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unprovable truths Conjectures

There is no certainty where it is not possible to apply any mathematical sciences or any of those based on mathematics.

Leonardo da Vinci

The June 7, 1742, Christian Goldbach wrote a letter to Leonhard Euler (one of the greatest mathematicians of all time), suggesting that he thought a demonstration for this statement because he could not find it:

All positive even number greater than two,
can be written as the sum of two primes.

A prime number is one that is only divisible by itself and one. For example, 2, 3, 5, 7 and 11 are prime numbers. But 6 and 15 are not. Six is \u200b\u200bnot prime because it is divisible by 2 and 3, while 15 is not because it is divisible by 3 and 5. In addition, the number one is not considered prime.





If a mathematician believes that a statement is true, but that truth can not prove you have the option of presenting it as a conjecture.
For mathematics, the term refers to a conjecture that is true statement, but was not proved or disproved so far.

The most famous conjecture is raised by a German mathematician who worked in Russia, Christian Goldbach (1690-1764). To explain, let us say that a prime number is any greater than 1 and only divisible by itself and 1. There are infinitely many primes. The former are 2, 3, 5, 7, 11, 13, 17, 19 and 23.

A Goldbach it seemed that any number greater than 2 could be expressed as the sum of two primes (sometimes more than one way.) So

4 = 2 +2, 6 = 3 +3, 8 = 5 +3, 10 = 5 +5, 12 = 7 +5, 14 = 7 +7, 16 = 11 +5;

18 = 13 +5, 20 = 13 +7, 22 = 11 + 11, 24 = 13 +11, 26 +13 = 13; 28 23 +5;

30 = 23 +7, 32 = 19 +13, 34 = 17 +17, 36 = 23 +13, 38 +19 = 19;

40 = 23 +17, 42 +19 = 23;

so.





No mathematician has ever found any even number greater than 2, that could not be expressed by the sum of two primes. Mathematicians are convinced that there is no such number, and Goldbach's conjecture is true. However, nobody has been able to test so far.
While all conjecture may be false, the respected opinion of experts in number theory is that what you thought Goldbach must be true and is only a matter of time until someone succeeds in establishing.


(Del lat. Coniectūra).

1. f. Trial forms of things or events by evidence and observations.

2. f. Ecd. Lesson not attested in the textual tradition and the critical edition reconstructed in accordance with other evidence.

Sources: Math You There? Adrian Paenza, DRAE
Photos: GM

Church St Station Is It Closed

Without a certain amount of madness,
firmly believe nobody can be in possession of truth, since
believe the truth is precisely madness
.

Nietzsche

was a logician Kurt Gödel, Austrian mathematician and philosopher-American, recognized as one of the most important of all time. His work has had a huge impact on the scientific and philosophical thought of the twentieth century. Gödel, like other thinkers such as Bertrand Russell, AN Whitehead and David Hilbert tried to use logic and set theory to understand the basics of mathematics. It is best known for his two incompleteness theorems, published in 1931 at 25 years old, a year after finishing his Ph.D. at the University of Vienna.

The most celebrated of his theorem says that for all co axiomáti system self-consistent recursive powerful enough to describe the arithmetic of natural numbers, there are true propositions that can not be proven from axioms. To prove this theorem developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.





In 1931 Gödel published his famous incompleteness theorems in "Über formal unentscheidbare Sätze der Principia Mathematica und Verwandte Systeme" ("On formally undecidable propositions of Principia Mathematica and related systems"). In that article postulated that for any computable axiomatic system that is powerful enough to describe the arithmetic of natural numbers (eg Peano axioms ), it follows that:

1-If the system is consistent can not be complete. (This is generally known as the Incompleteness Theorem.)

2-consistency of the axioms can not be established from within the system.

These theorems ended half a century of scholarly attempts (beginning with the work of Frege and culminating in Principia Mathematica and Hilbert's formalism) to find a set of axioms sufficient for all mathematics.






