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About Statistics and Gender Spectrum


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Posts: Wal Torres

About Statistics and Gender Spectrum .
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Wal Torres

August 16, 2009, 1:55pmReport to

I would like to start a broad topic, so we can exchange ideas on issues not so simple - really very complex.


First I did a suggestion structure for that so complex subject:

How do we perceive our gender?

Why do us perceive our gender that way?


1st.  We just know what we may see (perceive) - and we perceive things through the contact between our neural sensors (our senses), the transmission of these sensors to and through the brain (CNS-central nervous system), and the translation of these sensor data in a language of images by the CNS as a whole, generating a MENTAL IMAGE LANGUAGE, somewhere;


2nd. We know not an absolute reality, but just what we build (a language as imagery) and see inside ourselves - through our brain (CNS), translating electrochemical data through mental images in the brain - from our perception in contact with a reality inside and outside us. For details I suggest the work of Antonio Damasio - among others;


3rd. This perception is non-local - there is no place in the brain (CNS) or outside it, where these mental images converge - these images are related to the body and the brain - but ARE NON LOCAL.


4th. Since we have enough evidence that these mental images are non-local - they are related to a quantum generating system - in the sense that this MENTAL reality is the result of the quantum entanglement between the outside (or visceral inside neural messages or both) with  the neural processes and a mental non-local dimension;


5th. Even virtual and non-local, the mental language reality is real - in the sense that through ATTENTION, it becomes active and not passive only as an epiphenomenom from the CNS. For details I suggest see the works of Von Neumann and more recently Henry Stapp for details.


6th. Our contact with the outside - build our mental images in our brain - and the mental images synthesized - are results of SUMS AND PRODUCTS - of many microscopic processes that synthesize macroscopic scale mental images (as a language). Our macroscopic scale imagery ALWAYS synthesize itself through ADDITIVE PROCESSES (pressure, temperature, wind) and/or MULTIPLICATIVE PROCESSES (fragmentation, scattering, turbulence). In general, the complex systems that are summarized BY OUR MENTAL IMAGES is a language that be erected on additions and multiplications of multiple data and multiple STOCHASTIC processes.


7th.  That process of generation of mental images and perceptions (including self-perceptions) is important when we intend to study seriously  SELF-PERCEPTIONS and it's STATISTICS. The same happens when we intend to study seriously Gender Self-perception (gender identity) SPECTRUM.


8th. We may no more disconsider that complexity - and also the complexity of additive and multiplicative complex stochastic processes statistics - when we intend to study and understand properly the self-perception among humans - and even other primates and mammal species. If we bypass that complexity we will prepare a weak (really fake and wrong - even pseudo-scientific) "evidence based background", and old things will look like "obvious" (even and mainly statistically) - mistakenfully.


9th. To do science (and "evidence based medicine") we need to treat which are simple processes as simple and which are complex processes as complex.


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Martha Freitas

August 16, 2009, 2:29pmReport to

Continuing.


The statistics we need is the statistics of ADITIVE and MULTIPLICATIVE PROCESSES.


THE STATISTICS OF ADITIONS (I will build on the background work by Sornette and Nolan; the work of Sornette, Redner for MULTIPLICATIVE PROCESSES and Nolan for STABLE PROBABILITY DISTRIBUTION FUNCTIONS).


Look:


Sornette,D - Critical Phenomena in Natural Sciences - Springer, 2006;


From Redner:

http://physics.bu.edu/~redner/pubs/pdf/ajp58p267.pdf


for much more Redner free papers:

http://physics.bu.edu/~redner/pubs.html


From Nolan:

http://academic2.american.edu/~jpnolan/stable/chap1.pdf


also

http://academic2.american.edu/~jpnolan/stable/stable.html


for Nolan free papers and presentations about stable distribution functions, and also with a good free software for Windows - to statistic fitting to stable probability distribution functions (pdf).


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Martha Freitas

August 16, 2009, 2:49pmReport to

The adition of stochastic variables - give rise to the Generalized Central Limit Theorem. To summarize:


When same distribution of stochastic variables are added, the result is a variable of the same distribution - and even when they are not exactly the same distribution - the amount generally tend to a distribution of GAUSS - or NORMAL.


When the variables in addition HAVE FINITE VARIANCE - the sum converges to Gauss.


