Aida … or, Operation Desert Spiel

One could say that Verdi’s Aida is an opera about a love triangle.  A love polygon would be more accurate, as Aida has several more facets.    You see, Amneris, the high-priestess of Isis, is hot for Radames, who is hot for Aida, who is Amneris’ slave and, unbeknownst to anyone is also the daughter of Amonasro who is the king of Ethiopia, which is about to attack Egypt, the king of which is the father of Amneris.

With me so far?

Radames wants to impress Aida, and what would be more impressive than, say, winning a war against a rival nation? What woman wouldn’t be charmed by a gift of diamonds, gold, and a couple of slave pool-boys?  And the nation  Radames will conquer for her? Why, Ethiopia, of course! Radames hopes that Isis will choose him to be the conquering general. Knowing that Amneris has a thing for him, he figures he’s got an “in” with management.

As our story opens, Radames comes storming out of the gate with Celeste Aida, a brilliant tenor party piece with beautiful pianissimo high B-flats that no one ever sings pianissimo.1.   The name means “heavenly Aida”, but the gist of it can be summed up as “If I were a gen’ral … yedl deedle deedle didle didle didle didle dum.  All day long I’d yedl deedle dum, if I were a ge-ner-AL!”.   The Egyptian goddess Isis2 speaks, through Amneris3, saying that Radames will lead the armies of Egypt in battle against the Ethiopians.   The act wraps up with a big finale wherein Ramfis4, Amneris, and Radames lead the Egyptians in a ceremony of thanks and praise to the Egyptian god Ftha5. They beseech him to look upon them favorably and help them kick Ethiopian butt all the way back to the source of the Nile. All then retire to the banquet hall for a beautifully prepared buffet dinner and dancing.

Act II: Radames and his armies win the first battle and present the captured Ethiopians to the king as slaves. But, wouldn’t you know it! Amonasro, Aida’s father, is among these slaves. He whispers6 to her not to reveal his true identity. The king, always flattered by people’s gifts – especially when the gifts themselves are people – asks what honor Radames, as conquering hero, would like.  Aida discreetly pulls Radames aside to tell him that that slave, right there … no, the other one… yes, the big one … is her father, and suggests he ask for all the slaves to be freed as a sign of generosity and goodwill.  Radames, really turned on by her whispering in his ear like that, mindlessly repeats her suggestion to the king, who’s been politely pretending not to see or hear any of this exchange.     Amneris and the priests start to wonder whether maybe Radames has been sniffing the sacrificial incense a little too much, and counter his proposal by saying  Amonasro and Aida should remain in Egypt as hostages. The king agrees, and everybody – everyone except Aida and Radames, that is – goes off to party.

Act II: She’s not the sharpest ceremonial sword in the vestry, but it finally dawns on Amneris that Radames is in love with Aida. She tricks Aida into admitting this7, and then tells her that she’ll never be good enough for Radames because she’s not royal, like Amneris. Aida avoids what could have been a literal royal smack-down scene and keeps her royal standing to her royal self and goes off to console herself by singing something down by the river in the next scene. Amneris, meanwhile, stays put and sings about how great life will be once she’s married to Radames.

Act III, scene 2: Amonasro, having seen how whipped Aida’s got Radames, reckons he can prevail upon  her to get the inside dope on the Egyptian battle plan. First he tries the soft approach, telling Aida how much he missed her, how glad he is to see her, how great it’ll be when his army kills all the Egyptians so they can all go home, back to Ethiopia, and live happily ever after. Just one small problem. He needs her to get Radames to tell her where he plans to attack. She tells her father that she’s “very conflicted”, but decides that she cannot betray the man she loves. So, Amonasro starts to mess with her head. He berates her for denying her people, for forsaking her country and her heritage, for leaving the lights on after she’s left the room – it’s a “dad” thing, ok? — and reminds her of that time she crashed the family chariot right after she’d gotten her learners papyrus. This all cuts deep, but still, no sale. Finally, he goes all Reb Tevya on her and threatens to disown her, telling her that she’s no longer his daughter, just another slave of Egypt.   This is more than she can bear, so she relents and reluctantly agrees to get the information from Radames, adding that  it was her sister, Mildred, who was driving the chariot, not her.

