2009.11.02
Found a discussion on another blog
I recently stumbled onto a heated discussion on another blog. That discussion prompted some thoughts of my own.
The dramatis personae were Morgan Freeberg, Rick, and Sonja. Morgan is a blogger I read sporadically; I'm fairly familiar with his work. The other two are new to me. Rick appears to generally agree with Morgan, Sonja appears to generally not agree with either of them.
Morgan first came to my attention in a link from some other blog; he is distinctive in his respect for a nearly-forgotten ancient librarian in Alexandria. Sonja is unknown to me, but I recognize that she took an idea from Tolkien when she named her blog.
What piqued my interest was a comment by Sonja after she declared the original discussion closed. She said something about previewing comments, and deleting comments that didn't follow the rules of Logic.
Upon seeing that comment, I reviewed the discussion that preceded it. I looked for logic, illogic, and abusive attitudes.
The thoughts on mythology that were spawned by the name of Sonja's blog turned my mind in another direction.
I pictured a personified Logic in my mind. She seemed to be a lady, and one not to be trifled with. Logic has an almost-abrasive personality, a sharp mind, and no respect for persons. She only cares about groupings of ideas which can be labelled Consistent or Inconsistent. While quiet, Logic can be persuasive. If questioned carefully, Logic can produce many answers from a few beginning thoughts.
But the answers of Logic are only as trustworthy as the beginning assumptions that frame the questions asked.
In the history of human thought, one man brought a set of ten assumptions about lines, planes, and points to Logic. He began to ask questions. The results of this questioning, and careful questions based on the results, generated a vast edifice of knowledge.
For at least two millennia, this edifice of knowledge as viewed as Absolute Truth about measurement of lines, angles, shapes, and other objects in geometry.
Then someone wondered if the same results could be had if one of the original ten assumptions was removed, and the same questions asked.
The result was a different kind of geometry. (Actually, two entirely new kinds of geometry). The new system was internally consistent; it followed the rules of Logic.
This is an example of Logic giving surprising results. Given one set of assumptions, she tells us that the angles in a triangle add up to 180 degrees. Given another set, she may say that the angles add up to more than 180 degrees, or less, depending on what you've assumed.
Another man, named Charles Babbage, used the results of Logic heavily. He wanted to create a machine which would allow certain answers from Logic to be replicated automatically.
Babbage wanted to create a machine which would make it easier for scientists to ask questions, and use the answers that Logic provided to program the machine. The machine would then make lots of repetitions of certain computations very easy.
In his own words,
This question shows a misunderstanding of the way that Logic answers questions, and the way in which her answers can be used.
If Logic is provided with erroneous (or even conflicting) assumptions, she will not produce results that are in error (or self-contradictory).
Sometimes, Logic will simply answer the badly-posed question, and leave the questioner to discover the principle known as GIGO.
That is what I suspect happened in this case. Both Sonja and Morgan used a combination of logic, unspoken assumptions, and harsh assertions. Neither one used logic purely. (Though a case could be made that Morgan is the better logician of the two...)
There may have been abuses of Logic; but I doubt that Sonja was incensed about them. I suspect that she was incensed by the things assumed before any questions were asked of Logic. It is those assumptions that she likely disagreed with.
The dramatis personae were Morgan Freeberg, Rick, and Sonja. Morgan is a blogger I read sporadically; I'm fairly familiar with his work. The other two are new to me. Rick appears to generally agree with Morgan, Sonja appears to generally not agree with either of them.
Morgan first came to my attention in a link from some other blog; he is distinctive in his respect for a nearly-forgotten ancient librarian in Alexandria. Sonja is unknown to me, but I recognize that she took an idea from Tolkien when she named her blog.
What piqued my interest was a comment by Sonja after she declared the original discussion closed. She said something about previewing comments, and deleting comments that didn't follow the rules of Logic.
Upon seeing that comment, I reviewed the discussion that preceded it. I looked for logic, illogic, and abusive attitudes.
The thoughts on mythology that were spawned by the name of Sonja's blog turned my mind in another direction.
I pictured a personified Logic in my mind. She seemed to be a lady, and one not to be trifled with. Logic has an almost-abrasive personality, a sharp mind, and no respect for persons. She only cares about groupings of ideas which can be labelled Consistent or Inconsistent. While quiet, Logic can be persuasive. If questioned carefully, Logic can produce many answers from a few beginning thoughts.
But the answers of Logic are only as trustworthy as the beginning assumptions that frame the questions asked.
In the history of human thought, one man brought a set of ten assumptions about lines, planes, and points to Logic. He began to ask questions. The results of this questioning, and careful questions based on the results, generated a vast edifice of knowledge.
For at least two millennia, this edifice of knowledge as viewed as Absolute Truth about measurement of lines, angles, shapes, and other objects in geometry.
Then someone wondered if the same results could be had if one of the original ten assumptions was removed, and the same questions asked.
The result was a different kind of geometry. (Actually, two entirely new kinds of geometry). The new system was internally consistent; it followed the rules of Logic.
This is an example of Logic giving surprising results. Given one set of assumptions, she tells us that the angles in a triangle add up to 180 degrees. Given another set, she may say that the angles add up to more than 180 degrees, or less, depending on what you've assumed.
Another man, named Charles Babbage, used the results of Logic heavily. He wanted to create a machine which would allow certain answers from Logic to be replicated automatically.
Babbage wanted to create a machine which would make it easier for scientists to ask questions, and use the answers that Logic provided to program the machine. The machine would then make lots of repetitions of certain computations very easy.
In his own words,
On two occasions I have been asked, 'Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?' I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.
This question shows a misunderstanding of the way that Logic answers questions, and the way in which her answers can be used.
If Logic is provided with erroneous (or even conflicting) assumptions, she will not produce results that are in error (or self-contradictory).
Sometimes, Logic will simply answer the badly-posed question, and leave the questioner to discover the principle known as GIGO.
That is what I suspect happened in this case. Both Sonja and Morgan used a combination of logic, unspoken assumptions, and harsh assertions. Neither one used logic purely. (Though a case could be made that Morgan is the better logician of the two...)
There may have been abuses of Logic; but I doubt that Sonja was incensed about them. I suspect that she was incensed by the things assumed before any questions were asked of Logic. It is those assumptions that she likely disagreed with.
Posted by: karrde at
21:47
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