Arithmetic - What does it mean to you?

[Doug Freyburger]

Masonic ramblings,

The fourth in the list of the Seven Liberal Arts and Sciences is
arithmetic. Since Isaac Newton was alive at the time the first Grand
Lodge was founded in London in 1717 I will take arithmetic more
generally as algebra and I will use the two words interchangeably.
Arithmetic is reason quantified. It remains in the abstract realm but
it steps towards the physical world.

Like architecture, the progress of arithmetic can be traced throughout
history. Counting was learned, then addition, subtraction,
multiplication and division. Fractions were learned then abstracted
into algebra about a thousand years ago. In the same century as the
first Grand Lodge was formed, Newton and Leibnitz unified algebra and
geometry to form the calculus. Well educated Masons in the 1700s
probably saw the sequence of logic, arithmetic and geometry as a lesson
in building unity.

Algebra is more than logic. Algebra is a method and a set of rules
that can predict numbers and magnitudes based on the magnitudes of the
starting situation. Both arithmetic and geometry treat magnitudes.
Consider that in the sequence of the seven liberal arts and sciences.
Grammar is about being understood. Rhetoric is about convincing
others. Logic is about finding the truth. Algebra is about figuring
out how much the correct amount is. Looking back to the lessons of the
first degree logic is a tool to figure out how to adhere to the
principle tenet of truth and arithmetic is a tool to figure out how
much the cardinal virtue of prudence is.

Once we have the means of determining magnitudes we can begin to work
on our actions. What is too little or too much? Morality includes
proportional reactions and scheduler proactive planning. Arithmetic
ranges from a basis of our moral judgment to keep us from excess to a
basis or our planning to make us effective in pursuing our goals.

How do you apply arithmetic or algebra in your day to day life? How do
you fit it into the pattern of the seven liberal arts and sciences?

Fraternal regards,
Doug Freyburger
PM 2007/8 Arlington Heights 1162 Illinois AF&AM
PM 1999 Pasadena 272 California F&AM

[Chris H]

Post by Doug Freyburger
Masonic ramblings,
The fourth in the list of the Seven Liberal Arts and Sciences is
arithmetic. Since Isaac Newton was alive at the time the first Grand
Lodge was founded in London in 1717

Though Freemasonry was alive and well for well over a century before.

Post by Doug Freyburger
I will take arithmetic more
generally as algebra and I will use the two words interchangeably.

Algebra is not arithmetic it is mathematics.
Algebra should probably come under Logic in the Trivium

but I am just nit picking :-)

[Doug Freyburger]

Post by Chris H

Post by Doug Freyburger
I will take arithmetic more
generally as algebra and I will use the two words interchangeably.

Algebra is not arithmetic it is mathematics.

One good feature of symbolism is each person sees a different meaning in
each symbol. Since my discussion is symbolic and asks for other
interpretations, thank you for yours.

Arithmetic, geometry, algebra and calculus are all mathematics to most
who study them.

Post by Chris H
Algebra should probably come under Logic in the Trivium

Can logic be classed as a part of mathematics? It can but it usually is
not. Can mathematics be classed as a part of logic? It can but it
usually is not. Let's call them both allied fields within philosophy.

Calculus is the unification of algebra and geometry. That was a stated
goal for calculus. I've never encountered a history of algebra that
describes it as a unification of previous arts and sciences. I like to
view algebra as a unification of logic and arithmetic.

[Torence]

If you accept the common definition that “Algebra is the branch of
mathematics concerning the study of the rules of operations and
relations, and the constructions and concepts arising from them,” then
its application to FreeMasonry is made plain. Lodges and Grand Lodges
are incorporations for purpose, though I would state that to be viable
their purpose must be suitable for the time and place in which they
are at work. How we operate, who we incorporate, what constructions we
plan and the tenets that are then derived may just be capable of being
expressed in algebraic form.
Would any of you engineers like to have a stab at it?

Fraternally,
Torence Evans Ake
Secretary – Auburn Park Lodge No. 789 – Crete, Illinois
PM – Arcadia Lodge No. 1138 – Lansing, Illinois

[Chris H]

If you accept the common definition that “Algebra is the branch of
mathematics concerning the study of the rules of operations and
relations, and the constructions and concepts arising from them,”

I agree with that.
However algebra is not a branch of arithmetic.

are at work. How we operate, who we incorporate, what constructions we
plan and the tenets that are then derived may just be capable of being
expressed in algebraic form.

No. I don't agree there.

Would any of you engineers like to have a stab at it?

I am an Engineer.