Act III, Finale

Radames and Aida meet secretly in the sacred rock garden.   Radames shows up, all glad to see Aida. Aida, caught between a rock and … well … another rock, begs Radames to come and run away with her to some other country8.  Radames mutters something about leaving behind the fame, the glory, and the awful-tasting beer. Aida says, yes, but we’ll be together, dear. Radames, who’s beginning to sense that this is one of those “unwinnable arguments”, asks how she expects him to forget his home, his country, his beer? Aida gives him a look that says “Do I really need to answer that?” and gives him one last chance before she pulls out the big guns. Radames, now wishing she’d just asked him something he knows9 how to answer, like “Does this dress make my butt look fat?” tries to take the easy way out by changing the subject and sweet-talking her. No deal. Aida tearfully fires the next salvo: “I guess you must not love me anymore!” Radames thinks “Oh, Ftha! Here we go again.” “What do you mean, I don’t love you?” Aida replies, “I saw the way you were looking at her, I know you want Amneris.”  Radames swears this isn’t true. (We’re just friends, honest!) Aida stands firm, and Radames, who, with all that military training, knows when he’s beat, says “Fine! We’ll run away together.”

Now, the opera could have just ended right here. The story was a bit contrived, but still believable10. Aida and Radames could have run, ridden, chariot-ed, or otherwise been conveyed into the sunset to, say Chad, or maybe Argentina. Instead, we are now subjected to a climactic series of Really. Dumb. Moves.

Dumb Move#1: Instead of saying “ok, let’s go”, Aida asks Radames HOW they’ll escape. He says he knows where all the armies are, so he knows which road out of town is unguarded. “Which one might that be, honey?”, asks Aida. “Napata Drive.”, he replies. I guess Radames must have been cutting class at General School the day they went over why they put the word SECRET in the term MILITARY SECRET. Or maybe, since he lives in a desert, the meaning of “Loose Lips Sink Ships” was completely lost on him. In any case, Amonasro, who’s been hiding behind another rock, overhears this, bringing us to

Dumb Move #2: Suppose you’re commanding an army and you just found out where the other army’s gonna be hiding. Do you call up the other army and taunt “I know where you’re hiding, I know where you’re hiding! Neener neener neeeeeener!”? Of course not.  But, that’s pretty much what Amonasro does. He jumps out from where he’s been hiding and declares that he now knows where to attack the Egyptians. Understandably, Radames becomes pretty grumpy with Aida, and with himself for being so stupid, but … there’s still a chance to recover. He’s got options. Option 1: Kill Amonosro and tell Aida he’ll do the same to her if she breathes a word to anyone, then continue with tomorrow’s attack as planned. Option 2: pretend to run off in shame, but in actuality run back and tell the Egyptians that he’s tricked the Ethiopians into thinking Napata Drive will be unguarded so they’ll be lured there to their doom, unsuspecting. But he does neither, opting instead for

Dumb Move #3: He resigns himself to running off with Aida and her dad, leaving his armies to be slaughtered at the hands of the Ethiopians.

Right about this time, Amneris, who’s been lurking about behind yet another rock, has had about all she can stand of this idiocy (and there’s more to come) so she jumps out along with the priests and guards11, and declares Radames to be a traitor. Amonasro, backed up by basically no one, threatens to kill Amneris.  Radames stops him, asking, literally “Are you nuts?” This brings us to

Dumb Move #4: Radames urges Amonasro to take Aida and flee. Now, if you were Radames, wouldn’t you sorta want to get out of Dodge yourself, with them? Does he? No. He turns to Amneris and her posse and surrenders himself to them. The upside is that we have a really nice “tenor moment” when Radames cries “Sacerdote, Io resto a te.”, which, loosely translated means “I would like to speak with an attorney.

Act IV: Scene 1 – Judgement

Radames is called before the high priests and the king. Ramfis, the high priest, tells him to defend himself, to explain his actions, but Radames remains silent. (Considering it was his big mouth that got him into this mess to begin with, he’s probably better off not saying anything.) Amneris begs Radames to come up with an explanation that will make sense of what he’s done, and allow him to escape his doom. But, as we’ve already seen, Radames isn’t all that fast on his feet when it comes to thinking12, so … he remains silent. In the end, Radames is condemned to be entombed alive13.

Act IV: Finale – the Tomb Scene

Radames mopes about the tomb while an unimaginably large slab of rock is positioned over the only exit. “I’m so screwed” – or words to that effect – he mutters to himself. As he laments no longer being able see the light of day, and how he will no longer see Aida, the gravity and enormity of his blunders being to dawn on him. “At least Aida is still alive”, he says, trying to console himself. “I hope she will find happiness, and soon forgets what a big jerk I’ve been.” (Being somewhat anal-retentive he further laments not having had mail and newspaper delivery cancelled.)

