Lebesgue integral vs Riemann integral Updated 2025-07-16
Advantages over Riemann:
Video 1.
Riemann integral vs. Lebesgue integral by The Bright Side Of Mathematics (2018)
Source.
youtube.com/watch?v=PGPZ0P1PJfw&t=808 shows how Lebesgue can be visualized as a partition of the function range instead of domain, and then you just have to be able to measure the size of pre-images.
One advantage of that is that the range is always one dimensional.
But the main advantage is that having infinitely many discontinuities does not matter.
Infinitely many discontinuities can make the Riemann partitioning diverge.
But in Lebesgue, you are instead measuring the size of preimage, and to fit infinitely many discontinuities in a finite domain, the size of this preimage is going to be zero.
So then the question becomes more of "how to define the measure of a subset of the domain".
Which is why we then fall into measure theory!
The inaugural that predicted the Josephson effect.
Published on Physics Letters, then a new journal, before they split into Physics Letters A and Physics Letters B. True Genius: The Life and Science of John Bardeen mentions that this choice was made rather than the more prestigious Physical Review Letters because they were not yet so confident about the results.
Intel GPU Updated 2025-07-16
K-ary tree Updated 2025-07-16
MariaDB Updated 2025-07-16
Dude's a legend. Sells company for a few million. Then forks the open source project next year. Love it.
Trust (law) Updated 2025-07-16
Donald Trump Updated 2025-07-16
Trump's election was an act of protest by the people, because they felt, and rightly so, that the promises by the democrats to decrease social inequality were just full of shit.
So instead, the old voice of nationalism spoke louder.
Ciro agrees with analysis of Can't get you out of my head by Adam Curtis (2021) that this is largely because government is losing all power to do anything meaningful. So the only thing left to do is to speak empty words to calm, or exacerbate, people's fears and hopes.
Ciro believes it is important not hate Trump and his believers, no matter how disgusting Trump might seem, a large part of which is likely theater. We have to try and understand them instead.
Trump's election shows clearly how the democrats let down the poor. This understanding is a good thing. It shows that we all have to make greater efforts to help the poor. Just voting for some random democrat candidate who doesn't really care every four years is not enough.
Another positive point of Trump's election is that it further highlighted the power of social media even further: it now feels more likely than ever before that anyone can run for office, since a president without any previous political office was elected (of course, being filthy reach helps a lot still, which is a problem). And this further highlights the need for regulate social media, to prevent events such as the deplatforming of Donald Trump
We should calmly analyze and understand how someone that tries their best to appear disgusting managed to win. Some interesting analyses of Trump's character:
Most damning moments:
Video 1.
Fifth Republican Primary Debate - Main Stage - December 15 2015 on CNN
. Source. This perfectly summarizes the spectrum of republican politics. The only candidate who said anything decent were the two least popular ones, notably:
  • Rand Paul, saying that interventionism in the Middle East was a failure (Jeb notably still wants to repeat his brother's mistakes!), and supporting freedom of speech rather than censorship and violation of privacy
  • Carly Fiorina, saying that the people must take the country back
The others are mostly fear-mongering and saying "we will destroy ISIS", to avoid actually dealing with the more important questions: the people have no power anymore.
Video 2.
SMALL LOAN OF A MILLION DOLLARS - Remix Compilation by TwinkieMan (2015)
Source. Nothing synthesizes better how bad the democrats have failed to help the poor. This is who got elected.
Drew Berry Updated 2025-07-16
This is the dude that made many of the amazing WEHImovies animation.
Unfortunately, the process appears to be quite manual and laborious, more art than simulation, based on the software list used: www.drewberry.com/faq
Video 1.
Animations of unseeable biology by Drew Berry (2021)
Source. Presented at TED.

Unlisted articles are being shown, click here to show only listed articles.