Teorema de incompletitud de Gödel

Kurt F. Gödel, en «Sobre las proposiciones formalmente indecidibles de los Principia Mathematica y sistemas afines» [paráfrasis]:

«Existen argumentos lógicos imposibles de ser deducidos verdaderos o falsos; entre ellos, la coherencia de dichos razonamientos.»

La existencia verdadera o falsa de algo (por ejemplo, las piedras; al contrario, las hadas), no implica que la misma sea demostrable así, ni que deba o no tenerse fe en cualquiera de estas posibilidades.


La creatividad surge de hallar –pensando diferente del resto– ideas absurdas, para así nuevamente pensarlas y darles coherencia.

Ahí la importancia de la Lógica: porque sólo con ella es posible tanto hallar los absurdos como obtener la coherencia.


sábado, 13 de septiembre de 2014


Rudolf Clausius, a fundamental man
for the axiomatical establishment
of Thermodynamic's Laws.

The simplest things are the more probable to happen. For example, it is more complicated to cross the same hand fingers than keeping them free. Then, our fingers are free most of the time.

Nature needs energy to make things happen. What is, energy is the thing that makes things happen. Nature uses enough energy to make things happen, neither more nor less than the necessary.

In order to make simpler the things that happen, Nature tries to use the less energy it can. What is more, Nature liberates the energy that does not need to make things happen the simpler as possible.

Where does this energy go? To space, through time. Space contains unnecessary energy for Nature. This energy can make happen through time other things: that itself the energy turns into a particle, or that it makes collide other particles, or that makes move faster some objects, etc.

The simplest thing of those mentioned is that energy turns into a particle. One particle and no more, a simple thing. This particle will contain the energy that sometime was liberated by another event.

Particles are quantized: a particle is a particle and can not be divided into its components; in fact, those components does not exist. May be a particle can be transformed into other particles, but can not be divided. Then, energy, the origin of the particles, must be quantized too: it exists a fundamental quantity of energy that can not be divided. All effects that can be measured from particles are also quantized.

One of those effects is temperature: this quantity refers to the movement of two particles interacting (what is, colliding). When two particles interact, both try to divide in some way the energy they mean. Both try to have the same temperature. This is called the Zero Law of Thermodynamics.

Energy is quantized, and its division between two particles is also quantized. When two particles interact, the changes of temperature are quantized. May be a particle means an X temperature and another particle means a Y temperature. Both try to reach the Z temperature while colliding. The changes of temperature X–Z (minus) and Y–Z are quantized: there exists at least a minimum change of temperature, that is not soft.

Between bodies that mean the littlest energy, the quantum, the minimum change of temperature, necessary to allow things happen, is about 3 K (or 3 °C, it is the same).

Almost all the Universe is empty and almost has only quanta on it. Then, the changes of temperature that are frecuently registered are about 3 K from an hypothetical bottom of temperature, the absolute zero “R”.

This R value of temperature is the lowest that quanta mean. The existence of this value is only a supposition, that seems to function in order to explain how things happen: we are suggested (nowadays almost forced) to believe that this R value exists.

Why is R a supposition? Because it has not been measured and, actually, it can not be measured. A measurement is something that happens and that can be quantified. Things can possibly happen by themselves, but they can be quantified only if some comparison can be made between both and, eventually, they do are happening together.

A measurement needs two particles to occur: considering that one particle is the simplest thing that happens in Nature, two particles are the next simplest thing that happens in there. Two simple things that are comparing themselves constitute one simple measurement, the minimum required in order it occurs.

The R value could be measured by the interaction of two particles. But R is only meant by one particle, not by two particles: no measurement allow to determine the R value. It is conceptually impossible; to pretend it is absurd and that is why the existence of the R value is only a supposition. The R value may be exists, may be not, but we can not know if its existence is either true or false, because it is impossible to measure its existence or inexistence.

Nature needs enough energy to make things happen. It tries to make thing the simplest it can. Nature takes the energy from things happened before. Then, Nature uses the less energy to make things happen the simplest as possible. The energy that is not required to make things happen is liberated and stays in space, through time, making possible other things happen. If energy comes from quanta particles interacting, the 3 K change of temperature happen. This is the simplest thing in Nature and is the most common in empty space.

