Noether's theorem Updated 2025-07-16
For every continuous symmetry in the system (Lie group), there is a corresponding conservation law.
Furthermore, given the symmetry, we can calculate the derived conservation law, and vice versa.
As mentioned at buzzard.ups.edu/courses/2017spring/projects/schumann-lie-group-ups-434-2017.pdf, what the symmetry (Lie group) acts on (obviously?!) are the Lagrangian generalized coordinates. And from that, we immediately guess that manifolds are going to be important, because the generalized variables of the Lagrangian can trivially be Non-Euclidean geometry, e.g. the pendulum lives on an infinite cylinder.
Video 1.
The most beautiful idea in physics - Noether's Theorem by Looking Glass Universe (2015)
Source. One sentence stands out: the generated quantities are called the generators of the transforms.
Video 2.
The Biggest Ideas in the Universe | 15. Gauge Theory by Sean Carroll (2020)
Source. This attempts a one hour hand wave explanation of it. It is a noble attempt and gives some key ideas, but it falls a bit short of Ciro's desires (as would anything that fit into one hour?)
Video 3.
The Symmetries of the universe by ScienceClic English (2021)
Source. youtu.be/hF_uHfSoOGA?t=144 explains intuitively why symmetry implies consevation!
64 bits is still too much address for current RAM sizes, so most architectures will use less bits.
x86_64 uses 48 bits (256 TiB), and legacy mode's PAE already allows 52-bit addresses (4 PiB). 56-bits is a likely future candidate.
12 of those 48 bits are already reserved for the offset, which leaves 36 bits.
If a 2 level approach is taken, the best split would be two 18 bit levels.
But that would mean that the page directory would have 2^18 = 256K entries, which would take too much RAM: close to a single-level paging for 32 bit architectures!
Therefore, 64 bit architectures create even further page levels, commonly 3 or 4.
x86_64 uses 4 levels in a 9 | 9 | 9 | 9 scheme, so that the upper level only takes up only 2^9 higher level entries.
The 48 bits are split equally into two disjoint parts:
----------------- FFFFFFFF FFFFFFFF
Top half
----------------- FFFF8000 00000000


Not addressable


----------------- 00007FFF FFFFFFFF
Bottom half
----------------- 00000000 00000000
A 5-level scheme is emerging in 2016: software.intel.com/sites/default/files/managed/2b/80/5-level_paging_white_paper.pdf which allows 52-bit addresses with 4k pagetables.
Malus' Law Updated 2025-07-16
Matches the quantum superposition probability proportional to the square law. Poor Étienne-Louis Malus, who died so much before this was found.
SQL COUNT function Updated 2025-07-16
Have a look at some interesting examples under nodejs/sequelize/raw/many_to_many.js.
Khan Academy Updated 2025-07-16
Kudos for being a not-for-profit. Also, anyone can create content: e-learning websites must allow students to create learning content. Oh, but TODO is possible for anyone to make content publicly visible? Course join links lik: www.khanacademy.org/join/MJZ6NSV7 require login. webapps.stackexchange.com/questions/165132/how-to-create-a-course-that-is-publicly-visible-without-the-need-to-login-on-kha If that's the case, it is a fatal flaw not shared by OurBigBook.com.
Another cool aspect is that they have the "physical world teacher pull student accounts in" approach built-in quite well at course creation. This is a very good feature.
As of 2021 they were a bit struggling for money it seems: www.youtube.com/watch?v=I8XdUy-wyyM?
Kilogram Updated 2025-07-16
Unit of mass.
Defined in the 2019 redefinition of the SI base units via the Planck constant. This was possible due to the development of the Kibble balance.
NuNET Updated 2025-07-16
SQL transaction isolation level Updated 2025-07-16
Each transaction isolation level specifies what can or cannot happen when two queries are being run in parallel, i.e.: the memory semantics of the system.
Remember that queries can affects thousands of rows, and database systems like PostgreSQL can run multiple such queries at the same time.
Type-II superconductor Updated 2025-07-16
Figure 1.
Sketch of the typical superconducting phase diagram of a Type-II superconductor
. Source.
Particle decay Updated 2025-07-16
Can produce two entangled particles.
x86 Paging Tutorial / Application Updated 2025-07-16
Paging makes it easier to compile and run two programs or threads at the same time on a single computer.
For example, when you compile two programs, the compiler does not know if they are going to be running at the same time or not.
So nothing prevents it from using the same RAM address, say, 0x1234, to store a global variable.
And thread stacks, that must be contiguous and keep growing down until they overwrite each other, are an even bigger issue!
But if two programs use the same address and run at the same time, this is obviously going to break them!
Paging solves this problem beautifully by adding one degree of indirection:
(logical) ------------> (physical)
             paging
Where:
  • logical addresses are what userland programs see, e.g. the contents of rsi in mov eax, [rsi].
    They are often called "virtual" addresses as well.
  • physical addresses can be though of the values that go to physical RAM index wires.
    But keep in mind that this is not 100% true because of further indirections such as:
Compilers don't need to worry about other programs: they just use simple logical addresses.
As far as programs are concerned, they think they can use any address between 0 and 4 GiB (2^32, FFFFFFFF) on 32-bit systems.
The OS then sets up paging so that identical logical addresses will go into different physical addresses and not overwrite each other.
This makes it much simpler to compile programs and run them at the same time.
Paging achieves that goal, and in addition:
  • the switch between programs is very fast, because it is implemented by hardware
  • the memory of both programs can grow and shrink as needed without too much fragmentation
  • one program can never access the memory of another program, even if it wanted to.
    This is good both for security, and to prevent bugs in one program from crashing other programs.
Or if you like non-funny jokes:
Figure 1.
Comparison between the Linux kernel userland memory virtualization and The Matrix
. Source. Is this RAM real?

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