Problems with Visual vs. Abstract Thinking: Calculus

Examples from my college days preserve vividly the difference between those who think visually and those who are adept at abstract thinking. Although visual 'talent' as it was sometimes referred to, was a big bonus for studying geology, from geomorphology (landforms), to mineralogy (the crystal classification system) to structural geology (deconstructing relationships in space and time), in order to earn a degree, geology students were required to pass three semesters of Calculus and Calculus-based physics. I am not an abstract thinker; once mathematics leaves 'Concrete World' my visual mind simply goes blank - literally.  

No problemo! My visual brain could spin the wooden models that (no longer) are used to learn crystal forms, while other students were on the verge of emotional breakdown when tasked with this test. 

First panic, then strategy: I signed up for Calculus based physics before taking a Calculus course. I had to 'see' what Calculus looked like in the real world. It worked; I passed physics by sacrificing a few points on the mathematics while storing equations as whole images, and giving them names like, "the double violin with a thingy under the roof" and attached the image to a process for solving the equation. I had no idea what the equation described mathematically, but I could usually solve it. Calculus texts aid this approach since each chapter is organized by groups of similar equations.

 

I had no problem with the math that describes geologic processes like stream flow, because I could easily see the realization in nature. So, physics itself was understandable as it applies to the familiar world of motion, energy and behavior of objects, but getting through Calculus as a foreign language was like decoding signals from a very advanced and very alien civilization. 

Graphs! A visual window into the abstract language of mathematics.

From Paul's online math notes: http://tutorial.math.lamar.edu
"Now, let’s take a look at just how we could possibly get two tangents lines at a point. This was definitely not possible back in Calculus I where we first ran across tangent lines. A quick graph of the parametric curve will explain what is going on here. So, the parametric curve crosses itself!  That explains how there can be more than one tangent line.  There is one tangent line for each instance that the curve goes through the point."

 

For me graphic images, which can be quite a distraction due to their beauty, do help, but in order to 'do math' I had to approach maths as foreign languages. The analogy is fitting: one can learn the forms and grammar of another language, but never become fluent, nor speak it like a native.  

"Theory of Mind" Exposed as Delusional Thinking

It turns out that the vaunted psychological “Theory of Mind” is psychology's euphemism for delusional thinking; a supernatural, superstitious, and magical type of brain processing common to “normal” people. Anyone who demonstrates rational, science-based thinking is abnormal.
 
The fact that Scientific American would publish this is shocking.
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People with Asperger’s less likely to see purpose behind the events in their lives By Karen Schrock | May 29, 2010 |SCIAM BLOGS

BOSTON—Why do we often attribute events in our lives to a higher power or supernatural force? Some psychologists believe this kind of thinking, called teleological thinking, is a by-product of social cognition. As our ancestors evolved, we developed the ability to understand one anothers’ ideas and intentions. As a result of this “theory of mind,” some experts figure, we also tend to see intention or purpose—a conscious mind—behind random or naturally occurring events.

A new study presented here in a poster at the 22nd annual meeting of the Association for Psychological Science supports this idea, showing that people who may have an impaired theory of mind are less likely to think in a teleological way. 

Bethany T. Heywood, a graduate student at Queens University Belfast, asked 27 people with Asperger’s syndrome, a mild type of autism that involves impaired social cognition, about significant events in their lives. Working with experimental psychologist Jesse M. Bering (author of the "Bering in Mind" blog and a frequent contributor to Scientific American MIND), she asked them to speculate about why these important events happened—for instance, why they had gone through an illness or why they met a significant other. As compared with 34 neurotypical people, those with Asperger’s syndrome were significantly less likely to invoke a teleological response—for example, saying the event was meant to unfold in a particular way or explaining that God had a hand in it. They were more likely to invoke a natural cause (such as blaming an illness on a virus they thought they were exposed to) or to give a descriptive response, explaining the event again in a different way.

