[snowman]

Since you clearly cannot grasp the connection between mental manupulation of numbers and creative thought, there is little use in discussing it with you. Calculators are great, I use them, and computers all of the time. Yet they have only a very small place in the education system.

To truly understand something, how the world works, how physics work, how to build a building, an engine, anything, you must have a FEEL for it. This "feel" is developed by having a sense of the magnitude of things and the relative way they interact with each other. This "feel" can only be developed by becoming very very familiar with numbers and their magnitude. An instinctive feel. Computers only back up this sense. They only document what one "knows" to begin with. The computers can extend this "feel" but they cannot establish the basic concept that one develops by becoming "one" with them. This feel is developed by using math, without the use of calculators. Actually without numbers, although the numbers are necessary at first, to develop the correct relative relationships between variables. The concepts of twice as much, 10 times as much, infinity, cannot be realized without first getting a feel for the numbers. Numbers that are first counted on ones fingers.