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physics, dignity and butterfly effect

We are going through a serious global crisis that no one is sure how we will. Macroeconomic data are analyzed and plans are designed to stabilize the system, but nothing will work if you consider the main factor behind any crisis of a system: the human factor, a factor both stabilizing and destabilizing.

amazing thing about the story
Something amazing that I have always drawn attention to the story. It happened before, happens now and possibly ever will: humanity does not seem namely, not to actually control, where it goes. The events will happen and when all seems tied up and in place, comes a new incident that disrupts all, wars, revolutions, economic crisis or other catastrophe. In these situations the story, after they occurred, draws conclusions and helps us to prevent their recurrence, but there is always something that escapes us and everything returns to lead a new catastrophe, everything starts over again. Butterfly Effect


In physics there are some systems that are highly sensitive to initial conditions. No matter how well you know the variables that will influence its development, however sophisticated become the instruments that measure, there will be a minimum uncertainty influence decisively in the further development of the system. Cause minimal will be able to trigger large consequences. This effect is known popularly by the name of "butterfly effect." An exaggerated, but very graphic, explains that the simple flight of a butterfly in Africa, can lead, over time, a hurricane in China. The first such system to be studied back in the sixties, it was time weather forecast.

Butterfly Effect and history
From the first moment that I became aware of this curious type physical systems, I recalled the very course of history. We know thousands of small stories that influenced decisively in the further development of very important events. Any of these sensitive cases, to develop differently, would have changed the destiny of any country or world. History has passed, over thousands of years, curd million events of greater or lesser significance, randomly interleaved or not. In many ways, could be considered as a "very sensitive to initial conditions, a nonlinear system with many feedbacks. Fortunately, the manipulators who try, and try, change the destiny of nations, difficult, may take into account all the variables necessary to achieve its purpose. A very short term that their calculations may be correct, but in the medium and long term will make mistakes. Small errors of calculation, as events unfold, they have greater influence on the results up to deface. Intentioned actions will encounter, in principle, with the same problems with the multiplier effect of small miscalculations about the system. More so now that the effect of globalization transforms the world into a more sensitive and unstable.

"Dignity and stability?
Apart from the factor purely "physical", uncertainty, there is a crucial element in the historical development, the manipulator tends to forget and that is allied with the "butterfly effect" to disrupt their plans. It may seem unscientific, even unrealistic, but, far from it, actually obeys a verifiable and solid, and is an essential element of the human factor: human dignity. There is a driving force of history but rather as "channeler" the real engine. This, incidentally, is no stranger to selfishness in its various forms, perverse, to a greater or lesser extent.

selfish power tends stepped on all, without any consideration. It is a gross motor element, like a storm. But unlike the storm that acts without obstacles, obeying physical laws and constraints purely mechanical power is always faced with the dignity of the individual. The trodden a thousand times, the scorn, but ultimately come face to face, facing him in the seeds of revolution or change required. And be able to redirect the flow of history itself. That's the difference between physical systems chaotic in the sense that they can follow very different paths to the future, equally valid, and "sensitive system" of history whose only stable final trajectory after any change chaotic, passes through the respect for human dignity. The feeling that makes us feel unique, different, with an intrinsic value as the center of the world we perceive our world. It is a universal feeling born of self-awareness.

All lovers of natural justice and we welcome the fact that a physical effect "friend" is an ally of social justice against the selfish calculations of power. These calculations, organized by the most powerful of computers that may exist in the future, are unable to collect all information necessary and potentially influential in its smallest details. A simple flight, unplanned, uncalculated, a small butterfly can thwart most perfect and thoughtful. That simple flight will also be able to derail well-intentioned plans to try to handle any crisis if you do not have the stabilizing factor that introduces, in a multitude of unstable points, respect for personal dignity. Post

out of my collaboration with Book of Letters, Science and Letters .

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Infinity and beyond, transfinite numbers Aleph

late nineteenth century the original mathematical Georg Cantor proposed a beautiful theory of finite or transfinite numbers, whereby the total number of fractions, integers and natural numbers are the same number you called Aleph transfinite sub-zero.

At first sight it seems reasonable, as one might think that the number of integers is greater than the number of natives, and that every natural number is an integer while some integers (negative) are not natural numbers. Similarly one might think, too, that the number of fractions is greater than the whole, but one thing is what it seems and one that is.


The key lies in the strange properties infinite numbers and relationships can be established between them. For finite objects of two different sets if we can establish a "one-to-one, between them, we can deduce that have the same number of elements. For a finite number of natural numbers the same thing happens, but what is obvious to cease to be finite numbers to infinite.

can establish a one-to-one relationship between the natural numbers and integers as follows: 0 ( whole) -> 0 (natural ) -1 (integer ) - > 1 (natural ) +1 ( whole) -> 2 (natural ) and so we continue indefinitely with the following table:

Each integer and every natural number appears once and only once in the table. This correspondence between each pair of numbers-natural whole is what sets in Cantor's theory that the number of elements in the integer column is equal to the number of elements in natural column. Therefore, the number of integers is the same as natural. Similarly, although somewhat more complicated, it can prove that the set of fractions (rational) has the same number of elements as the set of integers. The number is infinite, but no matter, it is the same number.

The great mathematician David Hilbert was invented metaphor Hotel Infinity to intuitively explain the paradoxes we face the existence of an infinity of infinities:

"There was a hotel that had infinite rooms. One day there comes a new guest to stay there, but the concierge said he had bad luck, they were all full. The guest indignantly called the manager, and asks how it was possible in a hotel with infinite rooms. The manager agrees, but says he can not do anything, then the host responds quickly: "I know what you can do, which is in the room 1 it sends to the room 2, room 2 to 3 and so on, then Room 1 will be free for me. The manager

found ma Raville this solution and it did. "

" Some days later another guest arrives and asks to stay, to what responds that the hotel was full, but not to worry, they knew how to fix it. Then the host says there was a problem, he was not alone, but with a group of friends ... and that it was an infinite group. The manager again shocked I did not know what to do, but the host, skillful also told not to worry, to send the room 1 to 2, from 2 to 4, the 3 to 6 and so on. Thus all odd-numbered rooms would be free to its infinite friends. "

sets that can be placed on one-to-one with the natural numbers is called countable, so that infinite sets are countable sub aleph -zero elements.

Surprisingly, although the extension of the system from natural numbers to integers and rational, not really increased the number of objects that work !.

After this you might think that all infinite sets are countable, but not, not only one type of infinity, as the situation is very different to go to the real numbers. Cantor proved by the argument "crosscut" actually more real numbers than rational. The real number is the number transfinite C, continuously, another name for the set of real numbers.

might think about giving that number called aleph sub-one, for example. But that name represents the next transfinite number greater than sub-zero aleph to decide whether or sub C = Aleph-one is a famous unsolved problem, the so-called continuum hypothesis.

As a curiosity, since we are talking about infinite, the term googol (googol English) is a huge number 10 ¹⁰⁰ was coined in 1938 by Milton Sirotta, a 9-year-old nephew of American mathematician Edward Kasner . Kasner announced the concept in his book Mathematics and the imagination. Isaac Asimov once said about it: "We will have to suffer eternally a number invented by the baby."

The googol is of particular importance in mathematics and has no practical applications. Kastner he created to illustrate the difference between an unimaginably large number and infinity, and is sometimes used in this way in the teaching of mathematics. The google search engine was so named because of the number . The original founders were going to call Googol, but ended up with Google because of a spelling error Larry Page, one of the founders of Google.

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THE PHYSICAL CONDITION AND CAPABILITIES THAT DETERMINE. SPEED

Human beings have the ability to practice physical activity. For this requires energy it gets from the foods you eat. These are broken down into its most basic, essential elements, which are stored for later use.
The ability of people to practice physical activity, sport., Is called of fitness . The level that each person has the physical condition will depend on the level of their basic physical skills, whatever the level they have, the higher the level of fitness. The physical abilities
prerequisites are defined as basic driving guide and classified for physical activity, and they are: endurance, strength, speed and flexibility.
The resistance is defined as the basic physical capacity to support an effort for a long time without any performance decrease. We can distinguish 2 types of resistance:
R. Aerobics , which would be one that allows me to take an effort known for being highly durable (over 3 min.) And low intensity, and also by using oxygen to mix with the immediate early and get the energy needed to perform of that activity.
R. anaerobic, which would be one where the effort last a short time (less than 1 min.) And is performed at high intensity. Also does not require mixing oxygen with the immediate principles for energy.
The main systems used for training improvement are continuous running, interval training, circuit training, fartlek ...
The force Com defines the ability to withstand or overcome a resistance or weight (the body's own weight or is more than one outside the body).
is possible to distinguish various types of force:
F. maximum when the resistance to be overcome is the greatest possible and the time it takes to perform the movement is high.
F. explosive when resistance to overcome is very small and the time spent in making this movement is minimal.
F. resistance when resistance is overcome and the median time spent is intermediate.
The main training systems used to improve this capability are meétodo autoload, which must be overcome only the weight of the body, and method overloading, where you have to overcome the added weight of our (dumbbells, colleagues, medicine balls ,...)
speed is defined as the ability to perform a motor act the shortest possible time. A motor act is any move we make with our body, either a stride, a gesture like pulling a field goal, a bump on a martial art, etc.
is possible to distinguish various types of speed:
V. displacement or translation, defined as the ability to move from one place to another space in the shortest time possible.
V. reaction, which will be the ability of a movement INICA as soon as possible as a result of the perception of a stimulus. Stimuli may be visual (red light-green in Formula 1), auditory (pistolietazo career output of 100 m.), tactile, ...
V. mind that the speed with which we process the orders, the information we receive and emit the most appropriate response.
V. gesture, which will be the time it takes to perform a motor act (time it takes for the basketball player, fitting the arm to throw to the basket)
As for training methods that Capades, we find the repetition of sporting gesture questions added difficulty (races uphill field goal ,....); ballast balloon or otherwise minus difficulty (downhill running, ball throws light ,...). Tambo outputs from different positions and improving stride length through the work of the force capabilities (allows me greater impetus) and flexible (allowing an increase in size of the stride)
The suppleness defined as the capacity for which the joints reach their maximum amplitude. You can also Definis as the capacity for which the muscles reach their maximum extension.
may distinguish between active and passive flexibility based responsible for carrying out the movement. So when performing this movement is the responsibility of the person, it is called active flexibility, whereas when the movement, the force it generates, is responsible for another person, apparatus, there is talk of flexible working.
training methods for improvement are stretches, whether passive or active, ie ejecurados with the help of another person, device, etc., Or capable of the individual.



