Prices are used, not decoded
There’s no way to decode a price. Instead, there is a many-to-many mapping between the causes of prices and the resulting price system, i.e., the actual numbers, as well as the relationships between them, and there is a many-to-many mapping between the price system and the resulting allocation of scarce resources. For example, if you know the price of an apple is $1, you cannot use this information to deduce anything about the conditions of supply and demand, such as what the weather for apple-growing has been like, nor can you use such information about the weather to deduce, or even narrow down the possible range for the price of an apple. Nor can you use the price of an apple to infer anything about the resulting allocation of apples or vice versa.
This is because the meaning of prices is relationally real. The price of an apple doesn’t mean anything by itself, so there’s nothing to decode. Instead, the price of an apple only has meaning relative to other prices, such as the price of oranges and the price of strawberries. If the price of apples is $1 and the price of oranges is $2, then the meaning of the price of an apple is that if you buy one apple, you give up the opportunity to buy half an orange. This concept is called opportunity cost.
The relationship between apples and oranges where apples cost $1 and oranges cost $2 is really a relationship between their scarcities, which could be caused by many different combinations of events and which could cause many different allocative outcomes. As such, while we can decode relationally real prices in the sense that we can say, “Since apples cost $1 and oranges cost $2, this means that apples are half as scarce as oranges,” we cannot decode this any further, because we cannot decode either the $1 price of apples to tell us what the scarcity of apples is nor the $2 price of oranges to find out what the scarcity of oranges. We only get the relative information, and this information is consistent with so many different histories and futures that it is not useful for doing anything. Nevertheless, prices are used constantly to make economic decisions, despite the fact that there’s nothing of significance to decode. This is because prices don’t need to be decoded to be useful.
Buyers and sellers don’t decode prices, they use them. They decide with their own preferences what the meaning of a price is to them by determining what the relevant comparisons are. If you don’t like oranges, then the fact that buying an apple means giving up the opportunity to buy half an orange doesn’t matter. Buyers and sellers don’t need to know that relative prices correspond to relative scarcities. They just need to be able to use prices to determine what bundles of goods they can and cannot buy—e.g., if you have $3, you can buy 3 apples and no oranges, or one apple and one orange, but you cannot buy two oranges—and then decide which affordable bundle is their favorite according to their own preferences. Given the same set of prices, different agents with different budgets and different preferences will make different purchasing decisions.
Since price signals are analogous to bioelectric signals, the non-decodability of such signals has interesting implications for biology. The bioelectric signals cannot be decoded, so cells cannot simply read their meaning, since there is no such meaning to be read. Instead, the cells use the signals to make their own decisions, with the signals simply serving to warp what decisions the cells perceive as feasible. The same set of signals will produce different outcomes depending on the particular cells interacting with them. Neural and genetic signals will never command outcomes, just provide relationally real information that the agents interacting with the signals use to pursue their own ends.