Conning StarCon and Cartesian Dualism

Ever since being presented with the opportunity to cheat on the StarCon Aptitude Test by copying the answers of a fellow cadet with a remarkably large “brain pan”, I have been curious about the relationship of brain size and intelligence. The traditionally assumed positive correlation has apparently stood the test of time: a major recent study finds that there is a definite, albeit weak, correlation between brain size and intelligence, although one of the authors recommends against “measuring job candidates’ head sizes during the hiring process” (or, presumably, when determining whose answers to copy on aptitude tests):

Summary: Using a large dataset and controlling for a variety of factors, including sex, age, height, socioeconomic status, and genetic ancestry, scientists found that people with larger brains rated higher on measures of intelligence and educational attainment. Size was far from everything, however, explaining only about two percent of the variation in smarts.

The English idiom “highbrow,” derived from a physical description of a skull barely able to contain the brain inside of it, comes from a long-held belief in the existence of a link between brain size and intelligence. …

A new study, the largest of its kind, led by Gideon Nave of the University of Pennsylvania’s Wharton School and Philipp Koellinger of Vrije Universiteit Amsterdam, has clarified the connection. Using MRI-derived information about brain size in connection with cognitive performance test results and educational-attainment measures obtained from more than 13,600 people, the researchers found that, as previous studies have suggested, a positive relationship does exist between brain volume and performance on cognitive tests. But that finding comes with important caveats.

“The effect is there,” says Nave, an assistant professor of marketing at Wharton. “On average, a person with a larger brain will tend to perform better on tests of cognition than one with a smaller brain. But size is only a small part of the picture, explaining about 2 percent of the variability in test performance. For educational attainment the effect was even smaller: an additional ‘cup’ (100 square centimeters) of brain would increase an average person’s years of schooling by less than five months.” Koellinger says “this implies that factors other than this one single factor that has received so much attention across the years account for 98 percent of the other variation in cognitive test performance.”

“Yet, the effect is strong enough that all future studies that will try to unravel the relationships between more fine-grained measures of brain anatomy and cognitive health should control for total brain volume. Thus, we see our study as a small, but important, contribution to better understanding differences in cognitive health.” …

One of the notable findings of the analysis related to differences between male and females. “Just like with height, there is a pretty substantial difference between males and females in brain volume, but this doesn’t translate into a difference in cognitive performance,” Nave says.

A more nuanced look at the brain scans may explain this result. Other studies have reported that in females, the cerebral cortex, the outer layer of the front part of the brain, tends to be thicker than in males.

“This might account for the fact that, despite having relatively smaller brains on average, there is no effective difference in cognitive performance between males and females,” Nave says. “And of course, many other things could be going on.”

The authors underscore that the overarching correlation between brain volume and “braininess” was a weak one; no one should be measuring job candidates’ head sizes during the hiring process, Nave jokes. Indeed, what stands out from the analysis is how little brain volume seems to explain. Factors such as parenting style, education, nutrition, stress, and others are likely major contributors that were not specifically tested in the study.

Here’s a slightly older comprehensive review of the scientific literature on the topic, whose introduction surveys nineteenth and early twentieth century attitudes:

We review the literature on the relation between whole brain size and general mental ability (GMA) both within and between species. Among humans, in 28 samples using brain imaging techniques, the mean brain size/GMA correlation is 0.40 (N = 1,389; p < 10−10); in 59 samples using external head size measures it is 0.20 (N = 63,405; p < 10−10). In 6 samples using the method of correlated vectors to distill g, the general factor of mental ability, the mean r is 0.63. We also describe the brain size/GMA correlations with age, socioeconomic position, sex, and ancestral population groups, which also provide information about brain–behavior relationships. Finally, we examine brain size and mental ability from an evolutionary and behavior genetic perspective. …


Throughout the nineteenth and early twentieth centuries, the relation between whole brain size and GMA was almost universally accepted (Broca, 1861; Darwin, 1871; Morton, 1849; Topinard, 1878). The renowned French neurologist Paul Broca (1824–1880) measured external and internal skull dimensions and weighed wet brains at autopsy and observed that mature adults averaged a larger brain than either children or the very elderly, skilled workers averaged a larger brain than the unskilled, and eminent individuals averaged a larger brain than the less eminent. Charles Darwin (1871) cited Broca’s studies in The Descent of Man to support his theory of evolution:

No one, I presume, doubts that the large size of the brain in man, relatively to his body, in comparison with that of the gorilla or orang, is closely connected with his higher mental powers. We meet the closely analogous facts with insects, in which the cerebral ganglia are of extraordinary dimensions in ants; these ganglia in all the Hymenoptera being many times larger than in the less intelligent orders, such as beetles…

The belief that there exists in man some close relation between the size of the brain and the development of the intellectual faculties is supported by the comparison of the skulls of savage and civilized races, of ancient and modern people, and by analogy of the whole vertebrate series.

