[Correction of mistake--A new kind of infinitessimal] - A New Kind of Science: The NKS Forum

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Correction of mistake--A new kind of infinitessimal
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Posted by: Steve Zimmerman

My apologies--I inadvertantly posted a rough draft instead of my final copy of "A New Kind of Infinitessimal."

Here's the correct version of the classical infinitessimal--and this version grew from the rich soil of _NKS_.

Speaking as it were to Computation--for as there is the personification of Wisdom in the Hebrew scriptures (see the Book of Proverbs), so is there the personification of Computation due to _NKS_--one says,

"Describe a 135-degree angle.

"On a horizontal plane, rotate the leg of the angle that is orthogonal to the vertical (toward you would probably work better than away from you).

"At every increment of rotation during the rotation, ask whether the angle described by the rotation is indeed 135 degrees or if it is 45 degrees."

The infinitessimal is here defined technically as the time-point ambiguity between the time that the angle described by the rotation is 135 degrees and the time that it is 45 degrees.

Posted by: Val Smith

135 degrees is integer so you could
simply rotate + or - one half of the
former rotation.

Step 1:+360 degrees, too much
Step 2:-180 degrees, too much
Step 3:-90 degrees, not enough
Step 4:+45 degrees=135 degrees

A 135 degree angle is a rotation thrice-halved,
with a last half added to a second half.

Or 3/4 pi, or 3/8 pizza.

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