In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. Through him all things were made; without him nothing was made that has been made. In him was life, and that life was the light of all mankind.
St John 1:1-4
Without words, we have no thoughts nor reason. Without reason, there is no philosophy, nor mathematics. Some theoretical Physicists hold that: “The Universe is nothing but pure abstract mathematics.” If that is so, without words nothing exists, with them, everything exists.
The idea that The Word is the basis of existence and not mathematics is not new: as the quote from the Bible reminds us, this idea is well over 2000 years old.
Originally proposed by the Jews in The Bible between (4004 BC) circa 6020 years ago and up to approximately 10,000 years ago, if one supposes there are gaps in the genealogies. God and The Word have been interchangeable symbols for the same meaning in those scriptures for a very long time.
It was also proposed independently by Plato's forms circa 370 BC.
The reason for writing this is that most physicists believe that mathematics controls all the mechanics of the Universe. However, my point is that mathematics comes from words. Mathematics weeds out the inconsistencies and paradoxes. Mathematics is a smaller subset of words. Abstract existence extends beyond mathematics to include all words. If words control the Universe, that difference is huge.
You may ask "What is abstract existence?". Abstract existence is the existence of symbols and meanings attached to those symbols and the interconnections between those meanings. It is the most fundamental form of existence. We use words to describe, create or model every other form of existence. It is existence based only on words.
The English definition of a word, used here, is "A symbol used to share meanings". Symbols are anything used to share meanings, including letters, normal words, pictures, gestures, pheromone trails for ants and pollen dances for bees.
Words fall into five distinct sets:
- Nonsense - the chaos of the beginning of the Universe or more recently used in rhymes and love songs. Often there are only implied meanings, what is more important is the form; for a song the nonsense words, the rhythm, how they scan, their rhyme; For the chaos at the beginning of the Universe, while having no apparent meaning in itself, it has huge implications for the future of the Universe. It shapes the future of the entire Universe, including our very existence. That future was sown at the moment of the Big Bang even though we cannot see it.
- Lies or errors - intentionally or unintentionally deceive others as first used by life in camouflage. Some would hold that while lies use symbols, the symbols lose their status as words because they are not used to share meaning. However, we can talk about lies and discuss them and say such things as "That's a lie!". So the lies become symbols of themselves in their own right even if what they say is false and so they become words.
- Paradoxes - for the first time, we need analytical thought to discover if it is a paradox or not. For example, the simplest: "This is false." It is neither true nor false; it is a paradox.
- Every day truth, such as It is raining. It may be true today, but it is not a requirement of existence that it be true tomorrow.
- Lastly, existentially truth, things that are always true such as 2/2 = 1. It was true before the beginning of time and will be true after this Physical Universe ceases to exist. Pure mathematics is a part of this self-consistent truth that takes you step by step proof by proof to more true statements. We can then use mathematics to create computers, aeroplanes, spaceships or just to put up a shelf.
Mathematics is a subject that is split in two. Engineers, scientists, indeed almost anyone uses mathematics to measure things and use those measurements. This is called applied mathematics. One of the characteristics of applied mathematics is that it never needs to be 100% accurate it just needs to be accurate enough for the task we need it for. It uses approximations and rules of thumb, and it rarely needs to be absolutely exact.
However, where does mathematics come from? How was division first invented? Who invented calculus or set theory? This is the domain of pure mathematics. Pure mathematics is where new mathematics is invented.
However, where does mathematics come from? How was division first invented? Who invented calculus or set theory? This is the domain of pure mathematics. Pure mathematics is where new mathematics is invented.
In pure mathematics, everything has to be completely exact. Not to the nearest millimetre, nor a nano-metre if it is not absolutely exactly the same it is not exact enough. Even if two formulas come to exactly the same result but for different reasons that can be enough to exclude it from pure mathematics.
Pure mathematics has to be more than 100.ȯ% self-consistent, that ȯ means repeat zero forever, an infinite number of trailing zeros, it also has to be logically self consistent, otherwise it is not pure mathematics.
Pure mathematics achieves this complete accuracy by logical proof. Pure mathematics assumes certain things are true. These assumptions are called axioms. The axioms are believed to be true because they are evidently true. This is the only part of pure mathematics that is experimental in nature. Do the axioms match the world and do they lead to self consistent mathematics.
Axioms, are used as the foundations of new mathematics, at the very beginning. For a very long time mathematics was based on Euclid's principles. There was no need for any other axioms.
Pure mathematics has to be more than 100.ȯ% self-consistent, that ȯ means repeat zero forever, an infinite number of trailing zeros, it also has to be logically self consistent, otherwise it is not pure mathematics.
Pure mathematics achieves this complete accuracy by logical proof. Pure mathematics assumes certain things are true. These assumptions are called axioms. The axioms are believed to be true because they are evidently true. This is the only part of pure mathematics that is experimental in nature. Do the axioms match the world and do they lead to self consistent mathematics.
