[Mathematics and Physics – Ideal and Actual Worlds]: Mathematics is often called a language that describes nature or its changes or movements, and is also used as a tool to model logic and judge their right and wrong.

Is mathematics simply an artificial thing created by human beings? Even its representing symbols are artificial, is a concept or a logic inherent? If it is inherent, does it exist only together with nature, or does it exist more priory and originally than nature?

The various symbols and expressions used in mathematics must have been defined by humans. But it can not be said that the concepts and theories in it are also artificial things created by humans.

For example, when describing a natural law with an expression, the law can not be said to have been created by a human being, and when any right logic is expressed by a formula, the logic itself can not be said to have been created by man.

The law of nature – if the law is right, regardless of whether it is good or bad to human beings – is a description of mathematical modeling of the causal relationship that the same phenomenon always occurs in the same condition in the physical world. It is a logical problem that human beings can not intervene.

The main task of physicists is to find these laws or principles that exist in nature. And engineers – even though they find such laws or principles themselves – make them available as machines or products mediated through matter, so that the found laws or principles can be used in real life.

However, the individual cases that occur in nature or are applied in real life correspond to special cases of actual cases that – can be expressed as numerical values – are infinitely possible in these mathematically modeled natural laws and principles. Thus, realization in nature and everyday humans life can be said to be the realization of some cases of mathematics based on matter.

In this case, if the mathematical logic is wrong, the behavior of the manufactured product will not work consistently with the corresponding principle as it is predictable, and – especially for satellite or missile – remote observing, monitoring, control, adjusting, management and maintenance will not be possible.

The question is that if there is a perpetual logic that human beings have found or thought out through thinking, even not in nature, that is always judged to be right for anyone who thinks right, transcending the physical space and time, anywhere, anytime, then who made the logic and how can it always remain right?

Examples of such logic include the consequences of reasoning proven through various pure mathematical axioms or rational thought processes. As an example, the logic of the most basic arithmetic rules (addition, subtraction, multiplication and division) has been found and used separately in different parts of the world in the past when traffic and communication never developed, and the logic that the physical world is finite and always changes has never been denied and confirmed right in natural daily life.

Thus, mathematics, logic, and philosophy are more primitive than physics, and they are independent of the physical world – or have no relevance to physics – and have been able to study independently. Concept or right reason has been felt to exist before the physical world.

Plato felt mathematics as the domain of the Idea world and the God’s world. Mathematics deals with infinity, but physics rejects infinity. This is because the world of matter is fundamentally a finite world, and mathematics can handle any logical world away from the physical world.

For example, the theorem that the sum of two sides is greater than the other side in a triangle – corresponding to the pure concept of logic that the straight line distance is shorter than a certain curve distance – is right in the ideal world, but it is impossible to realize it perfectly in the actual world where refraction occurs even in light.

Repeating the process of bisecting each line of the oblique sides and attaching them to the base side on an equilateral triangle in an infinite number of turns, results in the final that the sum of the two oblique sides becomes equal to the base, and the above theorem becomes wrong. This means that it is not possible in the actual world to repeat the bisecting without any loss and infinitely.

The Pythagorean theorem that the square of the base of a right triangle plus the square of the height equals the square of the hypotenuse, and the mathematical formulas that determine the circumference or width of a circle are also ideal cases. In he actual world, we can not make perfectly right triangles or circles without error.

This is why some industrial products (eg, construction, machinery, electronics, etc.) used in the actual world can not be completely perfect, and – this is because the physical world is ceaselessly and interchangingly changing as a whole – have limited performances and life spans. And we may understand that the fact that the natural exponents and cosmological constants (eg, the ratio of the circumference of a circle to its diameter π, natural exponent e, light speed c, Planck constant h,

[Difference between mathematics and physics in 0 and infinite handling]: Physics deals with the physical world. And mathematics deals with the logic world. Physics deals with a world in which material existence exists, and mathematics deals with a logical world that may not require any material existence.

Therefore, in physics, zero (0) and infinity are not handled. The physical world treats the change mainly on the assumption that there exist somewhat physically in finite space-time, and it does not handle the case that existence is infinity. In other words, physics deals mainly with the existence of certain physical beings in a finite world.

However, mathematics can treat zero (0) without physical existence, and also treat infinity. The world without a physical being is a primordial world, and the world of infinity means to contain all possible cases.

Thus, physics corresponds to special cases of mathematics and can be explained based on mathematics. In other words, the laws of physics appear as mathematical expressions in special cases in various cases in mathematics. This shows that the physical world is a realization of a part of the logical world.