The basic idea of \u200b\u200bthe incompleteness theorem is rather simple. Gödel essentially constructed a formula that claims to be non-provable for some system formal. If it would demonstrably false, which contradicts the fact that in a system consisting of provable statements are always true. So there will always be at least one true but unprovable proposition. That is, for every set of axioms of arithmetic constructible by man there is a formula which is obtained from the arithmetic but unprovable in that system. However, to clarify that Gödel needed to solve several technical issues, such as proposals for codification and the very concept of provability in the theory of natural numbers. The latter is done through a process called Gödel numbering.

made important contributions to proof theory, to clarify the connections between classical logic, intuitionistic logic and modal logic. It also showed that the continuum hypothesis can not be disproved from the accepted axioms of set theory, if those axioms are consistent.

born April 28, 1906 in Brno, Austria-Hungary (now Czech Republic) and died on January 14, 1978 in Princeton, New Jersey.




truth.

(Del lat. Veritas,-atis).

1. Conformity of things with the concept that they form the mind.

2. Conformity of what is said with what feels or thinks.

3. Property that has always kept one thing from it without any mutation.

4. Trial or sentence that you can not rationally deny.


axiom.

(Del lat. Axiom, and it's gr. Ἀξίωμα).

1. So clear and obvious proposition that is accepted without proof.

2. Mat. Each of the fundamental principles and unprovable on which to build a theory.


theorem.

(Del lat. Theorema, and east of gr. Θεώρημα).

1. Demonstrable proposition logically from axioms or other theorems already demonstrated by accepted rules of inference.

Source: Wikipedia, DRAE
Images: GM

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Vacation And God said let there be Big Bang Particle

- So CERN has a throttle particle? A circular tube to break particles - Langdon thought, as the elevator down. When the elevator stopped, he was relieved to have solid ground under their feet, but when the doors opened, his relief evaporated. Robert Langdon was faced with a totally unknown world.

In "Angels and Demons Dan Brown starts his web of intrigue and conspiracy to murder in the bowels of the Large Hadron Collider. The center of the plot of the novel is the struggle between church and science to determine who or what created the Universe. The story of the novel takes up the debate over which humanity has continued since the Middle Ages. This debate is a long string of encounters and some simple and some quite tragic since led to the imprisonment or death of some of their players, usually on the side of scientists.

An example of this is Giordano Bruno, an Italian priest interested in science and philosophy. During his life traveling throughout Europe teaching their theories. He wrote many works in Latin about cosmology, physics, magic and the art of memory. Demonstrated, albeit with the wrong method, that the Sun is bigger than Earth.

was arrested by the Inquisition in 1591 and in 1601 the Roman church declared it heretical unrepentant, stubborn and obstinate. He died at the stake without repenting of their ideas. History has become a martyr to science made by the defense that the heliocentric ideas,

Perhaps the best known case is that of Galileo Galilei, physicist, astronomer of the Italian Renaissance was sentenced by the Inquisition because disclosure that made the Copernican ideas heliocentrism. Faced with the possibility of being sentenced to death the story goes that religious redemption against him prosecuted. However, the Church condemned him to remain confined at home for the rest of his days.

Times change and for the last 116 years the Vatican has its own cosmic research center: the Vatican Observatory. Its original headquarters in Castel Gandolfo has given the birthright of the modern Vatican Advanced Technology Telescope in Arizona, USA. The Observatory's website states that its mission is to be a bridge between church and science.

the Observatory Director Monsignor Jose Funes, an Argentine priest belonging to the Order of the Jesuits in charge of the operation of the center. Besides the vows of priesthood, Bishop Funes holds a doctorate in astronomy from the University of Padua. Somewhere between faith and science, Bishop Funes stated in September last year "has been and there will be conflicts between science and the church. But do not fear conflict, as they can overcome and help us grow. For José Funes

cosmological research is perfectly consistent with faith. "" The Big Bang is not in contradiction with the existence of a God who created the universe out of nothing. It is true that the Big Bang is not proof of the existence of God but neither denies "

