Here is a short, yet shot in High Definition HD, movie, inside view of Subaru Boxer 3.6 Liter DOHC Engine. Probably very educational for engine designers and thermodynamics fans. My previous post talks about actual physical principles behind internal combustion engine, http://goo.gl/JV0Tl.

## Friday, February 18, 2011

## Wednesday, February 16, 2011

### Mathematics and other fields and why math can be an independent discipline

Math took off as a separate discipline when thinkers realized that 2 + 3 = 5 no matter what are you counting. Then, axioms came into light, setting math on a firm footing of logical thinking. But, when you use math in real life situations or when you apply math in various disciplines, you do not go through axioms and theorems, not even proofs, at least until later. You state something, like Coulomb's Electric Force formula or Newton's Law of Gravitation, but, what are you stating, what is it, from the mathematical point of view?

You stated theorems, or premises, or postulates, directly provable from ZFC axioms! From inside math it looks trivial. But, the actual selection, what postulate, assumption, premise, you chose, as your starting point, really matters a lot from the point of view of discipline that stipulated that formula. Axioms can not tell you which postulate will be of special interest to you. Axioms just serves to tell you what operations and concepts you have at your disposal. And it's not much. You have a concept of a set, and few operations on sets, and that's, essentially, it!

Once you see, note, distinguish, things that are common to many other concepts,or objects, perhaps some common property, there is a big chance that that property and relationships between those properties, can take off as a separate discipline, with its own axioms and postulates, premises, theorems (and I am not talking only about math here!). World#1, is the world that has those objects with common properties between them. These common properties and their relationships, can be abstracted from World#1 into separate (possibly and desirably axiomatic) system. Then, World#1 will dictate the genesis of postulates and premises in that abstracted (axiomatic) system, let's call it World#2.

The postulates in World#2 can be generated from two sources. From World#1, with all descriptions and explanations using World#1's language, or, from World#2 axioms! Example in math and physics. Math expression y = ax^2 can be obtained directly from fundamental axioms of mathematics, which just tell you that you can, you are allowed, to do that. Hence, you can just chose to generate a function y = ax^2, without any further explanation. But, then, in physics, y = ax^2 can be E = mc^2 which required Nobel Prize way of thinking which objects to put in place of "a" and "x" in the formula y = ax^2. Here in physics, it matters what is counted and not only the mathematical form.

Hence, y = ax^2 can come from physics, engineering, economics, finance, and, while in math it is only counts what matters, in all those disciplines matters what you actually counted, or measured. The subject of kind or nature of countable objects, i.e. what is counted and reasons they are counted doesn't enter mathematics. Math only sees the count and what you require to do with the counts, namely you squared x, then multiplied it by a. Was it money (finance), was it production output (economics) or speed of light and mass (physics) math does not care. It will just deal with counts and give you result back after the multiplication.

You can read more "How math can be applied to so many different fields and how we can use math in real life".

Here are more links you might like as well:

You stated theorems, or premises, or postulates, directly provable from ZFC axioms! From inside math it looks trivial. But, the actual selection, what postulate, assumption, premise, you chose, as your starting point, really matters a lot from the point of view of discipline that stipulated that formula. Axioms can not tell you which postulate will be of special interest to you. Axioms just serves to tell you what operations and concepts you have at your disposal. And it's not much. You have a concept of a set, and few operations on sets, and that's, essentially, it!

Once you see, note, distinguish, things that are common to many other concepts,or objects, perhaps some common property, there is a big chance that that property and relationships between those properties, can take off as a separate discipline, with its own axioms and postulates, premises, theorems (and I am not talking only about math here!). World#1, is the world that has those objects with common properties between them. These common properties and their relationships, can be abstracted from World#1 into separate (possibly and desirably axiomatic) system. Then, World#1 will dictate the genesis of postulates and premises in that abstracted (axiomatic) system, let's call it World#2.

