Ciro Santilli @cirosantilli 37

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Sometimes you can debug software by staring at the code for long enough Updated 2025-07-16

Once upon a time, when Ciro Santilli had a job, he had a programming problem.

A senior developer came over, and rather than trying to run and modify the code like an idiot, which is what Ciro Santilli usually does (see also experimentalism remarks at Section "Ciro Santilli's bad old event memory"), he just stared at the code for about 10 minutes.

We knew that the problem was likely in a particular function, but it was really hard to see why things were going wrong.

After the 10 minutes of examining every line in minute detail, he said:

I think this function call has such or such weird edge case

and truly, that was the cause.

And so, Ciro was enlightened.

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Spacetime diagram Updated 2025-07-16

Why should I care when I can calculate new x and new time with Lorentz transformation?

Answer: it can give some qualitative intuition on what is larger/smaller happens before/after based only on arguably more intuitive geometric considerations, without requiring you to do any calculations, see e.g. Figure "Spacetime diagram illustrating how faster-than-light travel implies time travel".

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Spark-gap transmitter Updated 2025-07-16

The first type of device that allowed sending Morse code without wires, as opposed to the wired electrical telegraph that previously existed.

Naval communications was one of the first major applications, as you can't have wires on boats!

Wireless voice transmission came about with modulation.

Spark-gap transmitter at the at the The Museum of Radio and Technology Jeri Ellsworth (2017)

Marconi Spark Gap Transmitter Demonstration by Canada Science and Technology Museum (2012)

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Spherical cap model of the real projective plane Updated 2025-07-16

Ciro Santilli's preferred visualization of the real projective plane is a small variant of the standard "lines through origin in

R^{3}

".

Take a open half sphere e.g. a sphere but only the points with

z > 0

.

Each point in the half sphere identifies a unique line through the origin.

Then, the only lines missing are the lines in the x-y plane itself.

For those sphere points in the circle on the x-y plane, you should think of them as magic poins that are identified with the corresponding antipodal point, also on the x-y, but on the other side of the origin. So basically you you can teleport from one of those to the other side, and you are still in the same point.

Ciro likes this model because then all the magic is confined just to the

z = 0

part of the model, and everything else looks exactly like the sphere.

It is useful to contrast this with the sphere itself. In the sphere, all points in the circle

z = 0

are the same point. But this is not the case for the projective plane. You cannot instantly go to any other point on the

z = 0

by just moving a little bit, you have to walk around that circle.

Figure 1.
Spherical cap model of the real projective plane
. On the x-y plane, you can magically travel immediately between antipodal points such as A/A', B/B' and C/C'. Or equivalently, those pairs are the same point. Every other point outside the x-y plane is just a regular point like a normal sphere.

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Spin experiments Updated 2025-07-16

Stern-Gerlach experiment
fine structure split in energy levels
anomalous Zeeman effect
of a more statistical nature, but therefore also macroscopic and more dramatically observable:
- ferromagnetism
- Bose-Einstein statistics vs Fermi-Dirac statistics. A notable example is the difference in superfluid transition temperature between superfluid helium-3 and superfluid helium-4.

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Spin number of a field Updated 2025-07-16

I like relativistic quantum mechanics.

Best mathematical explanation: Section "Spin comes naturally when adding relativity to quantum mechanics".

Physics from Symmetry by Jakob Schwichtenberg (2015) chapter 3.9 "Elementary particles" has an amazing summary of the preceding chapters the spin value has a relation to the representations of the Lorentz group, which encodes the spacetime symmetry that each particle observes. These symmetries can be characterized by small integer numbers:

spin 0: $(0, 0)$ representation
spin half: $(1/2, 0) ⨁ (0, 1/2)$ representation
spin 1: $(1/2, 1/2)$ representation

As usual, we don't know why there aren't elementary particles with other spins, as we could construct them.

Bibliography:

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Spin (physics) Updated 2025-07-16

Spin is one of the defining properties of elementary particles, i.e. number that describes how an elementary particle behaves, much like electric charge and mass.

Possible values are half integer numbers: 0, 1/2, 1, 3/2, and so on.

The approach shown in this section: Section "Spin comes naturally when adding relativity to quantum mechanics" shows what the spin number actually means in general. As shown there, the spin number it is a direct consequence of having the laws of nature be Lorentz invariant. Different spin numbers are just different ways in which this can be achieved as per different Representation of the Lorentz group.

