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Series LC circuit by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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Fourier series by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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Approximates an original function by sines. If the function is "well behaved enough", the approximation is to arbitrary precision.
Fourier's original motivation, and a key application, is solving partial differential equations with the Fourier series.
The Fourier series behaves really nicely in , where it always exists and converges pointwise to the function: Carleson's theorem.
Video 1.
But what is a Fourier series? by 3Blue1Brown (2019)
Source. Amazing 2D visualization of the decomposition of complex functions.
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Satoshi Nakamoto by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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bitcoin.org registration: 2008-08-18
2008-08-22: first private contact to Wei Dai email. Reproduced at www.gwern.net/docs/bitcoin/2008-nakamoto on gwern.net from address satoshi@anonymousspeech.com. Email provider shutting down entirely on 2021-09-30 as per archive.ph/wip/RRNKx, homepage now juts contains useless Bitcoin stuff.
First public Bitcoin whitepaper announcement: 2008-10-31 www.metzdowd.com/pipermail/cryptography/2008-October/014810.html linking to www.bitcoin.org/bitcoin.pdf, email sent from from satoshi@vistomail.com. Claimed one year and a half development time. Provider apparently closed in 2014: www.reddit.com/r/Bitcoin/comments/3h80mi/vistomailcom_closed_and_domain_changed_owner_in/, as of 2021 just reads:
Once upon a time a man paid me a visit in cyberspace, at this very domain. He planted a seed in our heads that would become the path we are walking today.
Replies in November: www.metzdowd.com/pipermail/cryptography/2008-November/thread.html#14863 under satoshi@anonymousspeech.com claims source code shared privately by request at that point.
First open source release: 9 January 2009. Announcement: www.metzdowd.com/pipermail/cryptography/2009-January/014994.html "Windows only for now. Open source C++ code is included" Arghhhhhh how can those libertarians use Microsoft Windows??? Had a GUI already.
2011-04-23 Satoshi sent his last email ever, it was to Martti Malmi. www.nytimes.com/2015/05/17/business/decoding-the-enigma-of-satoshi-nakamoto-and-the-birth-of-bitcoin.html mentions:
May 2011 was also the last time Satoshi communicated privately with other Bitcoin contributors. In an email that month to Martti Malmi, one of the earliest participants, Satoshi wrote, "I've moved on to other things and probably won't be around in the future."
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GPL software by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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CGI comms by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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We've come across a few shallow and stylistically similar websites on suspicious ranges with this pattern.
No JS/JAR/SWF comms, but rather a subdomain, and an HTTPS page with .cgi extension that leads to a login page. Some names seen for this subdomain:
  • secure.: most common
  • ssl.: also common
  • various other more creative ones linked to the website theme itself, e.g.:
    • musical-fortune.net has a backstage.musical-fortune.net
The question is, is this part of some legitimate tooling that created such patterns? And if so which? Or are they actual hits with a new comms mechanism not previously seen?
The fact that:
  • hits of this type are so dense in the suspicious ranges
  • they are so stylistically similar between on another
  • citizenlabs specifically mentioned a "CGI" comms method
suggests to Ciro that they are an actual hit.
In particular, the secure and ssl ones are overused, and together with some heuristics allowed us to find our first two non Reuters ranges! Section "secure subdomain search on 2013 DNS Census"
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JavaScript memory usage benchmark by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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In this section we will use the file nodejs/bench_mem.js, tests are run on Node.js v16.14.2 from NVM, Ubuntu 21.10, on Lenovo ThinkPad P51 (2017) which has 32 GB RAM.
A C hello world with an infinite loop at the end has:
  • 2.7 MB
  • 770 KB
For a Node.js infinite loop nodejs/infinite_loop.js
topp infinite_loop.js
This gives approximately:
  • RSS: 20 MB
  • VSZ: 230 MB
Adding a single hello world to it as in nodejs/infinite_hello.js and running:
topp infinite_hello.js
leads to:
  • RSS: 26 MB
  • VSZ: 580 MB
We understand that Node.js preallocates VSZ wildly. No big deal, but it does mean that VSZ is a useless measure for Node.js.
Forcing garbage collection as in nodejs/infinite_hello.js brings it down to 20 MB however:
topp node --expose-gc infinite_hello_gc.js
Finally let's see a baseline for process.memoryUsage nodejs/infinite_memoryusage.js:
node --expose-gc infinite_memoryusage.js
which gives initially:
{
  rss: 23851008,
  heapTotal: 6987776,
  heapUsed: 3674696,
  external: 285296,
  arrayBuffers: 10422
}
but after a few seconds randomly jumps to:
{
  rss: 26005504,
  heapTotal: 9084928,
  heapUsed: 3761240,
  external: 285296,
  arrayBuffers: 10422
}
so we understand that
  • heapUsed seems constant at 3.7 MB
  • heapTotal is a very noisy, as it starts at 7 MB, but randomly jumps to 9 MB at one point without apparent reason
Now let's run our main test program.