[Torence]

Using that vast store house of accurate knowledge, Wikepedia, the
Seven Liberal Arts and Science (liberalia studia) are described as
the proper education for a free man “unlike the education proper for a
slave.” Perhaps that is why so many in my class of Mason, us
Secreataries, do not take much time to study them. I always point out
that in our positions we cannot be fired. Slaves have to be sold.
The subjects that would become the standard "Liberal Arts" in Roman
and Medieval times comprised the basic curriculum in the "enkuklios
paideia" or "education in a circle" of late Classical and Hellenistic
Greece. In the 5th century AD, Martianus Capella defined the seven
liberal arts as: grammar, dialectic, rhetoric, geometry, arithmetic,
astronomy, and music.
The term “dialectic” is decidedly different from Logic. It is
argument. Slaves, of course, would not be taught how to argue and I
wonder who altered (probably Hutchinson) our count of the seven to
omit argument and replace it with logic? Rehetoric is a singular
oration or monologue; and Grammar is the structure of words in context
to their use. So nearly half of the seven are focused on language and
the various forms used to communicate.
But of the other categories for study, Geometry, Arithmetic,
astronomy and music, it seems to me that the big “G”, little “a” & “m:
have little to do with each other. While Arithmetic, the big “A” is a
shared component of the other three.
Arithmetic, then, is important as the unifier; and like an
intelligent leader who has the capacity to bring men who would
otherwise remain at a perpetual distance together for one laudable
purpose or another, the use of Arithmetic and study of this particular
science should then be important for us all.

Fraternally,
Torence Evans Ake
Secretary – Auburn Park Lodge No. 789 – Crete, Illinois
PM – Arcadia Lodge No. 1138 – Lansing, Illinois

[Chris H]

Post by Doug Freyburger

Post by Chris H

Post by Doug Freyburger
I will take arithmetic more
generally as algebra and I will use the two words interchangeably.

Algebra is not arithmetic it is mathematics.

One good feature of symbolism is each person sees a different meaning in
each symbol.

In some cases but not all.... many symbols have VERY precise meanings.

Post by Doug Freyburger
Since my discussion is symbolic and asks for other
interpretations, thank you for yours.

I did say I was nit picking. :-)

Post by Doug Freyburger
Arithmetic, geometry, algebra and calculus are all mathematics to most
who study them.

Correct. Mathematics NOT Arithmetic.

Post by Doug Freyburger

Post by Chris H
Algebra should probably come under Logic in the Trivium

Can logic be classed as a part of mathematics? It can but it usually is
not.

Yes it can. Very much so. Ask any computer scientist.

Post by Doug Freyburger
Can mathematics be classed as a part of logic? It can but it
usually is not. Let's call them both allied fields within philosophy.

In philosophy anything can be anything :-)))))

Post by Doug Freyburger
Calculus is the unification of algebra and geometry. That was a stated
goal for calculus. I've never encountered a history of algebra that
describes it as a unification of previous arts and sciences. I like to
view algebra as a unification of logic and arithmetic.

Fair enough.

[SINNER]

Post by Chris H

Post by Doug Freyburger

Post by Chris H

Post by Doug Freyburger
I will take arithmetic more
generally as algebra and I will use the two words interchangeably.

Algebra is not arithmetic it is mathematics.

One good feature of symbolism is each person sees a different meaning in
each symbol.

In some cases but not all.... many symbols have VERY precise meanings.

Well, I went to a local conference this past weekend and it was made
abundantly clear that since we dont have the ability to ask those that
adapted the symbolism that what you say may be true as far as 'widely
accepted meaning' of a particular symbol, but it many cases there is
something left to the mason to interpret.

FWIW, the Conference was:

http://www.northtexashistory.org/?page_id=18

and the discussion in particular was The Winding Stairway.

I was hoping they would post the Powerpoint and notes that went along with
it but it has not been published yet.

[Mudge]

Doug Freyburger writes

Post by Doug Freyburger
Masonic ramblings,
The fourth in the list of the Seven Liberal Arts and Sciences is
arithmetic. Since Isaac Newton was alive at the time the first Grand
Lodge was founded in London in 1717

Though Freemasonry was alive and well for well over a century before.

Post by Doug Freyburger
I will take arithmetic more
generally as algebra and I will use the two words interchangeably.

Algebra is not arithmetic it is mathematics.
Algebra should probably come under Logic in the Trivium
but I am just nit picking :-)

Is it nit season in the UK ???

Careful - some of them can give one a narsty bite !

[David Simpson]

Post by Chris H

Post by Doug Freyburger
Masonic ramblings,
The fourth in the list of the Seven Liberal Arts and Sciences is
arithmetic. Since Isaac Newton was alive at the time the first Grand
Lodge was founded in London in 1717

Though Freemasonry was alive and well for well over a century before.

Post by Doug Freyburger
I will take arithmetic more
generally as algebra and I will use the two words interchangeably.

Algebra is not arithmetic it is mathematics.
Algebra should probably come under Logic in the Trivium
but I am just nit picking :-)

Exactly.

[Torence]

Post by Doug Freyburger
Masonic ramblings,
The fourth in the list of the Seven Liberal Arts and Sciences is
arithmetic. Since Isaac Newton was alive at the time the first Grand
Lodge was founded in London in 1717 I will take arithmetic more
generally as algebra and I will use the two words interchangeably.

