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Stas Cherkassky
Works at Intel Corporation
Lives in Haifa, Israel
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Stas Cherkassky

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IMAGINARY NUMBERS: AN ANOMALY OF FIRST ORDER

Without any doubt, the vast majority of people have full confidence in the scientific method as the best tool we have to understand the inherent physical of Universe. In fact, all we can say that our knowledge is based on it.
In part, this is so because we know all of physics can be expressed in mathematical terms. Even certain mathematical advances have allowed to know, subsequently, certain physical properties. Physics and mathematics from this perspective is a common body.

The mathematical method is, in turn, the judge, that validates or not any physical formulation. Under this dogma any progress, either physical or purely mathematical have to come confirmed by mathematical theory. Scientific progress is certainly a circular logic. Who do not perceive so only because the premise of the total and full acceptance of the inherent truth of mathematical logic.

But mathematical logic is circular too. Is a logical body of thought that can only be validated on the basis of its precepts. That is, any mathematical result is valid provided it does not contradict its assumptions. If not, whatever it is, is automatically ruled out; either a mathematics, physics or any other field formulation.

Now, the question is: Are the assumptions or initial conditions we accept math obviously correct? The answer is NO.

In the late nineteenth century, physicists thought that all the physics of the universe was no longer secret. Everything could be explained, they said. However, some uncomfortable physical anomalies that could not be explained from the perspective of classical physics led some scientists to go further. Thus, the maverick Max Planck, at the dawn of the twentieth century gave rise to what we now know as quantum physics. From that moment, nothing was ever the same in physics. This provides a way of understanding, in essence, the physical world. The anomaly was actually the tip of an iceberg.

A few years later, the Theory of Relativity from Einstein, showed that what we consider fully rational far from it. The fact that the time can contract and expand, like a gum odds with our common sense and our physical experience is involved. However, it has been demonstrated and, although difficult to assimilate, is accepted worldwide. Rationality in physics or even in mathematics, is a matter of definition.

In math today we find a first-order anomaly: imaginary numbers. Here, in my point of view, we could also include as an anomaly having so many outstanding mathematical conjectures resolution, though I doubt that mathematicians share this view. For them it is just a matter of time resolution, no matter that we speak of hundreds of years or even millennia.

All mathematical knowledge, in the background, is based on the definition of a logical or rational language. From here everything has been discovering relationships are just more or less simple, that occur between numbers. Yes, perfectly wrapped in a logical package. When these relationships are known become in formulations. In this process, we help functions, which are used as shortcuts to work more efficiently with numbers. When we apply the mathematical theory in physics, we include magnitudes that, in turn, are numerical relationships, but in essence the process remains unchanged. numbers are equivalent to physical?

Perhaps you might think that with all the mathematical theory that we know today unimaginable any numerical relationship? Well, the answer is clearly negative. In the XXI century we do not know how the numbers relate to each other completely. In fact, it has never known.

Imaginary numbers are based on an anomaly that, in essence, is this: the square root of a negative number does not exist. But, of course! all mathematical functions (first degree , second degree , etc ...) typically include such imaginary results. These results, in many cases certainly produce true solutions. That is, if you do not consider them we would be discarding obviously correct solutions.

Look at the essence of the problem: we define something that does not exist, something at odds with mathematical logic to include correct solutions. Not only that, but, this imaginary concept is absolutely essential in all fields of physics and especially quantum physics.

Normally in mathematics, we only need a single evidence of a result that contradicts a theorem so that it is invalidated. If we accept that the use of imaginary numbers mathematical theory contradicts, Should we invalidate a whole? 

The issue is deeper than you can imagine. We use a concept that does not exist, but that fits the physical reality. But there's more. Mathematically also used rationally true concepts but not physically exist. I refer to the concepts of zero and infinity. Both absolute nothingness, as the absolute infinity, are mere definitions without physical correspondence. In physics there is no vacuum or absolute nothingness.

Paradoxically, both in physics and in mathematics we usually discard the solutions that we define as irrational.

Something similar happens with the concept of dimension, so intimately linked with almost all current physical theories. Depending on what we define as a dimension or not, our understanding of the phenomena can vary significantly. A definition is an opinion, but does not have to be an absolute truth.

Imaginary numbers despite not exist, have unquestionable physical background. At this point one can wonder whether it is physical failing or simply fail mathematical definitions? Imaginary numbers refer to the square roots, closely related to the squaring function. It is therefore not surprising that our main physical laws are based precisely on it. Nothing is casual.
Surely, if you have mathematical knowledge, you will have noticed that a function of the first degree is not imaginary solutions. Error! Imaginary numbers just do not make reference to negative roots. A simple negative number is an imaginary number because, in the Universe, not anything negative. It is a simple matter of definition.

If we assimilate mathematics with the Big Bang, we could say that if we ignore the initial conditions, since everything seems to be correct. We can explain the evolution (not the source) according to the physical or mathematical parameters rationally used.

Now the Big Bang as a concept violates all laws of physics that we know, including the most important of all: common sense. Although this, is accepted. Something similar happens in mathematics, everything is exact and perfect if not asked ourselves if the initial conditions are correct or not. Tradition, in this sense, is contrary to evolution.
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Stas Cherkassky

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concert Solo Flamenco with Inbal Cohen and Sharon Sagi (15/03/2014)
http://www.soloflamenco.co.il/
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А, ну вот. Сангрию ведь не купили.
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Stas Cherkassky

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HelloFax - probably the most convenient way to send faxes from the PC .. Use this link to register and get extra 5 free fax pages ..
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Coffee in Carmela, MATAM
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guess :-) Как раз тому мишке в кофе !
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flamenco
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Нет, это все С.! ;-)
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Have him in circles
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You can now fax your Google Docs! Check ןא out and get a chance to win a Chromebook Pixel. 
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я тоже почти не помню, но некоторые отсталые организации пока еще очень их любят и хотят .. 
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ultimate table tennis robot :-)
 
Wow, I'm impressed. Also, the last part was pretty bad ass. More robots!!!
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Мнение известного и вменяемого человека (русского, но живущего в Украине) о текущих событиях
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It comes to table tennis - robot challenging human. Waiting to March ..
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Very promising experiment. Interesting if it would work for all kids or just these from relatively "good" families ..
 
An article about the interesting things that happened when a school got rid of its playground rules.
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Have him in circles
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