First a baseline case with an array of length 1:
node --expose-gc bench_mem.js n 1
This gives the same results as node --expose-gc infinite_memoryusage.js. The same result is obtained by doing:
a = undefined
with:
node --expose-gc bench_mem.js dealloc
Not let's vary the size of n a bit with:
node --expose-gc bench_mem.js n N
which gives:
NheapUsedheapTotalrssheapUsed per elemrss per elem
1 M14 MB48 MB56 MB1030
10 M122 MB157 MB176 MB1815
100 M906 MB940 MB960 MB99.3
"rss per elem" is calculated as: rss - 26 MB, where 26 MB is the baseline RSS seen on n 1.
Similarly "heapUsed per elem" deduces the 4 MB (approximation of the above 3.7 MB) seen on n 1.
Note that to reach MAX_SAFE_INTEGER we would need 8 bytes per elem worst case.
Everything below 100 million (8) is therefore very memory wasteful in terms of RSS.
If we use Int32Array typed array buffers instead of a simple Array:
node --expose-gc bench_mem.js array-buffer n N
we see that the memory is now, unsurprisingly, accounted for under arrayBuffers, e.g. for N 1 million:
{
  rss: 31776768,
  heapTotal: 6463488,
  heapUsed: 3674520,
  external: 4285296,
  arrayBuffers: 4010422
}
Results for different N:
|| N
|| `arrayBuffers`
|| `rss`
|| `rss` per elem

| 1 M
| 4 MB
| 31 MB
| 5

| 10 M
| 40 MB
| 67 MB
| 4.6

| 100 M
| 40 MB
| 427 MB
| 4
We see therefore that typed arrays are much closer to what they advertise (4 bytes per element), even for smaller element counts, as expected.
Now let's try one million objects of type { a: 1, b: -1 }:
node --expose-gc bench_mem.js obj
gives:
{
  rss: 138969088,
  heapTotal: 105246720,
  heapUsed: 70103896,
  external: 285296,
  arrayBuffers: 10422
}
Disaster! Memory usage is up to 70 MB! Why?? We were expecting only about 24, 4 baseline + 2 * 10 for each million int?!
And now an equivalent version using class:
node --expose-gc bench_mem.js class
gives the same result.
Let's try Array:
node --expose-gc bench_mem.js arr
is even worse at 78 MB!! OMG why.
{
  rss: 164597760,
  heapTotal: 129363968,
  heapUsed: 78117008,
  external: 285296,
  arrayBuffers: 10422
}
Let's change the number of fields on the object? First as a sanity check:
node --expose-gc bench_mem.js obj 2
produces as expected the smae result as:
node --expose-gc bench_mem.js obj
so adding properties one by one doesn't change anything from creating the literal all at once. Good.
Now:
node --expose-gc bench_mem.js obj N
gives heapUsed:
  • 1: 70M
  • 2: 70M
  • 3: 70M
  • 4: 70M
  • 5: 110M
  • 6: 110M
  • 7: 110M
  • 8: 134M
  • 9: 134M
  • 10: 134M
  • 11: 158M
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Ubuntu 18.04 by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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Break the meta by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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To break the meta means to find a new strategy that offers a significant advantage over the existing meta.
Video 1.
How One Man Changed the High Jump Forever by Olympics (2018)
Source. Dick Fosbury created and implemented the Fosbury Flop jump style in 1968.
Video 2.
Akiyo Noguchi asks the rules while climbing! | Beta Break Ep.1 by Albert Ok (2020)
Source. Happened at the 2015 IFSC Climbing World Cup during the Haiyang, China, bouldering event. The author has a playlist of such climbing meta breaks. In climbing, the meta is called "the beta". Climbing competitions are perhaps the sport in which the meta is broken the most often, since each stage is unique.
Video 3.
Lukas Hofer's Revolutionary Technique by IBU TV (2019)
Source. Lukas created a new technique to pack up his rifle during biathlon competitions.
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Capacitor by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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The fundamental intuition about capacitors is that they never let electrons through.
They can only absorb electrons up to a certain point, but then the pushback becomes too strong, and current stops.
Therefore, they cannot conduct direct current long term.
For alternating current however, things are different, because in alternating current, electrons are just jiggling back and forward a little bit around a center point. So you can send alternating current power across a capacitor.
The key equation that relates Voltage to electric current in the capacitor is:
(1)
So if a voltage Heavyside step function is applied what happens is:
  • the capacitor fills up instantly with an infinite current
  • the current then stops instantly
More realistically, one may consider the behavior or the series RC circuit to see what happens without infinities when a capacitor is involved as in the step response of the series RC circuit.
Figure 1.
Electronic symbol of a capacitor
. Source.
Video 1.
Finding capacitance with an oscilloscope by Jacob Watts (2020)
Source. Good experiment.
Video 2.
Capacitors Explained by The Engineering Mindset
. Source. 2019.