Suddenly, he hears something14. A sigh? A ghost? A vision? Nope. It’s

Dumb Move #515: Instead of heading back to Ethiopia with daddy, Aida decides, instead to hide out in the tomb and die with Radames. Why is this dumb? If she was able to sneak INTO the tomb without being noticed, don’t you think it might have been possible to sneak OUT of the tomb the same way? So she, too, had some options. Option 1: sneak in, leave a note, flowers, candy, one of those little plastic cats perpetually waving bye-bye, and sneak right back out. Her conscience would be assuaged, Radames would have his final “I love you” from her.  Sure, it’s still a sad ending, but, like the man said, at least she gets to live. Then there’s option 2: sneak in, wait until Radames shows up, then go to him RIGHT AWAY and show him how she snuck in and how they can both sneak out, run off to Monaco (don’t take Napata Drive – it’s a little backed up today), and live – I repeat, LIVE! – happily ever after.

No. She waits until the friggin’ tomb has been sealed shut with that humungous rock and only then does she pipe up. Rather than try to save some oxygen and prolong their last moments together, they use up what little breathable air they have left by singing what is arguably the most beautiful death scene in all of opera.   The opera comes to its tragic conclusion with Amneris singing a song she co-wrote with Ramfis praying for peace as the two lovers suffocate in each others arms.

Although the opera ends here, a recently discovered manuscript by the librettist offers us some clues as to what a sequel might have looked like:

Amonasro defeats the Egyptions and then goes back to Ethiopia.   Rather than die on the throne like all the kings before him, he turns over the family country to his first son-in-law – Mildred’s husband – and moves to Florida where he ended his days after suffering a stroke16.

The king of Egypt gets caught up in some sort of pyramid scheme, loses his entire fortune, and spends his final years living on cat food and dying in the Nile.

Amneris and Ramfis leave the priest[ess]hood and team up to pursue their common passion for music theatre, writing such hit musicals as “How to Succeed in Memphis Without Really Trying”, “Annubis Get your Gong”, and “A Horace Line”.

Copyright © 2011,2017 Nick Seidenman, All Rights Reserved.

Puccini’s “La Rondine”: Hard to Swallow

Opera connoisseurs all know the soprano aria from La Rondine.  It’s a fairly common party piece, it is beautiful, musically, and for sopranos who have the range and killer pianissimo high C’s  it’s a perfect showcase for these in concerts and auditions.   Yet, ask any of those same opera-lovers what the opera itself is about and most would be hard put to tell you.    As it happens, there’s a good reason for that:  it is dreadful.   The “good” thing about it is that, unlike nearly all other Italian operas involving a tragic romance, no one dies.1

To come up with this left-over stew of an opera, Puccini probably started with La Bohème: a starving poet (Rodolfo), suffering hack artist (Marcello), and their respective paramours, Mimi, conspicuously dying of consumption, and Musetta, who lives entirely to consume conspicuously.  Next, he switched Rodolfo and Marcello, and gave Mimi back her health. Scratch that.2  Switch Mimi out completely for Despina from Mozart’s Cosi fan tutte.    And that garret they were living in?  Too depressing.   Now Violetta’s Parisian digs in La Traviata … THERE’s a crib to envy, AND it comes with a posse:  Germont pater and Douphol.  Change all of the names to protect the composer from charges of abject plagiarism, make them all nauseatingly bourgeois,  give it a good stir, and voila`!    Out comes the tasteless slop of an opera  titled La Rondine (The Swallow).  

So, what’s this opera actually about?  A couple of rich, self-absorbed assholes prattling on to their long-suffering friends about their first-world problems. That’s what.

Act I takes place at a cocktail party at the home of Magda, who, as a young “working girl”, recounts the happy evenings she enjoyed dancing at Maxim’s  Bullier’s.   (This is the part where she sings that famous aria.  If this is your first time seeing this opera, leaving immediately after the aria is finished, while perhaps rude, is nonetheless strongly advised.)   Then in comes Alfredo Germont Ruggero Lastouc (seriously) with a letter from his father introducing him to one of Magda’s clients … er … guests, Douphol Rambaldo.  Prunier reads Magda’s palm which reveals she likes to swallow.  No, no!  She is like a swallow3, craving migration to sunnier climes, always looking for love, and so forth.   Ruggero, only just arrived and yet already bored to tears, tells the group he’s new in town and wonders where he can find a real party.  Lisette recommends Bullier’s, and Ruggero is off to it with nary a second kiss on the cheek.   Magda, hearing all this, heads off to change into her secret Working Girl identity after muttering something to Lisette about staying home for the rest of the evening.   Lisette, having heard that line before, grabs Prunier and they both make tracks for Bullier’s to get a front-row seat to the drama about to unfold there.

