The golden ratio and the number 40.
Four books of the Gospel have parts of a common puzzle
built into their stories of feeding thousands.
Just simple arithmetic.
There’s a math riddle in the Book of Mark that seems easy to solve.
Here’s the full text of the riddle:
“When I brake the five loaves among five thousand, how many baskets full of fragments took ye up? They say unto him, Twelve. And when the seven among four thousand, how many baskets full of fragments took ye up? And they said, Seven” (Mark 8:17-21 (KJV)).
It would appear that the solution to this math riddle is simple. Just add up the six numbers in the verses (5 + 5 + 12 + 7 + 4 + 7, dropping the “thousands”) and it adds up to 40, a special number in the Bible, as in:
>> 40 years of Hebrews wandering in the desert,
>> 40 days and 40 nights of rain in the Great Flood,
>> 40 days and 40 nights of Jesus’ fasting,
>> Moses receiving the Ten Commandments after fasting 40 days and 40 nights, and
>> bread-like “manna” in the desert feeding Hebrews daily for 40 years.
“Mark” has Jesus recite the riddle above and then has him hint, “How is it that ye do not understand?” This is after he has Jesus ask, “perceive ye not yet, neither understand? have ye your heart yet hardened? Having eyes, see ye not? and having ears, hear ye not? and do ye not remember?” I can’t prove to you that Mark intended this to be a math riddle. Maybe he had something else in mind. But something is supposed to happen at this point in the biblical text – why else all the questions from Jesus?
Maybe the events happened exactly as stated and the numbers actually added up to 40, and thus, Mark’s tally is actually an historical account. And maybe Mark is so excited about the numbers adding up that he can’t help pointing to them.
Then when I see that “Matthew” has exactly the same numbers in his “loaves and fishes” stories as Mark, yet he does not summarize the numbers like Mark, and thus does not point to the number 40 like Mark, I have to ask what is going on. Matthew, who supposedly wrote after Mark (even though Mark follows him in the Bible), does not know how to copy text? He inadvertently left it out? He doesn’t include the math riddle because he doesn’t get it? Quite a contrast. (I say “he” throughout without knowing the gender of each book’s contributor(s).)
I suppose Mark’s math riddle could be meant to impress the reader with a “special” number – 40. But were first-century readers so unsophisticated that they could be impressed just because the number 40 turned up? The answer may be that they rather expected to have their spiritual sustenance delivered with garnishments such as numerology. They were being served what they wanted. Would you go to a first-class restaurant and not order dessert? Same thing.
I find that the math riddle has the effect of releasing me, freeing me from attachment to the story, as I begin to realize that the story might be more figurative than literal, and the numbers could be a fabrication and could indicate that the whole story is simply a fabrication. All of it??. Maybe constructed in such a way that I can experience detachment.
I become aware that I am beginning to experience detachment. As I question the story and doubt builds, I am aware that the story is disintegrating and fading in front of me. I come to a realization of its fragility. I become aware of the impermanence of all forms. Quite a spiritual journey!
Did Mark’s author (and Matthew’s, also), fabricate some numbers and make them add up to 40 just to make the person Jesus seem more “special”? Or are the numbers real and they just happen to add up that way? It shouldn’t really matter to us if we understand that the author’s intention was not to record history, but rather to make a point. Somehow Mark’s mysterious number riddle helps the author make a point. And gets our attention!
I have come to understand that the texts are supposed to challenge the reader (especially where there are contradictions, discrepancies, or riddles), be stimulating, be a spiritual exercise, be uplifting, and increase our awareness. Sacred math is very appropriate to such purposes, as we contemplate the perfection of the Design and the intent of the Designer.
Well, I wrote all that, then I thought to myself, that the author of the Book of Mark must have had something more earth-shattering in mind than just making numbers add up to 40. It’s a simple riddle. Maybe too simple for the sophisticates of the 21st century, with so much available via videos, books, the Internet, etc.
But it made me feel pleased to figure out this riddle.
Of course Jesus’ insistent questions can be taken on another level – did the disciples understand the “loaves and fishes” happening? Do we?
Update – Easter Sunday, April 24, 2011:
Well, I was suspicious that wasn’t the complete puzzle and went at it again.
There are seven passages in the Gospel that tell about feeding crowds of thousands following Jesus. There are lots of numbers in these passages.
I carefully wrote out the numbers I found in each. I discovered that the sum of the numbers in the first three passages divided by the sum of the numbers in the remaining four passages equals the golden ratio to three decimal places:
23355 divided by 14428 = 1.6187 . . . .
Here are the numbers in each set of passages in the order in which the passages and numbers appear in the four books of the Gospel:
Matthew 14: 5, 2, 5, 2, 5000, 12
Matthew 15: 3, 7, 7, 7, 4000
Mark 6: 200, 5, 2, 100, 50, 5, 2, 2, 12, 5000
Total : 14428
Mark 8: 3, 7, 7, 7, 4000
Mark 8 (a summary of two feedings): 5, 5000, 12, 7, 4000, 7
Luke 9: 5, 2, 5000, 50, 5, 2, 12
John 6: 200, 5, 2, 5000, 12, 5
Grand total: 37783
Did the puzzle creator in the first century realize he/she had number totals whose first three digits are identical to some Fibonacci numbers – 144, 233, and 377? Fibonacci published in the 12th century. Nevertheless, the biblical author could have built the puzzle around such knowledge, if it existed earlier, while at the same time opting to include “special” numbers like 40, 12, and 7. Or the puzzle could have been built instead around a core number of 14428 based on (12 x 12 x 100) + (4 x 7), all special numbers I’ll guess since they are used so often in the New Testament.
I think I may have found the solution to this puzzle, not because I get a particular quotient (1.618), but because the answer falls out cleanly and very easily by comparing passages. I don’t have to mine for numbers – they are already arranged by the biblical author in discrete sets.
Is it an error to combine the various books of the Gospel to work a puzzle? Maybe it would be an error not to. I have no problem considering the possibility that this puzzle was inserted piecemeal into all four books by one person, or its construction within the four books was coordinated by just one person.
But maybe it’s just a coincidence that “1.618” shows up in the loaves and fishes stories.
Just a coincidence? What are the odds?
Can you find what isn’t there? Sure. Just squeeze the numbers enough. But I believe I know a real puzzle and a real solution when I see it, even though I can’t prove it’s real.
Does all that math ruin the spiritual lesson in the story for me? Not at all. I appreciate it even more, knowing that the author had an orderly and clear mind. It adds value for me. It makes me want to learn more about this person’s way of thinking.
Update – Sunday, July 17, 2011:
I finally realized I inadvertently left out the numbers in the summary of two feedings in Matthew 16:9-10. I was very tempted to just take down the golden ratio discussion in this post, but have refrained from doing so because I get such an interesting result by not including Matthew’s summary. I suppose there is a chance it might be just text added by an editing copyist trying to harmonize Matthew with Mark, and thus not part of the puzzle??