 

Once again we see that so-called scientific studies by psychologists are tainted by a bizarre insistence that delusional (magical-supernatural-religious thinking) is required in order to be a socially-acceptable human, and indeed that supernatural belief is necessary to social acceptance. Is it surprising then that American education is deficient in science and math instruction, and is instead focused on magical social ideas like the insistence that smiley face stickers 'create' self-esteem? 
It's unbelievable!

"Abracadabra" versus "Make It So"

This is the erroneous belief at the core of magic, that words have the power to create reality. Modern humans suffer from the ancient supernatural assurance that "saying" is the same as "doing." This is most obvious today in the institutional practice of stating the intention to "fix" a problem such as child poverty, but the actions taken result in...nothing. Stating intent to solve a problem is not problem solving: political statements are not based on correct analysis of the cause or causes and in practice can obscure or cancel out what might be effective strategies. The result is more laws, and the application of a modern magical remedy: money. Money is believed to solve problems, but it doesn't. The sums allotted to even minor projects have escalated over recent years into hundreds of millions, if not billions of dollars, which the U.S. government doesn't have, but must borrow, and the debt is converted to funds that are "upcycled" to the wealthy. Problems become chronic, institutionalized, and falsely believed to be unsolvable.

Stymied by their own lack of clear thinking, lack of science and technical knowledge, and belief in the magical power of words, officials and experts claim that no matter how simple the problem, it is extraordinarily complex, and that more funds must be allocated to initiate more studies which merely repeat the cycle and prolong the situation. The problem is PEOPLE who cannot take the step from magic to physical reality; people who believe that the social hierarchy is the only path to results, and that those results are conditioned on the "good will" and responsible feelings of those individuals who have gained power. Can you hear me laughing? Social people cannot seem to grasp this fatal roadblock to effective analysis and action. 

 

The anti-magic corollary to "abracadabra" is MAKE IT SO, used by Captain Picard on the bridge of the Starship Enterprise. This command is a call to action, based on the fact that the ship has been designed to perform its functions, and that the crew has been selected and trained to utilize the ship's capabilities, and then some. How ominous is it that a Sci-Fi TV show is a real model for teamwork, competence and success, while the social world spirals out of control?

How ironic, when violence against women has high social value, and is advanced and taught by the entertainment industry.

Myths about Asperger Women

This Esquire magazine cover is from the 1960's, and despite equal rights legislation, nothing has really changed, because hatred of women is embedded in American culture. Women are bombarded by the message that we are childlike idiots whose sole purpose is defined by men, and utterly disposable when we fail to conform to their prescriptions. Self-hatred is learned by girls through socialization, and demonstrates the susceptibility of the "normal" brain to "brain-washing."

Asperger females are accused of being unfeminine and unattractive. The old male prejudice that any woman who is competent, intelligent, and ambitious must therefore be 'masculinized' is still being propagated by psychologists. Asperger females are accused of having a "male brain," which effectively ejects us, and all smart women, from the female half of humankind.

It's quite a compliment, if you think about it.

What Asperger children are doing with their brains when regular people think we are standing around being defective.

I was an uncomfortable child. I didn’t like the world much, and it didn’t like me. The world was confusing - disturbing, jarring, and alarming. I was frightened most of the time and most everything frightened me. Within my mind I was adventuresome and fearless, but people and their invasive habits and their intrusive rules and demands, scared the shit out of me. I didn’t know it, I instincted it. They wanted to keep me from adventure, from thought, and from truth. I hid. I still hide, because I was right. Social people confine and limit each other in terrible ways.

Women are confident that the man they live with is a nice guy and a good father. He’s just an average man, not a leader. Leaders know how to bring out the killer in every man. That’s why they are leaders. Men were a giant intellectual obstacle when I was a child. In their estimation of how things work, I was an insatiable little monster whose curiosity, hidden passion, obstinacy, questions, and rational seeking would be fine…if only I had been born a boy. How I learned to hate that pejorative and final indictment. 