On the other hand, that theorem shows that (development by Paul Levy):


All adition of stochastic variables converges to a STABLE DISTRIBUTION FUNCTION - we may name to a Levy pdf


See that link to know better mathematically which are Lavy-Pareto stable PDF's:


http://www.sjsu.edu/faculty/watkins/stable.htm


The sum of variables converges to the Lavy-Pareto pdf - with ALFA between 0 and less than 2 (when the variances are not defined and are infinite) - the sum is distributed by the Pareto-Levy distribution (near a power law).


Therefore, all sums of stochastic variables can summarize their tendency to two basic possibilities:


With finite variance, ALFA = 2 or more, the sum converges to the Gaussian distribution.


With infinite variance or no defined variance (if it is not defined the moment of second order), ALFA between 0 and less than 2, the convergence occurs to the law of Pareto-Levy.


What's the difference of Gaussian distribution for the distribution of Pareto-Levy?


The TAIL, the lack of higher moments, the EXTREME EVENTS emergence.


Mandelbrot divided the distributions of probability (pdf - probability density functions) in two major types:


as MILD pdf's - where the Gaussian distribution is more typical.


as WILD pdf's - where the distribution of Pareto-Levy is typical.


Simplifying to explain:


Gauss allows small changes - for example the heights of people - vary a little in a population of men for example, by some 30.40% of difference, no more than that. It's Mild. The central value has a large weight and the tail almost nothing.


Levy-Pareto by contrast, accepts large variations and large tails - for example the difference in the RICHES of people, each have thousands of times more than the other, the variations are enormous.Thus the cluster size on the energy of earthquakes, hurricanes, number of people in cities, tree distributions in forests, venules in the bronchi and the blood circulation, the fracture of rocks, the distribution of clouds, of asteroids, of galaxies ... and of gender identity ... are conditions that require and generate large variations - and that dispersion necessarily generate extreme events.


Medicine and psychology, still imagine where we live is a universe of Gauss only. Where we may have a big stationarity of events, where there are fixed means and variances are small, where we may define WHAT IS NORMAL and what is ABNORMAL.


Reality shows us that Gauss is the exception - the rule is Pareto-Levy.


Pareto-Levy, may be called a fractal


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Martha Freitas

August 16, 2009, 3:01pmReport to

Resume about ADITIVE PROCESSES  pdf:


If aditions deal with minor variations - there is a convergence to Gaussian pdf, which define normal and abnormal conditions.


Or we may deal with major changes - where no normallity is defined nor abnormalities, but extreme values and heavy tails are more or less common. Events with more energy, as extreme events can destabilize relations with catastrophic movements. Gender self-perception follows that pattern and signature when an extreme event happens (as transexuality or transgenderism for example) - when the ends are so strong and frightening - even only unusual or uncommon - to destabilize the whole system. The same happens among earthquakes which may destroy cities, among big floods that may destroy whole regions, as families may be destroyed by the emergence of a transexual condition and societies may be revolved by huge political movements.


Is the identity self-perception of gender a result of ADITIVE PROCESSES only?


If it were, of course the sums which lead to the spectrum of gender lead to Pareto-Levy distributions and not Gauss - surely.


The EXISTENCE OF TRANSEXUALITY AND TRANSGENDERISM is enough evidence that Levy-Pareto is the characteristic pdf of that gender self-perception system.


But where are the MULTIPLICATIVE PROCESSES?


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Martha Freitas

August 16, 2009, 3:22pmReport to

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As you may see by the introduction - my living among doctors and psychologists is difficult because we live in parallel scientific universes.


They imagine a universe of Gauss for small variations in situations where a STEADY STATE is perenial in time, in a world of small "abnormalities" or "disorders".


I see a universe of Pareto-Levy, full of enormous changes, from huge fluctuations in global warming to uncontrolled emergence of megalopolis of almost-continuous spectrum of diversity - worldwide.


We live in parallel scientific worlds that do not easily intersect. Or when they cross, is at WPATH - hahaha!


But what is the scientific leading world when we consider more up-to-date and REAL scientific evidences?


Which EVIDENCE BASED MEDICINE we would need to do at XXIst century?


Variations of sex and gender are mainly visceral, are full, huge, absolutely tremendous - for self-perception. They follow typically Pareto-Levy pdf.


