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May 31st, 2010

10:16 am - The Coraniaid
This actually isn't a current obsession of mine, but I guess I felt like writing it down because I remember I didn't find it discussed in this way when I looked on the net.

There is a mediæval Welsh story, The Story of Lludd and Llefelys, written down in 12th or 13th century, usually published alongside the Mabinogion.  The story describes the counsel taken by Lludd, ruler of Britain, with his brother Llefelys, ruler of France, regarding three terrible plagues that afflict the former's kingdom.

The first of the plagues (and the only one I'm going to talk about) is described very briefly.  This plague consists of a people called the Coraniaid who have moved into Britain, and they apparently can hear anything that the wind hears, so it is impossible to plot against them (that's all we are told about how horrible they are).

It takes a little work for the brothers to discuss things; they have to use a brass horn to talk through so the wind (and thus the Coraniaid) won't hear them, and they need to wash a demon out of it with wine.  Anyway, Llefelys gives Lludd some insects in order to deal with the Coraniaid.  He's to set some of them aside for breeding (in case the Coraniaid ever come back), and mash up the rest in water.  Then call a big meeting of the Britons and the Coroniaid together, with the pretense of making peace between them, and sprinkle the water over the whole crowd.  The insect-water will utterly destroy the Coraniaid, but won't harm the Britons at all.

OK, am I the only one who finds this to be xenophobic almost to the point of offensiveness?  Nobody else seems to have noticed this.  These Coraniaid are described as a plague, and what horrible suffering do they inflict?  Apparently just being there and being impossible to be mean to.  And for this, our heroes are determined to lie to them, and trick them under false pretenses of peace, in order to exterminate them.  I guess it's sort of okay, since the fact that they're susceptible to these insects while decent, red-blooded Britons aren't shows that they're not completely human, right?

This sounds a lot like the basest of accusations leveled against various (immigrant) ethnic groups through the ages (especially against Jews, actually).  “Gee, something has to be done about these horrible people.  Well, no, they're not actually doing anything wrong, but they're too clever/hardworking/cunning/sharp-eared to compete with.  And they're taking up space/land/services/jobs that should be going to real Britons/Americans/locals.”

It just sort of struck me how blatant the bigotry was in this case.  I guess it makes a certain amount of sense in the small, local world back then.  People are bad simply by virtue of not being locals, and when they move in they're invaders, and any means are valid to repel them.

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May 11th, 2010

09:38 pm - Rhombic Hexecontahedron
I've been sitting on this one for a while; too lazy to take the pictures.  But it's pretty cool.  Once again straying slightly from just following instructions.  This is a rhombic hexecontahedron, a stellation of the rhombic triacontahedron (a d30 if you play RPGs).  It's a really cool shape; it also happens to be the logo of Wolfram Alpha, which is nice too.  I used a golden rhombus module from Moseley's book, and worked out what modifications needed to happen and also how to put it together.  Very cool.

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April 15th, 2010

05:54 pm - Praying to God
So the editorial in the March Scientific American quoted a tweet from Sarah Palin:
Copenhgen=arrogance of man2think we can change nature's ways.MUST b
good stewards of God's earth,but arrogant&naive2say man overpwers
Leaving aside the various media enjoyment over possible contradictions with her other statements, etc... Let's take a look at this.

I think I interpreted this maybe not exactly the way it was intended, but let's pursue it anyway.  So the implication here is that we mustn't think that humanity is responsible for any climate change, since it's all out of our hands.  Or perhaps (and this may be where I'm going off on a tangent), we mustn't panic and go nuts changing our habits to try to fend off climate change since it's all out of our hands.  Either way, it obviously leads to some pretty dangerous fatalism, of course.  If it's all out of our hands, then what does it matter if we do good or bad, are careful or careless?  Nothing more or less than what God wants will happen.  And of course that is a simplistic way of looking at it, and I doubt anyone seriously would take that view this far.

Still, let's take God's guiding hand as a given, rather than trying to fight the basic premise.  There are those that take comfort in that, contending that God would never let his world be damaged in the way global warming threatens.  But wouldn't he?  Maybe God does promise never to destroy the whole world again (just after the Flood), but he never said anything about massive drought, heat waves, rising oceans that don't flood everything but do take out most major coastlines, etc.  After all, things like plagues wiping out a large fraction of humanity have happened in the past (Black Plague, Smallpox, etc).  So there's little comfort to be gained from that.  What God wants to happen could very well be quite nasty.