Unbelievably, it was adult women who were most often the delivers of this life sentence of inferiority; women whose natural grace was replaced by restrictive clothing, rock hard hairstyles and icing-like make up, until nothing original remained. It was the 1950s and rigid sex rules demanded rigid bodies. Underwear was compiled in layers of girdles, brassieres, slips and garter belts, and stockings with seams that must be straight. Our mothers were Virgin priestesses who had been ceremoniously demoted by marriage, shamed and gagged by the function of their sex. I horrified my mother. I was not what she wanted in a child. My very existence challenged her acceptance of marriage as a woman’s inevitable defeat. My lively mind was a reminder of a dark female presence that she had murdered within herself.

The game unfolded: little girls were soon tamed. Female society ground on like a glacier that rolled over and pulverized every female that resisted its relentless power.

My father was a traitor to his gender. In matters of the mind he never slighted me. He was a mechanical engineer with wide interests, but his knowledge had one boundary, the artificial gulf between the priestly triumvirate of science, technology, and mathematics, the intellectual activities that divided the real world from everything else. He had an eidetic memory (he claimed) and rather than deflect my questions as unladylike annoyances, he fed me information about astronomy, geology, physics, chemistry, history, exploration and industry. He was not a creative person, but populated his mind with wonderful facts and figures in order to keep the world and his unhappy childhood at bay. He told me this, and let me know, without providing details, that he had idolized his father, a strict man who had used corporal punishment to toughen him up. 

Inexplicably, he hated his mother, whose sole flaw, as far as I could understand, was being a woman. His sister was also an object of his rage. He refused to provide any cause for his extreme feelings, and if my questions ventured to close to his wall of secrecy, he would turn on me. The experience was like that of trying to retrieve a bone from an ill-tempered dog that growls menacingly, curls its lip and commits a warning bite. Warning given: warning taken. I had to set aside this mystery concerning his female family members as a contradiction to the father I knew.

 

Cultural Imposition on Intellectual Pursuits

The modern arbitrary division between Art and Science was a childhood mystery. I read about men who during the Renaissance had created paintings, architecture, and sculpture, planned cities, invented weapons and battlefield strategies, uniting all these endeavors under the spell of a creative mind. There were priests who studied astronomy, painters who studied anatomy and chemistry, sculptors who studied the properties of stone and bronze and engineered monumental buildings. They were sought after by powerful families and institutions; the wider the range of their knowledge and skills, the more valuable their work. It never occurred to me that as a female I must be excluded from participation in such activities. Intelligent pursuits simply aren't sex-determined, but culture does its best to thwart women's ambitions by imagining that the intellect is gender-bound, that is, what you are permitted to do with your brain is culturally imposed.   

While looking at photographs of medieval architecture, a photo of Speyer Cathedral reminded me of the space shuttle on its launch pad - this impression is of course based on a particular view of the massive building. A supernatural thinker might claim that the similarity is proof that 'God' or some intelligent designer is at work, but both of these 'machines' were designed by humans working within the demands and limits of a universal physical system. Gravity, force, and mass must be balanced and environmental stresses accounted for. The deeper commonality between the massive 11th Century Romanesque cathedral (primarily a tomb for the Holy Roman Emperors, which has been damaged and rebuilt many times) and the Space Shuttle, is the will to obtain limitless technical power.

To read my book, Top Males - Anger by Design, go to: http://ginarex-angerbydesign.blogspot.com

 

The Asperger Mind Makes Art

My education is in geology, but I do not work in the field, rather, my appreciation for 'how the world works' is expressed through photography. I am fascinated by manmade objects being broken down (or not) by the desert climate, and most significantly, by the effects of wind that scours the landscape and by patterns generated by the freeze-thaw cycle. The desert remains a wilderness despite generations of human occupation; old dumps, although covered, have been exposed by natural forces.
     The photographs begin as color photos, which I then manipulate in the computer. My desire to make art began very early, but I had no dexterity - what I saw in my mind was impossible to create on paper. I worked as an advertising designer for many years, but could not draw a damn thing! I got around the problem by creating collages. Photography allows me to show what I see without the physical need to manipulate materials.