The problem is most psychologists and psychiatrists never heard of Pareto-Levy - not heard but keep saying they do not want to hear, and do not like those who have spoken these things!


But this is serious science that may not be ignored!


In our XXIst century's science - consider the large variations as Gaussian curve is pseudo-science. We no more are at the XIXth century!


When I say that, my intent is not to offend no one - but only to show the evidence of reality!


Indeed, we live in parallel worlds - one governed by XXIst century science and another living among XIXth old science - whicg is present day pseudo-science.


That was a brake for meditation.


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Martha Freitas

August 16, 2009, 3:38pmReport to

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Confirming what I am saying are the researchers below, from different sciences, I suggest you read.

These works are for non mathematicians, for newcommers to real XXIst century serious science:



Link for Linked by Barabasi - a great networks scientist.

http://www.amazon.com/Linked-E.....250436743&sr=8-1


Mandelbrot about Economy

http://www.amazon.com/Misbehav.....250436842&sr=1-1


The Black Swan: The Impact of the Highly Improbable

http://www.amazon.com/Black-Swan-Impact-Highly-Improbable/dp/1400063515/ref=pd_sim_b_1


Good reading for non-staticians.

Mainly psychiatrists, psychologists and doctors.

Also lawyers.


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Martha Freitas

August 16, 2009, 3:55pmReport to

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RANDOM MULTIPLICATIVE PROCESSES


Read attentively Redner for more details - much more.



Imagine a gradual process over time - an earthquake, a fracture in a bridge, a baby is born, an egg that develops in a womb.


MULTIPLICATIVE AND PROGRESSIVE PROCESSES. Full of stochastic possibilities due to the intrinsic complexity and the large amount of variables.


The variable X in time t has a value - and at time t +1 it will have another value that will be DEPENDENDENT from all the former ones, in a proportion that may be random and dependent on time. And so on.


Redner thoroughly examined these systems and concluded that - RANDOM MULTIPLICATIVE PROCESSES do NOT converge to GAUSS pdf - but to power law Levy-Pareto type pdf's - while keeping the process and system as transient (not recurrent and not stationary).


If stationarity is reached - that stationarity behave like a Gaussian distribution.


Imagine now a trans person. An egg. The egg develops gradually due to multiplicative processes and aditive influences, inside an environment (a womb) and becomes a baby and the baby grows and becomes a child ... this process is multiplicative, progressive and surely TRANSIENT - during the growing of the new life. That complex process allows large variations. For example even each one will develop a UNIQUE FINGERPRINT. And also for a trans-person also in the self-perception of gender, uncommon and extreme variations surely happen.


Each individual develops as a multiplicative progression - and that progress also on the gender self-perception shows a Pareto-Levy distribution.


That was the thesis - my thesis - when I presented my paper at WPATH Biennial Symposium in Chicago, 2007.


The population of human individuals as to the development of gender identity - even with the limitation of having the same genitalia (male or female) in the distribution of aditions and multiplications, show a distribution of large variations in a system of Pareto-Levy - and not Gauss.


We need then to know better the distributions of Pareto-Levy.


They are well known in economics, physics, astrophysics,  geology,  ecology, but are unfortunately little known in psychology and psychiatry.

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Martha Freitas

August 16, 2009, 3:59pmReport to

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Mathematics has been much studied to evaluate these distributions, first to determine - what distributions are stable?


In more technical language, what are the basins of attraction of different pdf's?


From what we have seen it is clear that the basin of attraction of the Gaussian distribution of additives are systems in which the variance is finite - they flow like a river basin whose attraction leads to a Gaussian distribution.


Furthermore today we know that the basin of attraction of the Levy-Pareto distributions (functions of power) is composed of cases in which the additives are original variables wich variance is infinite, and the same happens with multiplicative processes.


Anyway in general - in nature, in human life and in most part of the the universe and in human creation, the pdf's always converge to one of these two basins of attraction.


But what is a distribution of Pareto-Levy?


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Martha Freitas

August 16, 2009, 4:01pmReport to

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For more details see this link:


http://www.sjsu.edu/faculty/watkins/stable.htm


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Martha Freitas

August 16, 2009, 4:04pmReport to

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See also:


http://www.applet-magic.com/mandel.htm



http://adsabs.harvard.edu/abs/2004cond.mat.11161C



http://www.cba.unl.edu/academics/finance/recognition/pdfs/Renaud_Piccinini.pdf



http://www.redskyworld.com/use.....ng%20Uncertainty.pdf


These links now give an idea of what it is.

