Deconstructing Base-10

Not my own idea, came in large part from what I read in גנת אגוז of R' Gikatilia, but sunk in today with the right words so I'm writing it down. A little bit different way of looking at it than common perception.

We're use to the concept of Base-10 and it's unit markers: Ones Place, Tens Place, Hundreds Place, etc.... In truth though, in terms of actual real existing units, all you have is 9 digits, so that really what we're computing is Units of 9. When we pass the last final real digit of 9 we have no real digit further so we instead put '10' as if to say we've gone past one full set of 9's and yielded one (1) additional unit of the emergent כולל coming from that full set of '9'. In other words, '10' is 9 units of 9-based singular units (פרט) and '1' unit of כלל.

Another example: 47. On the one hand it's 4 sets of Tens and 7 units of Ones. On the other though, going by pure real digits i.e. 9 (because 10 is only a fantasy), it is 4 sets of 9's , 4 emergent units of כלל thereof, and 7 units of singular-unit Ones. 36+4+7= 47

My chavrusa and friend Shimshon Tabrikian formulated the equation for me:

Take any integer of abc.

In Base-10 it's essentially: a(100) +b(10) +c(1) = abc

What I said essentially subdivides the equation into the following:

[ a(99) +b(9) + c(1) ] + [a +b +c] = abc

The first portion being the calculation of the real units of פרט and the second portion being the emergent כלל.


With this perspective of looking at it it can become easily understood (after working through it somewhat) how an old mathematical "trick" of Digital Roots and '9' works. Essentially, take any integer in the world, calculate the Mispar Katan (Digital Root) of the integer, subtract that Mispar Katan from the original integer.... the remaining number will always have a Mispar Katan of '9' .
Example: '564' --> mispar katan is 15--> subtract 15 from 564 yields 549--> Mispar Katan of 549 is 18 which then becomes 9.

(Solution why it works: the initial calculating of Mispar Katan essentially parses out all of the "non-9" units i.e. the units of כלל and the units of Ones. Of course then when you subtract those units from the original number you're left with a number that is divisible by 9)

Now the Gemaras regarding תשיעי, עשירי, ואחת עשר by מעשר בהמה takes on a whole new depth of meaning. עיין שם Also, consider redemption of הקדש קרקע in פר' בחוקתי --  the 9 Yisraelim and one Kohen learnt out from the 10 mentions of Kohen.

Also see the mathematical concepts of Mispar Katan a.k.a. Digital Roots and also Modular Arithmetic for this.

[ועוד א ב ג ד ה ו ז ח ט , אדם. י-- ייחוד דיליה מלכות, עשיראה דאדם [זוהר פנחס רכד

Book Ends

ראיתי לעורר על ההבדל בין "ביאת קץ" של פרשת נח וספר יחזקאל לבין "לך לקץ" של סוף ספר דניאל וגדול הוא לענ"ד

Consider also :  "coming home" vs "going to the bathroom".... why not "coming to the bathroom"?

ויש להבתונן עוד בהדברים המשתייכים  -ביאת אשה ,עולם הבא, בא אל פרעה

ועי' פרי צדיק ריש פר' בא אל פרעה

Survival Mechanisms With Levels of Scaling

One of those floating thoughts that came to mind...:

Take for example the banging of a toe or the body's fighting of a cold. If scaled down to the localized level it's horrific, a complete holocaust of cell tissues and structures and what not... and yet we don't relate to it as a holocaust, as a complete destruction going underway as we go on throughout the day....why?...because our conscious mind is operating on a different (and higher) level of scale... at the end of the day the serrated finger or bruised toe is not Me/I .... rather, just a small component of the "I" that is Me.... the real Me/I is safely perched above the localized "holocaust" and instead relates to it as an inconvenience of sorts....

so maybe that's  the need for withdrawal (הסתלקות) sometimes into ourselves, into deeper layers of self-existential consciousness.... thereby reducing the forsaken external layers under attack as mere "shells", disconnected from the real I that we are so vulnerable to having damaged.....

Kever Yechezkel in Al Kifl

There is so much out there to see about this. Google "Tomb of Ezekiel Al Kifl" and enjoy.

I saw it written that the muslims have come to refer to Yechezkel as "dhu al-kifl" or, "the one who possesses double (כפל)" -- would be interesting to understand if there's any deeper connection of יחזקאל  to כפל....

