About the Matrix and the Process Physics of Reginald Cahill

Are we Living in The Matrix?

The Movie the Matrix states an ancient belief that we are living in a Dream World.

In the old Gnostic version the Matrix is created by the Demiurg, the Creator of our Material Universe.

In the new version the Dream World is created by a Computer Simulator.

At this moment Physicists and Mathematicians are exploring the Concept of the Matrix and are achieving remarkable results.

Process Physics

One of these scientists is Reginald Cahill. He has developed a challenging theory called Process Physics.

Measuring the Aether

One of the most important experiments in Physics was the Michelson and Morley experiment in 1887. The aim of this experiment was to discover the speed of the AEther. At that time the physicists believed space (aether) was moving. The result of the experiment was spectacular.

Michelson and Morley found that the speed of light was a constant (now called c) and the Ether (Space) was empty and static.

Cahill (and many others) analyzed the experiments and many other comparable experiments and detected a fatal error. The fatal error was a scientific “script”, the theory of Newton.

At that time Quantum Mechanics was not invented. Cahill found what they were looking for, the Absolute Motion of Space.

Relativity Theory

The result of the Michelson and Morley Experiment was used by Einstein in 1905 to create his Special Theory of Relativity.

This theory has been verified by many experiments so almost nobody started to question the theory of Einstein. Cahill proved that the absolute motion of space is not contradictory to the experiments that verified the theory of Einstein. Einstein was totally wrong!

Quauntum Space

Everything that is, is Space itself and Space is generating Space. This statement is a “self-reference” and can be formulated as an iterative function Space (i) = Function (Space (i-1)) + Randomness.

This Randomness is the result of Quantum Mechanics.

Every Self-Propelling Extension of Space has a Free Will to choose a “direction”. This “direction” can be organized as a causal system in which case Time appears. In general “space” is trying to create a Space-Time that is the most predictable to give the objects in Space-Time a chance to survive and grow.

Cahill found the “Function” and suddenly many disjoint fields of physics were united. Like every other big “paradigm shift” the theory of Cahill is officially banned.

Attacking Einstein is “not done” because when the foundation of Einstein falls the new (old) Physics falls apart

The paradigm shift of Cahill is not really a paradigm shift at all. It brings Physics back to a very ancient track that was abandoned a 100 years ago.

What is Happening

Space now called Quantum Foam is creating Space. In this process of continuous creation, every possible form is created.

Space is Relational, a connector of forms, and the connectors have a lot in common with the cells in our body. The fabric of Space is self-referential which means that the creative pattern behind every form is basically the same.

Cahill shows that the creation of space, the creation of the Stars and the Planets, the creation of the body and the cells is based on the same iterative process.

This process can be seen as the calculation of a very fast quantum computer that is creating itself. Cahill has discovered the software-design of the Matrix.

The interpretation of the output of the quantum computer is done by a conscious mind but the conscious mind is also the output of the quantum computer.

The Mind of Space

The feedback-loops in the cell-like structures of self-propelling space can be seen as a giant mind (a neural network) that is split into many (in)dependent minds. One of these minds is the mind of the Human but cells, the body, the brain, earth, our galaxy, and the universe are also mindful.

What we are able to see depends on what we are able to see. If we want to look through the lens of Special Relativity we are able to get a long way. At some point we get stuck.

Our interpretation system is desperately trying to fit our experiments with our theory. We measure what we want to see and we are able to get a long way. We develop instruments that contain our current theory and we prove the theory we want to prove.

Is there an end to our Interpretation System?

Our interpretation system fails if we don’t see a structure anymore. At that moment we think our interpretation system is seeing Chaos but Chaos is non-existent. Chaos is an interpretation of something we don’t understand.

The Limits of Chaos are just like Space extending every time we embrace a new form. Our Knowledge of our Reality expands just like the creator of forms, space, is expanding.

There is a Limit to our Understanding. This limit is the smallest self-referential pattern that is able to generate every form there is. Finding this pattern, the Essence is the Quest of Mathematics.

Wolfram

One of the most briljant mathematicians, Stephen Wolfram, the founder of Mathematica, a software package to program mathematics has spend many years, playing with his own software, to find this pattern. He even created a completely new science, a New Kind of Science, to explore this issue.

