Postcard from Bishkek

There are several songs about the “Perfect Day“, but the one that sticks in my mind is the one by Lou Reed from his 1972 album Transformer, (and which was the flip side of his, Walk on the Wild Side, released the same year and regraded by many people as his signature piece).

I was never that keen on Glam Rock, but there is something haunting about this song: the music with the repetition of the simple phrase “Perfect Day” together with the description of simple pleasures which go to make up such a “perfect day” … and … the promise in the closing refrain: “You’re going to reap just what you sow” (… or is it an implied threat?).

Anyway, Lou Reed’s song comes to mind because today, (28th June … 28/06), is a Perfect Day.  Both the day and the month are Perfect Numbers.

There is only one other date each year which might qualify, June 6th – 06/06, but today is even more special because it does not involve the repetition of the day and the month – they are different.

Perfect numbers are an obscure feature of mathematics, (number theory), which was known to the Ancient Greeks, and has proved the inspiration for a surprising amount of investigation by mathematicians down the years.   A Perfect Number is defined as one that is the sum of all its “proper divisors” – that is all its factors except itself.

OK – some examples:

• The number 6 has four factors, or divisors:  1, 2, 3, and 6 … 1×6=6 and 2×3=6.  Of these 1,2 and 3 are the proper divisors – that is, not including 6 itself.  If we calculate the sum of these proper factors we get: 1+2+3=6 … so 6 IS a Perfect number.
• The number 10 also has four factors, or divisors:  1, 2, 5 and 10 … 1×10=10 and 2×5=10.  Of these 1,2 and 5 are the proper divisors – that is, not including 10 itself.  If we calculate the sum of these proper factors we get: 1+2+5=8 … so 10 is NOT a Perfect number.
• The number 25 has just 3 factors, or divisors:  1, 5 and 25 … 1×25=25 and 5×5=5.  Of these 1 and 5 are the proper divisors – that is, not including 25 itself.  If we calculate the sum of these proper factors we get: 1+5=6 … so 25 is NOT a Perfect number.
• The number 28 has six factors, or divisors:  1, 2, 4, 7, 14 and 28 … 1×28=28, 2×14=28 and 4×7=28.  Of these 1,2, 4, 7 and14 are the proper divisors – that is, not including 28 itself.  If we calculate the sum of these proper factors we get: 1+2+4+7+14=28 … so 28 IS a Perfect number.

In fact there are very few perfect numbers … the ancient Greeks knew of just four of them, the firs four: 6, 28, 496 and 8128.  Apparently we know a few more these days … but the gaps between them seems to get larger and larger…

I suppose it would be a really perfect day if the day, month and year were all perfect numbers … but the last time that happened was on 28th June, 496, and the next time will be some time in the future … 28th June, 8128.

 

OK – I admit it … this particular postcard has nothing to do with Kyrgyzstan …

I did think about  trying to define what might make for a perfect day here in Bishkek: warm sunshine, (but not too hot, perhaps with a light breeze), a trip into the mountains, in the company of good friends, a picnic, a relaxing evening curled up with a good book or a an interesting movie … or, as he seems to have all the bases covered, trying to find a link with Lou Reed’s song such as drinking Sangia at the Mexican Cantina, taking a walk in the park, (of which we have many), and watching movies …  (feeding animals in the zoo would be particularly difficult as we don’t have one).

But it’s really a question taste … one person’s idea of a perfect day might be a torment for another … so I decided to leave it with a a tribute to a rock icon and a mathematical oddity.

For the record: the lyrics of Perfect Day, from the Album Transformer, by Lou Reed, (1972)

Just A Perfect Day,
Drink Sangria In The Park,
And Then Later, When It Gets Dark,
We Go Home.
Just A Perfect Day,
Feed Animals In The Zoo
Then Later, A Movie, Too,
And Then Home.

Oh It’s Such A Perfect Day,
I’m Glad I Spent It With You.
Oh Such A Perfect Day,
You Just Keep Me Hanging On,
You Just Keep Me Hanging On.

Just A Perfect Day,
Problems All Left Alone,
Weekenders On Our Own.
It’s Such Fun.
Just A Perfect Day,
You Made Me Forget Myself.
I Thought I Was Someone Else,
Someone Good.

Oh It’s Such A Perfect Day,
I’m Glad I Spent It With You.
Oh Such A Perfect Day,
You Just Keep Me Hanging On,
You Just Keep Me Hanging On.

You’re Going To Reap Just What You Sow,
You’re Going To Reap Just What You Sow,
You’re Going To Reap Just What You Sow,
You’re Going To Reap Just What You Sow…

Tags: Expat, Mathematics