In Islam, the idea of \u200b\u200bBig Bang is not opposed to the revelations of the Koran which reads" Do not the Unbelievers see that the heavens and the earth were a homogeneous whole and separate? (Quran 21:30) "later the prophet speaks of" the sky built it with strength. And certainly, we assign a vast space "(51:47). However

the ghost of the church speaking to science still seems to haunt the corridors of the Vatican. According to Steve Hawkin in his book "History of Time" in 1981, Pope John Paul II recommended that those attending a conference on cosmology organized by the Vatican to "study the evolution of the universe after the Big Bang, but do not investigate the Big Bang itself, because this is the moment of creation and therefore the work of God" Pope John Paul II spoke these words to attending a conference on cosmology organized by the Vatican, among them was Stephen Hawking who picked up the anecdote in his book "History of Time"

By a coincidence of fate Hawking was born exactly on the 300 anniversary of the death of Galileo Galilei. In "The History of Time", the most celebrated of relativistic cosmologists is happy that his meeting with the church would have been much more fortunate than its predecessor.


unanswered questions
Dr. Gustav Tammann be glad when the interview is over "Normally, when interviewing an astronomer Pegunta arises of how the universe was like before the Big Bang or the causes of this phenomenon. I am convinced that this is one of the things that the human race will never understand. I find it interesting that many researchers admit that there are questions that may never be answered. Theoretically we can raise 20 possibilities, but the scientific method does not allow us to accurately distinguish which is correct.

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Who created the universe is a question delicate when studying the process that formed the cosmos. So far we only know that constitute the building blocks (elementary particles) and "Hands" who put those bricks and that today keep them in place (the elemental forces). All this knowledge is accommodated in what physicists call the Standard Model, a theoretical proposal created in the early 70's and that after 30 years of experimental testing is very accurate.

"Until the middle of last century, life was relatively easy for the physicists who were engaged in studying atoms and fundamental particles that up "- physicist and popularizer writes Shahen Hacyan Mexican. - It was thought that the basic building blocks of matter were protons and neutrons in the nucleus while huddling clouds of electrons flying around. To study an atom or its nucleus was sufficient to hit it to break and explore other debris. When in 1950, the advance of technology allows increasing the energy of these collisions, the atomic model was made pieces, literally.

Luis Cabral Rosetti, Particle Physics Advanced Institute of Cosmology, explained that the researchers' surprise, the accelerator experiments revealed a wide "zoology" of subatomic particles. By the early 60's the types of particles reached a hundred. The sense of the physical was for posterity when Enrico Fermi, one of the physicists responsible for the Manhattan Project, was asked his opinion on the particle K02. Dr. Fermi looked at his partner and said: "Young man, if I had the ability to remember all these particles have been botanist."

In an effort to sort out all the information found three physicists (Winberg, Glasgow and Salam) established in the early 70's the so-called Standard Model of particles and forces. A case where 12 basic pieces fit constructing the universe and three of the four forces that govern them.

All the matter around us is composed of two types of particles, or building blocks --- --- explains Dr. Cabral family of quarks (which grouped form protons and neutrons) and the family of leptons ( one of which is the electron). Like any family, the particles are arranged in pairs and turn in generations of couples, three to be exact. In the same way that the marriage of the grandparents birth to the children and the marriage of these grandchildren. Particles older, heavier and less stable, the decay give rise to a next generation more stable and lightweight. Currently in nature available to us is only this last generation. The "genealogy" of subatomic particles was discovered by accelerator experiments.

the fundamental building blocks to settle down and stay in place requires forces which run on them to build a cosmos. Along with the particles are the 4 fundamental forces whose function is to unite and control matter and energy of the universe. Each has different strengths and different scope: the electromagnetic, long range, this means that the same is visible to the subatomic level in the macrocosm in which we live. Is responsible for interactions between charged particles, such as for example, keeping the atoms and a molecule attached. The strong force and weak force operating at very short range, ie at the quantum scale. The strong force is what keeps quarks together to form a proton. The so-called weak force is present in natural radiation processes such as uranium or plutonium. The last fundamental force is gravity that affects the cosmos on a global scale but its influence is negligible at the quantum level, a rather fortuitous because so far failed to include in the standard model.

