A proposal:

Take the equation O = I + R and see it as a machine. I and R are inputs and O is the output. We can define it precisely as a procedure and give it a name.
Plus
Read I
Read R
Do I + R ; any 2 input function can go here
Write O
GOTO Plus ; do this forever

When you think about this it logically divides into no input, single input and two input procedures.
Cos
Read I
Do Cos(I) ; any single input function here
Write O
GOTO Cos ;

Making these into hardware is easy. Each function becomes a node with input and output headers. So you can combine nodes in any manner with cables that carry the data.

Add two other functions, outside of mathematics to provide outside input and output.
Sensor
Read input
Convert to number
Write O
GOTO Sensor

Motor
Read I
Convert to action or display
Do the action
GOTO Motor

Now we can make mathematical structures and look at them.

Since we have moving data the calculus functions become simple one input functions because dt = 1 always here.

So we can write O = d(I) and O = i(I) for differentiation and integration. Other things come about. We have max and min functions, and an arithmetic logic that is beyond Boolean.

Going on this way, we eat up and unabstract some math. How much I don't know now.

Two input functions combine into n input trees that can be manipulated like numbers.

Are there any structures that cannot be made into a machine? Is any such structure meaningful?

Harold

Originally posted by hlreed
A proposal:
You've discovered functions, a concept taught to (I thought) every 7th grader.

- Warren

supposedly, harold has a degree in mathematics...

I didn't think elementary schools offered degrees.

This place is sometimes even worse than usenet.

- Warren

Warren,
What I am trying to do it to remove as much abstraction from language, including math, as possible. If you think a machine function is the same as a symbol function, you have not seen a machine.
Oops.
I hoped you could see a huge network of nodes cutting out the junk in math.

Happy = good - bad
good = corrections
bad = putdowns

This is a network. All these are working at the same time.

Just bringing this back up.

Originally posted by hlreed
Just bringing this back up.
Believe me, no one cares.

Your expansion of the succinct mathematical statement f(x,y) = x+y to
Plus
Read I
Read R
Do I + R ; any 2 input function can go here
Write O
GOTO Plus ; do this forever

does not benefit anyone, at least not by "removing abstraction from... math." Keep in mind that most mathematicians and physicists work to express different situations as different examples of a single abstract system, because this abstraction serves to illucidate commonalities of all the (apparently) different situations.

Abstraction is helpful. Unabstraction is not.

- Warren

Every thing is useful. The process of mathematics is to go from concrete to abstract to concrete. This is also what brains do.
You have sensor input, you abstract it, work on that and then your motors turn it into an action.

If you notice the aurguments here, they are mostly about abstract words. I want to point to numbers in a display. I want to mechanize language.

I also want mathematics to be redone from the beginning in a way that can be mechanized.

I appreciate your comments. I do not need put downs. I been there and done that. I knew functions in 1950.

Harold

Originally posted by chroot
You've discovered functions, a concept taught to (I thought) every 7th grader.

- Warren

I was never taught functions :mad:

Originally posted by hlreed
I also want mathematics to be redone from the beginning in a way that can be mechanized.
In what way? Like computer algebra systems or numerical methods? Both already exist, and work well.

- Warren

I want to add, not take away. I want to mechanize, and simplify so any one can see mathematics work.

Set theory cannot be mechanized. Set membership can, but only for numbers.

I want to add data streams, which are moving numbers and complete the number system. They also make integration and differentiation fundamental operations with + and -. They also add operations like MAX, MIN and a new arithmetic logic that is beyond Boolean.

Also, trees are not properly used. I have HalTrees which are functions of any number of inputs. These trees come in two types, full trees and sparse trees. Full trees themselves are a system of arithmetic in that they can be added and subtracted.
These trees can be made from any operation that has two inputs, and this includes functions.

And I would like all functions and operations defined as procedures so one can say "I mean this procedure" and can point to a script.

All this seems simple enough. Lets open up the closed mathematical society.

Originally posted by hlreed
I want to add, not take away. I want to mechanize... All this seems simple enough. Lets open up the closed mathematical society.
None of this would make math any easier, or more extensible to new problems. It would just make it look bigger on paper. I hardly see the use.

- Warren

Construction.
Simplification.
Order.
New form of logic.
Teach by showing.

I told you this was a closed society.

are you talking math?

Originally posted by emalius
I was never taught functions :mad: They probably called it something else.