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The spin and the strange twists of fermions

Of all the known physical quantities as spin is generally regarded as the most "quantum-mechanical." The word spin comes from the English "spin", meaning turn or rotate, and refers to a physical property of particles (1) subatomic, by which all elementary particle has an angular momentum intrinsic fixed value. Is a characteristic of the particle such as mass or electric charge, and a magnitude that remains as does the energy or momentum.

Unlike what happens with the angular momentum of macroscopic objects, which are used, which can take many different values \u200b\u200bdepending on the actions to which subjects see the magnitude of the spin of a particle is always the same for this particular type of particle. It is only the spin axis direction that can vary, but in a very strange way.

For an electron, proton or neutron spin quantity is always 1 / 2 of minimum value of time allowed (H) . Precisely why this amount of angular momentum would not be permitted for an object composed of a number of orbiting particles without any of them were turning on itself. Spin can only appear because it is an intrinsic property of the particle itself, ie not arising from the orbital motion of its parts around its center.

A particle like the electron, has an odd multiple spin ħ / 2 (h / 2, 3h / 3, 5h / 2, etc) is called a fermion, and presents a curious rarity: a full 360 º rotation transforms its state vector is not in itself but in the negative of itself, require therefore a rotation of 720 º to stay the same as before rotation. Most particles Nature are fermions, the remaining particles for which the spin is an integer multiple of h (h, 2h, 3h, 4h, etc.) are called bosons. Under a rotation of 360 º the state vector becomes a boson itself, not its negative.

If we take a particle of spin 1 / 2, for example the electron, the space of possible quantum-mechanical states turns out to be two dimensional, so we can take a base of only two states can be represented as [above> and [down below, for the first spin clockwise tour around the direction vertically upwards and the second is in the same way down. the same way as in a Euclidean plane any vector is a linear superposition of two orthonormal bases in question, in this case occurs as any possible state of the electron spin is a linear superposition , eg

w [up> + z [Down> where w, z complex numbers. Since the physical state represented remains unchanged if we multiply the two components by a non-zero complex number, the ratio z / q is the significant complex number that represents the state of the particle.


This complex number is represented on a Riemann sphere called, as shown in Fig. In Ecuador the same singular points are 1, -1, i-i.



The Riemann sphere plays a crucial role in any two-state quantum system, describing all possible quantum states. For a particle of spin 1 / 2, geometric role is particularly evident since the field points correspond to possible spatial directions for the axis of rotation. In other situations, the role of the Riemann sphere of possibilities is much more hidden, with a much less clear with the geometry space.


The strange turn of 720 ° of the electron to stay the same is quite a paradox. In many cases it seems that quantum mechanics phenomena has completely illogical, but to analyze every situation completely normal for us in the light of this amazing theory we note that without unexplained. The very cohesion of matter, as we know, or the existence of the four fundamental forces no sense. In the latter case at its foundations, paradoxically, is the very principle of uncertainty. A principle of "cumbersome" It seems that only measure is to prevent infinite accuracy.


(1) It is recognized that a "particle" may have individual parts that it can be treated as a whole quantum mechanical simple, with a well defined total angular momentum.