In Act II we find ourselves at Bullier’s, everyone’s already well in the bottle by the time Magda shows up, and several men (and perhaps one or two women) are instantly all over her like cheese on risotto.  Looking around she quickly spots Ruggero staring at his mobile and joins him on the ruse that she needs to look like she’s with him until those guys quit staring at her.  (Perhaps one or two are in fact staring at Ruggero?)  He closes his facebook app and tries to pay attention to her, trying hard (and mostly succeeding) to keep his eyes north of her collarbone.   Prunier and Lisette show up, arguing.  It seems Prunier wants to turn Lisette into a lady and she’s perfectly happy being a grotty little slut.   They see Magda and Ruggero and walk over to join them.    Ruggero, now swiping his way through snapchat, has thus far failed to recognise Magda in her disguise.   Again, Puccini lifts a scene straight out of another opera — Adele and Eisensten’s meeting in Act II of Die Fledermaus this time — and has Magda oh so subtly get Lisette (and Prunier, presumably) to go along with her charade.   Ruggero, who just can’t seem to put his damn phone down for few minutes, is now chuckling at cat videos on youtube.   Prunier then recites a poem he’s written, which somehow gets Ruggero’s attention.  The four of them face off in a quartet that is the opera’s only other bright spot.   (Leave NOW, I’m telling you.)   Enter Rambaldo.4  Prunier sees him before the others do and instructs Lisette to get Ruggero the hell outta there before the merde really hits the fan.  For once, she complies.   Rambaldo, who is clearly far more perceptive that Ruggero, heads straight for Magda and demands to know what’s going on.   Magda wordily tells him to shove off, which he does.   Ruggero and Lisette return and with dispatch that can be rivaled only by Rodolfo and Mimi’s hooking up scene, Ruggero and Magda decide they want to live together.   The act closes with Magda, who still hasn’t told Ruggero her real name let alone anything about herself, wondering if perhaps this isn’t such a good idea.

In yet another shameless imitation of La Traviata, Act III of Rondine takes place in a villa well outside of Paris, and as with Alfredo and Violetta, Ruggero and Magda have been shacked up living together in bliss for several months.   Regrettably, unlike Violetta, Magda is not suffering from consumption or any other terminal malady.   Moreover, after all these months together she has yet to tell Ruggero who  she really is.   As with Leonard and Penny5, Ruggero keeps proposing marriage to Magda and she keeps putting him off.  He sings of how great it will be when they have a little Ruggero or … saaaaay … What IS your name again? … running around.    Magda feels a migraine coming on.  Prunier shows up with a letter for Ruggero from his mother.  Ruggero takes this and goes off to find a letter opener or something.   Prunier tells Magda that Rambaldo wants her back and will take her on whatever terms she likes.   Her lips tell him she’s not interested while other parts of her anatomy beg to differ.  Ruggero returns and reads from the  letter wherein his mother tells him that if this woman is half as wonderful as he’s described her, they will have a long marriage filled with happiness. 6    Realizing that there is no way in hell her past would be acceptable to his family, and finding the prospect of being sentenced to this fiction for life growing less appealing by the day, along with the recollection of Rambaldo being way better in bed that Mr. Droopy-Drawers over there sends Magda over the edge.  She confesses everything to Ruggero and tells him they cannot be married and that she can no longer be with him.   He cries, stamps his feet and carries on like the spoiled little sook that he is.  The opera ends with Magda returning to Paris to be with Rambaldo leaving Ruggero there on the stage, sucking his thumb while staring at his facebook app.

Opera should be experienced, in large part because it is, after all, story-telling and the most interesting parts of any story are its characters.   The best stories captivate us by introducing us to characters we can strongly, or at least quickly identify with.   In La Rondine there are no such characters.  Well, perhaps Prunier (the name sort of gains something in translation, don’t you think?) and Lisette, who are sort of the Fred and Ethel7 of this little clique` aren’t so bad.   One might even regard them as “cute”, whereas Rodolfo … I mean Ruggero … and Magda (wait … Mimi?   No.  Magda. Got it right that time.)  swing from cloyingly codependent to gag-inducingly maudlin so often you’ll lose count by the time she finally ditches him for Douphol Rambo Rambaldo.  (nailed it!)  Maybe the opera would be performed more often if there were an app for that?

