Hexa anyone?

Hi,
Sorry that other concerns and considerations have kept me from writing more frequently than I intended. Anyways, today's post is about the number 6. The most obvious reason why I like the number 6 is that it is a multiple of 1, 2, & 3; and interestingly, it is also the sum of 1, 2, & 3!! I relate number six to indigo or dark blue but i also relate it to a backwards facing stork as shown here!

Typically, we are used to seeing 6 in many more ways than we can identify off the top of our heads! A hexagon is a polygon with six sides (Click here to see a hexagon). We see hexagons in many places around our house and life - think bolts & nuts, beehive structures (so we see these on honey bottles), soccer balls (usually have a combination of hexagons and pentagons), and basic structure of carbon (we don't see this, but Carbon is one of the basic elements we are all made of). We also see 6 in every cubic or cuboid object we see/use. Every cube/cuboid has six sides. A dice consists of 6 sides, for example. Another interesting and probably less known fact about 6 is that in calculator digits, 6 is written using exactly 6 lines! This only holds true for 4, 5, and 6!!

Another interesting aspect of 6 is that we use it every second of the day, literally... Our clocks are set up in increments of 60 --> 60 seconds to a minute, 60 minutes to an hour; 6 hours are 1/4th of the day, 6 are the days of work in most parts of the world and constitute almost 1/5th of a month, and last but not the least, 6 months constitute half a year! While 6 is (obviously) not a prime number itself, like i mentioned earlier, it is the sum and the product of the first three natural primes (1, 2, 3). Since 9 is also the inverted version of 6, a quick note here about 6 and 9 is in order - in our passion for 3s, 6 and 9 are the first two whole number multiples of 3!!

To check for divisibility by 6, all we need to do is check for divisibility by 2 and 3. I will cover divisibility by 2 when i write up the entry for the number 2 and have covered divisibility by 3 in the post about 3! 

6 also implies  half a foot - in fact if we look back at the non-metric systems around the world, we find that 4 and 6 show up prominently and not 10. Another aspect of 6 that is important is it's square - 36. As I discovered recently on my trip to the State Fair, 36 inches is the minimum height the park people allow for most rides! On further investigation about that I found that this is due to the fact that 36" is the average height of a 3-year old (gotta love the 3s!!), and the physical stability required to sit through and enjoy most rides (taking into account the femur length, etc. which allows for comfortable and safe seating). Another cool thing about 36 is that it is also the product of two squares - 4 & 9!!


Anyways, that's all i have to say about 6 for now... if i think of anything else, i will make another post for it at some point in the future. If you have anything to add, PLEASE send me/post your comments...

Until tomorrow or later... ADIOS!!!

The number 7...

I picked number 7 today for many reasons. The obvious one is that this is my 8th post and thus I have completed 7 posts till date! This is more than the total number of journal entries I have written in my entire life. I now realize my mistake. I tried to make the journal entries about me rather than about things that interest me...no wonder i never crossed 7!! One little known reason is that i associate 7 very emotionally with my son. I found out that i was expecting him on 10/06/2007 at 6:10 AM. If you sum up all the numbers from that date, you will get 7 and same thing for the time at which i learned about his existence!! This is probably a little sappy, but one of the very few things I am sappy about, indeed!! If you are anything like me and live your life by measuring numbers consciously or sub-consciously, you will realize that the fact that i remember the date and the time has less to do with the emotional importance of that moment and more to do with placing that information in a neat little packet in my brain's memory!!

The number 7 in my spectrum is represented by a "clear" color or "no color". I have had a few friends ask me how a "clear" band would work, and why. While I have found it difficult to explain, perhaps this figure representing 7 as a part of a flower vase will indicate why I always associate 7 with clear or negative space:

The Number 7 in a Flower Vase

As you can see in this figure, the black lines represent a 7!! The number 7 is many things...it is a prime number and if you google "the number 7" you will find out how many different mathematical functions involve 7 as a key number in their sequences! But let's just explore things that we use/hear/know on a regular basis:

1. 7 is the total of the two opposite sides of a regular dice! (1 and 6; 2 and 5; 3 and 4)

2. 7 is also the most probable sum if two dice are thrown together (6 out of 36 = 1/6) - so i guess you know what to bet on now when you are playing with two dice!! LOL

3. 7 is the number of deadly sins as described in some major monotheistic formalized religions - Pride, Envy, Gluttony, Lust, Anger, Greed, Sloth. Majority of the world religions have an unusually high occurrence of 7 in the theological books. I believe 7 is considered a magical number by many cultures and religions, but that is beyond my interest at this time!

4. 7 days of the week named after the 7 earliest acknowledged extra-terrestrial bodies - Sun, Moon, Mars, Mercury, Jupiter, Venus, Saturn! 7 months in the year have 31 days and the rest have either 30 or 28(29 in leap year) - January, March, May, July, August, October, December. 

5. A rainbow has 7 colors - VIBGYOR (violet, indigo, blue, green, yellow, orange, red); Music has 7 major notes - Do, Re, Mi, Fa, So, La, Ti (Sa, Re, Ga, Ma, Pa, Dha, Ni - in Indian classical)

6. The Big Dipper, also known as Saptarshi, is an easy to recognize stellar constellation that is formed out of 7 stars! Another major 7-star constellation is Orion.

7. We all are very familiar with 7 basic terms used to give directions - left, right, up, down, behind, front, beside! I am deliberately NOT focusing on the "Seven Wonders of the World" because I believe that 7 is too small a number to try to express the wonders in the world!!

Mathematically, 7 is interesting. The rule for identifying divisibility by 7 is almost more complex than actually manually doing the division. But i will attempt to explain, nonetheless. It is a three step  (O how i love thee, number 3!!) procedure:

1) Take the last digit of the number and double it

2) Subtract this doubled value from the rest of the digits

3) If the result is two digits, check if the two digit number is divisible by 7, otherwise repeat procedure.

e.g. Let's consider a number 595. Last digit is '5' so doubling it gives us '10'. Subtract 10 from '59' which gives us '49'. '49' is the square of 7 and therefore perfectly divisible by 7. This implies that '595' should be perfectly divisible by 7 (no fractional/decimal solutions!!). Testing --> 595/7 = 85!!

Well, my students are almost done with their midterm so i will get going...

Till tomorrow, or later...ADIOS!!

On Gandhi...

German author Herman Hesse, in his 1922 book "Siddhartha" includes a discussion that Siddhartha has with a trader regarding what his strengths are!  The trader asks Siddhartha (an ascetic who wants to work for the trader), "what are your strengths?" and the reply given by Siddhartha holds, in my opinion, the truth about India and Indians as observed by Hesse in 1910.

Siddhartha replied after a little bit of thought, "I can think. I can wait. And I can fast. These are my three strengths."  (Factor of 3 anyone???)


In a recent conversation with my father, he associated the lines from Herman Hesse's "Siddhartha" to Gandhi and it was as if a new world of thought opened up for me! How true it is that one of the most influential leaders of the 20th century survived on three major strengths and with three major principles. Gandhi's fundamental principles were truth, non-violence, and equality.

Here is a brief window to Gandhi - most of us know most of the logistical history of Gandhi, either because we grew up in India (a country that claims to function on Gandhian principles) or have watched Richard Attenborough's Gandhi. In either case, while this historical figure is impressive and attention-worthy, what is often overlooked is the sheer strength of character and commitment to truth that are demonstrated by the man!

Some day, when i have more time on hand, i will definitely devote a brief economic exploration into the ideas of Gandhi and how he, in terms of pure economic ideology, firmly establishes himself as a capitalist. In the mean time, I thought it was important to identify that along with his THREE principles, his THREE strengths were important to recognize.

1. I can think - Gandhi was an intelligent lawyer who was able to observe the conditions of Indians in a Colonial India when he returned from South Africa in 1915. He realized that the economic exploitation of local farmers and workers in India had resulted in a weak economic system that could not sustain itself even if the British left India immediately. He recognized that the root of the problem of colonization lay with economic interests and the only way to resolve the need for independence peacefully was to remove the economic incentive of the British in India. He quite literally thought things through to a point where removing economic incentives one after another led the British to finally, merely WALK out of India without further conflict.

2. I can wait - This is demonstrated by the fact that Gandhi spent 20 years in South Africa in order to get equal rights for Indians; and almost 30 years in getting the British to leave India. This demonstrates a strength of character - and a belief in truth. Having been influenced heavily by various religious texts, Gandhi realized that planning requires adequate amounts of time allocated for achieving success at any plan. The patience that is considered to be such a characteristic of the Gandhian philosophy comes out of the understanding that, in economic terms, at least - LONG TERM stability matters!!

3. I can fast - This is perhaps the most important learning from the Gandhian lifestyle. It is one of the easiest strengths to misunderstand, and one of the most difficult ones to follow. Fasting in this case does not necessarily refer to multiple fasts Gandhi undertook in order to establish peace and stability between groups of people. Fasting refers to the function of "doing without." I have found that fasting is a fairly foreign concept in the Western culture as a whole. Sacrificing personal convenience of any sort is almost looked down upon on the one hand or idealized on the other, without realizing the attainability of this goal and the value it has to survival. Don't get me wrong here, sacrificing personal convenience (also known as 'fasting") is NOT the same as "sacrificing" - a concept that abounds in the Western philosophy. The ability to do without is dwindling rapidly with each generation also. In a world of immediate gratification, i think it would serve us well to recognize the importance of surviving 'without.'

Once again, Gandhi does embody this very well. As a kid, i often made fun of the fact that Gandhi practically wore only a loincloth - i thought it was snobbish of him to be so "simple." To me, if a person's simplicity is encroaching on practicality,  it is basically a snobbery (a i-am-better-than-you approach). But, after a simple experiment carried out recently, i realized that something very powerful and goal-oriented is required within oneself to make a commitment of this nature. I had experimented with only wearing one pair of jeans and a couple of shirts throughout the semester (a couple semesters ago). I have seen my grandparents and my father live a very simple lifestyle by choice and was always thinking of the "snob" effect as i mentioned above. Once i started following the rules of limitation and simplicity, I have to honestly and embarrassingly admit, that i did not last for more than a week or two. The simplicity was not easy to stick with...it was boring, and yes, i did feel deprived to some extent. That was when i realized what a significant commitment Gandhi made to his cause of making the average Indian feel that he was understood!

Anyways, i am going to go start getting dressed for the State Fair of Texas!! Till tomorrow, or later...ADIOS!