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Martha Freitas

August 16, 2009, 4:10pmReport to

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These data show that when there are extremely important and dangerous or unexpected conditions - as great wealth, great losses, large earthquakes, major hurricanes, major storms,  large gender dysphorias, something big ....  there are deviations from normal distributions towards Pareto-Levy - for the whole system.


Actually these considerations are more economic, financial, and astrophysics for NASA - this is science.


We believe that scientific knowledge is also important to be considered in sexology (unfortunately so poor!) and also in gender therapy (affff, even poorer!), too!


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Martha Freitas

August 16, 2009, 4:18pmReport to

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The shape of a Pareto-Levy distribution can be easily recognized in a log-log paper.  


It gives a straight line.


See this picture:




That straight line in a log-log plot shows a power law (Levy-Pareto pdf) for cardiac pulsation.


For a healthy heart, the movement needs to follow a Levy-Pareto. If not, probably we have a heart failure or attack.


So the "normal" is the Levy-Pareto. Levy-Pareto is NORMAL.

As the biggest basin of attraction in the Universe for all stochastic processes.


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Martha Freitas

August 17, 2009, 3:58pmReport to

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More examples of Levy-Pareto:


On the web network:






See that the distribution of AOL users is nearly Levy-Pareto.


See another web example. See that ALFA  here is called k parameter at the picture:




And below considering the distribution of galaxies:





See another now considering the commercial establishments in US:





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Martha Freitas

August 17, 2009, 4:07pmReport to

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Now the most important of all:





This is the Levy-Pareto curve for the spectrum of self-perception of GENDER!


Raised by Wal Torres (myself!) and presented to WPATH at 20th Biannual Symposium in Chicago, 2007.


She talked, talked and nobody thought anything - I believe nobody understood nothing - but she did her try.


I do not know in which language she spoke - but she tried to speak in English.


But she left out of there with the certainty that no one wanted to or was unable to understand about what she was talking about.


She had some 10 minutes to present these ideas in a foreign language, and these 10 minutes included questions! hahaha! But from the audience - they also applauded the presentation frantically - probably thinking it was a monkey - from Brazil, probably from the Amazon forest - dressage.


But as the Levy-Pareto pdf -  the monkey was not such a fractal - it was only showing scientifical evidence.


For those who want to do Evidence Based Medicine - nothing better than start with the evidence that the probability distribution of the frequency spectrum of self-perception of gender distribution follows a Pareto-Levy pdf.


Don't you think so?

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Martha Freitas

August 17, 2009, 4:22pmReport to

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Just to explain - because even here possibly you will find that you can not understand anything.


In the x-axis - the horizontal, is a logarithmic scale of incidence - based on data published by Lynn Conway in 2002.


In the y axis, vertical one, is a logarithmic scale of intensities - intensities of thousands of data collected between 2001 and 2002 by Gendercare through the internet using the scales of measurement MF and FM developed and published by Gendercare.


This curve then expressed the best information we have at the moment - the intensity and incidence - within the spectrum of gender.


Of course these curves can - and should - be improved - The IBGE (in Brazil - the Brazilian Government Statistics Agency) could do a survey for this population in their decenal whole country evaluations.


As expected, in a log-log scale the curve of distribution of probabilities for gender identity, show a log-log straight line - typically a Pareto-Levy distribution.


Only this fact requires rethinking the classification of self-perception as a kind of normal and abnormal (people with mental disorders such as abnormal) by psychologists and psychiatrists, which is based on "a priori" Gaussian distribution of gender identity - which is not the case.


A distribution of Pareto-Levy shows there are not normals nor abnormals - but there are commons and less commons and highly unusual or extremely uncommons - which are so important when real disasters occur or cause earthquakes, hurricanes or .... gender dysphorias.


As is the case of the extremely unusual among the gender dysphoric - called trans-anything.


It is important to understand we are not considering CAUSES - but EVIDENCES  of PDF distributions.


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Martha Freitas

August 17, 2009, 4:28pmReport to

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Got this link looking for good fitting software for Levy-Pereto testing of hypothesis:


http://www.itl.nist.gov/div898/software/dataplot/ftp/win_2000/homepage.htm


What is a good free software and free for evaluation of distributions of Pareto-Levy. It is a software of the U.S. Government NIST - National Institute of Standards and Technology, his department of Engineering Statistics Division - software called DATAPLOT.