Requiem for Suzie

I first met Suzie at the Liberty Humane Society Animal Shelter almost 14 years ago.  She was one of a litter of four, nearly identical kittens.  Three of them were fast asleep with mamma.   Suzie, however, was wide awake, and completly engrossed in the obviously very serious business of catching a gnat.   She was still a bit too young to bring home that day, but I adopted her on the spot and picked her up from the vet, where she’d been spayed, a few weeks later.

 

Our dear little companion, Suzie, breathed her last at 8:31 this past Sunday morning while my wife held her.   As we lay awake, stroking Suzie to comfort her through her final hours, we could feel her start to purr a little.    You have to understand that Suzie always purred quietly, very softly, almost imperceptibly.  Yet now we could feel her quite unambiguously — I’d say even audibly — purring.   Whether it was a sign she was improving or just her letting us know she was alright, comfortable, didn’t want us to be sad, grateful for our being there with her, for her, I didn’t know.   I guess I do, now.   She yowled, weakly, once or twice during the night, in pain, sad to be leaving us, a bit of both?  It’s only natural to anthropomorphise whatever she was experiencing.   Seeing her yellow eyes, pupils now completely dilated brought to mind another little grey, yellow-eyed being that visited several years ago.

 

I was home alone one night not long after we’d moved to our present home, when I heard a commotion in the back garden.  I looked out and could see something jumping around in the dimly-lit shadows on the upper of the two terraces just outside our back door.  Torch in hand, I went to investigate further and found a tawny frogmouth — a small, grey species of owl common to these parts —  flapping about, dazed, perhaps wounded.    I went back inside and called our neighbours down the street who I knew to be trained in wild animal rescue.  They said to wrap it in

tawny frogmouthsomething warm — a towel — and bring it down.   I went back out with the towel, and gently picked up the wounded bird.   It weighed maybe half  kilogram at most, grey feathers, and had large,  yellow eyes.

 

I gently carried the bird down to our neighbours (Steve and Carol) and Steve was there waiting for me outside.    The owl, which I could feel still moving (if only a little) when I first picked her up was now still, it’s pupils completely dilated showing only thin bands of yellow-gold around the edges.    The bands of yellow gold in Suzie’s now lifeless eyes looked like well-worn wedding rings, and brought Edward Lear’s poem, “The Owl and the Pussycat” to mind.

 

The Owl and the Pussy-cat went to sea
In a beautiful pea-green boat,
They took some honey, and plenty of money,
Wrapped up in a five-pound note.
The Owl looked up to the stars above,
And sang to a small guitar,
“O lovely Pussy! O Pussy, my love,
What a beautiful Pussy you are,
You are,
You are!
What a beautiful Pussy you are!”

Pussy said to the Owl, “You elegant fowl!
How charmingly sweet you sing!
O let us be married! too long we have tarried:
But what shall we do for a ring?”
They sailed away, for a year and a day,
To the land where the Bong-Tree grows
And there in a wood a Piggy-wig stood
With a ring at the end of his nose,
His nose,
His nose,
With a ring at the end of his nose.

“Dear Pig, are you willing to sell for one shilling
Your ring?” Said the Piggy, “I will.”
So they took it away, and were married next day
By the Turkey who lives on the hill.
They dined on mince, and slices of quince,
Which they ate with a runcible spoon;
And hand in hand, on the edge of the sand,
They danced by the light of the moon,
The moon,
The moon,
They danced by the light of the moon.

It was a full Moon Saturday night.

 

Good bye, Beautiful Suzie.

 

Paris and Nicole’s Mayhem

In their frequent shopping sprees Paris and Nicole often have trouble checking the bill. To address their less than impressive numeracy skills they decide to return to school. After a year of maths training the teacher wants to test the class of 25 students and lines them up in a queue such that Paris and Nicole are standing next to each other. The teacher then writes a whole number on the board and the first person in the queue says “That number is divisible by 1.” Then the second person in the queue says “That number is divisible by 2,” and so on till the final student in the queue says “That number is divisible by 25.” After all this the teacher exclaims “Well done! Except for Paris and Nicole everyone made a correct statement.”  Find where Paris and Nicole were standing in the queue.

