Fun With Maths - Part 3 - The Bush Calculator

Fun With Maths - Part 3 - The Bush Calculator - by P.K.Odendaal

So we are in the bush, and we quickly need to calculate the number of stars in the night sky and our children are not there with their calculators. What do we do?

We draw a few lines in the sand.

We need to multiply two double digit figures with each other. Let's say 22 x 23 = 506.

Philosophy - Part 17 - Induction

Philosophy - Part 17 - Induction - by P.K.Odendaal - August 2012 

It is probable that all we know, we know from a process called induction - a very powerful mathematical and scientific tool, greatly neglected by fields like philosophy, psychology and religion. Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true for all natural numbers. In science and philosophy it is a kind of reasoning that constructs or evaluates general propositions that are derived from specific examples.

One such an example is a statement by Goldbach, called the Goldbach conjecture. In 1742 he conjectured in a letter to Euler that every even number from 4 onwards is the sum of two prime numbers like in 12=5+7. No proof of this is known other than that Tomas Oliveira e Silva proved in 2008 that it is true for all whole numbers up to 10¹⁸.

Fun with Maths - Part 2 - Squaring the circle

Fun with Maths - Part 2 - Squaring the circle - by P.K.Odendaal - August 2012. 

There are numbers which are not natural or rational numbers, and are called transcendental numbers. These are numbers which cannot be expressed exactly in our number system, having infinite decimals, like p and e - with the result that we will never know what the circumference of a circle is equal to exactly, if we have its radius. The formula is easy C (circumference)=2*p*R (Radius).

There are two ways of trying to establish it.

Fun with Maths - Part 1 - Divisibility

Fun with Maths - Part 1 - Divisibility - by P.K.Odendaal - August 2012

I find Maths exciting, fun and empowering. At its most elementary I know how old I am, what my bank balance is, and what my age will be at my next birthday. This opens up my world to comparisons and many other such useless things.

But, it is also the basis on which the Universe is created. Simple, powerful, logical, complex and mystical. No wonder the early Pythagoreans were thought to be mystic philosophers.

I have had coffee with a maths teacher of Canada once, and I thought that the coffee 'break' would be a very fruitful discussion on physics, until I found out that he knew nothing about physics. I was totally flabbergasted, and could not imagine that someone would know maths well, but would know nothing of physics. To me it was like a mechanic walking around with a box of spanners, not knowing what a spanner is used for.

The Importance of Nothing

The Importance of Nothing.
Revised 7 September 2011

In this blog I wish to pursue Nothing, no not nothing, Nothing the noun or more descriptively No-thing.

If Everything is Something then Nothing does not exist at all - a conclusion I reached when writing this blog. If it does not exist, we cannot even talk about it, although I know some people (including myself) who can talk about nothing for hours.

In the first blog I have dwelt on our own insignificance - and now I need to look at what is really important - as if that was not important.

I promised in my blog blurb that I would write satirically about what is not important, so, as this is important, it will not be a satire. If we, however, delve into it more deeply - as we should - we will find it to be satirical too, because we do not understand it quite well and also have to speculate a bit or a lot.

You might ask where do I get this notion from, or this fascination with Nothing (if it should ultimately turn out to be something), I must refer you to Creation itself. As we know today and according to the Bible, the whole of Creation was created from one Big Bang explosion of very high energy light, which became gas when it cooled, and planets and stars when it superheated, exploded and cooled again.

The million dollar question then is - What was this void creation was created in, before it was filled with creation ? Was it Nothing ? And if it was Nothing - what is Nothing ? Is such a thing as Nothing something or is it just Nothing ? Is it possible for Nothing to exist at all, or is it just a figment of the human mind.

This blog, therefore, is an excursion into the realm of meta physics for readers who do not know what either meta or physics means - and for the others as well.

We begin with God - as everything should begin and end with. Can God only create Something or can He create Nothing as well? Generally one can conclude that God can create Anything - so then he would be able to create Nothing.

Whether He would do such a thing is however debatable on the following premises :

1. God is the creator of life and the act of creating Nothing, a thing which is void and lifeless or dead, is not part of his repertoire.

2. We regard a void as being Nothing, but maybe we are wrong - maybe it is Something. A void could be Something we just do not see or understand, and may therefore contain wonderful elements with wonderful properties.

3. Although God can do anything, there are things that he just would not do - or could not do. For instance He cannot tell a lie and He cannot sleep. The injunction is therefore that He cannot create Nothing.

An alternative approach to finding Nothing is to approach it from its opposite side. Nothing is the opposite of Something - so, if we can only find out what Something means and we can find out what Opposite means, then we might get to the meaning of Nothing, but unfortunately we do not know what either means presently.

But we need to start at Something and work our way up (or down) to Nothing.

Not understanding it properly, I might write satirically about it, although I do not wish to scoff at it, being such a serious and heavy subject. In fact, I would not know how to contribute something tangible on this subject, other than classifying it. The reason for my present excursion into this, in the first place, was that I know so little of Nothing !!!!!!!!! By investigating it from different angles, viewpoints and perspectives, I feel I might touch some truths and realities about it.

Something can be anything - it can even be numbers - and this is where my journey starts - and more specifically it will start at the number 1 - a very easy number to remember indeed. Whether it is a round number I do not know, but it certainly is a prime number and in the first instance it is a rational number and further it is an integer.

Our forefathers held themselves busy with the discovery of numbers before they entered the arena of mathematics. It is still unknown whether numbers exist or whether it is something, but certainly the whole of creation was based on the uniqueness of numbers.

Integers include all whole numbers, positive, negative or zero. Wait .... ZERO ???? - I did not know it was a number - how can it be ? We are also told that integers are rational numbers.

More satirically, for those who are mathematically challenged, for whom this blog is meant, I will make it easier and speak of persons. It is like adding the numbers 1 and 2 together. It might help us to think in terms of apples and adding 1 apple to 2 apples is more understandable than the pure mathematical idea.

So we have this 1 person. If he is a zero person he will still be rational, and if he is a negative person he will still be rational. So my deduction is necessarily that all persons are rational. My further deduction is that a person who does not exist, like a Zero person is also rational.

Even a person who is only half (1/2 - also called a vulgar fraction) - such a person is also rational. So one can be vulgar (not meant to be vulgar in another sense of the word) and rational !!!

There are maybe more insights in the above statements that one might imagine.

Now we need to find out what is irrational then. Irrational is a number which cannot be expressed as a fraction - a number like Pi=3.14159265 .... (to infinite decimals) is one. So if Pi is a person, he cannot be rational - and he cannot be vulgar, but indeed he will be positive. There is hope for some of us then. Going around the world without being vulgar (in the other sense of the word) but being irrational and positive is also something to be jealous about.

Sorry for my digression into things which are Something. I had to do it to address Nothing.

To temper the ambience, I wish to digress further into things more mundane.
Things that gets bad, gets worse even quicker that we think - adage concocted by myself.

There are negative numbers and the negative numbers are integers and real numbers. If we apply our simplification to persons here, it turns out to be quite interesting.

In the first place - say we have an easy reckoning sum. What is 1 person + 3 persons + 5 persons. The answer is easy - it is 9 persons. If you got another answer we ignored some persons - which is not a very nice thing to do. One cannot ever make a correct assumption if one ignores certain persons.

Secondly. If a bus has 4 persons on it, and at the next stop 8 persons gets out. How many persons are left in the bus? Minus 4 persons of course - don't blink - negative persons do exist (if negative numbers exist), as we have already agreed on that). So we need to get 4 positive persons on board at the next stop to have an empty bus.

If this argument is wrong, then my assumption of taking apples instead of pure numbers is wrong - an eventuality I do not wish to contemplate - as it will lead me to doubt my own existence, whilst this blog is meant to define my own existence. So why do you want me to define myself out of existence.

Thirdly. Things turn out really complicated when we talk or say something. If we meet someone, we normally say less than what we could, specially when we like them. Is what which we did not say then the unsaid part - and does it exist ?

Now suppose we meet somebody whom we do not like, and say things we should not have said - as we mostly do. Will we be able to unsay that later? - and will that unsaid part have the same qualities as the unsaid part of the first example.

Back to basics.

Now we need to look at opposites. This is an even more slippery slope. Is the opposite of Something a non-something, or an un-something or an anti-something - like in - Is unhappy the opposite of happy? Maybe - then un-Something should be Nothing.

The word anti seems to be a good candidate for the simple reason that for anything in the universe there is normally an anti-thing. For millenia scientists thought that matter was matter, and that if it was not matter it was Nothing. These days however anti-matter has been discovered - weird as it may seem. So it is not unthinkable that anti-Something will also be discovered one day. If that is discovered, then Nothing will not be able to exist anymore. Will the mere discovery of anti-something all at once annihilate or destruct all Nothing?

I have no other option than to conclude that nothing is Nothing, but that anything is Something.

So far I have only looked at real numbers, but there are unreal, also called imaginary numbers, as well. An example of one such a number is the square root of minus 1. Our forefathers thought that this imaginary number cannot exist, but it does exist. We use it everyday when we calculte the voltages and currents in alternating currents. The way we solve this dilemma is by squaring it, because by squaring the square root of -1 we get -1 which is a real and rational number.

Can we not solve some of our other imaginary problems by squaring them?