I don't agree the area of the Koch snowflake is finite as claimed. The calculation may give the result of finite number - from a fixed point - but as the system is iterating infinity, as is assumed, the area of each added triangle will be real, and these areas infinitely diminishing - asymptotically. If we were to zoom into the 'last' iteration area size where the area goes finite, I am sure we would 'see' iteration continuing and with this diminishing added area. Infinite Series and convergence. There seems to be a paradox here, a practical result conflicting with a calculated result. I think in reality it is both: these infinite series must go on (convergi ng), presenting ever diminishing values, and thus the 'limit' must be irrational, not finite. But I am not going to challenge the finite calculation, I have not the authority or ability to do that. Interesting.
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By Blair Macdonald on
In response to hearing 'economists didn't pick the crash', I did . In 2004 I was teaching economics when I saw and recorded this program (below). I would show it to my student's, and spent the next 4 years being very unpopular to my friends and family saying it's going to slide and the global economy will go with it. They would laugh at me. Quite proud of that now. I had, at the time never heard of Austrian Economics, Peter Schiff or Michael Burry. I argued the crash on the property wealth effect (illusion) and the elasticity of goods in the developed world: if the 'wealth' bubble popped the elastic goods will dry up, and it would be over. Mortgage Madness (1/3): BBC2 - 29/10/2003 There is not a moment I don't think about the real slide coming. My current students don't know about 2008 where I live in Sweden, it was paved over; so I have to teach it as a kind of history lesson. And the current property market is rocketing - everywhere!