Inscription by tomb from what i can make out, I bolded everything that is questionable:

ענו לאל במהלל ושירים: אשר זיכה נדיבי עם ישרים

בבנין רב אדוננו יחזקאל: נביא האל לישראל בחורים

רעומיז הבחור? יופי עשאו: וטח אותו בציור ?ורואודים

אשר הושר ומשוח בששר: והון פיזר בזהב רב ספורים

לטוב מכר שם ודרך בנו שר?: נשיא ששון ויחס הגבירים

לבית דוד יברך צור מעונים: בברכת אל זקנים עם נערים

הנחל ששון לבית ששון בשמחה: בני חיי ומזוני רב לדורים

ונשתכלל על דנבאיראובן?: והוא פקיד תובר? שר בשרים

ועת נשלם .....[חסר

Ashur vs. Mitzrayim & Cush

In going through Yeshayahu it would seem that there is a constant counterbalance of Ashur אשור vs. Mitzrayim מצרים (and of course with Yisrael in the middle).

Noteworthy to point out the earlier roots drawing from מגדל בבל where הבה נלבנה לבנים is מצרים אמר לכוש (Brsh"Rabba 38:8) vs. מן הארץ ההיא יצא אשור .

Possibly even hailing back more fundamentally .... וְנָהָר יצֵא מֵעֵדֶן לְהַשְקוֹת אֶת-הַגָן וּמִשָם יִפָרֵד וְהָיָה לְאַרְבָעָה רָאשִים.....

Freezing Water To Make A Mikva

I was really surprised by this. I knew about the Mishna in Mikvaot that says snow and ice can be used for mikva waters, but I always took it as a foregone conclusion that that's barring any original psul of מים שאובין i.e. it just fell from the sky that way and you then transport it to the mikva. But to take already invalid מים שאובין and make it valid by way of freezing-- that I thought was crazy.

Then I looked up an Aruch HaShulchan (סימן ר"א) who brings from an explicit Tosefta (טהרות פרק ב) that freezing even removes the פסול שאובין! Frankly I'm in a little shock primarily because it runs against my whole sense of "coming-into-existence" theme of mikva that I had developed על פי דרוש. Particularly two points:

1) הויה על ידי טהרה - surprising that something demanding a concept like הויה על ידי טהרה would allow for just a freezing and thawing of an already extant invalid body of water. That dissolving would be seen as a new הויה I don't hear.

2) the sense of לידת\הויית גשמים -- see Bereishit Rabba 12:7 מטר יש לו תולדות, שנאמר (איוב לח): היש למטר אב -- I had assumed it was this element which was part of the effect of Mikva. The rebirthing. A new existence...

So I guess the upshot is that I'm wrong. :-) So be it.

כסף ישיב לבעליו והמת יהיה לו

 בראשית רבה לח ג-- רבי יוחנן פתח (משלי יז:ג) משיב רעה תחת טובה לא תמוש רעה מביתו

אמר רבי שמעון בר אבא: לא סוף דבר משיב רעה תחת טובה, אלא אפי' משיב רעה תחת רעה, לא תמוש רעה מביתו

עי' בעץ יוסף ובפי' מהרז"ו שמבארים קושיית המדרש הוא בלשון "משיב" דמשמע אותו דבר שקבל הוא מחזיר שוב בחזרה ומשום הכי דרשו כוונת הפסוק דהוא משיב רעה תחת רעה ולא רק פשטות הפסוק של "רעה תחת טובה", דתרוויהון אמשיב קיימי
-- "repaying evil instead of (repaying) good"

והנה היא היא גופא ענין דרשת רבותינו בכסף ישיב לבעליו לרבות אפילו סובין (עי' רבינו המלבי"ם עה"פ שם) ואולי גם כונת חז"ל בהבנת מלת תחת גבי עין תחת עין דשתיהן אמזיק קיימי וכונת הכתוב עין ממון ישלם תחת תשלום עינו ממש

ועפי מה שהקשו ודרשו רז"ל עה"פ של כסף ישיב לבעליו לרבות אפי' סובין רציתי להקיש בדרוש גם לשיבת חוטא בתשובה דהיא היא אותו סתירה של השבה בדבר שאי אפשר וקבלה בדבר של תמורה וא"כ ישיב לרבות אפילו סובין הוי ענין של תשובה שאינה מעולה

Etymology- Evil - אויל

The connection seems so obvious it frankly amazes me that none of the popular etymology sites reference it.... it's like they don't even bother to look at considering hebrew! Silly people.

It is interesting to point out the Malbim's explanation of אויל in משלי where he sees it deriving from the word אולי and interprets it as someone who is filled with intellectual skepticism and indecision. See there further.

[Found one. Hebrew Wikipedia mentions the connection at the end http://he.wikisource.org/wiki/Tnk1/kma/qjrim1/ewil . Ironically enough.... he's skeptic about it! Ha!]

The Hanging Gardens of Bavel

A ton of information out there. More than is practical to bring here. But just thought it fascinating to learn about the Hanging Gardens of Bavel that Nevuchadnezzar constructed-- one of the seven wonders of the world.
I think it would really enrich the various נבואות , particularly those of ישעיה, the more you understand just how magnificent מלכות בבל was.
Also, many Gemarot and Midrashim regarding Bavel make more sense when learning about it. One for example, the lack of any stones in bavel-- literally. Everything is made from mud.

See this youtube clip. http://www.youtube.com/watch?v=3i5uRoWT6w0

Was wondering if the Garden had anything to do with the account in Daniel 4:26...

Strange also that supposedly Nevudchadnezzar built the Gardens for his wife from Media מדי -- the very same kingdom that ultimately was Bavel's downfall.... and you thought your in-laws were bad!

Once we're on the subject, for those who can view KMZ files (i.e. have Google Earth), here's one opinion of the remains of the Migdal Bavel http://bbs.keyhole.com/ubb/ubbthreads.php?ubb=showflat&Number=845863&site_id=1#import

Etymology - Pirates

It would seem the Midrash gives the source of the first pirates of the world:

אמר רבי אבא בר כהנא, אמר רבי יהושע בן קרחה: כל מוניטא של מצרים אינה אלא בים. לודים, לודי ים, ענמים, ענמי ים, כשמן להבים, להב ים, נפתוחים, נפתוחי ים, פתרוסים, פרוויטות, כסלוחים, פקוסים.
אמר רבי אבא בר כהנא: פתרוסים וכסלוחים היו מעמידין הוטליסון, היו אלו מגנבין נשותיהן של אלו ואלו מגנבין נשותיהן של אלו. מה יצא מהן? פלשתים גבורים כפתורים ננסים

Note the appropriateness both of the sense of stealing and that of being sea-related.
Not sure what the word of פקוסים is though ......

The Value of Fantasy?

4 separate observations which seem to share one common denominator: allowance of false projection and fantasy can lead to objectively true values and advances. Consider:

1) The mathematical invention of the number zero '0' which furthered many advanced branches of Math, even though (it would seem) the Torah does not recognize it. [The closest thing would seem to be the word אין , but that still does not encompass the full effect of the mathematical zero]

2) (Part of) the mathematical concept of limits, essentially a matter of saying "I know this can never be but let's pretend it is and build upon that".

3) Once, during a difficult period of life, there was a girl I had a few exchanges with and became smitten with. Because the exchanges were few and far between my mind mentally projected alot of idealisms about her and who she was, 'till the thought of her became more like a vision of some utopian beauty to strive for, carrying me through alot of difficult times and hardship. [Similar to Viktor Frankl's account of his wife's vision in the book Man's Search For Meaning]. Some time thereafter, I got something of a "closer look" of who the girl was and 'click', like someone had just flipped a light switch my vision of her totally disintegrated-- it was all a fantasy, and yet it carried me through and helped me.

4) I personally was able to throw myself wholeheartedly in my studies in yeshiva because of the paradigmatic vision I had of the yeshiva's hashkafa and it's staff. Had I seen them then with the-less-than-impressed perspective I have of them now-- I never would have grown as I did those years...

[Many years later I heard a speech by one of the faculty being given in a community shul. It was horrible. Riddled with inconsistencies, misquoting Gemaras and showing a general impression of narrow-minded ignorance. If not for the speakers being held in high esteem in many circles I probably would have felt little compunction in telling him he was a moron]

So with all that said, if in fact this concept is true, it behooves us to know where we see it in the Torah.... I have my doubts as to whether it's the perfect answer but what comes to mind is what i've heard is a Rambam in the Moreh who says that in a sense all of עבודת בית המקדש is a בדיעבד insofar as it's a physically oriented activity trying to engage with a non-physical Being. The Rambam continues to explain that although it's a "false fantasy" we have no other choice being that we're physical beings and we naturally think in physical terms... not a perfect fit but it's related I think....

[Heard related (and deeper) concepts from my Rebbe, Rav Matis Weinberg, in discussions of Pr' B'Shalach and Metaphor http://www.thelivingtree.org/indexArchiveShemot.htm ]