Plato and the Seven Times Table: An Antidote To Chaos
The statement y= 6x+x is not a truth claim, it’s a description of a relationship. x and y represent quantities and if we know one then we know the other. It’s true to say “if x is 1 y is 7,” only if we voluntarily accept the premise that y=6x+x. Likewise, if we accept that relationship, we implicity acknowledge that “when x=6 y=42.” This is a harmonious result, except that for many of us the number 42 isn’t just a quantity. Numbers in the human mind have confusing semantic associations. In the context of 3rd grade math, 42 isn’t just an expression of a ratio, it is an Answer.
People are scared of 42, we find it mysterious, many of us feel pain when we see it. In Japan, 42 is known as the number of death because its pronunciation Shi-Ni sounds like the word for Death Itself 死神. To Science fiction fans, 42 represents the “Answer to the Ultimate Question of Life, the Universe, and Everything”. To the rest of us, it represents the pain of failing to memorize the 7 Times Table.
To a child, “What’s six times seven?” Isn’t a request to perform a mathematical operation, it is a demand, that the child say “forty two” as quickly as possible, or face consequences. Unfortunately for the child, the human memory works on associations and 42 is quite similar to 24, 43,45, 22, and even 67 since both are combinations of 6 and 7. The chaotic nature of the 7 times table prevents the human mind from discovering a pattern and forming the associations necessary to hold onto the the 12 numbers we require children to memorize for each of the primary numbers. This causes many children to associate arithmetic with humiliation and threat, which not only prevents them enjoying mathematics but conditions them to assign meaning and emotion to neutral quantities, a mistake which can lead to purchasing lottery tickets later in life on the grounds that “this number looks lucky”.
Damaging young minds in this way is a grievous sin, but it’s also a preventable one. When you force children to chant numbers they naturally seem magical and incomprehensible. You can help children “remember” the Seven Times Table by teaching it dialecticaly. The conversation below is inspired by Plato’s Meno. The Meno is a short Socratic dialogue in which Socrates demonstrates the innateness of mathematical knowledge by drawing a geometric formula out of a young boy by asking him questions.
To say that mathematical truths are “trivial once understood” is anther way of saying that they simply need to be “remembered”.
“Take three equal lines and make a triangle, how many points does it have?”: 3
“Take two triangles like the one you made and overlap them to make a star, how many points does the star have?”: 6, 3 for each triangle.
“How many points would two stars like that have?”: 12, three for each of the four triangles.
“Take a dot and put it in each star to represent an central point. How many points does that make?”: 14
“Draw another star with a dot inside. How many points on all of the stars?”: 18
“How many center points are there?”: 3
“What is 3 center points plus 18 star points?”: 21
“So if each star has 6 outer points, and the number of stars is equal to the number of central points what can we conclude about any number divisible by 7?”: Any number divisible by seven is equal to the number of sevens it contains plus 6 times the number of sevens it contains. (7x=6x+x or y=6x+x)
By teaching math as a conversation and by encouraging a visual rather than verbal conception of numbers, we can instill the basics of arithmetic without leaving a bad taste in children’s mouths. It would be nice to return to a time when mathematics was seen as a sacred branch of philosophy rather than as an obstacle to be climbed over in pursuit of financial success.