You need those because it is hard to do the following:
This is hard to do notably because when the update happens, several things might need to change on the webpage at the same time.
Notably, new elements might need to be added to the webpage, which in turn means that new bindings such as button clicks have to be added to those, in a way that keeps the page working.
The only way to do this basically is to have a functional dependency graph that keeps everything in the page in working state as updates come.
Random-access memory by Ciro Santilli 37 Updated 2025-07-16
In conventional speech of the early 2000's, is basically a synonym for dynamic random-access memory.
OpenShot by Ciro Santilli 37 Updated 2025-07-16
Ubuntu 20.10 crash...:
  exceptions:ERROR Unhandled Exception
Traceback (most recent call last):
  File "/usr/bin/openshot-qt", line 11, in <module>
    load_entry_point('openshot-qt==2.5.1', 'gui_scripts', 'openshot-qt')()
  File "/usr/lib/python3/dist-packages/openshot_qt/launch.py", line 97, in main
    app = OpenShotApp(argv)
  File "/usr/lib/python3/dist-packages/openshot_qt/classes/app.py", line 218, in __init__
    from windows.main_window import MainWindow
  File "/usr/lib/python3/dist-packages/openshot_qt/windows/main_window.py", line 45, in <module>
    from windows.views.timeline_webview import TimelineWebView
  File "/usr/lib/python3/dist-packages/openshot_qt/windows/views/timeline_webview.py", line 42, in <module>
    from PyQt5.QtWebKitWidgets import QWebView
ImportError: /usr/lib/x86_64-linux-gnu/libQt5Quick.so.5: undefined symbol: _ZN4QRhi10newSamplerEN11QRhiSampler6FilterES1_S1_NS0_11AddressModeES2_, version Qt_5_PRIVATE_API
web.archive.org/web/20181119214326/https://www.bipm.org/utils/common/pdf/CGPM-2018/26th-CGPM-Resolutions.pdf gives it in raw:
The breakdown is:
Unit circle by Ciro Santilli 37 Updated 2025-07-16
The unitary group is one very over-generalized way of looking at it :-)
Gamma ray by Ciro Santilli 37 Updated 2025-07-16
Most commonly known as a byproduct radioactive decay.
Their energy is very high compared example to more common radiation such as visible spectrum, and there is a neat reason for that: it's because the strong force that binds nuclei is strong so transitions lead to large energy changes.
Gamma rays are pretty cool as they give us insight into the energy levels/different configurations of the nucleus.
They have also been used as early sources of high energy particles for particle physics experiments before the development of particle accelerators, serving a similar purpose to cosmic rays in those early days.
But gamma rays they were more convenient in some cases because you could more easily manage them inside a laboratory rather than have to go climb some bloody mountain or a balloon.
The positron for example was first observed on cosmic rays, but better confirmed in gamma ray experiments by Carl David Anderson.
The orthogonal group has 2 connected components:
It is instructive to visualize how the looks like in :
  • you take the first basis vector and move it to any other. You have therefore two angular parameters.
  • you take the second one, and move it to be orthogonal to the first new vector. (you can choose a circle around the first new vector, and so you have another angular parameter.
  • at last, for the last one, there are only two choices that are orthogonal to both previous ones, one in each direction. It is this directio, relative to the others, that determines the "has a reflection or not" thing
As a result it is isomorphic to the direct product of the special orthogonal group by the cyclic group of order 2:
A low dimensional example:
because you can only do two things: to flip or not to flip the line around zero.
Note that having the determinant plus or minus 1 is not a definition: there are non-orthogonal groups with determinant plus or minus 1. This is just a property. E.g.:
has determinant 1, but:
so is not orthogonal.
If we didn't have GUIs, terminal multiplexers would be our desktop environments. E.g. they handle stuff like:
  • window switching
  • copy pasting across windows
  • screen locking
  • clock on the status bar (same one that holds tabs)
It is a thing of beauty.
We can then immediately see that the matrix is symmetric, then so is the form. We have:
But because is a scalar, we have:
and:

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