Today, while perusing Euclid's ELEMENTS, book 1, proposition 31, I was struck with this insight:
"Learning a principle is much easier than demonstrating its proof."
This is my second time through these early propositions of Euclid. There are 13 books. There are definitions, common notions, and postulates too.
I occasionally read Euclid for understanding, for mental exercise, for biological and historical analogies, and for fun!
But, there is not much 'fun' in confusion, only frustration and torment!
My deduction above, produced in parentheses about principles and proofs, grew out of my poignant frustration of endeavoring to anticipate Euclid's methods of proof, of his propositions, before reading and studying his methodology, using my own logic and invention.
Each time that I have done so, I have been, not only wrong; but worse yet, I have been also totally upended--flummoxed--by his efficiently elegant demonstrations of proof!
In doing so, Euclid, like a dutiful old school teacher, utilizes only previous propositions, postulates, or common notions, previously covered in class, to demonstrate, and to prove each proposition with graceful simplicity.
He is slowly building his case using what had gone before to prove every accretion of knowledge and nuance.
The thought alone is daunting: to prove everything and to build slowly upon appropriate proven precedents.
I finally just shook my head and rationalized that Euclid is a "nomme de plume" representing a secret guild of ingenious savants, from ancient Egypt and even more ancient Nubia, going back thousands of years.
There, in Africa, Euclid's earliest propositions and proofs have been discovered, found in writing, and are applied in still-extant monuments and megaliths, yet the marvel of the world over 4,000 years later.
From the foregoing I have deduced that I am a learner. Others must be demonstrators! I cannot do or be both!
So, why am I sharing this with you? Because misery loves company!
Wednesday, August 27, 2014
MISERY LOVES COMPANY: EUCLID'S GEOMETRIC PRINCIPLES AND THEIR ATTENDANT PROOF
MISERY LOVES COMPANY: EUCLID'S GEOMETRIC PRINCIPLES AND THEIR ATTENDANT PROOFS
Today, while perusing Euclid's ELEMENTS, book 1, proposition 31, I was struck with this insight:
"Learning a principle is much easier than demonstrating its proof."
This is my second time through these early propositions of Euclid. There are 13 books. There are definitions, common notions, and postulates too.
I occasionally read Euclid for understanding, for mental exercise, for biological and historical analogies, and for fun!
But, there is not much 'fun' in confusion, only frustration and torment!
My deduction above, produced in parentheses about principles and proofs, grew out of my poignant frustration of endeavoring to anticipate Euclid's methods of proof, of his propositions, before reading and studying his methodology, using my own logic and invention.
Each time that I have done so, I have been, not only wrong; but worse yet, I have been also totally upended--flummoxed--by his efficiently elegant demonstrations of proof!
In doing so, Euclid, like a dutiful old school teacher, utilizes only previous propositions, postulates, or common notions, previously covered in class, to demonstrate, and to prove each proposition with graceful simplicity.
He is slowly building his case using what had gone before to prove every accretion of knowledge and nuance.
The thought alone is daunting: to prove everything and to build slowly upon appropriate proven precedents.
I finally just shook my head and rationalized that Euclid is a "nomme de plume" representing a secret guild of ingenious savants, from ancient Egypt and even more ancient Nubia, going back thousands of years.
There, in Africa, Euclid's earliest propositions and proofs have been discovered, found in writing, and are applied in still-extant monuments and megaliths, yet the marvel of the world over 4,000 years later.
From the foregoing I have deduced that I am a learner. Others must be demonstrators! I cannot do or be both!
So, why am I sharing this with you? Because misery loves company!
Today, while perusing Euclid's ELEMENTS, book 1, proposition 31, I was struck with this insight:
"Learning a principle is much easier than demonstrating its proof."
This is my second time through these early propositions of Euclid. There are 13 books. There are definitions, common notions, and postulates too.
I occasionally read Euclid for understanding, for mental exercise, for biological and historical analogies, and for fun!
But, there is not much 'fun' in confusion, only frustration and torment!
My deduction above, produced in parentheses about principles and proofs, grew out of my poignant frustration of endeavoring to anticipate Euclid's methods of proof, of his propositions, before reading and studying his methodology, using my own logic and invention.
Each time that I have done so, I have been, not only wrong; but worse yet, I have been also totally upended--flummoxed--by his efficiently elegant demonstrations of proof!
In doing so, Euclid, like a dutiful old school teacher, utilizes only previous propositions, postulates, or common notions, previously covered in class, to demonstrate, and to prove each proposition with graceful simplicity.
He is slowly building his case using what had gone before to prove every accretion of knowledge and nuance.
The thought alone is daunting: to prove everything and to build slowly upon appropriate proven precedents.
I finally just shook my head and rationalized that Euclid is a "nomme de plume" representing a secret guild of ingenious savants, from ancient Egypt and even more ancient Nubia, going back thousands of years.
There, in Africa, Euclid's earliest propositions and proofs have been discovered, found in writing, and are applied in still-extant monuments and megaliths, yet the marvel of the world over 4,000 years later.
From the foregoing I have deduced that I am a learner. Others must be demonstrators! I cannot do or be both!
So, why am I sharing this with you? Because misery loves company!