Counting Sheep

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Well, what do you think about when you sleep? 

Many years ago, someone told me how to sum numbers from 0 to 100.  Essentially, just count by 100’s.  0 and 100=100, 1 and 99 = 100, 2 and 98 = 100, etc.  So, there 50 100’s, right?  0-49, plus the 50 left in the middle.  So 50 x 100 = 5,000, plus the 50 stuck in the middle = 5,050.

Easily done.  0 and 200?  100 x 200 = 20,000 plus the 100 in the middle = 20,100.  Keep the series going and you get 45,150, 80,200, etc. 

So, I can’t sleep.  Thinking it through is fine, but it would be pretty cool to have a formula!  Not useful, but… it’s something to think about.  So, converting how I explained it above to more mathematical terms, I take 100, divide by 2, then multiple it by 100.  And don’t forget to add the stray 50 in the middle.  That makes sense, but you can’t really have a formula without a variable, so… I’m essentially taking half of x, multiplying it by x, and then adding the change, which is x divided by two.   So x/2 (x) + x/2.  More properly:

… where x = the upper limit of the series, which begins at 0. 

So, 100 x 100 = 10,000.  Divide by two and add the change = 5,050.  It works, and I cede to sleep, my work completed.

It laid there a while, satisfied.  I go to sleep pretty quickly, so it was months later before I gave it another thought, expecting I’d have to move on to some non-mathematical thing before falling asleep.   Yeah.  But, wait…   There’s still the utility of the thing.   Where would I find that, exactly?  Well, back in grade school, I guess.  Math class.  The teacher asks for the sum for extra credit, and I can quickly do that.  They want a formula for it?  Ha.  I’m ahead of you on that one.  And then there’s another quiz, we’ll say, for summing numbers between, oh, 60 and 170, and well, I haven’t actually tried that

Those numbers are too much to deal with, so… I can handle a range of 10 to 20 without a calculator while noodling over this.  One might think, and hope, that just adding those particular sheep in my head would put me to sleep.  It didn’t.  The answer is 165. 

Now, admittedly, I didn’t actually add them.  Counting from 10 to 20, I have 11 base values of 10, and I can use my little formula for the change from each number (0 from 10, 1 from 11, 2 from 12… 10 from 20).  So, 11 x 10 = 110 from the base value, then my little formula works for the 0 to 10 of the leftover digits:  102/2 = 50.  Add the 5 left over, and we get 55.  110 + 55 = 165.  Maybe I should have just used 2- 7 for a proof?  

Anyway, following my original formula, 202/2 + 10 = 210.   Not good.  My little formula is no good for anything other than a very specific parlor trick.    

So, let’s backtrack and see what can work.  I need another variable, resetting to:

  • x = lower number
  • y= higher number

The numbers in the series no longer add to the upper number in the range, unless the range starts with zero, but the same “easy math” matching process is the same – 10 and 20 = 30, 11 and 19 = 30, 12 and 18 = 30, etc.  So, there’s a strong similarity to what I was doing before as that is the number I’m multiplying against, x + y.  Now I need to figure out how to express how many times I’m multiplying against it.

From 0 to 100, the midpoint happens to be the number of times to use, but that doesn’t apply in the range of 10 to 20, because there’s only 11 number being summed.  How many counts are there before I reach the midpoint?  Well, the midpoint is 15, so… 5.  So, it’s the difference between the two numbers, divided by two (y – x)/2, not the average (y + x)/2 which was implied when I started at zero in the original formula.   

So, the number of times is (y-x)/2.  Multiplied against the sum (x+y), then adding the change, which is now more properly described as half of the sum rather than the number in the middle of the range (x+y)/2.  Let’s test that. 

  • 20 – 10 = 10. 
  • 10/2 = 5. 
  • 5 x (10 + 20) = 150.
  • Plus the change, 30/2 = the 15 left in the middle.
  • 150 + 15 = 165.

Bingo.  And no bothersome “squaring” a number, either.

For not-yet-asleep fun, back to my original problem of 0 to 100:

  • 100 – 0 = 100
  • 100/2 = 50
  • 50 x 100 = 5,000
  • Plus the change, the 50 left in the middle = 5,050.

For your math quiz needs:

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Perhaps the more notable thing is that my blogging is at such a standstill on thoughtful content that this is what I felt most compelled to write about.  I don’t plan on losing sleep over it.

Note: My smarty-pants daughter informs me that my original formula is commonly known by smarty-pants people to be ∑ = n * (n +1)/2… 

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Grizzly Bear – Live at Tabernacle

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The night began with an expectation of mediocre Mexican food with friends who refuse to relocate from their weekly gathering spot.  Ah, the sway of margaritas.  A phone call changed all that, and off I went to battle traffic to downtown Atlanta for this show.  Note:  Surprisingly, there are not that many great spots for a pre-concert meal around Olympic Park.  If you’re in the area, try Der Biergarten, and perhaps the Jagerschnitzel. 

Grizzly Bear – I bought their 2012 CD, Shields, soon after it was released.  I was teased by a few of the songs, but it collected dust ever since.  A friend had bought tickets and someone dropped out, so aside from trading up on a meal, I was curious to see what the band was like live, especially coming off their latest release, Painted Ruins.

We arrived to find a full crowd, noticeably younger than my typical shows and also approaching gender equity.  In other words, it’s date night for a lot of folks.



Overall, the sound was pretty good.  Instrumental clarity was fine, and the vocals were probably suitable for those more familiar with their lyrics.  Each singer has their own style, Ed Droste fairly straightforward and Daniel Rossen with a penchant for a fairly unconventional delivery, ala Tim Smith of Midlake.  This provides good variety in their songs, which were roughly evenly split.

So, what is left is the performance.  Instrumentally, I liked what I heard.   Bassist Chris Taylor added sax and flute, which added good variety to the band’s keyboard heavy sound, not to mention his backing vocals which are key when then their songs are at their best. 

Drummer Christopher Bear was a pleasure to hear, playing a variety rhythms generally categorized as “things Ringo wouldn’t play.”  On the other hand, Ringo could play a big beat, and as “Indie” as this band is, an occasional sprite melody wouldn’t be unwelcome.  The band’s big hit, “Two Weeks,” isn’t their best song, but it was by far the biggest crowd pleaser – perhaps from familiarity but also because it has a simpler structure.



Visually, the band does not lack stage presence, but there’s not much to watch as each member stays close to their kits.  The Tabernacle’s lighting worked well, as the only visual focal point in the band was the drummer.



The band played a variety of songs from their last four albums – Veckatimest (4), Yellow House (5), Shields (3), and Painted Ruins (5).  As for their latest, I’m not certain that they chose the best songs.  That album closes well, and I was particularly surprised that they didn’t play “Neighbors.”

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Highlights included “Cut-out,” “Fine For Now,” and “Mourning Sound,” but most disappointing was the encore.  “Colorado” drones on and on repeating the song title and “What now, what now, what now?…” Answer?  Another song please.  “While You Wait for Others” is a fine song, but it’s not a parting gift.  I might have preferred a “gun-shy,” “Half Gate” combo.  Heck. Make it a triple with “Speak in Rounds.”



Overall, this was a very good concert.  Grizzly Bear is fully an Indie band, which might mean that from track to track, some people get it and some don’t.  I’m one of those, but I’ll remain curious for future releases to pick out their little treasures.

Setlist:
  • Losing All Sense
  • Cut-Out
  • Lullabye
  • Ready, Able
  • Four Cypresses
  • Mourning Sound
  • Sleeping Ute
  • Yet Again
  • Fine for Now
  • Two Weeks
  • On a Neck, On a Spit
  • Foreground
  • Knife
  • Three Rings
  • Sun in Your Eyes
Encore:
  • Colorado
  • While You Wait for the Others

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