Commutativity and Life

Sitting in a math class, and the professor announces that the next topic will be a brief study of matrices (matrix is the singular form). Then is asked a show of hands of those who have NOT had some previous experience in the topic. Up goes my hand, relieved to see that mine is not the only uncluttered mind, but saddened that there are so few of us. Those emotions are replaced when the professor announces that he will ‘go slow’ so that we midgets can keep up with the crowd. Thanks.

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As he takes us through the steps of ever increasing arithmetic manipulation, the point is made that some properties of matrices are commutative while others are not. It is the non-commutative properties that are of interest, he observes. For those of you who have my level of understanding, note that an arithmetic operation is commutative if the order of the process returns the same result; 3 * 2 = 6 and 2 * 3 = 6.

As the link above reports:

Records of the implicit use of the commutative property go back to ancient times. The Egyptians used the commutative property of multiplication to simplify computing products.[6][7] Euclid is known to have assumed the commutative property of multiplication in his book Elements.[8] Formal uses of the commutative property arose in the late 18th and early 19th century when mathematicians began to work on a theory of functions. Today the commutative property is a well known and basic property used in most branches of mathematics. Simple versions of the commutative property are usually taught in beginning mathematics courses.

But, predictably, there is a large portion of mathematics that is not commutative. I knew it was just too good to be true. As the professor observed, there are many, many examples in life where the order of a process is very important. As examples, he pointed out that opening the window and sticking your head out of the car window are operations where the order of things is critical.

Wikipedia expands on the idea:

Noncommutative operations in everyday life

  • Washing and drying your clothes resembles a noncommutative operation, if you dry first and then wash, you get a significantly different result than if you wash first and then dry.
  • The Rubik’s Cube is noncommutative. For example, twisting the front face clockwise, the top face clockwise and the front face counterclockwise (FUF’) does not yield the same result as twisting the front face clockwise, then counterclockwise and finally twisting the top clockwise (FF’U). The twists do not commute. This is studied in group theory.

    I’m confused but more impressed than ever with the nature of our existence. How can an idea as powerful as mathematics embrace contradictory behavior? Why do we think that mathematics can explain the physical world when it is riddled with inconsistency? Could it be that the nature of our existence transcends the universe of mathematics?

    Am I having a metaphysical moment?

    Sharpening the Axe

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    From a forum for beginners in Java:

    Question:

    What is the best way to improve logics. Since most of the coding works on developing quick/good logic. Is there a book or resource for developing logics which will be used in coding. Most of the times I end up speding time thinking abt the logics.How can one improve his logical thinking.

    Answer:

    I don’t know of any book, method, or formal plans, but i’d simply suggest practice.

    a lot of folks will tell you it’s GOOD to spend a lot of time thinking, and less time writing code. Abraham Lincoln allegedly once said “If i were given 8 hours to chop down a tree, i’d spend the first 7 hours sharpening my axe.” I think the same principle applies to coding – more time spent thinking about things up front will make writing the code much easier down the road.

    We have had this concept hammered into our brains in my two classes in programming. It still hasn’t sunk in…….I still start thinking about code before logic. It doesn’t work……

    Mr. Parkinson, Meet Mr. Murphy

    As a boy, I read every Horatio Hornblower book that has ever been published. So great was my addiction that I even read a reference book written about my hero: “The Life & Times of Horatio Hornblower”, by C. Northcote Parkinson, who, I quickly learned, way back then, was the father of the famous Parkinson’s Law.

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    In my journey through life, I have never forgotten Hornblower, who overcame rejection, enduring tragedy, and persecution in a series of stories that surely must have provided some understanding about the life that lay in my murky future.

    Parkinson’s law, one of the most profound, if little understood, principles of business, has, as well, been a frequent visitor in the cabin of my little ship of life.

    The law may be succinctly stated thusly: “Work expands so as to fill the time available for its completion.

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    Parkinson’s Law, at least as manifested in my existence, is often accompanied by that other famous natural law, Murphy’s Law, whose principle effect is summed up this way: “Whatever can go wrong will go wrong, and at the worst possible time, in the worst possible way.

    These two great forces have met, formed a vortex of immense power, and have begun sucking the faint essence of my soul-being from my physical existence. Let me explain……

    It is spring break, so I have one week to catch up on domestic duties, school work, and to prepare for a large social function for an organization that takes this event very seriously.

    On Sunday, the electrical components of our castle began to flicker. Televisions and computers were most severely affected. A call to the local utility, an astonishingly quick response, and the matter was taken care of, or so I thought. Within minutes of their departure, the terrible on-off cycle began again. We had no choice but to power down our two main connections to the world, television and internet.

    On Monday, while feverishly completing school work on my computer, the utility company returned, to install a recording device to monitor the flow of electricity into and out of the crib. Flickering continued unabated. On Tuesday, work on the social function was partially completed, amidst truly alarming bangs and bumps as volts and amperage surged through our delicate devices. Wednesday dawned to the sound of more noises, with electrical devices that acted as if they had just left the set of Poltergeist. A call was placed to the electrician, who, agreeably, arrived within 30 minutes.

    Yessir, he noted, you do have some problems. The only way to fix them is to track down the ‘gremlins’ in your wires. And so commenced the search, with every device that drinks electricity turned on, switches switched, and even additional consumers like very high powered lights brought in from the truck and turned on; all apparently designed to cause my home’s electrical system to fail. And fail it did not. But one thing did die, the one thing that I absolutely had to have this week in order to fulfill all of my responsibilities; the one thing that has become irreplacable (we all know that humans/employess are not irreplacable, but that’s another story)……yes, my desktop pc gave up the ghost.

    Order has been restored to the grid. An even supply of juice is now available. But the one thing that really, really needs the juice is not here. It’s at the computer emergency room, where my new best friend is attempting to revive the exhausted, but vital component of my life. Like a family member in the waiting room, I await the visit from the doctor. What news will he bring?

    If I require another computer, can he give me back the data that lives only on the old hard drive…..the hard drive that holds all of my software, data, and connections for school, work, and social obligation? Can I get a working device before the week is out, so as to finish my tasks before this eye of the hurricane (spring break) passes overhead and the furies recommence?

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    I await, helpless as a new born babe, the decision that will be rendered by those great natural jurists, Parkinson and Murphy.