People gifted in mathematics tend to be (very much a generalization) very judgemental, love symmetry, almost obsessively orderly, emotionally distant, become easily obsessed with problems, stoic in their self image, etc... — SkyLeach

What is your basis for that claim?

You're not wrong (last statement).

[note]Developmental, evolutionary and neuronal modeling inferred explanation for how and why the brain needs math for modern communication (and its limits)[/note]

I see that as: mathematics is missing constructs for allegorical analogy which are an essential base component for practical daily use languages.

Language is a serialization of 4D reality as it is "understood" by the speaker that uses shared context and perspective to allow the listener to reconstruct the serialization in the prefrontal cortex as a cognitive narrative (series of causal set functions applied to models).

That process relies very heavily on allegorical analogy to compare properties and functions of sets to completely different sets and infer meaning from the exercise.

Returning to mathematics; the purpose of mathematics is to validate the properties and functions applied to the sets. It makes no assertions, descriptions or assumptions about the nature of the sets. It's intended to strictly regulate validation of function and derived outtcome only.

The entire idea is that if you have applied mathematics to the properties and functions (as many as makes sense at least) and if two individual's precision of definition of a set in question is sufficiently detailed they can be relatively certain of reaching the same cognitive result and thus certain of objective agreement.

One of my favorite examples of the difference between linear calculus and set theory elegance is to compare Euler Angles with Quaternions. In linear algebra the quaternion equation iterates over vectors and translates (rotates) their position in 3 coordinate planes. It tells you the new location of each member of a vector. With Euler angles, however, the description of the matrix is what gets rotated, not the matrix.

- Me

I quoted myself because you seemed to have missed my detailed comparison when you asked where Quaternions came into things.

demographics

ZFC

Jung help us I just skimmed back and now I know why this thread is 10 pages long. We have an ISFJ judging everyone for daring to think instead of accept dogma.

Returning to mathematics; the purpose of mathematics is to validate the properties and functions applied to the sets. It makes no assertions, descriptions or assumptions about the nature of the sets. It's intended to strictly regulate validation of function and derived outtcome only — SkyLeach

You refer repeatedly to "sets". Care to expand on that ?

A set is just a group of things. In the brain every concept is a superset of neural cells and their relationships both to one another and to other associated sets in other regions of the brain. Relationships are also a set of measurable dynamics such as sodium ions, potassium ions, neurotransmitters, inhibitors, hormonal markers, synaptic pathways and their reinforcement with same.

So in this context a set is the boundary of associations encapsulating a concept as distinct from others. It is best defined given current technology by an fMRI showing active regions experiencing state change during specific cognition. Typically it includes the Parietal, Occipital, Temporal and Prefrontal for real-world objects and their allegorical associations. Distinctions between regions are associated with how concepts are introduced (visual, written and spoken instigation as well as direct vs. representational association with cognitive burn-in (reinforced mapping)).

Math is an abstraction of determinism such that you can apply the same series of functions to apples, oranges and the loves of your life because even though two of the former are physical sets of atoms that can be seen and touched while the latter is an allegorical association of evaluated relationship qualifications between a concept of self and a concept of other; all three are treated by the human brain identically. That's because they are cognitively identical processes.

Well, that's an interesting approach to mathematics. I'm always curious about how laymen interpret the subject. :cool:

demographics — SkyLeach

Obviously, just saying "demographics" is not a basis for claiming:

People gifted in mathematics tend to be (very much a generalization) very judgemental, love symmetry, almost obsessively orderly, emotionally distant, become easily obsessed with problems, stoic in their self image, etc... — SkyLeach

Obviously, just saying "ZFC" is not a meaningful answer to the questions I asked.

https://thephilosophyforum.com/discussion/comment/659140

instead of just assuming you should learn a bit more about the humanities and what kinds of research are regularly done

I never said I was explaining jargon.

It's the only one you're getting. You're a limbrain ISFJ with an ego the size of a mountain that has repeatedly demonstrated he's here to stroke his ego not discuss philosophy.

And no, I'm not going to ignore you but I'm also not going to argue (as in fight) with your ego instead of your rational mind. It's a waste of my time.

