mainstream standard physic, not to any «alternative» physic).
Anyways, this universe of nibs certainly exists, as a logical system, in the meaning we said that logical systems exist, in the previous chapter III-3. And if we do for instance a computer simulation, we shall be able to observe the phenomena which take place into it. And if somebody else does a different computer simulation, he will still observe the same phenomena (principle 5 in chapter III-3). So we are compelled to say that this universe of nibs exists, at least as a logical building, after our primary definition of existence in chapter III-2. In more, it passes the test of existing independently of any primary cause or external object! This happens by the only virtue of the creative absurdity. So this way of creating an universe qualifies as a truly explicative metaphysical system. (We shall discuss the question of the divine creation further, in chapter xxx)
But does this nib universe exist in the meaning of our concrete daily experience of existence? Of course, we cannot see it, but what about its «inhabitants»? Are they only appearances, figures in a computer, or can they indeed experience like us consciousness and the feeling of reality? The reply of classical science is «no», and anyway it would be naive to just reply «yes» without first assessing the exact meaning of words such as «concrete» or «observable».
Well, then let us see those who use these words, and ask them what they mean with them.
Ideas, texts, drawings and realization: Richard Trigaux.
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