(Extracted from OnCharm Lee’s book “Humans & Truth”)

See http://www.dialectics.org : division by 0 [renamed ‘empty zero’] is readily performed, and yields a finitary, ‘quanto-qualitative’ value [called ‘full zero’], in the axiomatic system of the ‘Mu’ dialectical arithmetic. This arithmetic also enables a fully arithmetical, fully algorithmic, fully ideographical expression of “dimensional analysis”, instead of the historically retrograde, “syncopated”-algebraic form presently prevalent, e.g., (1)[gm.], (2)[cm.], (3)[sec.], etc.

In this ‘Mu’ dialectical arithmetic, ‘quanto-qualitative’ subscripts/denominators behave analogously to the conventional superscripts extracted by logarithm functions: script-level multiplications translate to subscript-level, non-amalgamative additions; script-level divisions translate to subscript-level subtractions.

Dynamical system state variable and control parameter ‘arithmetical quantifiers’ can be expressed in forms fully ‘‘‘qualified’’’ by ‘metrical arithmetical qualifier meta-numerals’, and by ‘ontological arithmetical qualifier meta-numerals’, in this ‘Mu’ system of arithmetic.

As a consequence, dynamical “singularities”, arising in finite time, resulting from division by zero in the dynamical differential equation itself, and/or in its solution-function, can be ‘semantified’ — rendered in their real, Gödelian-like meaning — in a way which naturally avoids ‘infinity residuals’, i.e., the ‘infinitely erroneous’ values that result from interpreting “singularities” as signifying physical “purely”-quantitative infinities.

Dynamical singularities typically signify a change in the physical ontology that the dynamical equation models — a change that goes beyond what the language and ‘‘‘ontological commitments’’’ of the model specification, implicit or explicit, can encompass. That is, they signify an ‘ontological revolution’.

Thus, the arising of the ‘full zero’ value ‘meta-numeral’ is typically a sign-post that the dynamical trajectory has reached a point where such ontological incompleteness of the model specification becomes explicitly manifest.

‘Arithmetical qualifiers’ are not a new ‘ideo-phenomenon’ in the history of human cognitions regarding numbers, or «arithmoi». In the prelude to cuneiform in ancient Mesopotamia, ideograms representing both ‘ontological qualifiers’ and ‘metrological qualifiers’, as well as their ‘‘‘quantifiers’’’, eventually emerged, as documented in the work of Dr. Denise Schmandt-Besserat.

The circa 250 C.E. proto-algebraic text by Diophantus of Alexandria, entitled “«Arithmetiké»”, which pioneered the movement toward symbolic or ideographical algebra, featured a syncopated proto-symbol, ‘M^o’, short for «Monad», or “unit”, which denoted a qualitative unit of a given kind of object, or, indifferently, of a metrological unit — i.e., of a “qualitative unit” in either case.

In Western mathematics after the Renaissance, the presence of ‘arithmetical qualifier meta-numerals’ in mathematical expressions entered a long eclipse and elision, in favor of “purely quantitative” ideographies — except for the unrecognized presence of ‘metrological unit qualifiers’ in “syncopated” form, e.g., units of measurement like “sec.”, “gm.”, and “cm.”, when expressing “physical quantities”.

Later, an immanent re-emergence of a new kind of ‘arithmetical qualifiers’ ensued, with the discovery that the square root of negative unity could be represented by the so-called “imaginary unit”, i, with rich mathematical consequences, and with the subsequent development of the “hypernumbers” involved in, e.g., the Hamilton Quaternions, the Cayley/Graves Octonions/Octaves, and the “Grassmann [hyper]numbers”, all of which involve “qualitative units”. This kind of ‘arithmetical unit qualifiers’ involves the formation of arithmetical “qualitative units” that represent different basic forms of motion in arithmetical — analytic-geometrical — space.

“Vector” symbols also represent something beyond the “purely quantitative”, combining “scalar” quantity with ‘directionality’, or orientation.

Likewise, the recent development of set theory, and of the various “orders” of predicate calculus in mathematical logic, all involve the ideographical symbolization of ‘‘‘idea-objects’’’ that are not “pure quantities”, e.g., that represent “qualities”.

After visiting the land of Pythagoras and Archimedes, I realized the importance of this 14k stamp and this drawplate and mandrel. I don't know why there was no scratch test or chemical test, but drawing 22 gauge wire from an ingot is pretty difficult. Then, I bought some binoculars for astronomy read up on horology and astrology, and read some occult from al- Majriti. I don't see a richer pastime.

## 13 comments

[Mathematics and Physics – Ideal and Actual Worlds]: Mathematics is often called a language that describes nature or its changes or movements, and is also used as a tool to model logic and judge their right and wrong.

Is mathematics simply an artificial thing created by human beings? Even its representing symbols are artificial, is a concept or a logic inherent? If it is inherent, does it exist only together with nature, or does it exist more priory and originally than nature?

The various symbols and expressions used in mathematics must have been defined by humans. But it can not be said that the concepts and theories in it are also artificial things created by humans.

