# Geometry on Jeopardy



## pointwithinacircle2 (Jul 11, 2015)

Wednesday night I am watching Jeopardy, minding my own business, when suddenly the answer is "In 240 B.C. Eratosthenes used geometry to accurately calculate the circumference of this".  The answer was the Earth.  What!?!  2255 years ago someone knew how to calculate the size of the earth using geometry?  I never heard that in my geometry class!

I jumped up in the middle of Jeopardy, ran to my computer, and googled this guy.  It turns out that he was a pretty fascinating dude.  His work was studied for hundreds of years after his death (until his was original paperwork was destroyed by religious fervor against science).  Interestingly, his measurement of the earth was much more accurate than those used by Columbus and Magellan 1750 years later.

If you want to read how he did this I suggest you check out this page: http://www.aps.org/publications/apsnews/200606/history.cfm

I also discovered that he accurately measured the tilt of the earths axis.  That story is here: http://www.astro.cornell.edu/academics/courses/astro201/eratosthenes.htm


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## hanzosbm (Jul 11, 2015)

It took me a bit to even figure out how the method he used produced the given results.  Very impressive!


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## pointwithinacircle2 (Jul 12, 2015)

Here is a graphic: http://www.wired.com/2012/06/june-19-240-b-c-the-earth-is-round-and-its-this-big/


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## dfreybur (Jul 13, 2015)

I remember learning of Eratosthenes in elementary school history when we learned about how Columbus pitched Spain to fund his exploration expedition.

I remember the angle of the shadow as a trigonometry problem in high school algebra to show practical applications of trigonometry.

Wasn't he before Hindu-Arabic numerals?  Doing the calculations must have been a bear in his era.  He didn't have a book of tables the way I learned it or an electronic calculator the way it would be done today.


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## hanzosbm (Jul 13, 2015)

dfreybur said:


> I remember learning of Eratosthenes in elementary school history when we learned about how Columbus pitched Spain to fund his exploration expedition.
> 
> I remember the angle of the shadow as a trigonometry problem in high school algebra to show practical applications of trigonometry.
> 
> Wasn't he before Hindu-Arabic numerals?  Doing the calculations must have been a bear in his era.  He didn't have a book of tables the way I learned it or an electronic calculator the way it would be done today.


No joke.  It's been a long time since I've done it, but I'm trying to imagine calculating out the cosine of an angle by hand...repeatedly.  No thank you.


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## pointwithinacircle2 (Jul 18, 2015)

Further ponderings on Geometry:  In reflecting on how Eratosthenes measured the circumference of the Earth I have realized something that I find interesting.  I guess it is a simple thing really, it just never occurred to me before.  In order to know that the angle between two plumb lines could be used to measure the Earth's circumference, he had to have realized that what a plumb line measures is the direction of gravity AND that the center of gravity is the center of the Earth.  I have always thought of being plumb in relation to physical objects.  But in reality it means being aligned with a _force_.  Eratosthenes used a plumb, a fairly small tool, to measure a force so large that pervades the entire universe.  Of course that is Operative Geometry, Operative Masonry, and we work in Speculative Masonry only.

But what if there is a Speculative lesson in there?  Perhaps my old idea of plumb as being "upright enough to stand on my own" is incomplete?  Being Plumb means to to be aligned with a force.  I find that thought worthy of speculation.


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## Canadian Paul (Jul 18, 2015)

That is a very interesting speculation, Brother! It definitely deserves further thought. Might I suggest that you consider re-wording it to read 'to be aligned BY a Force'?


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## hanzosbm (Jul 18, 2015)

So other things that could use some reflection:

Being plumb is perpendicular to being level. Is there a lesson here?

On a sphere, a level would be a tangent. Where have we seen a circle with a tangent, or two? Is there a connection?


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## Archangel Raised (Jul 18, 2015)

You are expanding knowledge, Brother!  The best and brightest use of this sacred forum!

Booyah!


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## Archangel Raised (Jul 18, 2015)

hanzosbm said:


> So other things that could use some reflection:
> 
> Being plumb is perpendicular to being level. Is there a lesson here?
> 
> On a sphere, a level would be a tangent. Where have we seen a circle with a tangent, or two? Is there a connection?




Boom!  Head exploded!  

Puttin' on my thinkin' cap!


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## pointwithinacircle2 (Jul 20, 2015)

If the plumb is used to align objects with a force, what force are we talking about?  In operative Masonry of course that force is gravity, but what force are we talking about in Speculative Masonry?

In the EA lecture we are introduced to the idea that Masonry is supported by Three Great Pillars, denominated Wisdom, Strength, and Beauty, and represented by the three principal officers of the Lodge, the JW, SW, and WM.    Interestingly the column of Wisdom does not belong to the WM, he is assigned the column of Beauty.  The Column of Wisdom belongs to the JW, whose jewel is the Plumb.  It seems to me that the lesson here is that we should align our actions with wisdom.  But even if we accept that the first lesson of Masonry is that we should align ourselves with Wisdom, how are we to understand the nature of Wisdom?  What is it exactly?


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## pointwithinacircle2 (Jul 20, 2015)

This EA trestleboard shows the JW column in the South, the letter W for Wisdom, and leaning against it the Plumb.


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## Canadian Paul (Jul 20, 2015)

These are some very interesting speculations and worth careful thought. May I contribute the following possibility?

It is the Junior Warden's place 'to mark the Sun at its meridian' - that is, when it's rays fall perpendicular to the earth. (That is, if we ignore declination and the curvature of the earth, which, as we are speculative masons moralising on the working tools and other masonic emblems, we are, in my opinion, justified in doing.) As the Sun represents the Divine spreading its influence over the earth then 'wisdom' represents our ability to interpret the vessel of that influence, the VSL, in directing ourselves how to live upright lives. 'Wisdom' is the sum total of the 'hidden mysteries of the Craft' we have been directed to make our study.

Of course, other interpretations are possible. We must each decide for our self which we prefer.


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## pointwithinacircle2 (Jul 20, 2015)

JamestheJust said:


> So what did the God of Israel mean when he said that he had put a plumb line amidst his people and that he would no longer overlook their faults?
> 
> How was that plumb line visible?
> 
> Could that plumb line be used in a moral sense, directly to distinguish right from wrong - or at least obedience from disobedience?


Gravity cannot be detected with the five physical senses.  It's existence can only be deduced by observing it's effect on other things.  I submit that this meets the definition of faith.  My VSL says "Now faith is the substance of things hoped for, the evidence of things not seen."   Belief in the existence of gravity is based on "the evidence of things not seen".  Evidence provided by the plumb.  Of course that would be operative Masonry.

What can this teach to the Speculative Mason?  It has been suggested that we are "aligned with" or "aligned by" a certain force.  And that this force is "intelligence" or "an intelligence".  I wonder if intelligence in it's simplest form would be described as "correct thought"?  Certainly to become aligned with correct thought is a good starting place for any endeavor.  But the question remains, What tool shall we use to determine if our thinking is correctly aligned?


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## dfreybur (Jul 21, 2015)

pointwithinacircle2 said:


> If the plumb is used to align objects with a force, what force are we talking about?  In operative Masonry of course that force is gravity, but what force are we talking about in Speculative Masonry?



The force would be moral rectitude.  I'm dubious that anyone ever intended to push the symbolism to mean moral relativism, but "towards the center" does make sense.  If you're off course steering your moral compass towards the center makes sense.  But which center?  With morality when does it not make sense to move towards the universal center, yet in astronomy we know that there are very many local centers.  The image breaks when expanded too far.



> In the EA lecture we are introduced to the idea that Masonry is supported by Three Great Pillars, denominated Wisdom, Strength, and Beauty, and represented by the three principal officers of the Lodge, the JW, SW, and WM.    Interestingly the column of Wisdom does not belong to the WM, he is assigned the column of Beauty.  The Column of Wisdom belongs to the JW, whose jewel is the Plumb.  It seems to me that the lesson here is that we should align our actions with wisdom.  But even if we accept that the first lesson of Masonry is that we should align ourselves with Wisdom, how are we to understand the nature of Wisdom?  What is it exactly?



The lecture I learned assigns Wisdom to the Master and to Solomon and to the square.


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## hanzosbm (Jul 21, 2015)

pointwithinacircle2 said:


> It has been suggested that we are "aligned with" or "aligned by" a certain force.  And that this force is "intelligence" or "an intelligence".  I wonder if intelligence in it's simplest form would be described as "correct thought"?  Certainly to become aligned with correct thought is a good starting place for any endeavor.  But the question remains, What tool shall we use to determine if our thinking is correctly aligned?


I would say that correct thought or that intelligence that you're speaking of is, and always has been, within us.  It is a force giving us direction, but the force is not easily understood by our five senses.

Using gravity for the allegory, as we stand upright, we know the general direction of what is plumb.  Our senses let us know when we have gone dramatically out of plumb.  And for everyday life, perhaps this is sufficient.  But when building that temple not made by hands, 'good enough' is not.  Therefore, we must be exacting.  As the force of gravity can be used to ensure an exact perpendicular, perhaps we must use the tools we are given outside of our senses to determine the more exact path and uprightness. 
Regarding your question of 'what tool shall we use to determine if our thinking is correctly aligned', that is the question.


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## pointwithinacircle2 (Aug 3, 2015)

dfreybur said:


> The lecture I learned assigns Wisdom to the Master and to Solomon and to the square.


Just curious - to which degree are you referring?


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## dfreybur (Aug 3, 2015)

pointwithinacircle2 said:


> Just curious - to which degree are you referring?



I learned wisdom to the Master as a part of the first degree lecture.  In the slide show version there was a slide showing the three ancient orders of architecture with the pedestal symbols.  Solomon is known for wisdom and for being in charge at the building of his temple.  Hiram of King Tyre is known for strength for funding the construction.  The other Hiram is known for beauty because his design of the temple was beautiful to behold.  Each ancient grand master taking the pedestal seat and symbol per current tradition.

Similar wording appears for the number 3 in the Senior Deacon work in the Staircase lecture as well.  In Texas that lecture got abbreviated and moved to the East.


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