So, again staying with God's guiding hand, we are often told that we can help influence God's decision by praying.  But there are other things God seems to care about much more.  When doctors started washing their hands between autopsies and deliveries, God very conspicuously started sentencing a lot fewer mothers to death in childbirth, and a lot fewer babies to death in infancy.  It seems that certain practices, like health and safety protocols and such, have a profound effect on God's decision-making process.

I wonder why it might not be looked at this way.  Rather than the somewhat uncomfortable, almost adversarial view of "the scientists/doctors do what they can on earth, but we will pray to God" (with the implication that prayers are what really matter), why not think of earthly procedures simply as some really ultra-effective forms of prayer.  Rituals, if you like.  If you perform the handwashing ritual, God will protect you from infection.  If you have the appendectomy ritual performed, God will cure you of your stomachache.

This is actually pretty cool.  Might be especially inspiring to deeply religious doctors.  If prayer is a way of communing our needs to God with the intent/hope that this will influence God's decision about them, and if the ultimate decisions are made by God, then there isn't much room to escape the conclusion that for whatever reason, God likes it when your prayers for health are accompanied by hygiene, medicine, etc.  God likes it when prayers for healthy children and lives are accompanied by vaccines, seat belts, building codes, and other safety protocols.

This sort of opens up a whole new avenue of empirical theology.  Study what God likes by what he has (very clearly) demonstrated to us that he likes.  There are some obvious conclusions to be drawn, like those above.  God seems, on the whole, to like science: when we use it, he makes decisions that favor what we want.  So why does religion feel so threatened by science?

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April 13th, 2010

08:49 pm - Tetrakis Hexahedron
So I found myself revisiting some geometry obsessions lately (background: at my brother's house for Passover his children and mine began to be interested on playing Dungeons & Dragons, which led to talk about polyhedral dice, and so forth), including modular origami construction of interesting polyhedra. I dragged out my old copy of Paperfolding Stellated Polyhedra by Jeannine Mosely to look up how to make a rhombic dodecahedron etc. (Jeanine, if you are out there and by some bizarre chance ever read this, a friend gave me a copy of some paper or another you wrote with that title back when I was in high school; I don't know if you ever meant for it to be seen). I thought about making other die-like polyhedra, some of the other Catalan Solids, like, say, a tetrakis hexahedron, sometimes used as a 24-sided die. I've never designed one of these modular shapes before, only followed other peoples' directions for them. But I read and i reckoned and I pondered and actually designed the thing—and it worked! See picture...

(the smaller one is the first one I made; I worked out a simpler way to approximate the ratios needed and made the larger one.)

I record this accomplishment here for posterity so at least I don't forget I did it. I wrote down the instructions and everything too so maybe it could be repeated.  I suppose for some people working this out would be simple, but what I think is cool is how little I started with. I had done none of the calculations to find shortcuts and formulas for all this, and besides, it isn't like my 3D geometry is even all that good. I remember a few simple formulæ from plane geometry and trigonometry and that's about all I have to go on; I re-derive everything when  I need it. I couldn't even find good data on the shapes of the triangles etc (actually, MathWorld did tell me the edge lengths, but I didn't even look at them so I didn't realize how easy it was to derive their very simple 4:3 ratio); I derived everything from only the description of the shape as a cube with each face replaced with a pyramid of height ¼s.  Hey, I thought it was cool.

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April 9th, 2010

05:29 pm - Oh the Horror!
Saw this today in Best Buy, on a display advertising the Blu-Ray edition of the Lord of the Rings movie trilogy.  Oh, this hurts.

Let's read that text: “Best Buy Exclusive Includes: Andruil™ Sword Letter Opener (a $30 Value)”

Andruil™[sic]?  Really?  As John Cowan asked, "The Flame of the Wset"?  On the one hand, this is so geeky it is perhaps embarrassing to have noticed it.  On the other hand... dude!

(If you really are lost: the sword's name is Andúril, dammit!)

