Ciro Santilli @cirosantilli 37

Take the group of all Translation in ${\mathbb{R}}^1$.

Let's see how the generator of this group is the derivative operator:

The way to think about this is:

So let's take the exponential map:and we notice that this is exactly the Taylor series of $f(x)$ around the identity element of the translation group, which is 0! Therefore, if $f(x)$ behaves nicely enough, within some radius of convergence around the origin we have for finite $x_0$:

This example shows clearly how the exponential map applied to a (differential) operator can generate finite (non-infinitesimal) Translation!

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:

The first thing the colleague said: join those three commands into one:And so, Ciro was enlightened.

A compiled executable under /usr/bin/csvtool, has an Ubuntu 23.04 package: manpages.ubuntu.com/manpages/lunar/en/man1/csvtool.1.html

There seems to be no sane filtering mechanism however: stackoverflow.com/questions/46540752/using-csvtool-call-to-filter-csv-in-bash

After the 2019 redefinition of the SI base units it is by definition exactly $1.60217663410^{-19}$ Joules.

Incredible that there hasn't been a Nobel Prize for it as of 2022, e.g. as mentioned at: theconversation.com/no-nobel-but-epigenetics-finally-gets-the-recognition-it-deserves-18970

Some old dudes getting another prize in 2016: www.cuimc.columbia.edu/news/pioneers-epigenetics-awarded-horwitz-prize

The dot product is a positive definite matrix, and so we see that those will have an important link to familiar geometry.

In Ciro Santilli's view, the following three artists form a Holy Trinity of popular Brazilian music:

Elis Regina is not far though.

Ciro remembers quite clearly when he was riding the car with his parents when he pre teen, and he could not understand why they seemed so obsessed with The Trinity et al. Ciro in particular remembers listening to Video "Refazenda by Gilberto Gil (1975)". They had picked it up of course from the 70's and 80's when they were younger.

Young Ciro would also always confuse who was whom from the three of them.

Then Ciro got older, and he understood, they are mind blowing. You do have to look back in time a bit though, lots of lukewarm stuff on later periods. The military dictatorship in Brazil was good for music.

The only cases where formal proof of theorems seem to have had actual mathematical value is for theorems that require checking a very large number of case, so much so that no human can be fully certain that no mistakes were made. Some examples: