Ciro Santilli @cirosantilli 35

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Product definition of the exponential function by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

e^{x} = lim_{n \to \infty} (1 + \frac{x}{n})^{n}

The basic intuition for this is to start from the origin and make small changes to the function based on its known derivative at the origin.

More precisely, we know that for any base b, exponentiation satisfies:

$b^{x + y} = b^{x} b^{y}$ .
$b^{0} = 1$ .

And we also know that for

b = e

in particular that we satisfy the exponential function differential equation and so:

\frac{d e ^{x}}{d x} (0) = 1

One interesting fact is that the only thing we use from the exponential function differential equation is the value around

x = 0

, which is quite little information! This idea is basically what is behind the importance of the ralationship between Lie group-Lie algebra correspondence via the exponential map. In the more general settings of groups and manifolds, restricting ourselves to be near the origin is a huge advantage.

Now suppose that we want to calculate

e^{1}

. The idea is to start from

e^{0}

and then then to use the first order of the Taylor series to extend the known value of

e^{0}

to

e^{1}

.

E.g., if we split into 2 parts, we know that:

e^{1} = e^{1 / 2} e^{1 / 2}

or in three parts:

e^{1} = e^{1 / 3} e^{1 / 3} e^{1 / 3}

so we can just use arbitrarily many parts

e^{1 / n}

that are arbitrarily close to

x = 0

:

e^{1} = (e^{1 / n})^{n}

and more generally for any

x

we have:

e^{x} = (e^{x / n})^{n}

Let's see what happens with the Taylor series. We have near

y = 0

in little-o notation:

e^{y} = 1 + y + o (y)

Therefore, for

y = x / n

, which is near

y = 0

for any fixed

x

:

e^{x / n} = 1 + x / n + o (1 / n)

and therefore:

e^{x} = (e^{x / n})^{n} = (1 + x / n + o (1 / n))^{n}

which is basically the formula tha we wanted. We just have to convince ourselves that at

lim_{n \to \infty}

, the

o (1 / n)

disappears, i.e.:

(1 + x / n + o (1 / n))^{n} = (1 + x / n)^{n}

To do that, let's multiply

e^{y}

by itself once:

e^{y} e^{y} = (1 + y + o (y)) (1 + y + o (y)) = 1 + 2 y + o (y)

and multiplying a third time:

e^{y} e^{y} e^{y} = (1 + 2 y + o (y)) (1 + y + o (y)) = 1 + 3 y + o (y)

TODO conclude.

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Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

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List of data breaches by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

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Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

Too restrictive. People should be able to make money from stuff.

The definition of "commercial" could also be taken in extremely broad senses, making serious reuse risky in many applications.

Notably, many university courses use it, notably MIT OpenCourseWare. Ciro wonders if it is because academics are wary of industry, or if they want to make money from it themselves. This reminds Ciro of a documentary he watched about the origins of one an early web browsers in some American university. And then that university wanted to retain copyright to make money from it. But the PhDs made a separate company nonetheless. And someone from the company rightly said something along the lines of:

The goal of universities is to help create companies and to give back to society like that. Not to try and make money from inventions.

TODO source.

The GNU project does not like it either www.gnu.org/licenses/license-list.en.html#CC-BY-NC:

This license does not qualify as free, because there are restrictions on charging money for copies. Thus, we recommend you do not use this license for documentation.
In addition, it has a drawback for any sort of work: when a modified version has many authors, in practice getting permission for commercial use from all of them would become infeasible.

en.wikipedia.org/wiki/Creative_Commons_NonCommercial_license#Defining_%22Noncommercial%22 also talks about the obvious confusion this generates: nobody can agree what counts as commercial or not!

In September 2009 Creative Commons published a report titled, "Defining 'Noncommercial'". The report featured survey data, analysis, and expert opinions on what "noncommercial" means, how it applied to contemporary media, and how people who share media interpret the term. The report found that in some aspects there was public agreement on the meaning of "noncommercial", but for other aspects, there is wide variation in expectation of what the term means.

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Dan Kaminsky by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

A superstar security researcher with some major exploits from in the 2000's.

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Kinesis Advantage 2 keyboard by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

kinesis-ergo.com/shop/advantage2/

For Ciro Santilli, this is not a computer keyboard. It is a fetish.

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P (complexity) by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

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Cloud computing market share by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

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Inner source by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

If you are going to do closed source, at least do it like this.

Basically the opposite of need to know for software.

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The development cycle time is your God by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

A slow development test cycle will kill your software.

New developers won't want to learn your project, because they would rather shoot themselves.

This means that build time, and the time to run tests, must be short.

5 seconds to rebuild is the maximum upper limit.

Of course, at some point software gets large enough that things won't fit anymore in 5 seconds. But then you must have either some kind of build caching, or options to do partial builds/tests that will bring things down to that 5 second mark.

You also have to spend some time profiling execution and build from scratch times.

A slow build from scratch will mean that your continuous integration costs a lot, money that could be invested in a new developer!

It also means that people won't bother to reproduce bugs on given commits, or bisect stuff.

One anecdote comes to mind. Ciro Santilli was trying to debug something, and more experience colleague came over.

To reproduce a problem, ciro was running one command, wait 5 seconds, run a second command, wait 5 seconds, run a third command:

cmd1
# wait 5 seconds
cmd2
# wait 5 seconds
cmd3

The first thing the colleague said: join those three commands into one:

cmd1;cmd2;cmd3

And so, Ciro was enlightened.

Figure 1.
xkcd 303: Compiling
. Source. They should be benchmarking and fixing their shitty build system instead.

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KISS principle by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

The software engineer phrasing of simplicity is the ultimate sophistication.

Like all other principles, it is not absolute.

But it is something that you should always have on the back of your mind.

You aren't gonna need it is closely related, as generally the extra unnecessary complications are set in place to accommodate useless features that will never be needed.

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Office space design and remote work by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

Working remotely is hard if you don't already highly master the software and enterprise systems used.

Also you don't feel people's love as strongly, and usefulness is built on love, see also Steve Jobs's Pixar office space design philosophy.

But please, give workers a small silent office so that we can concentrate instead of a silly open space, and create an internal social network so people can see what others are doing.

Remote working is much better if the majority of the team also does it, otherwise you will get excluded. Maybe after VR...

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X chromosome by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

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Church of England by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

Political division:

nominal leader: British monarch
toplevel arch-dioceses/provinces of Cantebury and York. One archbishop each, who is also bishop of Cantebury and York diocese
within provinces: one cathedral and bishop per diocese

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Microarchitecture by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

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Causality and quantum jumps are incompatible by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

If something does a quantum jump, what causes it to decide doing so at a particular time and not another? It is expected that a continuous cause would have continuous effects.

This concern was raised immediately by Rutherford while reviewing the Bohr model in 1913 as mentioned in The Quantum Story by Jim Baggott (2011) page 32.

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Radiocarbon dating by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

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Monosaccharide by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

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University of Campinas by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

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Hydrogen cyanide by

Ciro Santilli 35  Updated 2025-01-06  +Created 1970-01-01

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