Defactoring terminology proposal: Difference between revisions
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These new terms were coined by [[Dave Keenan]] in collaboration with [[Douglas Blumeyer]] in June of 2021<ref>Many, many other terms were considered before arriving at defactored and enfactored, including but not limited to: repeated, (up/down)sampled, decimated, divided/multiplied, divisive/multiplicative, completed/depleted/repleted/pleated, efficient, brown, dry, spongy/holey, fluffy, corrugated, copied, shredded, tupled, tupletted, enphactored (where the ph stood for possibly hidden), reduced, simplified...</ref>. | These new terms were coined by [[Dave Keenan]] in collaboration with [[Douglas Blumeyer]] in June of 2021<ref>Many, many other terms were considered before arriving at defactored and enfactored, including but not limited to: repeated, (up/down)sampled, decimated, divided/multiplied, divisive/multiplicative, completed/depleted/repleted/pleated, efficient, brown, dry, spongy/holey, fluffy, corrugated, copied, shredded, tupled, tupletted, enphactored (where the ph stood for possibly hidden), reduced, simplified...</ref>. | ||
The arguments in favor of "defactor" and "enfactor" are: | |||
# They do have obvious mathematical meaning in this context: the absence/removal ("de-") vs. presence/introduction ("en-") of a common factor ("-factor") in linear combinations of a matrix's rows or columns. | |||
# "Enfactored" sounds a bit like "infected", better suggesting the [[The pathology of enfactoring|pathological case]] of unsaturation. | |||
# They don't have any of the problems listed for the other terms. | |||
== Defactoring, to replace saturation == | == Defactoring, to replace saturation == | ||
Several | Several problems with the term "saturation" may be identified: | ||
# It does not have any obvious musical or mathematical meaning in this context, while defactoring and enfactoring clearly refer to the common factor found in linear combinations of matrix rows or columns. | # It does not have any obvious musical or mathematical meaning in this context, while defactoring and enfactoring clearly refer to the common factor found in linear combinations of matrix rows or columns. | ||
# It has another unrelated meaning within xenharmonics that it would conflict with: https://en.xen.wiki/w/Anomalous_saturated_suspension | # It has another unrelated meaning within xenharmonics that it would conflict with: https://en.xen.wiki/w/Anomalous_saturated_suspension | ||
# To "saturate" in everyday use means to ''add'' to something, whereas in this mathematical sense it means to ''remove'' something, which can be very confusing. We suggest an effective way to look at it is that saturating is accomplished not by adding more information into the container but rather by shrinking the container itself so that it has no wasted capacity, and thereby attains a saturated state, but still feel that this is a bit of a stretch. | # To "saturate" in everyday use means to ''add'' to something, whereas in this mathematical sense it means to ''remove'' something, which can be very confusing. We suggest an effective way to look at it is that saturating is accomplished not by adding more information into the container but rather by shrinking the container itself so that it has no wasted capacity, and thereby attains a saturated state, but still feel that this is a bit of a stretch. | ||
# The most common everyday usage of that word is for "saturated fats", which are the bad kind of fats, so it has negative associations, despite "saturation" being the ''good'' state for a matrix to be in | # The most common everyday usage of that word is for "saturated fats", which are the bad kind of fats, so it has negative associations, despite "saturation" being the ''good'' state for a matrix to be in. | ||
# Furthermore, there is another common but conflicting sense of saturation for matrices which clamps entry values to between -1 and 1<ref>See https://math.stackexchange.com/questions/1964814/linear-transformation-of-a-saturated-vector and https://faculty.uml.edu//thu/tcs01-june.pdf</ref>. | # Furthermore, there is another common but conflicting sense of saturation for matrices which clamps entry values to between -1 and 1<ref>See https://math.stackexchange.com/questions/1964814/linear-transformation-of-a-saturated-vector and https://faculty.uml.edu//thu/tcs01-june.pdf</ref>. | ||
== Enfactoring, to replace torsion and contorsion == | == Enfactoring, to replace torsion and contorsion == | ||
As for the term "torsion", the | As for the term "torsion", the problems with it are: | ||
# Again, it does not have any obvious musical or mathematical meaning in this context. | # Again, it does not have any obvious musical or mathematical meaning in this context. | ||