Double loop LO26087

From: Leo Minnigh (
Date: 02/09/01

[Arbitrarily linked to LO26078 by your host.]

Dear LO'ers

Recently, the expression *double loop* appeared several occasions in
several contributions. The words of Jan Lelie in LO26057, referring to the
"picture galary" of Maurits Escher, triggered a flash in my mind.

At de Lange spend also some words on the double loop (LO26078):

>Using my imagination, I can think of many kinds of "double loops" like
>two loops next to each other ( O O ), a single loop twisted into the
>figure eight ( 8 ), two loops linked into each other to form a chain,

My brain flash was this:

Let's not think in 2 dimensions when thinking of double loops. We probably
all know the band of Moebius. It is 1 loop of a twisted surface (the twist
makes it a double loop). Following the surface of a band of Moebius is
meandering from inside to outside until no distinction could be made
anymore. My own learning looks somewhat like that.

We probably also know what will happen when cutting a band of Moebius
lengthwise: 2 interlinking loops (the number depends on the number of half
twists of the band). Is the appearance of 2 loops out of 1 not a fantastic

Question to At: You have written about intensive and extensive factors and
that extensive factors are scale sensitive and scale dependent: deviding a
battery in two halves means that the extensive factors will be reduced to
half size too. What are the intensive and extensive factors in a band of

Good thinking and learning,

dr. Leo D. Minnigh
Library Technical University Delft
PO BOX 98, 2600 MG Delft, The Netherlands
Tel.: 31 15 2782226
        Let your thoughts meander towards a sea of ideas.


Leo Minnigh <>

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