For example, when describing a natural law with an expression, the law can not be said to have been created by a human being, and when any right logic is expressed by a formula, the logic itself can not be said to have been created by man.

The law of nature – if the law is right, regardless of whether it is good or bad to human beings – is a description of mathematical modeling of the causal relationship that the same phenomenon always occurs in the same condition in the physical world. It is a logical problem that human beings can not intervene.

The main task of physicists is to find these laws or principles that exist in nature. And engineers – even though they find such laws or principles themselves – make them available as machines or products mediated through matter, so that the found laws or principles can be used in real life.

However, the individual cases that occur in nature or are applied in real life correspond to special cases of actual cases that – can be expressed as numerical values – are infinitely possible in these mathematically modeled natural laws and principles. Thus, realization in nature and everyday humans life can be said to be the realization of some cases of mathematics based on matter.

In this case, if the mathematical logic is wrong, the behavior of the manufactured product will not work consistently with the corresponding principle as it is predictable, and – especially for satellite or missile – remote observing, monitoring, control, adjusting, management and maintenance will not be possible.

The question is that if there is a perpetual logic that human beings have found or thought out through thinking, even not in nature, that is always judged to be right for anyone who thinks right, transcending the physical space and time, anywhere, anytime, then who made the logic and how can it always remain right?

Examples of such logic include the consequences of reasoning proven through various pure mathematical axioms or rational thought processes. As an example, the logic of the most basic arithmetic rules (addition, subtraction, multiplication and division) has been found and used separately in different parts of the world in the past when traffic and communication never developed, and the logic that the physical world is finite and always changes has never been denied and confirmed right in natural daily life.

Thus, mathematics, logic, and philosophy are more primitive than physics, and they are independent of the physical world – or have no relevance to physics – and have been able to study independently. Concept or right reason has been felt to exist before the physical world.

Plato felt mathematics as the domain of the Idea world and the God’s world. Mathematics deals with infinity, but physics rejects infinity. This is because the world of matter is fundamentally a finite world, and mathematics can handle any logical world away from the physical world.

For example, the theorem that the sum of two sides is greater than the other side in a triangle – corresponding to the pure concept of logic that the straight line distance is shorter than a certain curve distance – is right in the ideal world, but it is impossible to realize it perfectly in the actual world where refraction occurs even in light.

Repeating the process of bisecting each line of the oblique sides and attaching them to the base side on an equilateral triangle in an infinite number of turns, results in the final that the sum of the two oblique sides becomes equal to the base, and the above theorem becomes wrong. This means that it is not possible in the actual world to repeat the bisecting without any loss and infinitely.

The Pythagorean theorem that the square of the base of a right triangle plus the square of the height equals the square of the hypotenuse, and the mathematical formulas that determine the circumference or width of a circle are also ideal cases. In he actual world, we can not make perfectly right triangles or circles without error.

This is why some industrial products (eg, construction, machinery, electronics, etc.) used in the actual world can not be completely perfect, and – this is because the physical world is ceaselessly and interchangingly changing as a whole – have limited performances and life spans. And we may understand that the fact that the natural exponents and cosmological constants (eg, the ratio of the circumference of a circle to its diameter π, natural exponent e, light speed c, Planck constant h,

[Difference between mathematics and physics in 0 and infinite handling]:

Physics deals with the physical world. And mathematics deals with the logic world. Physics deals with a world in which material existence exists, and mathematics deals with a logical world that may not require any material existence.

Therefore, in physics, zero (0) and infinity are not handled. The physical world treats the change mainly on the assumption that there exist somewhat physically in finite space-time, and it does not handle the case that existence is infinity. In other words, physics deals mainly with the existence of certain physical beings in a finite world.

However, mathematics can treat zero (0) without physical existence, and also treat infinity. The world without a physical being is a primordial world, and the world of infinity means to contain all possible cases.

Thus, physics corresponds to special cases of mathematics and can be explained based on mathematics. In other words, the laws of physics appear as mathematical expressions in special cases in various cases in mathematics. This shows that the physical world is a realization of a part of the logical world.

(Extracted from OnCharm Lee’s book “Humans & Truth”)

Thanks for this excellent upload

Since mathematics is the science of order and logic is the science of making correct inferences then how can they be related?

What an enjoyable, wide-ranging lecture. Thank you.

Excellent! Read Ray Monk's biography on Oppenheimer, you can get it through Amazon, now in PB.

Interesting… in the Cohen Brothers flick 'A Serious Man', one character purports that, "Mathematics is the art of the possible."

See http://www.dialectics.org : division by 0 [renamed ‘empty zero’] is readily performed, and yields a finitary, ‘quanto-qualitative’ value [called ‘full zero’], in the axiomatic system of the ‘Mu’ dialectical arithmetic. This arithmetic also enables a fully arithmetical, fully algorithmic, fully ideographical expression of “dimensional analysis”, instead of the historically retrograde, “syncopated”-algebraic form presently prevalent, e.g., (1)[gm.], (2)[cm.], (3)[sec.], etc.

