- #1
Ashish Shukla
- 1
- 1
Hey,
I have often times wondered what is multiplication? Repeated addition is OK but for some reason it doesn't satisfy me. For example:
2*2cm is linear because it scales 2cm on the same dimension but 2cm*3cm is not scaling, it spans 2 dimensions. It seems as if the flow of operation takes a 90 degree turn when 2nd term i.e. 3cm is multiplied, whereas 2cm + 3cm keeps the operation confined to 1 dimension, if we again multiply 4cm to it i.e. 2cm*3cm*4cm, the flow takes another 90degree turn and now spans 3 dimensions. This makes me think there is much more to multiplication than just repeated addition.
Same with division: if I divide 2cm*3cm*4cm = 24cm^3 by 8 cm, then there are 2 distinct operations here, either divide the value i.e. 24 by 8 first, that would result in 3 cubes of 3cm^3 volume, OR you divide the dimensions first cm^3/cm which would result in an area cm^2 of value 24.
So I think * and / signify construction and deconstruction somehow which is way more than repeated addition and I don't even know what to say for division.
Please help...
I have often times wondered what is multiplication? Repeated addition is OK but for some reason it doesn't satisfy me. For example:
2*2cm is linear because it scales 2cm on the same dimension but 2cm*3cm is not scaling, it spans 2 dimensions. It seems as if the flow of operation takes a 90 degree turn when 2nd term i.e. 3cm is multiplied, whereas 2cm + 3cm keeps the operation confined to 1 dimension, if we again multiply 4cm to it i.e. 2cm*3cm*4cm, the flow takes another 90degree turn and now spans 3 dimensions. This makes me think there is much more to multiplication than just repeated addition.
Same with division: if I divide 2cm*3cm*4cm = 24cm^3 by 8 cm, then there are 2 distinct operations here, either divide the value i.e. 24 by 8 first, that would result in 3 cubes of 3cm^3 volume, OR you divide the dimensions first cm^3/cm which would result in an area cm^2 of value 24.
So I think * and / signify construction and deconstruction somehow which is way more than repeated addition and I don't even know what to say for division.
Please help...