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February 17th, 2010

02:09 pm - 4D Thinking.
So a few weeks ago someone wrote to me about my page about hyperspheres.  She had been thinking about what I wrote and trying to reconcile it with her own conceptions, and we discussed a little of how her perception would fit in with the model I was using, etc.  It was interesting, and it reawakened my interest in the subject, so I started thinking more about higher-dimensional geometry, using that as something to ponder while waiting to fall asleep, and I feel like I'm getting a better grip on picturing four dimensions.

So I saw how flat planes can intersect at a point in 4D (in 3D they're either parallel or intersect along a line), or are skew (neither parallel nor intersecting); how hyperplanes (3D “planes”, as spaces in 4D) intersect and interact, how rotations work a little more, etc...

Nothing that I learned is actually new.  The geometry of four dimensions is very well-studied, and the mathematics is not terrifically complicated.  Quick visits to Wikipedia will tell you all about the known 4D (and higher) regular polytopes (which actually is an interesting topic; 4D has an unusually high six regular convex polytopes, whereas 3D has five (the Platonic solids), and everything above 4 has only three), and all kinds of details about how things can be arranged in many higher dimensions... It's interesting reading, but for me, I'm trying to learn to “picture” it better, improve my intuition about such spaces (I still have to put “picture” in scare quotes, because it isn't quite picturing it).  I seem to be most successful with the “red/blue” dimensional that I describe on my hypersphere page, and which I read about in Ian Stewart's book Flatterland.  Picture the fourth dimension as a color, in this case running from red through purple to blue.  Things have to be in the same location and color to be in contact, etc.  It's reasonably successful.

Anyway, something else occurred to me about this.  We can't really picture four dimensions particularly well, in part, I think, because we have specialized mental machinery dedicated to picturing spatial relationships that we're trying to cram it into, and that machinery is of course designed for three dimensions.  But if we were doing this all the “hard” way, actually keeping track of co-ordinates of vertices and whatnot and doing the various trigonometric calculations to compute rotations and everything, there is nothing intrinsically harder about doing it for four dimensions than three.  Well, there is more to keep track of, but nothing qualitatively different.  So a putative artificial intelligence, something that had access to its own thought-processes and modeling systems, could presumably think in four (or five, etc) dimensions just as comfortably as in three, though perhaps a bit slower.

This sort of plays into the feeling you get when you first study this sort of thing, of “Gee, we could access this fourth dimension if we only knew which direction it was,” as though our limited experience with only three dimensions was all that was stopping us.  But a computer (even a non-intelligent one) thinking in four dimensions perceives it just as clearly as it does three.  Even if you “knew what direction” it was, it doesn't help you point anything there if you don't have any accessible physical processes that exert a force with any component that way.  Something to ponder.

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February 2nd, 2010

12:04 am - Reunion
So, last night (31 January 2010) I attended my high school class' 25th reunion.  Wow, who'd have thought it was 25 years already?  Not me, certainly.  But see previous entries on my state of denial regarding my age.

No denying, it was nice to see folks again, even if some people I wanted to see didn't make it.  You start to remember how well—or not well—you knew or remembered people from back then, and what people were like, and how they've changed.  I discovered I still tended to wind up standing by myself when everyone else was chatting in groups... but not as frequently, and not for as long, and not as awkwardly.  And even discussed that fact with one or two people there.

Kind of pleased to discover one classmate of mine (Hi, Mimi, if you're reading this!) had googled me and read my website already.  It's nice to get stalked a little now and then.

Naturally, it seemed like everyone was so much more successful than I am, but a good part of that is just my usual self-deprecation.  Someone did remark that it sounded like I was still having trouble deciding what I wanted to be when I grew up, which actually is not a bad description.  I expected rather more business networking there (it's probably better that there wasn't); still, it'll be nice to keep in touch with a few more of these folks.  Guess that means I'll have to peek into Facebook a little more frequently.

Also was reminded once more of the feeling that I really need to write more.  At least two of my classmates (one of whom was present) are quite well-known writers.  I wouldn't think of approaching their level of renown, but I have to have enough stuff to be worth setting down for posterity.

OK, enough wallowing.  I'm allowed a maudlin blog post like everyone else now and then.

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November 8th, 2009

06:47 pm - More Talmud Thoughts
Sorry, another post on Talmudic thought.  Maybe if I post shorter posts more often...  Anyway, I have some thoughts on higher dimensions coming up later.

