Ciro Santilli @cirosantilli  40

 Articles (13k) Discussions (30) Comments (68) Follows  Received likes Files

New Updated  Top  Announced  A-Z  Liked  Followed

List of Stack Overflow users Updated 2025-09-09

 Read the full article

Physics Stack Exchange Updated 2025-07-16

physics.stackexchange.com/

 Read the full article

Matrix ring Updated 2025-07-16

The matrix ring of degree n

M_{n}

is the set of all n-by-n square matrices together with the usual vector space and matrix multiplication operations.

This set forms a ring.

Related terminology:

math.stackexchange.com/questions/412200/what-is-the-notation-for-the-set-of-all-m-times-n-matrices

 Read the full article

Ciro's Edict #5 / Link to an image or video in another file that has an \x on title from another file Updated 2025-07-16

= Programming language

\Image[https://raw.githubusercontent.com/cirosantilli/media/master/python-logo.jpg]
{title=The \x[python-programming-language] logo}

== Python
{c}
{disambiguate=programming-language}

Now, when rendering \x[image-the-python-logo], we would need to fetch two IDs:

But after group all SQL queries together was done, there was no way to know that rendering image-the-python-logo would imply also fetching python-programming-language.

This was solved by adding a new database entry type, REFS_TABLE_X_TITLE_TITLE to the existing References table, which tracks dependencies between IDs.

After this was setup, we can now know that image-the-python-logo depends on image-the-python-logo, and then fetch both of them together in a single JOIN.

 Read the full article

Hermitian matrix Updated 2025-07-16

 Read the full article

Invariance of the speed of light Updated 2025-07-16

This single experimental observation/idea is the basis for all of special relativity.

Special relativity is the direct result of people bending their backs to accommodate for this really weird fact.

 Read the full article

History of special relativity Updated 2025-07-16

Bibliography:

Subtle is the Lord by Abraham Pais (1982) chapter III "Relativity, the special theory" has a good sketch as you may imagine.

 Read the full article

Special relativity experiment Updated 2025-07-16

moving magnet and conductor problem: the more experiments confirm Maxwell's equations, the more special relativity has to be correct
aberration TODO more precisely how it is evidence.

 Read the full article

Einstein synchronization Updated 2025-07-16

 Read the full article

Lorentz transformation Updated 2025-07-16

The equation that allows us to calculate stuff in special relativity!

Take two observers with identical rules and stopwatch, and aligned axes, but one is on a car moving at towards the

+ x

direction at speed

v

.

When both observe an event, if we denote:

$(t, x, y, z)$ the observation of the standing observer
$(t^{'}, x^{'}, y^{'}, z^{'})$ the observation of the ending observer on a car

It is of course arbitrary who is standing and who is moving, we will just use the term "standing" for the one without primes.

Then the coordinates of the event observed by the observer on the car are:

t^{'} x^{'} y^{'} z^{'} = γ (t - \frac{vx}{c ^{2}}) = γ (x - v t) = y = z

where:

γ = \frac{1}{1 - ( \frac{v}{c} ) ^{2}}

Note that if

\frac{v}{c}

tends towards zero, then this reduces to the usual Galilean transformations which our intuition expects:

t^{'} y^{'} z^{'} = t x^{'} = y = z = x - v t

This explains why we don't observe special relativity in our daily lives: macroscopic objects move too slowly compared to light, and

\frac{v}{c}

is almost zero.

 Read the full article

Maxwell's equations require special relativity Updated 2025-07-16

The following aspects of Maxwell's equations make no sense without special relativity:

the Lorentz force would be different observers have different speeds, see e.g.: charged particle moving at the same speed of electrons thought experiment
Maxwell's equations imply that the speed of light is the same for all inertial reference frames

When charged particle though experiment are seen from the point of view of special relativity, it becomes clear that magnetism is just a direct side effect of charges being viewed in special relativity. One is philosophically reminded of how spin is the consequence of quantum mechanics + special relativity.

Bibliography:

 Read the full article

Spacetime Updated 2025-07-16

 Read the full article

Relativistic mechanics Updated 2025-07-16

 Read the full article

Special linear group of dimension 2 Updated 2025-07-16

 Read the full article

S L (n)

Updated 2025-07-16

 Read the full article

Finite special general linear group Updated 2025-07-16

Just like for the finite general linear group, the definition of special also works for finite fields, where 1 is the multiplicative identity!

Note that the definition of orthogonal group may not have such a clear finite analogue on the other hand.

 Read the full article

The best code is no code at all Updated 2025-07-16

Some blogs:

blog.codinghorror.com/the-best-code-is-no-code-at-all/ The Best Code is No Code At All (2007)
www.skrenta.com/2007/05/code_is_our_enemy.html Code is our enemy (2007)

Also resonates with backward design.

 Read the full article

Use The Source Luke Updated 2025-07-16

wiki.c2.com/?UseTheSourceLuke

 Read the full article

Playstation Updated 2025-07-16

 Read the full article

Static program analysis Updated 2025-07-16

 Read the full article

 There are unlisted articles, also show them or only show them.