Re: LOGO-L> Re: Total Turtle Trip

[mikedoyle@cix.compulink.co.uk (Mike Doyle)]

In-Reply-To: <v03007808b074865622f3@[139.132.40.201]>
John Gough <jugh@deakin.edu.au> wrote in reply to my comments on Turtle 
Circles that:

> Keep in mind that Logo can handle turtle steps and turtle turns that are
> tiny, regardless of the actual pixel-clumsiness of the resulting 
> graphics.

> What about this? It's not non-standardly infinitesimal, but how small   
> can your brain go?

> to smooth.poly
> repeat 36000000 [fd 1 rt 0.00001]
> end

This illustrates my point beautifully.
Whatever the number input, the procedure is always of the form:

to poly :sides :side
repreat :sides [forward :side right 360/:sides]
end

Which is a definition of a regular polygon. A polygon is not a circle. The 
interesting aspect of Turtle Geometry is in its capability to draw 
polygons far more easily that we can with a pencil and ruler. Thus we are 
able to produce a polygon which is perceptually a circle. I had assumed 
that one purpose of mathematical description was to overcome naive 
perception.

More interestingly, the Logo procedure is a description of the operation 
of moving forward a distance then turning an amount. It is my 
understanding that such process descriptions are new to mathematics, 
arriving only with the computer. Is it legitimate, therefore, to mentally 
extend these process descriptions, which operate only within the finite 
medium of the computer, to the mental realm? Even admitting this, I cannot 
see how a procedure the words of which describe the drawing of a polygon 
may ever be considered to be a description of the process of drawing a 
cirlce.

Michael Doyle (aka Micheal O Duill)
37 Bright Street
SKIPTON BD23 1QQ UK
Tel/fax: +44 (0)1756 794601
Email: mikedoyle@cix.co.uk

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