Top photo: the coils of an old box springs.
Left: Children's hand prints in paint on the side of a house.

Brilliant!

https://m.youtube.com/watch?v=BKorP55Aqvg

The absolutely most true and hysterical video of what it's like to be an Asperger forced to deal with Neurotypicals.

Childhood: A Female Asberger Mystery

My relationship to my own childhood is sketchy; I think it must be due to being Asperger, because most of the people I know remember almost everything that ever happened to them, and to friends and family. I remember pictures, as if I had stopped once in a while to take a snapshot of what happened, but then left the images behind. The image is the memory. Read more: Post 6/25   

  

Trying to Remember My Mother.

Months ago I assigned myself the task of remembering good things about my mother. Ours was an unhappy relationship, and my first attempt resulted in an image of glass bottles on a window sill. Some were filled with colored water; a few had marbles in them, but I may have added the marbles just now. My imagination inserts objects with similar physical qualities into my memories, a habit that has caused the family to accuse me of lying.

     Weeks later, the image of bottles filled with colored water remained the sole entry on the "Good things about my mother" list, so I tried again, but instead of a touching scene of her doing something motherly, a vivid yellow shoe intruded. The leather was shiny and smooth. Unless I’m lying again, these shoes refer to a Polaroid taken of me as I walked across a polished gym floor between rows of folding metal chairs during eighth grade graduation. The yellow pumps matched a sleeveless dress; a yellow band held back my hair, which had been done up at a beauty salon in a style that advanced my apparent age from thirteen to about twenty-seven. Pointy black eyeglasses exposed a nerdy streak. My recall of this event, and indeed of that year, begins and ends with this photograph, which may or may not exist.

     A second pair of shoes then popped into mind: sturdy leather loafers accented with brass buckles, easily identified as those that were purchased for my freshman year in high school. During winter I changed to snow boots for the trek to and from school and carried my shoes. One afternoon a single loafer vanished, and despite retracing the route back to school and home again, the shoe was lost, even though it had to be somewhere. I had chosen the loafers myself, but discovered that I didn’t like them much, so it’s possible that the shoe accidentally-on-purpose dropped out of my life, but that could be my mother talking.

     One spring day during junior year, my best friend and I decided to walk to Chicago, about fifteen miles distant from our town. I wore a beautiful pair of boots made from thin buttery leather, lined with elastic, which left no room for socks. Within the first mile multiple blisters swelled and popped, but had I stopped to inspect the damage, I wouldn’t have been able to get the boots on again. Regardless, my friend and I made the city without incident and recorded our excursion at a subway photo booth, which I know is true, since my friend has the pictures.

    We took a train home; neither of us could have walked the last two miles. Our faces were black from auto fumes and our raccoon eyes were a giveaway that we had been up to something. When my mother picked us up she only commented on how dirty we were. At home I locked myself in the bathroom and peeled away my beautiful glove-tight boots. One toenail came off and I swabbed the blisters with mercurochrome, but my blazing orange feet drew no notice. My parents ignored me; I thought it was because they trusted my judgment, but in truth, they didn’t want to know anything that might upset them. Of course, I could be lying.

     It was beginning to look as if good memories of my mother either didn’t exist, or were weirdly inaccessible, so I switched to searching for instances when my mother was happy, but I’m not sure she ever was. Everything she said sounded like, “I’m broken. Fix me.” 
 

My mother's ideal woman, Zsa Zsa Gabor. For an Asperger girl, this female model was terrifying and soul killing.

