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Brief Summary
Why 153 Fish in
John 21:11 ?
Sections :
Introduction
Church Fathers : Sts. Jerome, Augustine, Gregory the Great, Cyril A.
No Reason ?
Why Church Fathers’ Answers Could Not Be John’s
Problems with Square Root of 3 Answer
Context Points to the Answer : An Explanation That Works
Archimedes : Context of Time and Place
Greeks and Wisdom
Fish
Calculating the Measure of the Fish
John’s Purpose
Why Church Fathers Did Not (could not?) Give John’s Idea
Conclusion
Archimedes and The Greeks and Their Works
The following article gives more additional
information on Archimedes and about the following two questions besides
what is already presented in the main article about John 21:11 and the meaning of “153 fish.”
First Question
If John’s reference to “153 fish” was a sure
reference to the wisdom of the Greeks as exemplified by Archimedes in
his Proposition 3 and with John’s pastoral objective of designating that
all wisdom comes from Jesus who is the Son of God, then why do the early
Church Fathers not recognize and state this connection ?
A second question.
Is there a reasonable likelihood that the Greeks of
Ephesus at the time of John’s writing would have had knowledge of
Archimedes new method for calculating the value of π in the
Measurement of a Circle, Proposition 3?
This article below on Archimedes relates how his
work was not as wellknown as Euclid’s. Euclid’s book Elements was a
systematic work that began with the basic principles that progressed
into deeper mathematics. It was a compilation of others’ works. It was
a primer for education. On the other hand, many of Archimedes’ works
were on specialized topics. And so, Archimedes’ work itself was not as
well published as Euclid’s.
The inventions and the glory of Greek
mathematical wisdom were enormous.
Notes from Wikipedia
Euclid's Elements
… Euclid's Elements has been referred to
as the most successful^{[5]}^{[6]}
and influential textbook ever written. Being first set in type in
Venice in 1482, it is one of the very earliest mathematical works to
be printed after the invention of the printing press and was
estimated by Carl Benjamin Boyer to be second only to the Bible in
the number of editions published,^{[7]
… }For centuries, when the
quadrivium was included in the curriculum of all university
students, knowledge of at least part of Euclid's Elements was
required of all students. Not until the 20th century, by which time
its content was universally taught through other school textbooks,
did it cease to be considered something all educated people had
read.^{[9]}
Archimedes of Syracuse (c. 287 BC – c. 212 BC)
was an Ancient Greek mathematician …
Archimedes died during the Siege of Syracuse
when he was killed by a Roman soldier despite orders that he should
not be harmed. …
Unlike his inventions, the mathematical
writings of Archimedes were little known in antiquity.
Mathematicians from Alexandria read and quoted him, but the first
comprehensive compilation was not made until c. 530 AD by Isidore of
Miletus in Byzantine Constantinople …
The relatively few copies of Archimedes'
written work that survived through the Middle Ages were an
influential source of ideas for scientists during the Renaissance,^{
}
^{
[6]} ….
During his youth, Archimedes may have studied
in Alexandria, Egypt, where Conon of Samos and Eratosthenes of
Cyrene were contemporaries. He referred to Conon of Samos as his
friend …
According to the popular account given by
Plutarch, Archimedes was contemplating a mathematical diagram when
the city was captured. A Roman soldier commanded him to come and
meet General Marcellus but he declined, saying that he had to finish
working on the problem. The soldier was enraged by this, and killed
Archimedes with his sword. ...
The last words attributed to Archimedes are "Do
not disturb my circles", a reference to the circles in the
mathematical drawing that he was supposedly studying when disturbed
by the Roman soldier. This quote is often given in Latin as "Noli
turbare circulos meos," …
Writings
The works of Archimedes were written in
Doric Greek, the dialect of ancient Syracuse. The written work of
Archimedes has not survived as well as that of Euclid, and seven of
his treatises are known to have existed only through references made
to them by other authors. Pappus of Alexandria mentions On
SphereMaking and another work on polyhedra, while Theon of
Alexandria quotes a remark about refraction from the nowlost
Catoptrica.[b] During his lifetime, Archimedes made his work known
through correspondence with the mathematicians in Alexandria. The
writings of Archimedes were first collected by the Byzantine Greek
architect Isidore of Miletus (c. 530 AD), while commentaries on the
works of Archimedes written by Eutocius in the sixth century AD
helped to bring his work a wider audience. …
Surviving works
This is a short work
consisting of three propositions. It is written in the form of a
correspondence with Dositheus of Pelusium, who was a student of
Conon of Samos.
(see note below on the numbering of the
propositions.)

Although Arhcimedes lived
in Syracuse, that was part of what was then considered Magna
Graecia (Latin meaning “Great Greece”) or Greek:
Μεγάλη Ἑλλάς, Megálē Hellás 

See
Map

https://en.wikipedia.org/wiki/Conon_of_Samos
Conon was born on
Samos,
Ionia, and possibly died in Alexandria, Ptolemaic Egypt, where
he was court astronomer to Ptolemy III Euergetes.
So, we can see that as we examine cultures outside
of the area of Greece Archimedes text would have become less known.
Surely, they would have known about his final conclusions on the value
of π, but the Church Fathers may not have had his actual text so that
could see the importance that the number 153 played in his calculations.
As for the second question, the Greeks in Iona, in
Ehpesus would have placed a high value on knowing and having Archimedes
actual text. The 250 to 300 year time span between Archimedes writing
and that of John was sufficient for Archimedes work to have been circulated
to the Greek areas. At the time of John the Greek culture in Ephesus
would have still been strong and not yet given way to the influence of
the Romans. While by the time the Church Fathers wrote the Greek
influence would not have been as strong in the other areas of the Roman
Empire where they lived.
The Greeks had ruled the whole
Mediterranean Sea.
Ancient Greek culture was probably at its
peak about the time of John writing his Gospel. The Romans, the Latins,
had ruled since the time of Julius Caesar, but the Greeks probably
thought of them as just an occupational force. The culture was still
Greek in Ephesus.
Why was Archimedes so
important?
To understand this we
need to understand ancient Greek culture. Above all else the Greeks
esteemed philosophy, mathematics and wisdom.
https://en.wikipedia.org/wiki/Greek_mathematics
Greek mathematicians
lived in cities spread over the entire Eastern Mediterranean, from
Italy to North Africa, but were united by culture and language. The
word "mathematics" itself derives from the ancient Greek μάθημα (mathema),
meaning “subject of instruction”. …
One of the most important characteristics of the Pythagorean
order was that it maintained that the
pursuit of philosophical and mathematical studies was a moral basis
for the conduct of life. Indeed, the words philosophy
(love of wisdom) and
mathematics (that which is learned) are said^{ }to have
been coined by Pythagoras. From this love of knowledge came many
achievements. It has been customarily said^{ }that the
Pythagoreans discovered most of the material in the first two books
of
Euclid's
Elements.
The Greek’s pride was in their wisdom.
Every Culture worship something or at least
that idealizes something
Every culture has a cult. I mean this in
the good sense of the word. Archimedes was more influential and was a
greater hero than the Apollo mission astronauts were to Americans in the
1970’s. The Greek culture in the time of John would have esteemed
Archimedes more than our current culture looks up to Albert Einstein.
Archimedes and his use of
the number 153 was more important to the Greeks than Albert Einstein is
to the Americans, and so we can reasonably conclude Archimedes work was
well known among the Geeks, as Albert Einstein and his formula E=MC^{2},
is known to the Americans.
Surely some will argue
that many of Archimedes other accomplishments were more profound than
his work on Pi. Archimedes himself valued his favorite mathematical
proof on a sphere and a cylinder of the same height and diameter.
Archimedes had proven that the volume and surface area of the sphere are
two thirds that of the cylinder including its bases. He had even
requested that his tomb be surmounted
by a sphere and a cylinder.
However, most people will
only need to know this on a math test. On the other hand every culture
has shown a need for an accurate value of Pi. No one wants to travel
across the arc of a bridge that almost spans the width of a river from
one side to the other. No one wants to walk under an arch of a doorway
that is precariously balanced between door posts because it is almost
wide enough to fit safely. Even if one does not need to know the value
of π directly, he has an indirect need that others know it such as
architects.
The detail of 153 fish
seems too specific to be insignificant.
More from Wikipedia
Pythagoras of Samos
c. 570 –
c. 495 BC)^{[3][4]}
was an
Ionian
Greek philosopher, mathematician, and has been credited as the
founder of the movement calle d
Pythagoreanism. … He was born on the island of
Samos, and traveled, visiting Egypt and Greece, and maybe India,
and in 520 BC returned to Samos.^{[5]}
Around 530 BC, he moved to
Croton, in
Magna Graecia, and there established some kind of school or
guild. ...
…
Pythagoras (c. 570 – c. 495 BC) as it is he who, by tradition,
is credited with its first recorded
proof. ...
Magna Graecia (Latin meaning "Great Greece",
is the name of the coastal areas of Southern Italy on the Tarentine
Gulf that were extensively populated by Greek settlers; particularly
the Achaean settlements of
Croton, … The settlers who began arriving in the 8th century BC
brought with them their
Hellenic civilization, which was to leave a lasting imprint in
Italy,