 

So, we’re looking for a number that can be divided by all numbers from 1 through 25 EXCEPT two of them, that are also consecutive. The number 1 will divide anything, so, that’s trivial. We can also come up with a number that can be divided by ALL of the numbers by simply taking the product of all of those numbers. This doesn’t quite give us our answer, and it also results a number that is much bigger than we really need since some factors would be repeated. (e.g. any number for which 4 is a factor will also have 2 as a factor, so if we don’t need to include both 4 (i.e. 2 x 2) and 2 as factors. Take this a bit further, you see that by including 16 as a factor (2 x 2 x 2 x 2) we include 2, 4, and 8 as well.)

 

Let’s create such a product, expressed in a form that is prime-factored, though assuming all of the students’ answers were correct:
2: prime 
3: prime 
4: 2 x 2 
5: prime 
6: 2 x 3 
7: prime 
8: 2 x 2 x 2 
9: 3 x 3 
10: 2 x 5 
11: prime 
12: 2 x 2 x 3 
13: prime 
14: 2 x 7 
15: 3 x 5 
16: 2 x 2 x 2 x 2 
17: prime 
18: 2 x 3 x 3 
19: prime 
20: 2 x 2 x 5 
21: 3 x 7 
22: 2 x 11 
23: prime 
24: 2 x 2 x 2 x 3 
25: 5 x 5
Combining these (e.g. the factored forms of 4 and 8 are implicit in the factorised 16) we get
2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 7 x 11 x 13 x 17 x 19 x 23 = 26771144400. 
This number is divisible by all of the numbers from 1 to 25. It should be easy to see that by removing, say, 13, we get a number that is still divisable by all of the other numbers from 1 through 25. (13 x 2, the smallest of the other numbers, equals 26, which falls outside range of factors.) Removing 13 we get
2 x 2 x 2 x 2 x 3 x 3 x 5 x 5 x 7 x 11 x 17 x 19 x 23 = 2059318800,
But, we need TWO CONSECUTIVE numbers. Suppose we stick with 13 and try removing 12 as well. But, 12 = 2 x 2 x 3, so, we’d have to either remove both of the 3’s as factors, or at least 3 of the 2’s to have no 12. Suppose we remove both 3’s to give us
2 x 2 x 2 x 2 x 5 x 5 x 7 x 11 x 17 x 19 x 23
Now we’d have no 13, no 3, no 6, no 9, no 15 … already we have more than two numbers that don’t divide whatever was written on the board. So, 12 won’t work. How about 14? Same problem. You’d need to remove either all of the 2’s or the 7, but, removing all of the 2’s gets rid of all even numbers as valid factors, and removing the 7 gets rid of 14 and 21 as well. So neither Paris nor Nicole occupy the 13th place in line.

Let’s try 17. Like 13, when you remove this as a factor from the original factorization, above, you get a number that is divisible by all other numbers except for 17. We then need to look at 16 and 18 as possible second candidates. 16 = 2 x 2 x 2 x 2. Take out just one of those 2’s and we can still keep every other product in which 2, 4, or 8 is a factor, so removing just one 2 results in the loss of only 16 as a factor. Looks like Nicole and Paris were the 16th and 17th students in the line. For completeness we can look at 18 and see that it doesn’t work since 18 = 2 x 3 x 3, so we’d need to drop all of the 2’s which means we’d have a product with more than two wrong answers in the list.

So, our answer is
2 x 2 x 2 x 3 x 3 x 5 x 5 x 7 x 11 x 19 x 23 = 787386600.
To see if I got the right answer, I googled the problem and found this site (page 3) with the exact same problem and a solution. They get the same places for Paris and Nicole as I did (16 & 17) but their number (that the teacher wrote on the board) is different: 2362159800. This looks like it’s about 3 times what my answer is, and in fact it is exactly 3 times my answer. In other words, they have an extra “3” in their factorization, for whatever reason. So, both answers are correct, but mine is the SMALLEST number that is a factor of all numbers from 1 through 25 excepting 16 and 17.

Radical Maths

This little puzzle popped up the other day and I thought it would make a good, simple example of how to deal with square roots.

First, a little terminology:  The word for root in latin is radix from which we get words like radius and radical. Mathematicians refer to the square root symbol √ as the radical symbol, and the stuff we’re taking the square root of they’ll refer to as what’s under the radical.

We start with this.