Axioms, are used as the foundations of new mathematics, at the very beginning. For a very long time mathematics was based on Euclid's principles. There was no need for any other axioms.
Please note, that it took about 2300 years to spot the first issue with Euclid's principles. Euclid's 5th axiom that given a straight line and a point, not on that straight line: There is only 1 straight line that does not eventually touch the first line; that the second line is said to be parallel to the first line.
It was the 18th century before mathematicians saw the possibility that Euclidean axiom might be wrong in certain circumstances. e.g. when navigating around the Earth. If the underlying space is bent as on the surface of the Earth, then the axiom is no longer valid.
It was only in the 20th century that astronomers "scientifically proved" that the Universe is non-Euclidean because gravity bends the fabric of space.
This means there is nowhere in the Universe where Euclid's 5th principle is true. There is no 3D graph paper that could match the Universe because all the "would be cubes" are bent.
The differences are only visible at cosmological scales. This is why we still use Euclidean geometry for almost all applied mathematics, where the differences do not matter.
As an Aside during the infancy of set theory George Cantor put forward an axiom that allowed sets to contain themselves. This led to Russell's paradox so that axiom was abandoned, which is why we ended up with the axioms of set theory we use today, The Zermelo–Fraenkel Set theory with the axiom of choice.
We can define all the mathematics just using the 9 ZFC axioms. They describe the rules of set theory. These can then be used to create the various number systems we use every day and then those can be used to express the geometric axioms that were first expressed by Euclid about 2300 years ago and the rest is history.
So those ZFC axioms are now used as the foundation of all accepted mathematical statements.
From those axioms, pure mathematics creates logical statements, that is, statements that are true, false, or paradoxes using nothing but the logical tools of "and", "or", "not" and occasionally "exclusive or" that is one, and only one of two statements has to be true. These logical operators combine the accepted mathematical statements into new statements. It then excludes the false and paradoxical statements and includes the statements that are always true into the list of accepted mathematical statements as "logically proven to be true". The whole of pure mathematics is built this way, excluding the false and paradoxes and including the logically proven true ones.
It was only in the 20th century that astronomers "scientifically proved" that the Universe is non-Euclidean because gravity bends the fabric of space.
This means there is nowhere in the Universe where Euclid's 5th principle is true. There is no 3D graph paper that could match the Universe because all the "would be cubes" are bent.
The differences are only visible at cosmological scales. This is why we still use Euclidean geometry for almost all applied mathematics, where the differences do not matter.
As an Aside during the infancy of set theory George Cantor put forward an axiom that allowed sets to contain themselves. This led to Russell's paradox so that axiom was abandoned, which is why we ended up with the axioms of set theory we use today, The Zermelo–Fraenkel Set theory with the axiom of choice.
We can define all the mathematics just using the 9 ZFC axioms. They describe the rules of set theory. These can then be used to create the various number systems we use every day and then those can be used to express the geometric axioms that were first expressed by Euclid about 2300 years ago and the rest is history.
So those ZFC axioms are now used as the foundation of all accepted mathematical statements.
From those axioms, pure mathematics creates logical statements, that is, statements that are true, false, or paradoxes using nothing but the logical tools of "and", "or", "not" and occasionally "exclusive or" that is one, and only one of two statements has to be true. These logical operators combine the accepted mathematical statements into new statements. It then excludes the false and paradoxical statements and includes the statements that are always true into the list of accepted mathematical statements as "logically proven to be true". The whole of pure mathematics is built this way, excluding the false and paradoxes and including the logically proven true ones.
But the false statements and the paradoxes still exist they are a part of the abstract existence of our conversations, dreams and imaginations. We can talk about them.
The reason I have explained the foundation of mathematics like this is that this book and the ideas it proposes, start from the ideas put forward here and builds on them in exactly the same way.
Step by step, they grow into a description of the Love of God in Abstract Existence. While it starts with, some would say a boring style, defining terms logically and then repeatedly building new terms in the same way. It arrives at something that is totally beautiful: The Love of God.
Here we use some extra logical 'self-evident' beliefs or axioms if you will:
- Abstract existence is based on Words. As this is the definition of abstract existence, this hardly disputable.
- Mathematics's foundations are in abstract existence. As explained above, it excludes the falsehoods and paradoxes, leaving a set of self-consistent rules that are exceedingly useful for measuring the world. The rest of abstract existence still exists. It is just that it is not used in mathematics.
This is an assumption of the study of Pure Mathematics that is rarely explicitly stated but is none the less an essential part of the foundations of mathematics and can hardly be disputed. - There are "Laws of Physics", and most physicist believe these are based on mathematics. The Laws of physics are the mechanics of how the whole Universe works.
This last belief is commonly thought to be true by physicists.
However, let us look at making our first logical deduction. Physics is based on mathematics, and abstract existence is mathematics's foundation, among the falsehoods and paradoxes, that means that The laws of physics are actually founded on words.
So the third Axiom is actually that The laws of physics are based on words.
