Remarkable mathematical truths

Kurt Gödel

Deductive systems are either incomplete or inconsistent. Meaning

  • Inconsistent: they contain contradictions. Statements can be true and false in the same deductive system.
  • Incomplete: Statements can be found that can not be proven to be true or false.

Gödel proved this for us.

Wittgenstein formulated something similar:

The truth is built of true facts and untrue facts: facts that are not based on a system of observation yet are true anyway. Nevertheless, Wittgenstein seems to disagree with Gödel’s incompleteness theorem. Food for a lasting scientific debate. Anyway, Wittgenstein was looking at language and philosophy, not at mathematics.

Final remarkable mathematical truth for now from Cantor.

Cantor proved that one infinity is not the same as the other infinity. He developed a way to compare infinite sets and describe how infinite sets with different characteristics exist.

As an example, Cantor proved that real numbers are more numerous than the set of natural numbers. While both are infinite. He also invented a way to operate on infinite sets.

Cantor ended up in a mental hospital, which seems to be viewed as as heroic achievement among mathematicians—an opinion I do not share.

I recall reading The Mystery of the Aleph by Amir D. Aczel about Cantor. Unfortunately, I have lost my notes and the book. This book was very accessible, I do recall that.

Murakami’s Norwegian Wood reread

On the plane back from Prague, I finished reading Norwegian Wood—re-reading, actually. I don’t often re-read books, but Murakami is a favorite of mine.

Watanabe is in love with Naoko. She is the girlfriend of their mutual friend, who died at a very young age. Naoko can not cope with life and commits suicide in the end, while Watanabe is torn between emotions he is not able to identify or is not even conscious of. The girl who falls in love with him must tell him he is in love with her. An old friend tells him he has to choose for himself. While perfectly capable of analyzing other people’s situations, he is unable to analyze his own issues. Let alone that he is able to come up with a choice for his own problems he is not even aware of.

Photo movies

I (re)started making picture movies from my photo projects. I publish them on my YouTube channel. It’s a kind of slide show, but I’m trying to make a bit more of it and augment pictures with some video I made during the photo shoots.

I started this before with low success but now decided to take this more systematically. Nobody seems to exhibit his photography products like this, at least not so systematically. The first new set I created during the Scotland trip. Created a separate playlist for this trip.

This weekend, I created a video using pictures I took during a business trip to New York City and upstate New York.

And I have a large backlog of similar trips. Having fun with this.

Subscribe to the channel if you like it with this button here.

Glasgow Central, in pictures

I almost forgot to look up to get a good look at how this light could fall so beautifully into the hall of Glasgow Central station.

Exploring Ethical Search Engines Beyond Google

There is no good reason why you should still rely on Google search for your search engine. Read this excellent article on Google’s practices, and Big Tech chills run down your spine. There are ample good alternative search engines these days that do have integrity:

DuckDuckGo

Ecosia

Bing (though also Big Tech and historically suspect)

Brave

StartPage

And there are more.

Lately, I’ve been using Ecosia and DuckDuckGo side by side. I don’t feel like I’m missing anything about Google.

Vacation Photos; and the fun of always taking pictures

Toeristen fotograferen

Kronkeling has the most fun blog about photography.

Kronkeling has a hard time photographing on vacation. I don’t share this struggle. I always takes pictures. Sometimes it’s for the image, the beautiful picture, sometimes for the subject, so just the snapshot. I decide the goals afterward, but then I am different from Kronkeling.

Tips for your holiday pictures from Kronkeling are here.

Sometimes, there are miniseries, like when our car broke down, and we had to wait until a mechanic came to help us. I photographed all the trash in the parking lot.

Or, during vacations, photographing tourists.

Or hotel rooms.

Hotelkamer
Hotelkamer
Hotelkamer
Hotelkamer
Hotelkamer

Or art on the wall.

Or numbers.

47
104

Nina Katchadourian is a super creative source of inspiration.