Thanks, for your attention, Mr. Chandy. I think the problem here is my biplane brain compared to your starship brain. :-) I've often wondered if maybe the "deliberativeness" (shall we say) of mine affords me a better than average peak at the wheels turning in there. And as hard and as carefully as I have looked, I have never observed anything other than basic addition and addition facts called into play to work through every ("numbery") math problem I've ever met, 1st-grade through grad school. But I certainly wouldn't mind being proven wrong. All it would take is to present a problem from one of the "numbery" maths (arithmetic, algebra, analytical geometry, trigonometry, probability, statistics, calculus, for example) that one would not naturally solve by a sequence of fundamental additions and/or multiplications.
Can anyone come up with a "textbook" problem that shoots my assertion down?
Anyone looking in at this stage might be interesting in reading my web page on the subject:
Since it's just electrons, I'll copy a relevant paragraph here that appears in my pages devoted to basic addition and multiplication:
ds> I'll devote a web page to it one day, but think of math as being divided into two "rooms" - the addition room and the multiplication room. Each room has its own set of tools, many of which correspond to, but are not identical with, tools in the other room. For example, each room has a "do nothing" number called the "identity element". In the addition room that number is 0; in the multiplication room it's 1. You must always be totally aware of which room you're operating in, addition or multiplication. No matter how complicated a math problem gets, your brain only ever operates in one room at one time. At any moment you are doing either addition or multiplication, nimbly stepping back and forth between the rooms as needed. And, to repeat myself, no matter how complicated the addition or multiplication gets, your brain only processes a pair of single digits at a time. In a nutshell: all of math is just a big mixture of single-digit addition and single-digit multiplication.! [end quote]
Which sort of leads to the point of all this, that students would be very well served--that there might be a math education breakthrough, or revolution, even--if they were shown how all of math is just basic addition and basic multiplication, and were trained to see the distinction between the two in crystal clarity, and to only ever "do" just one of them at a time.