[eesmith]

What do you regard as the first digital, Turing-complete (if given enough memory) computer?

ENIAC, for example, was not a stored-program computer. Reprogramming required rewiring the machine.

On the other hand, by clever use of arithmetic calculations, https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.37.... says the Z3 could perform as a Universal Computer, even though, quoting its Wikipedia page, "because it lacked conditional branching, the Z3 only meets this definition by speculatively computing all possible outcomes of a calculation."

Which makes me think the old punched card mechanical tabulators could also be rigged up as a universal machine, were someone clever enough.

"Surprisingly Turing-Complete" or "Accidentally Turing Complete" is a thing, after all, and https://gwern.net/turing-complete includes a bunch of them.

[kragen]

let me preface this with the disclaimer that i am far from an expert on the topic

probably numerous eddies in natural turbulent fluid flows have been digital turing-complete computers, given what we know now about the complexity of turbulence and the potential simplicity of turing-complete behavior. but is there an objective, rather than subjective, way to define this? how complicated are our input-preparation and output-interpretation procedures allowed to be? if there is no limit, then any stone or grain of sand will appear to be turing-complete

a quibble: the eniac was eventually augmented to support stored-program operation but not, as i understand it, until after the ias machine (the johnniac) was already operational

another interesting question there is how much human intervention we permit; the ias machine and the eniac were constantly breaking down and requiring repairs, after all, and wouldn't have been capable of much computation without constant human attention. suppose we find that there is a particular traditional card game in which players can use arbitrarily large numbers. if the players decide to simulate minsky's two-counter machine, surely the players are turing-complete; is the game? are the previous games also turing-complete, the ones where they did not make that decision? does it matter if there happens to be a particular state of the cards which obligates them to simulate a two-counter machine?

if instead of attempting to measure the historical internal computational capability of systems that the humans could not perceive at the time, such as thunderstorms and the z3, we use the subjective standard of what people actually programmed to perform universal computation, then the ias machine or one of its contemporaries was the first turing-complete computer (if given enough memory); that's when universal computation first made its effects on human society felt

[eesmith]

> is the game?

Sure. One of the "Surprisingly Turing-Complete" examples is that "Magic: the Gathering: not just TC, but above arithmetic in the hierarchy ".

See https://arxiv.org/abs/1904.09828 for the preprint "Magic: The Gathering is Turing Complete", https://arstechnica.com/science/2019/06/its-possible-to-buil... for an Ars Technica article, and https://hn.algolia.com/?q=magic+turing for the many HN submissions on that result.

[_a_a_a_]

Could you explain "above arithmetic in the hierarchy" in a few words, TIA, never heard of this

[eesmith]

Nope. The source page links to https://en.wikipedia.org/wiki/Arithmetical_hierarchy . I can't figure it out.

An HN comment search, https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu... , finds a few more lay examples, with https://news.ycombinator.com/item?id=21210043 by dwohnitmok being the easiest for me to somewhat make sense of.

I think the idea is, suppose you have an oracle which tells you if a Turning machine will halt, in finite time. There will still halting problems for that oracle system, which requires an oracle from a higher level system. (That is how I interpret "an oracle that magically gives you the answer to the halting problem for a lower number of interleavings will have its own halting problem it cannot decide in higher numbers of interleavings").

[BoiledCabbage]

This appears to discuss it a bit more. Not certain if it's more helpful than the comment (still going through it), but it does cover it more in detail.

https://risingentropy.com/the-arithmetic-hierarchy-and-compu...

[kragen]

mtg is more recent than things like the johnniac, but plausibly there's a traditional card game with the same criteria that predates electronic computation

but then we have to ask thorny ontological questions: does a card game count if it requires a particular configuration to be turing-complete, but nobody ever played it in that configuration? what if nobody ever played the game at all? what if nobody even knew the rules?

[eesmith]

The MtG preprint suggest people have been looking for such games but failed to identify any. From "Previous Work", first page, column 2:

> Prior to this work, no undecidable real games were known to exist. Demaine and Hearn (2009) [10] note that almost every real-world game is trivially decidable, as they produce game trees with only computable paths. They further note that Rengo Kriegspiel {Rengo Kriegspiel is a combination of two variations on Go: Rengo, in which two players play on a team alternating turns, and Shadow Go, in which players are only able to see their own moves.} is “a game humans play that is not obviously decidable; we are not aware of any other such game.” It is conjectured by Auger and Teytaud (2012) [1] that Rengo Kriegspiel is in fact undecidable, and it is posed as an open problem to demonstrate any real game that is undecidable.

> The approach of embedding a Turing machine inside a game directly is generally not considered to be feasible for real-world games [10].

Regarding your ontological question, that we don't know if something is Turning complete doesn't mean it isn't.

People explored the Game of Life before it was proven to be Turing complete. The 1970 SciAm article says "Conway conjectures that no pattern can grow without limit." so Martin and Gardner didn't even know about gliders then. People don't say GoL wasn't Turning complete in 1970.

I pointed to a 1998 paper claiming the Z3 machine from the 1940s was Turing complete, that author clearly believes that a particular physical configuration is not required.

Nor did Turing construct a physical representation for his paper.

FWIW, the MtG preprint gives a concrete example of a 60-card initial deck. I would be surprised if neither the authors nor anyone else has ever tried it.

The ontological question is even more fully resolved because no one has ever created a real Turing machine. We always have the proviso "if given enough memory".

Similarly, the video game "Minesweeper" is NP-complete as the size increases, and with an infinite board - clearly not physically realizable - is Turing complete. https://en.wikipedia.org/wiki/Minesweeper_(video_game)#Compu...

[kragen]

i don't have much to add here but wanted to express my gratitude for having had the opportunity to read your wonderful comment

well, maybe one thing: if it doesn't matter whether anyone played the game or knew the rules, then magic: the gathering was turing-complete before the first magic deck was printed, before the first human was born, before the first star was formed, perhaps before the big bang

[eesmith]

Thanks, I appreciate it!

If you go down that route you'll realize there are an uncountable number of games that have never been created, and will never be created, which are Turing-complete.

And start wondering if mathematics is created or discovered.

[midasuni]

Colossus was before eniac, but was also programmed by plugging up. Baby was a stored program machine and had branching