Value close to 0
Value close to 0
You think it is zero, but in fact it is just very small and may not be zero.
The time it took for light to get from here to there seemed to be zero, but it was not zero, just very small.
Position and momentum were conventionally considered scalars. This implicitly assumed that XY=YX. Transforming the equation, XY-YX=0. This is called "zero exchanger. In quantum mechanics, however, the exchanger between position and momentum is not zero. (about 1e-34 smaller)
Conversely, many problems are made easier by assuming that a value close to zero is zero. For example, "When x is sufficiently small, the term x^2 can be ignored. It is better to be able to calculate even if there is an error than to aim for exactness and not be able to calculate anything.
__BELOW_IS_AI_GENERATED__
0に近い値 2023-09-05 01:11 omni.icon
Summary of notes.
A note discussing "values close to zero," pointing out the possibility that values that appear to be zero are actually just very small and not zero. He gave an example from quantum mechanics to show that the exchanger between position and momentum is not zero. He also pointed out that the problem can be simplified by assuming a value close to zero to be zero. He concluded that it is better to be able to calculate even with errors than to pursue rigor.
Relation to Fragment.
The fragment on the "Still No Picture Blind Spot Card," like the note, discusses the difference between a value close to zero and zero. Using an example from quantum mechanics, it shows the possibility that a value that seems to be 0 is actually just very small and not 0. This illustrates the same idea as the note, and the two are closely related.
deep thinking
This note highlights a problem with our everyday approximate calculations: the fact that a value that seems to be 0 is actually only very small and not 0 has a significant impact on our perceptions and calculations. On the other hand, however, there is also the reality that the problem is simplified by assuming that a value close to zero is zero. This shows a realistic viewpoint that it is better to be able to calculate even with errors than to pursue rigor.
summary of thoughts and title.
The difference between near-zero values and zero has a profound effect on our perceptions and calculations." But in practical terms, the problem is simplified by assuming a value close to zero is zero."
Title: "The Subtle Difference Between Near Zero and Zero."
extra info
TITLES: ["Still no picture blind spot card"], "Kozaneba Development Diary 2021-09-06", "Coyote analysis", "Not distance", "In infinite dimensional matrices, right inverse and left inverse are not equal", "Identifies what is not equal and cannot be identified by increasing difference"," I'm paraphrasing, not thinking."]
generated: 2023-09-05 01:11
---
This page is auto-translated from /nishio/0に近い値 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.