analysis

Mathematics

Mathematics relates to everything in our world. You do not think about it but everyday you use math. When you are walking and you gauge how far your target destination is. Spacial relationships that tell you if something is within arms reach or within how many paces. In driving people are concerned with time and fuel needed to get to a destination. Whenever you look for the right socket or wrench to fit a bolt and how much force to use when tightening or using the correct torque specification. We fairly accurately tell how heavy something is just by looking at the overall mass with just our eyes. It is pretty amazing what the human mind can do. If you were to write a program for a robot with sensors to do the same things as us it would be very complicated. It might look something like this:

***Tellling robot how to pick up a ball from a basket on the ground***

Visually lock on to target ball
Move till within arm span distance
Bend torso till arm can reach ball
Extend arm
Rotate at shoulder
if (ball is down) Bend at elbow to decrease arm reach
if (ball is up) Straighten at elbow to increase arm reach
if (ball is left) Swing arm left
if (ball is right) Swing arm right
if (ball is reachable) Extend fingers
if (touch ball) Close fingers gradually
if (ball is grabbed) Try to pick up with small amount of force
while (ball weighs less than max AND ball == not moving)
 increase force by 5% in both grasp and up force
if (ball is moving) bring arm in to torso

This is over simplified but when you think about how the signals from our brain can multi-task several commands at once and then try to duplicate that in something like a robot it becomes extremely complex. This demonstration is to prove to you that everything can represented by mathematics.

Here is an excert from Math.Mit.Edu:
With this you get the ability to find the effects of changing conditions on the system being investigated. By studying these, you can learn how to control the system to do make it do what you want it to do. Calculus, by giving engineers and you the ability to model and control systems gives them (and potentially you) extraordinary power over the material world.

The development of calculus and its applications to physics and engineering is probably the most significant factor in the development of modern science beyond where it was in the days of Archimedes. And this was responsible for the industrial revolution and everything that has followed from it including almost all the major advances of the last few centuries.

Here we will connect abstract math with tangible anchors in the world. In a way I find it fun and exciting and hope you will as well.

References and Citations