The mathematician Chaitin has proved that we, the Humans, are unable to find this pattern, with the help of programming languages and computers. He proves that we are able to get a long way but at a certain moment, Time is going to bother us. We will simply not be able to beat the speed of the creative wave of ever-expanding Space.

Is there an end to the expansion of space?

In our current thinking space looks like a bubble and bubbles can be expanded into eternity. The new forms of space are different

The interpretation of space is changing and space could be expanding until eternity in a closed system.

Space could be bounded by itself. It is not impossible that space could find another form to expand again and again.

If space is creative and mindful it could create every space that is possible but we the Humans have no idea what this could be because we are moving behind space itself.

If we could become space itself we could imagine everything we wanted.

How could we move out of the Matrix?

We are a part of the consciousness that contains the consciousness that..

If we merge the splits in our simulated consciousness and merge the splits between our consciousness and the consciousness of the other simulated consciousnesses and ….we could move out of the Matrix.

What are we doing in the Simulator?

The ancient Gnostic Mystics believed that Our Universe was created by Demiurg, the Great Architect. The Demiurg was a “high level’ Consciousness that was allowed by the Creator (The Light, The Void) to create a Universe that would speed up the awareness of many “splitted” consciousnesses, The Sparks of the Light.

The Earth Simulator is a Learning Device and every Soul is allowed to enter the Simulator to (re-)play a Game.

When the Soul enters the Matrix his memory of past lives, other games played, is erased (the Veil). On Earth we are playing the Games we have chosen. When you are aware of the Game you are able to move out of the Simulator to move to another place to play different games of creation.

What are the possibilities when you leave the Simulator?

Create Your Own Universe. You don’t need to be a Game Designer to do this. The Simulator is already in place and Old Designs are never repeated in the Multi-Universe.

Our Universe could contain tiny Universes we are not aware of

How to compress space

Reginald Cahill, About the Michelson and Morley Experiments

Constructur Theory of David Deutsch

A lot of documents about Process Physics

Why Numbers are Waves

Pythagoras, the inventor of the Music of the Spheres, thought that the principles governing Number are the principles of all things.There are many principles behind the Numbers. The most intriguing is called the Riemann Hypothesis. It defines a spiraling relationship between the Prime numbers.

What is a Number?

A Number is a Symbol that represents an Object we use to Count and to Measure. The Number-Object 1 is often represented by the symbol “1” and the sound “One”.

When we Count we are able to Tell How Many Objects are available in a certain Set. In mathematical terms the Amount of Objects in a Set is called the Cardinality.

To define a Set we have to define “What the Objects Are”. If we don’t do this we are not able to See, to Observe, the Objects. To Count we have Define “What we are Counting“.

To define what we are counting we have to Classify and to Describe. To Classify we have to Name. The name “Sheep” is connected to a Mental Picture of something that “looks like a” Sheep.

There are Names who are not represented by a Mental Picture. An example is the name “number”. This Class of Objects contains Abstractions of Real, Visible, Objects or of Actions that are Performed on Visible Objects. Abstract Objects/Actions are related to, Mapped, to Visible Objects/Actions by Metaphors. One Apple “is representing” the Number One.

There is no fundamental law that Tells us How to Classify. Classifications are highly Culture and Time Dependent. The effect is that different people will count different amounts of objects when they don’t agree about “What they are Counting“.

When we have Counted a Set of Sheep we are able to Add when we have counted another Set of Sheep at another Place. We are only able to Add when the Sheep at both places are “the Same“.

It is impossible to add Sheeps and Cows unless we define a more abstract Set called Animals. Again the problem of classification arises.

When we want to Count Every Thing we have to find the Cardinality of The Set of All Sets. The Cardinality of this Set is “not knowable“. Most scientists would say that the cardinality of this set is infinite (“not bounded“). Mathematicians would say that this Set maps to the Set of Numbers or to a Sub-set of the Set of Numbers. The paradox of Russell shows that the Set of all Sets “does not exist“.

It does not matter in what order we Add Numbers. A+B = B+A. This is called the Commutative Quality of the Numbers. Remember that this Quality only applies when we are counting the Same Objects

Another Quality of Addition is called Associativity. It does not matter in what order we add a sequence of numbers. 1+(2+5)+3 = (1+2) + (5+3). Remember that this Quality only applies when we are counting the Same Objects.

