Ciro Santilli @cirosantilli 37

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x86 Paging Tutorial / Multiple addresses translate to a single physical address Updated 2025-07-16

The same linear address can translate to different physical addresses for different processes, depending only on the value inside cr3.

Both linear addresses 00002 000 from process 1 and 00004 000 from process 2 point to the same physical address 00003 000. This is completely allowed by the hardware, and it is up to the operating system to handle such cases.

This often in normal operation because of Copy-on-write (COW), which be explained elsewhere.

Such mappings are sometime called "aliases".

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x86 Paging Tutorial / Single level paging scheme numerical translation example Updated 2025-07-16

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Suppose that the OS has setup the following page tables for process 1:

entry index   entry address       page address   present
-----------   ------------------  ------------   -------
0             CR3_1 + 0      * 4  0x00001        1
1             CR3_1 + 1      * 4  0x00000        1
2             CR3_1 + 2      * 4  0x00003        1
3             CR3_1 + 3      * 4                 0
...
2^20-1        CR3_1 + 2^20-1 * 4  0x00005        1

and for process 2:

entry index   entry address       page address   present
-----------   -----------------   ------------   -------
0             CR3_2 + 0      * 4  0x0000A        1
1             CR3_2 + 1      * 4  0x12345        1
2             CR3_2 + 2      * 4                 0
3             CR3_2 + 3      * 4  0x00003        1
...
2^20-1        CR3_2 + 2^20-1 * 4  0xFFFFF        1

Before process 1 starts running, the OS sets its cr3 to point to the page table 1 at CR3_1.

When process 1 tries to access a linear address, this is the physical addresses that will be actually accessed:

linear     physical
---------  ---------
00000 001  00001 001
00000 002  00001 002
00000 003  00001 003
00000 FFF  00001 FFF
00001 000  00000 000
00001 001  00000 001
00001 FFF  00000 FFF
00002 000  00003 000
FFFFF 000  00005 000

To switch to process 2, the OS simply sets cr3 to CR3_2, and now the following translations would happen:

linear     physical
---------  ---------
00000 002  0000A 002
00000 003  0000A 003
00000 FFF  0000A FFF
00001 000  12345 000
00001 001  12345 001
00001 FFF  12345 FFF
00004 000  00003 000
FFFFF 000  FFFFF 000

Step-by-step translation for process 1 of logical address 0x00000001 to physical address 0x00001001:

split the linear address into two parts:
```
| page (20 bits) | offset (12 bits) |
```
So in this case we would have:
*page = 0x00000. This part must be translated to a physical location.
*offset = 0x001. This part is added directly to the page address, and is not translated: it contains the position within the page.
look into Page table 1 because cr3 points to it.
The hardware knows that this entry is located at RAM address CR3 + 0x00000 * 4 = CR3:
*0x00000 because the page part of the logical address is 0x00000
*4 because that is the fixed size in bytes of every page table entry
since it is present, the access is valid
by the page table, the location of page number 0x00000 is at 0x00001 * 4K = 0x00001000.
to find the final physical address we just need to add the offset:
```
  00001 000
+ 00000 001
  ---------
  00001 001
```
because 00001 is the physical address of the page looked up on the table and 001 is the offset.
We shift 00001 by 12 bits because the pages are always aligned to 4 KiB.
The offset is always simply added the physical address of the page.
the hardware then gets the memory at that physical location and puts it in a register.

Another example: for logical address 0x00001001:

the page part is 00001, and the offset part is 001
the hardware knows that its page table entry is located at RAM address: CR3 + 1 * 4 (1 because of the page part), and that is where it will look for it
it finds the page address 0x00000 there
so the final address is 0x00000 * 4k + 0x001 = 0x00000001

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Xah Lee Updated 2025-07-16

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fuseki.net/home/List-of-Patreon-Subs-with-Justification.html describes him well:

Outsider, formerly homeless, extreme person interested in CS and culture. Self-publishes a website with thousands of tutorial / opinion pages. Possibly similar to Sam Sloan - extremely productive, wide interests, obsessive, and pretty disagreeable.

Homepage xahlee.org/ says:

Siphon my knowledge into your brain. Assimilate my sensibilities to your spine.

Nice Second brain vibe.

Figure 1.
Xah Lee with some weird statuettes of himself
. Source. 2019.

Let's see:

LinkedIn: www.linkedin.com/in/xahlee/
youtu.be/a6J62TwOreY?t=271 OMG he also uses a Kinesis Advantage 2 keyboard-like keyboard! Maybe there is something here after all.
he's also a mad tutorial writer: xahlee.info/Wallpaper_dir/c4_Derivation.html#gc2.2.2.1 like Ciro's Stack Overflow
www.patreon.com/xahlee £835.2/month from ony 27 members as of 2023, holy crap not bad!
he was in a bad spot as of 2014: xahlee.info/emacs/misc/xah_as_good_as_dead.html
i live on $3 per day for food in past 3 years. Eating noodles and oats with salt
Thread: www.reddit.com/r/programming/comments/25pypq/im_about_as_good_as_dead_the_end_of_xah_lee/
One is reminded of Chill and eat your bread in peace and Quote "Omar Khayyam's chill out quote". xahlee.org/PageTwo_dir/Personal_dir/xah.html autobiography is also of interest.

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Yang-Mills existence and mass gap Updated 2025-07-16

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www.youtube.com/watch?v=-_qNKbwM_eE Unsolved: Yang-Mills existence and mass gap by J Knudsen (2019). Gives 10 key points, but the truly hard ones are too quick. He knows the thing though.

Video 1.

Yang-Mills 1 by David Metzler (2011)

Source.

Playlist: www.youtube.com/watch?v=j3fsPHnrgLg&list=PL613A31A706529585&index=13

A bit disappointing, too high level, with very few nuggests that are not Googleable withing 5 minutes.

Breakdown:

1 www.youtube.com/watch?v=j3fsPHnrgLg: too basic
2 www.youtube.com/watch?v=br6OxCLyqAI?t=569: mentions groups of Lie type in the context of classification of finite simple groups. Each group has a little diagram.
3 youtu.be/1baiIxKKQlQ?list=PL613A31A706529585&t=728 the original example of a local symmetry was general relativity, and that in that context it can be clearly seen that the local symmetry is what causes "forces" to appear
- youtu.be/1baiIxKKQlQ?list=PL613A31A706529585&t=933 local symmetry gives a conserved current. In the case of electromagnetism, this is electrical current. This was the only worthwhile thing he sad to 2021 Ciro. Summarized at: local symmetries of the Lagrangian imply conserved currents.
4 youtu.be/5ljKcWm7hoU?list=PL613A31A706529585&t=427 electromagnetism has both a global symmetry (special relativity) but also local symmetry, which leads to the conservation of charge current and forces.
lecture 3 properly defines a local symmetry in terms of the context of the lagrangian density, and explains that the conservation of currents there is basically the statement of Noether's theorem in that context.

Video 2.

Millennium Prize Problem: Yang Mills Theory by David Gross (2018)

Source. 2 hour talk at the Kavli Institute for Theoretical Physics. Too mathematical, 2021 Ciro can't make much out of it.

Video 3.

Lorenzo Sadun on the "Yang-Mills and Mass Gap" Millennium problem

. Source. Unknown year. He almost gets there, he's good. Just needed to be a little bit deeper.

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Year 4 of the physics course of the University of Oxford Updated 2025-07-16

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Students choose only one of the Cx courses.

Then there are PhDs corresponding to each of them: www.ox.ac.uk/admissions/graduate/courses/mpls/physics

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Zeeman effect Updated 2025-07-16

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Split in the spectral line when a magnetic field is applied.

Non-anomalous: number of splits matches predictions of the Schrödinger equation about the number of possible states with a given angular momentum. TODO does it make numerical predictions?

