Wonderfest 2010: Is Mathematics More Art Than Science?

Euler's Equation and the Reality of Nature. =. Mr. Dexter Sinister wrote: ' I understand Euler's Identity, and I know what it means, and I know how to prove it, there's nothing particularly mystical about it, it just demonstrates that exponential, trigonometric, and complex functions are related. Given what we know of mathematics it shouldn't surprise anyone that its various bits are connected. It would be much more surprising if they weren't, that would almost certainly mean something was badly wrong somewhere.' Mr. Gary wrote: Mathematics is NOT science. Science is knowledge of the REAL world. Mathematics is an invention of the mind. Many aspects of mathematics have found application in the real world, but there is no guarantee. Any correlation must meet the ultimate test: does it explain something about the real world? As an electrical engineer I used the generalized Euler's equation all the time in circuit analysis: exp(j*theta) = cos(theta) + j*sin(theta). So it works at that particular level in electricity. Does it work at other levels, too? Logic cannot prove it. It must be determined by experiment, not by philosophizing. ====.. Thinking about theirs posts I wrote brief article: Euler's Equation and Reality. =. a) Euler's Equation as a mathematical reality. Euler's identity is "the gold standard for mathematical beauty'. Euler's identity is "the most famous formula in all mathematics". ' . . . this equation is the mathematical analogue of Leonardo da Vinci's Mona Lisa painting or Michelangelo's statue of David' 'It is God's equation.', ' It is a mathematical icon.' . . . . etc. b) Euler's Equation as a physical reality. "it is absolutely paradoxical; we cannot understand it, and we don't know what it means, . . . . .' ' Euler's Equation reaches down into the very depths of existence' ' Is Euler's Equation about fundamental matters?' 'It would be nice to understand Euler's Identity as a physical process using physics.' ' Is it possible to unite Euler's Identity with physics, quantum physics ?' ==. My aim is to understand the reality of nature. Can Euler's equation explain me something about reality? To give the answer to this question I need to bind Euler's equation with an object - particle. Can it be math- point or string- particle or triangle-particle? No, Euler's formula has quantity (pi) which says me that the particle must be only a circle . Now I want to understand the behavior of circle - particle and therefore I need to use spatial relativity and quantum theories. These two theories say me that the reason of circle - particle's movement is its own inner impulse (h) or (h*=h/2pi). a) Using its own inner impulse (h) circle - particle moves ( as a wheel) in a straight line with constant speed c = 1. We call such particle - 'photon'. From Earth - gravity point of view this speed is maximally. From Vacuum point of view this speed is minimally. In this movement quantum of light behave as a corpuscular (no charge). b) Using its own inner impulse / intrinsic angular momentum ( h* = h / 2pi ) circle - particle rotates around its axis. In such movement particle has charge, produce electric waves ( waves property of particle) and its speed ( frequency) is : c>1. We call such particle - ' electron' and its energy is: E=h*f. In this way I (as a peasant ) can understand the reality of nature. ==. I reread my post. My God, that is a naïve peasant's explanation. It is absolutely not scientific, not professor's explanation. Would a learned man adopt such simple and naive explanation? Hmm, . . . problem. In any way, even Mr. Dexter Sinister and Mr. Gary wouldn't agree with me, I want to say them ' Thank you for emails and cooperation' =. Best wishes. Israel Sadovnik Socratus. =. P.S. ' They would play a greater and greater role in mathematics - and then, with the advent of quantum mechanics in the twentieth century, in physics and engineering and any field that deals with cyclical phenomena such as waves that can be represented by complex numbers. For a complex number allows you to represent two processes such as phase and wavelenght simultaneously - and a complex exponential allows you to map a straight line onto a circle in a complex plane.' / Book: The great equations. Chapter four. The gold standard for mathematical beauty. Euler's equation. Page 104. / # Euler's e-iPi+1=0 is an amazing equation, not in-and-of itself, but because it sharply points to our utter ignorance of the simplest mathematical and scientific fundamentals. The equation means that in flat Euclidean space, e and Pi happen to have their particular values to satisfy any equation that relates their mathematical constructs. In curved space, e and Pi vary. / Rasulkhozha S. Sharafiddinov . / ===============...

Time, Space and Quantum of Light. / My opinion./ =. Can Time Exist Without Matter? 1. According to Newton the answer is " Yes" 2. According to Einstein (SRT & GRT ) the answer is " No" Who is right? Who is wrong? What is the resolution of this apparent paradox? There are four kinds of time: a) the proper (individual) time b) the planetary time c) according to SRT the ( -4D) spacetime d) and according to GRT relative time. How can we unite them? ===. The individual time and planetary time are so familiar that we rarely give them thought. Don't we know, that time for living being is limited and the planetary time is absolute for us ? It is. Maybe therefore Newton declared that time is absolute and wrote in 1687 that time " flows equably without relation to anything external". But Einstein had another opinion. He wanted to know: " Where does the conception of time come from?", " What is the essence of time?". And to explain these questions he created two theories: SRT and GRT and declared that time is relative, changeable. 1. SRT explains behavior and the proper time of light quanta /electron. Why do I think so? a) One law (postulate) of SRT says that speed of light quanta is constant c=1. Second law ( postulate ) says no another particle can reach this speed. So there are two incommensurable quantities. Is it possible to bind them together? No. I was taught at school from the first class that the incommensurable quantities cannot be compared. The connection between these incommensurable quantities is similar to the decision of a problem: "What will be if the whale attacks the elephant?" We can see whale in a ocean and elephant in a savanna, but they never meet and fight in the same " frame of reference". And the same is about light quanta and another particles. We cannot see them together in SRT. We can meet only the light quanta in SRT and no other particles in it. b) SRT was born from Maxwell's theory and it is a continuation of the electrodynamics' development . The electron is a main and single hero in the Maxwell's theory and SRT. There isn't the Maxwell's theory / SRT without electron. It is not correct to compare electron/ light quanta with another particles (protons...etc) and bodies (billiard balls, satellites, astronauts, "twins") because they cannot produce electromagnetic fields. The electron and the another particles are also incommensurable quantities. They are absolutely different objects. c) Every epoch has its own delusion. Maxwell and Boltzmann tried to explain electromagnetic fields using balls, wheels, cog-wheels, springs...etc. H. Hertz, who demonstrated the existence of the electromagnetic waves, wrote that the electromagnetic waves didn't have practice use. Etc.... Now we try to compare electron/photon ability with astronaut's and "twins' " opportunities. It is mistaken, but what to do? We do it because this is our way of cognition: " From vague wish to the bright thought". 2. So, how SRT explains time from electron/ light quanta point of view. a) When light quanta is in state of a rest its time is frozen, and its own clock shows zero. b) When photon moves with constant speed c=1 its time is also frozen, and its own clock still shows zero. c) Only when photon moves with speed c>1 its zero time changes and limited time appears. In this situation we know photon as an electron. Photon works as an electron and SRT and Lorentz transformations explain this process. d) And when , for example, electron emits from an atom and interacts with Vacuum all its parameters change. Its limited time ends and its own clock shows zero again. Now it lives in infinite/ eternal Vacuum until new incarnation, until its new work, maybe, in an atom (molecule), or in a cell, maybe, in a blade of grass or in a tree, maybe, in an animal or in a person. In another words:" We are living beings until Light quanta/ Electron is present and works in our body." Is it true? Yes, it is true. Why? Because W. Pauli in 1924 wrote:" Each quantum state in the atom is not limited of two electrons, but only one electron". It means in the atom can be only one, single electron. The electron manages the atom. If the atom contains more than one electron (for example - two), this atom represents " Siamese twins". Save us God of having such atoms and cells. And the living being begins its life from one, singe cell. What I am introducing here is what ' thinking photon/ electron' exist . I applied the quantum of light/ photon/ electron with a consciousness. And His own consciousness is not static but can develop. The development of conscious scale goes " from vague wishes up to a clear thought ". This evolution proceeds during hundred millions (billion) years. e) Trying to understand " the electrodynamics of moving bodies" Einstein wrote that it is the result of time and space changes. It is not exactly correct , because these changes are secondary in SRT. And the first point of SRT is that Quantum of light changes its spin. The former Planck/ Einstein's spin (h) changes in Goudsmit / Uhlenbeck's spin (h = h / 2pi), and as a result of this act all its parameters change and the time and new space appear. 3. GRT explains the conditions of gravitation and the secret of planetary time. Why do I think so? a) When Einstein worked on GRT, he asked astronomers: " What is the average mass of matter in the Universe?" The result was lamentable. The quantity of mass was insignificantly small. It was impossible to keep gravitation law with such insignificantly little mass and so, the Universe must be "open", endless. But what to do with the infinite space, Einstein didn't know. Therefore he took (from the heaven) " the cosmological constant" in order to "close" the Universe. The taken mass was enough for creating the condition of gravitation. Without " the cosmological constant" the Universe is endless. b) In 1922 Friedman wrote, that we could not take " the cosmological constant" in calculation. Instead of it, it is enough to take "time" and the Universe will be "closed". Friedman was correct, but why? Because "time", by its nature, is a limited physical quantity and, be taken in mathematical calculation, automatically gives "closed" result. c) So, the detected material mass of the matter in the Universe is so small (the average density of all substance in the Universe is approximately p=10^-30 g/sm^3) that the gravitation law doesn't work. Astronomers and astrophysicists know about this fact and therefore (to save the gravitation law) invented new matter a "dark matter", a new energy a "dark energy" and another abstract objects. This " invention" is only a result of our mentality , which says: " If in a theory you meet infinity it means the theory is nonsense". It is very hard to take that the Universe is infinite. It is no easy matter to give up a lifetime of habit . d) In my opinion it is impossible to use GRT to Universe as a whole. The Newton/ Einstein's gravitation laws are correct only in the local parts of Vacuum. The Universe / Vacuum as a whole is endless. e) So, how does GRT explain time? According to GRT the time depends on the mass and speed it means, of moving matter. It means that different masses and speeds can create different time. For example, our planet Earth has its own time but for us it is absolute. The other planets have another mass and speed and therefore they have their own time. This time according to GRT is relative. But their habitants will think that their time is absolute. But if they know GRT they will not make this mistake. ============= According to SRT and GRT time is relative. SRT says about proper/ individual time of an electron/ light quanta. GRT says about planetary time of a Planet.. The time cannot exist without matter and speed, in another words, without moving matter. But different reasons and different moving of a matter create the proper and planetary time. =================.. Is it possible to see the different manifestation of time in a human being? Here is an article " Even the time is pressed from fear" by Dr. Vadim Chernobrov (collaborator of MAI - - Moscow Aviation Institute). He wrote, that we usually think time is a constant quality. But Einstein's relative theory says time is relative. Question. Is it possible to check it in our life? Answer. Russian and foreign researches say it is possible. The documents (secret in the past) testify that "cataclysm of time", " phenomenon of time's perversion "," the changes (its deceleration) of time" often is observed by people whose profession connected with risk: astronauts, pilots, drivers, soldiers. 1. The test pilot Mark Gallay wrote in his book "The test in the sky" when his airplane was caught with fire " the time began to go in another scale. The time almost stopped. Every second took ability of expansion, and in this situation it was possible to do many things." He confirms that tested such feeling many times. 2. The test pilot Marina L. Popovich said the same, in the dangerous, catastrophic situations " the time is stretches". 3. In June 1989 the soviet airplane MIG-29 crashed near Paris, in Le Bourget airport , in the time of its air show. The notes of "the black box" showed that during the four (4)seconds the test pilot Anatoly Kvochur made as many operations as in normal situation it would take some minutes. The test pilot later said: " the time was stretched". 4. The captain N.Z.(fought in Afghanistan) remembers: "the fly of the bullet was so beautiful that I didn't guess to evade from it, although I have enough time to do it". 5. The sergeant V. Ch (fought in Afghanistan) told: " The black barrel of gun seems very big, even enormous. Time is stopped and full silence came. And I moved slowly a step a side and saw as the bullet passed close to me." 6. Etc... His conclusions. The people in a critical situation, on the border of death, suddenly for themselves begin to see everything as in the slow down film and in this time their speed reaction and power increase in tens and hundreds times. And this explains: a) why a man who escaped from wolves, can quickly reach up the top of the naked tree, b) an old woman took out a big trunk from her burned house, which later two strong firemen couldn't rise. c) etc... =============.. My experience. The speed on the curve was so fast that to keep the balance of the car I went on other road line and flew straight at the "forehead' of a green mercedes. The driver of the mercedes was in panic, in horror. He threw the wheel and closed his face with his hands. Suddenly the time stopped and the sound disappeared for me and I made many actions before my car kicked only the side back door of the mercedes. It was long time ago, but writing this article I understood better what happened. Our computer-brain works on a dualistic basis (on two different neurons systems): 1) usually under logic program, 2) sometimes on intuition (subconscious). Brain of a man approximately consists of sixteen milliards neurons. All of them form the system that manages human body. That is why that with the work of all the sixteen milliards neurons of brain, a man cannot catch a single impulse of his Electron, of his Quantum of light, of his Soul: (mass of electron is equal 10^-31 kg., charge of electron is equal 10^-19 k.) But in that time ( critical time ) most neurons of my brain stopped their electric pulse (time almost stopped) and my Light Quanta/Electron in this new condition (superconductivity) had possibility to increase my speed reaction and power on a short period of time . So, as SRT says, the Light Quanta in different systems ( even in the brain) can show us a different Time. The Light Quanta plays major role in the Nature, in the Physics, in our Life. ==========. Best wishes. Israel Sadovnik. Socratus. =======================.

It's hard not to take offense as a mathematician by Alejandro's take on the field. Basically, the more "pure"-oriented mathematicians, whose work is obviously arcane to him, are the only people he would consider to be mathematicians. All other math is "not real math," and is some kind of... for lack of a better word, application of a science. That point in and of itself seems to jump out as an obvious contradiction with his thesis. I don't see how you can separate "whether math works" from "whether math works in the universe." It's kind of like saying that if you haven't found an application of an algorithm, then there is no application of that algorithm. Not only myopic, almost tautologically wrong. Very little respect earned for Alejandro today.