Video 1. "Quantum Mechanics 9a - Photon Spin and Schrodinger's Cat I by ViaScience (2013)" explains nicely how:

incorporated into the Dirac equation as a natural consequence of special relativity corrections, but not naturally present in the Schrödinger equation, see also: the Dirac equation predicts spin
photon spin can be either linear or circular
the linear one can be made from a superposition of circular ones
straight antennas produce linearly polarized photos, and Helical antennas circularly polarized ones
a jump between 2s and 2p in an atom changes angular momentum. Therefore, the photon must carry angular momentum as well as energy.
cannot be classically explained, because even for a very large estimate of the electron size, its surface would have to spin faster than light to achieve that magnetic momentum with the known electron charge
as shown at Video "Quantum Mechanics 12b - Dirac Equation II by ViaScience (2015)", observers in different frames of reference see different spin states

Quantum Mechanics 9a - Photon Spin and Schrodinger's Cat I by ViaScience (2013)

Quantum Spin - Visualizing the physics and mathematics by Physics Videos by Eugene Khutoryansky (2016)

Understanding QFT - Episode 1 by Highly Entropic Mind (2023)

. Source. Maybe he stands a chance.

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Ciro's Edict #4 / China front Updated 2025-07-16

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Ciro's Edict #4 / ourbigbook.com Updated 2025-07-16

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Ciro's Edict #4 / The table of contents shows across different files via \Include Updated 2025-07-16

README.cironot-readme.cirothe table of contents for index.html also contains the headers for not-readme.ciro producing:

This will be especially important for the website because initially I want users to be able to edit one header at a time, and join all headers with \Include. But I still want the ToC to show those children.

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Ciro's Edict #5 / Completely rebrand Cirodown to OurBigBook Updated 2025-07-16

I have also squatted OurBigBook on all major social media handles for near future usage, e.g.: twitter.com/ourbigbook and so on.

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Ciro's Edict #8 / List topics on home page Updated 2025-07-16

Doing this required in particular calculating the best title for a topic, since it is possible to have different titles with the same ID, the most common way being with capitalization changes, e.g.:would both have topic ID javascript.

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Ciro's Edict #8 / Next steps Updated 2025-07-16

I guess ended up doing all the "how things should look like" features because they clarify what the website is supposed to do, and I already have my own content to bring it alive via ourbigbook --web upload.

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Spontaneous parametric down-conversion Updated 2025-07-16

Phenomena that produces photons in pairs as it passes through a certain type of crystal.

You can then detect one of the photons, and when you do you know that the other one is there as well and ready to be used. two photon interference experiment comes to mind, which is the basis of photonic quantum computer, where you need two photons to be produced at the exact same time to produce quantum entanglement.

One Photon In, TWO Photons Out by JQInews (2010)

Features Alan Migdall of the National Institute of Standards and Technology. Produced by the Joint Quantum Institute (JQI).

Mentions that this phenomena is useful to determine the efficiency of a single photon detector, as you have the second photon of the pair as a control.

Also briefly describes how the input energy and momentum must balance out the output energy and momentum of the two photons coming out (determined by the output frequency and angle).

Shows the crystal close up of the crystal branded "Cleveland Crystals Inc.". Mentions that only one in a billion photon gets scattered.

Also shows a photomultiplier tube.

Then shows their actual optical table setup, with two tunnels of adjustable angle to get photons with different properties.

How do you produce a single photon? by Physics World (2015)

Very short whiteboard video by Peter Mosley from the University of Bath, but it's worth it for newbs. Basically describes spontaneous parametric down-conversion.

One interesting thing he mentions is that you could get single photons by making your sunglasses thicker and thicker to reduce how many photons pass, but one big downside problem is that then you don't know when the photon is going to come through, that becomes essentially random, and then you can't use this technique if you need two photons at the same time, which is often the case, see also: two photon interference experiment.

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SQL contiguous ranges Updated 2025-07-16

stackoverflow.com/questions/17046204/how-to-find-the-boundaries-of-groups-of-contiguous-sequential-numbers/17046749#17046749 just works, even in SQLite which supports all quoting types known to man including [] for compatibility with insane RDBMSs!

Here's a slightly saner version:

rm -f tmp.sqlite
sqlite3 tmp.sqlite "create table mytable (id integer primary key autoincrement, number integer, status integer)"
sqlite3 tmp.sqlite <<EOF
insert into mytable(number, status) values
  (100,0),
  (101,0),
  (102,0),
  (103,0),
  (104,1),
  (105,1),
  (106,0),
  (107,0),
  (1014,0),
  (1015,0),
  (1016,1),
  (1017,0)
EOF
sqlite3 tmp.sqlite <<EOF
SELECT
  MIN(id) AS "id",
  MIN(number) AS "from",
  MAX(number) AS "to"
FROM (
  SELECT ROW_NUMBER() OVER (ORDER BY number) - number AS grp, id, number
  FROM mytable
  WHERE status = 0
)
GROUP BY grp
ORDER BY MIN(number)
EOF

output:

1|100|103
7|106|107
9|1014|1015
12|1017|1017

To get only groups of length greater than 1:

sqlite3 tmp.sqlite <<EOF
SELECT "id", "from", "to", "to" - "from" + 1 as "len" FROM (
  SELECT
    MIN("id") AS "id",
    MIN(number) AS "from",
    MAX(number) AS "to"
  FROM (
    SELECT ROW_NUMBER() OVER (ORDER BY "number") - "number" AS "grp", "id", "number"
    FROM "mytable"
    WHERE "status" = 0
  )
  GROUP BY "grp"
  ORDER BY MIN("number")
) WHERE "len" > 1
EOF

Output:

1|100|103|4
7|106|107|2
9|1014|1015|2

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SQL histogram Updated 2025-07-16

OK, there's a billion questions:

SQL Server
- stackoverflow.com/questions/485409/generating-a-histogram-from-column-values-in-a-database OP did not know the difference between count and histogram :-) But it's the number one Google result.
- stackoverflow.com/questions/19103991/create-range-bins-from-sql-server-table-for-histograms has a minor extra group by twist, but otherwise fine
- stackoverflow.com/questions/16268441/generate-histogram-in-sql-server
SQLite
- stackoverflow.com/questions/67514208/how-to-optimise-creating-histogram-bins-in-sqlite perf only, benchmarking would be needed. SQLite.
- stackoverflow.com/questions/32155449/create-a-histogram-with-a-dynamic-number-of-partitions-in-sqlite variable bin size, same number of entries per bin
- stackoverflow.com/questions/60348109/histogram-for-time-periods-using-sqlite-regular-buckets-1h-wide time
MySQL: stackoverflow.com/questions/1764881/getting-data-for-histogram-plot MySQL appears to extend ROUND to also round by integers: ROUND(numeric_value, -2), but this is not widely portable which is a shame
stackoverflow.com/questions/72367652/populating-empty-bins-in-a-histogram-generated-using-sql specifically asks about empty bins, which is amazing. Amazon Redshift dialect unfortunately, but answer provided works widely, and Redshift was forked from PostgreSQL, so there's hope. Those newb open source server focused projects that don't use AGPL!

Let's try it on SQLite 3.40.1, Ubuntu 23.04. Data setup:

sqlite3 tmp.sqlite 'create table t(x integer)'
sqlite3 tmp.sqlite <<EOF
insert into t values (
  0,
  2,
  2,
  3,

  5,
  6,
  6,
  8,
  9,

  17,
)
EOF
sqlite3 tmp.sqlite 'create index tx on t(x)'

For a bin size of 5 ignoring empty ranges we can:

sqlite3 tmp.sqlite <<EOF
select floor(x/5)*5 as x,
       count(*) as cnt
from t
group by 1
order by 1
EOF

which produces the desired:

0|4
5|5
15|1

And to consider empty ranges we can use SQL genenerate_series + as per stackoverflow.com/questions/72367652/populating-empty-bins-in-a-histogram-generated-using-sql:

sqlite3 tmp.sqlite <<EOF
select x, sum(cnt) from (
  select floor(x/5)*5 as x,
         count(*) as cnt
    from t
    group by 1
  union
  select *, 0 as cnt from generate_series(0, 15, 5)
)
group by x
EOF

which outputs the desired:

0|4
5|5
10|0
15|1

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sqlite3 Node.js package Updated 2025-07-16

Includes its own copy of sqlite3, you don't use the system one, which is good to ensure compatibility. The version is shown at: github.com/mapbox/node-sqlite3/blob/918052b538b0effe6c4a44c74a16b2749c08a0d2/deps/common-sqlite.gypi#L3 SQLite source is tracked compressed in-tree: github.com/mapbox/node-sqlite3/blob/918052b538b0effe6c4a44c74a16b2749c08a0d2/deps/sqlite-autoconf-3360000.tar.gz horrendous. This explains why it takes forever to clone that repository. People who don't believe in git submodules, there's even an official Git mirror at: github.com/sqlite/sqlite

It appears to spawn its own threads via its C extension (since JavaScript is single threaded and and SQLite is not server-based), which allows for parallel queries using multiple threads: github.com/mapbox/node-sqlite3/blob/v5.0.2/src/threading.h

Hello world example: nodejs/node-sqlite3/index.js.

As of 2021, this had slumped back a bit, as maintainers got tired. Unmerged pull requests started piling more, and better-sqlite3 Node.js package started pulling ahead a little.

github.com/mapbox/node-sqlite3/issues/1381 FATAL ERROR: Error::ThrowAsJavaScriptException napi_throw with Node.js worker_threads vs better-sqlite3 Node.js package github.com/JoshuaWise/better-sqlite3/issues/237

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SQL RECURSIVE prevent infinite recursion Updated 2025-07-16

Example under: nodejs/sequelize/raw/tree.js

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SQL tree traversal Updated 2025-07-16

Example: nodejs/sequelize/raw/tree.js

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SQL TRIGGER Updated 2025-07-16

SQL's implementation of database triggers.

This feature is really cool, as it allows you to keep caches up to date!

In particular, everything that happens in a trigger happens as if it were in a transaction. This way, you can do less explicit transactions when you use triggers. It is a bit like the advantages of SQL CASCADE.

Sequelize: SQL TRIGGER in Sequelize

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