EDIT: I mixed up two replies in one. Glad I caught it on the editorial re-read. That's what I get for typing in the middle of a family in full Saturday boogy.

1 infinity + 1 infinity = 1 infinity
— Agent Smith

Again, there is no object that is infinity (other than such things as points of infinity on extended numbrer lines). There are sets that have the property of being infinite.

That cardinal arithmetic is idempotent for infinite sets (especially for the set of natural numbers) is not really not problematic if you bother to read the proof. — TonesInDeepFreeze

:ok:

I quoted myself because you seemed to have missed my detailed comparison when you asked where Quaternions came into things. — SkyLeach

Were (are) you an aeronautical engineer or Naval person? I know little of rotation theory, but the gimbal lock problem can occur in one of these schemes but not the other. The short paper I linked is as close to this as I get. I almost always work in the complex plane.

I was joking about the behavior of fellow mathematicians. In all my days I never saw a rant. And your description of a math person's personality is valid sometimes, but more often they are social animals - the practice of mathematics is a very social activity. I recall being at an autumn meeting at the Luminy campus of the University of Marseilles in 1989 at which there was communal dining and quite a jovial atmosphere. And a summer meeting at the University of Trondheim in 1997 where a member of the royal family attended a convivial banquet overlooking a ski jump where their Olympic team put on a performance. Other international meetings displayed similar atmospheres.

Sorry about the ramble above, but many assume math talent means the sort of personality you have described. Which, incidentally, omitted the fact that many in the profession have musical talent.

@TonesInDeepFreeze, is an uncountable infinity a mathematical object?

ooh you're right I forgot about that one and yes, it's a problem with rotating space instead of rotating the object in space. You can actually have the problem with either implementation depending on how you're treating your overall scene because quaternions still operate on the three axis and, depending on what you're doing in the scene, become mathematically ambiguous due to loss of precision (i.e. the square root problem and other things).

I am an engineer but software, not mechanical/chemical/structural/etc...

[hr/]

As for

I was joking about the behavior of fellow mathematicians. In all my days I never saw a rant. And your description of a math person's personality is valid sometimes, but more often they are social animals - the practice of mathematics is a very social activity. I recall being at an autumn meeting at the Luminy campus of the University of Marseilles in 1989 at which there was communal dining and quite a jovial atmosphere. And a summer meeting at the University of Trondheim in 1997 where a member of the royal family attended a convivial banquet overlooking a ski jump where their Olympic team put on a performance. Other international meetings displayed similar atmospheres. — jgill

Please allow me to clarify using my own quote:

...gifted in mathematics tend to be (very much a generalization) very judge... — SkyLeach

I am very aware of the problems of bias in generalization and that's why I pointed out it was a generalization. Any time you combine multiple data points in a demographic you wind up with a much flatter distribution curve. "... tend to be ..." drops to 12% instead of the 50:50 median split of a single data point. Most people conceptualize bias generalizations at 50+ during conversation because... well I'll avoid going into why right now...

As soon as you add any other variables you can completely invalidate the metric. I was using my knowledge of Jungian and the MMPI which are the most widely used and thus easiest to draw inferences from. They have their limits, however, so I try to make it clear that I'm generalizing and try never to use them to evaluate any individuals (or prejudice my behavior). The operative word being try, I'm human too.

EDIT: one further thing to add. When it comes to a discipline, generalizations become much more appropriate because we are very much social animals and when we make choices about our own bias which is essential to cognitive function we must choose between social consensus and personal time investment for validation (hopefully those, not the bad ones like bigotry, faith or inanity). Academics is, at its core, an appeal to authority.

I have read some of what the others said and my good question is, what kind of infinite are you looking for? As long as you live this mortal life, you will not possess any knowledge of the True Infinite, aka God, at least in the sense that you will have no real evidence of this mysterious Infinity. Any belief in the Infinite must be accepted with faith. And to an extent, even lesser infinities are unknown, until you actually encounter them. Before that, we can only speculate on the nature or existence of infinities.

