Fascinating stuff! Thanks for bringing these ideas to light. I'd be interested if you have any suggestions for further reading on these kind of real-world applications of mathematical concepts.
The expansion of a family tree through succeeding generations is my favorite example. The contrast of arithmetic vs. geometric growth made me think of the phrase "the whole is greater than the sum of its parts."
So, wouldn't the next scheme be multiplying exponentially, taking geometric expansion to a new dimension? Would exponents require a 3-D graph to show successive growth?
- By Hand and Eye by Walker & Toplin (about woodworking & design)
- A Pattern Language by Christopher Alexander, Murray Silverstein, and Sara Ishikawa (about city development, social development, and design in general)
- There's probably an agricultural text on this topic but I don't know of it yet. Science in Agriculture seems to be the closest I can think of.
- New Polity's recent podcast on Subsidiarity also goes into some of why "the whole is greater than the sum of its parts" isn't quite the right frame of mind, but is pointing at something.
I've been taking this thought very loosely, really - which I think is fitting. The world is very often nonlinear - it may be multiplicative, exponential, etc. - the exact nature is always different - but the key is that, to quote John Kempf, "we are finding very often that one plus one equals eleven, not two." Don't expect linearity.
Fascinating stuff! Thanks for bringing these ideas to light. I'd be interested if you have any suggestions for further reading on these kind of real-world applications of mathematical concepts.
The expansion of a family tree through succeeding generations is my favorite example. The contrast of arithmetic vs. geometric growth made me think of the phrase "the whole is greater than the sum of its parts."
So, wouldn't the next scheme be multiplying exponentially, taking geometric expansion to a new dimension? Would exponents require a 3-D graph to show successive growth?
Thank you! Some further reading:
- By Hand and Eye by Walker & Toplin (about woodworking & design)
- A Pattern Language by Christopher Alexander, Murray Silverstein, and Sara Ishikawa (about city development, social development, and design in general)
- There's probably an agricultural text on this topic but I don't know of it yet. Science in Agriculture seems to be the closest I can think of.
- New Polity's recent podcast on Subsidiarity also goes into some of why "the whole is greater than the sum of its parts" isn't quite the right frame of mind, but is pointing at something.
I've been taking this thought very loosely, really - which I think is fitting. The world is very often nonlinear - it may be multiplicative, exponential, etc. - the exact nature is always different - but the key is that, to quote John Kempf, "we are finding very often that one plus one equals eleven, not two." Don't expect linearity.