Wild geese flying over a lake don't intend to cast a reflection
and the water has no mind to retain their image
Wandering the information superhighway, he came upon the last refuge of civilization, PoFo, the only forum on the internet ...
If by imaginary numbers we're talking about negative numbers on a Cartesian scale these could be considered just labels in many cases.
I don't know what that means.
I do know that what I'm talking about is abstract math, math without it's roots in everyday things, numbers that aren't fractions or whole for example. I understood the characterization of non-Euclidean was correct.
I'll grant I suck at math. That doesn't mean there isn't something to the topic. I can clearly see what I'm trying to say, but I'm no specialist in this branch if learning - which is a good reason to bring it up unless this is a house of bullies who only will tease instead of teach.
Suska wrote:I think that after a certain threshold, say the start of the 20th century, with the advent of imaginary numbers and leading to things like String Theory and Quantum Physics - when people ceased to be using math for practical straight-forward things dealing with clear objective matters - we have entered a terrain of thought experiment better suited to an understanding of inner matters such as thought itself and even metaphysics. Quantum physics in particular, though pointed at the sub-atomic realm seems to me to be looking at an ink-blot. String theory is similar in that it seems to begin with sets of pure symbolism, cosmology, the realms of the very large, like the realms of the very small reveal more about what symbols a mind needs to function than they do about what is actually out there.
Potemkin wrote:You clearly know nothing about imaginary numbers, Suska. Stop babbling before you embarrass yourself any further.
Potemkin wrote:'Negative numbers on a Cartesian scale" are just... negative numbers. Imaginary numbers are orthogonal to the real number line, so that complex numbers form a 2-dimensional surface rather than a 1-dimensional line.
That's just one way of visualizing it, and the easiest way to plot it. Imaginary numbers don't LITERALLY exist in a new dimension relative to real numbers.
Suska wrote:Potemkin, you seem to be suggesting that new math extends old math, it does so by systematically abandoning the rules that made it coherent. Again, I think what you mean by rigorous is "self-consistent" and this is a fine thing in principle, but it allows for anything apart from an inconsistent application of rules. We can substitute up-quarks or dimensions with anything, imaginary bananas or imaginary cups of coffee that obey their own rules, and what I'm suggesting is that the value of the exercise is the same - the language, the method - because it's more about achieving that consistency then it is about what we see in the world.
Einstein is the star of this sort of effort; applying metaphysical assumptions to astronomical observations, it just happens that barring evidence to the contrary these assumptions have been used in connection with other assumptions to climb out onto a a very fine limb and beyond like a cartoon character standing in space until the fact is noticed. If the answer is so strange that no one can explain it we must return to our original assumptions. What we're seeing in the higher maths of today are artifacts of where we look, or rather how.
You're right I'm babbling. I think there's something to it but it's based mostly on impressions since I don't have several lives to devote. Mind you, I've read on the subject and I'm echoing opinions of fairly esteemed commenters, I just don't have time right now to track them all down. I was hoping the more learned members here might help me ferret out where this is going but apparently the tendency is disinterest.
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This is the single greatest question ever asked.