I recently encountered a nineteenth / early twentieth century source not cited by the paper, the always fascinating Rav Eliyahu Kalatzkin’s endorsement of the correlation between brain size and intelligence. Due to a curious intersection of the timeless principle that correlation does not imply causation and some classic nineteenth century scientific confusion, however, he rejects the common assumption that brain size affects intelligence, arguing that this is actually an example of reverse causation: the self-evident (to him) nature of an extreme form of Cartesian dualism – “it is inconceivable that the brain, combined of phosphorus and albumen and the like, can engender intelligence and knowledge” – prompts his suggestion that it is actually greater intelligence that causes greater brain size, rather than the reverse:

וההכרח לומר דהא דקאמר שמעת מימיך אומר חמור זה יוצא צינה עליו, הכוונה שאינה מסובבת לו יסורין וחולי, כאשר הרגש הכאב הוא בעצבי ההרגשה המובילין להמוח, ואין שוטה נפגע, וביחוד החמור המצויין בסכלותו,1

ובהבעלי חיים הפקחים כמו הקוף ירבה כמות המוח,

[ויש שאמרו כי גם באנשים ירבה כמות המוח לפי ערך תבונתם, ומזה ישפטו כי המוח יראה פעולתו על כח השכל, ופליאה דעת איך יחולל המוח המורכב מפאספאר ואלבומין וכדומה, את כח השכל והמדע, וקרוב הדבר אשר יחליפו הסיבה להמסובב וכי יגדל וירבה כמות המוח על ידי עבודת העיון והתבונה, והעבודים בעמל ידים ירבה מרוצת הדם בשרירי ידיהם, ומזה יגדלו ויתחזקו שרירי ידיהם, ואנשי מדע אשר יעמלו ברעיוני חכמה והרגשות עדינות יעוררו רגשות עדינות וקלות בהעצבים ומרוצת הדם, וכאשר הקל יצוף למעלה, מקומן בראש ומוח, ורגש תאוה מוחשית מקומה באברים תחתונים, ורגשות זכות המחוללים תנועה זכה בדם ועצבים, מקומן הגבה מעלה, ובעבדות המוח אשר יתעצם שמה מרוצת ותנועת הדם, מזה יגדל וירבה כמות המוח, אם אך לא יחלישו ברוב יגיעה ועבודה שאינו לפי כחו, ובקלקול ופצע במוח יאבד האדם כח תבונתו, אף כי התבונה והשכל הוא ענין רוחני, כאשר יסתמא בקלקול העין, כאשר מוחש ההבטה הרוחנית, תראה פעולתה על ידי העין]

ובהם יוסיף גם הרגש ומכאוב2

R. Kalatzkin acknowledges that damage to the brain will impair the intellect; I do not understand his reconciliation of this fact with his stance of substance dualism.

[Further reading: another review of the scientific literature; some popular articles; Wikipedia discussions.]

  1. It is unclear where the donkey gets its reputation for foolishness. claims (also without any sourcing): “In general donkeys are quite intelligent, cautious, friendly, playful, and eager to learn. Donkeys have a notorious reputation for stubbornness, but this has been attributed to a very strong sense of self preservation.” []
  2. אמרי שפר סימן ל”ד אות י”ב []

Frankenstein: Origins

An Account of some Experiments made on the Body of a Criminal immediately after Execution, with Physiological and Practical Observations. By Andrew Ure, M.D.M.G.S.

Read at the Glasgow Literary Society, Dec. 10, 1818

Convulsions accidentally observed in the limbs of dead frogs, originally suggested to Galvani, the study of certain phenomena, which from him have been styled Galvanic. He ascribed these movements to an electrical fluid or power, innate in the living frame, or capable of being evolved by it, which he denominated Animal Electricity. …

Many experiments have been performed, in this country and abroad, on the bodies of criminals, soon after their execution. Vassali, Julio, and Rossi, made an ample set, on several bodies decapitated at Turin. They paid particular attention to the effect of Galvanic electricity on the heart, and other involuntary muscles; a subject of much previous controversy. …

Most of the above experiments were however made, either without a voltaic battery, or with piles, feeble in comparison with those now employed. Those indeed performed on the body of a criminal, at Newgate, in which the limbs were violently agitated; the eyes opened and shut; the mouth and jaws worked about; and the whole face thrown into frightful convulsions, were made by Aldini, with, I believe, a considerable series of voltaic plates.

