Big numbers
The Eddington number
They are a few, but some of them are really big. I'm talking about the 'constants' of the physical universe that surrounds us. For example, the speed of light is 299,792,458 metres per second. Another example is the Avogadro's number, NA= 6.022 141 99 * 1023 that is the amount of atoms or molecules needed to make up a mass equal to the substance's atomic or molecular mass, in grams.
But how do scientist come out with those huge numbers? By theory implications or deductions, and by laboratory experiments.
The Arthur Eddington's number NEdd = 15 747 724 136 275 002 577 605 653 961 181 555 468 044 717 914 527 116 709 366 231 425 076 185 631 031 296 comes out by none of the above.
This 'constant' --the mother of all of them-- is the brainchild of only one person: Sir Arthur Eddington. According to him, this number is the exact amount of protons in the visible universe.
What are the implications of this number for the scientific community? Read the full article here.
Random numbers
One million random digits
Rolling dice is a somewhat addicting game for its randomness in the numerical outcomes. For a perfectly balanced dice, any one of the faces has the same chance of coming the uppermost. But modern science needs much more than the six outcomes of a dice for testing experimental events, specially when the sample needed is very large.
Having a table of random numbers is always a good idea because you never know when it will be handy. How about a one million random digits table? There are not many of them. Can they be used to predict the future? What relation do they have with the Manhattan Project and the production of the atomic bomb? Read the full article here.
Myths
Some myths about the infinite
Our surrounding world is made up of finite things. No object that we can touch or hear or sense in any way is infinite. Then, how we invented the idea that some things can be infinite? Do they really exist?
There are some myths and stories around this subject (or the whole matter is the myth?). Some people think that the grains of sands are infinite, but Archimedes settled this problem thousands of years ago. But there are some surprises in the horizon, like this one: can an object be finite and infinite at the same time? Read the full article here.
Number systems
The imaginary numbers are not so imaginary, and the complex numbers are not so complex
Why is it that for some people the imaginary and the complex numbers are so difficult to understand? Possibly, because they were pushed to solve complex equations without a clear understanding how they were invented and how our number system has evolved.
Humankind began counting with simple objects and with their hands, but as the abstract thinking developed as an indispensable tool to understand the surrounding world, the counting process and the mathematical tools were also refined.
The imaginary numbers are not "imaginary", and the complex numbers are simple as the natural numbers. See how they were developed.... read the full article here .
Transfinite numbers
The Book of Sand is a Transfinite Book
One controversial aspect of the modern mathematics is the introduction of the concept of transfiniteness by George Cantor when he developed his Theory of Sets.
The transfinite concept is used in those cases where the elements of a set cannot be countable. Theoretically, we can count all the grains of sands in our planet, or we can count all the molecules of the available water, or all the molecules of uranium or gold. But can we count all the fractions? Can we count all the decimals?
Counting is mainly a one-to-one correspondence between between the natural numbers and the objects we want to count. The argument of this article is that all the instances of The Book of Sand is uncountable. Read the full article here .
Set Theory
The Book of Sand of Borges and the Continuum of Cantor
No doubt that The Book of Sand is an infinite book. It is a book with no beginning page and no ending page. It is a book where you see a figure only once. It is a book where pages are randomly numerated, but is there any connection or any relation of this short story with the Theory of Sets that created the controversial and largely humiliated George Cantor? Read the full article here .
This article is a continuation of another article: Nobody understands the infinite so well as Borges .
The Book of Sand
Nobody understands the infinite so well as Borges
Why is it that the Argentinean literary writer Jorge Luis Borges is cited so many times in the math and philosophy books that deal with the concept of the infinite? Why is his short story The Book of Sand a fountain of inspiration for so many controversial articles and essays?
Learn more about how this famous writer manipulates the idea of the infinite without complex math and in an amusing way using the metaphor of a book with no beginning and no end. Read the full article here .
The fourth dimension
What is the shape of a wheel in the fourth dimension?
In most of the books and articles we read about the fourth dimension authors seldom describe the shape and behavior of bodies in those dimensions. The reason is simple: it is easy to describe the fourth dimension as a continuation of the first, second, and third dimension, but it is not easy to predict the properties of our daily objects in higher dimensions.
Dr. Henry Parker Manning, the author of the book The fourth dimension simply explained takes the challenge. Read the full article here .
Graphing equations
A Short history of the Cartesian Coordinates
The Cartesian coordinate system is a wonderful achievement that let us visualize the behavior of the mathematical functions. Once we are comfortable with graphing equations in a 2D-plane it is very easy to do it with a 3D-space: we take everything for granted. However, drawing figures taking as reference two mutually perpendicular lines externally to the graph was a big breakthrough in the history of algebra and geometry.
On the other hand the negative numbers, and even the zero, were not always accepted as part of the computational mathematics. Then, how were they integrated in the Cartesian coordinate system? Read the full article here.
SETI
What do you know about the Paradox of the Great Silence?
Since 1962, scientists have been sending radio messages to the outer space. The first one was a three-word message sent from Evpatoria, in Ukraine. A few years later, a second message was sent to the cosmic space from Arecibo, Puerto Rico, and some years later two more messages were sent from Evpatoria again. In all cases the messages were sending information about all us, to unknown civilizations that may capture those well-intentioned signals, but that can be used for who knows what purposes.
However, in order to take no risks should we stop sending data from us while at the same time keep silently trying to hear their messages? A couple of years ago, the Russian astrophysicist Alexander Zaitsev saw a contradiction in this attitude. This contradiction is what is now know as The Paradox of the Great Silence. Read the full article here.
You can also go to the
- Articles page for general articles, or to
- The Transcomplex Surfaces page for complex variables transformations from the standpoint of the Transcomplex numbers, or to
- 4DLab - the Blog, for many others related articles.