Philosophy Now Forum

I understand walking the circumference of a radius 1 circle about the origin counterclockwise, and making mental notes about theoretical position on a 2 dimensional plane in relation to all other points; but no, I don't equate spinning in empirical circles with imaginary mathematics... Have you see...

I have yet to meet anyone who has empirically experienced the square root of -1 I have. You have too. The complex number i is just a gadget that keeps track of how many times you made a counterclockwise quarter turn in the plane. If you're facing east that's 1 on the real line if you are in the usu...

I agree with pretty much everything you said before this so I am not going to respond on any of it. For every Mathematical denotation there is a clear philosophical interpretation. I much prefer science/engineering to philosophy so I want to elaborate on WHY I think lazy evaluation matters to Mathe...

π + π√5 ‾‾2π‾‾ = Φ But this is just a restatement of the defining property of Φ. You could plug in any real number whatsoever and it would still be true. You have (pi + pi sqrt(5) / 2pi = (pi(1 + sqrt(5))) / 2pi = (1 + sqrt(5)) / 2 = Φ. Just as the pi cancelled in the numerator and denominator; you...

π + π√5 ‾‾2π‾‾ = Φ But this is just a restatement of the defining property of Φ. You could plug in any real number whatsoever and it would still be true. You have (pi + pi sqrt(5) / 2pi = (pi(1 + sqrt(5))) / 2pi = (1 + sqrt(5)) / 2. Just as the pi cancelled in the numerator and denominator; you cou...

It is designed as a universal 'orientation' system that tends away from all suffering and towards all knowledge. If applied to the spiral, the pentagram has two orientation "poles" with each being some configuration between the two: knowledge and belief-based ignorance. This is beyond my ...

I've had a bit of a rough day so I am not on my best game choosing my words - if you pick up on any irritability/crankiness in my tone - it's not you.... No worries. You wrote a long post and I'll only respond to a little of it today, but hopefully it's the heart of the matter. So it seems to me th...

No, as I don't want or expect anyone here to take me seriously - I don't even! Ah. Sorry I took the trouble then. I am aware of Euler's but do not see e^(2πi)=1 e^(2pi i) = cos 2pi + i sin 2pi = 1 + 0 = 1. If x is a real number, the function f(x) = e^(ix) wraps the real line around the unit circle ...

I figured you'd click on the blue up-arrow next to the quote which will take you to the relevant post (so i don't spam the thread again). Duh, got it!! Will check it out. But every time you write down a number - whether to paper; or to memory - you are handling a representation. Of course. But the ...

I'm afraid I see no polynomial with integer coefficients here. Do you? Honestly yes but that is because I do not abide by the restrictions of what a 'polynomial' is (or can be) according to mathematical orthodoxy. Ok that's fine. But then do this. Say, "A standard polynomial is such and so. Bu...

The relevant quote is in this post: (...) You seem to have omitted the quote. And so the implication seems to be exactly that. Representation (base, choice in precision) matters. In practice, if not conceptually or symbolically. It could never matter in the question of whether a real number is comp...

π actually can be the solution to a polynomial with integer coefficients: https://i.postimg.cc/0QtRWvtn/base-of-pi.jpg I'm afraid I see no polynomial with integer coefficients here. Do you? "2π" does not arithmetically equal '1', True. If you don't mean equality you should try to say what...

Thanks for the article, looks good. I know a bit about constructive math. Not only from the computational viewpoint but also from higher category theory and topos theory in abstract algebra. Non-constructivism is all the rage these days. It's good to remember that foundations aren't cage matches to...

Yes it's the standard definition in the computer science curriculum. And that would be dandy, but I side-stepped academia. I am an autodidact. I understand computer science (engineering?) by having done it for 20+ years. Now that I am reading the theory, I am joining all the dots to the practice. Ok.

Didn't you claim to have read Turing 1936? So when you say you don't know the standard definition of a computable number, you are, shall we say, dissembling. I have read it. You have quoted it. I have that definition committed to memory. In 2020 is that still what you refer to as "the standard...