In this ‘Mu’ dialectical arithmetic, ‘quanto-qualitative’ subscripts/denominators behave analogously to the conventional superscripts extracted by logarithm functions: script-level multiplications translate to subscript-level, non-amalgamative additions; script-level divisions translate to subscript-level subtractions.

Dynamical system state variable and control parameter ‘arithmetical quantifiers’ can be expressed in forms fully ‘‘‘qualified’’’ by ‘metrical arithmetical qualifier meta-numerals’, and by ‘ontological arithmetical qualifier meta-numerals’, in this ‘Mu’ system of arithmetic.

As a consequence, dynamical “singularities”, arising in finite time, resulting from division by zero in the dynamical differential equation itself, and/or in its solution-function, can be ‘semantified’ — rendered in their real, Gödelian-like meaning — in a way which naturally avoids ‘infinity residuals’, i.e., the ‘infinitely erroneous’ values that result from interpreting “singularities” as signifying physical “purely”-quantitative infinities.

Dynamical singularities typically signify a change in the physical ontology that the dynamical equation models — a change that goes beyond what the language and ‘‘‘ontological commitments’’’ of the model specification, implicit or explicit, can encompass. That is, they signify an ‘ontological revolution’.

Thus, the arising of the ‘full zero’ value ‘meta-numeral’ is typically a sign-post that the dynamical trajectory has reached a point where such ontological incompleteness of the model specification becomes explicitly manifest.

‘Arithmetical qualifiers’ are not a new ‘ideo-phenomenon’ in the history of human cognitions regarding numbers, or «arithmoi». In the prelude to cuneiform in ancient Mesopotamia, ideograms representing both ‘ontological qualifiers’ and ‘metrological qualifiers’, as well as their ‘‘‘quantifiers’’’, eventually emerged, as documented in the work of Dr. Denise Schmandt-Besserat.

The circa 250 C.E. proto-algebraic text by Diophantus of Alexandria, entitled “«Arithmetiké»”, which pioneered the movement toward symbolic or ideographical algebra, featured a syncopated proto-symbol, ‘M^o’, short for «Monad», or “unit”, which denoted a qualitative unit of a given kind of object, or, indifferently, of a metrological unit — i.e., of a “qualitative unit” in either case.

In Western mathematics after the Renaissance, the presence of ‘arithmetical qualifier meta-numerals’ in mathematical expressions entered a long eclipse and elision, in favor of “purely quantitative” ideographies — except for the unrecognized presence of ‘metrological unit qualifiers’ in “syncopated” form, e.g., units of measurement like “sec.”, “gm.”, and “cm.”, when expressing “physical quantities”.

Later, an immanent re-emergence of a new kind of ‘arithmetical qualifiers’ ensued, with the discovery that the square root of negative unity could be represented by the so-called “imaginary unit”, i, with rich mathematical consequences, and with the subsequent development of the “hypernumbers” involved in, e.g., the Hamilton Quaternions, the Cayley/Graves Octonions/Octaves, and the “Grassmann [hyper]numbers”, all of which involve “qualitative units”. This kind of ‘arithmetical unit qualifiers’ involves the formation of arithmetical “qualitative units” that represent different basic forms of motion in arithmetical — analytic-geometrical — space.

“Vector” symbols also represent something beyond the “purely quantitative”, combining “scalar” quantity with ‘directionality’, or orientation.

Likewise, the recent development of set theory, and of the various “orders” of predicate calculus in mathematical logic, all involve the ideographical symbolization of ‘‘‘idea-objects’’’ that are not “pure quantities”, e.g., that represent “qualities”.

For further details, see: http://www.dialectics.org/dialectics/Applications.html , starting with — http://www.dialectics.org/dialectics/Applications_files/Glossary,E._D._Notation_Definition,'Full_Zero'_Sign,Sheet_1_of_7,19APR2015.jpg .

My blog: https://feddialectics-miguel.blogspot.com/2017/08/division-by-zero-in-mu-dialectical.html

where is the transcript?

like a cut out of a piece of cardboard, math is a man made stencil where you can look through and find pieces of reality.

Are you the guy who ordered the 22 gauge wire and needed the 14k test?

After visiting the land of Pythagoras and Archimedes, I realized the importance of this 14k stamp and this drawplate and mandrel. I don't know why there was no scratch test or chemical test, but drawing 22 gauge wire from an ingot is pretty difficult. Then, I bought some binoculars for astronomy read up on horology and astrology, and read some occult from al- Majriti. I don't see a richer pastime.

I hate math im bad at it whyyyyyy is this on YouTube I mean wtf but I will try I think maybe probably I don't know

Excellent!