When we are Counting Sets of Sheep that contain the Same Amount of Sheep we are able to create a new operator “*” called Multiplication. Multiplication is a Repetition of the Same Amounts (another word for Cardinality) of Counting.

When we Multiply the same Qualities of Addition are applicable. Multiplication is Commutative and Associative. 6*7=7*6 and 6*(7*8)=(6*7)*8.

What is a Prime?

We have finally reached the Primes. A Prime is a Number that can only be divided by 1 and Itself OR Every Number can be written as a Multiplication of One or more Primes.

Mathematicians Think that the Set of Prime Numbers is the Foundation of the Set of Numbers.

Nobody thought that this Foundation contains another Foundation until Riemann formulated his famous hypothesis. Riemann observed that the frequency of prime numbers is very closely related to the behavior of the so called Riemann Zeta function, ζ(s) = 1 + ½**s + 1/3**s + ¼**s + . The hypothesis is still not proven but is verified by computer programs that generate very big numbers (1,500,000,000) and until now it still holds.

The operator “**” is called Power or Exponent. It represents a Repetition (s) of the multiplication of the same number. 2**2 = 2*2=4. The operator “/” represents the operator Division. Division is the “opposite” of Multiplication.

A Foundation is something that is used to build on. It is the “lowest” layer of all the layers. If a Foundation contains a Foundation many theories that were formulated using the old foundation are at stake. One of the most important theories is the theory about the Numbers themselves. If the Numbers are not what they are thought of new mappings, new metaphors, are possible. In this blog I will try to explain that Numbers are not Distinct Isolated Objects. Numbers are not Parts.

Numbers are Waves.

The Primes are the Foundation of the Number System if we Accept that:

• A Number is something we use to Count Objects
• We are Counting the Same Object
• Multiplication is Repetitive Counting
• the Quality of Commutativity in Multiplication and Addition Applies

We are not Counting the Same Object at All.

We are always Counting Cows and Sheeps because every Object is Unique. If we make a Picture of one Sheep we see a Lot of Detail. We ignore these details because we are not interested in them when we are Counting Sheep. The Sheep are treated as Objects.

When we want to Articulate the Details of One Sheep we Run Out of Words to describe all the details. We are unable to define all the attributes to classify all the details.

When we are Counting, Every Thing has to be treated as an Object because Counting implies the Perspective of the Object.

The Quality of Commutativity in Multiplication and Addition does not Apply.

If we want to treat Every Thing As It Is, the Commutative Law is not applicable: A+B is not equal to B+A. When we want to treat Every Thing As It Is, Every Thing is One. If we Map every Unique Object on the Number Line every Number is representing a Unique Object. A Number is a Unique Key, An Identifier.

If we are not able to Add we are not able to Multiply. If we are not able to Multiply the Primes are non-existent. If we accept that Every Thing is Unique we are not able to Talk about Anything. We have be Silent and Observe. We could also accept that Language is a Funny Game We Play (Wittgenstein) or Accept that a Picture Paints a Thousand Words.

When we want to Quantify or Qualify we are always Equalizing.

When we want to Count we have to accept that we have to make Some Things the Same when they are really not the Same. If we want to Quantify we have to accept that we are making Mistakes all the Time.

If we want to Qualify we have to accept that Numbers are not usable. If we want to Qualify we have to accept that Classifications are not usable. If we want to Qualify we have to Accept that somewhere we are using the Numbers and are Quantifying.

When we use Language to Qualify somewhere we introduce concepts like High and Low and are forcing an Order on Reality. The only thing that is left is to use the Emotions to do this. We could Say that Every Thing is Beautifull and produce a Sound (“Ahhhhhhhhhhh” or “Wauw“).

When we want to Quantify or Qualify we have make sure we are not equalizing something that is really unique. We have to Make a Choice and think about the Consequences. If we define a Selection Criterium or Define an Attribute of a Unique Object or Define a Filter, we have to be aware that the Attribute simply defines a new Object. This Object is always an Abstraction. When we define the Attribute or Quality of Race we Divide Reality in Races.

Language always Divides The Whole in Parts.

Multiplication is Repetitive Counting.

When we Multiply we make use of two Types of Numbers. We are using a “repetition factor” and we use a “counting factor“. These types of Numbers are not the same. When they are not the same the Commutative Law is not applicable. 7*6 is different from 6*7. The first statement is about 7 times a Set of Sheep with Cardinality 6. The other is about 6 times a Set of Sheep with a Cardinality of 7.

Primes are Frequencies.

A Repetition Factor could be defined as a Frequency. If we move from the domain of the Rectangular frame, Cubes, to the Circular frame of Mathematics, Waves, the Riemann Hypothesis changes into a statement about the Musical or Harmonic Behavior of the Primes. The primes have Music in them. You can even Listen to this Music. Pythagoras was Right.

If Primes are Frequencies What are Numbers?

If every Number is a combination of one or more Prime Numbers, every Number contains one or more repetition factors. If we move to the Circular Domain, Multiplication changes into Addition. A Number is the Sum of Waves. A Mapping from the Rectangular to the Circular Domain is called a Fourier Transformation.

If Numbers are Waves what are Objects?

Objects are also Waves.

If Objects are Waves is there a Boundary between Objects?

No. They are All One. In a Circular World there is no Beginning and there is no End. In a Spiraling Spiral World Everything is Closed in Itself. We are an Enfolding of the One that is Closed in Itself. The One is Aware. It is Consciouss. Every Thing Contains a Conscioussness, A Spark of the One.

What is Behind Every Thing?

0. It all starts with the Primal Void, 0.

1. Out of the Primal Void the One is Created. The One is The Mover that Moves Itself, The Center. It Enfolds in Itself.

2. The One is Observing Itself so there are Two. The One becomes Conscious.

3. The Two Expand and Compress so there are Three, the Trinity. The Two are named Control and Desire. The One, Conscioussness, stays in the Center. The One Voids the Two (-1 + 1 = 0).

4. The Two are split in Two so there are Four Forces or World Views. Control and Desire are “compensated” by Spirit and Soul.

5. The One, Consciousness, is always in the Middle. Now there are Five, the Pentagle. The Five are called the Hu-Man. It contains Control, Desire, Spirit (Creativity), Soul (Love, Emotion) and Conscioussness. The last part connects the Human to the One. A Human is a Dynamic Instability where the Four Forces are constantly trying to find Harmony. The Conscioussness Observes and Reflects. It helps the Forces to find Balance.

6. The Four Forces combine. There are Six or Twelve combinations. This depends on the way the combinations are made. Four independent Forces generate 1*2*3 combinations when the Combinations, the Relationships or the Mappings, are considered Unique. When a Relationship is a Two-Way Connection (A Dialoque), the amount of combinations is 2* (1*2*3) =12. Six is the first Perfect Number. The Sum and the Product of its Divisors is Equal. 1+2+3 = 1*2*3.

7. The One is always in the Middle so there are 6 + 1 = 7 Relationships. There are Seven Chakra’s. The Chakra in the Middle, The Heart, is related to the Centre, The One (-3,-2,-1, 0, 1, 2, 3).

9. This is a Pattern where the Four Forces are connected in a Circular Pattern. One Pattern moves with the clock and the other counter the clock. The complete pattern looks like a Moebius Ring

10. This is the Lowest Level in the Sephirot, The Tree of Life. It is called Malchut, the Kingdom of God. It exists outside the Pattern of the Nine.

12. See 6. The four Forces are now in their Dialogic State. 12 is a Highly Composite Number (HCN). A HCN is a Social Number. It contains Many Divisors. HCN’s are used in situations where many divisions are needed like Clocks and Calenders. HCN are used to avoid conflicts. Other HCN’s are 24 (hours), 60 (seconds) and 360 (degrees).

There are twelve signs of the Zodiac, twelve Tribes of Israel, twelve Apostles of Jesus and twelve Houses in Astrology. Every number is a Relationship between Two Powers of the Four Powers and can be interpreted as such. The Four Powers are the cornerstones. Examples are the Apostles John (Spirit, Eagle), Marc (Control, Laws. Lion), Luc (Desire, Bull, Ox) and Matthew (Soul, Human/Angel).

13-24. With the Thirteen a new Cycle on Another Level Starts. The 13th Card of the Major Arcana of the Tarot is called Death, a New Beginning. The Soul has travelled in the UpperWorld (Earth, 1-12, Our Material Reality) and moves to the Under World (Heaven, The World of Souls, 13-24) to Clean itself and to start a new Cycle as the Fool (0).

The Tarot spelled as TARO-T is a Cyclic Structure that operates on Three Levels. In every level the four Forces (T, A, R and O) are combined in different ways. The Highest Level is called the Major Arcana and contains 24 (1*2*3*4) Cards. The last card indicates the End of the Cycle of the TARO. Every card in the Higher Arcana is named with a Permuation (without Repetition) of the letters T,A,R and O.

25-36. The Second Level contains 12 Cards (3*4). The King, Queen, Knight and Page represent the four Forces.

37-76. The Third Level (40 Cards) contains the Ace (1) and the numbers 2-10. The four Forces are called Sword (Mind, Control), Cups (Soul, Emotions), Wands (Spirit, Creativity) and Pentacles (Senses, Desire).

The One Enfolds into a Spiraling Spiral.

New Numbers and New Levels are Created.

We are One AND we are Many. We are The Same AND we are not The Same. We are Music AND we are Producing Music. We are Repetitons AND we are Creating Repetitons. We are Primes AND we are not Primes.

Chaitin, About the Russell Paradox and other Controversies concerning the Foundations of Mathematics

Listen to The Music of the Primes

About the Same and not the Same

A Book about The Music of the Primes

Explaning the Riemann Hypothesis

Every Thing You want to know about The Riemann Hypothesis

I have never believed reason and the final implementation of reason, the Computer, would help mankind. Reason is a terrible trap. It compresses our reality to a single point in which we finally will vanish.

The Reason We are Here is not reason but non-reason. We are here to fight reason until it finally disappears.

The weapon with which we have to fight reason is reason itself. If we understand the simple fractal pattern behind everything we are ready to experience the spectacular effects of the simple pattern.

When you look at my blog about the Limits of Reason you can see that the solution is easy to find.

The solution is to move to the level the computer and reason never can reach, the world beyond Point Ω of Chaitin into Total Madness. It is the place where the Creative Force creates unique patterns that nobody can explain. The only thing we can do is Experience them.

The step into the world beyond Ω is in essence a step into madness. We have to leave everything we know behind. We have to skip all our patterns.

There are many types of madness but the madness I am talking about is named schizophrenia or psychosis.

I have experienced Psychosis when I suddenly jumped into the Unknown two years ago. I did not know my state was named this way. I experienced the state and tried move out of it because it was killing me. It was killing me because I received too much information. My brain was unable to find a pattern and the effect was almost total madness.

Luckily I did not go to a psychiatrist and I also did not take any pills. I just started to use the Internet to find out what was happening to me. Finally I knew I was the “victim” of something the old scientists call “Kundalini Rising“. I was experiencing something the Old Scientists call Enlightment.

When you are moving into the state of Enlightment you know there is another world behind this world and you know this world is real. It exists but the majority of humans are not aware of this world.

When you have experienced this state you suddenly understand what other enlightened humans are trying to tell. You understand the Gnosis but you also understand certain Philosophers who are trying to grasp the Reality behind our Reality.

One of them is Gilles Deleuze. Deleuze worked together with the psychiatrist Félix Guattari. One of their “Inventions” is the Plane of Immanence.

A few citations:

Here, there are no longer any forms or developments of forms; nor are there subjects or the formation of subjects. There is no structure, any more than there is genesis.”

We will say of pure immanence that it is A LIFE, and nothing else” […]

A life is the immanence of immanence, absolute immanence: it is complete power, complete bliss

There are only relations of movement and rest, speed and slowness between unformed elements, or at least between elements that are relatively unformed, molecules, and particles of all kinds. There are only haecceities, affects, subjectless individuations that constitute collective assemblages. […] We call this plane, which knows only longitudes and latitudes, speeds and haecceities, the plane of consistency or composition (as opposed to a plan(e) of organization or development

Deleuze and Guattari are using very difficult language but what they are trying to grasp is the experience of Union that occurs when your kundalini is moving. Many other people that have experienced this state of pure love have tried to find all kinds of metaphors to explain something you cannot explain.

The first time in my life the state of Union took only 30 minutes because somebody was able to drag me out of it. I wanted to stay there for ever. The second state lasted more than a week and because I was alone nobody was able to help me. It was much stronger and it came with huge flashes of Insight.

What will come in the near future is total Madness. Many people are already moving inside to find a state to cope with the Madness. The Total Madness has many names. Terrence McKenna calls it Point Omega. Funny enough the state when we pass the Limits of Reason carries the same name.

