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Thursday, November 3, 2011

Numbers and little numbers

 I was reading the other an article of Scientific American entitled Cracking a century old riddle, written by  Davide Castelvecchi (April, 2011) and simply  author explains the numeric subdivisions. He explains  with  apples and little  balls that this concept is  not rather than a number can be split into parts, and as example  is mentioned that the number 2 can be represented by 1 +1, while the 3 represents 1 +1 +1 or 1 +2 ... and as the number increases, the partition becomes more and more complex, let 4 with the logic of which is equal to 1 +1 +1 +1 or 1 +2 +1 or 2 +2 also, while 5 would be: 1 +1 +1 +1 +1 +1 * 1 +1 +1 +2 * 1 +1 +3 * 1 +2 +2 * 1 +4 * 2 +3.

Do you begin to feel seasick?, well,  mathematicians express this as p which represents the number in parentheses, and record the number of combinations, for example 2 (1), 3 (2), 4 (3), 5 (6) The magazine says 5 (7) but I see no other possible ... in short, becomes large as the number to divide, of course, the parenthesis  grow older, and I love the big number  you do with 100 (190,569,292) I swear I did not try to check it, don't believe I'm so obsessive, I trust what the author says.

Well, this is a topic that made me remember when a child; I used to be fascinated by the numbers ... but the truth is most of teachers are always looking for ways to make you know numbers are not your subject. And I say this because if we ask: what is a number?, When we ask this to a child, we do hope that the answer will be: a number is a measure ... but then if the child asks, but what is a number?, maybe we will end up saying the same thing that teacher said to me when I replied that 0.5 was not a number, but half of a number ... is it not logical? If we have a 1 to the middle and is represented as 0.5, is not it the middle of a number?.

And now seeing that a 5 is a combination of possibilities what is 5? is half of 10, double the 2.5 ... it's  5 times  1, is it a number ?

I swear it's not my desire to make you feel confuse ... but what is the logic when someone spits on the face of a child that a number is just a number? ... And then we teach ... we split into pieces what? Bits of numbers?, broken numbers?, Ah, no! I remember, are fractions, fractions of what? Is it a number? ... Ok, under that idea ... 4 is the fraction of 8, which is half of 8, a quarter of 16 ... do you want to continue? ... Ok, well 4 is the tenth of 40 ... is 40 already a number? No! Because I can imagine that one day an obsessive mathematician will divide googol which theoretically is a large number since a googol = 10100 and this is represented as:

A googol is roughly equal to the factorial of 70, and its only prime factors are 2 and 5 (one hundred times each) and is said that it would occupy the 333 binary bits.

The googol is of particular importance in mathematics but has no practical uses. Kastner created it to illustrate the difference between an unimaginably large number and infinity, and is sometimes used this way in the teaching of mathematics, and if you teach this to a child may think he or she  finally met with a number, but ... is it a number?

The reason for this is that when a child has problems with arithmetic, it's not for lack of fascination with numbers, actually we are genetically programmed to understand quantities, but it's cognitively hard to understand the numbers, if not the logic with which we teach it. And of course this traditional educational idea does not help, because there is only one correct answer and anything that looks different is not correct...

Now, can anyone explain what a number is?

Alma Dzib Goodin

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Castelvecchi, D. (2011) Cracking a century-old enigma mathematicians unearth fractal counting patterns to explain a cryptic claim. Scientific American. April.

Sagan, C. (2001) Cosmos. Editorial Planeta. España.


  1. I've been thinking and it's a hard question to solve, I believe what I learned with no more than faith. What is a number?

    1. It's a complex question, after many hours in a group we found out a number is a measure and they are the alphabet of maths... so we need them to understand the word:)