How an MIT Professor Proved the Existence of God Using Mathematics


“Jacob Wrestles with God” Alexandre Louis Leloir, 1865 The Big Bang, which suddenly occurred about 13.8 billion years ago, marked the beginning of history. Several billion years after this, galaxies formed from clouds of slightly cooled gas; after some time, stars formed from nebulae inside the galaxies, and planets appeared around the stars. On one of these planets, chemical life arose in the water near the hot hills of underwater volcanoes. Gradually, this life became more complex and evolved - first into the simplest viruses and bacteria, and then into birds and mammals. And in the end, the brain of one of the species of mammals developed enough to, based on indirect evidence, reproduce the entire path it had taken to its own existence. But despite all its achievements, this mammal is still tormented by the question: what happened before the Big Bang?

Opinions differ on this matter. Many consider this question to be incorrect, since time itself did not exist before the Big Bang. Some consider our Universe to be the interior of a black hole formed in some “outer” Universe. And some believe that everything that exists is a simulation running on a powerful computer in the “real” world. Who knows, maybe our whole world really is just a school programming project for a sixth-grader from a developed civilization. But even if our world is inside the “superuniverse” or “real universe,” then why does this external universe itself exist? What gave birth to it? Why does everything exist at all?

Creator

The most popular answer to this question has long been considered the existence of God, the creator of our world. Proponents of this point of view view the Big Bang directly as an act of Creation.

The logical chain of reasoning leading to proof of the existence of God is called a cosmological argument. It says that since the law of cause-and-effect relationships strictly operates in the world and everything has a cause, then the world itself must also have a cause, and such a root cause is God.

True, the existence of God gives rise to a logical question: where did God himself come from in this case? In response to this, medieval Christian scholastic theologians argued that the question “what was before” and “where did it come from” is not applicable to the concept of God, because God is an absolute outside of time and space. Therefore, in a strictly formalized form, the cosmological argument looks like this:

  • Every thing in the universe has its cause outside itself (children have a cause in their parents, a rolling ball has a cause in the person who pushed it, etc.)
  • The universe, as consisting of things that have their cause outside themselves, must itself have its cause outside itself
  • Since the universe is matter existing in time and space, therefore, the cause of the universe must be outside these categories
  • Therefore, there is an immaterial cause of the Universe, not limited by space and time
  • Such a root cause can be called the word “God”

The doctrine of an eternal and infinite God, who created all things, and the cosmological argument itself were not the original ideas of Christian theologians, they were not even created by Christians themselves. The whole point is that despite the fact that Christianity in the religious aspect is a product of Judaism, in the ideological aspect it is a direct descendant of ancient Greek philosophy.

Parmenides - being and non-being

Parmenides
The ancient Greek philosopher Parmenides did not ask the question of why everything that exists (“being”) exists. He considered a much more interesting question: does non-existence exist? His train of thought, pardon the pun, revolved around the thought itself.

About being, Parmenides argued that its existence is absolutely self-evident for us, since only what we think already speaks of the existence of something - thought itself. Many centuries after Parmenides, the famous French philosopher Rene Descartes formulated this statement most succinctly: “I think, and therefore I exist.”

Regarding non-existence, Parmenides argued that it does not exist because it is unthinkable. If you try to imagine nothingness, then most likely you will imagine absolute blackness and emptiness. But blackness is just our idea of ​​the absence of light, and emptiness is our idea of ​​the absence of objects. Real non-existence is the absence of anything at all: space, time, matter, even thought itself, complete oblivion. This is impossible to imagine, and therefore, according to Parmenides, non-existence does not exist. In addition, the philosopher noted that the existence of non-existence is logically contradictory, because it comes down to the statement “There is something that does not exist.”

From the existence of being and the non-existence of non-being, Parmenides draws two conclusions: that being is not generated by anything, otherwise it would have to admit that it came from non-being, which does not exist, and that being is eternal and indestructible, otherwise it would turn into nothingness that does not exist. As can be seen, already in the time of Parmenides, views about a certain eternal absolute, having neither beginning nor end, began to form in Greek philosophy.

In addition, from the existence of being and the non-existence of non-being, Parmenides deductively derives a picture of the world very similar to modern ideas about our Universe, which the philosopher also calls being:

  • There is one being, and there cannot be two or more beings, otherwise they would have to be delimited from each other by non-existence, but it does not exist
  • Being is continuous and united, that is, it has no parts. If existence had parts, they would be delimited from each other by non-existence, but it does not exist
  • Being is motionless, homogeneous, perfect and limited, has the shape of a ball
  • Being has neither past nor future, being is pure present

It is unknown how exactly the philosopher came up with the idea of ​​a spherical form of existence, but we can say with confidence that he guessed the real shape of our Universe.

Names of God

As paganism was replaced by a religion glorifying the one God, people began to be interested in the name of the Creator in order to be able to turn to him in prayer.

Based on the information given in the Bible, God personally revealed his name to Moses, who wrote it down in Hebrew. Due to the fact that this language subsequently became dead, and only consonants were written in names, it is not known exactly how to pronounce the name of the Creator.

The four consonants YHVH represent the name of God the Father and are the verbal form of ha-vah, meaning “to become.” Different Bible translations add different vowels to these consonants, giving completely different meanings.

In some sources he is mentioned as the Almighty, in others - Yahweh, in others - Hosts, and in fourths - Jehovah. All names denote the Creator, who created all the worlds, but at the same time they have different meanings. For example, Hosts means "Lord of Hosts", although he is not a god of war.

Disputes about the name of the Heavenly Father are still ongoing, but most theologians and linguists are inclined to believe that the correct pronunciation sounds like Yahweh.

Pythagoras - the cult of the unit


Pythagoras
Shortly before Parmenides, another ancient Greek philosopher and mathematician, Pythagoras, lived in Greek Italy, and is still known today for his famous theorem on the relationship between the lengths of the legs and the hypotenuse of a right triangle. Pythagoras was delighted by the relationship he discovered between the height of the sound produced by a harp and the length of its strings - after this discovery, Pythagoras created the first mathematical theory of music in history. Seeing that other laws of nature, like music, are described by mathematics, Pythagoras put forward the hypothesis that mathematics underlies everything that exists, or, in other words, that “everything is a number.” By analogy with music, Pythagoras called the mathematical beauty of the world order the great harmony of the Universe.

Pythagoras adored numbers, he was especially fascinated by the unit - Pythagoras called it a monad and worshiped it, considered it the highest absolute, a symbol of the single and indivisible fundamental principle of all things, a deity. Pythagoras considered the two to be the principle of the bifurcation of all things into opposites: the limiting and the infinite, the even and the odd, the one and the multiple, the right and the left, male and female, rest and movement, straight and crooked, light and darkness, good and evil.

This belief led Pythagoras to create his own religion. Having collected ideas from the monotheistic religion Orphism, which was popular in Greece at that time, he created the Pythagorean school - a religious and mathematical interest group. The Pythagoreans worshiped the One, and they chose the Sun as the material embodiment of the One. The Pythagoreans looked for their sins and made confessions. According to ancient historians, Pythagoras punished his disciples: “Let the sleep that closes your eyelids not touch your eyes before you have sorted out the affairs of three days in order: “What have you sinned?” What did you do? What did I not do that was due?” Despite the mathematics of the Pythagorean school, they had many prohibitions and superstitions: Pythagoreans were forbidden to eat beans, step over the crossbar, touch white roosters, look in a mirror near the fire, break bread and much more. They also practiced vegetarianism, since they inherited the doctrine of the transmigration of souls from Orphism.

The Pythagorean hypothesis about the mathematical structure of the Universe became very popular among scientists - Newton, Kepler, and Einstein were inspired by it. This hypothesis is confirmed even in modern scientific research. If we look at quantum mechanics, which describes our world at the micro level, we will see that there the solid material world crumbles into pure mathematical abstractions: Hilbert space, complex numbers, Schrödinger wave equations, tensors and linear operators.

Plato - the eternity of the soul

Plato
Another famous ancient Greek philosopher, Plato, had great respect for Pythagoras and mathematics. Above the gates of the academy he founded in Athens, he wrote the phrase that went down in history: “Let no geometer enter.” But most of all, Plato is famous for creating the doctrine of ideas. Strictly speaking, this teaching began to be formed by Plato’s teacher, the famous Athenian philosopher Socrates, but it was Plato who developed it into the philosophy now known as idealism. The easiest way to understand Plato's “idea” is through the following example.

There are many round tables in the world, but none of these tables are perfectly round. Some of the tables have small cracks and imperfections, some are well made but are still not completely round at the atomic level. Despite this, we have the idea of ​​a perfect geometric circle in our heads. That is why we usually call such a circle ideal. In addition, there are a great many tables of different shapes in the world, but in our minds there is an abstract idea of ​​a table, under which all the tables existing in the world fall. Thus, an ordinary round table in the material world, according to Plato, has a prototype in the world of ideas: the idea of ​​a round table, which is a combination of the idea of ​​an abstract table and the idea of ​​a circle.

The best examples of Platonic ideas are mathematical objects and relationships. If we think about whether two plus two would equal four if no universe existed at all, then we will come to the conclusion that yes, it would. After all, this equality is not something material and dependent on some properties of the universe - it exists only in the world of ideas. Moreover, we can endlessly combine different ideas and their combinations, generating more and more complex ideas. Thus, Plato comes to the conclusion that the world of ideas, unlike the material world, is eternal and infinite. In addition, according to Plato, the world of ideas, despite all its diversity, is something One.

Developing this idea, Plato asks the question: if our mind, or figuratively speaking, the soul, is the sum of a huge number of ideas, and ideas are eternal entities, then it turns out that our soul is also neither born nor dies. Plato believed that after physical death, the human soul returns back to the world of ideas and achieves complete unity with it. This is how Plato comes to the doctrine of the immortality of the soul and its posthumous return to God, which will later be adopted by the fathers of the Christian church.

History of Christianity with the coming of the Messiah

The birth of Christianity occurred in the 1st century AD. e. in Palestine, which at that time was under Roman rule. Another connection with the people of Israel is the upbringing that Jesus Christ received as a child. He lived according to the laws of the Torah and observed all Jewish holidays.

According to Christian holy scriptures, Jesus is the incarnation of the Word of the Lord in a human body. He was conceived immaculately in order to enter the world of people without sin, and after that God the Father revealed himself through him. Jesus Christ was called the consubstantial son of God, who came to atone for human sins.

The most important dogma of the Christian church is the posthumous resurrection of Christ and his subsequent ascension into heaven.

This was predicted by numerous Jewish prophets many centuries before the birth of the Messiah. The resurrection of Jesus after death is a confirmation of the promise of eternal life and the incorruptibility of the human soul that God the Father gave to people. In Christianity, his son has many names in holy texts:

  • Alpha and Omega - means that he was the beginning of all things and is its end.
  • The Light of the World means that he is the same Light that comes from his Father.
  • Resurrection and life, which should be understood as salvation and eternal life for those who profess the true faith.

Many names were given to Jesus by both the prophets and his disciples and the people around him. All of them corresponded either to his deeds or to the mission for which he found himself in a human body.

Aristotle - creation of the material world

Aristotle
Plato's student, philosopher Aristotle, analyzing his teacher's thoughts about the world of ideas, asked the question: if the prototypes of real material things are ideas, then what forged our material world according to the patterns of ideas, what breathed life into ideas, materializing them? Aristotle considered the existence of a Prime Mover to be the only reasonable answer to this question. It was Aristotle who first formulated the cosmological argument - if everything has a cause, then there must be a very first cause, the beginning of every action in the world - the Prime Mover. Thus, Aristotle completes the formation of the image of God, which was later adopted by Christians - the eternal and infinite, immaterial Absolute and Prime Mover of all things.

Who created God

A good question to which there are many answers and hypotheses. But who created the creator? Nowadays, the Internet brings together many people. And we can learn what they think about important and timeless issues. And here we have collected answers that come closer to solving a not simple situation about who created God, and maybe the gods. It’s just as interesting and exciting as the solution to the trailer for the latest “Avengers” and the hypotheses about who among the superheroes will die and what the ending will be.

I came across the problem of the “root cause” as old as Ancient Greece. As is known from Christian teachings, the world where we live has a starting point - the moment of creation of the world. According to various biblical chronologies, this date ranges from 3000-7000 BC. The creation of the world itself took one week.

And now the question itself: how long did God exist before this?

An answer with any finite number leads to the question: who then created God and what came before him? More interesting is the option “God has always existed,” i.e. we can look at time as a number line that is infinite in both directions. The point that we will mark as 0 is the moment of the creation of the world, and we are now somewhere at the coordinate ~5000-9000 years from the origin.

And this is where an interesting situation arises, since the interval on the left is open, it took God an infinite amount of time to come up with the idea of ​​the world and then create it. I heard somewhere that it seems that God’s perception of time is such that for him a millennium flies by in a minute. But even if our million years lasted a second for God, God would still have to go through an infinite amount of time before creating us. Not to mention that it seems strange that God had nothing to do all this time, having spent eternity in the void, probably wondering what he would eventually do.

Moreover, the process of creation itself, as it is described in the Bible, is more like an improvisation (something like, God made the ocean, he liked it, then he created the sky and it was even more fun for him) than a plan, the preparation for which took forever . Well, if God did not use magic to jump over eternity (and if he did, then it turns out that there is a whole eternity in which there is no God?), then we still do not exist, because the waiting time for God until the moment of creation is infinite, write down the number with any number of zeros, but God would still have to wait longer.

Not a bad answer from one of the Orthodox sites:

Who created God? In short, no one; God is not created. To answer this question in more detail, we will need to pay attention to the difference between two concepts - conditional and absolute being. For some, these concepts may sound unusual, but there is nothing particularly complicated about them. For example, my existence is conditioned by the marriage of my father and mother, the food I consume, the air I breathe—many causes outside of myself. The existence of the computer on which I am typing this text is determined by the intention of the manufacturer, the history of the development of technology, the materials from which it is made, and so on.

The existence of the Sun is determined by the star formation processes occurring in the Universe, the laws of physics and the existence of the matter from which it was formed. Everything we see around us - from a cup of tea on the table, to stars and galaxies - has a conditioned existence: all these things are not eternal and are generated by some underlying causes. They were brought into existence by something else - for example, (if we talk about galaxies) the movement of matter formed during the Big Bang, which developed according to certain laws. But what brought into existence matter itself and the laws according to which it develops? Even the great pagan thinker Aristotle said that by tracing the chain of causes, we will inevitably come to the root cause - or the prime mover, as defined by the philosopher himself. The Church, on the basis of Biblical Revelation, confesses that the root cause of everything, the source of all being, is God. “You brought us from non-existence into being,” says the liturgical prayer.

Unlike everything created, God has absolute existence, as is sometimes said, He is Self-existent, that is, His existence is not conditioned by anything outside of Himself, He does not need any causes external to Him in order to exist. The question “who created” or “what is the cause” is meaningful only in relation to a conditioned being such as ours; in relation to God it simply does not make sense.

Who created God? This question is not logical, Don Baten.

“So who created God?” This question is one of the main arguments put forward by atheists to justify their disbelief. Bertrand Russell (1872–1970), a famous British philosopher, put forward this question as his first argument in his highly influential essay entitled “Why I Am Not a Christian.” Modern atheists repeat this argument, including Richard Dawkins (The God Delusion) and Australian scientist Philip Adams, who said at the 2010 World Atheist Congress in Melbourne, Australia:

“The biggest argument in favor of the existence of God is that there was a certain Creation, a beginning... But this argument is easy to refute. If God was in the beginning, then who gave the beginning to God?

The universe had a beginning, almost no one argues with this, since the laws of thermodynamics require it: the universe is depleting, but it could not always be depleted, because in this case, by now it would have been completely depleted. The stars wouldn't radiate their energy, and we wouldn't be here.

Some have suggested that one universe gives birth to another, but again there cannot be an endless series of such births and deaths, since for each such cycle there must be less and less energy available for work, and if this continued forever, the death of everything would have come long ago.

There had to be a beginning

One of the proven principles of logic/science/reality is the principle of causation: everything that has a beginning must have a proper cause. This principle does not say that “everything happens for a reason.” Bertrand Russell voiced it incorrectly. No, the principle is: “Everything that has a beginning must have a proper cause.” And just a minute of reflection will confirm this conclusion - that which has no beginning does not need a reason. Moreover, the reason must be proper or adequate. The words “You were found in a cabbage” are not a proper explanation of your existence.

This principle of causality is so fundamental that if I were to say that the chair you are sitting on must have had a beginning but came into existence without any cause, you would probably think that I needed the help of a psychiatrist.

Modern atheists, who like to use the words “rational,” “justified,” and “scientific” to describe their beliefs, believe that the greatest of all principles—the beginning of the universe—had no cause! Some of them admit that this is a problem, but argue that the explanation “God created her” does not explain anything, because it still needs to explain where God himself came from. However, how valid is this argument?

What could be the reasons for the creation of the universe?

The cause of the universe had to be immaterial, because if that cause were material/natural, it would be subject to destruction, just like the universe itself. This means that the beginning would have to lie in itself, and here you face the same problem as in the theory with the cycles of birth and death of universes. So, the reason for the beginning of the universe had to be supernatural, i.e. immaterial, spiritual - a reason that is beyond the boundaries of space-matter-time. Such a cause should not be subject to the law of decay/corruption, and therefore it should not have a beginning. This means that the reason would have to be eternal in spirit.

Moreover, the cause of the universe would have to be incredibly powerful; this is evidenced by the enormous scale and energy that we observe in the universe, and this reason had to be proper/sufficient.

To me, all these descriptions resemble the God of the Bible. In the Bible, God the Creator of the universe is described as:

- eternal

Before the mountains were born, You formed the earth and the universe, and from everlasting to everlasting You are God. (Psalm 89:3)

- Your almighty, Lord, greatness, and power, and glory, and victory and splendor, and all [that] in heaven and on earth, [Your]: Yours, Lord, is the kingdom, and You are above all, as the Sovereign. And wealth and glory are from Your presence, and You rule over everything, and in Your hand is strength and might, and in Your power to magnify and strengthen everything. (1 Chronicles 29:11–12)

- spiritual (immaterial) God is spirit, and those who worship Him must worship in spirit and truth. (John 4:24)

Notice that the Bible says, “In the beginning God created the heavens and the earth” (Genesis 1:1). Here God created time itself. This could only be created by the One who is beyond the boundaries of time, who is not subject to time or is eternal.

This means asking who created God or where this Eternal God who has no beginning came from is the same as asking “Who is this bachelor married to?” This question is irrational. The Bible corresponds to reality, and this is not surprising if you think about the fact that the Bible was given to us by the Creator Himself.

Two “great beginnings” without a reason!

People who reject the existence of a Creator are forced not only to believe that matter came into being without any cause, but also that life itself came into being without an adequate cause. Even the simplest single-celled organism is incredibly complex. A simple bacterium is full of incredibly complex nano-mechanisms that it needs to maintain life. A single cell requires more than 400 different proteins to function mechanisms absolutely essential to its life. How could these protein-based mechanisms arise on their own, even if all the necessary components were present (20 different amino acids, each of which is present in large quantities)? For every protein to function, it is necessary that amino acids, of which there are often thousands, combine together in a specific, correct order.

Just think about the one crucial mechanism that copies pieces of DNA to create each of the proteins. Let's take just one protein component of this mechanism, accounting for less than 10%. This protein consists of 329 amino acids. What is the probability that this protein appeared by chance, even assuming that all the necessary and only correct ingredients were available? Let's calculate it this way: 1/20 x 1/20 x 1/20... and multiply by 329!6 The probability is 1 in 10,428... that's a one followed by 428 zeros! Even if every atom in the universe (1080 is a number with 80 zeros) represented an experiment for every possible molecular vibration (1012 per second) over the estimated evolutionary age of the universe (14 billion years = 1018 seconds), this would give the possibility of "only "For 10,110 experiments - and this is much less than the number necessary for there to be even a small chance of the formation of this one single protein - they no longer talk about the remaining 400 proteins necessary for this process.

Not surprisingly, Richard Dawkins admits that scientists may never know how life could have arisen through natural processes. However, he rejects the creation theory for the erroneous reason discussed above.

What reason can be considered appropriate to explain the origin of life? This reason must be incredibly intelligent - far beyond our understanding of reason. We admire scientists who discover nanotechnology in living things - and this is a truly amazing branch of science. But what then should we say about the One who created all this? How big is He in His mind? And this question reminds me of another characteristic of God, about whom the Bible says that He is all-knowing. See Psalm 139:2-6, Isaiah 40:13-14


Looking at God's creations, we know enough about the Creator to be "unresponsive." Romans 1:18-22 says:

“For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men, who suppress the truth in unrighteousness. For what can be known about God is obvious to them, because God has revealed it to them. For His invisible things, His eternal power and Godhead, have been visible from the creation of the world through the consideration of creatures, so that they are irresistible. But how, having come to know God, they did not glorify Him as God and did not give thanks, but became futile in their speculations, and their foolish hearts were darkened; calling themselves wise, they became fools.”

And here the Bible explains why people decided to believe in impossible things - that first the universe, and then life on it, came into being without any adequate cause. They decided without any logic to accept that their two "great principles" had no good reason, instead of recognizing and glorifying their Creator."

Brahman

In the ancient Indian philosophical school there was a concept of the One similar to the Greek one - the Indians called it Brahman. They believed that our entire world in all its diversity: every leaf on a tree, every pebble on the ground, every living creature, every moment of time, are particles of a certain superbeing - Brahman, and all physical, chemical, biological and historical processes in The Universe are the life processes of this super being. This being is not a personal God, Brahman is rather the soul of the world, an indifferent absolute, it is directly reality itself. This creature did not appear from anywhere, and will not disappear anywhere, it is existence itself. They argued that Brahman cannot be given any affirmative definition, it can only be defined through negation: Brahman is infinite, Brahman is unchanging, Brahman is motionless. The ancient Indians, who believed in Brahman, were the first pantheists.

It is interesting to note that the famous physicist Erwin Schrödinger was an ardent admirer of the Indian philosophical school of Vedanta and wrote an entire treatise on the connection between quantum mechanics and Brahman. But unlike Schrödinger, not all philosophers of ancient India agreed with the idea of ​​Brahman, and one of them will be discussed further.

Holy Spirit

In the Old Testament, the concept of the Holy Spirit is found infrequently, but the attitude towards it is completely different. In Judaism it is considered the “breath” of God, and in Christianity it is one of his indivisible three hypostases. Thanks to him, the Creator created everything that exists and communicates with people.

The concept of the nature and origin of the Holy Spirit was considered and adopted at one of the councils in the 4th century, but long before that, Clement of Rome (1st century) united all 3 hypostases into a single whole: “God lives, and Jesus Christ lives, and the Holy Spirit , faith and hope of the elect." Thus, God the Father in Christianity officially acquired the trinity.

It is through him that the Creator acts in man and in the Temple, and in the days of creation he actively took part in them, helping to create visible and invisible worlds: “In the beginning God created the heavens and the earth. The earth was formless and empty, and darkness was over the deep, and the Spirit of God hovered over the waters.”

Buddha - Dependent Origination

Siddhartha Gautama - Buddha Shakyamuni
During the time of Pythagoras and Parmenides, at the other end of Indo-European civilization lived the great Indian philosopher Siddhartha Gautama, better known as Buddha Shakyamuni. The central idea of ​​his philosophy was shunyata - the underlying emptiness.

Buddha argued that absolutely all things (objects and phenomena) in the world are composite, that is, they can be decomposed into two or more parts. The interaction of these parts gives rise to the illusion of the existence of this thing itself; the thing has no properties of its own - its nature is “empty” . For example, a hydrogen atom consists of a proton and an electron, and all its properties are generated by the interaction of these elementary particles. The hydrogen atom itself is just an idea in our head; in fact, there is no atom, there is only the interaction of a proton and an electron.

The Buddha pointed out that when the composite things themselves interact with each other, more and more complex composite things are generated, and there is no limit to this. Just as the interaction of elementary particles generates atoms, the interaction of atoms generates molecules, the interaction of molecules generates cells, the interaction of cells generates living organisms, and the interaction of living organisms generates ecosystems and civilizations. The philosopher wisely noted that all composite things and phenomena are short-lived, tend back into the void and, sooner or later, disappear into oblivion.

In addition, the Buddha pointed out that things and phenomena arise around emptiness only interdependently and symmetrically. For example, the concept of low arises mutually with the concept of high, the concept of stupid arises mutually with the concept of smart, day arises mutually with night, heat with cold, light with darkness, past with future, cause with effect, wakefulness with sleep, and a slave can exist only with the existence of the owner.

Shunyata is closely related to mathematics - the Indians called the number “zero”, invented in the eighth century AD, by the Sanskrit word “shunya”, which means “empty”. In addition to the main meaning of zero as emptiness, that is, the absence of countable objects, this name emphasized the sacred meaning of zero: just as according to Indian philosophical ideas, emptiness lies at the basis of all things, so zero lies at the very foundation of all mathematics. It is relative to zero that positive and negative numbers mutually arise.

We can also find confirmation of the philosophical views of the Buddha in the physics we know. Forces such as gravity and electromagnetism occur between two objects only reciprocally - both objects attract each other or repel each other with the same force. In the case of electromagnetism, pairs of positively and negatively charged particles also exist symmetrically. And so everything tends back into emptiness, towards zero, then differently charged particles attract each other, and equally charged particles repel.

According to the laws of quantum physics, even in a vacuum, energy cannot be constantly zero. It constantly fluctuates and is zero only on average. Zero-point oscillations of the polarized vacuum constantly generate symmetrical pairs of virtual particles and antiparticles. When they collide, particles and antiparticles annihilate, returning back into the void.

There is the zero-point energy hypothesis of the universe, which states that the total amount of energy in the universe is zero because the amount of positive energy in the form of matter is equal to the amount of negative energy in the form of gravity. And according to Noether’s theorem, each conservation law corresponds to some continuous symmetry of a physical system: thus, the law of conservation of energy corresponds to the homogeneity of time, and the law of conservation of momentum corresponds to the homogeneity of space.

Symmetry in general is one of the main properties of our Universe: galaxies have axial symmetry, spherical stars and planets are spherically symmetrical, most living creatures on our planet are bilaterally symmetrical, there are even creatures like siphonophores that form colonies with sliding symmetry. Moreover, we like symmetry subconsciously: most of human art, architecture, painting, sculpture, photography, music is characterized by symmetry in one form or another.

If we apply the Buddhist principle of dependent arising to the issue of being and non-being, we see that non-being simply cannot exist without the existence of being. They must coexist symmetrically. Even purely logically, both for the definition of “not A”, “A” must be defined, and for the existence of non-existence, being must necessarily exist. Moreover, we can say that Plato’s world of ideas and our material world also arose interdependently and symmetrically.

Nagarjuna - reality and unreality

Nagarjuna Statue in Scotland
A few hundred years after the death of Siddhartha Gautama, another Buddhist philosopher, Nagarjuna, pondered the question: can we even find differences between the ideal and material worlds and tell what is real and what is not?

Let's take for example the already mentioned hydrogen atom. Since this atom is just an illusion generated by the interaction of a proton and an electron, and exists only in our head in the form of an idea, it means that it is not part of the material world, which means it is unreal. But everything else in our world is built from atoms—molecules, cells, organisms, planets—and is a collection of layers of abstractions of component ideas. This means that all material things are also unreal. Moreover, even the very nucleus of an atom, the proton, is a composite illusion of the interaction of quarks, and an electron spinning in orbit around a proton can be represented as an illusion generated by the interaction of physical forces described by mathematical formulas. That is, the parts of the atom are also illusory and unreal and exist only as an idea in our head.

Even such a seemingly fundamental property of our Universe as time is just an illusion. We divide time into past, present and future. The past is defined in relation to the present and the future, the future is defined in relation to the present and the past, and the present is defined in relation to the past and the future. The past no longer exists, the future has not yet arrived. So where then is the present - that very moment between the past and the future? Between that which no longer exists and that which does not yet exist. This means that the present and time itself are just as “empty” as everything else.

Of course, in the time of Nagarjuna, they had not heard of quarks, but having analyzed in a similar way all the things and phenomena known to him, the philosopher came to the conclusion that nothing real and material exists at all, that all matter is just ideas and impressions in our consciousness, and therefore the material and ideal world are one and the same. Developing this idea, Nagarjuna came to thoughts very similar to the thoughts of the famous 20th century Austrian philosopher Ludwig Wittgenstein that our language, in principle, cannot adequately describe reality, and all our philosophy is not reasoning about the world, but reasoning about our ideas about world. A spoken thought is a lie. Everything that is real is indescribable, everything that is described is unreal, and no other reality exists except the world of ideas.

Tegmark - in search of God

Modern physicist and cosmologist, MIT professor Max Tegmark comes to similar conclusions. In his book Our Mathematical Universe, Tegmark reflects on the problem of Pythagoras and questions posed by two great physicists: Eugene Wigner and Stephen Hawking. Wigner marveled that mathematics was so incomprehensibly effective at describing the physics of our Universe. And Hawking thought that even if in the future we complete work on the theory of everything and obtain all the equations by which our Universe works, we will immediately be faced with questions: “Why exactly these equations?” and “What breathes life into them?”

Tegmark believes there is only one way to answer these questions. And this answer is that our entire Universe is mathematics, or rather, only one of the possible mathematical structures. According to Tegmark, existence itself is any consistent mathematical structures, of which there are an infinite number, and each such structure is a separate Universe with its own laws. In each such mathematical Universe, the interaction of its simplest parts gives rise to more and more complex substructures, some of which are so complex that they can even have consciousness and contemplate all the divine beauty of this very Universe.

It turns out that Pythagoras, Plato and Nagarjuna were right. Mathematics is truly the basis of all things, an eternal and infinite truth that exists in itself, the only reality. Mathematics is the same all-generating God that the Greeks spoke about, the same all-encompassing Brahman that the Indians spoke about.

There is a story that in the 18th century, at the court of the Russian Empress Catherine II, a dispute took place between the great Swiss mathematician Leonhard Euler and the French philosopher Denis Diderot about the existence of God. In response to Diderot's assertion that God does not exist, Euler wrote a formula on the wall and commented on the entry: “therefore God exists.”

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