Entropy gives me much.

For this time, I want to blog about the relation between math and physics of human beings.

The second law of thermomdynamics is that in general the total entropy of any system will not decrease other than by increasing the entropy of some other system. (from wikipedia http://en.wikipedia.org/wiki/Entropy)

So what is entropy? Entropy is a theromodynamic property that is the measure of a system's thermal energy per unit temperature that is unavailable for doing useful work. Perhaps the most familiar manifestation of entropy is that, following the laws of thermodynamics, entropy of a closed system always increase and inheat transfer situation, heat energy is transferred from higher temperature components to lower temperature components. (from wikipedia Entropy)

It's like gravity. An article on a higher position is moving to a lower position if there is no obstraction of friction or resistance. We know the gravitational acceleration, which can be described as quadratic function.  Here is the brigde between math and physics.

Math has a long history more than 2000 years, but it can be said that physics was born from Sir Isacc Newton in 17 century and math had been so powerful to establish the physics system.  Despite of this fact, I think that it would be physics that can include math.  The reason is that human beings discovered and created the math world, but math can't make human.  There must be a possibility that physics can rule chemistry and chemistry has an ability to depict how biology works, it means that physics can answer the question who we are and where we are going to.

Let's create a new society according to the nature of this world.

Math can be a thread of light as Language is.

We are sometimes cheered up by some words and phrases.  Language can be a thread of light to show our way forward to our goals.  Why can't math or numbers?

So the first and the final question is that what is the difference of words and numbers?  Thinking about them, there would be no critical difference in the region of brain, but the meanings are obviously different.  Then let's take a look for the case of coincidence or lucky. By describing the situation by language, someone happens to meet his acquaintance on a corner of a city.  In the brain, There may be a certain impact of the event.  Unimaginable but meaningful combination has a surprised power.  Each numbers can be combined by addition, subtraction, multiplication and division.  You know only calculation never gives us any surprise but just annoying.  But as Jigsaw "puzzle" can give us some pleasure by its completion, well-tuned numbers calculation can also have a possibility to be pleased.

What I want to say here is that as mentioned above, math or numbers can be a thread of light or energy by well-tuned question.  Furthermore to be happy may be Tuning yourself to keep balance.  If we can tuning something by proper numbers, which can be called a system, our technical level will dramatically increase. 
Math is not a direct tool and so is language.  People who have made a success may know something special, but we, all individuals are also special respectively. So the real key to success may be quite different from each others.  The indirection nature of math and language have common meanings which are so powerful.  These are our treasures remained unknown, despite we are unconsciously using them.

Let's continue the journey from ancient to future, which is about happiness by searching and developing our life.

Now let me introduce again and again about Math apps on Google Play.  Differentiation for points of max and minimum extreme is released on free version.  http://play.google.com/store/apps/developer?id=MathContext

Thank you for reading. I hope that we will live in the sucessed society by our cooperation.

You are a tree.

When you see a tree in a forest, you can't see the whole part of the forest by your own eyes without tool like camera.  It is obvious that you are in the forest, and to see the forest needs a higher position outside of the forest to look down.

You are a tree in your forest called society.  Of course I also a tree in my society.  Furthermore everyone is a part of the society.  But at the same time, you are a forest of your body.  Here is the essence of life.

Let me quote my favorite story "Alchemist" written by Paulo Coelho.  His blog http://paulocoelhoblog.com/ is actually, definitely and no-need-to-explainly more sophisticated and powerful.  But going my own way is much more important than just getting his points.  I also hope you reading this blog are on your way and cooperation between us beyond the physical distance will drive our own ways forward respectively.  Now back to the Coelho's quote;

"Well, there is only one piece of advice I can give you," said the wisest of wise men. "The secret of happiness is to see all the marvels of the world, and never to forget the drops of oil on the spoon."

