In ZFC set theory, indexed family over a set (possibly uncountable or even bigger), is just syntactic sugar for a function.

So let's say you have a set U (possibly uncountable). To say let {u_i}, i in I (another set, possibly uncountable) is equivalent to asserting existence of function f:I -> U, such that f(i) = u_i. Note that this does not even require axiom of choice, since you are allowed to postulate that a function exists.

Of course if I is uncountable you can't list the elements of I, but that is not important in this case.

I prefer this test: "Imagine a ball resting on a table. A person walks up to the table and pushes the ball". Question for the test subject: "What will happen?"

Everyone answers correctly the ball will roll of the table and fall to the ground. But then ask them" "What was the color of the ball? What was the size of the ball? What was the gender of the person pushing the ball, what clothes were they wearing?"

People with aphantasia are usually stunned by the follow up questions. People who don't have aphantasia really have seen the table, the material its made of, imagined a ball of certain size/type color (e.g. multicolor beach ball, or basketball or what ever), and they saw an actual person pushing the ball, they saw the ball rolling on the table an falling to the ground and can answer details about their vision.

> Everyone answers correctly the ball will roll of the table and fall to the ground.

For me the ball kept rolling off the table and rolling through air but not falling to the ground, even while realizing I should be causing it to fall to the ground, but rolling straight just "felt" natural at that moment because it's in make-believe land it can do whatever.

Brings back memories. Aztec C was my first C compiler on Amiga 500 way back in 1990. I learned C, I learned vi. Still have fond memories of those early days.

Can you please elaborate? How are you running ollama? I just build it from source and have written a shell script to start/stop it. It runs under my local user account (I should probably have its own user) and is of course not exposed outside localhost.

How did you end up with TM backup larger than original source? Sure, total storage consumed on TM drive can be larger than source, but that is because older versions of files are stored as well. But restoring most recent versions of files should be equal to source in size.

I had only 600-700 gb of data on my Mac. Installed OneDrive, did not know that I had configured my NAS to do 800gb of cloud backups to OneDrive. And Time Machine downloaded that data into its backup. Although I had configured OneDrive not to download that folder to my Mac. So time Machine screwed up in the first place.

Ah, ok, that's a nasty bug/scenario. I long for the good old days one could just rsync the internal drive and bless it and you have a bootable clone, or make compressed disk image. Those were the days.

I view CAP theorem as statement about the universe we live in (information travels at speed of light, "instantaneous" is observer dependant etc), and not as a consequence of information theoretic definitions we chose to adopt (strength of consistency or availability). Yes, when stated simplistically (you have 3 properties C, A, P choose 2) can be extremely misleading, since you can't really choose P, you can only decide what to do in case of P. But like any mathematical theorem one has to understand the preconditions when the theorem applies, understand the various computing model assumptions etc. to actually use it.

Notwithstanding, I still find it very useful as a general guide when designing distributed systems.

As fellow mathematician tutoring my son I found all of the articles incredibly useful. Thank you for writing them and making them freely accessible. Awesome work.

That's very lovely to hear! Thanks for sharing that.

Signal perhaps does not allow you to export your message history through the front door, however decrypting and exporting your message history is relatively low effort.

You messages are stored in encrypted SQLite3 database. The Signal encryption key is in

    ~/Library/Application\ Support/Signal/config.json

in plain text. If you have SQLCipher (https://github.com/sqlcipher/sqlcipher) compiled you can decrypt your Signal database:

Navigate to

    ~/Library/Application\ Support/Signal/sql/

and type

    sqlcipher db.sqlite
    sqlite> PRAGMA key = "x'<your_key_here>'";
    sqlite> .schema

and query away.

Of course there is a Python package to automate all of this here:

https://github.com/carderne/signal-export

This exports your message history as markdown and HTML files for your convenience and it will do incremental exports as well.

For iOS the same holds true, considering iOS has had a jail break most of its existence.

So, in retrospect your Signal messages are only as secure as computers of the people you talk to and of course your own device.

I would go a step further and assert that there is no such thing as secure communication.

GP here. Signal allows chats to be backed up on Android. It’s a built in feature.

You probably don't need to learn C and program in it, but I do think knowing material covered in say [1] Computer Systems - A Programmer's Perspective will make you a better engineer, and historically computer systems were implemented in C and that heritage is still with us. So, being able to read C at least is a prerequisite to understand some of it.

[1] - https://www.amazon.com/Computer-Systems-Programmers-Perspect...

Yet another background daemon. No thanks. Update when you need to, it's not like it's mandatory.