For there to field any of the four forces, quarks and leptons must interact through a carrier particle, called bosons. For every force there is a particular Bozon, the best known is the photon, carrier of the electromagnetic force in such phenomena as light., The strong force has the Gluon (of glue = glue) so called for being the glue that makes up protons, the weak force interactions exist by Bozon W and Z boson

Standard Model is a strong theory that successfully explains a large number of phenomena. "The model is so good, he is boring," jokes Dr. Guy Paic to emphasize the perfection with which the model predicts the particles and forces that shape our universe. However, although we have not seen it all, in the box of the standard model are still gaps where we draw the outline of the experimental work that there must accommodate. The most visible of all the mass.
According to our theoretical instruction, none of the elementary particles should have mass, the universe would be insubstantial as light. To remedy this little forgotten, physicist Peter Higgs proposed in 1960 that among the forces that govern the physics of the cosmos should be a field everywhere in the universe whose "divine breath" on the particles would make them heavy and slow. The bearer of the Higgs field is known as the Higgs boson, also called "Particle Divine "as its interaction with quarks and leptons is what gives them mass, transforming energy into matter. Its existence is essential to the model we have created our universe. Despite all our efforts have not been able to detect. Looking
invisible


To witness the collisions between the particle whose remains emerge divine the CMS, one of the four giant detectors installed in underground caverns carved around the four collision points available to the LHC.

The purpose of the detectors is to identify the secondary particles produced in collisions, says Guy Paic The parameters for determining the nature of a particle trajectory are described from the moment of impact, electric charge, speed, mass and energy. To accomplish this, the detectors are built in layers or sub-detectors each of which has a very particular role in the reconstruction of the collision. A magnetic system is responsible for separating the different particles according to their charge to determine when a magnitude related to the mass and velocity of the particle.

The detector layers are arranged two types instruments. One is the path detectors, usually a series of sensory fibers that identify the point and time when a particle touches then to relate the signs and all filaments is reconstructed velocity and trajectory of the particle. The other is a calorimeter instruments that analyze the energy of the particle stopping and measuring the amount of energy released.

detectors are shaped like a barrel with caps at the ends. Thus there is no space without instrumentation around the impact point which prevents any particles can escape undetected CERN explains in his press kit.

LHC detectors are

ATLAS (A Toroidal LHC aparatus), the largest detector ever built. Its main feature is a system of magnets in the form of donut surrounding the point of impact. It is designed to detect a wide range of phenomena which is known as a general purpose detector.

LHCb (Large Hadron Collider Bottom) is to study antimatter to understand why our Universe "chose" to settle the matter and not antimatter.

The CMS (Compact Muon Selene) is the other LHC multipurpose detector. Its most important task is to find the Higgs boson miraculous. Although the number of collisions is very large, the production of "divine will be very small particles, which require 2 to three years of experimentation in order have sufficient data to determine if the elusive particle was pleased to arise.

ALICE (A Large Ion Collider Experiment) will be responsible for looking at the creation. Inside Lead protons collide to produce the plasma quark - gluon soup of particles from which our universe evolved to what it is.

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divine And in the beginning, who said let there be light? And when the dinosaur

" The decision I took to be an astronomer to four years because of a traumatic experience " - says Gustav Tammann, one of the most renowned astronomers worldwide - "Four years told me that God was in heaven. It is traumatic when you look at the sky, you can not see it. Then I thought: 'He must be further away, so I can not see. " So I became an astronomer to see further . "

Contrary to the assertions of Dr. Tammann, it seems that the divine hand will not be in the vastness of outer space, but in the depths of a circular tunnel excavated 100 meters below the border between Switzerland and France. The tunnel, 8.6 km in diameter, contains what is probably the largest machine built by humans. Its primary function is to manipulate atomic particles to produce them region in space with a density so high that it becomes as it were in the beginning, a "soup" of fundamental particles. Under conditions of high density and high energy atoms crumble in his fundamental particles, a phenomenon that our universe has not seen since the time of its creation during the Big Bang

The Large Hadron Collider (LHC by its acronym in English) is operated by the European Organization for Nuclear Research (CERN) and is both a microscope and a time machine. To get to open the tiny window to the past requires a team of 100 thousand tons of scientific instruments. Thousands of components are organized into complex Meccano pieces ranging from a computer chip to machines large enough to fill half of the Metropolitan Cathedral in Mexico City. The parties from every continent and have been designed with great precision so that the degree of error is hundredths of a millimeter, it depends to handle and observe particles that are below the atomic scale. So far the effort has required an investment of three billion euros and years of hard work. It is not an easy task emphasizes Guy Paic, one of 40 Mexican researchers involved in the project engineering has to be gigantic to the infinitesimal work "

When asked Dr. Paic by the objective of such an effort, his answer is the very foundation of science, "the human desire to know." From the observatory at Chichen Itza to the Hubble telescope, man has sought to answer two fundamental questions How did the Universe? And why I become what it is?

The Time Tunnel

Enrique Fernández, researcher at the Autonomous University of Barcelona and President of the Scientific Policy Committee explains CERN particle physics and understanding of the creation of the universe are intimately linked. The logical connection is the Big Bang because the initial time of the cosmos were free elementary particles and the properties of the time largely determine the shape and structure of both the quantum cosmos and the macrocosm.

If we have done good job, it appears that all started about 13.700 million years ago, when all we know, and still do not know, are squeezed into tiny point no bigger than an atom. In an instant, this super-dense speck of matter and energy exploded in a great bang! And the universe began to exist.

The recipe to recreate the building is deceptively simple, we just have to concentrate as much energy we can into the smallest space possible. Over 50 years of experiments, scientists have found that the easiest way to achieve this lies in using brute force is to smash particles. But get this amazing "grip" is not simple, the size and complexity of the LHC is a clear example.


The LHC is a race track, two-way with 27 km in circumference. The characteristics of this track make it the most special in the world. For starters we have the runners. As the LHC accelerator can only accelerate certain kinds of particles: Requiring charged particles due to their size because only can be manipulated by electromagnetic fields. Second must be stable we do not want to start the race with a type of runner and end with a completely different person. The requirements we are left with two candidates: electrons and protons. The latter being the higher density, density being a key factor in the experiment, chosen to tell the secret of creation are protons.

runners properties imposed on the track a number of very specific requirements. Must be free of any obstacles within the Large Hadron Collider will be the empty space of the solar system. To prevent the proton beam collide with molecules gas inside the HCL is the ultra high vacuum, similar to what we find in interplanetary space communicators explain CERN.

The heart of the LHC are two tubes that run the 27 miles of tunnel. It is just inside the pipes where they fly in opposite bunches. The tubes are covered by an armor composed of 9300 superconducting electromagnets whose function is to accelerate the protons, to guide the particle beam to keep it within the "road" and then compress the beam to achieve the most impact ..

electromagnets represented the greatest challenge in the design of the collider because the maximum possible acceleration is directly proportional to the magnetic field strength. Normal electromagnets are not practical for the needs of the machine. Those used in the LHC cables are made of an alloy of titanium and niobium to be cooled to -263 degrees Celsius become superconductors, this is can conduct electricity without resistance. Once the LHC is ready, the cryogenic system is the world's largest refrigerator cooled using liquid helium to keep the magnets at optimum operating temperature.

The particles used in the collider will hydrogen protons or lead. Once extracted from their original atoms, protons are accelerated firing the duoplos (electromagnets) in sequence to "pull them." It is as if a group of teens we put Salma Hayek at the end of a street, says Dr. Arturo Menchaca, a researcher at the Institute of Physics of the UNAM and the Mexican team member who works in the construction of the Collider. The boys begin to run toward her. When they were about to reach it, put a little later. As the boys pick up speed, Miss Hayek move more quickly, which would force the group of teenagers to move ever faster and more energy. You put this in a ring road and will have an accelerator.

Once operating at full power within a tube, trillions of protons will travel 11.245 times per second the LHC ring traveling to a 99.99% speed of light. In the other tube as a group it circles in the opposite direction. In four points of the ring, the two routes intersect Collider to collide proton packs. Upon impact, the energy generated by the two trains would cause particle density and temperature levels similar to those existing during the Big Bang and for a moment will create an energy-dense broth in which there will be free, fundamental particles created the Universe.