Consistency in Arithmetic
Double the debt: 2 −1 = −2 *Ok
But: −2 −1 = 2 *Ok?
Who will allow you to multiple your debt with another’s debt to get rid of it?
2 −1 + −2 − 1 = (2 − 2) −1 = 0 −1 = 0
But...
2 −1 + −2 −1 = −2 + −2 * −1 = 0
Therefore...
-2 * −1 = 2
Ian Stewart, Professor Stewart’s Cabinet of Mathematical Curiosities, Profile Books, 2008, pages 37-38;
So mathematics is mentally-created, it looks objective because of primordial choices we have made? As a form of a subconscious of the Species and we’ve created computers because we think that way and choose to think that way? Our truths may be grounded on habit and rationality may be a self-imposed restriction, nature being more non-bivalent than we would like it to be. Under the same logic, the furniture in our room might have been subject to similar primordial choices. Oh, and especially I, Ourselves, Identity.
The degrees of what’s available in nature might be infinitely greater than we think and a self-imposed boundary might be inherently limiting.
Hofstadter opens with the story of J.S. Bach’s Musical Offering for King Frederick, which contains a particular canon that sneakily shifts from one key to another before its apparent conclusion, and when this modulation is repeated 6 times, the piece ends up at the original key but one octave higher. This is our first example of a “Strange Loop”:
The “Strange Loop” phenomenon occurs whenever, by moving upwards (or downwards) through the levels of some heirarchical system, we unexpectedly find ourselves right back where we started. (Here, the system is that of musical keys.)
Other examples occur in the drawings of M.C. Escher, for example this famous one.
Is the water going up or down?
I think you meant (-2 * −1 = $2) I meant, multiply by a negative count of debt and not itself. So a debt multiplied by a negative count of debts leads to no debt at all, a positive. I’m not sure how you can have a negative count of debts.
$2 debt squared does make sense, though, it is $4 and no debt. So by our mathematics, I could call the bank and ask them to multiply my debt with yours, I would return a positive.
The point I am making is that we’ve made it this way because have chosen to. It says to me that mathematics is more of a mental creation, albeit a very useful one and that nature might be infinitely greater than our own self-imposed boundaries.
Take a look at this picture does the water goes up or down? Is bivalent thinking necessarily nature or simply a mental creation? When it comes to truths (true or false) or computers (by primordial decisions) (1 or 0)