Apple Pi
December 30th, 2004 by Jess StrattonNotwithstanding the fact that I can’t even do basic addition to save my life, math has always been a passion of mine. Though my lack of understanding may be the enticement, however, as I love a good enigma.
Mathematical algorithms are behind every aspect of life and nature, from being able to calculate the largest package that will fit in your mailbox, right down to the reduction of a recipe from four to two people instead.
I have just stumbled upon one answer of which the question had been driving me nuts for ages:
Which came first ? the mathematical principles themselves, or our counting system, in which 1+1=2, which enables all the mathematical principles to actually work?
The answer I found here, in a paper called The Magnificent Perfect Square, by Roger Logan:
‘Over the centuries, mathematicians have expanded the number system four times. Each new expansion was required because the then existing number system was not sufficient to solve certain problems.’
So it would seem the first problem is that my original question was not correct at all? 1+1=2 is not complex enough to enable all the principles to work in the first place.
Apparently, mathematics has four number systems in addition to the natural system (1, 2, 3, 4 etc.):
1. Integers (the natural system, but expanded to include 0 and -1, -2, -3 etc.)
The introduction of integers allowed many more algebraic equations to be solved, which would have been impossible to solve previously.
2. Rational (the introduction of fractions)
3. Real (which accounts for infinite decimal point ability)
4. Complex (an ordered pair of real numbers, imaginary)
I was a little disappointed in this learning? my first thought was almost a letdown, that maybe the natural system I love so much wasn?t so natural after all. But then I read this paragraph in the same paper:
‘The age old question is, “Which came first, the chicken or the egg?” This simplistic summary regarding the expansion of the number system makes it appear that the mathematicians’ main concern was to expand the number system so as to solve the then current number problems. However, solving the number problems is what caused the creation, discovery or invention of new numbers, thereby forcing the expansion.‘
After my reading, I now have a new question.
Are the expansions considered a discovery, or an invention? And would the answer be fact, or a debatable opinion?
If I tally the facts, I’m sure I’m oversimplifying everything. But I warned you I couldn’t do basic addition to save my life.