Euclid
(300 BCE), sometimes called Euclid of
Alexandria,
was a Greek mathematician, often referred to as the "father of
geometry". ...
Euclid's Elements has been referred to as the
most successful[5][6] and influential[7] textbook ever written.
Being first set in type in Venice in 1482, it is one of the very
earliest mathematical works to be printed after the invention of the
printing press and was estimated by Carl Benjamin Boyer to be second
only to the Bible in the number of editions published,[7] with the
number reaching well over one thousand.[8] For centuries, when the
quadrivium was included in the curriculum of all university
students, knowledge of at least part of Euclid's Elements was
required of all students. Not until the 20th century, by which time
its content was universally taught through other school textbooks,
did it cease to be considered something all educated people had
read.^{[9]}


Notes:
One Wikipedia web page has Archimedes' third
proposition on Pi mislabeled as his second. Perhaps the mislabeling was
based on the error below.
Quote:
http://web.archive.org/web/20151124100810/https://en.wikipedia.org/wiki/Measurement_of_a_Circle
Proposition two
Proposition two states: ...
This proposition could not have been placed
by Archimedes, for it relies on the outcome of the third proposition.^{[3]}
This argument has no foundation. An examination of
different cultures reveals how values and priorities vary. While we
might value having things numbered according to historical sequence
there is no overarching reason why others would need to value that more
than some other standard. Standards vary. When personal computers were
first becoming popular one computer geek made famous the line, “One
thing nice about standards is that there are so many.” Individuals
think differently from others. Cultures separated by thousands of
years, do so even more.
There are a host of reasons why Archimedes might
have desired to number his work on Pi as his Third Proposition. My
personal favorite guess is that since Pi has a value of about 3, he
thought it appropriate that it be placed 3^{rd}. For Archimedes
the number 3 might have held some special personal importance that made,
in his mind, a certain appropriateness for his work on Pi.
On the other hand, he may have started to explain
his second proposition to someone who already was aware of his work on
Pi, but after he started writing down his second proposition he later
decided to include his work on Pi for the benefit of others who did not
know about it. The inclusion of Pi could have been an afterthought.
Rather than discard expensive sheepskin, and valuable labor, and start
over he just decided to append his previous work.
The Greek tended to place a certain importance on
numbers that may seem odd to our standards. Consider the early Church
Fathers and the number 22 in regards to the Canon of the Old Testament.
Many of the early Church Fathers placed some
importance on the number of letters in the Hebrew alphabet. When listing
the books that belonged in the Old Testament, they stated that there
were 22 books in it. How they numbered them seems quite forced in order
to arrive at the number 22. Not all the books always made the cut in
order to get the total to equal 22. Finally, St. Augustine who does
include the full Old Testament canon found himself needing to double the
total to “44 books” in order to get them all included. But, even then he
seems to have the need for the total to equal a product of those 22
letters, 2 x 22 = 44.
St. Athanasius in The ThirtyNinth Festal Letter,
Jurgens 1:341, PP 791
“Old Testament … 22 books”
St. Cyril of Jerusalem in Catechetical Lectures,
4:34, Jurgens 1:352, PP 819
“Old Testament … 22 books”
St. Hilary of Poitiers, Jurgens 1:383, PP 882
“Old Testament … 22 books”
St Gregory of Nazianz, Poems, Jurgens 2:42
“twelve historical books … therefore, 22 old books,
Corresponding to the number of the Hebrew letters.”
St. Jerome, The Galeatic or Helmeted Prologue,
Jurgens 2:207, PP 1397,
“ … there are 22 letters ... so too there are 22 books”
St. Augustin of Hippo, Christian Instruction,
2.8.13, Jurgens 3:53, PP 1585.
“ … 44 books the authority of the Old Testament is concluded.”
St. John Damascene in The Source of Knowledge,
3.4.17, Jurgens 3:340, PP 2373
“ … 22 books, one for each letter of the Hebrew language”
(Jurgens Book# : Page #, PP = paragraph #) 
Continue ...
Fish 
Sections :
Introduction
Church Fathers : Sts. Jerome, Augustine, Gregory the Great, Cyril A.
No Reason ?
Why Church Fathers’ Answers Could Not Be John’s
Problems with Square Root of 3 Answer
Context Points to the Answer : An Explanation That Works
Archimedes : Context of Time and Place
Greeks and Wisdom
Fish
Calculating the Measure of the Fish
John’s Purpose
Why Church Fathers Did Not (could not?) Give John’s Idea
Conclusion
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