The postulates in World#2 can be generated from two sources. From World#1, with all descriptions and explanations using World#1's language, or, from World#2 axioms! Example in math and physics. Math expression y = ax^2 can be obtained directly from fundamental axioms of mathematics, which just tell you that you can, you are allowed, to do that. Hence, you can just chose to generate a function y = ax^2, without any further explanation. But, then, in physics, y = ax^2 can be E = mc^2 which required Nobel Prize way of thinking which objects to put in place of "a" and "x" in the formula y = ax^2. Here in physics, it matters what is counted and not only the mathematical form.

Hence, y = ax^2 can come from physics, engineering, economics, finance, and, while in math it is only counts what matters, in all those disciplines matters what you actually counted, or measured. The subject of kind or nature of countable objects, i.e. what is counted and reasons they are counted doesn't enter mathematics. Math only sees the count and what you require to do with the counts, namely you squared x, then multiplied it by a. Was it money (finance), was it production output (economics) or speed of light and mass (physics) math does not care. It will just deal with counts and give you result back after the multiplication.

You can read more "How math can be applied to so many different fields and how we can use math in real life".

Here are more links you might like as well:

- Real world examples for rational numbers, for kids
- Math and its relationship with real world
- How math can be applied to so many different fields?
- Where the graphs in mathematics and physics come from?
- Tweets about math, physics, and how to approach math calculations
- One insight about mathematical axioms, logic and their relation to other disciplines
- How the ideas are born and notes on creative thinking
- Mathematics Axiomatic Frontier
- Why math can be an independent discipline?
- More on creative thinking, math, innovations, physics, emotions
- Comparison between making movies and math and physics
- More tweets about math
- Domains of math applications and math development
- Where all those number series in math are coming from?
- How to understand the role of math in economics, physics, engineering, and in other fields

Labels:
applied math,
creative thinking,
fiction,
fiction writing,
idea,
ideas,
innovations,
inspiration,
math,
physics,
thoughts

## Tuesday, February 15, 2011

### More on creative thinking, innovation, art, math, physics, emotions

Invention is picking right premises from a real world axiomatic systems. How we pick them? By intuition, emotion, feel, trial and error.

We sometimes use our emotions, what we value, to make decisions. What are the decisions picked? They are premises in well defined axiomatic systems of the real world.

Intensity of emotions can be quantified. Intensity exists. It's a different story why we can't show exact biochemistry process taking place.

Our emotions come from our values. Also, our values come from our emotions. The two neural systems provide continous feedback to each other.

It is beyond me why the concept of a function, in math, has to be introduced so late in education. It's just pairing of numbers....

How to Easier Understand the Role of Mathematics in Physics, Economics, and Other Fields - http://tiny.cc/ji8fw #math #physics

Premises in math are theorems in fields in which math is applied. That's why, even math is built from axioms, it can link with real world.

I like when a physicist postulates! Using fancy word "postulate" to say "I have no idea where this formula comes from, but it might work!"

Axioms in one system are theorems in the other.

Axiom: your home light switch can be ON or OFF. Theorem 1: You switched to ON. Theorem 2: You switched to OFF. Proof: directly from Axiom.

From "About..." section of book "Mathematical Physiology": Of interest both to applied mathematicians and quantitative physiologists :-)

As long as you explain students that math deals with counts only and logic applied to it can be applied eslwehere freely, it's a good start.

Math should help you to think more freely, not to prohibit your all other thoughts and thinking in order to correctly add two numbers.

I've watched a movie, I've read a book, I've listened to a song. How about I've written a book, I've made a movie, I've composed a song?

Precise logical processing in thinking is necessary but not sufficent to succeed. Assumptions must be correct and valuable.

Your brain logical unit will process anything with same accuracy, be it input from an emotional response or from strict scientific thinking.

It's hard not to be emotionally attached to your scientific thinking :)

Emotions continuously make axiomatic systems and your logical brain process it, because it only deals with raw truth values.

Sometimes emotions create an axiomatic system and then present it to your brain logical center for processing. Bad input gives bad output :)

Your brain has amazing logical mechanism that can process any axiomatic system presented to it. That's why car salesman can sell you a car!