But some things are not happening due to quanta. They, of course, liberate more energy than the minimum and do not imply the 3 K of empty space, but more. It would mean that actually in Universe should not be happening the 3 K that, nevertheless, has been measured in several times.

How to solve the “paradox”? Space should have increased the minimum temperature change since the 3 K started to occur, because much energy has been liberated since that. However, it is not happening. The absurd is originated if we consider that space is saving and keeping energy: in fact, it is not true.

What happens is the following: the quantity of space is increasing and distributes the energy all over it (we might remember that energy is in space, through time). Then, space is not saving and keeping energy, but it distributes energy by increasing its size. The result is that the 3 K minimum change of temperature between quanta is constant, due to the energy distribution.

It seems to continue like this. It should not be seen as rare: the simplest thing is the one that Nature searches and happens with a 3 K minimum temperature change, and not by other way. Then, Universe space increasing its size must be also part of that simplest thing: this “expansion” is something very simple, may be the simplest thing related to space. May be when all energy is distributed, space “expansion” will stop.

Nature tries to make everything the simplest as possible. Then, it intends that things happening liberate their unnecessary energy the fastest as possible.

That is why a person falling from a very high place reaches the ground and dies: because the unnecessary energy in order to that person stay on the ground is liberated quickly; this energy gets quickly into the person, by a very strong hit with the ground, but the person can not survive that enormous quantity of energy in a very little period of time.

People try to avoid Nature's energy liberation. Then, people use energy that makes that avoiding possible (we might remember that the only thing that makes things happen is energy, no matter if that thing is to avoid energy liberation).

This avoiding of energy is the same size the energy that Nature would liberate. «Fire is fought with fire», is said. Actually, the avoiding energy is energy that Nature liberates, but in a controlled way, directed by people or other things that are not precisely Nature.

Anyway, either people, or a machine, or anything else, are liberating Nature's energy, the energy that makes things happen is the same. It does not matter if the liberation is fast or slow. That expresses the First Law of Thermodynamics: Things happen by a sufficient quantity of energy, neither more, nor less.

If a quantity X of energy is involved with an event and a quantity Y different to X is pretended to obtain the same event, it would not happen: it is needed exactly X. May be the obtained event is similar, but not the same. As it was said before, «Nature uses enough energy to make things happen».

There is a difference between Nature and people or machines, or anything else: Nature takes its own energy to make things happen. On the other hand, things that are not Nature take energy from Nature to make things happen. «Taking energy from Nature» is a thing that happens and requires energy to occur.

Nature only uses energy to make happen an event. Other things use the same energy that Nature would use, but added to the energy required to «take energy from Nature» and make happen the whole event.

Then, the quantity of energy required to make something happen is 1) the only necessary or, 2) more than the necessary. That expresses the Second Law of Thermodynamics: Things happen by a sufficient quantity of energy, but may be requiring more energy to obtain the former.

It does not contradicts the First Law: when Nature works, an A event happens, where Nature needs an X quantity of energy. When things that are not Nature work, a B event happens (may be similar to A, but not the same), where those things require the X quantity to make A occur, and an extra Y quantity to eventually make happen B.

The Second Law says that may be more than the exact quantity of energy is required, but never less than that in order to make something happen.

It is useful to calculate the “extra” energy required with the entropy: it is defined as the “extra” energy over the change of temperature since the R value to the actual value related to the thing that is happening. In other words, is “extra” energy over the temperature meant by the event happening.

However, things that are not Nature belong to Nature and, eventually, the searched events are exclusively generated by Nature. Then, in the case of the Second Law, Nature is also using its own energy and, at the end, the First Law is the only one manifested.

The Second Law is used to describe the things that happen due to people, or machines, or something else, but not directly (actually indirectly) by Nature. Nevertheless the First Law is conceptually the most fundamental law of both, showing that Nature is the “chief”.

That is why some physicists think Nature's (and our) destiny is fixed: Nature takes its own energy to obtain the simplest things. Nature is not wrong and things happen as in the present because it is the only way to reach the goal of a “lazy Universe” without complexity.

September 13th, 2014

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