Short dialog

I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgot their use.

Galileo Galilei

Following the definitions we made about theory, law, hypothesis and conjecture in science, we can understand the next dialog.

- I think we may teach intelligent design in schools. Evolutionism is only a theory
- Exactly, it's only a theory, but intelligent design is not even a conjecture. It will be a conjecture the day the intelligent designer appeared in an experiment... and the experiment were reproducible! Even in that case, intelligent design wouldn't be a theory, neither only a theory.

Time vs Time

The only reason for time is so that everything doesn't happen at once.

Albert Einstein

If you are searching me from Spain, now it will be one hour later than last week. However, next week, the time will be the same as before. On the other hand, if you are searching me from Japan, the time is the same, but next week, it will be one hour before.

If you don't understand anything, here is a clue:

• In Spain, the summer time adjust was made last week.
• In Canada, the summer time adjust is made next Sunday.
• In Japan, there is no time adjust.

I love standards!

Last MacGyver episode

One of my biggest problems is I can never leave a puzzle alone.

MacGyver

For the Video of the Week (although it could be named, Video of the Month), we have a special guest, the hero of engineers, the god of the tools, the "i-can-fix-it-with-gum-and-a-Swiss-knife" man... MacGyver!

A well known credit cards company has recovered the 80s character for a commercial. Richard Dean Anderson is a little bit older, but he keeps the charisma of MacGyver.

Win 1 million dollars!

No one who cannot rejoice in the discovery of his own mistakes deserves to be called a scholar.

Donald Foster

I've received an email asking for the truth of the Riemman hypothesis from the last post. I'm glad to read those kind of questions.

In Mathematics, and in every science, there are several steps from an idea to become an Universal Law. First, the scientist discovers something that can't be explained with the current science, so he or she designs an idea to explain that situation. If the supposition is not backed by observation is known as a conjecture, and if backed by observation it is a hypothesis.

It's important to note that every hypothesis must be testable and based on previous observations or extensions of scientific theories.

Then, the scientist develops a theory, which is an explanatory statement of what has been observed, explaining the why and how. Most theory evolves from hypotheses, but the reverse is not true: many hypotheses turn out to be false and so do not evolve into theory.

If the theory can be logically deducted from a set of axioms, it's called a theorem. An axiom is an idea that it's true or we assume that, for example A=A.

Finally, a physical law is a model of reality, which not only explains the observed data, but also predicts future observations.

We have presented some mathematical hypothesis in this blog, like Riemman hypothesis or the normality of pi. Both are really interesting, but the first one is more... profitable.

Six years ago, the Clay Mathematics Institute (CMI) named seven Prize Problems. The Board of Directors of CMI designated a $7 million prize fund for the solution to these problems, with $1 million allocated to each. They became the Millennium Prize Problems.

1. Birch and Swinnerton-Dyer Conjecture
2. Hodge Conjecture
3. Navier-Stokes Equations
4. P vs NP
5. Poincaré Conjecture
6. Riemann Hypothesis
7. Yang-Mills Theory

There are 3 conjetures, 1 hypothesis, 1 problem, 1 (currently irresoluble) equation and 1 physics theory with a mathematical problems.

Solve it, and you'll win 1 million dollar for each one.

Basel problem: Leonard Euler (2)

Although to penetrate into the intimate mysteries of nature and thence to learn the true causes of phenomena is not allowed to us, nevertheless it can happen that a certain fictive hypothesis may suffice for explaining many phenomena.

Leonhard Euler

Comes from here.

Yesterday, we showed that there is a relationship between pi and the Basel problem. Let's see where it is.

The idea of Euler consisted on extending observations about finite polynomials and assumed that these same properties hold true for infinite series. More precisely, he can express the infinite series as a product of linear factors given by its roots, just as we do for finite polynomials. The agreement he observed gave him sufficient confidence to announce his result to the mathematical community.

Euler first recall the Taylor series expansion of the sine function

Dividing through by x, a infinite polynomial which roots (zeros) occur precisely at x = ±nπ, where n = 1, 2, 3,... If we factorize using the roots and we multiply the positive and negative elements, we have

The next step is very tricky. Let's analyze the coefficient of x². In the first equation, the coefficient is -1/3! = 1/6, but in the last equation, the coefficient is the result of the sum of infinite elements

So, we have

And now, we have found the relationship between pi and the series.

