Much Ado about Nothing

  Both the Greeks and the Romans lacked something in their mathematics that we now take for granted, ‘nothing’, a concept we don’t even think about anymore.  The number Zero, while common isn’t well understood, and as many school boards adopted the ‘new math’ the confusion only grew, a move that has typically been rescinded.  This writing is going to try to sort things for both the author and the audience.

  Starting with some of the basics, zero (0) is a whole number which represents an absence of value or quantity.  Zero is not a natural number, a natural number is the whole number greater than zero; probably a throwback to the Greeks and the Romans.  Also, zero is an even number as it fits the requirements: flanked on each side by an odd number, divisible by two (2), and it ends in the digit zero.

  Many people get confused about zero in that they don’t understand what zero actually does; and while zero represents ‘nothing’: the question must be asked – nothing of what?  As an example, we can take the number one thousand (1,000) and examine it from right to left: there are zero ones, zero tens, no hundreds, and a single thousand; showing once again that zero represents a lacking of value or representation. 

  Now we get to the catalyst for this paper, as here there are potentially three conflicting rules.  Zero also gets a pass on some of the other rules within mathematics.  This is the area where things get confusing: as A) any number divided by itself equals 1 (5÷5=1), though B) with zero it equals itself (0÷0=0), and C) zero divided by a number also equals zero (0÷5=0).  So, did mathematicians break the logic inherent in mathematics or perhaps it was slightly broken all along?

  Seemingly, when zero is used in the numerator slot the result is always zero, however when in the denominator position things turn tricky if you let them.  Before starting this writing, my position was that any number divided by an absence of value or representation remains the same and yet this is where Google and I disagree as Google reports it as ‘undefined’, also MS Excel throws a ‘division by zero error’ and so I carried on looking into it.

  Here is how it works, when one goes just to math, please play this out with the equations shown in A, B, and C above; take the denominator and move it to the other side of the equal sign and multiply;  via this method, all of the equations work as intended.  So now we can try the equation 1÷0=1.  This breaks, for once you move the zero to the right side of the equal sign and multiply, one ends up with 1=1×0, which results in 1=0 which is impossible; and so there you have it; I was wrong.

  In a recent conversation, my confidence superseded my competence and this writing was an attempt to re-balance that problem. 

Some Thoughts on Education

  Government funded education has lost purpose and maybe the blame can be laid at the feet of the band Pink Floyd and their song ‘Brick in the Wall’ with the opening line – “We don’t need no education.”  The song was, in hindsight, prophetic though the song could also have set the tone for how to move forward as it was released in 1979; please lookup the lyrics to get the full story.  It must be noted that the noted introductory line in the song a double negative and so, yes, they do need an education.

  Another factor that has influenced education is the female to male ratio within the education system especially from K-12.  According to Statistics Canada the data shows that approximately 75% of educators are female, with a higher proportion (89%) in elementary schools and a lower but still substantial proportion (59%) in secondary schools.  (Source https://www150.statcan.gc.ca/t1/tbl1/en/tv.action?pid=3710015303)  It is understood via the statistics, that boys and young men raised in a single mother home are more likely to end up battered, in prison, or even dead: thus leaving the question, has the formative years for a child’s government driven education has effectively rebuilt the ‘single mother sydrom’, more simply put: it has and been injected into the school system.

   Back when I was in high school I tutored my classmates in Algebra, Calculus, and in Functions and Relations.  More recently I tutored a young man, and went old school on him including, though not limited to, the times-table, and what I call Greek math.  Greek math is what one can do with a ruler, a compass, and protractor; which was done through observation and reasoning.  The most common example of this sort of math is known as the Pythagorean Theorem.

  Pythagoras of Samos, or someone before him, figured out that a equiangular quadrilateral, such as a square or a rectangle, can be cut in half between two opposite corners, which forms a triangle resulting in the equation which is presented as A² + B² = C² where C is the diagonal line from one corner to the opposite corner.  Pythagoras sorted this out without the aid of a teacher, and as such a PHD, posthumously of course, should be awarded by whichever university is of the highest rank in Greece if this hasn’t already been done.

