Tri maths
To say I struggle with maths is an understatement but that is not to say that I do not appreciate the problems and puzzles that maths works to solve. On that basis I was reading an interesting book on Philosophy of Maths. I was following a particular line of argument when they were explaining some theory or other using triangles. The theory they were talking about is not relevant here but what got me was when they described starting with a triangle, draw a line to divide the triangle down the middle. This was easy to follow and then they started talking about the 3 triangles.
What 3 triangles? Divide a triangle in two so where is the 3rd triangle. Of course it was obvious (I am slow). The original triangle and the two internal triangles. That makes 3 right? Obvious really.
But it struck me what this means for numbers. I have one thing, I divide it in two and get 3 things. Not conventional maths. 1/2 is 0.5. So where am I going wrong. Well it must be to do with how we treat numbers rather than values. Is the comparison of dividing a triangle down the middle to result in 3 triangles with dividing 1 by 2 and getting 0.5
More brain power is needed on this. But there seems to be a difference between 1 thing and the value of 1. Triangles are 'things' We have one triangle (1 thing) and then divide it and have 3 things. This is actually comparable to dividing 1 by 2. You end up with two halves (2 things) and arguably the original 1. So you have 3 identifiable things.
If this were right then we could also look at subtraction. If you have the divided triangle (3 things) and take away one of the triangles completely you have only 1 thing. Only 1 triangle is left. So equate that to the numbers. You have 1, you divide by 2 to get the 3 things. Take away on of the halves and you get 1 thing left, a half.
So the treatment of 'things' that can be counted is different to numbers and their values.
What 3 triangles? Divide a triangle in two so where is the 3rd triangle. Of course it was obvious (I am slow). The original triangle and the two internal triangles. That makes 3 right? Obvious really.
But it struck me what this means for numbers. I have one thing, I divide it in two and get 3 things. Not conventional maths. 1/2 is 0.5. So where am I going wrong. Well it must be to do with how we treat numbers rather than values. Is the comparison of dividing a triangle down the middle to result in 3 triangles with dividing 1 by 2 and getting 0.5
More brain power is needed on this. But there seems to be a difference between 1 thing and the value of 1. Triangles are 'things' We have one triangle (1 thing) and then divide it and have 3 things. This is actually comparable to dividing 1 by 2. You end up with two halves (2 things) and arguably the original 1. So you have 3 identifiable things.
If this were right then we could also look at subtraction. If you have the divided triangle (3 things) and take away one of the triangles completely you have only 1 thing. Only 1 triangle is left. So equate that to the numbers. You have 1, you divide by 2 to get the 3 things. Take away on of the halves and you get 1 thing left, a half.
So the treatment of 'things' that can be counted is different to numbers and their values.
posted by So long and thanks for all the fish at
9:49 pm
1 Comments:
Blackadder attempts to teach Baldrick how to add, asking if he had "two beans, and [I] add two more beans, what does that make?". Baldrick's conclusions ("Some beans", "Three beans... and that one", and "a very small casserole"), lead Blackadder to comment "To you, Baldrick, the Renaissance was just something that happened to 'other people', wasn't it?" and that "The ape-creatures of the Indus have mastered this"
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