The spoon of  oil drops is handed by you.  This situation may be only in having the oil drops like taking medicine or soup.  But if you do something with behavior of handling the spoon with oil drops, the action can be totally different from doing something only, because you need much more care for the spoon additionally. 

Concentrating on the spoon requires rest of all things.  It looks like that when you see a tree, you lost the vision of the forest.

Math is a world of numbers.  For example, when you see number of 2, you may lose the number world.  Considering the Riemann Hypothesis about prime numbers, we have not seen the whole image of the world, despite we have already achieved to see the whole sphere of the earth from space.  But math has its own history over 2000 years and on the course, it can be said that physics was born from Math.

To cooperate is difficult or sometime impossible.  To fly like a plain was impossible only before 100 years ago.  Understanding how thing works is powerful.  Math can be a tool for getting an index of what is going on. 

Here is my new math program of differentiation to find the point of extreme.  http://tobea.sakura.ne.jp/mathcontext/dif.html

Math app for calculation, geometry and linear function is now on Google Play.
https://play.google.com/store/apps/developer?id=MathContext

Thank you for reading.  Now I totally forget the spoon of drops.  Changing myself can lead to a different place whether it is good or bad.  Needless to say, I am challenging to find my best, and you too.






 

Force of Pen and Power of Sword

It is frequently said that Pen is mighter than Sword. As you of course know, you can't win the battle with a real pen as a sword toward a real sword.  What is the point of the quote?

Both pen and sword are used by human being.  If you use more stronger tool like a gun rather than sword, you will win.  Then, what is the strongest weapon?

It may be an intelligence.  That is why the pen is mighter than sword.  So what is an intelligence?  I think, as blogging before, that "way", "course" or "path" is the one which is dependent on time and its existence in brain widely in physical body.

Then how to improve an intelligence to be stronger than anything else?  It is the intelligence that improve an intelligence. The recrusivity cost a huge energy to construct the structure of the loop, but once you make it properly, the technique is reusable and it can save energy.

Math can be an intelligence.  Furthermore Math can be the intelligence to brush your intelligence up by thinking recrusively.  Of course there are another intelligence, like logic using language.  But why not to lose the chance to earn the powerful tool, math using numbers and notes.

Now I am introducing you to Math Apps on Google Play.  Please check them out! http//play.google.com/store/apps/developer?id=MathContext


Thanks for reading and let's get the intelligence!

Inside or Outside of You?

When you do math, what happens?

You see a quetion and begin to think about it as compared with what you have learned.  Then sometimes you reach the answer and occasionally lose your way.  At the end, whether your output answer is correct or wrong, the course to the answer is from the inside of you. Let us think about the course at the inside, especially in brain, and widely in body.

Any examination or test requires the result, which is determined by others, so your thinking about questions must be output from your inside.  We have met these kind of situation so many times that we care so much about our outputs.  Of course, the outputs are from inside which can't been clearly seen, compared with the outputs. So brushing your insde up is definetly important, but the true step is ambiguous except the step of keeping practice.

We are bound to miscalculate. But the probability of miscalculation can be decreased by training. Math can be a training, not only for calculation but thinking widely about this world.  Math field seems too narrow that many students are bored to learn.  If the door of Math is calculations, for some students the door is so heavy, but a training can make the door lighter.  When you feel that something has just become lighter, it is the pleasure that drive you forward and into good spiral.

I am now challenging to give you the pleasure by following the course to the answer in these app.  They are far from completion, but I hope you feel something. Please check them out! https://play.google.com/store/apps/developer?id=MathContext

Thank you for reading. Have a nice your course of life.

Thinking about Mathematical Model of Thinking

A mathematical model is a description of a system using  mathematical concept and language. (from wikipedia http://en.wikipedia.org/wiki/Mathematical_model ) The mathematical model is constructed by human brains, but our thoughts can not be modeled as mathematical system.   On the contrary, logic by mother language is so powerful to describe our thoughts.   Let's thinking about mathematical and logical model of thinking.