Again they made a movie from all the things you already know and you are aware of. but again you failed to link them in that particular way.

Stand-up comedian may not make more logical connections than a good mathematician, but, impact of result is much greater. Chose right links.

While repeatedly asking "Why?" can eventually bring you to quantum physics, asking "How I can link things " will lead you to new inventions.

One postulate in logic can be interpreted in billion ways.

I have a strong feeling about that axiomatic system.....

Statement ''you might have a chance'' is better than ''you never know''.

We sometimes use our emotions, what we value, to make decisions. What are the decisions picked? They are premises in well defined axiomatic systems of the real world.

Intensity of emotions can be quantified. Intensity exists. It's a different story why we can't show exact biochemistry process taking place.

Our emotions come from our values. Also, our values come from our emotions. The two neural systems provide continous feedback to each other.

It is beyond me why the concept of a function, in math, has to be introduced so late in education. It's just pairing of numbers....

How to Easier Understand the Role of Mathematics in Physics, Economics, and Other Fields - http://tiny.cc/ji8fw #math #physics

Premises in math are theorems in fields in which math is applied. That's why, even math is built from axioms, it can link with real world.

I like when a physicist postulates! Using fancy word "postulate" to say "I have no idea where this formula comes from, but it might work!"

Axioms in one system are theorems in the other.

Axiom: your home light switch can be ON or OFF. Theorem 1: You switched to ON. Theorem 2: You switched to OFF. Proof: directly from Axiom.

From "About..." section of book "Mathematical Physiology": Of interest both to applied mathematicians and quantitative physiologists :-)

As long as you explain students that math deals with counts only and logic applied to it can be applied eslwehere freely, it's a good start.

Math should help you to think more freely, not to prohibit your all other thoughts and thinking in order to correctly add two numbers.

I've watched a movie, I've read a book, I've listened to a song. How about I've written a book, I've made a movie, I've composed a song?

Precise logical processing in thinking is necessary but not sufficent to succeed. Assumptions must be correct and valuable.

Your brain logical unit will process anything with same accuracy, be it input from an emotional response or from strict scientific thinking.

It's hard not to be emotionally attached to your scientific thinking :)

Emotions continuously make axiomatic systems and your logical brain process it, because it only deals with raw truth values.

Sometimes emotions create an axiomatic system and then present it to your brain logical center for processing. Bad input gives bad output :)

Your brain has amazing logical mechanism that can process any axiomatic system presented to it. That's why car salesman can sell you a car!

Again they made a movie from all the things you already know and you are aware of. but again you failed to link them in that particular way.

Stand-up comedian may not make more logical connections than a good mathematician, but, impact of result is much greater. Chose right links.

While repeatedly asking "Why?" can eventually bring you to quantum physics, asking "How I can link things " will lead you to new inventions.

One postulate in logic can be interpreted in billion ways.

I have a strong feeling about that axiomatic system.....

Statement ''you might have a chance'' is better than ''you never know''.

## Friday, February 11, 2011

### Comparison Between Making Movies and Physics, Mathematics

You will rarely see the movie whose sole purpose is to explain events from the point of view of physics (not talking about educational movies or documentaries). While the events presented in the movie can be analyzed from the physics point of view, like, calculating energy, motion, mass exchange, speed, force, these kind of results are not the purpose of the movies. In the movies you will use "What..if" method to construct events in order to explore their humanistic values, their emotional, moral, ethical values.

When you want to make a movie, you don't have to wait for an invention to be actually made and available. Let your imagination go its way by assuming that some inventions and discoveries are already there, but focus on humanistic part of the story and emotional, moral, ethical messages.

A good movie has an axiomatic system of its own. Otherwise the movie will be unrealistic, incoherent, inconsistent at least. Don't think that mathematics only has axiomatic systems.

In movies you use "What..if" constructs to make a story and within it to explore human experiences and values, while in mathematics you use "what..if" to construct new propositions and theorems. However, underlying logical thinking is the same in either case of creative work.