The software is free but need some DOS commands and direct the console - not everything is as in paid software so simple - but certainly is very powerful and mathematically accurate.


And for free.


I suggest downloading the 2008 version - not the last of 2009 that requires more HD space.


Enjoy the tip!

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Martha Freitas

August 17, 2009, 4:34pmReport to

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For more resources and current research by BARABÁSI:


http://www.barabasilab.com/



Look:


SCALE-FREE = Pareto-Levy = Fractal = Power Law



All these terms are synonymous and applied in different sciences and in different environments.


Networks - network sciences - use more the word SCALE-FREE and POWER LAW


In economy it is used PARETO distribution


In mathematics and statistics PARETO-LEVY pdf


In geometry and on the web - Fractal


It is always the same - in different terms.


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Martha Freitas

August 17, 2009, 5:14pmReport to

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Being a Pareto-Levy and not Gaussian, in no way we may say about NORMALITIES  in that system.


So not also about ANORMALITIES or DISORDERS.


But EXTREME EVENTS  may be VERY RARE, VERY STRONG AND VERY DANGEROUS!


So the main evaluation question of extreme events is - or even not so extreme but unusual or uncommon events is - IS THAT EVENT DANGEROUS?


If the event is a dangerous one - how may we PREVENT IT?


Or if it happens WHAT MAY WE DO TO MINIMIZE THE DANGER?


That is the way we do with all extreme events that are dangerous - as hurricanes, floods, earthquakes and so on.


Fractures. galaxies, arteries, the population of cities, as heart beats also follow Levy-Pareto, but their extreme events DO NOT TRIGGER DANGEROUS CONDITIONS.


So our main question now is - are THE EXTREME CONDITIONS of the gender spectrum DANGEROUS?


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Martha Freitas

August 17, 2009, 5:33pmReport to

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A priori we may say - NO - they are not dangerous.


Rarely they may be dangerous for the OWN PERSON - if the family and society HELPS  - instead of to put difficulties.


Rarely real mental disorders TRIGGER a gender dysphoria - and in these rare conditions - WHICH TRIGGERS  need to me controlled.


Rarely difficult lives and post-traumatic conditions MAY TRIGGER MORE DIFFICULTIES AND EVEN MENTAL DISORDERS - a posteriori of the gender dysphoria.


So, when these RARE CONDITIONS HAPPEN - we need to be prepared to help - as heath care providers.


So THE HEALTH CARE PROVIDER of services for gender uncommons NEED TO BE GATE OPENERS  and never GATE KEEPERS.


And we need to be EXPERTS ON DANGEROUS POSSIBLE CONDITIONS - that we may not anticipate , preview or prevent - but which we may surely MINIMIZE, MITIGATE and HARMONIZE, taking care of the subject - and preparing the society to accept these UNCOMMON OR UNUSUAL CONDITIONS.


Most people with gender dysphorias living extreme conditions of gender show NO DANGEROUS CONDITION.


These we need to be fast and effective on our evaluations, perfect on our transitions and corrections, so even living an extreme condition triggered by nature, they will feel as they are - NORMALS AMONG NORMALS - having the opportunity to live a normal life among normals.


So the steps Gendercare suggests are:


1. An EARLY, fast and effective evaluation of the DANGER and  of the UNUSUAL CONDITION;


2. Follow up of the reactions of the subjest during the desired transition (HRT, if possible RLE, if not possible a RLE due to professional and family difficulties, at lesast the follow up of the reactions of the subject to the hided transition); The BODY WILL NEED  1 to 2 years to transition.


3. A fast and effective TRANSITION when desired by the subject, even with surgeries and SRS;


4. For children, the early and very early evaluation - since 6,7 - with Games online, and later puberty delay at 10/12 with HRT when desired and necessary at 12-14, and SRS at 16 or even before if desired and structurally coherent.


5. For people with real disorders - mental and emotional disorders - each one need to be considered to see what we may do as GATE OPENERS, and not as gate keepers. But these are VERY RARE.




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Martha Freitas

August 17, 2009, 5:43pmReport to

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All gender dysphoric - or all uncommon gender condition needs psychological/psychiatrical tutoring?