Anomalous: evidence of spin.

www.pas.rochester.edu/~blackman/ast104/zeeman-split.html contains the hello world that everyone should know: 2p splits into 3 energy levels, so you see 3 spectral lines from 1s to 2p rather than just one.

p splits into 3, d into 5, f into 7 and so on, i.e. one for each possible azimuthal quantum number.

It also mentions that polarization effects become visible from this: each line is polarized in a different way. TODO more details as in an experiment to observe this.

Well explained at: Video "Quantum Mechanics 7a - Angular Momentum I by ViaScience (2013)".

Video 1.

Experimental physics - IV: 22 - Zeeman effect by Lehrportal Uni Gottingen (2020)

Source.

This one is decent. Uses a cadmium lamp and an etalon on an optical table. They see a more or less clear 3-split in a circular interference pattern,

They filter out all but the transition of interest.

youtu.be/ZmObNFAqkBE?t=165 passes the lines through a polarizer, which shows how orbital angular momentum is carried by photon polarization
youtu.be/ZmObNFAqkBE?t=370 says they are looking at 1D2 to 1P1 changes.

Video 2.

Zeeman Effect - Control light with magnetic fields by Applied Science (2018)

Source. Does not appear to achieve a crystal clear split unfortunately.

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ZX-calculus Updated 2025-07-16

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As en.wikipedia.org/w/index.php?title=ZX-calculus&oldid=1071329204#Diagram_rewriting tries to explain but fails to deliver as usual consider the GHZ state represented as a quantum circuit.

How can we easily prove that that quantum circuit equals the state:

\frac{∣000 > + ∣111 >}{2}

(1)

The naive way would be to just do the matrix multiplication as explained at Section "Quantum computing is just matrix multiplication".

However, ZX-calculus provides a simpler way.

And even more importantly, sometimes it is the only way, because in a real circuit, we would not be able to do the matrix multiplication

What we do in ZX-calculus is we first transform the original quantum circuit into a ZX graph.

This is always possible, because we can describe how to do the conversion simply for any of the Clifford plus T gates, which is a set of universal quantum gates.

Then, after we do this transformation, we can start applying further transformations that simplify the circuit.

It has already been proven that there is no efficient algorithm for this (TODO source, someone said P-sharp complete best case)

But it has been proven in 2017 that any possible equivalence between quantum circuits can be reached by modifying ZX-calculus circuits.

There are only 7 transformation rules that we need, and all others can be derived from those, universality.

So, we can apply those rules to do the transformation shown in Wikipedia:

Figure 1.
GHZ circuit as ZX-diagram
. Source.

and one of those rules finally tells us that that last graph means our desired state:

\frac{∣000 > + ∣111 >}{2}

(2)

because it is a Z spider with

m = 3

and

n = 1

Video 1.

Working with PyZX by Aleks Kissinger (2019)

Source. This video appears to give amazing motivation on why you should care about ZX-calculus, it mentions

Bibliography:

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ZynAddSubFX Updated 2025-07-16

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askubuntu.com/questions/220802/no-sound-zynaddsubfx-and-jack-wont-run/1297988#1297988

Contains a large database of instruments, and allows you to edit them. This is a fun toy.

Instruments are edited on a GUI. It is a multi-window program, and you open new windows from new windows from new windows, all filled with hundreds of virtual knobs that you drag with your keyboard, and which would be better done from textual software like Csound. It is a thing of beauty.

It does not seem possible to program arbitrary modular synthesizer circuits therefore. But if you understand additive synthesis and subtractive synthesis well, you can make some funky sounds with it.

It is basically a superset of all popular hardware synthesizers ever made.

Has its own built-in MIDI keyboard which is nice.