When you want to make a movie, you don't have to wait for an invention to be actually made and available. Let your imagination go its way by assuming that some inventions and discoveries are already there, but focus on humanistic part of the story and emotional, moral, ethical messages.

A good movie has an axiomatic system of its own. Otherwise the movie will be unrealistic, incoherent, inconsistent at least. Don't think that mathematics only has axiomatic systems.

In movies you use "What..if" constructs to make a story and within it to explore human experiences and values, while in mathematics you use "what..if" to construct new propositions and theorems. However, underlying logical thinking is the same in either case of creative work.

Labels:
fiction,
fiction writing tips,
movies,
screenplay writing,
story writing

## Tuesday, February 1, 2011

### My Tweets About Innovation, Inspiration, Math, and Physics

Integration, in math, is just a summation, with limiting process added into the picture.

Engineer sees clay and wants to make a brick. Artist sees clay and wants to make a sculpture. Architects do the both.

Dare to think differently.

Integral equations have integration boundaries open, unspecified. That's the point your creativity, as an engineer, inventor should kick in.

You can not use amorphous blob of matter, put it through physics equations of aerodynamics and obtain an airfoil. It does not work that way.

Politicians can not solve your integral or differential equation but they will tell you what the solution should be.

You spend years in school to learn how to quantify an invention, without enough focus to inquire how invention is made at the first place.

The amorphous blob of matter is used to explain governing equations in aerodynamics. But it is not explained how the blob became an airfoil.

It is always more interesting what is said (calculated) than which underlying language grammar (mathematical) rules are used.

If you link Maxwell's equations, magnetic flux, EM induction, motor torque, speed with electric tattoo machine, physics lecture will rock!!

Surface and volume integrals should be explained using tattoos. They are a good example for arbitrary surface and ink volume calculation.

I think my goal is to make student understand 100% what math is about and only then to say "I don't like it".

Interesting career path: AirAsia Airliner Pilot (First Officer, right seat in cockpit) is model and Miss Thailand (2005), Chananporn Rosjan.

Length of a musical note as a mathematical property has way less significance than emotional perception of the sound (note) of that length.

Britney Spears way to create integers (as oppose to Peano Axioms): "Baby, One More Time".

In many fields you have to prove why certain calculations are necessary. In math you can just say "I can do that because axioms said I can".

In physics, we can quantify things without knowing what they are and where they come from. That's apparently called knowledge.

Most of the physics is developed using an equation for which we don't know where it comes from and why it is there. Schroedinger's Equation.

Once you start defining your own initial, boundary conditions for differential equations in physics you've entered world of real creativity.

Once you start defining your own path, volume, surface, time interval, of integration, in physics, you've entered world of real creativity.

Strict, precise Newton's Law of Gravitation does not prevent you to enter into it a completely random number for mass or distance.

While a proof, in math, has to be very logical and precise, the genesis of it is usually described as art or unexplainable inspiration.

Different arguments what belongs to a certain set, and why, are not part of math. They are things called disciplines (physics, gambling..).

It's puzzling how math can accept any given set cardinality, yet it takes so much argument to say what belongs to a set at the first place.

If you were to invent mathematics, possibly from scratch, what would you invent first? What would be the situation to start it? Which rules?

Some time ago I borrowed from a library a computer science book. Beside the problem about Dinning Philosophers somebody wrote "Why??".

You can't apply math to real life like you apply paint to the wall. But you can use math way of thinking for some real life situations.

You can supply to math any number that comes first to your mind. Math will count how many are there of each. And that's prob. distribution.

Math does not care where the numbers are coming from. It's like a cashier in supermarket. No matter what's in basket there always be a sum

Functions in math should be introduced to students as pairs of numbers (arbitrary, to start with), and not as algebraic formulae.

From math point of view, calculus could've come from simple "Let's assume that...". It was not necessary to analyze a physical process.

Some parts of mathematics relationships are developed by quantifying completely non mathematical relationships.

Coulomb did not have any idea where the electrical charges are coming from or what they are, yet he formulated powerful Coulomb's Law

Quantifying something does not mean you explained it. Newton did not have the slightest idea what gravity is yet he defined Law of Gravity.

