Saturday, August 29, 2015

Anxiety about math may be a mis-understanding


"Gaa!" is usually the reaction I get to that word, and I think that's too bad. Math is a handy tool we use to understand the world around us, we made it up, and use it for many purposes. Tools can be mis-used; and the consequences of that could be bad, but the tool itself isn't something to be scared of, even just a little bit.

By learning where math came from and why we use it, we can appreciate and understand it much easier than repetitive memorization. Math is the fundamental technology, and how technology is defined will help understand that line a little better.


Math is also art, with very practical uses. How is it an art? If you learn math as an art the practical aspects will emerge.

  1. Reasoning and critical thinking
  2. Elegance of solutions. Math is good when the solution has removed all needless complexity.
How do math relate to other arts?
  • painting is both art, and practical when you paint rooms in a house
  • music is art, is it practical? would the world be better off without music? of course not.
Practical as problem solving
  • A defined, repeatable structure of problem solving can be transferred to any parts of life. Use the How to Solve it steps for any problem:
    • Understand
    • Plan
    • Execute
    • Review

Models that reflect real life

Why math? The patterns of life are all around us can be added up, so they were. There are hours in a day, and things to do. There is stuff to measure all the time, so a way to measure it was needed that everyone could understand. How do you count when you are small and learning? Usually its with your fingers: one, two, three, four, or five fingers can signal between two people the count of something. Once we got past 10 things to deal with, then it can get a bit complicated. This is where the tool called math shows its most basic and important value; the ability to model the real world with symbols and notation so we can understand them, and be able to understand the same thing together.

You can create it all with the basic fundementals, so learn those techniques and you will realize that more complex solutions are just extending these fundamentals. Don't Memorize solutions; memorizing math is like memorizing colors and shapes. Just create them with the basics

The real world problems early math was dealing with and help solve were not that complicated. Way back, you would have been farming, or maybe making pottery. If you are farming, you would have to know where to plant the crop seeds, or tend the herd of animals. How to measure this land?
To measure the land people used numbers to indicate how many steps (feet) they took around the land, and this was usually the shape that we know now to be a square or rectangle. (graphic). Now that all this land has been measured, it can be measured again to divide up what goes where. All of those smaller pieces can be added up to make the whole piece.

Adding (+) enabled us to go past counting on our hands, and was soon followed by subtracting (-).

At this point in history we just have numbers and geometry. This was the world of math for a long, long time.


In the west, roman numerals were replaced with the set of numerals. 117 is easier than CXVII, and enabled the same operations to work on different bases then 10. Base 2 enables modern computation. These numbers originated in Arabia and India. Lots of important math advances occurred there while western Europe was in the dark ages.


As people interacted and traded with each other, they needed to know how many potatoes they were trading for those 4 chickens. Currency was used, and basic math ensured that people could trust it as a mechanism to trade fairly.


This did a whole lot to help us work with each other and understand how things worked in the world around us. How far something was and how long it would take to get there could be calculated.


The size of the world was becoming comprehensible once we realized it wasn't flat, so the geometry of a sphere was discovered to understand that. It also works with a soap bubble and a basketball. That's a powerful tool!


It was a lot, and now valuable, so the sways of people and the ideologies they brought with them shaped the development of math and its understanding in the general public. This continues to this day!


Technology is a term used to describe the set of tools that we have made for ourselves. Math is the underlying technology to it all.
The size of the house and how big or small that can be. This enabled more and more technology through the correctness that math enables in engineering and architecture. Houses, buildings, trains, automobiles and airplanes, followed,
Computing and computing machines is an example of applying many types of mathematics to enable many amazing things we have around us today.
To build any technology we use math to define and tie all the components together, this is why its the fundamental technology

Who does math?

This is a list of my favourite characters from the long history that mathematics has.


John Holland