SQL histogram by Ciro Santilli 37 Updated 2025-07-16
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
Bought: January 2020 from store.google.com/ for 350 pounds.
Front camera video on Android 11: about 100MiB / minute. The encoding is however super inefficient, a FFmpeg re-encode without any options reduces it by 1/3.
For Fastboot mode: Power and Volume down simultaneously for 10-15s. It is OK if screen sleeps. On "no command", power then volume up to see options.
2023-10: touchscreen not registering touches anymore. Still displays images. Manage to regain access with wired USB mouse + a simple USB-C adapter. RIP. Will attempt replacement: store.ifixit.co.uk/products/google-pixel-3a-screen-genuine?variant=42388954448071, partly to get Authy access which I had never properly tested... Replaced screen, but at exact same status as before: shows image but no touch. thus I wasted my money and time (minus the learning) something else is broken.
~1TB.
Internal hard drive likely removed from some old computer I lost track of, kept in a crappy case, incredible stuff.
Ubuntu 20.04 gnome-disks benchmark, NTFS partition: 40MB/s.
Marked read speeds up to 150 MB/s
Write speed burning 5 GB Ubuntu ISO from Dell Inspiron 15: 5.4 MB/s
For clean Dell Inspiron 15 3520 cryptocurrenty laptop bootstrap and backup.
This form is not really an inner product in the common modern definition, because it is not positive definite, only a symmetric bilinear form.
Mathematically, we can decide if two events are timelike-separated or spacelike-separated by just looking at the sign of the spacetime interval between them.
On the light cone, these are events on the left/right part of the cone.
Different observers might not agree on the order of two spacelike-separated events.
Further discussion at Section "Light cone".
The opposite of those events are timelike-separated events.
Standard Model by Ciro Santilli 37 Updated 2025-07-16
As of 2019, the more formal name for particle physics, which is notably missing general relativity to achieve the theory of everything.
cds.cern.ch/record/799984/files/0401010.pdf The Making of the Standard Model by Steven Weinberg mentions three crucial elements that made up the standard model post earlier less generalized quantum electrodynamics understandings
Faster-than-light by Ciro Santilli 37 Updated 2025-07-16
One argument of why, is that if you could travel faster than light, then you could send a message to a point in Spacetime that is spacelike-separated from the present. But then since the target is spacelike separated, there exists a inertial frame of reference in which that event happens before the present, which would be hard to make sense of.
Even worse, it would be possible to travel back in time:

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
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    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 5. . 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.
  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