On Ubuntu 20.04 Version: 3.0.5:

sudo apt install zynaddsubfx
zynaddsubfx -O alsa

as per askubuntu.com/questions/220802/no-sound-zynaddsubfx-and-jack-wont-run/1297988#1297988
To do anything of interest, switch to the Advanced UI:

Misc
Switch Interface Mode

The UI is completely different form what is shown on the website as of 2020: zynaddsubfx.sourceforge.io/, it looks instead like: www.youtube.com/watch?v=iVPr6iUuO3g Maybe on the website it is the new zyn-fusion UI... www.reddit.com/r/linuxaudio/comments/bxn3ur/some_help_for_installing_zynfusion_zynaddsubfx/ so confusing.

And they have some crappy policy of asking for 45 USD for binary downloads.

Compiling from source:

git clone https://github.com/zynaddsubfx/zynaddsubfx
cd zynaddsubfx
git checkout a789866de4d45a784c1f4d95fcf5a1938347baef
sudo apt build-dep zynaddsubfx
mkdir build
cd build
cmake ..
make -j`nproc`

fails with:

Traceback (most recent call last):
  File "/usr/bin/cxxtestgen", line 7, in <module>
    import cxxtest.cxxtestgen
  File "/usr/share/cxxtest/cxxtest/__init__.py", line 33, in <module>
    from cxxtest.cxxtestgen import *
  File "/usr/share/cxxtest/cxxtest/cxxtestgen.py", line 18, in <module>
    import __release__
ModuleNotFoundError: No module named '__release__'

Ciro gives up for now.

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OurBigBook.com Updated 2025-10-27

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ourbigbook.com is a website created by Ciro Santilli.

The website is the reference instance of OurBigBook Web, which is part of the OurBigBook Project, the other main part of the project are software that users can run locally to publish their content such as the OurBigBook CLI.

The source code for ourbigbook.com is present at: github.com/ourbigbook/ourbigbook/tree/master/web

The project documentation is present at: docs.ourbigbook.com#ourbigbook-web-user-manual

This page contains further information about the project's rationale, motivation and planning.

Video 1.

Intro to the OurBigBook Project

. Source.

Figure 1.
The topics feature allows you to find the best version of a subject written by other users user
. Live demo: derivative.

Figure 2.
Take a look at my GitHub, there are great projects!

OurBigBook's weird specialization towards the weird overly niche interests of its creator Ciro Santilli, notably "I want to create the perfect documentation for every atom in the universe, is undoubtedly partly to blame for the project's failure to gain even a single user outside of its own creator.
However, Ciro does also believe that innovation requires to some degree specializing weirdly in some niche direction. Success comes perhaps from both going into a novel and valuable direction, while still being anatomic enough for enough people.

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Asian fetish Updated 2025-10-27

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All interests are based on fetishes.

The fetish of beauty. The fetish if intelligence. The fetish of kindness.

What's wrong with the fetish of Asianess?

Whenever Ciro's wife starts with "the Asian fetish talk", Ciro reminds her of her own claimed "tall person fetish", and they call it quits.

Asian fetish is much more than sex. It is about the culture, the history, the language. It is the same fetish that makes great mathematicians an Artists do what they do.

When Ciro Santilli was at École Polytechnique, he had to do a presentation for his stupid English courses that all students were forced to take, no matter how good their English was.

The topic was likely something like "pick a country", and Ciro was delighted when he managed to pick "China", after it had gone around a table with many many people before him.

The PowerPoint presentation Ciro made over the weekend was so amazing (and making it was actually fun to make, Ciro actually remembers it a bit!), drawing partly from stuff his wife then girlfriend showed him, that at the end the one of the other students asked him if he had lived in China.

It is a shame Ciro couldn't find the presentation when he wrote this line many many years later. Anything that is not in a BLOB-free monorepo, will disappear, heed my words. But he's certain about two things which it contained:

en.wikipedia.org/wiki/Asian_fetish#History_of_origins

In the United States, women of East and Southeast Asian descent are sometimes stereotyped as subservient, passive, mysterious, villainous in nature, and hyper-sexual.

subservient, passive, mysterious are understandable. But Hyper-sexual and villainous? OMG have these people never seen real Asians?
en.wikipedia.org/wiki/Asian_fetish#Pornography:

Several studies have implied that Asian women are over-represented in the American pornography industry. Asian women make up perhaps 20% of all female performers, despite being roughly 2.5% of the U.S. population. Asian men also appear to be considerably over-represented, at 10% of male actors.