Before 1717 there were many gatherings of Grand leadership for the
Operative Craftsmen, York -926, Strasburg – 1275, Ratisbon-1464,
Spire-1469, Cologne-1535, Strasburg – 1563, etc. and for them the use
of Arithmetic was a more of a practical necessity then a speculative
science. Though the average workman was illiterate, all needed to
measure and fit. As for the leadership, a good grounding in arithmetic
was required as they were tasked with the details of funding the large
building projects going on in those places. The people built the
cathedrals while the rich only invested in them to either save their
debauched souls or to puff themselves up in grandiose expression. The
care that the Grand Leadership exercised in spending public funds
became famous particularly at Strasburg and indicative to define who
we Masons are and of what stuff we are made of …our love of
Arithmetic, then, goes to argue for our more sensible and practical
qualities.
You mention Sir Isaac Newton. I always imagined him, Indigo Jones
and Christopher Wren in collaboration; and I think that there is room
here to ponder the connection, if any, that FreeMasonry had to the
Royal Society.

Post by Doug Freyburger
Well educated Masons in the 1700s
probably saw the sequence of logic, arithmetic and geometry as a lesson
in building unity.

We owe our discussion along these lines, IMHO, to the interests of
Augustus, HRH the Duke of Sussex. Augustus thumbed his nose at his
father to marry who he chose in Rome against the Royal Marriage Act.
He fathered Augustus Fredick d’ Este who also became a Grand Officer
upon his majority. Augustus was made a Mason in Berlin and then,
having had this continental experience, joined the Prince of Wales
Lodge when he was back in England. His interests in the sciences were
so great that he spent his fortune to build a library. After all, no
man can take “it” with him.
Wholesome popular entertainments of the day were usually of the
religious sort. Unwholesome entertainments have always been what they
have been. Lecturing on science, music recital and other intellectual
pursuits offered another opportunity for a man to better himself and
it was the Duke who saw to it that these subjects were offered to the
Craft. So, your theorem is correct in a very specific way. Discussion
on these three topics did assist in healing the split and unifying our
fraternity.

Post by Doug Freyburger
Algebra is about figuring out how much the correct amount is.

Arithmetic, IMHO, is all about raising questions. The mathematician
opens up for us a problem and we are tasked with solving it. The 47th
Problem , IMHO, is more beautiful in its expression than it is in its
solution. Masons must be able to solve problems and if the skill is
not natural to a man who makes himself into a Freemason, then that
ability is one to be developed. We have been at all times and in all
places problem solvers. Arithmetic, then, is essential for us all.

Post by Doug Freyburger
How do you apply arithmetic or algebra in your day to day life? How do
you fit it into the pattern of the seven liberal arts and sciences?

In daily life, particularly for those of us who operate a business,
the numbers are all about making connections. There is a dance that
goes on with pricing where too much margin will stunt product
movement, too little will make the investment in the cost of the goods
and their handling not worthwhile. Labor hours must be invested
properly. Too much and the business goes broke. Too little and
customer service fails. Making it all add up is the pursuit of many;
but like power, success with it is the privilege of too few. Assaults
on the formula come from many selfish sources and good arithmetic will
always argue for a man to do better business that will prove itself to
be a benefit to all that are concerned with it.

Fraternally,
Torence Evans Ake
Secretary – Auburn Park Lodge No. 789 – Crete, Illinois
PM – Arcadia Lodge No. 1138 – Lansing, Illinois

[Doug Freyburger]

Post by Torence

Post by Doug Freyburger
Since Isaac Newton was alive at the time the first Grand
Lodge was founded in London in 1717 I will take arithmetic more
generally as algebra and I will use the two words interchangeably.

You mention Sir Isaac Newton. I always imagined him, Indigo Jones
and Christopher Wren in collaboration; and I think that there is room
here to ponder the connection, if any, that FreeMasonry had to the
Royal Society.

http://www.cafreemason-digital.com/cafreemason/20100607#pg16

There was an article on that topic in the most recent edition of the
California Freemason. After readin I tend to leave my copy at one of
the lodges I attend in case some brother takes an interest.

Jean Deaguiliers was active in Masonry around the time the first Grand
Lodge was formed. Isaac Newton "was godfather to one of Desaguiler's
daughters" according to the article. Newton definately knew Masons.

Masonry is a social order. Newton was notoriously anti-social. No
wonder there's no evidence he was a Mason.

[Chris H]

Post by Torence

Post by Doug Freyburger
Masonic ramblings,
The fourth in the list of the Seven Liberal Arts and Sciences is
arithmetic. Since Isaac Newton was alive at the time the first Grand
Lodge was founded in London in 1717 I will take arithmetic more
generally as algebra and I will use the two words interchangeably.

You mention Sir Isaac Newton. I always imagined him, Indigo Jones
and Christopher Wren in collaboration; and I think that there is room
here to ponder the connection, if any, that FreeMasonry had to the
Royal Society.

Nothing much to ponder it is VERY well documented. Also several other
Royal Societies.

See the links at
http://www.jagraphics.co.uk/abcdef/1234/

For Robert Lomas lecture (video and ppt slides) on this very subject and
other related subjects.