I finally figured out the real key difference between Talmudic thinking and secular legal thinking.  Well, not the only difference, but the important one for... what I'm thinking about.  You'll see what I mean.

It isn't the kind of logic used.  It isn't the fineness of the hairs being split.  It's the goal, the aim of the canon of law being produced.  Secular law aims to produce a canon of law that can be followed by people more or less like the ones who promulgated it (with all their faults).  So when it comes to, say, the validity of a contract, if a litigant contests the validity of the signatures on a contract, the law will say (or even leave unsaid, since it is “obvious”) something like “the party contesting the contract shall present what evidence it has supporting forgery, the other party shall attempt to demonstrate that the signatures are valid, they should bring testimony from handwriting and document-tampering experts, blah blah blah...” (though the “blah blah blah” might be in Latin.)  The details of how the case should be judged is left up to the presumed competence of the judge adjudicating the case, and also whatever precedence and case-law that has built up over the years.

In contrast, the Talmud goes into exhaustive detail about what kinds of tampering is suspect, how the signatories can approve erasures and changes to the text (N.B. Talmudic contracts are signed by witnesses, attesting to the transaction, and not by the parties to the transaction).  So it discusses the exact effects of the placement of the witnesses' signatures, and how much blank space can be around them, and when we may suspect that the contract was tampered with by the addition of an extra line of text... What happens if there is one blank line, what if there are two, what if there's space for just one and a half lines...  This is just from skimming quickly from Tractate Baba Batra, Chapter 10 (in English at sacred-texts.com).  There is a very clear attempt to try to cover all the possible situations that may arise, so that a future judge need only look up the answer and not have to apply too much actual judgment.  They talk about exactly which arguments or claims by litigants in various cases should be or should not be believed, and why, as though future judges in these cases need all the help they can get.  I suppose in some sense it's like trying to establish case-law, but it isn't: they talk in hypotheticals, suggest possible arguments and claims and propose rules to decide when they should or should not be believed!  See, for example, some of the discussion in this explanation of part of Tractate Ketubot.  The terminology is highly “Yeshivish,” mixing a lot of Aramaic with the English, but maybe you can get the gist.  The actual details of the cases aren't even the point, just the way that they are handled.

Combine this with the ancestor-veneration in Judaism which I have complained about before, and you have a system that is not only resistant to change, it's positively resistant to remaining itself.  Especially now, with notions floating around that the Talmud rabbis were somehow inerrant, and when they talk about things that are contrary to science as we know it, it's not because they didn't know better, but because we don't know better, and they're still right (even though they themselves admit that they don't know everything.  See the discussion in Pesachim 94b that I discussed at the end of this post almost two years ago).

What do I mean by “resistant to remaining itself”?  I suppose in many ways this post is a repeat of a lot of what I said in the one linked at the end of the last paragraph (I guess the main new insight is the way the Talmud tries to lessen the role of future judges).  Because Judaism does not confer onto itself the authority to decide and change and rule itself, and because the Talmud is so structured as to make such decisions unnecessary, Judaism has difficulty adapting to the changing world (which is nothing new, though it must in fairness be remarked that for something that has trouble adapting to the changing world, it is doing a pretty good job of it anyway), but this doesn't mean that by remaining true to these old principles, Judaism is maintaining its identity.  On the contrary, if the Talmud-rabbis were alive today, I am certain they would have all kinds of rulings on modern conundrums that are very different than the stringencies that we have adopted in their name.  Read how they dealt with the world in their time, and imagine how they would have dealt with ours.

(This turned out to be more of a downer than I thought it would).

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August 31st, 2009

11:06 pm - Religious “Sources”
So a week or two ago I got a message from a reader out there (I doubt he reads this blog, but hey, he might (hi there!)), writing to me in my capacity as Samaritan Pentateuch Dude.  He was asking about the laws in Deuteronomy 21:10-13, which details procedures to be followed when a conquering Israelite soldier sees a “beautiful woman” among the captives.  He was troubled by what he saw as an implied sanction of rape by the Bible, and wanted to know if the Samaritan text read this section differently (it doesn't; well, not significantly anyway).

For whatever reason, I didn't simply answer that it didn't change things and leave it at that; I let things develop into a larger discussion about puzzling concepts in the Bible and how they are interpreted.  After all, that particular section is fairly tame compared to some other questionable quotes.  So I mentioned Numbers 31:15-18, which speaks of giving virgin captives to soldiers, and various places in Joshua which discuss destroying whole towns right down to the women and children.  And this led to Deuteronomy 25, which prescribes death for raping a betrothed woman (and death for both if it was consensual), yet raping an unbetrothed woman is a simple matter of 50 sheqels and marrying her (which, at first reading, does seem to imply that she is forced to marry her rapist.  The Rabbinic interpretation of this is that it applies only to a very particular stage of female maturity, between 12 and 12½ years, and that marrying the rapist is at the girl's option.  Even so, it seems pretty mild).

The point I was trying to make was that the Bible is just full of troubling quotes and lines, and this is nothing new: people have been writing commentary to interpret and explain them for centuries.  You won't find anything that can't be explained or interpreted away, simply because someone else would have already found it, and if it really really couldn't be explained, the Bible would have already lost a lot more respect than it has.  And I noted such things as the Bible's dietary prohibitions (in the case of certain fish, an “abomination” no less) and its apparent support of slavery, death penalty for gathering wood on Sabbath, etc.  The Bible certainly does seem, at least, to espouse morals and ideals that are at odds with our modern views, and there are various ways of reconciling the two.  There are various re-readings and re-interpretations of the Bible, or conversely actually rejecting one or the other viewpoint (e.g. rejecting the Bible altogether, or something like Orthodox Judaism rejecting the idea that eating shellfish is permitted).

This tends to lead people (like my correspondent) to appeal to some sort of “logic” or “common sense,” which really means “what I think is right.”  My correspondent reckoned that Biblical dietary laws were really just health advice (and thus presumably are not as relevant today) and death penalty for Sabbath-breaking was a corruption introduced by the generations of scribes passing the text down.  And he thought that death penalty for adultery but a 50-sheqel penalty for rape “makes no sense and lacks consistency,” and that such an explanation was “something bizarre psycho wacko.”  Why?  Because it doesn't fit his expectations, apparently.  At this point people are no longer talking about what the Bible says, but rather what it should have said, i.e. essentially putting words in God's mouth because we know what he should have said better than the text does.  Now, human-based morality is okay (I personally have my doubts that there is any other kind), but people should at least recognize that they are invoking it.  Once you start picking and choosing what the Bible “should” have said or meant, any claim to Divine authority (if any) is severely weakened.  Who are we to say which laws are no longer relevant and which are not?  If dietary laws were just health advice, maybe the prohibition against homosexuality was just to increase fertility, in a society with a high infant mortality rate.  Or conversely, maybe dietary laws have some deep cosmic meaning that is utterly beyond our understanding (God does say, after all, that his thoughts are infinitely beyond ours, see Isaiah 55:9).

Now, Christians perhaps have a slightly better answer to the above, with the concept of Supersessionism, which I readily confess to not knowing very well.  Yes, there are some things more or less explicitly de-emphasized by Jesus (like the dietary laws, see Matthew 15:11), but what can we say about the rest?  Sabbath is one of the Ten Commandments; has that one been rescinded?  And generally very few of the reinterpretations credited to supersessionism actually have a basis in the text.  Most are still more variants of “well, that law just doesn't make sense to me.”

So, rape might be a horrible crime to us, and thus not to be discounted with a mere fine, but it wasn't always seen so.  I seem to recall in medieval Japanese literature, at least, rape was considered an expression of powerful, impulsive love: he would not even let her objections stand in the way of his love of her, and thus something actually borderline laudable.  A woman's rights to her own body are a comparatively modern concept, at least in universal application.  Slavery is universally reviled in modern Western culture, but it was a completely normal part of life in ancient times.  The Bible discusses the laws of slavery (as something that is part of its society) in great detail, perhaps a little surprising for a people just rescued from slavery, but not so incredible.  Certainly debtor's slavery was perfectly understood: when you have no money, you have to sell yourself.

OK, so this has been a lot of talking as if I'm trying to push Biblical divinity or something… quite the opposite.  I don't make any such claims, and the point really is that I don't think anyone else should either.  What I mean is, even if you believe that the Bible is divinely-inspired or whatever, unless you're willing to accept all of it at face-value (which itself would require a lot of interpretation), you really have no right to point self-righteously at the text to support your particular morals, since you have essentially rewritten it to your own meaning, and everyone else's rewriting is no less valid.  This is something all too often forgotten by Bible-thumpers.

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July 15th, 2009

05:40 pm - Shabbat Yitro
After the previous portion's famous content—the Song of the Sea—we now have an even more famous part for this one: the Ten Commandments.  Once again, I think we'll have to face that part first before we look at anything in the rest of the portion.

Most of the start of the Decalogue is pretty much the same, except for small differences in spelling, etc.  One particularly notable difference is in the Fourth Commandment (by Jewish counting, see below), “Observe the Sabbath day to make it holy.”  The Bible includes the Decalogue in two places: once here, and once in Deuteronomy chapter 5.  In the Masoretic text, this commandment is worded slightly differently in the two places: here in Exodus, it says זכור את יום השבת “Remember the Sabbath day” but in Deuteronomy it says שמור את יום השבת “Observe the Sabbath day”, or “Keep…”  The rabbis explain that the two terms stand for the two aspects of the laws of Sabbath: “Remember” refers to the positive command­ments, and “Observe” refers to the negative command­ments, and the two words were miraculously pronounced by God (and just as miraculously heard and and understood by the Israelites) simultaneously.

The Samaritan text, as usual, is more consistent: שמור “Observe” in both places.  This is the less well-known of the two versions to most non-Samaritans, I think, which makes it a little more noticeable.

We already know that Jews and Christians count the Commandments a little differently from each other.  Jews consider “I am YHWH your God…” to be the first commandment, and “You shall have no other gods before me” is the second (note that the term used for the Decalogue in Hebrew isn't the Ten Commandments, but עשרת הדברות, which is more like “the ten utterances,” which explains how “I am YHWH your God…” can be a Commandment—it doesn't have to be, it's an utterance).  Then the commandment-numbers are off-by-one wrt the Christian count (which considers “I am…” to be just introductory, or else part of the first commandment along with “You shall have no…”, until the end, where Jews consider “You shall not covet your neighbor's house” and “You shall not covet your neighbor's wife…” to be the same commandment.  Hey, it's all just “Don't covet, mmkay?”  Christians count coveting wives to be a distinct commandment from coveting houses.

Samaritans begin the count like Christians but end it like Jews, because they have more text to include.  Their version of the “coveting” commandment also includes the word “his field,” thus including that in the list of things not to be covetted, and it has the conjunctions structured a little differently, so as to group slave and maidservant together, and ox and donkey.

The Samaritans have one more commandment.  Recall that probably the central disagreement that caused the schism between Jews and Samaritans was where to put the Temple, i.e., where this place that God “set his Name” was, that is referred to many times in the Torah.  Jews say it is Mt Moriah in Jerusalem, and Samaritans say it is Mt Gerizim near Shechem (Nablus).  Both texts specify Mt Gerizim as the mountain of blessing for a ceremony to be performed by the Israelites upon crossing the Jordan (See Deuteronomy chapters 11 and 27), so even according to Jews the Samaritan position is not completely without support.

The Masoretic text frequently refers to “the place where YHWH will choose to set his Name,” the place where sacrifices are brought, etc.  In the Samaritan text, all these references are in past tense: “the place where YHWH has chosen to set his name.” In their version of the Torah, right here in no less distinguished a spot than the Ten Commandments, Just after the commandment against covetting, the Samaritan text spells out, in words similar to those used elsewhere, the commandment to set up an altar and a monument of plastered stones with the law written on it on Mt Gerizim and bring sacrifices there (See Deuteronomy chapter 27; in the Masoretic text the location is given as Mt Ebal).  I suppose it isn't actually any more explicit about designating it as the place than the Masoretic text is in Deuteronomy, but certainly the placement here does add importance.

In Moses' retelling of the events surrounding the giving of the Ten Commandments, in Deuteronomy chapter 5, he gives details about the Israelites' reactions and God's reactions to them which are not in the text here… but they are in the Samaritan text.  It looks like it isn't a simple restatement of what's in one place either; it seems that what is stated here is stated again elsewhere in smaller pieces. 

OK, I stalled on finishing this up for weeks; I better get this published without messing with it any more.

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