In the beginning was the Word!
The first statement of St John 1:1
That last conclusion is shocking to most scientists and changes the whole of physics. The third axiom becomes:
3. Physics is based on words.
It is so shocking, let us check whether it is actually true.
If the mechanics of the Universe were purely mathematical, lies would be impossible. If the Universe and our understanding of it was absolutely and completely the self-consistent truth of mathematics because falshoods and paradoxes have been stripped out of mathematics. So lies would be impossible and yet lies are common place.
Scientific experiments do support the idea that many Laws of Physics appear to be mathematical. However, communication, including lying, has to be baked into the laws of physics. Consciousness and the ability to choose is intrinsic to all life. It is in everything alive where words become king.
This is looking at the possibility that we have to go back to the word as the foundation of the Universe to explain life. J. K. Rowling is also rich. Similarly
Terry Pratchett would not have been so rich if he had not got a vividly inconsistent mind. Those inconsistencies in his thoughts earned him a physical reward.
These are two physical experiments, the life and works of Terry Pratchett and J. K. Rowling prove to my mind the Universe is based on words and not mathematics.
Another is that there is no purely mathematical explanation as to how a man decides to walk up a hill against the mathematical laws of gravity. We can explain parts of it, such as how the levers of the arms and legs work, but we cannot explain the decision that causes the events to happen. The mechanics of making those decisions have to be a part of "The laws of physics". Those decisions are based on words including lies and not purely on mathematics. The communication of ideas has to be built into physics. Otherwise, we would not be able to do it.
The point is that words are not something laid on top of the physics. It is the mathematics that is built out of words, and it is impossible for the laws of physics to exist without mathematics, and it is impossible for mathematics to exist without all the meanings including the inconsistent ones that are filtered out of mathematics. The two authors mentioned created worlds just out of words with very little mathematics involved, and as a result, if one looks, one can see their worlds are not self-consistent. Some of these inconsistencies are what make these worlds entertaining.
Our actions are based largely on other people's opinions and more importantly our own opinions. Our actions have physical effects that have no mathematical basis. So anyone who thinks the future is inevitable because physics follows mathematical laws will be sadly mistaken as the success and failure to transfer information has a fundamental random effect on every event and every later event.
For example it causes vases
to shatter in random unpredictable ways.
The path taken by a crack or a bolt of lightening is not the path of least resistance. It is the path that appears to be the path of least resistance when the decision occurs and that is affected as is all information transfer by Quantum effects.
Why? because our information about reality is never correct. Whether the decision is made by a lightening bolt travelling through the air or a crack breaking a vase or an army attacking an enemy stronghold.
This is a very fundamental form of communication theory. It suggests that every physical state also has a meaning attached to it as well, and that atoms can misunderstand those meanings as much as we can. Those meanings fall into one of those five categories, mentioned earlier.
Science is based on finding patches of self-consistent truth and trying to connect them; bringing them together to make a larger self-consistent body of knowledge.
This is a quick look at the implications of how changing the foundation from mathematics to words, that is symbols, and their shared meanings changes our understanding of existence.
If existence is founded on the word, then words are: always present; they contain all knowledge; they contain all possible outcomes. So words could be thought of as omnipresent; omniscient; omnipotent. By and large, words are benevolent because they are used for sharing information, and the whole of existence just looked at as a collection of words is timeless and eternal. Maybe this difference in foundation unveils all the attributes of God?
Why? because our information about reality is never correct. Whether the decision is made by a lightening bolt travelling through the air or a crack breaking a vase or an army attacking an enemy stronghold.
This is a very fundamental form of communication theory. It suggests that every physical state also has a meaning attached to it as well, and that atoms can misunderstand those meanings as much as we can. Those meanings fall into one of those five categories, mentioned earlier.
Science is based on finding patches of self-consistent truth and trying to connect them; bringing them together to make a larger self-consistent body of knowledge.
This is a quick look at the implications of how changing the foundation from mathematics to words, that is symbols, and their shared meanings changes our understanding of existence.
If existence is founded on the word, then words are: always present; they contain all knowledge; they contain all possible outcomes. So words could be thought of as omnipresent; omniscient; omnipotent. By and large, words are benevolent because they are used for sharing information, and the whole of existence just looked at as a collection of words is timeless and eternal. Maybe this difference in foundation unveils all the attributes of God?
Table of Contents
Chapter 1 The philosophies of physics; the theories and the laws of physics
Chapter 2 In the Beginning
Chapter 3 What is thought?
Chapter 4 Intelligence
Chapter 5 Life as we know it
Chapter 6 An introduction to Infinity
Chapter 7 Your eternal soul
Chapter 8 A basic introduction to quantum mechanics
Chapter 9 M-Theory, Heaven and Earth?
Chapter 10 Why quantum mechanics? Because of Judgement Day!
Chapter 11 The multiverse and other places
Chapter 12 Understanding God
Chapter 13 Understanding Religion
Chapter 14 A Child's prayer, a daydream