[Ure spends some time discussing various theories of the relationship between electricity and life, and then continues:]

These general physiological views will serve, I hope, as no inappropriate introduction to the detail of the galvanic phenomena, exhibited here on the 4th of November, in the body of the murderer Clydsdale; and they may probably guide us to some valuable practical inferences.

The subject of these experiments, was a middle sized, athletic, and extremely muscular man, about thirty years of age. He was suspended from the gallows nearly an hour, and made no convulsive struggle after he dropped; while a thief executed along with him, was violently agitated for a considerable time. He was brought to the anatomical theatre of our university in about ten minutes after he was cut down. His face had a perfectly natural aspect, being neither livid nor tumefied; and there was no dislocation of his neck.

Dr. Jeffray, the distinguished Professor of Anatomy, having on the previous day requested me to perform the galvanic experiments, I sent to his theatre with this view, next morning, my minor voltaic battery, consisting of 270 pairs of four inch plates, with wires of communication, and pointed metallic rods with insulating handles, for the more commodious application of the electric power. About five minutes before the police arrived with the body, the battery was charged with a dilate nitro-sulphuric acid, which speedily brought it into a state of intense action. The dissections were skilfully executed by Mr. Marshall, under the superintendance of the Professor.

Exp 1. A large incision was made into the nape of the neck, close below the occiput. The posterior half of the atlas vertebra was then removed by bone forceps, when the spinal marrow was brought into view. A considerable incision was at the same time made in the left hip, through the great gluteal muscle, so as to bring the sciatic nerve into sight; and a small cut was made in the heel. From neither of these did any blood flow. The pointed rod connected with one end of the battery was now placed in contact with the spinal marrow, while the other rod was applied to the sciatic nerve. Every muscle of the body was immediately agitated, with convulsive movements, resembling a violent shuddering from cold. The left side was most powerfully convulsed at each renewal of the electric contact. On moving the second rod from the hip to the heel, the knee being previously bent, the leg was thrown out with such violence, as nearly to overturn one of the assistants, who in vain attempted to prevent its extension. …

Exp. 3. The supra-orbital nerve was laid bare in the forehead, as it issues through the supra-ciliary foramen, in the eyebrow: the one conducting rod being applied to it, and the other to the heel, most extraordinary grimaces were exhibited every time that the electric discharges were made, by running the wire in my hand along the edges of the last trough, from the 220th to the 227th pair of plates; thus fifty shocks, each greater than the preceding one, were given in two seconds: every muscle in his countenance was simultaneously thrown into fearful action; rage, horror, despair, anguish, and ghastly smiles, united in their hideous expression in the murderer’s face, surpassing far the wildest representations of a Fuseli or a Kean. At this period several of the spectators were forced to leave the apartment from terror or sickness, and one gentleman fainted. …1

These experiments of Ure (or perhaps those of his predecessors) are mentioned by the unfailingly interesting Rav Eliyahu Kalatzkin:

וזה איזה שנים אשר אנשי החברה מגיני בעלי חיים (טהיערשוטץ פעראיין) [Humane Societies] החלו לחקור ולדון על דבר שאלת השחיטה, ובאיזה מחוזות במדינות שווייץ, מצאו האנטיסעמיטין תואנה להוציא חוק לאסור השחיטה, ולהנהיג הטביחה על ידי הבוטעראל, שיסמאסקע או מכונה עלעקטרית, ובעוד אשר ילכו לצוד ציד ויגרו כלבי הציד בטרפם, לעונג ושעשוע נפשם, יהפכו לרגע כרחמנים, ותחת מסוה החמלה והרחמים, יתנפלו להציק רבבות אנשים, ולהכרית אוכל מפי אחינו בני ישראל, ולא ישימו לב למופתי החכמה אשר הראו לדעת גדולי הפראפעסארין כי השחיטה נעלה וטובה מכל אופני הטביחה ומיתה האחרים, ובא קבוצת דבריהם במחברת הד”ר עהרמאן מטריער, אשר נקראה בשם טהיערשוטץ אונד מענשען-טרוטץ והובא דבריו במכה”ע יידישע פרעססע 18 אפריל שנה תרמ”ה, …

