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Brief Summary
Why
153 Fish in John 21:11 ?
What is the significance, meaning, or symbolism,
that John’s Gospel records how Jesus and the disciples caught 153 large
fish in the miraculous catch of John 21 ? What is the Catholic Church
Fathers tradition ? 153 large fish is metaphor for wisdom.
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 : Context of Time
and Place It is
necessary to understand the cultural context of the time and
place when John's Gospel was written. He used the literal event
of the 153 fish in John 21 to doubled as simple
metaphor.
We must not assume our
modern cultural standards were the same as John’s. We
need to train ourselves to look from John’s perspective.
John’s Gospel is commonly
dated as the last one written. The Church at this point was
already actively reaching out to the Greeks. We need to
look through the eyes of a Jewish fisherman who converted to
Christianity, who was writing a Greek Gospel,
from the
ancient
Greek city of Ephesus, at a time in history when the
Church was fully engaged at trying to help convert the
Greeks to the Gospel. St. Irenaeus tells us the Apostle John
lived in Asia and
expressly declares that he wrote his
Gospel at Ephesus
(Against
Heresies III.1.1)
This area of the world had been
heavily influenced by Greek culture even before
Alexander the Great (died 323 BC)
had conquered this whole area all
the way down into Egypt. It was only later that the Romans
came. Pilate had his inscription on Jesus’ cross translated
into Hebrew and Latin, but also into Greek. Cf. John
19:1920. The Old Testament translation that was most often
used by the New Testament writers was the Greek Septuagint
rather than the Hebrew text.. And much, if not all the New
Testament was written in Greek.
Understanding the Greek culture of this
time holds the key to understanding what John meant by 153
fish. 


As will be
explained later, the sequence 3.14 would have
appeared as a completely random number with no significance
to the Greeks in the first century. And
conversely, the number 153 which seems to be a totally
random sequence in today’s culture would have been very
recognizable to the common Greek man in the first century.
So, John could easily use it as a metaphor without the need
to explain its meaning.
The Greeks
To understand why John does not explain his metaphor and why
his meaning would have been obvious to the Greeks, we need
to understand what the Greeks valued. 

What do we
know about the Greeks ?



Greeks and Wisdom
The Greek culture esteemed natural wisdom,
which includes mathematics.
Later we will examine 1 Corinthians 1:2224 and its connection to
John’s use of 153 Fish.
Greek Mathematicians
… 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.
Wikipedia
The Greeks excelled in
natural philosophy and mathematics. They are even credited for creating
the
world’s oldest mechanical computer in about 100 BC. Their
culture esteemed their philosophical and mathematical heroes.
Archimedes was their greatest mathematician and his work on Pi was his
most influential, and most used work. Because of their national pride they would have wanted to
know about his new method for calculating Pi that separated him, and in
essence all Greek culture, from all those who preceded
him.
A few hundred years earlier, the
Pythagoreans had made a ground breaking discovery and proved
what is now called Pythagorean theorem. Pythagoras was from
Samos, just off the coast of Ephesus. This enabled
mathematicians to calculate the sides of a right triangle.
Building on that in the 3^{rd} century BC, was one
of the greatest mathematicians of all time, Archimedes. He
was able to compute with great accuracy the value of pi, π,
using the value of the square root of 3 in his
calculations.
Archimedes, in his book the
Measurement of a Circle, Proposition 3, provided an
entirely new, ingenious, and accurate method for solving for
the value of Pi. His method did not involve any
measurements and was based entirely on mathematical
calculations. It allowed a person to calculate Pi with as
much accuracy as one desired. He began by using √3 and the
ratio 265:153. This ratio
represents the most accurate value of √3 that can be
expressed by using small whole numbers.
Archimedes : Measurement of a Circle :
Proposition 3. 

Here Archimedes begins his calculations
on solving for π, Pi, the measurement of the circumference
of a circle divided by its diameter. Notice how frequently
the number 153 is used.
In the first section, Archimedes calculates
Pi to be slightly less than 3 and one seventh.




Notice above, that in his calculations for the
value of Pi, Archimedes solves for the value
of 10 different line segments. He calculates their values to be the 10
mathematical equations above. If all the mathematical steps had
been written out it would be
over 15 pages long. However, Archimedes just tells how to
construct his diagram and most of the rest of his work consists
only of the ten conclusions, or ten statements above. Even with the 15
pages of calculations  that apparently Archimedes did in his head
 it is
quite amazing that most all these equations end with the number 153.
(Although, the tenth equation does not have 153 in
Archimedes’ original text the equation that I have labeled as number
nine is stated twice by Archimedes, so we still have at least 10 citations,
and usually several more depending on how another author might explain
Archimedes’ work.)
Is this by pure chance ? Rather, it is an
indication of the brilliance and the simplicity of the design of
Archimedes’ solution for solving for Pi, π, where he uses 153 as
the key denominator to which he brings his equations to express.
Why is John’s allusion to Archimedes work not
usually recognized ?
Horizontal Fraction Bar :
Linear
verses Professional Format
While a person might be wise enough to consider the
Greek cultural context during the time of John when he wrote his Greek
Gospel while living in the ancient Greek city of Ephesus and consider
Archimedes and his work which had a tremendous influence on that
culture, such a person is prone to examining Archimedes work written in
modern notation.
However, the
early Greeks wrote their fractions or ratios in
linear form, as seen in the equations above. The use of the horizontal fraction bar came much
later. The
horizontal fraction bar is first attested in the work of AlHassār in
A.D. 12^{th} Century. See
Wikipedia Source.
More details on :
Horizontal Fraction Bar and 153
For example, equation 10 expressed in linear form
above is more likely to be expressed today in modern "Professional"
format as seen below.
Fractions, or ratios, expressed in modern format using the horizontal
bar causes the number 153 to be less conspicuous.
And so, in modern times the number 153 seems to get lost
in the midst of all the other numbers. This could not have been
the case at the time John wrote his Gospel. In his time only the
linear format could have been used.
So, this means that Archimedes would write the
denominator, 153, at the end of his conclusions, at the end of his
equations. This made his use of the number 153 much more
prominent.
And the important point here, is that Archimedes
prominent use of the number 153 made it very easy for St. John the
Evangelist to allude to Archimedes’ wisdom, and by extension to all
wisdom, by using that number, 153, in his Gospel, cf. John 21:11.


See :
Archimedes Math Made Simple and Easy :
A detailed explanation of each mathematical step.



See image below of Archimedes'
work, translated into English 



There is a red underscore to each reference to “153.”
See
Complete Quotation of Archimedes First Section on Pi, π
See
:
Archimedes Math Made Simple and Easy :
A detailed explanation of each mathematical step.
In
the Introduction, Chapter 4, page lxix, this author, Heath, and
expert on Archimedes explains the Greek numbering system.
He picks a “random” number to give an example on how they
wrote numbers. And this random number just happens to be,
yes you guessed it, 153. In other words, you cannot read
through Archimedes work without recognizing the significance
of this key number, 153.
When the Greeks read John’s Greek
Gospel and saw his reference to 153 they could not but help
think of Archimedes, and his greatest work in terms of what
had the greatest influence on others, his work on π, Pi. Pi
is even
called Archimedes’ constant.
Archimedes is “Generally considered the greatest
mathematician of antiquity and one of the greatest of all
time,[3][4]”
The Greeks would have recognized that
by John referring to “153,” John was alluding to all
wisdom, but especially that of the Greeks as represented by
Archimedes and his work on the calculations for the value of
π.
Continue ...
Greeks and Wisdom
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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