\sqrt{x + 15} + \sqrt{x} = 15

We can get rid of square root symbols by just squaring what’s under them, which will leave just the terms under the radical and nothing else.   Since this is an equation, we’ll need to do this to both sides:

(\sqrt{x+15} + \sqrt{x})^2 = 15^2 = 225

When we multiply this out, it looks like a real mess:

x + 15 + 2(\sqrt{x+15}\sqrt{x}) + x = 225

We can combine the two x’s to make this

2x + 15 + 2(\sqrt{x+15}\sqrt{x}) = 225

But, it isn’t all that much simpler.  Let’s try another approach.   Having two different radicals on the same side of the equation is what makes this messy, so, let’s move one of them to the other side of the equals sign.   We can move the \sqrt{x} term by subtracting it from both sides.

\sqrt{x + 15} = 15 - \sqrt{x}

Now let’s square both sides of the equation like we did before and see what we get:

x + 15 = 225 - (2)(15)\sqrt{x} + x = 225 - 30\sqrt{x} + x

I know, it doesn’t look all that much simpler, but, notice how there is a solitary x term on both sides?  We can get rid of that by subtracting x from both sides:

x + 15 -x = 225 - 30\sqrt{x} + x -x

leaving us with

15 = 225 - 30\sqrt{x}

It’s looking easier already!   Let’s subtract 15 from both sides, and then add 30\sqrt{x} to both sides.  We get

30\sqrt{x} = 225 - 15 = 210

Now we have simple terms for both left and right hand sides of the equation.   Divide both sides by 30 to get

\sqrt{x} = 210 / 30 = 7

Square both sides (yes, again) to get rid of the radical, and we end up with

x = 49

Let’s see if this is right.  Plug 49 in for x in the original equation:

\sqrt{49 + 15} + \sqrt{49} = 15

We can add the 49 and 15 under the first radical to get

\sqrt{64} + \sqrt{49} = 15

The square root of 64 is 8 (8 x 8 = 64) and we already have square root of 49 being 7, so

8 + 7 = 15

So, the answer checks out!

Totally RADICAL, eh?

What does the Quran really say about a muslim Woman’s Hijab? (TED Talk)

In recent times, the resurgence of the hijab along with various countries’ enforcement of it has led many to believe that Muslim women are required by their faith to wear the hijab. In this informative talk, novelist Samina Ali takes us on a journey back to Prophet Muhammad’s time to reveal what the term “hijab” really means — and it’s not the Muslim woman’s veil! So what does “hijab” actually mean, if not the veil, and how have fundamentalists conflated the term to deny women their rights? This surprising and unprecedented idea will not only challenge your assumptions about hijab but will change the way you see Muslim women.

Samina Ali is an award-winning author, activist and cultural commentator. Her debut novel, Madras on Rainy Days, won France’s prestigious Prix Premier Roman Etranger Award and was a finalist for the PEN/Hemingway Award in Fiction. Ali’s work is driven by her belief in personal narrative as a force for achieving women’s individual and political freedom and in harnessing the power of media for social transformation. She is the curator of the groundbreaking, critically acclaimed virtual exhibition, Muslima: Muslim Women’s Art & Voices.

Linear Thinking

I read this article in MotherJones a few months ago when it first came out. I thought the author’s analysis of how rural Trump voters think was particularly insightful given that many of the people the author came to know during his time among them largely agree with it. He summarized it this way:

You are patiently standing in the middle of a long line stretching toward the horizon, where the American Dream awaits. But as you wait, you see people cutting in line ahead of you. Many of these line-cutters are black—beneficiaries of affirmative action or welfare. Some are career-driven women pushing into jobs they never had before. Then you see immigrants, Mexicans, Somalis, the Syrian

Yard of Trump Supporter
Yard of Trump Supporter (photo: Stacy Krantitz)

refugees yet to come. As you wait in this unmoving line, you’re being asked to feel sorry for them all. You have a good heart. But who is deciding who you should feel compassion for? Then you see President Barack Hussein Obama waving the line-cutters forward. He’s on their side. In fact, isn’t he a line-cutter too? How did this fatherless black guy pay for Harvard? As you wait your turn, Obama is using the money in your pocket to help the line-cutters. He and his liberal backers have removed the shame from taking. The government has become an instrument for redistributing your money to the undeserving. It’s not your government anymore; it’s theirs.

What these poor souls fail to understand is that There Is No Line.

Yet, people have been sold the notion that there is a line, and it has become the basis for an otherwise unfounded sense of entitlement. “Good things come to those who wait.” How often do we hear that? Antithetically, we also hear “God helps those who help themselves.” Which is it?

Confused? Maybe that’s the point. Maybe that’s the purpose of constantly pounding conflicting messages into people’s heads: to confuse them. And if you make sure those same people never develop even a basic capacity for critical thinking, you can keep them befuddled, confused, dependent on authority figures to tell them what to do throughout their lives.

We liberals are told we don’t know how to talk to this part of the country, to these people. We’re told they feel disconnected, feel that their country has been taken over by those who they see as cutting in line, robbing them of their due. Well, to us liberals, they sound like petulant children, whining “It’s not fair!” when they feel they’ve been denied the cookie, the ice cream cone, equal turns (or time, right down to the last darn second) on the swing, or suffer any one of seemingly thousands of such injustices. The naive parent tries to reason with their child, tries to explain the how and why. Sooner or later, many of these parents (myself included) resign themselves to the reality that they are trying to reason with people who are unreasonable, and long-winded, thoughtful explanations are being ignored. The best answer turns out to be the simplest, and applies here, too: Life is not fair. Get used to that.

The overwhelming majority of people who think this way live in states that in fact receive more from the federal government than their residents pay out in federal taxes. If anything, those of us who live and work in “liberal” states, like New York or California, should be crying about how unfair that is. We don’t. Liberals operate on the principle that we’re all in this together, and that the purpose of any benevolent government is to be a tool for all of us to use to make life better for all of us. Does that mean each and every one of us will receive an equal portion? Ideally, sure; in reality, it’s not possible nor is it a reasonable expectation.

In an ideal world, life is fair, no one ever goes without, and everyone is always happy. I think the rural, benighted folk of the heartland need to grow up, need to understand that life indeed is not fair, the universe does not owe them anything, and that their life will be what they make of the opportunities chance bestows on them coupled with the character they exhibit when chance kicks them in the gut.

That’s the bottom line.

Judging for Ourselves

References to and comparisons with Hitler’s rise may be valid, however, I think a more accurate comparison can be drawn with Romania’s pre-WWII  “Iron Guard” movement  and its leader Corneliu Codreanu.   This became the basis for Eugene Ionesco’s “Rhinoceros”, a play that depicted the transition of a group of ordinary people into a herd of these animals, one by one, each with their own rationale for accepting them and then becoming one themselves.   We read this in high school (mid-70s) and it comes to mind whenever I see people I thought I knew and even respected begin to embrace right-wing authoritarianism, something I thought they abhorred as much as I.

Right-wing fascism has reared its ugly head many times throughout history, wearing many masks.   The players, populations, and languages differ, but, the circumstances and warning signs are nearly always the same:

The good news is that, notwithstanding claims of “the death of liberalism” that fascists and their apologists seem often chant these days, it is in fact fascism, authoritarianism that is typically short-lived.   Like its economic concubine, speculative capitalism, it survives on the necessarily increasing output and consumption of it’s own excrement, and soon meets its end by starvation, or sepsis from having swallowed too much of its own shit.   Democracies, or at least regimes that recognise their power as being derived from the compliance (or complacency) of the governed survive for centuries; authoritarian regimes rarely last more than a few decades.

I’d be willing to bet that the articles of impeachment against Trump were drafted even before he took office — possibly even before the election.   Both Putin and the Republicans saw him as a “useful idiot” and they’ll continue to pull his strings until the FBI and other investigative agencies have all of the ducks lined up to bring him down.  At which point, Trump will either be convicted and removed, or he’ll resign, or 25A will be invoked.  In any case, Pence will be installed and, whereas Trump was a useful idiot, we’ll now have to deal with a complete moron until 2020.   With any luck enough of the benighted fly-over (by then they’ll be more aptly-named fucked-over) states will have seen the folly of voting for Trump and use their votes to say “fuck you” right back.

In the mean time, however, we’ll see a rise in anti-anyone-who-ain’t-white-christians-like-us violence and threats to persons and American Democracy itself.  The last, best defense, there, will be the courts.  My greatest fear, is that we’ll start to see judges assassinated, as has happened when such regimes have taken over in Latin America, for example.   We can worry ourselves over the circus going on in Washington and state capitols across the country, but such assassinations are, to me, far more worrisome.   Two of our government’s three branches have been weakened by three decades of relentless, right-wing undermining of people and principles, leaving the judiciary to stand against it, alone.  Unless and until we see that start to happen, I have great confidence in the ability of our constitution and the democracy that it implements to endure and prevail.