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Materialism claims that the entire reality comes up from matter. Unfortunately, some facts do not belong to matter. It means that Materialism is wrong.

Moreover, the external reality can only be a mathematical thing. It means that matter does not exist anymore.

By the end, we shall explore the thinking system that constitutes our universe.



We shall place ourselves in the best situation for the materialist theory: A mineral world without any living creature and any consciousness.

Science includes laws of nature such as the law of gravitation. Do these laws just exist in our mind or do they exist by themselves in the external reality? Of course, the laws are not a product of our mind. We do not invent them. We discover them and there is an underlying order in the nature (1). In fact, materialists just do not like the word “law” because it implies a lawgiver and a God. Therefore, we shall not use that word. We shall focus our analysis on some scientific laws based on constant ratios between varying quantities, such as most of the chemical laws (2). Thus, we shall demonstrate the existence of immaterial constant ratios. Consequently, and according to its own premise, Materialism is wrong.

A constant ratio means that a phenomenon C advents when a quantity A mixes with a quantity B according to the same proportion. For example, in the next drawing, some quantities of A and of B are in relations. The yellow squares indicate the combinations that give a new phenomenon C.


As you can see, according to situations O, P, R, and S, the relation does not bring any results. On the contrary, situations Q and T give a new phenomenon C. It means that C is the result of a constant ratio such as 2A/1B = 4A/2B.

The cause of C is neither in A alone nor in B. It is not in the contact of any undefined quantities of A or B. The cause would be in A and B if each of them had the virtue of being able to count themselves and then to meet in the exact required proportion! As it is obviously not the case, it means that the cause is not in the matter by itself. The cause is a constant ratio that is to say a proportion.

Well! You may object that things are just as they are. Proportion is just a word and some juxtapositions of determined quantities of matter produce some determined effects. Let us suppose that we agree with that and just examine the consequences: we suppose two quantities of water (crossed circle) and one quantity of energy (heat: White circle). The juxtaposition of these determined quantities of water and energy produce an effect and the water is converted into steam ( Yellow Square). Now let us suppose that we have four quantities of water and two quantities of energy ( White Square) and look at the next drawing.

There is again a juxtaposition of determined quantities of matters. However, if we keep the preceding explanation, it is clear that the juxtaposed quantities are not equal. It is therefore impossible that we get in the second case the same effect that in the previous! In fact, we know that the effect is the same due to the constant ratio between the quantities! This example shows that a constant ratio cannot be considered as the simple juxtaposition of measurable quantities of matter.

Neither a matter nor juxtaposition can produce the same effect as a constant ratio. It means that a constant ratio is not material. Since we have agreed that the ratios existed independently of our mind, it becomes obvious that the external world contains some immaterial entities. Of course, the materialists may invent many arguments about the origins of constant ratios (3) but it should be out of the subject. Our single question was: does a constant ratio is material or immaterial. Clearly, it is immaterial. So, we can conclude:

-Materialists say that everything is made up of matter.

-We have found immaterial ratios.

-Consequently, Materialism is wrong.



At first glance, the existence of immaterial relations does not eliminate matter because ratios link elements. More largely, the scientific laws are the instructions by which all matter operates. The laws are information (4). Indeed, they could be compared to the software transmitting instructions to the material hardware. However, may we admit that matter and immaterial relations interact themselves? It should be a return to the illogical dualist problem (5) and the only solution is to agree that the external reality is by itself immaterial.

Until recently, such an idea was not obvious. Today, it becomes acceptable thanks to progress in physics: for contemporary scientists, the ultimate particles express interactions between quantum fields that are themselves immaterial. For example, in the previous lesson, we have seen that any object is a number of elementary particles and a pattern of relations between the particles of the collection. Moreover, number and relations, and not the stuff, create the properties that distinguish the different objects. Consequently, the concept of material elements has no more significations. Deprived of their properties, elements look like geometrical points

As a result, many scientists posit that the external reality can only be a mathematical thing. The Nobelist physic Wiener Heisenberg said that the ultimate reality could be made up of numbers (6). Recently, Max Tegmark, a cosmologist at the Massachusetts Institute of Technology has speculated that mathematics does not describe the universe: it is the universe. Dr. Tegmark wrote in New Scientist that we are part of a mathematical structure. Everything in our world is purely mathematical, including you!

