Non-Euclidean Math is Psychology - Politics Forum.org | PoFo

Wandering the information superhighway, he came upon the last refuge of civilization, PoFo, the only forum on the internet ...

Pollution, global warming, urbanisation etc.
Forum rules: No one line posts please.
#14149699
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.
#14149715
I guess so. It's not really what I had in mind. I think people using abstract math quite rigorously are actually on to something useful, I just don't think it's exactly what they say it is. Sure, it's not categorically different than your random pattern recognition kook, in that case Quantum Physics looks goofy - I don't mind saying - but on the other hand it's on a different qualitative level altogether.
#14149723
Quantum physics is just as scientific and just as rigorous as Newtonian physics. You're babbling nonsense again, Suska.
#14149729
I've just stated I find it rigorous, as I understand it the idea is to be self-consistent. This allows for almost anything though.

Don't be a hater Potemkin.
#14149747
Are you trying to suggest that abstract mathematical concepts are only used in mostly abstract/theoretical subjects? Such abstract concepts as imaginary numbers have very real meaning in areas such as Fourier Analysis, which is extremely useful (critical even) in areas such as signal processing and frequency/vibration analysis (both of which are very practical and straight forward). You would be hard pressed to put metaphysical concepts on the same level as Quantum Mechanics (one has the virtue of scientific rigor, the other does not).
#14149762
I don't agree that metaphysics is not scientifically rigorous, it's a different sort of science. If by imaginary numbers we're talking about negative numbers on a Cartesian scale these could be considered just labels in many cases. My point - once again - was not to slander the discipline, but more along the lines of the suggestion that in as much as we begin with hard to study subjects and therefore have to rethink the symbols we use to study them - in as much as this becomes a study in itself, for instance Set Theory, these tools we use and on which certain very abstract matters depend, are more about what is thinkable and what is necessary to thought and therefore the study itself is of a secondary use to the development of them - as a study of thought.
#14149844
If by imaginary numbers we're talking about negative numbers on a Cartesian scale these could be considered just labels in many cases.

You clearly know nothing about imaginary numbers, Suska. Stop babbling before you embarrass yourself any further.
#14149855
'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.
#14150039
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.
#14150049
I don't know what that means.

Evidently.

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.

Your objection seems to be that complex numbers cannot represent quantity. Traditionally, numbers have been used to represent a given quantity of something. Indeed, the need to represent quantity in an abstract sense is probably the origin of mathematics. However, there is no logical connection between numbers and quantities. And, indeed, what 'quantity' does a negative number represent? The discovery of imaginary and complex numbers (which involve the square root of -1) made it absolutely clear that numbers and quantities are different things.

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.

Don't wait for someone else to teach you - educate yourself. In this age of teh internets and Wikipedia, there's really no excuse not to.
#14150241
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.


I'm not sure exactly what you mean, but I have drawn some vague connections between quantum mechanic concepts and the nature of our self existence, and the possible workings of our minds.

String theory is a bit harder to visualize. I enjoyed Kurt Vonnegut's "Slaughterhouse Five" version of reality as a metaphor for higher dimension existence, but it's not a very realistic metaphor. Rob Bryanson's Imagining the Tenth Dimension is an interesting way of looking at string theories and higher dimensional existence. It also suggests implications about the existence of the mind if it has any basis in reality.
Potemkin wrote:You clearly know nothing about imaginary numbers, Suska. Stop babbling before you embarrass yourself any further.

Sometimes I fall into the trap of assuming that if someone says something that makes no sense to me, they must be smarter or understand something I don't. This is clearly a logical fallacy. I'm going to name it the onemalehuman fallacy.

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.
#14150277
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.

Define 'literally'. It is in fact a completely rigorous statement to say that the imaginary number line is orthogonal to the real number line. They therefore do exist in a new dimension relative to real numbers; that's as literal a statement as it's possible to get in mathematics.
#14150350
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.
#14150429
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.


No, it is about "what we see in the world". Negative numbers have been recognised as useful for hundreds of years, in areas like finance - is your bank balance positive or negative? What is the charge on a proton, electron or neutron? They're used all the time to solve real world problems, not just to be self-consistent, and the same goes for complex numbers, which are used in electrical engineering, for instance. Quantum theory and relativity arose to explain experimental results that nothing else could; and they made predictions of new phenomena that were later confirmed experimentally. String theory has not, as far as I know, made any predictions that can currently be verified, so your characterisation may be more apt there; but people are formulating it to try and explain what our observations have found.
#14150442
Prosthetic Conscience has pretty much said it all. I have nothing to add.

Lemme get this all straight. You can't be bothere[…]

https://twitter.com/adamjohnsonNYC/status/88995582[…]

The long and boring tantrum by zionists about BDS.[…]

A Left-Libertarianism-ist Manifesto

He didn't simply not give a reason like you said […]