In her “diagram of development,” Lovelace gives the
fourth operation as v5 / v4. But the correct ordering
here is v4 / v5.
I was recently at the Musee des arts et metiers in Paris, and they have several original Pascalines on display. So many marvels packed into a very tight space, it is one of my favorite in Paris and I would highly recommend it. I'm not sure what they have on Lovelace, I'll admit I was pretty overwhelmed with the collection. Their computer collection alone is a museums worth, and they cover much, much more than just computer history (a lot of mechanical engineering for starters). If they don't have this algorithm on display, they absolutely should.
A leather-bound first edition Lovelace including this algorithm recently sold for about $120,000. That actually seems like a bargain when you think about the level of the accomplishment. 
I agree with OP that most likely the bug is in the transcription and not present in the original manuscript.
 - https://www.theguardian.com/books/2018/jul/24/ada-lovelace-f...
To be the first, you have to believe Babbage designed a general purpose computer that could accept instructions and never wrote any instructions.
“I confirm that the manuscript evidence clearly shows that Babbage wrote ‘programs’ for his Analytical Engine in 1836-7 i.e. 6-7 years before the publication of Lovelace’s article in 1843. There are about 24 of such ‘programs’ and they have the identical features of the Lovelace’s famous ‘program’,” adds Swade. The historian says that the new tests are “unarguable” and that they “do not support, indeed they contradict the claim that Lovelace was the ‘first programmer’.”
Ada Lovelace was the first to realise that the analytical engine would perform arbitrary tasks and wrote programs for those arbitrary task, beyond computational operations. Of course Babbage who designed the hardware had some idea of what programs it could run and presented examples, but he did not have the forethought to go beyond as Lovelace is quoted in your articles, "an original understanding of where the power and potential of computers lay."
There has always been a controversy of how much of Lovelace's work is hers and how much is Babbage's in the Menabrea papers, and I don't think Babbage writing a few simple programs settles this controversy one way or another. Lovelace had unique and original insights that should not be downplayed.
A [computer] program is a sequence of instructions executable by a machine (the computer).
> Would you argue that the Euclidean algorithm from two millenia prior was a program?
It's in the name: EA is an algorithm.
Btw, this human "compiler" job was for a long time considered to be inferior work and part of the reason why the first professional software developers in mid 20th century were largely women: it was considered clerical work to translate algorithms from paper into computer programs. The Computer Girls is a good article that describes these attitudes.
The string "x=1" can both be a computer program, and something intended only for humans to read. The Euclidean Algorithm was written specifically for humans to understand, with no intent for them to ever be interpreted by a machine. The fact that someone at some point did implement it doesn't retroactively make it the first program. Lovelace's "Diagram" was also not something a machine could directly execute. But the key difference was the intention, she specifically intended that her instructions could be interpreted and executed by a machine.
"Babbage also wrote more than twenty programs that he never published.19 So it’s not quite accurate to say that Lovelace wrote or published the first program, though there’s always room to quibble about what exactly constitutes a “program.” Even so, Lovelace’s program was miles ahead of anything else that had been published before. The longest program that Menabrea presented was 11 operations long and contained no loops or branches; Lovelace’s program contains 25 operations and a nested loop (and thus branching)..."
Also note that apparently Babbage later did consider exactly the implementation of the said missing hardware functionality:
It's also debated whether these were bugs from Ada or transcription errors. But, yes, it does seem like an interesting milestone
Transcription errors would make this the first bug due to bit rot in a special sense! Still quite remarkable :)
Quiet and completely excellent, The Museum of Heritage and Architecture.
The Army Museum is worth a visit - it is interesting to see a less Anglo centric view of the wars, particularly WW1. The paintings are deeply grim - not ideal if you have young kids.
The Museum of the Middle Ages is currently being renovated but is well regarded.
Probably a candidate for best museum in the world, the Louvre is a great way to completely waste a day with massive crowds, sore feet, food and water shortages, closed exhibits, intense heat and even more crowds. Get a map ahead of time and check that the things you want to see aren’t closed before you go.
If you're into modern art and/or architecture, it's a must-see. The center itself is a beautiful mess of industrial design, and they have everything ranging from modern paintings to furniture to contemporary sculptures to technological inventions.
Two of the current exhibitions are an installation by Ryoji Ikeda , which is one of the most superb audiovisual pieces I've seen (you sit in a completely dark room and watch a huge projection) and Coder Le Monde , a history of generative art (digital 2D and 3D, as well as physical), computer graphics and visualization. Both are fantastic.
The nearby Palais de Tokyo is also fun, as is the Museum of Modern Art, which is next door to it.
Everyone mentions the Louvre, but it is incredibly crowded and touristy, and the 90% of the paintings are portraits of 19th century nobility. The gardens surrounding the Louvre are much enjoyable than the inside, in my (possibly unpopular) opinion.
Used to go there all the time as a kid, especially to read 2600 magazine in the library.
The author is saying that Ada deserves the title of first programmer both because she did publish an elaborate algorithm and because she understood the potential of the Analytical Engine better than Babbage and Menabrea.
Jonathan Blow's presentation is more about that second point and how computers (or rather, sufficiently complex dynamical systems) can "give you something back that you didn't put in".
System theory is nothing new so it might not be exact equivalent of thinking about engines that can compose music in 1842, but it seems to me that it is not a widespread and well-understood concept as it should be, and that the public opinion is re-discovering it mainly through Deep Learning advancements.
>in the context of manufacturing methods Babbage calculates that the total number of teeth to be formed for a store with 1,000 registers would be 1,800,000.
It's definitely far from being trivial!
Also note the use of floats in the C version. A lot of simpler CPUs didn't and still don't have floats.
Fascinatingly, the Analytical Engine's number representation was 40 digits (and later: 50)(!) base 10 (but not "floating" but "fixed" point):
Moreover, a lot of simpler CPUs also don't have the "division" in the "instruction set", the Engine has it!
Given the emulator already existing, maybe somebody will now create the cards from Lovelace's program, and run it as intended?
10 PRINT "HELLO WORLD"
Even the horrible crap I wrote as an novice is probably less embarrassing to me that the stuff I wrote as a journeyman who shoulda known better.
Thankfully, the most embarrassing things are, like, spending 2 days configuring postfix and not realizing that I could just read the log files and it tells me specifically what isn't working. A valuable lesson, but embarrassment has its cost.
mov ah, 2
mov dl, 7
Does anyone know what "should repeat" means? Was the machine capable of repeating or does this mean the human operator needed to do the repeating?
If you're interested in that kind of thing I wrote a description of the entire instruction set a while back: http://h14s.p5r.org/2012/11/punched-cards.html.
Thanks for the in-depth, and wonderfully clear write-up.
The London Science Museum built a fully working Difference Engine, to Victorian tolerances so it could have actually worked.
I heard of a project to build a modern working replica but I don't know if anything ever came of it.
It's really just a series of mathematical steps with a store of values in between. Notions that would have clearly taken it from being a series of mathematical steps, to a program, such as branching, looping, or jumping are left completely unspecified. So her 'loop' was specified literally as "here follows a repetition of operations 13-23".
In other words, "should repeat" is left an as exercise to the reader.
 - https://i.imgur.com/HSWjbUl.jpg