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Wayback Machine full text search by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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Personal web page by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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Usenet newsgroup by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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Eternal September by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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Shaun Bridges by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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OpenStax by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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These people have good intentions.
The problem is that they don't manage to go critical because there's to way for students to create content, everything is manually curated.
You can't even publicly comment on the textbooks. Or at least Ciro Santilli hasn't found a way to do so. There is just a "submit suggestion" box.
This massive lost opportunity is even shown graphically at: cnx.org/about (archive) where there is a clear separation between:
  • "authors", who can create content
  • "students", who can consume content
Maybe this wasn't the case in their legacy website, legacy.cnx.org/content?legacy=true, but not sure, and they are retiring that now.
Thus, OurBigBook.com. License: CC BY! So we could re-use their stuff!
TODO what are the books written in?
Video 1.
Richard Baraniuk on open-source learning by TED (2006)
Source.
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MediaWiki instance by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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Nupedia by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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Download all Wikipedia categories by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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Let's observe them in MySQL:
mysql enwiki -e "select page_id, page_namespace, page_title, page_is_redirect from page where page_namespace in (0, 14) and page_title in ('Computer_storage_devices', 'Computer_data_storage')"
outputs:
+----------+----------------+--------------------------+------------------+
| page_id  | page_namespace | page_title               | page_is_redirect |
+----------+----------------+--------------------------+------------------+
|     5300 |              0 | Computer_data_storage    |                0 |
| 42371130 |              0 | Computer_storage_devices |                1 |
|   711721 |             14 | Computer_data_storage    |                0 |
|   895945 |             14 | Computer_storage_devices |                0 |
+----------+----------------+--------------------------+------------------+
mysql enwiki -e "select cl_from, cl_to from categorylinks where cl_from in (5300, 711721, 895945, 42371130)"
gives:
+----------+-----------------------------------------------------------------------+
| cl_from  | cl_to                                                                 |
+----------+-----------------------------------------------------------------------+
|     5300 | All_articles_containing_potentially_dated_statements                  |
|     5300 | Articles_containing_potentially_dated_statements_from_2009            |
|     5300 | Articles_containing_potentially_dated_statements_from_2011            |
|     5300 | Articles_with_GND_identifiers                                         |
|     5300 | Articles_with_NKC_identifiers                                         |
|     5300 | Articles_with_short_description                                       |
|     5300 | Computer_architecture                                                 |
|     5300 | Computer_data_storage                                                 |
|     5300 | Short_description_matches_Wikidata                                    |
|     5300 | Use_dmy_dates_from_June_2020                                          |
|     5300 | Wikipedia_articles_incorporating_text_from_the_Federal_Standard_1037C |
|   711721 | Computer_architecture                                                 |
|   711721 | Computer_data                                                         |
|   711721 | Computer_hardware_by_type                                             |
|   711721 | Data_storage                                                          |
|   895945 | Computer_data_storage                                                 |
|   895945 | Computer_peripherals                                                  |
|   895945 | Recording_devices                                                     |
| 42371130 | Redirects_from_alternative_names                                      |
+----------+-----------------------------------------------------------------------+
So we see that cl_from encodes the parent categories:
So to find all articls and categories under a given category title, say en.wikipedia.org/wiki/Category:Mathematics we can run:
mariadb enwiki -e "select cl_from, cl_to, page_namespace, page_title from categorylinks inner join page on page_namespace in (0, 14) and cl_from = page_id and cl_to = 'Mathematics'"
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Wikipedia dumps by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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Per-table dumps created with mysqldump and listed at: dumps.wikimedia.org/. Most notably, for the English Wikipedia: dumps.wikimedia.org/enwiki/latest/
The tables are "documented" under: www.mediawiki.org/wiki/Manual:Database_layout, e.g. the central "page" table: www.mediawiki.org/wiki/Manual:Page_table. But in many cases it is impossible to deduce what fields are from those docs.
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Deletionism on Wikipedia by Ciro Santilli 35 Updated 2025-04-18 +Created 1970-01-01
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Some examples by Ciro Santilli follow.
Of the tutorial-subjectivity type:
Notability constraints, which are are way too strict:
There are even a Wikis that were created to remove notability constraints: Wiki without notability requirements.
For these reasons reason why Ciro basically only contributes images to Wikipedia: because they are either all in or all out, and you can determine which one of them it is. And this allows images to be more attributable, so people can actually see that it was Ciro that created a given amazing image, thus overcoming Wikipedia's lack of reputation system a little bit as well.
Wikipedia is perfect for things like biographies, geography, or history, which have a much more defined and subjective expository order. But when it comes to "tutorials of how to actually do stuff", which is what mathematics and physics are basically about, Wikipedia has a very hard time to go beyond dry definitions which are only useful for people who already half know the stuff. But to learn from zero, newbies need tutorials with intuition and examples.
Bibliography:
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Pinned article: ourbigbook/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!
Video 1.
Intro to OurBigBook
. Source.
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
    Video 2.
    OurBigBook Web topics demo
    . Source.
  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 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
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