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.