♾? If I understand you, the only thing the infinity symbol in mathematics means is that the limit isn't known (thus it can't be summed).

♾? If I understand you, the only thing the infinity symbol in mathematics means is that the limit isn't known (thus it can't be summed) — SkyLeach

Well, all I meant to ask was whether something uncountable (an example of an uncountable infinity is the set of real numbers R) can be considered mathematical? After all, math is, bottom line, about countability (0, 1, 2, 3,...).

Academics is, at its core, an appeal to authority. — SkyLeach

In a sense. An appeal to the authority of consensus.

I don't really know what you meant by that.

Not really. That's just the first traditional axiom (self-evident truism in the philosophy of mathematics).

Then again, as I said, there is a very strong and growing debate about that since the argument for sets being the the first self-evident truth has a lot to offer and, of course, can't (or hasn't been) invalidated.

The essential argument is that numbers are simply a form of measurement and mathematics is a precise language for making falsifiable linear statements about those measurements. Numbers are, after all, assigned to representations of sets. Apples/fruit/kilometers/distance/seconds/time... you get the idea.

I'm somehow not convinced by your words. Uncountability is, in a sense, beyond (conventional) mathematics seen as a counting activity.

True that the variety of numbers has expanded over history. Yet we seem distinctly more comfortable with the category of natural numbers than with any other I can think of.

Continuity is infinite and uncountable. Though you can have one continuity, two continuities, three continuities, more continuities, many continuities, enough continuities, ànd no continuities. How many points reside in a continuity? Is a point a zero dimensional continuity? Does continuity require one dimension at least?

Academics is, at its core, an appeal to authority. — SkyLeach

In a sense. An appeal to the authority of consensus. — jgill

↪jgill I don't really know what you meant by that. — SkyLeach

Mathematics is what a consensus of mathematicians says it is. That's the "authority".

is an uncountable infinity a mathematical object? — Agent Smith

I know this wasn't a question for me, but have to say: Yes, it is a mathematical object.

Just as is even Cantor's Absolute infinity. (Which he didn't talk much about, but still...)

instead of just assuming you should learn a bit more about the humanities and what kinds of research are regularly done — SkyLeach

Assuming what? I infer that you don't have any actual studies to cite, since you continue to reply without mentioning them.

And I know a little about the notion of studies in psychology and sociology. Asking you to cite an actual study that justifies your claims is not a fault from my own understanding.

It's the only one you're[/] getting — SkyLeach

With emphasis on 'you're', I guess you mean that you have a better response but you're holding it close to vest because I'm the one asking?

Anyway, my point stands that just saying 'ZFC' is not a plausible response to the questions I asked.

You're a limbrain — SkyLeach

What's a limbrain?

ISFJ — SkyLeach

You don't know that I am an ISFJ. And even if I were, being any one of the types does not contribute to disqualifying a person from having asked pertinent questions.

with an ego the size of a mountain that has repeatedly demonstrated he's here to stroke his ego — SkyLeach

I would guess that most people who post do so with motivated to enhance their sense of self-worth by exercising their prerogative to express their ideas, and many people often with criticisms of the ideas or claims of others. You have no evidence that my motivation is any more for gratification of ego than average. Especially, I come nowhere close to the kind of egotism found in a forum such as this that is displayed by people with terrible grandiosity when they bloviate their personally devised philosophies, with irrational arguments denying any weight to, and insulting other views by people who know something about the subject, and doing that by way of egregious distortions of even the rudiments of the subject.

And even if my motivation were entirely egotistic, that would not disqualify my points themselves.

not discuss philosophy. — SkyLeach

I am interested in mathematics and philosophy of mathematics. I find that it is worthwhile not to distort or misrepresent the mathematics itself when philosophizing about it. Clearing up misinformation and misunderstanding that is posted about mathematics is a worthy first step toward discussion of philosophy about it.

I'm also not going to argue (as in fight) with your ego instead of your rational mind. — SkyLeach

You have not mentioned anything I've said that is irrational.

Any time you combine multiple data points — SkyLeach

On what data points do you base your characterization of the personalities of mathematicians?