This website used to allow embedding text messages with OP_RETURN, here's an archive from 2015: web.archive.org/web/20150718052659/http://eternitywall.it/
As of January 2024, it seems to read-only mode, where it simply indexes matching transactions that were made via other means: web.archive.org/web/20230929075331/https://eternitywall.it/
There were 3191 hits for the search term:
git grep '\bEW '
in our data starting with tx a3b3af21514bd79a4cbcac9916a8514636a72d813539192214542fd85247082e (2015-06-24):
EW Eternity wall is live
up to the last entry on tx 28820bc14cf2cfda58ecbc9ac6df3f41a1cb90f4246543f01ba42a5e9dac3cf8 (2023-06-15)
EW May our friendship endure, signed by hg, kty, wjj, and xyz.
no doubt initials of 4 Chinesepeople. A blood brother oath comes to mind, akin to the Oath of the Peach Garden. Will these four be the ones to take down the evil dictator Xi Jinping?
The very first message gives away the name of what we assume is a web-based upload system, "EW" being its advertisement signature added to every message.
Running bitcoin-cli:
bitcoin-core.cli getrawtransaction a3b3af21514bd79a4cbcac9916a8514636a72d813539192214542fd85247082e true
shows that the messages are encoded with OP_RETURN:
  "vout": [
    {
      "value": 0.00000000,
      "n": 0,
      "scriptPubKey": {
        "asm": "OP_RETURN 455720457465726e6974792077616c6c206973206c697665
Every vector space is defined over a field.
E.g. in , the underlying field is , the real numbers. And in the underlying field is , the complex numbers.
Any field can be used, including finite field. But the underlying thing has to be a field, because the definitions of a vector need all field properties to hold to make sense.
Elements of the underlying field of a vector space are known as scalar.
Test buy 2023-04-10 in the UK:
  • fee: 0.99 pounds, minimum buy: 1.99 pounds
  • bought 10 pounds, minus 0.99 fee, totalled: 0.00039162 BTC (£8.92) presumably after further fees/spread
  • bitcoin price on Google on that day: 22,777.54 GBP / BTC
  • bitcoin transaction fees were about 2.7 BTC on that day
Sending 5 pounds to wallet 12dg2FaiZLp3VzDtLvwPinaKz41TQcEGbs
  • network fee: 0.00001989 BTC
  • total bitcoin cost: -0.00023928 BTC
  • new balance: 15,234 satoshi (39,162 - 23,928).
  • total spent: £5.45
  • time est.: about 30 minutes
This worked and I received 21939 satoshis (23928 - 1989) on Electrum on one of the outputs of transaction 1177268091cbeaacbcaac5dc4f6d1774c4ec11b4bcffafa555cd2775eafb954c.
Sending 1 satoshi back! The lowest fee in Electron is 1120 Satoshis targeting 25 blocks (4 hours). Let's do it. Failed, server forbids dust, minimum is 1000 satoshi. OK, sending 1000 satoshi, at 1139 fee.
Cayley graph by Ciro Santilli 40 Updated 2025-07-16
You select a generating set of a group, and then you name every node with them, and you specify:
  • each node by a product of generators
  • each edge by what happens when you apply a generator to each element
Not unique: different generating sets lead to different graphs, see e.g. two possible en.wikipedia.org/w/index.php?title=Cayley_graph&oldid=1028775401#Examples for the
Normal subgroup by Ciro Santilli 40 Updated 2025-07-16
Only normal subgroups can be used to form quotient groups: their key definition is that they plus their cosets form a group.
One key intuition is that "a normal subgroup is the kernel" of a group homomorphism, and the normal subgroup plus cosets are isomorphic to the image of the isomorphism, which is what the fundamental theorem on homomorphisms says.
Therefore "there aren't that many group homomorphism", and a normal subgroup it is a concrete and natural way to uniquely represent that homomorphism.
The best way to think about the, is to always think first: what is the homomorphism? And then work out everything else from there.
Video 1.
Why Relativity Breaks the Schrodinger Equation by Richard Behiel (2023)
. Source. Take a plane wave function, because we know its momentum perfectly. Apply a constant voltage to an electron. You can easily bring it beyond the speed of light at about 255.5 keV.
In this section we list charitable organizations that support education or research:
Crankstart Foundation by Ciro Santilli 40 Updated 2025-07-16
At crankstart.org/grants the organization's website describes mostly California activities, but they do at least also act in the University of Oxford, see: Section "University of Oxford study costs".
Presumably the name refers to crank starting an old car, as in helping out those in difficulty like poor students get started in life. But is also an obscure slang for a type of handjob according to Urban Dictionary.
LibreTexts by Ciro Santilli 40 Updated 2025-07-16
Follows the "certified teacher only" approach which is in Ciro Santilli's opinion a fatal flaw of most elearning systems out there, OurBigBook.com won't suffer from that!
But that is a very, very good project.
All notes appear to have been extracted from existing notes, as noted on the bottom of each page.
TODO how does it work exactly? Do they ask for permission from authors in every case, including when the content has open license? Or when it has open license, do they just do it? In some cases, the notes have no license, so they must have asked.
TODO what is the source code that authors write? LaTeX or something else? LaTeX feels extremely likely given that it is what most original materials were already written in.
They are attempting a "model up this entire university" thing: phys.libretexts.org/Courses which is good. E.g. they have a bunch of "quantum mechanics ones under: phys.libretexts.org/Bookshelves/Quantum_Mechanics
Appears to be UC Davies-based mostly.
They claim to use this closed source backend: www.nice.com/resources/cxone-expert-knowledge-management? Seriously? For a publicly funded project with low-tech requirements?? It is mind blowing.
Some issues:
OK let's database it:
Fundação Estudar by Ciro Santilli 40 Updated 2025-07-16
Video 1.
What I learned in Harvard part 1 by Jorge Paulo Lemann (2012)
Source. Portuguese talk about his experiences. A bit bably, but has a few good comments:
  • You don't learn the Harvard experience, you absorb it.
  • Being amongst excellent people makes you learn what excelent people are like, just like only by tasting many different types of wine can you know what good wine is like.
    This one does have bias danger though. But detecting greatness, is as type of bias arguably.

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