Da Vinci, Fibonacci, & the Divine Proportion

In CategoryTV/Movies, mathematics
Bylab

I enjoyed the book and I enjoyed the movie – The Da Vinci Code that is.  All the codes and puzzles are right up my alley.  Most of these were breezed over in the movie, for time’s sake, so I was glad I had read the book and really got the full affect.  The Fibonacci sequence used at the beginning of the story was fun, the sequence being a set of numbers where the next number is calculated by the addition of the previous two numbers.  Fibonacci numbers appear all over nature – the branching pattern of leaves or the spiral patterns found in shells are a couple of examples.  This also reminds me of the study of chaos theory in mathematics and how fractals are formed.  A friend of a colleague at work started his own website based on his love of nature and mathematics.  Some of his nature photos are truly breath taking, and they really show how things like Fibonacci numbers and the Golden Ratio are subtly  interlaced in everything around us.   His fractal images are equally astonishing.

Speaking of the Golden Ratio, ~ 1.618033989, apparently Dan Brown did not get it quite right.  There were some references in the 20th chapter of the book to how Da Vinci was influenced by the Golden Ratio, and in many of his paintings, the proportions that he used were based on this number.  A recent article disputes that theory …..

there’s no proof Da Vinci, nor any of the artists, musicians or architects whose works are often cited as examples of the Golden Ratio in action, were really influenced by the mathematical notion or used it as a basis for their work.

The Greek Parthonon and the modern day United Nations building are examples of where this Golden Ratio is used in architecture.  There may not be proof that Da Vinci was using the Golden Ratio on purpose, but I think it’s possible he used the golden number without even knowing it.  Since this divine proportion is so ascetically pleasing to the eye, and Da Vinci’s work is revered as genius, wouldn’t it make sense that this ratio was something that Da Vinci subliminally used when he painted, something his genius incorporated into his works automatically.

sisters, chatting …

In Categorymisc
Bylab

kobe … he just went out with jordan

i wish i had a dog walker

a dog walker or a dog?

both

haha … a puggle?

i want someone to take me out on walks every day

so you wish you were a dog?

sometimes

me too … although I think a cat would be better because you could just sleep all day

true … but then you’d have to poop in a closet

4 8 15 16 23 42 [execute]

In CategoryTV/Movies, mathematics
Bylab

Am I the only one who was dying to type that?  According to this, I don’t think so.  If you are lost reading this right now, you are missing out on one of the smartest shows on television – LOST. 

One theory posits a huge psychological experiment. Another tinkers with numerical analysis. Other schools of thought examine collective consciousness, electromagnetism and theology.

I of course, am drawn to the numerical analysis theories.  The fact that 4+8+15+16+23+42 = 108 and these numbers must be punched into the computer every 108 minutes is intriguing.  Also, the number 108 appears strategically hidden in different scenes,  such as in the hatch where the number is inscribed in a mural on the wall.  I did some additional tinkering with the numbers and came up with these facts:

  1. Adding up each digit yields: 4+8+1+5+ …. + 2 = 81.  Interesting because the same digits 8 and 1 are seen in both sums.
  2. 812=6561, 6+5+6+1=18.  I thought it was neat that the digits 81 became swapped after a square and addition series. 
  3. Looking at the deltas between each number yields 4, 7, 1, 7, and 19.  Note that 4+7+1+7 = 19.  So the first 5 number’s deltas equal 19, as does the delta between the last two numbers.  Maybe this shows how the numbers can be separated from each other.

Whether any of this analysis means anything or not, is yet to be determined, but these numbers were obviously chosen for a specific reason.  One idea notes that they are all retired numbers of the New York Yankees.  It is true, I googled it, but since I am a Sox fan, I choose to ignore that theory.  Oh, and for any anti-numberers out there, there are other non-numeric clues [BOR-ING ;-) ] hidden throughout the show – the titles of the books in the hatch is one example.  I’ve always loved giant puzzles, so this is definitely fun for me to theorize about.  Hopefully we’ll get some answers about these numbers by season’s end.