Video 1.

How my boyfriend CHEATED with another Asian girl by Jenny Tian

. Source.

Video 2.

Sam Rockwell monologue about being an Asian girl on The White Lotus

. Source.

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Ciro Santilli's sinophily Updated 2025-10-27

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Two things come to mind when Ciro Santilli thinks about his sinohpilia.

There is a strong "Ciro Santilli's knowledge hoarding" side to it. Ciro has decided that he has to know EVERYTHING about China. It's culture. It's people. It's art. And so once that has been decided, it becomes inevitable.

But of course, there is also the "which part of Ciro's inner being led to that hoarding decision" part of things. Mishima's quote often comes to mind:

Every night I return to my desk precisely at midnight. I thoroughly analyze why I am attracted to a particular theme. I drag it into my conscious mind. I boil it into abstraction.

Exoticism is undoubtedly part of it.

Maybe it has something to do with growing up observing 5th+ generation Japanese Brazilians immigrants, well, being Asians and crushing it academically. But also being quiet people, and sometimes misfits. I.e., nerds.

Maybe there is also something to do with the influence Japanese anime, highly popular during Ciro's childhood in Brazil. Ciro, unlike many of his friends, left that relatively early, as he got into the deeper pleasures of natural sciences and then more traditional Asian culture. But still.

And finally perhaps the correlation between sofware engineers and Asian fetish and the correlation between software engineers and Buddhism.

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Fluid mechanics Updated 2025-10-27

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Boooooring. Except for Navier-Stokes existence and smoothness. That's OK.

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Navier-Stokes existence and smoothness Updated 2025-10-27

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Video 1.

A report on the Navier-Stokes Problem by Vladimir Šverak

. Source. 2025.

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Sylvain Poirier Updated 2025-07-16

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Ciro Santilli feels a bit like this guy:

he's also an idealist, even more than Ciro. So cute. Notably, he he also dumps his brain online into pages that no-one will ever read
he also thinks that the 2010's education system is bullshit, e.g. settheory.net/learnphysics
trust-forum.net/ some kind of change the world website. But:
Started with Vue.js + Node.js. Details reserved for developers willing to contribute
is a sin to Ciro. Planning a change the world thing behind closed doors? Really? Decentralized, meh.
antispirituality.net/ his atheism website

One big divergence: obsession with translating every page into every language.

His Mathematics Genealogy Project entry: www.genealogy.math.ndsu.nodak.edu/id.php?id=56185

Old French website: spoirier.lautre.net/

singlesunion.org/ so cute, he's looking for true love!!! This is something Ciro often thinks about: why it is so difficult to find love without looking people in the eye. The same applies to jobs to some extent. He has an Incel wiki page: incels.wiki/w/Sylvain_Poirier :-)

Figure 1.
Sylvain's photo from his homepage.
Source. He's not ugly at all! Just a regular good looking French dude.

Video 1.

Why learn Physics by yourself by Sylvain Poirier (2013)

Source.

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Coursera Updated 2025-07-16

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Some courses at least allow you to see material for free, e.g.: www.coursera.org/learn/quantum-optics-single-photon/lecture/UYjLu/1-1-canonical-quantization. Lots of video focus as usual for MOOCs.

Some are paywalled: www.coursera.org/learn/theory-of-angular-momentum?specialization=quantum-mechanics-for-engineers

It is extremely hard to find the course materials without enrolling, even if enrolling for free! By trying to make money, they make their website shit.

The comment section does have a lot of activity: www.coursera.org/learn/statistical-mechanics/discussions/weeks/2! Nice. And works like a proper issue tracker. But it is also very hidden.

November 2023 topics: