[robski]

The fans of Monty Python will probably recall the line "What did the Romans do for us" and after some thought a long list of innovations were revealed. Well we can twist this and say "What did the French do for us" and I am sure a equally long list could be produced. As far as we are concerned they produced two interesting branches of mathematics. We are going beyond the simple idea of adding up a shopping list. We are into the realms of Roger Penrose helping Stephen Hawking produce a Mathematical proof that Black Holes exist in space.

Sounds very complex but the concepts stem from a very simple idea. These ideas get extended and become very abstract and can be applied to all sorts of problems. Take the French gamblers who were trying to work out the odds or devise a system to win at the Casino. They were responsible for statistics. In fact if you touched on the subject at school the typical example was what is the chance of throwing a dice and getting a 6. Then what is the chance of throwing two 6s in a row. This leads us to workout the probabilities of events and as we saw earlier it is used in some compression schemes.

French engineers came up with a concept of using a mathematical model to solve problems. Any object or structure can be made up from smaller components.
For example a house is made up from bricks. If they need to calculate the strength of a house, bridge or dam they would test the strength of a single component. That is test a brick to destruction. Then workout the relationship of a few bricks joined together with mortar. This information can then be extended to larger buildings. In some real world situations the mathematic is too complex or long winded to process. In these cases a simpler approximation is used to replace some of the components. A bit like using a clear piece of plastic instead of glass because the required properties are similar. Another extension of this is to transform something in to something else because it is easier to work with. An example could be to turn solid ice into liquid water or a gas steam.

I am hoping the above has extended your mind into a way of lateral or abstract thinking as this is required to follow the next stages of the jpeg processing.