For extensive details on the show and all the theories, check out this wikipedia entry  … man, does that site have everything!  I remember when Britannica was IT … all 50 volumes of IT!

a salute to summer, and dirty bone noses

In Categorykobe
Bylab

Summer is here!  Or is it?!  We have had 7 days of continuous rain.  Steady, cold, wind blowing … rain.  I am so sick of it.  I find this weather extremely depressing.  At least summer has hit LAB Unleashed.  You’ll notice some of my favorites pics from last summer up in my new masthead.  I was inspired to put that together after a cold, wet, excursion late last night ….

Kobe dragged me out in the rain and he was on a mission.  I gave him a bone earlier in the day.  Obviously, my first mistake because he was not in the mood for a bone.  Instead, he wanted to hide the bone in a secure location so that he could enjoy it later.  He paced around the house for a while, and then the whining began.  Those droopy eyes, bone in mouth, standing by the door and whining.  It was late by that point, dark, and SO rainy.  Torrential down pouring and wind swirling down our corridor like a sideways water twister.  The last thing I wanted to do in the world was go outside with him so he could hide his bone.  I opened the door and kind of shooed him out … but he was not having it.  He insisted that I walk him around the corner of our building to his favorite pee spot.  Fine.  I bundled up and braved the weather.  Once we got to his spot, bone in mouth, he looked at me like I should turn around … as if he needed some privacy.  He did not want to show me his secret bone stash.  He knows of course, that soggy raw hide bones are my favorites snack.  So, I played along …  Anything to get him to finish quicker … I turned around, umbrella whipping this way and that, pants soaking wet from the sideways rain, and Kobe runs off behind some bushes.  He literally does not come out for 2 LONG ASS minutes.  I finally yell for him and he hops out from behind the bush as if I had spooked him with my voice, the expression on his face says, "Damn it, she knows where I hid my bone"

I was so pissed by this point until I saw that sweet little snout … covered in mud.  He did a lot of digging to get that bone in there just right, and it just cracked me up.

Dirty Bone Nose

When we came inside, I dried off and decided to liven up my attitude by looking at some of last summer’s pictures.  I know summer is right around the corner, but it’s hard to believe on this 8th day (and counting) of cold, rainy, weather. 

I now have my own chauffeur

In Categorymisc
Bylab

Kevin and I just picked up our new car the other night.  Now, some may accuse us as being serial car buyers, but let me set the record straight.  KEVIN is a serial car buyer, I am merely an innocent by-standard.  Although … he definitely has become much better in recent years, mostly due to my angelic influence.  In any case, this new purchase is completely justified by one important fact.  Our warranty was up on the old car, and with over 100,000 miles on it, we were afraid of getting hit with very expensive repairs.  We are now back under warranty, and not paying for any service or oil changes is a nice perk as well!

With the new car comes all kinds of fun extras including a 3 inch thick user’s manual paired with an informational cdrom.  With all this extensive information, you would think this car is the Bat Mobile … and in that scenario we would definitely fight over who gets to be Batman.  I’m almost afraid to operate it though, so I might settle for Robin.  You should probably have some sort of rocket science license to operate it properly. 

Anyway, we popped the cd in last night for some easy listening.  The first thing it went over was the car’s safety features.  Airbags, check.  Anti-lock brakes, check.   We really should have poured a glass of wine before I heard the next piece of information, because I was floored and appalled.   "Children under 13 years old or less than 5 feet tall should always ride in the rear" of the vehicle.  No lie … this is exactly what the robot woman on the cd said … we replayed it about 10 times!  I just can’t believe it … and if you can’t either … check out the sound clip here.

My initial shock has turned into a mischievous interest  … there is a huge opportunity here.  For safety reasons, I could now require Kevin to chauffeur me around.  I now have my very own driver.  I may even get him a uniform.  I think a Batman costume will do.

Enjoy being herded like cattle?