  Another thing that is not being taught, as far as I can tell, is that the basic explanations on the how or the why things work, are no longer being taught.  In the last few yeas I’ve explained to, to many people, why a number squared or cubed is called as they are. Let’s see if I can explain why those mathematical terms are used.  Going back to the good old days of times-table, when one looks at the times-table again, one can see that when you go 3 across on the top and 3 down on the left the result is 9 which forms a square as there are only two dimensions; and yet it still results in a square.  An additionally good task would be to bring in another piece paper for the third dimension, and when one thinks on this idea, one can see why 2^3rd = 16 is referred to as two cubed.  Also, there is no name for 2^4^th as there are no physical dimensions left.

  According to multiple studies, it is said that if a person learns more than one language by the time they reach the age of twelve, they will always know the basic and will be able to speak it without an accent.  This was known to my father, as I was instructed to do times-tables and writing every weekend when I was young, the school system also knew this as I was not allowed a calculator until somewhere around grade ten.  It should be noted that when America put men into space the math was done by hand or by using a slide ruler; oh and I typically add up my shopping list to within two dollars and after that I can tell what the change should be, yes I still use cash.

  The purpose of the paragraph directly above is that if you put in the work manually at a young age then you will reap the reward for most of your life.  The current problem is that age where ‘the toys’ are being introduced and while the toy can give the answer the how it works is being lost; this will only get worse as AI is introduced.  There is program called Grammarly that can write personal letters, reports, legal documents and more.  The problem is going to be that reliance destroys resilience; we are now going to play a game in the form of a narrative.

  The power grid goes down for a week, and so people in homes can not cook, no access to the Internet, or charge their phones and cars, also the gas pumps will stop; also, restaurants won’t be able to cook meals, refrigerate, those who deliver food can’t charge their bikes, and so people will get hungry: can you imagine the level of chaos and violence that will ensue?

   If you don’t use it, you loose it; or perhaps you never really learned writing in the first place; I never really did and I typically only use pencil for words, though I do use a pen when I do maths.  I tend to misspell words all the time, though I’m still working on it, so I can be a better, this is part of the reason for my others writings you can read; the ideas are more important than the spelling.  So this is where I am part from both spelling and grammar, as I just never got it right, it took me about a decade to learn how to type the word dyslexia, though I can now with out error

  Additionally, the rhetorical talent amongst 20-35 year olds seems to be only parroting the current talking point(s), all the while not being able explain what the words coming out their own mouths mean.  I have run into this quite often as of late, and so ‘What do you mean by that’ become my go to response with the current youth; how is that after about 3,000 years the battle against Sophistry has resurfaced or perhaps it had never stopped, and just went into hiding for a while.

  I left grade thirteen around 40 years ago, so I’m not sure how the curriculum is being taught today.  Though based on anecdotal evidence, I feel that things have changed and not for the better.  Two factors must be taken into account at this point, the first being that I have three to four decades over the youth and that most of them live in Google.  A problem with living within Google is that most of the people know the what, while not knowing the why.  This is why teaching history is important, because while the faces change; the human character has not changed for thousands of years.  “Those who forget history are doomed to repeat it”, the question then must be riddled: what happens when history is never really even being taught in the first place? 

  Returning to rhetoric for the final moment, there was a man about 3,000 years ago who stood up against the Sophists and he was sentenced to death for his deeds; his name as you may have guessed was Socrates.  Socrates is best known for the Socratic Method, which is all about asking a person to explain their position and expand on it, which was seen as an attack on the orthodoxy.  The concern is that we have returned to a position of Sophistry and orthodoxy all the while abandoning the Socratic Method: and I’d like to know the how and why that could have happened outside the changes in education systems.