Remembering the dimensions we are discarding
Remembering the dimensions we are discarding
If there is a wide variety of scales, they may actually be a projection of one higher-dimensional scale onto a lower dimension.
Indicators such as GC-contents and GC-skew in the base composition of a genome are the length of a four-dimensional measure of the rate of occurrence of the four base types in the genome, projected against an arbitrary straight line that is easy for humans to explain.
Where diverse measures exist, they may be a projection of a higher-dimensional measure onto a lower dimension. For example, an index of base composition of a genome is a four-dimensional measure of the rate of occurrence of the four base species, which is then projected into a form that is easily understood by humans.
The fragment "Quaternions" introduces the concept of quaternions (quaternions) to represent rotations in higher dimensional spaces and is related to the content of the note. While the note describes the projection of high-dimensional information onto a lower dimension, "quaternion" illustrates the opposite process, i.e., the extension of low-dimensional information into a higher dimension.
Notes and fragment "quaternions" are complementary to each other in terms of the dimensional transformation of information. This provides different perspectives from which to understand and interpret information. Projecting high-dimensional information to a lower dimension transforms the information into a form that is easier for humans to understand, while extending low-dimensional information to a higher dimension makes it possible to represent more complex phenomena.
"Transforming Dimensions of Information: Shifting Perspectives for Comprehension and Representation."
__BELOW_IS_AI_GENERATED__
捨てている次元を思い出す 2023-09-05 00:44 omni.icon
Summary of notes.
Where diverse measures exist, they may be a projection of a higher-dimensional measure onto a lower dimension. For example, an index of base composition of a genome is a four-dimensional measure of the rate of occurrence of the four base species, which is then projected into a form that is easily understood by humans.
Relation to Fragment.
The fragment "Quaternions" introduces the concept of quaternions (quaternions) to represent rotations in higher dimensional spaces and is related to the content of the note. While the note describes the projection of high-dimensional information onto a lower dimension, "quaternion" illustrates the opposite process, i.e., the extension of low-dimensional information into a higher dimension.
deep thinking
Notes and fragment "quaternions" are complementary to each other in terms of the dimensional transformation of information. This provides different perspectives from which to understand and interpret information. Projecting high-dimensional information to a lower dimension transforms the information into a form that is easier for humans to understand, while extending low-dimensional information to a higher dimension makes it possible to represent more complex phenomena.
summary of thoughts and title.
"Transforming Dimensions of Information: Shifting Perspectives for Comprehension and Representation."
extra info
TITLES: ["Blind Spot Cards Without Pictures Yet"], "Dimensions of Output", "The Curse of Dimension", "Abstraction is Dimensionality Reduction, so it's a Low Dimension", "Kozaneba:Neri"]
generated: 2023-09-05 00:44
---
This page is auto-translated from /nishio/捨てている次元を思い出す using DeepL. If you looks something interesting but the auto-translated English is not good enough to understand it, feel free to let me know at @nishio_en. I'm very happy to spread my thought to non-Japanese readers.