4 - three part invention.pdf
TRANSCRIPT
8/17/2019 4 - Three Part Invention.pdf
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Chapter
4
ThreePartInvention
I
hope
I
didn’t
brain
my
damage
–
Homer
Simpson
4.1 Abstract
Bachwrotefifteen three-part inventions. In this three-partDialogue, theTortoiseandAchilles–
themainfictionalprotagonists inthedialogues–are“invented”byZeno(as infacttheywere,to
illustrateZeno’sparadoxesof motion). Very short, it simplygives theflavorof theDialogues to
come. GEB
pp.
viii
4.2 StudyQuestions
1. TowhatEscherprintdoesAchillesreferatthebeginningof thedialogue(Imean,whatdoesthatprint looklike)?
2. What isaMobiusstrip?TowhatprintdoesAchillesrefer?
3. What is the relationshipbetween thehole in theflagand theMbius strip? As soon as the Tortoise
introduces
the
term
Capitalized
Essences,
capitalized
terms
seem
to
abound.
What
are
their
significance?
Write
down
those
whose
significance
you
dont
see
immediately
on
your
Open
Mysteries
page.
4. IsZenothesixthpatriarchor ishenot? If he isn’t,thenwhydoesAchillesthinkhe is?
5. Whatstory isrecreated inthisdialogue?
6. Inwhatways isthisdialogueself-referential?
7. Doyouunderstandthecruxof theparadox(Achilles paradox )thatZenorelates?
8. AreyoufamiliarwiththeDichotomy
Paradox towhichtheTortoiserefers?
9. Isthereanysignificance inpositioningtheTortoiseupwindof Achilles?
10. Useordinaryalgebratofindhowlong itwilltakeforAchillestocatchtheTortoise. AssumethatAchillesrunswithaspeedof 1rodpersecond,sothathispositionisgivenby:
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A(t)=positionof Achillesovertime=0rodsfromstart+(1rod/sec)(tsec)
AssumealsothattheTortoiserunswithaspeedof 1/2rodpersecondandhasaheadstartof 10rods,sothathisposition isgivenby:
T(t)
=
position
of
Tortoise
over
time
=
10
rods
from
start
+
(1/2
rod/sec)(t
sec)
Playaroundwithdifferentvaluesforthespeeds,thensee if youcanderiveaformulaforthetimeatwhichAchillescatches theTortoise intermsof their running speedA (forAchilles)andT(fortheTortoise).TheTortoisealwaysgetsa10rodheadstart.
11. What(if anything) iswrongwithZeno’sargument?
12. What isa“rod”anyway?
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MIT OpenCourseWarehttp://ocw.mit.edu
Gödel, Escher, Bach: A Mental Space Odyssey
Summer 2007
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