Checking proofs is easy. I would like to learn more about computers constructing proofs.

Computers are supremely good at *arithmetic*, which is a tiny part of mathematics.
I like to think of mathematics as a struggle to understand quantity, symmetry, and relationships.
You can go a long way by asking questions like "If *this* doubles, what happens to *that*?"
Now generalize the word "quantity" to include things like integer, real number, complex number, length, area, volume, vector, matrix, function.

And don't forget about the word "proof."

In 1972, I wrote a tiny program in machine language for an IBM 1620. It was a decimal machine (sort of: see below) with 12 digit instructions and 40000 digits of memory. I punched the program onto cards. The program read a punched card, added two numbers on the card, and punched a card with the result.

The machine had a disk operating system, a macro assembler, a Fortran II compiler, and a useful set of file manipulation programs. You could enter commands from a teletype machine. We had a washing machine sized disk drive and a line printer.

We were required to start at the bottom with machine language so we knew what was really happening. The instructor introduced addressing, conditional branches, loops, subroutines, etc before we were allowed to use Fortran. He then convinced us, not rigorously, that it was at least possible for a computer to parse, translate, and compile. Only then were we allowed to use Fortran.

I left home at 6AM to ride the New York City subways to school, arriving one hour before first class so I could learn assembly language from a manual I found in the closet. I struggled to write programs that were too advanced for me. When I eventually learned a technique, I had been primed with a problem that required it.

For every type of computer I have ever programmed, I programmed it first in assembly language. I retired when this stopped being practical,

http://tincansandstring.net/co...

(Footnote) The hardware actually used 8 bit bytes. Six bits represented the usual characters, and the remaining 2 bits per byte where used for special purposes.

--
Hi to all my friends at NSA.

I will mostly leave this discussion to others, but I have a problem. I don't know in what circumstances I can use conservation of momentum. I used to rely on it all the time in physics classes, and now I can't. What should I do?

Without work as a TA, my wife could not have earned two Master's degrees. She wouldn't have her career. I wouldn't have met her. That would be very, very bad.

How is our economy supposed to work?

I mostly agree with you, but ...
Every version of Windows has extensive documentation, even if not organized the way I want it. Are the details you want documented? Should they be on the standard installation screens?

Back in XP, I did the research and registry edits and group policy changes to make Windows use local NTP and DNS servers, but then I burned out trying to research each security update. I don't have a solution for real-time certificate revocation. Important stuff ran on Linux, but it has some of the same issues.

[ I can't tell if others have commented on this ]

The kind of traffic matters. Some external communication is reasonable.

NTP, to synchronize clocks.
Checking for certificate revocation.
Checking for the existence of security updates.
Downloading lists of sites known to be malicious.

You can take responsibility for these functions, but servers need to get them done.

I'm surprised by comments that Ahmed "just" took things apart and put them together. Do you remember getting your first chemistry set, or bicycle, or learning how switches work? I'll bet that you tried things out, many times.

If you played basketball, I bet you went out to shoot baskets, just because you could.

If you took shop class, did you invent wood, or drills, or nails? I bet you did things that somebody showed you.

If you played a musical instrument, I bet you played the same practice pieces over and over.

Those activities are "play" and most mammals do that. They practice their skills, even if they are not immediately needed to survive. That is a developmentally appropriate thing to do! There are parts of your brain that are not wired up to the rational, language using parts, and those parts need to develop.

I don't care if all Ahmed did was take something apart and put it together again. That was encouraged in me, and I hope it will be encouraged in others.

Last year, I had my first recurrence of an atypical meningioma. That's a growth between the skull and the brain. Not something to play around with.

The hospital "tumor board" recommended one of two treatment options: (1) The proton accelerator. (2) An older technique. I found out how extraordinarily expensive the proton accelerator was, and just couldn't stomach consuming that much health care. I chose (2).

Making something "mandatory in all grades" breeds dislike. Young kids often like programming, (or math, or art, or language, or music) and understand right away that it can be fun. Then the schools mess it up. If you haven't read it, I recommend the essay known as Lockhart's Lament:

A musician wakes from a terrible nightmare. In his dream he finds himself in a society where
music education has been made mandatory. “We are helping our students become more
competitive in an increasingly sound-filled world.” Educators, school systems, and the state are
put in charge of this vital project. Studies are commissioned, committees are formed, and
decisions are made— all without the advice or participation of a single working musician or
composer.

My wife, an educator, just heard me ranting and popped into the room: "Preschoolers need to play. That is the developmentally appropriate thing for them to be doing." She also reminded me that Steve Jobs didn't want his children looking at screens - he wanted them talking and reading.

I believe that ocean acidification is one of the planet's greatest problems. But I am ignorant about the timing.

The article is about the Permian Extinction. It took place 250 million years ago. When geologists or biologists say that something happened "fast" they might be talking about 10 years, or ten thousand years, or ten million years. That matters. If the scale is long then I don't care because we have *no idea* what life will be like then.

After a major health crisis, one doctor told me: "We don't cure people so they can live miserable lives without wine."

When I gather wood or water or food, I won't be walking.

I have a strong bias in favor of kids who are growing up in the most chaotic environments.

In the poor neighborhoods I know, schools don't let kids take home *books*. What fool thinks taking home computers is a good idea? Anyway, who lets hardware manufacturers influence educational policy?

Signed,
bleeding heart liberal.