The algorithmically minded will have noticed that paging requires associative array (like Java Map of Python dict()) abstract data structure where:
  • the keys are linear pages addresses, thus of integer type
  • the values are physical page addresses, also of integer type
The single level paging scheme uses a simple array implementation of the associative array:
  • the keys are the array index
  • this implementation is very fast in time
  • but it is too inefficient in memory
and in C pseudo-code it looks like this:
linear_address[0]      = physical_address_0
linear_address[1]      = physical_address_1
linear_address[2]      = physical_address_2
...
linear_address[2^20-1] = physical_address_N
But there another simple associative array implementation that overcomes the memory problem: an (unbalanced) k-ary tree.
A K-ary tree, is just like a binary tree, but with K children instead of 2.
Using a K-ary tree instead of an array implementation has the following trade-offs:
  • it uses way less memory
  • it is slower since we have to de-reference extra pointers
In C-pseudo code, a 2-level K-ary tree with K = 2^10 looks like this:
level0[0] = &level1_0[0]
    level1_0[0]      = physical_address_0_0
    level1_0[1]      = physical_address_0_1
    ...
    level1_0[2^10-1] = physical_address_0_N
level0[1] = &level1_1[0]
    level1_1[0]      = physical_address_1_0
    level1_1[1]      = physical_address_1_1
    ...
    level1_1[2^10-1] = physical_address_1_N
...
level0[N] = &level1_N[0]
    level1_N[0]      = physical_address_N_0
    level1_N[1]      = physical_address_N_1
    ...
    level1_N[2^10-1] = physical_address_N_N
and we have the following arrays:
  • one directory, which has 2^10 elements. Each element contains a pointer to a page table array.
  • up to 2^10 pagetable arrays. Each one has 2^10 4 byte page entries.
and it still contains 2^10 * 2^10 = 2^20 possible keys.
K-ary trees can save up a lot of space, because if we only have one key, then we only need the following arrays:
  • one directory with 2^10 entries
  • one pagetable at directory[0] with 2^10 entries
  • all other directory[i] are marked as invalid, don't point to anything, and we don't allocate pagetable for them at all
MAC address by Ciro Santilli 40 Updated 2025-07-16
Hardcoded and unique network addresses for every single device on Earth.
Started with 48 bits (6 bytes), usually given as 01:23:45:67:89:AB but people now encouraged to use 64-bit ones.
How they are assigned: www.quora.com/How-are-MAC-addresses-assigned Basically IEEE gives out the 3 first bytes to device manufacturers that register, this is called the organizationally unique identifier, and then each manufacturer keeps their own devices unique.
Like PCR, but does not require thermal cycling. Thus the "isothermal" in the name: iso means same, so "same temperature".
Not needing the thermo cycling means that the equipment needed is much smaller and cheaper it seems.
Video 1.
Loop Mediated Isothermal Amplification (LAMP) Tutorial by New England Biolabs (2015)
Source. Explains the basic LAMP concept well.
Crime by Ciro Santilli 40 Updated 2025-09-11
Video 1.
FBI vs Un-Defuseable Bomb by Qxir (2021)
Source. Tells the story of Harvey's Resort Hotel bombing (1980)
The art of programming by Ciro Santilli 40 Updated 2025-07-16
Just art:
  • useless mathy stuff
  • incredibly nifty little tools that are just so satisfying to use it is mind blowing:
  • media related stuff
Matrix mechanics by Ciro Santilli 40 Updated 2025-07-16
It is apparently more closely related to the ladder operator method, which is a more algebraic than the more analytical Schrödinger equation.
It appears that this formulation makes the importance of the Poisson bracket clear, and explains why physicists are so obsessed with talking about position and momentum space. This point of view also apparently makes it clearer that quantum mechanics can be seen as a generalization of classical mechanics through the Hamiltonian.
Inward Bound by Abraham Pais (1988) chapter 12 "Quantum mechanics, an essay" part (c) "A chronology" has some ultra brief, but worthwhile mentions of matrix mechanics and the commutator.
Sister transaction of 4373b97e4525be4c2f4b491be9f14ac2b106ba521587dad8f134040d16ff73af with another variant of the XSS but without IF and OP_FROMALTSTACK, thus making it spendable:
OP_ADD OP_ADD 13 OP_EQUAL <large xss constant> OP_DROP

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact