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Mark Balaguer defends the proposition that mathematics belongs to an eternal realm. This realm is frequently referred to as the Platonic realm.
Mathematics is like nothing else. The truths of math seem to be unrelated to anything else—independent of human beings, independent of the universe. The sum of 2 + 3 = 5 cannot not be true; this means that 3 + 2 = 5 would be true even if there were never any human beings, even if there were never a universe!
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Crap. Sums are not in nature because discrete objects are not in nature.
2 + 3 = 5 is not a natural statement because particles are not natural. Nature is all waves.
Math is just a form of language, inherent in the human brain like words and sentences. Integers are an arbitrary and crude sampling of continuous reality, just as digital audio is an arbitrary and crude sampling of a real analog wave.
Even if you think in terms of atoms, countable objects are still an arbitrary grouping, only valid in certain ways at certain scales. We sense areas of atoms as single objects like apples because we’re not looking closely enough. From the viewpoint of a VERY SMALL observer the boundaries of one apple are invisible.
The sum of two apples is meaningless on its own. Nature doesn’t combine the apples into one object. When nature does combine things, the result is an entirely different object. Inanimate combinations lead to rivers or avalanches. Animate combinations (eg eating or sex) lead to more life.
Me + Apple doesn’t automatically turn into MeApple. Me + Apple becomes (me with more energy).
We could consider the total area occupied by the two apples, or the total nutrition imparted by eating the two apples, or the total mass of the two apples. Each of these totals can only be approximate, never exact.
But the two apples are NEVER a single thing unless you grind them up into applesauce, in which case they’re no longer discrete at all.
We don’t need discrete math for construction or repair. All measurements are analog. We do need discrete math for commerce. If I have two apples on a tray, I can sell both of them for a single price, which may happen to be the sum of the two unit prices but more likely will be discounted. The discount will increase for larger quantities.
But here we’re not dealing with a passive inert number, we’re dealing with a MOVEMENT of value. The two apples move into your hands, and a token of abstract value moves into my hands. Money is always a vector.
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Think of currency in a dynamic way.
A coin represents a DELTA of value. If you have HONESTLY acquired a coin, it means you have INCREASED THE VALUE of something. You have cut down a tree, or turned the tree into paper, or helped to print a book with the paper, or arranged books attractively in a store to raise the sale price.
Gresham’s law in vector form: The skill that yields the greatest number of coins for a given amount of effort will become a collectible, no longer freely transferred.
What’s the highest-value skill? Counterfeiting. PLATONIC money, money as pure numbers. What’s the SKILL or EFFORT that creates counterfeit money? No skill at all, just access to the treasury. If you belong to the correct caste you have access to counterfeit money. It’s an inherited trust from the start!
Among other traditional skills, what’s the lowest-value? Farming. Requires long ownership of property and generations of skill development. Payoff depends on weather, speculators, and the actions of other farmers. BUT farming is critically important to the existence of civilization, so a sane civilization (ie FDR) takes steps to subsidize farmers.
Most other skills are in the middle. Pottery, welding, weaving, programming, cooking, selling. These are available to anyone with some innate talent, but the genetic aspect is non-exclusive. Doesn’t depend on your caste. You can learn them in a year or two of apprenticeship.
These skills qualify as currency. They can be transferred freely to anyone who can use them, and they can be used freely by the recipient. The resulting delta of value depends on all sorts of internal and external factors that don’t apply to simple coins, but the basic idea is still the same.
Because these skills can be acquired (comparatively) easily, they don’t need subsidies… BUT a sane civilization will take steps to maintain their value, just as it maintains the value of coins.
Our insane “civilization” is depriving ordinary skills of all value. Hyperinflation of skill currency, leaving ONLY ledger money, aristocrat money, PLATONIC money, with any value.
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Polistra's Mill 