What does it mean? Just consider the numbers like some sets of units organized in space. As you can see, each number is like a domino. Since we reason on these specific numbers, each distinct set of units requires a specific network of relations. According to this fact, any number is not only a quantity of units. It is also a network of relations between the units.


These networks of relations bring a configuration of the units and give to each number a specific property. Plato used to represent these distinct properties by some figures such as point, line, triangle or square. Since each number offers a specific property, it is fruitless to add or to substrate. It should just be like adding tomatoes and potatoes! It means that these numbers are very different of our ordinary numbers and we should have better to do not use anymore the word "number". In order to avoid confusion, we shall call "form" these sets of units closely related to relations and properties. A form is a network of units with the different relations between its units and the properties that result of them .

Clearly, this definition is the same as for the objects that science describes. . Therefore, these mathematic forms could really correspond to the reality of the mineral world. They could also represent the reality of the living world. For example, your own body is just like the other objects. Of course, it is far more complex than the simple atoms of the mineral world. However, this complexity does not result of the stuff of "matter" but depends only on the complexity of the relations. Consequently, we may posit that your body is also a mathematical form implying billion of separate units linked by billion of relations. It includes many elementary forms such as the mineral forms (for example the calcium and the salt). What is more, this complex form is constantly in relation with some simple other forms (For example the oxygen you breathe).

Clearly, the external reality (and consequently our own body) could be made up of mathematical forms (7).Nevertheless, a mathematical form is an idea. On the other hand, an idea only exists in a thought. Since these mathematical forms are independent of our human mind, it means that they must exist in a universal mind.



Materialism posits that there is a material universe composed with objects. We contend that there is a thinking universe composed with mathematical forms . We must underline that we do not add any mysterious new hypothesis. We do not have to invent a God or a supernatural spirit. We just posit that the entire universe is a thinking system. What is it?

31-Thinking rules

The nature of a thinking system may be deduced of the properties of the mathematical forms that we have studied in the previous chapter!

Firstly, the forms cannot enter in calculations such as addition. However, we can conceive a synthetic relation : Two forms are combined and give a new form that brings new properties in accordance with the properties of the two previous forms. In the case of a complex form, you can imagine an analytical relation: The complex form is divided into several forms. The properties of the complex form are lost but the properties of the several simple forms can be nevertheless deduced from the previous. As a result, the thinking system is always connecting billions of forms . Indeed, the forms appear and disappear but any dissociation of a complex form must stop to its final units, which are used to build up new forms.

Secondly, the thinking system does not associate the forms at random. Let us us compare the forms with the letters of an alphabet. The letters must be disposed in order to form words expressing a meaning. Therefore, at each creation of a single form, the thinking system constitutes a partial meaning. Moreover, it must keep its meaning in all the sentences where it would enter. Now, replace the letters by the mathematical forms: The word with its constant meaning must be replaced by constant ratios giving the same constant results. It means that the constant ratio created at the beginning must be kept to guide the further creations. Moreover, in accordance with the constant ratios, the thinking system never associates some forms and on the other hand, it constantly associates some others. Clearly, this process explains the laws observed in the nature.

Thirdly, as we have seen and due to the conception of numbers like set of points, any form is by itself a configuration and a network of relations that are the causes of its properties in the thought. Their logical place must obey to an order in relation with the association or dissociation whom they come from. It does not mean that the forms have a shape or occupy an extended space. It just means that they are not confused and that they represent an order of coexistence. .

Obviously, all these rules look like those described by the chemical and physic schoolbooks.

32-Procession of forms

Of course, a thought always follow an order. At the beginning, there is the simplest mathematical form: the idea of the Unity, which is the cause of all the numbers and relations (8). Then the thinking system duplicates some simple numbers and thinks the other forms through association or dissociation. By the end, it goes toward the complex forms of living creatures.

