4 ms·
How do we do things like electrical engineering without imaginary numbers? Is this method an actual improvement?
by 7thaccount 1y ago
How do we do things like electrical engineering without imaginary numbers? Is this method an actual improvement?
- michaelsbradley 1y agoimaginary numbers are not the same thing as irrational numbers
- vlovich123 1y agoHow do you rationalize pi or e?
- aarestad 1y agoBy fiat, of course. :) (e.g. https://en.wikipedia.org/wiki/Indiana_pi_bill https://en.wikipedia.org/wiki/Indiana_pi_bill)
- empath75 1y agoYou don't. He basically defines numbers like pi and e not as numbers, but as iterative functions, which you can run to whatever level of accuracy that you want. It's sort of a silly argument, because _all_ numbers can be treated like the output of a function, including the real numbers, so he has basically smuggled in all reals through the back door, because any real number can just be thought of as a function with increasingly precise return values with an infinitely long description, just like pi is.
- MarkusQ 1y agoYou can't get all the reals that way. The reals that can be produced by an algorithm make up a vanishingly small (e.g. countable) subset. Almost all of the reals are inexpressible.
- LPisGood 1y agoTo an ultrafinitist, there is no such thing as a number that is inexpressible.
- kragen 1y agoRight, but to be clear, it's not that ultrafinitists like Wildberger believe that they can express all the real numbers; rather, they believe that those inexpressible real numbers don't actually exist.
- vlovich123 1y agoHow does that work for calculus which regularly looks at the limits of functions as x approaches infinity and has very real real world applications that stem from such algorithms?
- drdec 1y agoMath in general needs to have a big blinking "don't confuse the map for the territory" label on it. E.g. when you calculate the area of a plot of land do you take into account the curvature of the Earth? You have to make a bunch of compromises in the first place to even talk about what the area of a plot land means. Math is a bunch of useful systems that we humans have devised. We tend to gravitate towards the ones that help us describe and predict things in the real world. But there is plenty of math which doesn't do either. It's just as real as the math that does.
- vlovich123 1y agoI agree. I’m just trying to speak to the “realist” argument that Wilderberg presents claiming that some numbers aren’t real and there’s no point talking about them when they come from very practical mathematics let alone the ones that aren’t. In no way was I trying to claim that some part of maths aren’t real - I was trying to understand the consistency of what to me seems like a confusing argument to make.
- empath75 1y agoHe doesn't work with imaginary numbers, either. He treats complex numbers as matrices of rationals.
- numpy-thagoras 1y agoWhich is the same thing for all intents and purposes. An ultrafinitist is still allowed to call that 'i'.
- dhosek 1y agoStill kind of freaked out that a Möbius transform can be expressed as a matrix multiplication.
- 7thaccount 1y agoI never said they were, but could've sworn that the Wikipedia page or parent comment did (I can't find it now and am questioning my sanity). I couldn't understand how he could try to get rid of them, although this isn't surprising as mathematics is basically magic to me once you get past calculus. I guess this is only about removing irrationals though.
- griffzhowl 1y agoIt depends on the particular construction. You could construct the "complex rational field" by adding i to the rationals with the rule i^2 = -1. That seems to be what Wildberger is ok with. The standard complex numbers involve adding i to the real numbers, which Wildberger doesn't like. I don't know how you'd do electrical engineering with the rational complex field, because electrical engineering and physics in general involves a lot of irrational quantities and calculus, and the standard foundations of these concepts use real numbers. It's really up to finitists to show that there are problems with these methods and that they have a better way of doing things, because so far the standard way seems to work very well.
- fuzzfactor 1y agoElectricity has always been standing by to do the same things regardless of how far your imagination wanders away from where it started.
- clickety_clack 1y agoElectricity is not standing by, it is malevolently trying to burn out your equipment. If you allow your imagination run too far it’ll heat up your equipment and burn it out. You need to increase your capacity to keep your imagination in check.
- numpy-thagoras 1y agoImaginary numbers, quaternions, octonions, Clifford Algebras, etc. can still have finite expressions. After all, the Cayley-Dickson construction is not an infinite affair.