## A proposed revision for the current MBTI model

The current model of the MBTI (Myer-Briggs Type Indicator) has been, in my opinion, one of the most convincing attempts at generalizing how axiological principles and emotions interact, such as to produce what is referred to as character. However, I would like to say that there are several questions which, if answered, might stand to dramatically improve how useful and falsifiable the model actually is. Therefore, I would like to impose a few goals, in order to explicitly show what my model does, that is different.

1. Establishment of the validity of proposed delineations from psychological, evolutionary biological, and game theoretic perspectives.
2. Further development of the theory of temperament and function, such as to explain the distributions in letter groupings.
3. Relation of letters to predisposition toward pleasure and stress of various types, as well as the effects those types of pleasure and stress have on the other types.
4. Development of a theory of context dependent typal gradience. (CDTG’ing from type to type, as per changes in external and internal context)
5. The development of a theory of interpersonal interaction.

For, it is after we have accomplished these things, that we will better be able to establish why it is that we make the decisions we do, so that we can ensure that we have an overall beneficial effect on each other, as individuals, and member of the same species.

In any case, for a along while (2 years ago), I had been attempting to reduce the number of emotions a human being is able to feel, to a set of primitive emotions (though, as opposed to some, I also included anticipation and inhibition)

from which the, seemingly, extensive variety of feelings may be generated by mixing the primitives with varying intensities. In this sense, there is some basis set of emotions, and the rest of them are just vectors in the space over which the basis spans. However, I didn’t exactly have a formal method for deciding upon how any particular emotion should lead

However, when I learned about the MBTI, I realized that there might be a way to explain how axiology, temperance, and social forces guide the development of personality, and how personality responds to stimuli of various types. I thought that, if one is an extrovert or introverted, there should be reasons, both negative and positive, for why they go about behaving in the manner they do. Indeed, if each letter was associated with a type of negative an positive consequence, it would be sufficient explanation for it’s behavior, like a context sensitive massage/shock collar. Indeed, from this prospective, it seems clear that this serves the purpose of shaping our learning styles and, as such, the proportions of people who have such predispositions is maintained by the degree of reproductive success their actions have on the species as a whole (as is the case with homosexuality and bisexuality, in the case of bonobos). That is, the fact that there are so many SJ types is probably supported by the danger imposed by having a majority of people with characteristics commonly associated with NP types. That being said, the means by which society innovates toward a better future is by way of NP types. Hence, I seems as if SJ types enforce what is, while NP types generate what could be. In addition, the lower frequency NJ types are those that get changes implemented (which can be quite dangerous), and the SP types are those that attempt to show the importance of convention (less dangerous).

## Quora Moderation

I’m not sure it even makes sense anymore to listen to the moderators about who to contact in the event that one has an issue with their determinations. Let it be known, if they tell you to contact the email addresses, at all, just don’t. It won’t work. My girlfriend and I, for completely unrelated reasons, attempted to get into contact with Quora, via email, pertaining to these matters, but she hasn’t gotten a response, and it’s been over 3 months. When the moderators tell you to try emailing, they are not, themselves, privy to the statistics regarding response rates. They do not know how long it will take for them to get to you. Their job is to assume that this aspect of the company is a fully functioning and effective means by which to handle issues that present. Tell them explicitly that the apparent means they provide for resolving issues, does not work as they think it does, and you’ll be needing another means by to voice your concerns.
As well, apparently it is harassment to attempt address an issue with a moderators interpretation of events, as exemplified here;
What explains Deepak Chopra’s behavior when debating with Sam Harris and Michael Schermer?

I was blocked just recently. Can’t upvote (Except on the mobile version, thanks devs ❤ ), post comments, ask questions, answer questions, follow people, ect, as a result of my conduct here;
What explanations has Quora given for the banning of Dorothy Clark?

The decision for my being blocked, was made completely without my being given a chance to defend myself in any regard. The violations, as expressed to me from a generic company account from which no one has attempted further contact.

Quora Moderation

Wed

You are being edit-blocked for one week for violations of Quora's “Be Nice, Be Respectful” policy.

Please note that the issue is that your comments in aggregate are hostile and consist of micro-aggressions.

Quora Moderation
(I would encourage others to decide, for themselves, whether or not my comments are aggressive in aggregate.)

Now, I was already blocked when I received this message, so if anyone wants to say something like;

“I haven't seen the question you're referring to but I know it's Quora company policy to warn people before banning and to make the warning clear. If you have any questions then the mods are contactable on the site and there are multiple questions that deal with policy and how they're enforced.”

Don't believe it. They don't know actually know this to be true, and are mostly just being defensive of Quora because of the high degree of emotional significance it has to them. In addition, if you

“Then it's time we realised that we're not investigators. We have no investigative power. You and I are users of website owned by a Private Company. If they want to kick you out for having a surname that rhymes with Garfield, or me out for being Australian then they can. Because it's their site and their rules.

