Obvious Leo wrote:
Scott Mayers wrote:To me, it is like accepting only natural numbers (1, 2, 3,...) ignoring the whole numbers (0 plus the natural numbers), Negative numbers, etc to cover all numbers in a theory about numbers.
This is the truth of numbers, Scott. They are an abstract construct invented by a human mind to model a certain procedure of thought. Numbers can tell us nothing about the nature of reality. Numbers tell me that if have a bowl containing two apples on my table then I can take three apples out of this bowl and have a negative apple left. This will not provide me with my lunch.
I urge you to actually try to create a REAL computer without the things that reference number as a real thing. Or are computers unreal?
Maybe it might help to note another kind of comparison using graphics applications like Adobe's Photoshop vs Illustrator. What do you think is the difference between vector and raster graphics? If you already know, 'raster' type graphics draws frames by some form of scanning the whole screen while vector's merely formulates things as 'objects that mathematically give a generic formula for things on the screen in 2 dimensions. Raster graphics treats the whole 2D frame using a linear 1D type of drawing.
Example, just using 1s and 0s, I'll draw a simple picture:
000000
011110
000010
000100
001000
001000
Can you see how the one's create the character, '7'?
A raster program treats the information as one stream. By laying it out from left to right, and top to bottom, this is
000000011110000010000100001000001000.
A vector-type program begins with the 'object' akin to how you perceive matter without concern of the spaces. Thus, it might speak only of 1s here and explain how it is generically drawn by a form:
Beginning with a given starting address (like 2 across and 1 down), find another address x units to the right and join them with 1s.
Go down x/4 units down and fill that line with 1s.
Find a point x/2 down and x/2 left; draw 1s joining this to the last point.
Lastly find a point x/4 units down and join this to the last point with 1s.
This formula describes any '7' based on a standard size, 'x', for the shape.
I used this explanation because both have uses to describe reality but the vector form acts independent to any space it is in. This is similar to how you perceive matter as real but not the spaces. Yet notice that the monitor still draws the whole frame using a raster that still demonstrates the reality of the page as a whole by turning the given vector into a raster as it is being viewed on a monitor.
Also notice that even directions within the vector description require understanding directions that exist as directions that must exist or would mean nothing. It also requires the background to be real.
Does this REAL analogue demonstrate how your thinking is like your preference to bias your description via the objects rather than the background. Yet both need the background ('0 or 1' variable spaces) and the '1s' representing the object. The '0s' may not have to be placed as it is by default there already. But they still represent and shape how the objects in them have meaning too.
Also, the same formulation can occur by reversing the 1s with the 0s so the default background would be 1s but the objects would be defined by 0s.