My mother was always on the hunt for shoes, and our arrival in any shoe department was a dark day for the clerk. Stacks and stacks of boxes holding pumps or sling backs were brought forth, but none fit. My mother was a Cinderella for whom no shoe was good enough and she delighted in the fiction that her feet were impossibly unique, even though stores always had a selection in her size. No matter which pair of shoes she purchased, by the time we got home they hurt her feet; her closet floor was a mosaic of wasted cow hides. Perversely (from her point of view), my feet found satisfaction everywhere. Any style of boot or shoe would do, which reminds me of a pair of blue boots I once owned. All I can say is that I wish I still had those boots.

     My mother saw this democratic aspect of my anatomy as an indictment of commonness, which she reinforced with cutting questions such as, “Why is it that only the wrong type of men look at you?” The truth was that I was young and pretty and men looked at me, but it could be that I was a she-devil and didn't know it.

     One twenty-something birthday my mother sent a pair of Jesus sandals as a gift. These articles of 1st Century torture were clearly marked two sizes smaller than the size I had worn since I was twelve. Mom was one of those gift-givers who require that unwanted items be returned to her, so I phoned to say that the sandals were in the mail.  She became furious, and then pathetically hurt, which is what one expects of a tyrant. She insisted that the sandals weren’t too small, my feet were too big. She had gotten them at a clearance sale and could not return them. Couldn't I squeeze my feet into them if I really tried? Refusing to try  meant that I didn't love her. Besides, I had to be lying about my shoe size, since I lied about everything.

Support for the Asperger Experience of Emotion as Pain

FROM:  Your Brain: Your Pharmacist. Brain prescribes opioids for rejection – and rewards social acceptance with opioids! Posted on November 20, 2013 by consummatenovice

For the last decade researchers have found that emotional pain experienced from social rejection activates the same region of the brain that physical pain activates – the pain center. (see previous post "The Science of Pain, Empathy and Emotion) 

Scientists believe that since mammals live in social groups that are crucial to survival, social rejection is akin to a physical threat to our brain. A recent paper by Hsu et al. from the University of Michigan, has now shown that the same opioid receptors located in the brain’s pain center activated in response to physical pain are also activated by emotional pain and that the more opioid response an individual releases, the more that person scores high on the trait “resiliency”.  The study also found that the brain rewards social acceptance with activation of opioid receptors located elsewhere in the brain.

The brain protects itself from feeling too much physical pain by dosing itself with endogenous opioids. It lets you feel pain so you know that whatever it is you are doing should stop, but then alleviates its own pain by activating opioid receptors located in the pain center of the brain. Presumably, this neat self-soothing mechanism exists so when we get hurt we don’t just lie down and cry. (My personal experience points to the failure of this quenching or dampening of pain; the result is panic and anxiety that will escalate to unbearable levels.)

 

Given the similarities in the experience of physical and emotional pain, scientists have hypothesized that emotional pain also results in opioid receptor activation. In this study, Hsu and Zubieta used a radiotracer specific for opioid receptors to visualize the release of endogenous opioids with PET imaging in response to stimuli.

Expectedly, rejected subjects felt more “sad and rejected” and less “happy and accepted,” while accepted subjects felt the opposite. Interestingly, subjects with high opioid activity rated themselves as lower in the “sad and rejected” scale. These findings suggest that individuals with a robust opioid response bounce back more quickly in the face social rejection. This data corroborates a study by Way et al. from 2009 which examined the differences in activation of the brain’s pain center in response to social rejection between people who have a normal opioid receptor gene and those who have a mutation in the receptor. The mutated receptor is thought to have greatly reduced function and carriers of this mutation have been shown to need greater amounts of opioids to treat physical pain (ex: post-surgical pain). Way and Eisenberg saw that carriers of the mutation had greater activation of the pain center than non-carriers.

These findings will hopefully lead to new therapies and interventions with individuals suffering from depression, social anxiety, and other psychological disorders.

Hsu, D. et al. Response of the μ-opioid system to social rejection and acceptance. Molecular psychiatry 18, 1211–7 (2013).