That's it. No magic. The bunny was in the hat.

Euler generalized his previous result to define the Riemann zeta function, for every complex number.

What is more, he found the connection between the function and the prime numbers. Surprisingly, later the Riemman hypothesis about the distribution of the zeros in the zeta function provided the elements for the prime counting function.

In Mathematics, everything is tied, and Euler showed it. How?

To be continued...

The Mathemagician: Leonard Euler (1)

Read Euler, read Euler. He is the master of us all.

Pierre Simon de Laplace

For those who have dealt with Engineering, Physics, Mathematics or almost every science, the name of Euler is not unknown. Born in Basel in 1707, is probably one of the biggest mathematician in the History. If you want to read a brief summary of his work, you can read the Eulogy to Mr. Euler, by the Marquis de Condorcet. Despite the 16 pages of the eulogy, Euler work was even bigger, including mechanics, astronomy, optics, acoustics, architecture, ballistics, navigation, cartography, precision instrument manufacture, music and philosophy. Opera Omnia, is the coursebook of 86 volumes that covers his published works.

But also the quality of his work was incredible for a human being. As a curiosity, he started using the symbols e for the base of natural logarithms, i for the imaginary numbers and f() for the functions. Now, they are used even in the schools worldwide. He had also a good memory and an incredible ability for calculus. He was able to say all prime numbers until 100, their squares, cubes, even to the power of six. When he died, he was working on the Uranus orbit. Those equations, years later, were used to investigate and discover Neptune.

Today, I want to show one of the most amazing mathematic demonstration. It was the year 1735, Euler were only 28, he had studied with Johann Bernoulli. Years ago, the Bernoulli brothers tried to solve the, so called, Basel problem, the series of the inverse of the squared naturals. Johann Bernoulli had proved the divergence of the harmonic series (the sum of the inverse of the natural numbers). Even the great Leibniz, who discovered the series of the inverse of the triangular numbers in a very elegant and convincing manner, failed solving the Basel problem. It seemed to be a hard problem.

But then, Euler appeared with an amazing solution. It was amazing because the solution were... pi squared over 6!

It was a very simple and at the same time a very astonishing solution. The result was the sixth part of the area of a square with a side equals to the lenght of a circunfenrence of unity radious. What were the connections between pi and the series?

To be continued...

Based on:
http://tiopetrus.blogia.com/
http://historias-de-la-ciencia.blocat.com/

Welcome Spring

My religion consists of a humble admiration of the illimitable superior spirit who reveals himself in the slight details we are able to perceive with our frail and feeble mind.

Albert Einstein

Today, at last we can say: "Farewell, Mr. Winter. Hello, Mrs. Spring."

The other day, I watched on TV a program that said this Winter was the warmest in the last 50 years on Vancouver. Ok, it was warm. In January, it was about 8-10º C on average. But now, almost in April, it reamains 8-10º C!! Fortunatelly, the rain is progresively decreasing. I guess I won't see another 40 days raining in a row.

Anyway, the rain has an advantage. It makes you really appreciate a sunny day. Specially in Vancouver, where it seems to be a competition to have the most awesome garden in the town. A sort ride or walk becames a nice experience. Cherry blossoms, bush sculptures, green grass everywhere; everything framed by the quiet bay and the huge mountains.


The picture was taken on the cementery. I'll talk about that in the future. Just take a look at the tombstones... do you see something special?

Think green

No one goes there nowadays, it's too crowded.

Yogi Berra

Last Friday was Saint Patrick day. The Ireland day. It's amazing, there are Irish everywhere. Until Friday, I didn't realize the number of Irish (or Irish sons) that live in Vancouver.

Saint Patrick means green. Saint Patrick means leprechauns. Saint Patrick means celtic music in a pub. But, specially, Saint Patrick means beer. Pints, pints and more pints of beer.

The only problem is that I couldn't find the pot of gold. Although, a leprechaun drove me home in his magic cart.

I know what you think. No, it wasn't the beer. It's because the bus driver wore a funny costume. What a pity, I forgot my camera.