If you don't like that situation then you are free to leave at any moment. But Quora has made it clear that they don't discuss the reasons behind individual bans out of respect for the banned users.”

Sure, whatever (Isn't that the same sort of think Americans say to Americans who don't like the actions of America?), but for whose protection is it, really, that a person is given no information pertaining to a decision regarding their own conduct? Do moderators not even have to bother explaining their rational before taking action? Is there not a means by which moderator misconduct might also be addressed?

Anyway, just a bit of friendly, constructive criticism.

## Faith

One of the defining problems with faith, as a means of justifying belief in some proposition $A$, is that there is nothing about the definition of faith, as a strategy for making decisions, that precludes someone from using it to justify $\sim A$. That is, the negation of $A$ is just as reasonably true, before one is prompted by the strategy to make a decision regarding which to believe. What makes science and mathematics useful is that, regardless of what your opinions are about the evolution of some system, you can deduce what it should be (based upon your axioms) and, if you should fail in your attempts at prediction, decide whether or not either to reject your previous conclusions or the premises by which you came to them. They work as the means to check our conclusions, by making attempts to derive their own, independent of what we think should happen. And, truly, if there is any point in asking the question “what will happen”, we must admit that there are other actions within the universe that give rise to the emergent properties we observe, which may or may not be dependent on what you believe. Indeed, if it is possible for one to be wrong at all, it is either that one’s belief, sometimes, forces founding propositions (or, the reasons why one believes) to become false, or that, sometimes, reality does what it does regardless of what one believes. Indeed, the latter seems the proper setting in which to talk about the nature of objects in our universe, as the former seems to imply that defining their nature changes what their definition should be, in such a manner that is always nontrivial.

Often, as well, we find that the premises we hold may not be allowed to coexist with one another, without adding some form of inconsistency to our system, making it difficult to use for representing a something that, conceivably, should have none. It is not reasonable for people that God both exist, and not exist, and rightly so. For, if anything is predicated on his existence, so too should they be in the limbo of existing and not existing. Sin would both exist and not exist and, hence, you would and wouldn’t go to hell for sinning. In other words, everything contingent on the existence of something undecided, becomes undecided itself. If a mathematician has a belief they want to test, they can assert it to be true, in an attempt to transform it’s description by valid processes, into an expression that is acceptable or not. If the result is acceptable, doing the proof backwards should work to prove the initial assumptions, as long as the relations are bijective. If the conclusion is unacceptable, the argument is a reductio ad absurdum proof of the negative.

For instance;

$(x+1)^2=x^2+2 x+1$

$(x+1)(x+1) = x^2+ 2 x+1$

$x*x+1*x+1*x+1*1= x^2+2 x+1$

$x^2+2 x+1 = x^2+ 2 x +1$

$x^2+2 x+1-(x^2+2 x + 1) = 0$

$0 = 0$

Where, if I had started with;

$(x+1)^2=x^2+ 2 x$

I would have concluded in;

$1=0$

Which should not be the case, if equality distinguishes numbers by their magnitudes and signs.

It is here that we find the superiority of science and mathematics to faith, in matters of deciding what to believe. A mathematician that believes strongly in the truth of $(x+1)^2=x^2+ 2 x$, can free themselves from this belief by using it in a proof, in order to establish whether or not that assumption leads to inconsistency when used in combination with other, more foundational beliefs. As for faith, however, it seems to be useful only in referring to one’s preconceptions, and should not be regarding as evidence for anything other than to suggest that one hold’s that belief.

## Emotion and Heuristics

For humans, and many other species, emotions have been a critical part of survival. For, the faster and more precisely a threat is capable of changing our environment, the less time we are given to derive a complete enough analysis to guarantee that we could take action that would “advantage” us, in some sense we deem “valuable”. As well, a deductive proof, ideally, works better than a heuristic (for solving the same problem), but any non-rigorous proof $P_n$, sampled from a rigorous proof $P$ can be thought of as heuristic. The questions one must ask themselves, when considering whether or not a deductive or heuristic system will be acquired randomly, are (assuming that the proof or heuristic is intended to reveal the true value of some symbolic reference A);

1. How many deductive proofs are there that are intended to expose the true value of $A$?

2. How many heuristic proofs are there that are intended to expose the true value of $A$?

Now let us, for a moment, consider the class of heuristics that are lists of steps sampled from deductive proofs, though by no means do I consider this a technique of enumerating all heuristic processes. We understand that, whether or not this is a quality maintained by all heuristic procedures, that it satisfies the expectation of taking less work to perform than some deductive procedure to which it is related, which is typically what justifies it’s use. Any heuristic, of the class above, that is distinct from the proof from which it’s steps have been selected, must have fewer steps than that proof. Hence;