As the series of forms is by itself a thought, their number is necessarily finite, because a thought with an infinite object would remain uncompleted and meaningless. Just imagine a sentence with an infinite number of words: It should be a non-sense. Since the quantity of forms is limited, our present universe, despite its innumerable galaxies, is finite.

Since the quantity of forms is finite, the thinking system ends its course once it has thought all the possible forms according to a logical trajectory. As it cannot stop thinking, it comes back to the starting point. Then, it begins a new course. Each course corresponds to a cycle. When one cycle is over, another begins. Consequently, the present sentient universe will finish. Then, another universe will begin and so on. On the contrary, the thinking universe is eternal since the number of cycles is infinite (9).

All the cycles have the same beginning because the logical choices are limited among few simple forms . However, when the complex forms are reached, many possible forms are available. As a result, the course can differ from one cycle to another. If a human could visualize several cycles at the same time, he would observe the same geological history of the universe (since it corresponds to the simple forms). On the other hand, he would distinguish different evolutions of animals and plants depending on the cycle (since complex forms offer a great diversity).

This process is fully compatible with the story of the universe as Science describes it. On the contrary, materialism is unable to explain the cause of universe. Moreover, its theory of evolution looks like a fairy tale with many miraculous events. In fact, we bring a basic change because evolution follows a goal.

33-The alien observer

Let us imagine an alien observer who could introduce himself into the thinking system to observe what is happening into it. At the lower level of the forms, he will see the single units and he will call them ultimate particles or space-time like points. Visioning the first associations of these units in simple numbers, he will call them quarks, leptons, gluons and finally atoms through their higher associations. Regarding the complex forms, he will depict them like molecules and through the same process, he will reach the most complex networks corresponding to the cells of the living creatures.

All the forms are associated or dissociated by the thought and the cause of this animation is in the thinking process . Our observer who ignores the thinking process will deduce energy and motion of that animation. Finally, in calculating the position and the movements of the units, he will forecast the future state of any form. In contemplating the mathematical forms, our observer thinks, represents and deduces exactly like the scientist who attempts to perceive the ultimate reality of the universe.



A thinking universe does not disturb the scientific habits. It does not need any new hypothesis. The thought just replaces the matter. This theory brings more answers than the materialism. As a result, the existence of matter becomes a useless hypothesis!

Now, we have to come back to the daily life. We shall see that our theory does not change anything to your daily perception of the reality.



1- Do the laws just exist in our mind? Do they exist in the external reality? Considering a mineral world deprived of any living creature and consciousness, the first question seems to be a non-sense. If the laws were a product of our mind, it should mean that no laws existed before the apparition of the man. Therefore, we would imagine that in the early earth, the mercury was changing sometimes in water and sometimes in carbon! Nevertheless, Relativists claim that we choose some facts and that we establish arbitrarily some laws. For example, the drawing 1 shows many various shapes.

Among these shapes, we can choose a serial of circles, of squares, of large or small figures, of yellow figures and so on. If we choose the circles, we could say that there is the "circle law"! Moreover, another individual could choose the squares and establish the "square law". What is the truth? The square or the circle law? With Protagoras, relativists answer that the two laws are equally true. It means that truth is always relative to each observer according to the choices he has made. In fact, we choose a serial of facts in order to get a result. Some of them do not bring any results: for example, to offer gifts to an idol to get health. Other provide with regular results: To take drugs in order to cure.

Most scholars admit effective connections in nature but they deny that they obey to a law. In short, they say that experiment provides with data concerning regularities and no more. This position appears false because a regularity of effective connections is never self-sufficient. For example, look at the drawing 2: The first serial shows regularity because each circle gives Y.

Now look at the second serial:

-Your initial observation based on regularities (each singular circle gives Y) is false because it appears that several circles also give Y.

-The assert that every quantity of circles gives Y is also false.

-The truth is that every odd number of circles gives Y

In the first case, the regularity was self-sufficient: Why did every single circle bring Y? The answer was simple: It is in the nature of a circle to bring Y. The necessity to bring Y is in the circle itself. In the second case, you cannot just describe regularity: Why does every odd number of circles bring Y? The answer is no more obvious because none circle and not any quantities of circles contain by itself the concept of odd number. To explain it, you have to discover a law. As this law is not a product of your mind, it must be engraved in the reality.

