One day in Alaska

https://picasaweb.google.com/102381076648563287639/OneDayInAlaska#

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.

One day in Dubrovnik

https://picasaweb.google.com/102381076648563287639/OneDayInDubrovnik#

Adult Sunday School - Part 8 - Joseph

Adult Sunday School - Part 8 - Joseph as a type for (of) Jesus - by P.K.Odendaal - August 2012

We find the story of Joseph in Genesis chapters 30 to 50, and nowhere else in the Bible has one man gotten so much coverage as Joseph, except Jesus Christ, and the point is that it is a very important story. Not so important as a story of Joseph, but much more importantly, as a foreshadow of the story of Jesus Christ.

The story of Joseph contains numerous intrigues, prophecies, examples and lessons interspersed with the best mankind has in terms of courage, long-suffering, forgiveness and love - characteristics we find in Jesus Christ himself. So we are not going to read this story as a story of Joseph. We are going to delve deeper into it and regard it as a story of the life and times of Jesus Christ.

One day in Barcelona - Sagrada Familia

Another series in my photobook :

https://picasaweb.google.com/102381076648563287639/SagradaFamiliasASymphonyOfBeauty#

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.

Philosophy - Part 15 - For King and Country

Philosophy - Part 15 - For King and Country - by P.K.Odendaal - August 2012

How many innocent, non-suspecting and honest people have been killed because of King and Country? And if you think that conscripted soldiers are not innocent, what are they then? Most countries do not have standing armies, so the soldiers are conscripted from the non-suspecting, innocent and honest population - and if they are pacifists, like myself, they go to jail for refusing. I did not go to jail, but complied with the call to arms, and did not protest against such, as I did not even know or care a hoot of why we were in that war - and that is why all countries take their youngest men. These men do not even know what the war is about - and it always happens the same, fighting for some pie in the sky.

And the truth is always the first casualty in any war. And a war is not about who is right, it is about who is left.

Adult Sunday School - Part 7 - The Law

Adult Sunday School - Part 7 - The Law - by P.K.Odendaal - August 2012

We find ourselves in the beginning of the world. Adam and Eve, who knew God personally, may have died already. What do we find? Violence, revenge, war, aggression - and people in bondage, even slavery. And this despite God's will that we be kind to each other and enjoy His creation.

How did this transpire then? It is because we could sin with impunity. There was no law. God wanted us to be free and not subject to any laws other than the one forbidding us to eat of the fruit of the tree of knowledge of Good and Evil.

But we had eaten of this fruit - we now know what sin and evil is, and we are going to pursue this line for survival, not knowing that it leads to death.

Of course we will not be punished for our sin and evil, other than dying because of it one day. So there is this uneasy peace with God, and it is building up tension between us and God and between us and our fellow men. We were on a path of self-destruction.

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.

Philosophy - Part 15 - What do you see?

This part was written by Annemie Odendaal on invitation.

As a painter, you are required to look at things a little differently, a little deeper. Paint that emotion behind the eyes, capture the magic that isn't visible on the surface. You have to look at an object and see how things really are. You can not draw from memory, you have to really look investigatively. We have to examine every angle, it is the only way to develop or grow in your style.

Years ago the Impressionists tried this for the first time,followed by the post-impressionists, expressionists and cubists. Until then, everybody painted just what they saw on surface and from memory. Everything was picture perfect and pretty. Almost documentary, which make sense, since there wasn't any cameras.