We johny-come-lateleys to mathematics kind a think maths is fractions and algebra and notation. Yeuk!:insane:
So we think this cos despite years of teaching, this is all we get when maths pops up. We could be having an ineresting normal conversation when suddenly :ninja: blamow!:yikes: a bit of maths slips into the conversation. Everybody kind a glazes over and looks at their watches. Time to go?
You know it was not always like that. Mathematicians of old were gentlemen, carpenters, builders,educated people with something interesting to say about the ordered world, and people would listen to their "rhetoric"
People will listen to rhetoric, but mathematicians will not,so does that make them "not people?"
I guess so judging by others reactions.
So why did we abandon rhetoric in favour of notation?
Well most mathematicians are on the autistic spectrum somewhere toward the Aspberger end. This makes them not very smart socially. Don't get me wrong, they have plenty of smarts!. They just don't get this social thing. Many mathematicians are actually "in love" :love: with some number, or some calculating machine,or some symbolic representation or some geometrical form.
Hey! we have to have our hobbies!:D .
So going back to rhetoric may not be a bad thing at all.
At the head of this post is a conversation a mathematician wanted to have with me.
Many would ask "what is it?", if they were not so scared :no: .
This is an "expression". First and foremost it is a communication. It is not mathematics, it is language, writing, a written conversation but condensed into a brief code. It is a language coded down to a few pen strokes.
Mathematics is Manipume: apprehnding reality with every part of your being and thinking about the dynamic relationships you are experiencing. Communicating that experience and response to experience is not unique to mathematicians. Scientists do the same because mathematics is the Greek idea of science.
Along with obscuring our "talk" we dissected our "walk" away from the general development of science and technology to stand apart in our own right as "The big M's", the Mathematicians.
Hey we are nothing more or less than specialists in every scientific and technological field and in any constructive art,… in all art!
So communicating this experience was done rhetorically:
"I say, chaps, i was trying to find out what the volume of a box was. i chose a box shaped like a cube, all its sides the same length, easy!
I used the standard governmental issue of volume and started measuring. I soon found that i could always get the volume of the box by multiplying the length by the length and then multiplying it again."
"jolly good old bean, i think the Greeks found that out years ago, so i think you are on the right track. By the way, what do you think? Should we call this type of multiplying a cube?"
"Ha ha ha!. Nice one, chap. sounds really cool! so what do i say:i cubed the length? is that what i write?"
"Hmm, i guess so. I am not sure if everybody will get it though. I guess we ought to explain what it means when we introduce it"
"Yeah!. I totally see where you are coming from, chap. I looked at it and felt a bit queasy, but if i put: that means multiplying the length by itself and then by itself again that makes sense."
"Nice one! Sooo…. What are the other thingies?"
" Those, my dear chap, are some extra things to say about finding the volume of a cube!"
"Oh yeah! extra things eh? I am intrigued…"
"I thought you might be, well at least i hoped you would be. I put the extra stuff in "terms" of a cube box which in general i know the volume of. I wanted to see how in general "terms", the volume changes when i increased the side lengths of the box by 1 unit, keeping the cube box form. `i did not want to look at other box shspes, just yet"
"Okay,old bean, i except your "terms" for the "expansion" of the box cube. Is that the right idea? You are not thinking in terms of shrinking the box cube?"
"No , No , chap. Capital! You have the right idea. So i drew a few cubes on some paper and added one unit to the length of each of the sides. The original cube i drew in black ink to make it stand out. It always ended up being in the corner of a much larger cubed box!
So using the drawings i thought i would make one out of a block of wood.
My first attempts were not very successful until i realised i needed to account for the width or thickness of the saw!"
"Oh my god! Yes! Of course! I had not thought of that part. Well spotted old bean!"
"Thanks ,my good fellow!. What that meant was that i could saw out the original block
cube,but then i had to measure and saw out several rectangular blocks of unit height. 3 to be exact, and again 3 parallelepiped blocks of unit height and width and i unit cube!"
" Ha! I see where this is going old bean! If you know the original cube volume you can find the new cube volume by assembling these other blocks around it in the shape f the new cube!"
"Yes! Yes! Yes! Capital old chap! You have truely got it. Of course i could immediately see how this could generalise to any additional length on the sides simply by making these additional blocks thicker accordingly"
"My god , man! You could even generalise that generalisation!"
'I say old chap, you wouldn't care to take me through what you mean by that remark would you…..?'
Well that dear reader is another story.