In conclusion, we can say that the laws are not a product or an interpretation of our mind. We do not invent these laws. We discover them. Indeed, there is an underlying order in the nature that corresponds to necessary laws.

2- For example, Joseph Proust's law and Dalton's law

3- Materialists frequently argue that the relation cannot be separated from matter and treated separately. For example, the ratio between O and H would be inherent to the molecule of water. This statement is not clear. Firstly, the relation is not the result of the properties of the material stuff that are linked. In fact, as we have seen in the previous lesson, properties are the result of numbers and relations. Secondly, imagine that the relation is a material entity distinct from the terms that it links. If A and B are in proportion and if this ratio is itself a material element, such as C , there would have to be two new ratios between C an A on one hand, and between C and B on the other hand. This leads to an infinite regression that illustrates the impossibility of assigning a material consistency to any ratio whatsoever. Thirdly, let us suppose that this molecule had existed at the beginning of the world; there would be an inherent relation. However, science shows that electrons, quarks and atoms preceded molecules in the history of universe. These ratios which seem innate actually come from other ratios further and further back in time as we go back to the big bang. However, at that moment, only photons existed, which in turn transformed themselves into the electrons and quarks that make up atoms and molecules. Therefore, in the beginning, there was only one unique indefinite, homogeneous substance made up of identical photons. It is evident that they did not have some "inherent" ratios. Materialists object that some combinations appearing by chance in time do not disappear because they are compatible with earlier combinations. It is then explained that a logical necessity formed with constant ratios seems to replace mere chance as this series advance. It supposes that there is at the beginning one stable combination that could give the support to the next stage. However, how could any stable combination emerge from the myriad of identical elements? New materialists answer that the earlier stable combination just comes from the main parameters of the Universe. Well, once again we are facing an infinite regression because the first parameters are by themselves some ratios between fundamental constants of nature. None of these materialist arguments sounds right

Moreover, a ratio has none of the attributes of matter. For example, the ratio that explains the boiling point of water in the recipient of the pharaohs is the same that we observe today. The proportional combinations of A an B can be distinct in space or separated by intervals of time without changing their unique and constant ratio. Unlike material objects, ratios are ubiquitous and permanent. These properties are incompatible with the notion of materiality.

4- The cover story of the a recent Scientific American said that "Ask anybody what the physical world is made of, and you are likely to be told "matter and energy."
Yet if we have learned anything from engineering, biology and physics, information is just as crucial an ingredient. The robot at the automobile factory is supplied with metal and plastic but can make nothing useful without copious instructions telling it which part to weld to what and so on. A ribosome in a cell in your body is supplied with amino acid building blocks and is powered by energy released by the conversion of ATP to ADP, but it can synthesize no proteins without the information brought to it from the DNA in the cell's nucleus. Likewise, a century of developments in physics has taught us that information is a crucial player in physical systems and processes. Indeed, a current trend, initiated by John A. Wheeler of Princeton University, is to regard the physical world as made of information, with energy and matter as incidentals."

5- Since the early origins of philosophy, any dualistic position confronts itself to a logical hurdle. A spirit cannot be in connection with an extended matter. This spirit is supposed to be our mind or our soul while the external world is supposed to be made up of matter. The dualists cannot overcome the mind body relation because it is impossible to explain how your free will could move your body. Consequently, the dualists are obliged to refer to God who realizes the constant relation between mind and body. Descartes, Leibniz, Malebranche, and some other philosophers have spent much time in trying to construct some ingenious concepts such as "Occasionalism" and "Pre established harmony". Anyway, all these explanations rely heavily on a supernatural cause and are outside the scientific knowledge. Of course, the materialists are very happy with the dualists: They play with them just like a cat with mice’s! It is easy to critic dualism and by contrast to promote Materialism. With scientific Idealism, there is quite another business!

