ר’ יעקב ב’ר חיים יוסף בנימיני ז’ל הרב
אדר תשמ’ג’נשמתו עלתה למרום ב
Black Swan English completeתנצב”ה
מרת נחמה זלאטע בנימיני בת אבא מנחם ז’ל
נשמתה עלתה למרום טו’ סיון תשס’ז
תנצב”ה
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pdf – The Black Swan and the Torah- 8
February 12, 2013
ב אדר- תשעג
The Black Swan and the Torah
When the Dutch explorer Willem de Vlamingh discovered black swans on the west coast of Australia in 1697 and the news filtered back to Europe, it became the model for things we can and cannot know with certainty.
John Stuart Mill, the classical economist and philosopher, explained this as follows it: “No amount of observations of white swans can allow the inference that all swans are white, but the observation of a single black swan is sufficient to refute that conclusion.”
Elaborating on this idea, Donald Rumsfeld, the former US Secretary of Defense stated:
“Reports that say that something hasn’t happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don’t know we don’t know.”
Four Types of Randomness:
1. Epistemic randomness: random events in human affairs. There is not enough information to know that something will happen. (i.e., the Japanese bomb Pearl Harbor, 9/11, the Arab Spring.)
2. Brownian motion or pedesis (from Greek: πήδησις Pɛɖeːsɪs “leaping”) is the presumably random moving of particles suspended in a fluid (a liquid or a gas) resulting from their bombardment by the fast-moving atoms or molecules in the gas or liquid. The term “Brownian motion” can also refer to the mathematical model used to describe such random movements, which is often called a particle theory.
3. The Uncertainty Principle
In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle, such as position x and momentum p, can be known simultaneously. The more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.[1] The original heuristic argument that such a limit should exist was given by Werner Heisenberg in 1927, after whom it is sometimes named the Heisenberg principle. A more formal inequality relating the standard deviation of position σx and the standard deviation of momentum σp was derived by Earle Hesse Kennard[2] later that year (and independently by Hermann Weyl[3] in 1928), where ħ is the reduced Planck constant.
4. Randomness and Mathematical Proof
The information in a random series of numbers cannot be “compressed or reduced to a more compact form. The number series is without pattern.
01010101010101010101
01101100110111100010
The first could be specified to a computer by a very simple algorithm, such as “Print 01 ten times.” If the series were extended according to the same rule, the algorithm would have to be only slightly larger; it might be made to read, for example, “Print 01 a million times.” The number of bits in such an algorithm is a small fraction of the number of bits in the series it specifies, and as the series grows larger the size of the program increases at a much slower rate.
For the second series of digits there is no corresponding shortcut. The most economical way to express the series is to write it out in full, and the shortest algorithm for introducing the series into a computer would be “Print 01101100110111100010.” If the series were much larger (but still apparently patternless), the algorithm would have to be expanded to the corresponding size. This “incompressibility” is a property of all random numbers; indeed, we can proceed directly to define randomness in terms of incompressibility: A series of numbers is random if the smallest algorithm capable of specifying it to a computer has about the same as the series itself.
By Gregory J. Chaitin
Randomness and the Torah
Randomness as a great Organizing Mechanism and contrast to the unique aspects of Torah and Torah study. The uniqueness of the Torah is highlighted by comparison and contrast to what it is not.
