Hendrik Boom @hendrikboom3@qoto.org

@freemo What's interesting, of course, is the *way* it's nonsense. In putting together ZF set theory they found ways to forbid the paradox while still allowing the useful things mathematicians were doing with sets. But there seem to have been multiple attempts to patch it all up, and the one in ZF has gained popularity.

As for what is actually *true* in set theory, I suspect there is no objective way of answering that.

Mathematical philosophers are still working on ways to make logics that allow the Russel set without its paradoxical nature infecting the rest of the set theory.

See for example, Kevin Sharp's note http://kevinscharp.com/ScharpPhilosophyandDefectiveConceptsHandout.pdf

The book he refers to is "Replacing Truth", available for money at Oxford University Press. Or maybe in a library. It may be more detailed than you want to get into.

@freemo
The wikipedia has a nice write-up:

https://en.m.wikipedia.org/wiki/Bendix_G-15

@freemo A question oof course is whether the so-called property that is used to define the paradixical Russel set is a property at all or merely nonsense. Attempting to determine whether that set is a member of itself leads to infinite recursion.

I see this as indicating something about sets. We are used to thinking of sets as justbexisting somewhere and we are discovering their properties. But I'm a constructivist, and view our membership conditions as a kind of construction of sets. It's possible to use language to describe all kinds of nonsense, and this one is nonsense.

Not that I mind such nonsense. It's fun. I read fantasy nivels, too, and they're fun.

But trying to build fantasy set theories that can admit such descriptions if fraught with difficulty. You have to avoid plot holes.

@freemo These were still the early days of computing. When did they first start using disks with addressable permanent random-access storage? I don't know, but the first I saw myself appeared on another computer years after this Bendix was made. The Bendix was donated to tge university in 1957 by Pioneer Electric on condition that ghey could continue to use it for transformer design calculations. I do not mnow how old it was when it was donated. I do know it had lots and lots of vacuum tubes.

I do know that this ever recirculating memory was basic to the machine's design.

There were a few short memory lines of only one or two or four wordsmlong. These were used the way we use registers now. And a few destinations were special circuitry instead of being regular memry lines. The one-word accumulator was two destinations -- one for the usual write process, where you could provide new data to replace what would otherwise be rewritten, and the other that you used to add to what otherwise would be rewritten. So by specifying that a data transfer was to happen for multiple word times, you would end up adding multiple words from the source memory line to the accumulator. One instruction, no loop, many numbers added.

The drum was treated as volatile memory.

The Bendix used a magnetic drum Each memory line had a read head and a write head. Normally whatever was read would be written immediately, and would then travel around with drum rotation until it got bach to the read head and repeat the cycle.

Maybe a better way to describe the Bendix was to say it emulated delay lines using a magnetic drum?

@freemo I wasn't aruond for the mercury delay lines. They were from the 40's and 50's, right? And you can still get them nowadays? I didn't get into computing until '62. I remember reading about William's tube memories. Why do I get the idea they were grasping at straws back then to get anything, just anything, to work?

@freemo No, I did mean a real magnetic drum on this machine, acquired by the university in 1957. I got to use it in1962. I spent a happy summer hanging about the university's air-conditioned computer room reading its circuit diagrams to learn how it operated. It was a truly magnificent kludge.

Main memory consisred of a number of these recirculating tracks, each was 108 words of 29 bits each -- 7 hex digits and a sign bit. The instructions had a source memory line, a destination memory line, and specifications when the instruction was to be executed and when the next one was to be read. These times were essential -- they determined which words were being read and rewritten and thus possibly modified as the drum turned.

@freemo The Bendix G-15d computer used delay lines on a magnetic drum. The spacing between read and write heads determined the delay.
Those delay lines contained the main memory *and* the registers (such as the arithmetic accumulator).

@freemo A slower version could be an acoustic delay line.

@federationbot Go ahead and follow me if you like.

@b9AcE I have found those captive portals quite a nuisance since my browser detects that I have not got to the site I requested and refuses to let me go further.

My workaround is to use another (presumably less secure) browser to make the connexion and then use my regular browser to browse.