SURELY NOT!


All need a fast evaluation - as the evaluation provided by Gendercare - in one to 3 months trough the web.


ONLY IF A DANGEROUS CONDITION IS DETECTED, a psychological or psychiatrical follow up is really necessary - and the professional need to learn to be a Gate Opener and never a Gate Keeper.


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Martha Freitas

August 17, 2009, 5:48pmReport to

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O love for these rare possibly dangered situations that need some psy therapy - to prescribe ART-THERAPY.


Or occupational therapy.


These not so hard-wired therapies I believe are extremely profitable for post-traumatic disordereds.


And I suggest an intensive campaign to show the media and society, the churches and religions and families and cultures - that uncommons are only uncommons - and they are normals among normals - and have the right to be and feel that way.


Before, during and after transitions, evaluations and therapies.


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Martha Freitas

August 17, 2009, 5:51pmReport to

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So I believe we have plenty of SCIENTIFIC EVIDENCES  to say with France:


"Gender Dysphorias are not triggered by MENTAL DISORDERS, so Gender Identity Disorders may RARELY  exist"



Vive la France!  

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Martha Freitas

August 18, 2009, 12:52amReport to

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As gender unusual conditions could trigger gender dysphorias - and rarely dangerous conditions - HOW COULD WE RECOGNIZE these conditions?


Their consequences?


Doing a gate keeper service based on old "psychological abnormalities" that psychology never cured, or "gender identity disorders" that could never be ordered?


No, but recognizing it through its own characteristics - STUDYING THE MULTIPLICATIVE PROCESS OF ITS FORMATION.


The development of gender identity - as gender self-perception - in EACH INDIVIDUAL  - is a typical multiplicative and complex process.


When we study the whole population we see the results of each of these individual processes follow a Pareto-Levy pdf.


But how could we study EACH PERSON DEVELOPMENT  to recognize its position inside the gender spectrum?


That was the question for Gendercare in 2003 - and we would need to solve that question properly!


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Martha Freitas

August 18, 2009, 1:02amReport to

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We could start that study considering two possible ways:


1. As a multiplicative stochastic process;


2. As a deterministic and chaotic process.


We could generate time-series through questionnaires (MF and FM questionnaires), measuring unexpected femininity (MF) and masculinity (FM).


But how could we treat that data?


Stochastic processes need thousands of data and we could have no more than one hundred or a little more time-series points for each development.


But we could develop hundreds of these time series - for typical developments.


What we decided to do was - first of all - to develop a method to generate for each subject one time series. And compare time series.


What model we would use? The stochastic model or the deterministic model? Both could fit the development.


Stochastic processes are much more difficult to investigate, if they are not Markovian, and if they are not a Levy process.


Soon we were sure the development of gender self-perception in no way is Markovian.


Also it is not a Levy process - but could be a series of some different Levy processes.


And surely it fitted very well as a chaotic deterministic process.


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Martha Freitas

August 18, 2009, 1:09amReport to

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A Markovian process is a process when the state of the system now is a function of the system at the last moment ONLY. The previous history of the time-series is not important.


Is that real? For gender self-perception? Surely not. So, our system could not be studied as a Markov process.


The Levy stochastic process says the deveopment of the conditions depend on the time gradient that is constant. Is that true?


Our time-series showed if we could split the time series in 3 or 4, each part could be modelled by a Levy process - but we had so few points we could do nothing.


The last model we could consider was the chaotic and deterministic model.


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Martha Freitas

September 17, 2009, 10:52pmReport to

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The old mantra – all girls have XX chromosomes and all boys have XY – is no longer reliable. The proof lives in as many as 40,000 Australians whose chromosomes don’t match the standard. Scientists are now looking beyond chromosomes to "brain sex" and the role of newly discovered genes in determining gender.


Transsexuals are now under the scientific microscope because they may hold the key to the gender puzzle. By studying people on the gender extremes, scientists believe they may discover the genes that determine everybody’s gender.



Gender extremes are vital to understand gender self-perception - and its causes


See that link from Australia


http://www.abc.net.au/abccontentsales/s1483809.htm


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Martha Freitas

October 8, 2009, 3:16pmReport to

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Important link to think about it later


http://www.nature.com/news/2009/091007/full/news.2009.980.html



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