The Torah touches upon randomness in at least three ways:
1) בחקתי
2) סמוכית הפרשיות
3) כי לא דבר רק הוא מכם
בחקתי
ויקרא פרק כו
(כא) ואם תלכו עמי קרי ולא תאבו לשמע לי ויספתי עליכם מכה שבע כחטאתיכם:
(כב) והשלחתי בכם את חית השדה ושכלה אתכם והכריתה את בהמתכם והמעיטה אתכם ונשמו דרכיכם:
(כג) ואם באלה לא תוסרו לי והלכתם עמי קרי:
(כד) והלכתי אף אני עמכם בקרי והכיתי אתכם גם אני שבע על חטאתיכם:
(כה) והבאתי עליכם חרב נקמת נקם ברית ונאספתם אל עריכם ושלחתי דבר בתוככם ונתתם ביד אויב:
(כו) בשברי לכם מטה לחם ואפו עשר נשים לחמכם בתנור אחד והשיבו לחמכם במשקל ואכלתם ולא תשבעו:
(כז) ואם בזאת לא תשמעו לי והלכתם עמי בקרי:
(כח) והלכתי עמכם בחמת קרי ויסרתי אתכם אף אני שבע על חטאתיכם:
“And if you walk contrary unto Me, (as if all is by chance), and will not hearken unto Me; I will bring seven times more plagues upon you according to your sins. And I will send the beast of the field among you, which shall rob you of your children, and destroy your cattle, and make you few in number and your ways shall become desolate. And if in spite of these things ye will not be corrected unto Me, but will walk contrary unto Me (as if all is by chance), Then will I also walk contrary unto you (as if by chance); and I will smite you, even I , seven times for your sins.”
כו:כא רש”י ויקרא פרק
ואם תלכו עמי קרי – רבותינו אמרו עראי, במקרה, שאינו אלא לפרקים, כן תלכו עראי במצות. ומנחם פירש לשון מניעה, וכן (משלי כה יז) הוקר רגלך, וכן יקר רוח (משלי יז כז), וקרוב לשון זה לתרגומו של אונקלוס לשון קושי, שמקשים לבם להמנע מהתקרב אלי.
שבע כחטאתיכם – שבע פורעניות אחרים במספר שבע כחטאתיכם
Rashi:
Our Rabbis have explained (the term Keri) as denoting chance”, “by accident” (Bemikreh). i.e., it is only occasionally; similary you follow the commandments occasionally. And Menachem explains it as denoting “withholding”; and similarly (Proverbs 25:17) “Withhold thy foot”, and also (17:27) “He that restraineth his spirit”. And this meaning is close to the translation of Onkelos “in hardness”, as denoting “hardness,” and they harden their hearts and refrain from coming close to Me.
סמוכית הפרשיות
(Juxtaposition of Passages)
ויקרא פרק יט פסוק טז
לא תלך רכיל בעמיך לא תעמד על דם רעך אני יקוק
Do not be a tale bearer among your brethren. Do not stand idly by when your brother’s blood is shed. I am Hashem.
ויקרא פרק ה
א) ונפש כי תחטא ושמעה קול אלה והוא עד או ראה או ידע אם לוא יגיד ונשא עונו
And if any one sin, in that he heareth the voice of adjuration, he being a witness, whether he hath seen or known, if he do not utter it, then he shall bear his iniquity.
ספרא קדושים פרשה ב
ח) ומנין שאם אתה יודע לו עדות אין אתה רשאי לשתוק עליה תלמוד לומר לא תעמוד על דם רעך.
The Sifra asks from where do we know that we are obligated to give testimony as an eyewitness to an event? The Torah states : “Do not stand idly by while your brother is being attacked or killed.”
רש”י ויקרא פרק ה
(א) ושמעה קול אלה – בדבר שהוא עד בו, שהשביעוהו שבועה שאם יודע לו בעדות, שיעיד לו:
Translation: In that he heareth the voice of adjuration in a matter in which he is a witness, ie.e., they had adjured him by oath that ifhe knows any testinomony for him, he should testify for him (Siphra).
המלבי”ם
אמנם פשוטו של מקרא, שאם רואה חברו בסכנה, לא יעמוד ויטמון ידו בצלחת, רק יעשה כל השתדלות להצילו, אולם מן הסמיכות של “לא תלך רכיל בעמיך” ל”לא תעמוד על דם רעך” הוסיפו חכמים ואמרו שפירושו, שהגם שהזהרתי מרכילות, בכל זאת אם ידעת עדות לחברן, אף על פי שבזה תלך רכיל ותגלה סוד, צריך אתה לגלות ולהעיד, כי אין זה בכלל לשון הרעץ
The Malbim comments on this:
The plain meaning of this passage in the Torah is that if you see your friend in danger, you cannot just stand idly by with your hands folded. You must make every effort to save him. However, from the juxtaposition of the phrases “Do not be a tale-bearer on your people” and “Do not stand idly by while his blood is being shed” the Rabbis have explained that even as I am warned against tale-bearing, but in any event if I am an eyewitness to a crime, even if this seems like tale-bearing and that you are revealing a secret, nevertheless this act of being a witness does not come under the category of evil-speech (leshon hara).
