Summary
The origin of cognitive inequality is a hot, divisive topic. The existence of cognitive inequality is hardly controversial.
Highlights
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I found out that many prominent mathematicians had tried to articulate the idea that their talent was first and foremost a cognitive attitude. A famous example is that of Descartes who, in the opening lines of his Discourse on Method, insisted that he wasn’t particularly gifted:
For myself, I have never presumed my mind to be any way more accomplished than that of the common man. Instead, he attributed his successes to his chance discovery of a miraculous “method” that, for all practical matters, is an assortment of metacognitive techniques aimed at improving the clarity and reliability of one’s intuition. If you were to generate a tag cloud of his favorite words, intuition, clear and distinct would stand out with massive fonts. The same themes can be found over and over again in the writings of Poincaré, Hadamard, Thurston, Grothendieck, and many others. This is part of a broader pattern where some of the biggest names in science have rejected the notion that they were born with unique abilities, insisting instead on their curiosity and stubbornness
Esto está muy alineado con lo planteado en el libro “Peak”.
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We have no good words to discuss these things. No one ever explained to us what it means to think, meditate, imagine, reason, or dream. What is the neurological basis of these activities? What do they have in common? What differentiates them? What are their long-term effects on our brains? Could it be that some people practice them the wrong way, while others have stumbled upon remarkably effective techniques that radically transformed their capabilities?
Anders Ericsson y Robert Poole estarían de acuerdo.
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I have no idea how “normal” people approach a question like this one, but it is very hard for a mathematician like me to take it as a satisfactory test of “working memory,” “processing speed,” or “logical thinking”—whatever these expressions mean. I hardly have to think to get the right answer. When looking at the picture, I get the eidetic perception of three superimposed permutation matrices (one for the background geometric shape, one for the color of the foreground rectangle, one for the angle of the foreground rectangle.) And, thanks to this eidetic perception, I perceive this question as requiring the same cognitive load as computing 132 + 37. Subjectively, it feels that by projecting mathematical structure onto the picture, I am able to reduce the need for “working memory”.
Es exactamente lo que plantea Ericsson: las representaciones mentales apalancan recursos básicos compartidos para multiplicar sus capacidades en base a heurísticas cognitivas.
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The Flynn effect applies to all mathematical structures, including the ones that feel obvious to “normal” people. Two thousand years ago, in Ancient Rome, my comparison “trivial” problem (132 + 37 = 169) would have constituted a more challenging IQ test question (CXXXII + XXXVII = CLXIX.) Our number sense has substantially evolved over the past millennia. We live in a world where (almost) everybody understands Hindu-Arabic numerals, (almost) everybody understands zero, and (almost) everybody understands negative numbers—three notions that had long been out of reach of ordinary people. This large-scale anthropological transformation, which cannot be explained by changes in our genomes, is directly attributable to changes in our cultural and technological environment.
Argumento a favor de la teoría de los dispositivos cognitivos.
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we have no biologically meaningful words to express the specific unseen actions that we can perform in our heads when we think, meditate, imagine, reason, daydream
Realidad que hace difícil estudiar estas diferencias.
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In a fascinating 2016 fMRI study, Marie Amalric and Stanislas Dehaene observed that professional mathematicians process complex mathematical statements by recruiting brain areas that aren’t typically mobilized in language processing, specifically in the inferior temporal and parietal regions. This happens regardless of whether the statements belong to their specific domain of research. By contrast, the control population of non-mathematicians with equal academic standing activate the expected language-processing regions when exposed to the same mathematical statements.
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When hearing that brains of professional mathematicians have specific activation patterns, people feel vindicated in their hereditarian beliefs. Yet they accept non-genetic causes for the biceps of a bodybuilder or the liver of an alcoholic. Because cognitive activity takes place under a veil of invisibility, people underestimate the magnitude of the practice gap.
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From a machine-learning perspective, the conjecture can be viewed as a natural consequence of the prior ones. Indeed, our synaptic connectome reconfigures in response to not just primary stimuli—the raw sensory signal we receive from the world—but also secondary stimuli, the stream of mental imagery that we continuously elaborate. This is the fundamental reason why educational interventions so often fail to move the needle. While they deterministically alter the primary stimuli, their impact on the secondary stimuli is always indirect and contingent to uncontrolled factors.
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No theory of cognitive inequality would be complete without a discussion of fear. Why did we evolve cognitive inhibition, this bizarre response to intellectual difficulty, this visceral panic, this brain fog that prevents us—among other things—from even engaging with mathematical abstractions?
Interesante que afecte tanto a los matemáticos, y que la capacidad de gestionar ese miedo sea tan crucial para su capacidad de pensamiento.
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Progress involves reinforcing self-confidence, finding the right sparring partners and ecosystems, and developing new ways of thinking.
Creo que esto aplica en general, más allá del campo de las matemáticas.