Axiomatic systems, as a way of thinking, need not to be a part of mathematics only.

Knowledge of physics laws are only necessary but not sufficient condition to be a good, innovative engineer. Innovation is an art.

Inventors play with initial conditions, final solution ranges for force, movements, speed, and not with exact solutions of PDEs in between.

Engineer sees clay and wants to make a brick. Artist sees clay and wants to make a sculpture. Architects do the both.

Dare to think differently.

Integral equations have integration boundaries open, unspecified. That's the point your creativity, as an engineer, inventor should kick in.

You can not use amorphous blob of matter, put it through physics equations of aerodynamics and obtain an airfoil. It does not work that way.

Politicians can not solve your integral or differential equation but they will tell you what the solution should be.

You spend years in school to learn how to quantify an invention, without enough focus to inquire how invention is made at the first place.

The amorphous blob of matter is used to explain governing equations in aerodynamics. But it is not explained how the blob became an airfoil.

It is always more interesting what is said (calculated) than which underlying language grammar (mathematical) rules are used.

If you link Maxwell's equations, magnetic flux, EM induction, motor torque, speed with electric tattoo machine, physics lecture will rock!!

Surface and volume integrals should be explained using tattoos. They are a good example for arbitrary surface and ink volume calculation.

I think my goal is to make student understand 100% what math is about and only then to say "I don't like it".

Interesting career path: AirAsia Airliner Pilot (First Officer, right seat in cockpit) is model and Miss Thailand (2005), Chananporn Rosjan.

Length of a musical note as a mathematical property has way less significance than emotional perception of the sound (note) of that length.

Britney Spears way to create integers (as oppose to Peano Axioms): "Baby, One More Time".

In many fields you have to prove why certain calculations are necessary. In math you can just say "I can do that because axioms said I can".

In physics, we can quantify things without knowing what they are and where they come from. That's apparently called knowledge.

Most of the physics is developed using an equation for which we don't know where it comes from and why it is there. Schroedinger's Equation.

Once you start defining your own initial, boundary conditions for differential equations in physics you've entered world of real creativity.

Once you start defining your own path, volume, surface, time interval, of integration, in physics, you've entered world of real creativity.

Strict, precise Newton's Law of Gravitation does not prevent you to enter into it a completely random number for mass or distance.

While a proof, in math, has to be very logical and precise, the genesis of it is usually described as art or unexplainable inspiration.

Different arguments what belongs to a certain set, and why, are not part of math. They are things called disciplines (physics, gambling..).

It's puzzling how math can accept any given set cardinality, yet it takes so much argument to say what belongs to a set at the first place.

If you were to invent mathematics, possibly from scratch, what would you invent first? What would be the situation to start it? Which rules?

Some time ago I borrowed from a library a computer science book. Beside the problem about Dinning Philosophers somebody wrote "Why??".

You can't apply math to real life like you apply paint to the wall. But you can use math way of thinking for some real life situations.

You can supply to math any number that comes first to your mind. Math will count how many are there of each. And that's prob. distribution.

Math does not care where the numbers are coming from. It's like a cashier in supermarket. No matter what's in basket there always be a sum

Functions in math should be introduced to students as pairs of numbers (arbitrary, to start with), and not as algebraic formulae.

From math point of view, calculus could've come from simple "Let's assume that...". It was not necessary to analyze a physical process.

Some parts of mathematics relationships are developed by quantifying completely non mathematical relationships.

Coulomb did not have any idea where the electrical charges are coming from or what they are, yet he formulated powerful Coulomb's Law

Quantifying something does not mean you explained it. Newton did not have the slightest idea what gravity is yet he defined Law of Gravity.

Axiomatic systems, as a way of thinking, need not to be a part of mathematics only.

Knowledge of physics laws are only necessary but not sufficient condition to be a good, innovative engineer. Innovation is an art.

Inventors play with initial conditions, final solution ranges for force, movements, speed, and not with exact solutions of PDEs in between.

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