As mentioned above, thinking itself uses logic, but logic itself is not mathematically restricted.  Furthermore creativity, imagination or humor seems non-logic one.

To see this world, the earth goes around sun.  The air's elements are nitrogen, oxygen and carbon and so on.  Even plants, animals and micro-organisms are formed from cells which are constructed by molecules.  All of them are in the field of science.  So thinking must be based on mathematical models, but we cannot have found out it.  But considering prime numbers model,  Riemann hypothesis remains unsolved, it is no doubt to solve the thinking model by mathematical models.

Now thinking about solved question, Poincare conjecture, the way to the answer gives us some points.
1.  From Geometrization conjecture (http://en.wikipedia.org/wiki/Geometrization_conjecture ), any world, 3-dimension space, i.e. 3-manifolds can be classified into only 8 types of construct.  For the mathematical model of thinking, classification can be useful.

2.  It is differential geometry or Ricci flow equation that resolved the topological question, Poincare conjecture.  For the model, we can sometimes uses topology, logic model, and in another occasion, differential geometry, mathematical model.  "Double standard" or multi-standard is much more powerful, if the standards are controlled.

Anyway thinking deeply beyond a language needs mathematics.  If you hate math in class, it is like dropping money.  As you know, you don't actually drop some money by hating math, and sometimes to earn something requires to lose others.  But math can be a tool to see the world from another angles.  Please check out math apps. 
http://play.google.com/store/apps/developer?id=MathContext

Thanks for reading.

Observation and Measurement

When you see an object, you can't see it objectively.  You can't see anything without your own subjective view, even if it is scientific data.  Further more, when you feel that you have an objective mind, it becomes more difficult to have suspicion about your vision.

Any observation must be based on some measurement.  We know that our sense is depend on our emotion which is moved or moves time by time. So the proper measurement is necessary, but there are no objective view as mentioned above.

Therefore objective or scientific is important.  Math is tool for objective measurement in its field.  But the field is too narrow compared with the real world.

It's like darkness.  But recognition of the darkness can be a thread of light.  Math can be true to "touch" the light.  Let us light out this world again with a bland new stuff.  Concerning Math, please check these apps. http://play.google.com/store/apps/developer?id=MathContext

Differential geometry and topology

What is this world? How can we see it from which point of view?

When you see, hear, touch, smell, taste, or feel this world, mather language is so powerful to draw the experience. A color of red can be related to anything which you have memorized with the color.  From the point of view of common sense, a color of red is blood, sun, passion, danger or stop of trafic light.  So as mentioned above,  a sense of this world is usually described by mother languages.

As you know, there are many mother languages in the world and the meaning is different from each others as well as the difference of individuals even in the same language speaker. 

In same world, there are mathmatics, physics, biology and science. To see or feel this world by observation can have many problems about the observation tool.

Math has its history over 2000 years, and Sir Issac Newton who wrote The Principia, one of most important scientific book, developped differetial and integral calculs in 17 century.

Once you recognize something as what you think, it needs a huge amount of energy to amend the concept, which may be one of human brain nature. In 20 century, as the Newton's world had became familier with scientist and the concept of differetial geometry was systemized, topology was born.  It is amazing that new concept changes the world, even though this world is always changing under the principle of entropy.

Now for me, I would very like to develop my Apps of Math to see and feel how this world can be. It would not be a teacher, but programs that lead people to next paradime.

Thank you for reading, and please check http://play.google.com/store/apps/developer?id=MathContext

Hellow world! The first principle.

It must be the turth that the very first principle is, literaly ironical, second  law of thermodynamics in which the total entropy of any system will not decrease other than by increasing the entropy of some other system.  So, in a system isolated from its environment, the entropy of that system will tend not to decrease, usually increase. ( Entropy Wikipedia http://en.wikipedia.org/wiki/Entropy) Considering the fact, I am very very pleased that I am now liveing, despite of the principle.