Yevamot 3B:
The specific Torah passage which the Gemara deals with is the following:
דברים פרק כב
(יא) לא תלבש שעטנז צמר ופשתים יחדו: ס
(יב) גדלים תעשה לך על ארבע כנפות כסותך אשר תכסה בה: ס
Translation:
Thou shalt not wear a mingled stuff, wool and linen together. Thou shalt make thee twisted cords upon the four corners of thy covering wherewith thou coverest thyself.
תלמוד בבלי מסכת יבמות דף ד עמוד א
דכתיב: +דברים כ”ב+ לא תלבש שעטנז, גדילים תעשה לך, ואמר רבי אלעזר: סמוכים מן התורה מנין? שנאמר: +תהלים קי”א+ סמוכים לעד לעולם עשוים באמת וישר; .****************************************
3) The Torah is Infinitely Dense
דברים לב פרק
מז) כי לא דבר רק הוא מכם כי הוא חייכם ובדבר הזה תאריכו ימים על האדמה אשר אתם עברים את הירדן שמה לרשתה:
Translation:
For it is no vain (literally-“empty”) thing for you; because it is your life, and through this thing ye shall prolong your days upon the land, whither ye go over the Jordan to possess it.
רש”י דברים פרק לב
מז) כי לא דבר רק הוא מכם – לא לחנם אתם יגעים בה, כי הרבה שכר תלוי בה, כי הוא חייכם. דבר אחר אין לך דבר ריקן בתורה שאם תדרשנו שאין בו מתן שכר, תדע לך שכן אמרו (בראשית לו, כב) ואחות לוטן תמנע, (שם לו, יב) ותמנע היתה פלגש וגו’ לפי שאמרה איני כדאי להיות לו לאשה הלואי ואהיה פילגשו, וכל כך למה, להודיע שבחו של אברהם שהיו שלטונים ומלכים מתאוים להדבק בזרעו.
Rashi:
Not for nought will you toil in it, for a great reward depends upon it: “because it is your life.” Another interpretation: There is no empty (superfluous) thing in the Torah which , if you expound it, does not contain a reward. The proof to you is that thus have the Sages said: “And Lotan’s sister was Timna” (Gen. 36.22) “/And Timna was concubine (to Eliphaz, Esau’s son),” etc. (v. 12), for she said: If I am not worthy to be his wife, would that I be his concubine. Why is all this “necessary)? To make now the praise of Abraham, that rulers and kings desired to join with his seed. (Siprhre).
רבינו בחיי בראשית פרק יח
כי לא דבר רק הוא מכם”, ודרשו רז”ל: (ירושלמי שביעית א, ה) ואם רק הוא, מכם הוא רק.
Translation:
“It is no empty thing” and the Rabbis have explained this: “If you find it empty, it is because the emptiness comes from you.” (Yerushalmi, Shviit,1:5).
Conclusion
A detailed study of the Torah text reveals that randomness is non-existent in the Torah. This premise is a major feature in all of Torah study, a pervasive unifying concept. Stating it would appear obvious, trivial, and superfluous to the majority of Torah scholars Nevertheless, as we have shown, Rashi felt compelled to state it, for the idea gives us the focus and perspective to appreciate the uniqueness and distinctiveness of all Torah study.
All Torah Study demonstrates this principle, that there is no Randomness in the Torah. Hence an entire lifetime of study will continue to uncover the infinite density of the Torah.
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The Black Swan and the Torah- 8