### The physics of everyday miracles

Are there really miracles?

We are accustomed to hear --and repeat-- that the laws of physics are unalterable through time, and that everyday there is a miracle --visible or not-- around us.

All everyday activities are supposed to be ruled by  immutable laws. The force of gravity is the most representative and easily recognized of all the physical laws.

In opposition to that, the miracles are supposed to be a break of some physical law.

If there is an deadly car accident but nobody dies, people say its a miracle, but if somebody die in the same accident, its because "such  is life", or that "its the will of God".

However, the awesome miracles and the immutable physical laws are the same thing. It is hard to digest, but every time somebody comes alive out of a deadly accident is because of the same physical laws that provoked the accident.

Everything that happens around us has some physical explanation. If some action is unexplainable then it is just that: "not yet explained".

A book that explains many everyday physical phenomena.

Physics for entertainment, by Jakov  Perelman is a simple book easy to read and follow. It answers hundreds of questions like:
•  Is it possible to make fire with ice?
• What's the secret of painting people and drawing faces that seem to follow us everywhere we move?
• Is it possible to make soap bubbles that last ... for years?

### What are ordered pairs?

An ordered pair is the intuitive idea that objects can be flipped in different positions in such a way that the order in which we take them make different entities.

This "definition" may sound a little abstract, but a few examples should bring the idea comprehensible.

When we think about the basic Cartesian coordinate system of two axes, we immediately think of two "real number lines" intersecting at 90 degrees.

The figure above shows an example of how we intuitively use ordered pairs when we plot graphs of real functions.

In this example, The function is any abstract one-one (1-1) rule Y = f (x). When the variable x on the X-axis assumes or takes the value a, then the function f assigns the value b on the Y-axis to that choice x= a of on the X-axis.

Hence, we are necessarily and intuitively talking about the ordered pair (a, b). This entity (a, b) is an ordered pair because the function f explicitly and uniquely assigns the value b to the unique value a.

The notion of ordered pair is not limited to the usage of the real  numbers.  We can choose the second entry of the ordered pair to be an imaginary number. In that case, the Y-axis is no longer a real-numbers axis, but an imaginary numbers axis. In that case the ordered pair is simply a complex number.

The ordered pairs are very useful when we deal with transformations, specially transformations of plane figures.

For example, the following transformation, made up of two parametric equations:
transforms a circular area of the plane into a  dome in space.

To dramatize the results, a picture of a cat is shown before this transformation, and after the parametric equations are applied to the cat's photo.

In this example we are implicitly using triplets, that is, ordered pairs of three entries, like (x, y, z). The first two entries of the triplet are for the locations of the points of the cat's photo, and the the third entry of the triplet is for the amount of "deformation" applied to each point of the photo.

Transformations and ordered pairs are very interesting subjects, because they are not so abstract after all.

Interested in more examples of transformations as in the example above? Then download this free E-Book: The Golden E-Book of Graphs of Mathematical Functions: A selection of some beautiful mathematical surfaces from the domain of the real and the transcomplex numbers system.

Interested in an in-depth development of the foundation of the complex numbers from the standpoint of the ordered pairs? Then download this free E-Book: Foundations of Transcomplex Numbers: An extension of the complex number system to four dimensions.

Or simply remember this link:   http://4DLab.info   as a source of free E-Books and critical articles about mathematics and mathematics.

### Is the search for perpetual motion an utopia?

The pursuit for perpetual motion is, maybe, as old as the invention of the wheel. Everybody wants to save energy, specially human energy.

People want to be creative, no doubt about this, but people also hate to do the same thing over and over again. Therefore, inventing a machine that could create workforce with virtually a minimum of input energy is the perfect artifact to substitute the human sweat.

The earliest recorded intent to create a non-stop rotating device dates back to the thirteenth century. The sketch was made by Wilars de Honecort, a French architect.

Many a time have skillful workmen tried to contrive a wheel that shall
turn of itself: here is a way to make such a one, by means of an uneven
number of mallets, or by quicksilver.
How was it supposed to work? By what logic was this wheel supposed to keep turning and turning indefinitely?

Perpetual Motion, by Percy Verance is the book that explains it all. Perpetual Motion, the EBook recently edited by Datum is a source book that not only collects all the historic efforts and contrivances to create ever-spinning wheels, but in addition to that, in it we can find the explanations why the machines, or sketches, can't work.

About the sketch shown above he says:
Seven mallets, or arms, each loaded with a heavy weight at the end, are jointed at equal distances to the circumference of the wheel, so that those which happen to have their joints below the diameter of the wheel will hang freely down, but if the wheel be turned round by hand or otherwise, the weights of those which are on the ascending side will,
in succession, rest on its circumference, and will, in that position, be
carried over the highest part of the wheel and downwards on the descending side, until the arms that bear them are brought into a vertical
position and a little beyond it, and then the weight will fall suddenly
over and rest on the opposite position on the circumference of
the wheel, until its further descent enables it to dangle freely as before.
According to modern physics, a truly perpetual motion machine can never be accomplished because it would violate the basic laws (or principles) of thermodynamics.

The most basic of the thermodynamic principles states that:
Energy can neither be created nor destroyed. It can only change from one state to another.
In every machinery, in every kind of work, some heat is lost or dissipated, and since heat is a form of energy, the energy output is always less than the energy input, thus, we cannot retrofit the output energy as an input feed, because in the next cycle we are feeding less energy than in the first cycle. No matter how well are machine parts lubricated, every moving part generates friction, thus, everything that moves is a potential energy loser.

However, some people still claim having invented some kind of perpetual motion machinery --and believe it or not-- in some rare cases, they obtain invention patents for their claims. In the EBook Perpetual Motion the author includes some old cases where patents were granted for those esoteric devices, even when they could not withstand real-world tests.

Registering an invention is not an easy process. It takes specialized attorneys or lawyers. It takes making specialized drawings, and it takes clearly defining your claims. The invention must be new; you must claim and sustain and prove that your patent claims patent are genuinely new. The hardest part is answering the Examiner's comments to your claims. Those people will respond to your invention with a lot of other claims from similar inventors, and you have to prove that your idea is different and your claims are unique.

To conduct some preliminary search about existing patents you can use the excellent Google patent search. There you can read and download millions of patents applications, their drawings, and their claims; be it space vehicles, toys, lamps, dolls, car seats, stoves ---or a soap dispensing method as shown in the accompanying illustration--- or whatever invention you can think of.

Every society needs good and ingenious inventors. But the process of inventing is not achieved by merely drawing ideas on paper. Those ideas must be in accord with the laws of physics that keep the world running. Ignoring those laws and ignoring those principles is a loss of time, a loss of money, and creativity lost.