What is the Reason We are Here

I think Leibniz was not far away from his statement that Our Universe is “the most simple in hypotheses and the most rich in phenomena“. There are just a few rules that determine the Game of Life. It does not take a long time to find these rules. We can spend our whole life to prove these simple rules are not there. In this case Reasoning detracts us from the real thing.

You can always find an infinite amount of equations that fits a finite set of points.

When the set of points changes the equation changes. This represents a major problem when you want to find a general pattern. The solution is to assume that the pattern behind the set of points has to be a Simple Equation (or a Simple Law).

A  theory has to be simpler than the data it explains, otherwise it does not explain anything.

To define Simplicity we have to define a tool that measures the simplicity of an equation. Mathematicians have tried to solve this problem in many different ways. The problem seamed unsolvable until computers and software-languages were invented.

A law of nature is a piece of software, a computer algorithm, and instead of trying to measure the complexity of a law via the size of an equation, we now consider the size of programs, the number of bits in the software that implements a theory.

If every theory is represented by a string of bits we are able to analyze what a computer (our “thinking mind”) is able to represent. The problem is transformed to the problem of representation. Behind this problem lies the problem of Compression.

Our Reality is represented by the simplest equation (the shortest (most compressed) binary set) that when it is expanded represents the most complex binary set that represents our reality.

One of the conditions we have to add is the condition of “understand ability”. Perhaps the expression exists but we are unable to grasp the law. Leibniz calls this law the principle of sufficient reason.

Leibniz formulated this principle as follows: “Dieu a choisi celuy qui est… le plus simple en hypotheses et le plus riche en phenomenes” (God has chosen that which is the most simple in hypotheses and the most rich in phenomena)”. “Mais quand une regle est fort composée, ce qui luy est conforme, passe pour irrégulier” (But when a rule is extremely complex, that which conforms to it passes for random)”.

The interesting point in the statements of Leibniz is de term “irrégulier“. It is translated by the term “random“. This term can be interpreted in many ways. In the world of Statistics it means that a certain event is unpredictable. In algorithmic terms it means that we are unable to find a pattern behind the pattern we observe. A random pattern is an essential pattern. It cannot be compressed.

Science ends when we have found randomness and have reached the Limits of Reason.

Everybody has a Limit of Reason and this limit expands in time but for every mind that will be born there is an absolute limit of Reason. When we have reached this limit we will know there are still patterns to find but we will be unable to prove they are real patterns.

Gregory Chaitin is the expert of the Limits of Reason and he is highly influenced by Leibniz.

By running a program you can eventually discover that it halts, if it halts. When it halts you have found a theory. The problem is to decide when to give up on a program that does not halt.

A great many special cases can be solved, but Turing showed that a general solution is impossible. No algorithm, no mathematical theory, can ever tell us which programs will halt and which will not.

We are never certain that we have found a theory because when we wait a little longer (collect more facts) we find the final theory that explains what we want to explain (if we understand the theory).

We could use a computer to search for patterns (this happens already) but the computer presents an incomprehensible theory (this happens already) or it has to search a little longer. A computer could run “for ever” when there is enough energy but a human has a fixed lifetime. The halting problem shows that we will not know how long “for ever” is. We also will not have enough minds to analyze the output. The Halting problem is proved to be unsolvable.

Chaitin defined a constant Ω that shows our progress in reaching the Limit of Reason. It shows our progress to reach the Incomprehensible.

We still have a long way to go.

The Halting Problem cannot be solved because we (the Humans) are unable to define the Limits of Reason. Even the Brightest Minds will not be able to understand all the patterns that are available in Our Universe. Even Mechanical Devices programmed by the Brightest minds will not solve the Mystery. Somewhere we will make a Mistake.

The Mistake will start a new process of Inquiry and New Theories will be created that will always contain a Mistake. We will be Busy until Enternity to Create because we are not perfect. Only Perfect Solutions are Impossible.

I want to close this blog with a statement of Leibniz: ”Sans les mathématiques on ne pénètre point au fond de la philosophie. Sans la philosophie on ne pénètre point au fond des mathématiques. Sans les deux on ne pénètre au fond de rien”(Without mathematics we cannot penetrate deeply into philosophy. Without philosophy we cannot penetrate deeply into mathematics. Without both we cannot penetrate deeply into anything)”.