In Categorymathematics, travel
Bylab

We just flew AirTran Airways from Boston to Hilton Head last weekend.  Besides the dated decor, nappy cloth seats, and numerous delays, the thing that perplexed us the most was how the airline implemented its boarding process.  We were always seated at the back of the plane, around row 24.  To begin boarding they would first call rows 25 to 29 to board, which made sense.  Most airlines seem to start boarding at the back of the plane.  Kevin and I would get our stuff ready to board next, but then we would hear them call rows 5 to 10.  Rows 5 to 10??  We weren’t sure if we were hearing things right.  It really seemed counter intuitive.   Wouldn’t all the people boarding in rows 5 to 10 block the rest of us trying to get to the back of the plane?  This atypical boarding process was sparked by a study done by some mathematicians in Arizona.

The two then developed a mathematical formula that measured the number of times passengers were likely to get in each other’s way during boarding. "We knew that boarding time was negatively impacted by passengers interfering with one another," explains van den Briel. "So we built a model to calculate these incidents."

Villalobos and van den Briel looked at interference resulting from passengers obstructing the aisle, as well as that caused by seated passengers blocking a window or middle seat. They applied the equation to eight different boarding scenarios, looking at both front-to-back and outside-in systems. "Ultimately, the issue America West needed to address was time," explains van den Briel. "We figured a system that reduced interference between passengers would also cut boarding time."

Last July, AirTran Airways launched a boarding system that the airline’s Judy Graham-Weaver refers to as a rotating zone system. AirTran first seats the back five rows of the plane, then the front five, and continues rotating back-front-back until boarding is complete. Graham-Weaver says that this system is one reason AirTran enjoys turnaround times in the 20- to 30-minute range.

We found this zone system extremely inefficient.  We were the 3rd group to board, and no surprise to us, we were held up by passengers in rows 5 to 10.  We stood on the bridge-way for a good 10 minutes before stepping onto the plane.  I appreciate the fact that they are trying to come up with better boarding processes, and it’s cool that the airlines are relying on mathematics and statistics.  I love hearing about real world mathematical applications.

Southwest Airlines, who does not assign seats, but allows its passengers to board in groups and pick their own spot, has the fastest boarding times in the business.  I’ve flown Southwest before and have definitely made fun of the giant paddles you are issued, and how you are then herded into one of three corrals.  It makes you feel like a piece of meat.  But it’s interesting to note that when humans are left to self-organize, our nature allows us to do a very efficient job of it!

Where have I been?

In Categorymisc
Bylab

There has been a long pause on LAB Unleashed.  A kind of awkward silence has crept in.  Have I abandoned the blog?  Do I have nothing to write about?  Have I been busy proving P=NP?   All valid questions.  The truth is, I came down with a nasty flu.  I was pretty useless for about a week.  I barely made it through my work, let alone had enough energy to blog.  And at that point, I don’t think anyone would want to hear about my nasty flu symptoms.  That is TMI, even for the blog. 

Just as I was beginning to feel better, we hopped on a plane to Hilton Head Island, South Carolina for our BCFs’ (that’s Best Charlestown Friends’) wedding.  The weather was awesome, the wedding was beautiful – we really couldn’t have asked for a better weekend.  The warm air helped to clear up the remnants of my flu turned lingering cold, so I was really able to enjoy our little get-a-way.

So …. the wedding … A gorgeous ceremony, was followed by an extravagant cocktail hour, and of course a kickin’ reception.  The festivities ended on a couple of high notes.  One, The groom leading a pack of the wedding party into the pool.  It was absolutely hilarious, and such a perfect way to end the evening.  It was even funnier on Monday morning when I got back to the office and commenced my regular routine.  The routine includes coffee, email, and reading through (and ripping off) the past days from my Spanish Phrase calendar.  For their wedding day, May 6, 2006, the Spanish phrase read "La piscina no es tan profunda" – translation – "The swimming pool is not so deep".  Coincidence??  I think not!!!  This leads me to believe that my Spanish Phrase calendar is really a daily glimpse into the future.

And the second high note, Kevin, aka The Dancing Machine, giving the bride a huge farewell hug.  Did I say Dancing Machine??  Because … WAS HE EVER!!!  And if you know Kevin, you know he would have to be severely intoxicated for this to occur.  Did I mention the extravagant cocktail hour??

All in all .. it’s been a crazy couple of weeks – filled with flem, flights, festivities, and even a little fun.  The blog is back, I am coding away … keeping it classy on and off the web.

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