Nos estan timando

Hoy voy a saltarme mi norma de escribir en Inglés, porque el tema afecta principalmente a Españoles y creo que es de suficiente importancia como para que quede claro.

En España, como en muchos paises, el desconocimiento de la ley, no exime del delito. Si bien es cierto que es humanamente imposible que una persona física esté al corriente de todas y cada una de las leyes que se promulgan, con todos sus detalles. Por otro lado, el Gobierno, el máximo poder ejecutivo, es el encargado de que velar por el cumplimiento de esas leyes; ergo, como persona juridica, debe conocerlas con la máxima precisión. Para eso existen los diversos gabinetes, consejerías, ministerios, delegaciones, subdelegaciones y demás burocracia politica.

Y cual es mi sorpresa, cuando yo, como persona física y cuya unica conexión con el mundo legal es -usando terminología informática- a nivel de usuario, me encuentro con la ley 22/1999, por la que se modifica la ley 25/1994 por la incorporacion de la Directiva 89/552/CEE, relativas al ejercicio de actividades de radiodifusión televisiva. Se puede encontrar el texto integro en el BOE del 8 de Junio de 1999.

Me llama especialmente la atencion la sección diez, parrafo tercero.

Igualmente, son ilícitas la publicidad y la televenta que inciten a la violencia o a comportamientos antisociales, que apelen al miedo o a la superstición o que puedan fomentar abusos, imprudencias, negligencias o conductas agresivas. [negritas mias]

Curiosamente, desde 1999, cualquier difusion con fines publicitarios de temática pseudocientifica y supersticiosa es ilegal. Bueno, ahora veamos que define como publicidad esa misma ley. Lo encontramos en la sección tres.

c) Publicidad por televisión: cualquier forma de mensaje televisado emitido, mediante contraprestación y por encargo de una persona física o jurídica, pública o privada, en relación con una actividad comercial, industrial, artesanal o profesional, con el fin de promover la contratación de bienes muebles o inmuebles o de servicios de cualquier tipo.
Los mensajes dedicados a la autopromoción tendrán, a efectos de esta Ley, la consideración de publicidad.
También se considerará publicidad, cualquier forma de mensaje emitido por cuenta de terceros para promover determinadas actitudes o comportamientos entre los telespectadores. [otra vez negritas mias]

Según mi inocente opinión, cuando alguien llama a un telefono de pago, y solicita una consulta -astrológica, cartomante o similar- esta solicitando un servicio que conlleva una contraprestación para la otra parte. Pero aunque eso no fuera cierto, si que promueve una actitud hacia los espectadores, y en este ultimo caso ni siquiera se habla de contraprestación.

Es decir...

• Cada vez que aparece en televisión Anthony Blake intentando adivinar el último decimal de pi empleando lo que él mismo denomina "poderes mentales", es ilegal.
• Cada vez que Iker Jimenez o J.J. Benitez cuentan sus fantasías lisergicas como noticias de actualidad, es ilegal.
• Cada vez que Octavio Acebes o Aramis Fuster nos recuerdan que hay que encender velas el dia anterior al ultimo domingo de Mayo mientras pelas naranjas en sentido contrario a las agujas del reloj para que todo te vaya bien, es ilegal.
• Cada vez que se cuentan remedios y tratamientos de medicinas alternativas, sin ningun tipo de fundamento, basados en las tradiciones y supersticiones populares, es ilegal.

Para terminar, añado el texto de las disposiciones finales.

Disposición final primera.
Esta Ley, en cuanto regula el contenido de los medios audiovisuales, se dicta al amparo de lo establecido por el artículo 149.1.27.a de la Constitución, teniendo por tanto el carácter de norma básica.
Disposición final segunda.
El Gobierno dictará las disposiciones que sean necesarias para el desarrollo y aplicación de esta Ley.
Disposición final tercera.
Esta Ley entrará en vigor el día siguiente al de su publicación en el «Boletín Oficial del Estado».

Por tanto,
Mando a todos los españoles, particulares y autoridades, que guarden y hagan guardar esta Ley.
Madrid, 7 de junio de 1999.

JUAN CARLOS R.