וכבר העיר בצדק החכם מהרי”ם ראבינאוויץ בחוברת “יסודי השחיטה”, שאין הפרכוס ותנועות של הבהמה אחר שחיטתה, מוכיחין שתרגיש אז צער וכאב, כאשר גם אחר כריתת כל הראש במכונת הגוילאטינע [guillotine], נראה בה לפעמים קריצת העינים וכדומה עכ”ד, והחוקרים בחנו בהגישם גוף אדם תלוי לצירי עמוד הגאלוואני, וראו שפרפר בתנועות מוזרות2

But while Ure understood his experiments to demonstrate that electricity could actually restore life to the dead, R. Kalatzkin rejects this interpretation:

In deliberating on the above galvanic phenomena, we are almost willing to imagine, that if, without cutting into and wounding the spinal marrow and blood-vessels in the neck, the pulmonary organs had been set a-playing at first, (as I proposed) by electrifying the phrenic nerve (which may be done without any dangerous incision,) there is a probability that life might have been restored. This event, however little desirable with a murderer, and perhaps contrary to law, would yet have been pardonable in one instance, as it would have been highly honourable and useful to science. …

It is known, that cases of death-like lethargy, or suspended animation, from disease and accidents have occurred, where life has returned, after longer interruption of its functions, than in the subject of the preceding experiments. It is probable, when apparent death supervenes from suffocation with noxious gases, &c, and when there is no organic lesion, that a judiciously directed galvanic experiment, will, if any thing will, restore the activity of the vital functions. …3

ואשר יש שישפטו מזה כי כח העלעקטרי יפעול על הנפש, לא כן הוא, ואך כאשר נשאר עוד בגופו כח חיים בלתי מורגש שב לתנועה מורגשת בכח גירוי הזרם העלעקטרי, וכאשר נראה כי הזרם העלעקטרי לא יפעול מאומה על הגוף אשר כבר אבד ממנו כל כח חיים, ופעמים נשאר בו כח חיוני, גם כשלא נראה בו אות ורגש חיים, וכמפורש בנדה (דף ס”ט) דזב וזבה שמתו מטמאין במשא עד שימוק הבשר, דאז הוא דהוי מת בודאי, ובפ”ת דמסכת שמחות שפוקדין על המתים עד ג’ ימים ומעשה שפקדו אחד וחיה כ”ה שנים, ועיין מ”ש בזה החת”ם סופר (חלק יו”ד תשובה של”ח), וכן יאמרו הרופאים שביחוד בתליה וחניקה, יארע כזאת, ולזאת פעל עליו הזרם העלעקטרי כמבואר

R. Kalatzkin’s cited remarks occur at the end of his long discussion of צער בעלי חיים, which we have previously discussed here and here. His essay was also the subject of a recent Reading Responsa lecture of mine, available at the Internet Archive.

  1. The Journal of Science and the Arts, Edited at the Royal Institution of Great Britain, Vol. VI, London 1819, pp. 283-290. See Lauren Young, The Real Electric Frankenstein Experiments of the 1800s, and John Simkin, Andrew Ure. []
  2. אמרי שפר סימן ל”ד אות י”ז []
  3. Ibid. pp. 292-93. []

Faulhaber’s Formula Of the Figurate Numbers

For Dr. Pinhas Grossman, recently promoted to Senior Lecturer at the School of Mathematics and Statistics of the University of New South Wales

Several years ago, we noted the procedure given by the Tosafos to calculate the triangular numbers. I recently came across an analysis by the non-pareil Rav Eliyahu Kalatzkin of the Tosafos and a cognate source, which concludes with a parenthetical excursus into the case of the square pyramidal numbers. This analysis seemingly has no significance at all for any point of Torah, and R. Kalatzkin apparently engages in it merely for the joy of doing mathematics. See his שו”ת אבן הראשה סוף סימן כ”ד1.

R. Kalatzkin’s concluding line notes that his method can be extended to the calculation of the sum of the first n cubes (the four-dimensional hyperpyramidal numbers), although he leaves this as an exercise for the reader.

The general formula for the sum of the p-th powers of the first n positive integers is known as Faulhaber’s formula, named after the sixteenth / seventeenth century German mathematician Johann Faulhaber.

  1. I have not reproduced the text here as I usually do, due to the difficulty and tediousness of getting the HTML necessary to represent the mathematical notation, combined with the bidirectionality, correct. Furthermore, reading mathematical equations written (as R. Kalatzkin does) from right to left is an experience everyone should have at least once. []