What's Special About This Number?
Invalid techniques of proof
My favorites:
Proof by cosmology
The negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of God.
Proof by semantic shift
Some standard but inconvenient definitions are changed for the statement of the result.
Proof by religious belief
God told us that X is true
Proof by parent
“Because I said so.”
Proof by slippery definitions
The definitions are not so well-defined that the reader can tell exactly what they mean.
Proof by eminent authority
“I saw Karp in the elevator and he said it was probably NP-complete.”
David Karp?
Links Roundup #2
ART OF SCHIZOPHRENIA, BIOLOGY OF MORALITY, ADULT NEUROGENESIS, DANCING PLAGUE, PREDICTION TO LEARN MATH, ARACHNOPHOBIA & PERCEPTION, SUPER BABIES…OR NOT.
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The Fairy Fellers’ Master-Stroke by Richard Dadd (1817-1886). Richard Dadd was an Enlish painter who developed a mental illness, something like skizophrenia, and underwent a dramatic personality change becoming delusional and violent. He murdered his father and attempted to kill another man. His life and work are the subject of a book by Nicholas Tromans.
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Frans de Wall, a biologist and “monkey watcher”, author of The Age of Empathy: Nature’s Lessons for a Kinder Society, says that human morality has its biological basis in the need to cooperate to survive, reproduce, and pass genes.
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For most of the last century one of the central dogmas of neuroscience was that the brain couldn’t grow new cells once embryonic development was ended. In 1980 Fernando Notthebhom found evidence that “the adult canary brain undergoes seasonal changes in size. Males sing to serenade females, but the song-producing brain regions decrease dramatically in size after breeding season. The following spring, they are regenerated by neurogenesis so the male can learn new songs.” Nowadays adult neurogenesis is one of the hottest topics in neuroscience.
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How do you decide if a neuroscientific interventions for dyslexia is a valid treatment or an hoax? Some useful criteria could be: Who is behind the treatment? Is there a credible scientific basis to the treatment? What is the attitude of those promoting the intervention to conventional approaches?
The same criteria can be used to judge also other kind of treatments.
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In 1374 strange episodes were reported across Europe. People started dancing, uncontrollably, screaming, shouting and singing, appearing to neither see or hear nothing but their hallucinations. These events are known as dancing plague.
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”[…] using prediction during instruction can create learning opportunities to enhance the understanding and doing of mathematics”. Students asked to predict “how linear and exponential factors work—before this information was taught—became more curious about the content of the lessons they then proceeded to learn.” Engaging math in this way promotes reasoning, and the students appear to understand the material more deeply compared to when math is proposed (implicitly or not) and viewed, only as a matter of memorizing facts and procedures.
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A new research investigate the connection between fear and perception in spider phobic individuals showing how they are biased by their fear and perceive spiders as larger than they really are. / “[…] perception is just as much about construal, belief, the interaction of environment and memory as it is about sensory inputs”
“It was as big as my head, I swear!”
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Are babies super? A reasoned critique to development psychology studies claiming babies have incredible hidden abilities.
The great snare of the psychologist is the confusion of his own standpoint with that of the mental fact about which he is making his report. I shall hereafter call this the ‘psychologist’s fallacy’ par excellence.
William James, Principles of Psychology
Links Roundup #1
IMPOSSIBLE FIGURES, GRIEF≠DEPRESSION, MATH+CHILDREN, REVERSE ENGINEERING, NUMBER HYGIENE, SPACEWALK & SPACE MUSIC.
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When we admire the artwork of M.C. Escher, or we see some impossibile figure like the Pensore triange, how does the brain processe impossible objects?
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“The DSM-5 Mood Disorders Work Group has proposed eliminating in DSM-5 the major depression criterion E, “bereavement exclusion” (BE), which recognizes that depressive symptoms are sometimes normal in recently bereaved individuals.”
The failing in recognizing the difference between a proportionate response to a devastating emotional event and a mental illness carry the risk to make a caricature of psychiatry. Psychiatrists must think better.
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“Children as young as three to five years of age have the potential to learn mathematics that is surprisingly complex and sophisticated”, and, more impressive, infants by two months understand that unsupported objects will fall, and that hidden objects still exist and by five months of age they expect non-cohesive substances like water and sand to pour. This suggests that babies born with a basic understanding of how things in their environment operate.
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Ray Kurzweil is convinced that ”[…] by 2020 we’ll have computers that are powerful enough to simulate the human brain […] By 2029 […] we will have completed the reverse engineering of the human brain.”
Mh. I’m not sure.
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The Royal Statistical Society proposes 12 rules of “number hygiene” for journalists to at least achieve a basic understanding of numbers, statistics, graphs and so on (all of which are far too loved by journalists).
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“An EVA is probably the most physically demanding task an astronaut can undertake.”How astronauts learn to “spacewalk”.
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“Musics in space is something very important for the moral of the crew and for the psychological support of the crew.”
If you’re sharing a pizza with another person, there’s no need to cut it into precisely equal slices.Make four cuts at equal angles through an arbitrary point and take alternate slices. You’ll both get the same amount of pizza.
Also: If a pizza has thickness a and radius z, then its volume is pi z z a. (via Futility Closet)