El Presidente del Gobierno,
JOSÉ MARÍA AZNAR LÓPEZ

Es decir, esta ley es norma básica, al amparo de la constitución y firmada por el Rey y el entonces presidente del Gobierno. El texto de la ley deja bien claro que es DEBER del Gobierno dictar las disposiciones para la aplicacion de la ley. Y que se deberia estar haciendo desde HACE 7 AÑOS.

Dado que eso no se esta llevando a cabo, es nuestro deber, como españoles, el hacer que se cumpla, si es necesario, por mandato real.

Canada vs Spain

Comedy is simply a funny way of being serious.

Peter Ustinov

Some people ask me about the cultural differences between Canada and Spain. I remember a funny and cool animation comparing Italy with the rest of Europe. If you exchange Italy-Spain and Europe-Canada, the results are also valid.

Enjoy!

Snowy sunset

I am not one of those who in expressing opinions confine themselves to facts.

Mark Twain

Finally, there was a little sun after two days of soft snow. So, I thought to walk to the beach and see the beatiful sunset in Vancouver. The picture says everything.

(click on it to enlarge)

Let's open Pandora's box

I think it would be a good idea.

Mahatma Gandhi
when asked what he thought of Western civilization

I owe you a lot of post. I know. I have a lot of ideas, but few time.
Meanwhile, have you ever listened to a band or a song and though: "Ey man, I like this music. It could be more music like that one"? Now, you can find it. You can listen your favorite music, even that you don't know you like.

How is it possible? Introduce a name of a band or song and a computer will find any similar music in the database. And then, you'll have your own radio station, acording to your preferences!

I tried it, and now, I can't quit.

Canadian Private Copying

Politicians are the same all over. They promise to build a bridge even where there is no river.

Nikita Khrushchev

Whenever you buy a CD (or any other recording device), in Canada or in Spain, you are paying a tax to music industry. Theorethically, this is based on a law called private copy, that allows you to copy music that you have purchased.

"...Es obvio que cada vez que se hace una copia de un disco para uso privado, se deja de vender un ejemplar del mismo..." (from SGAE)

Free translation:
"...It's obvious that every time a private duplicate of a disc is done, a copy isn't sold..."

This reminds me my old high school phylosophy classes. My teacher loved fallacies, so we studied it deeply. He liked to show very clear examples like...

1) Everything that is made of gold shines
2) The sun shines
3) Ergo... the sun is made of gold!

You see. It's obvious! Now, he can use SGAE for his classes.

If it isn't clear. Let's say why it's a fallacy:

First: A CD is a devide to store DATA, not music. In fact, it stores digital data. Music must be converted to digital data before being in a CD.

Second: Private copy was invented because those devices have short life. I have paid for information (music, movies, programs...). So, it's logical to create back-ups of what I paid BEFORE.

Third: That statement is agains one the most basic rules of market: the demand curve. The number of elements solds Q is inversely proportional to the price P. Since the price of a private copy is only the tax, that statement would be true when a music CD costs exactly the value of the tax. Here, I challenge music industry to do that.

Four: In Spain, the way the tax is distributed is unfair. It should be controled for a public statement and used to incentivate music, not industry. In fact, it should be used to incentivate data creation, information creation...


Now, let's do a comparative of countries:

Canada:
Tax: 0.21 CAD = 0.155 EUR
100 CDs price: 69.99 CAD = 51.72 EUR (Maxwell, Future Shop)
Percentaje: 30 %
Beneficiary: Copyright Board of Canada (Goverment agency).
Status: Public

Spain:
Tax: 0.22 EUR
100 CDs price: 45,02 EUR (Benq, PCbox)
Percentaje: 49 %
Beneficiary: SGAE (among other societies).
Status: Private

Update (for spanish): A ver si la SGAE tiene narices de leerse mi blog, como hizo con la Frikipedia. Aunque se supone que esta reabierta (con la pagina de la SGAE bloqueada en blanco), en estos momentos, parece que no funciona.

Update 2 (for mañicos): Campaña de Compartir es Bueno en Zaragoza a las 12 horas del día 3 de Marzo en la Calle Bretón nº12, frente a la sede de la Sociedad General de Autores y Editores (SGAE).

"...Animamos a acudir con películas, musica, libros y otras obras culturales en soporte informático para compartirlas entre todos los presentes. Desde la organización traeremos CDs con material variado para intercambiar..."