6- The theory of numbers comes up from the Greeks. The first attempt was the Pythagorean analysis. Pythagoras said that all things were formed with numbers. Unfortunately, his doctrine was unclear about the real substance of these numbers: grains of matter or ideas in the thought? Indeed, if the units are material, the doctrine is in short the idea that bodies are made up of grains that can be counted. Objects are not numbers any more but groups of points and the doctrine looks like a prelude to that of Democritus. What is more, it was not possible with such numbers to explain the qualitative differentiation of bodies observed in nature. For example, let’ us suppose that a horse corresponds to the number 3 and a man to the number 6: According to this theory, each man would be equal to two horses! In fact, we have not any texts from Pythagoras and his doctrine is known to us through the books of his disciples Archytas and Philoaos and the writings of Aristotle. Go to:

Plato taught that the universal spirit was made up of eternal divine forms, which were the causes of the sensible world. The problem of understanding how an individual object was a copy of its form worried Plato for his entire life.Go to: . By the end, he was deeply inspired by Pythagoras and he thought that these divine forms could be some mathematical forms. Plato said that these numbers instead to be material were ideas in God consciousness. It was a dramatic progress compared to the earlier Pythagorean's: These numbers were by themselves ideas and so objects of a thought: Of course, not our own thought but some universal thought (Go to: Click on encyclopedia, then on "friends of wisdom" and finally on Proclus. You will find here the famous Proclus's commentary of the Timaeus of Plato)

Once again, the hurdle was to define ideal numbers qualitatively different one from another in order to launch a bridge toward the material properties of the particles of matter. Plato used to represent these distinct relations by some figures such as point, line, triangle or square. This representation was a useful milestone on the road. However, Plato never explained his theory in writing papers. We only know it through the testimony of Aristotle. As Aristotle was opposed to such a theory, he wrote a devastating criticism in the books M and N of his famous Metaphysic.

By this time, all the attempts to launch a bridge between numbers and matter had failed. However, this profound intuition traveled secretly through the centuries. Indeed, with the new physic, there is no more such a gap between "matter" and numbers. Among the modern philosophers, Bachelard is maybe the sole who saw the philosophical importance of this fact. In a book titled "the rational materialism», he wrote the following sentence «The material properties are the result of a composition. There are not such properties in the intimate substance of the elements". As a result, he forecasted the resurgence of a new and extended Pythagorean theory

7- I submit you another argument based on the manufacturing process and demonstrating that the external reality is mathematic.

-Let’s suppose one human facing an object. This compact object is a sensation (brown form X) in his mind and he ignores what is really the nature of the external reality A causing it.


-Now, let’ suppose that the observer applies a numeric analysis to the sensation (brown form X). For example, he tries to decompose the sensation into a multitude of elementary sensations. Once he has attained the limits of his sentient perceptions, he continues this decomposition by forming the representation of even smaller particles and then of units and numbers. It means that starting with a rough sensation; he creates a mathematical representation in his mind. This mathematical representation is the square B.

-Our observer is an engineer. From this representation B, he imagines in his mind a new combination in order to get a new product. The triangle C is the mathematical representation of this new product.

-Then, he manufactures this new product. In doing so, he is modifying the external reality A, but since he does not know it, he cannot expect a specific result. However, a new sensation appears: The triangle D (brown triangle) corresponding to the sketch C!

-Now, consider the entire drawing 2. If B was different from the external reality A, the sketch of the triangle, as a new combination of B, should only be some dream and you never could get a real triangle! It means that the success of the experiment is possible only if B is by itself the same thing as the external reality A.


-Since B is a mathematical representation, it means that the true being of the external reality A is also a mathematical form! In short, we may posit that the external reality is not made up of matter:It is by itself made up of mathematical numbers.

8 -According to an old Pythagorean tradition, several philosophers such as Plotin, Proclus and Avicenna stated that the One was the subject of the Universe.

9- The cyclical theory is as old as the humanity. Nietzsche adopted it but he thought that all the cycles were identical due to an absolute determinism. Funnily, Engel, the Marxist philosopher, shared this belief and he wrote that the human brain would reappear in the series of cycles.


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