$0< |P_n| < |P|$

But, the number of steps in the longest heuristic proofs that can be sampled from P (without being equal to P) is $|P|-1$ . This means that each heuristic of length $|P|-1$ may be derived by removing a single step from P, which contains $|P|-1$ possible steps to remove (due to the fact that the conclusion cannot be removed, since these are heuristics of what is proven by P). Hence, there are at least $|P|-1$ heuristics of length $|P|-1$. As well, each of these heuristics may have one step removed from them (excluding the conclusive step), in order to produce heuristics of size $|P|-2$, such that there are $(|P|-1)*(|P|-2)$ heuristics of size $|P|-2$. More generally, this generalizes to;

$|H_P| = \prod_{k=1}^{|P|-1}{(|P|-k)}$

where $|H_P|$ is the number of heuristic samplings from P, intending to demonstrate the conclusion $A$. This demonstrates that the number of heuristics is strictly greater than the number than the number of proofs, and establishes why we should believe that a heuristic will be used to approach the problem, as opposed to a deductive proof.

So, it is more likely that emotions, if they might be used to prescribe action that has us avoid danger, are heuristic procedures, based solely on the fact that it is, in some very real sense, easier to produce a heuristic than it is to produce a deductive proof, in about the same sense as selecting an integer amongst the reals. There are simply more restrictions imposed upon being an integer than being a real, as there are more restrictions on being a proof than a heuristic (where any heuristic might as well be considered a sequence of expressions).

So emotions are probably heuristics, as are most things we consider to be proofs. The best heuristics appear to be those that come from relieving a proof of it’s least often applicable, and most taxing steps.

Emotions, however, are not informative in the same manner as proofs or heuristics. Rather, they can be used to change how an experience is to be interpreted by manipulation of feelings alone, such as to support the development of a heuristic of the type above. One avoids things that smell bad, not as a conscious acknowledgment of their danger, but as an inbred heuristic for recognizing something as uncomfortable quickly and without much thought. In regard to smell, humans resoundingly interpret the feeling of being persistently subjected to an unpleasant odor as if something is wrong that is worth being anxious about. and often, offended by (From which that phrase “Do I offend?” must have originated). This begs the question, to what should be we taking offense? There are many mechanisms by which our bodies detect, and urge us to satisfy our needs. And much like hunger is used to compel a person to find and consume food, it seems that anger is used to detect and confront issues with enough confidence to follow through with a decided strategy. When a smell is indicative of bad hygiene, frustration is a useful reaction in bringing attention to and resolving the issue as, without alternative methods of recourse, others need to be taught how to live, in order not to become a detriment to themselves and those around them. But, it is not always the case that a smell, however similar to those smells which are dangerous, indicates the existence of something dangerous. In most cases, a single smell is not enough to uniquely indicate danger, just as the similarity of a pattern on a snakes back does not indicate the level of danger posed by that snake.

—King Snake—-            —Coral snake—

I doubt, however, that one should be expected to delay their reaction merely because they cannot decide about what distribution of red, yellow and black are most highly correlated with this particularly breed of snake. One is expected to be convinced that they should be afraid, before they are appealed to via some means of higher comprehension (even, still, not ensuring that the initial fear response is sufficiently attenuated in subsequent relevant scenarios.)

The function of the Orbitofrontal cortex, seems very much, to provide us with the illusion of well-founded expectation, that comes with feelings of curiosity, joy, anger, sadness, fear and all others.

http://en.wikipedia.org/wiki/Orbitofrontal_cortex#Functions_of_the_human_orbitofrontal_cortex

## Connections between Calculus and Statistics

The most widely known definition of the average of a series of values, takes the form;

$A_{v_0}^{v_{n-1}}(v)= \frac{1}{n} {\sum_{k=0}^{n-1}} {v_k}$

Where, $v_k$ is an array of values. As to how those values had come to be contained at those indices in said array, however, is unassumed by our model. We do, however, tacitly assume that the values contained in $v_k$ are real, and any function is restricted to being either continuous or discontinuous in the reals for all real valued inputs. However, since any discontinuous function, whose range is restricted to the reals, may be made smooth by defining a function that must contain that set of reals for the same inputs, it not is a problem to say that the discontinuous function is a result of sampling from a continuous function, conventionally referred to as;

$f(x_k)$; $A_{x_0}^{x_{n-1}}(f(x))= \frac{1}{n} {\sum_{k=0}^{n-1}} {f(x_k)}$

However, we may also observe that there is nothing stopping us from distributing  $\frac{1}{n}$ into the sum, such that it becomes the coefficient of every term in the series;

$A_{x_0}^{x_{n-1}}(f(x)) = {\sum_{k=0}^{n-1}} {\frac{1}{n} f(x_k)}$

Initially, we presumed that the role of the value $n$ was to allow each value to pull the magnitude of our average with a force defined by it’s own value, giving no bias to any contestant not already inherent in them. But, there is nothing stopping us from assuming that the difference in consecutive $x_k$ is precisely equal to $\frac{1}{n}$, such that;

$A_{x_0}^{x_{n-1}}(f(x))= {\sum_{k=0}^{n-1}} {(x_{k+1}-x_k) f(x_k)}$ where; $x_{k+1}-x_k = \frac{1}{n}$ giving;

$x_{k+1} = \frac{1}{n}+x_k$ where, if $x_0 = 0$, then; $x_k = \frac{k}{n}$ which justifies; $A_{0}^{x_{1}}(f(x))= {\sum_{k=0}^{n}} {\frac{1}{n} f(\frac{k}{n})}$

Where, it should be clear that, as n approaches infinity, $\frac{1}{n}$ becomes infinitesimal, while the function is evaluated at every value, spaced by that infinitesimal, from 0 to 1.

This, in other words, is equivalent to a left Riemann definite integral, on the interval 0 to 1; $\int_{0}^{1}{f(x)}dx = \lim_{n \to \infty} \sum_{k=0}^{n-1} {\frac{1}{n} f(\frac{k}{n})}$ To generalize the interval, however, one need only, first, change the lower limit such that;

$A_{a}^{x_{a+1}}(f(a+x))= \lim_{n \to \infty} \sum_{k=0}^{n-1} \frac{1}{n} f(a+\frac{k}{n})$

After which, all that is required is stretching the step-size from $\frac{1}{n}$, to $\frac{b-a}{n}$ , so that we ensure that all values from a to b are captured, as;

$\int_{a}^{b}{f(x)} dx= \lim_{n \to \infty}A_{0}^{1}(f(a+(b-a)x)) = \lim_{n \to \infty}{\sum_{k=0}^{n}} {\frac{b-a}{n} f(a+(b-a)\frac{k}{n})}$

Where, for clarity, I will replace b and a with their values referred to as being selected from the array x, as; $\lim_{n \to \infty} \int_{x_0}^{x_{n}}{f(x)} dx = \lim_{n \to \infty} \sum_{k=0}^{n-1} \frac{x_{n}-x_0}{n} f(x_0+(x_{n}-x_0)\frac{k}{n})$

But, if it is still our intention to derive the average of the values sampled from the function, no matter their actual spacing from one another on the x-axis, we are required to remove the factor of b-a that results, such that;

$\lim_{n \to \infty} \frac{\int_{x_0}^{x_{n}}{f(x)} dx}{x_{n}-x_0} = \lim_{n \to \infty} \sum_{k=0}^{n-1} \frac{1}{n} f(x_0+(x_{n}-x_0)\frac{k}{n})$

As well, one may refer to the general form of the weighted average as;

$W_{x_0}^{x_n}(f(x))= \frac{\sum_{k=0}^{n-1} (x_{k+1}-x_k) f(x_k)}{\sum_{k=0}^{n-1} {x_{k+1}-x_k}}$

Where, it may be very easily shown that; $x_{n}-x_{0}= \sum_{k=0}^{n-1} x_{k+1}-x_k$ Giving us the following relation between the average and the definite integral, as;

${\frac{\int_{x_0}^{x_n}{f(x)} dx}{x_n-x_0}} = {\frac{\sum_{k=0}^{n-1} (x_{k+1}-x_k) f(x_k)}{\sum_{k=0}^{n-1} {x_{k+1}-x_k}}}$

In addition, It seems to me that the variance is best represented by something akin to;

$V_{x_0}^{x^n} = 1-\frac{x_n - x_0}{\int_{x_0}^{x_n}{\sqrt{(f'(x))^2+1}}dx}$

Which is one lessened by a measure of the length of a line with 0 variance on that interval, against the arclength of the function from a to b. As it seems that, if there our function is unchanging, the function is equivalent to it’s expected value on any interval. Thus, the variance becomes zero. However, the function above, curiously, is normalized, as opposed to the common series definition of variance, given as;

Which is clearly not bounded. __________________________________________________________________________________ June 21 2015

Following from;

$\frac{\int_{a}^{b}{f(x)}dx}{b-a} = \lim_{n \to \infty} \sum_{k=0}^{n-1} {\frac{1}{n} f(a+\frac{b-a}{n}k)}$

We may interpret $f(x)$ to be some function $(g(x)-\mu)^2$ . such that;

$\frac{\int_{a}^{b}{(g(x)-\mu)^2}dx}{b-a} = \lim_{n \to \infty} \sum_{k=0}^{n-1} {\frac{1}{n} (g(a+\frac{b-a}{n}k)-\mu )^2}$

Which gives us;



Where $\mu$, the expected value, is determined by;