User:FloraC/Critique on D&D's terminology: Difference between revisions
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== "Domain basis" == | == "Domain basis" == | ||
''Domain'' and ''domain basis'' are D&D's replacements for ''subgroup'' and ''subgroup basis'', respectively. They | ''Domain'' and ''domain basis'' are D&D's replacements for ''subgroup'' and ''subgroup basis'', respectively. Currently the main reasoning is based on pedagogical needs. They argue for using linear algebra, the less advanced math theory, rather than group theory, the more advanced, since they believe the difference between the vector space and the free abelian group is negligible for practical purposes. | ||
<blockquote> | <blockquote> | ||
This is because group theory is a relatively obscure and advanced field of mathematics, and this article prefers to leverage terminology from the more well-known and basic field of linear algebra whenever possible. […] some argue that RTT cannot be sufficiently described using only linear algebra. This article, however, prioritizes pedagogy of the basics over any potential considerations arising from such advanced RTT problems. | |||
</blockquote> | </blockquote> | ||
Here they admit that ''subgroup'' is technically more correct than ''subspace''. It should be pointed out that their reason seems to be one ''for'' taking the correct terms, not ''against''. Specifically, they draw the comparison between the two math disciplines, and it appears that RTT would be more difficult by taking the correct terms. The problem in their logic is, if "advanced RTT problems" only arise occasionally, the actual difficulty levels should be similar. | |||
The story behind it is that RTT does not make use of the full power of group theory. RTT only concerns free abelian groups, which as they appropriately noted, are similar to vector spaces. | |||
My suggestion: use ''subgroup'' and ''subgroup basis''. These are technically correct, consistent, and as clear as they can get. Maybe even ''sub-'' is not needed, just ''group'', but that is another topic. | |||
=== | === Resolved issues === | ||
==== Consistency ==== | |||
<s>First, they argue ''subgroup'' and ''basis'' are inconsistent terms since they are a mix from different mathematical fields. | |||
<blockquote> | <blockquote> | ||
The term "subgroup basis" mixes mathematical terminology from different mathematical fields: "subgroup" comes from group theory, while "basis" comes from linear algebra. The equivalent term for "subgroup" in linear algebra is "subspace", and the equivalent term for "basis" in group theory is "minimal generating set". | |||
</blockquote> | </blockquote> | ||
That is not correct. The basis is a concept that is used across linear algebra and a particular sector of group theory: the study of free abelian groups. If you look up the definition of the free abelian group, it is simple: a free abelian group is an abelian group that has a basis. Indeed, in RTT, JI is modeled as a free abelian group, rather than a group or module in general. That is why bases are used. | |||
Since a free abelian group is a group, it naturally has subgroups. It is not a vector space, so we do not speak of subspaces – but that has to do with their next point below. </s> | |||
=== Specificity === | ==== Specificity ==== | ||
<s>At this point, they further argue for ''domain basis'' than ''subspace basis'': they prefer more specialized tuning terms to general mathematical terms. | <s>At this point, they further argue for ''domain basis'' than ''subspace basis'': they prefer more specialized tuning terms to general mathematical terms. | ||
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To understand this point of theirs, we must look back at the time before they changed ''interval basis'' to ''domain basis''. Back then, ''interval basis'' was indeed more ''specialized'' for tuning, though not more ''specific'' in its form. Yet that is no longer the case. ''Domain'' is by no means more specialized or specific than ''subgroup'', if not less. So the reason is obsolete. </s> | To understand this point of theirs, we must look back at the time before they changed ''interval basis'' to ''domain basis''. Back then, ''interval basis'' was indeed more ''specialized'' for tuning, though not more ''specific'' in its form. Yet that is no longer the case. ''Domain'' is by no means more specialized or specific than ''subgroup'', if not less. So the reason is obsolete. </s> | ||
==== Inclusivity ==== | |||
=== Inclusivity === | |||
<s>Finally, they argue that ''subgroup'' is often assumed to be nonstandard subgroups, and to exclude the standard type, while ''domain'' is designed to include both standard and nonstandard types. | <s>Finally, they argue that ''subgroup'' is often assumed to be nonstandard subgroups, and to exclude the standard type, while ''domain'' is designed to include both standard and nonstandard types. | ||
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The hope for a term that invariably includes standard subgroups does not hold itself because language does not work like that. So long as prime limits continue to be used, chances are the actual usage of ''domain'' will turn out the same as ''subgroup''. </s> | The hope for a term that invariably includes standard subgroups does not hold itself because language does not work like that. So long as prime limits continue to be used, chances are the actual usage of ''domain'' will turn out the same as ''subgroup''. </s> | ||
== "Prime-count vector" == | == "Prime-count vector" == | ||