Hypercomplex money

Money is currently quantified in real numbers, including debt, credit, interest, cost, profit, loss and other quantities. Taxation is also in real quantities.

When i was a member of a LETS scheme, i used to charge leaves for my services and money for my goods, so people would pay me in two separate units. There was a problem with units based on time because it meant, for example, that if you needed childcare to do something for someone else, that would "cost" exactly the same as the units one received for the service one offered. Another problem was that governments sought to tax it and to deduct a notional conversion rate from benefits, making it difficult for people to operate if the work they offered was normally paid as well.

There are also values which are less quantified, as i've mentioned before.

This is my solution: Buy and sell in the normal way using real units of currency, but at the same time trade using currency units defined in terms of complex numbers, not as a way of indicating interest as in the linked idea, but as a way of measuring qualities not normally taken into consideration in monetary terms at all. Thus, you might go to a small shop where you have a more personal relationship with the shopkeeper and pay them for the quality of service and positive experience you get there in mathematically imaginary terms, or you might pay a second price in imaginary quantities for an item which was locally sourced, more sustainably produced, more durable or something else, where this is not taken into consideration by the real number of the price. Alternatively, you might sell something with an extra imaginary value if it had extra sentimental or ceremonial value to you, so a family heirloom, a napkin with one's future partner's telephone number on it or the signature of a famous person could be valued in those terms rather than in the terms of the cost of the item. This could also be flipped over so that the real value of a napkin with Elvis's signature on it corresponded to its auctionable price, but the imaginary value corresponded to the cost of the materials.

Introduce this second dimension of currency in everyday trading. When you offer a tip, carry on doing so in real money anyway, but also give them a cheque, like a LETS cheque, which represents the value of that person's politeness and consideration to you in imaginary "monetary" terms. Give a shop assistant at a checkout counter a similar cheque personally as a compensation for their boring, repetitive work. Use them for and as random acts of kindness and paying forward. Get it to creep gradually into society until it becomes mainstream, maintaining an organisation like those involved in running LETS to keep track of the imaginary currency units. Mark prices in shops using complex numbers by two sets of price tags. Donate to charity with these units. Above all, mark these units clearly and unambiguously as being in imaginary numbers in the mathematical sense.

At some point, should this become successful, the government will attempt to intervene, as it did with LETS, to tax or establish a conversion rate to conventional currency so it can deduct from welfare. However, under current legislation this would be impossible. All financial transactions currently involve operations on real numbers alone. The imaginary portion of prices in complex numbers cannot be taxed or converted to conventional money because they are in a different dimension from real numbers.

It was hard enough for governments to deal with LETS, which were in real numbers. They would have considerably more difficulty dealing with these, particularly as everyone would still be paying tax, receiving income and buying things using real money at the same time.

Edit: I agree with [bigsleep] about the hypercomplex point and i want to amend the idea to include that.