well, hmmm... I'm not certain this actually describes a fractal; sounds more like an odd sort of Fourier expansion. if I remember correctly, fractal attractors are everywhere non-differentiable, which would never apply to sine curves. I mean, I can see the analogy to a Koch snowflake, I just don't think it flies (the basic element of the snowflake is non-differentiable at three points, but that approaches total non-differentiability as the line length approaches 0...).

I'll point out, in passing, that this is a variation on Zeno's paradox - arguing that an arrow can never hit a target, because first it has to get half way there, and before that, it has to get halfway to that halfway point... the classics are always the best. :-)

that being said, though, problems only occur with these kinds of arguments when the relational chain between objects or events is improperly specified. it's really a question of proper vs. improper induction, and as such it can't really be called a fallacy. it's just a theory that's subject to examination and/or refutation.

Fairly high on a Mac site. Skydivers aren't all that rare, and , based on my observations, freefall videographers use Macs at a rate that is higher than the population as a whole.


If you want to believe that, you are certainly entitled to do so. However, for the purposes of this particular discussion, why the argument fails or doesn't fail IS the topic of discussion. I only needed one example, no matter how unrealistic and contrived (my example was admittedly both), to show that it is misuse, not use, of the slippery slope strategy that leads to a fallacious conclusion.

That's the whole point of the Slippery Slope argument. The first step implies the last step, hence the name slippery slope. (It can also be valid if the first step just increases the probability of the last step, provided that is all that is asserted.)

I've seen more than one cameraman board without a rig. Those damn helmets can be quite distracting. I know of at least one (beginning) skysurfer who did it also. He was most of the way to altitude before anyone noticed. Usually when they check their handles and find they are not there, they become aware of the problem.

Regretfully, I've yet to attempt to find the actual mathematics of the pattern. It was actually by studying Taoism that I thought of it in those terms. But should you come across said mathematics, please let me know. :)

From what little I've read of Chaos Theory, there seems to be a distinction between mathematical fractals and natural fractals. You make a very valid point about the differentiability. I just use the term fractal to represent the self-repeating aspect of the appearance, no matter how closely one zooms in, much like the Mandelbrot set. (If I recall correctly, the Mandelbrot set has only a finite number of "dimensions.")

Yes, I did steal Zeno's process, but eliminated the (since resolved) paradoxical aspect.

True. In the previous thread in System, I mentioned how one can use division improperly to prove that 1 = 0, but it's the improper use of division that creates the fallacy, not division itself.

all fractals have finite dimensions, though generally they are fractional (that's where the name 'fractal' comes from - a corruption of 'fractional dimension'). basically that means that the set is infinite without filling an entire dimension - Mandlebrot, if I remember correctly, is around 1.3 dimensions, meaning it's more than a line but less than an entire plane. also you have to distinguish between the computer enhanced patterns which you see and the attractor, which is more of a mathematical abstraction. for instance, with the Mandelbrot set, the attractor is the set of all points C on the complex number plane such that iterations of the equation Z=Z^2+C never exceeds 2. 2 is not arbitrary or chosen, that's just the way it happens to work out - if it exceeds 2 the equation heads off to infinity. when you see Mandlebrot images, the Mandlebrot set is always in black - colors are generated for points outside the set, according to how quickly Z passes 2 for that value of C.

fun, hunh? :)

they resolved Zeno? seems I missed something. :) what was the resolution?

J Christopher-
It was not my intention to create a math test. I enjoyed the thought exercise, as I too believe in the patterns of nature providing insight into life. I am trying to find my path on the Way.

IMHO the definitive translation of the Tao Te Ching was done by R.L. Wing. If you have not seen it, I highly recommend checking it out at your book store.

Calculus (limits, geometric series, the understanding of instantaneous velocities, etc.)

The Tao that we can speak of is not the eternal Tao.

:D

I will have to track that version down and read it. Thanks for the heads up.

No worries about the maths test. I enjoy maths. No matter how much I learn, I wish I knew more.

ah... that. :rolleyes:

there is no definitive translation of the taote. there is only the tao, ineffable and serene, and the maunderings of old men entranced by its beauty...

that being said, though, I'll look it up. :D

One problem with Zeno's paradox, and probably a problem with the OP's example, is that what actually exists is a continuum; the divisions into smaller parts is imposed by the observer and are artificial, not intrinsic to the situation at all.

That's exactly what the slippery slope argument is meant to highlight.

Having said that, Zeno was one clever fellow, IMO, but I'm more inclined to accept Einstein's conclusions (which built on Newton's work) about motion. :)

Nicely spotted. There's an old joke about a male Engineer and Mathematician being offered the services of a lissome lass standing unclad before them provided only that they approach her by halves. The mathematician declines because he knows he'll never get there, but the engineer accepts eagerly because he knows he'll get close enough.

lol - that joke is almost too true... :)

tw-

Good point.

Perhaps I should have said that I found it to be the most insightful and resonant translation I have read. Have a peek and let me know what you think.