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complex numbers are not interesting because they are 2d; otherwise we would just use xy coordinates instead of bringing in this whole sqrt(-1) business. Complex
by zwkrt 8y ago
complex numbers are not interesting because they are 2d; otherwise we would just use xy coordinates instead of bringing in this whole sqrt(-1) business. Complex numbers are useful because the definition of complex multiplication fundamentally says something about rotations.
If you start at 1+0i and multiply twice by 0+1i, you end up at -1+0i. If you try to imagine this in the xy plane (where we pretend x and y are currencies) then this would mean that multiplying a positive amount of one currency (1x + 0y) by a positive amount of another currency (0x + 1y^2) would put you in debt (-1x + 0y). This would be a very strange property to have in your currency!
- lifeformed 8y agoWell, what does multiplying two values of currency mean at all?
- deleted 8y ago[deleted]
- umanwizard 8y agoIt means nothing. That's why it doesn't make sense to model with something that was invented specifically as a way of multiplying pairs of numbers. That's the entire point of the message you're responding to.
- ianai 8y agoYes, go into the complex plane because the phenomena somehow mirrors a circle or sphere. But there is definitely something lacking from reducing everything down to a one dimensional measure. For instance, there are many pieces of real estate improvements that ought to be torn down and replaced with new improvements (homes, commercial buildings, etc). But the economy rarely offers incentives or even the abilities to tear down and rebuild - despite the huge benefit construction is to an economy. For things like this, I conclude the economic system is not closed. It’s not creating a self sustaining relationship between all participants.
- umanwizard 8y agoThe person you're responding to wasn't arguing against this 2-dimensional currency idea. They were explaining that it would make no sense to model as complex numbers. A lot of the confusion in this thread seems to come from people believing that the main idea of complex numbers is that they are just pairs of real numbers. That is wrong -- pairs of real numbers are just pairs of real numbers. Complex numbers are pairs of real numbers with a particular multiplicative structure.
- ianai 8y agoI made it clear I agreed. I should have added that it only becomes circular if you add the point at infinity. Otherwise it’s more similar to a plane. But yes, it’s not simply x,y numbers when you assume y^2=-1. The geometric interpretation of the complex numbers matters, and you have to do it correctly. Gets very hard to imagine quickly.
- jandrese 8y agoI can't believe people in this thread are talking about denoting currency in complex numbers. I'm trying to imagine how I would explain this to my grandmother.