I found a 55 year old bug in the first Lunar Lander game

There were on the order of hundreds of high school students with computer access in the US in 1969, and even fewer with computer literacy. Growing up in the Space Age probably was inspirational, but that doesn't change the fact that computers basically didn't exist to the general public at that time. Unlike now, software development wasn't a widely known career. There wasn't a CS major in the US until 1962. I think that makes it pretty notable he was a high school senior in 1969.

I needed to know what language that is written in. Turns out it's something called FOCAL, as mentioned in this article about the game:

https://retro365.blog/2021/12/02/bits-from-my-personal-colle...

Wikipedia on FOCAL:

https://en.wikipedia.org/wiki/FOCAL_(programming_language)

Though famous as the first lunar lander game, the impressive part was the specific numerical techniques used.

I thought it was a little odd that he mentioned "impressive for a high school senior in 1969" multiple times throughout -- honestly I would imagine that growing up in the Space Age would have had a massive influence on technically minded folks, reminds me of that movie from a while back called October Sky.

OP here. I see your point. But think of what's needed to create this game:

- From high school physics, you know to start with a free body diagram. There are two forces, gravity and thrust. So far, your average high school student with an A in physics should be able to do that.

- Gravity depends on the distance to the center, which of course is changing, that's the whole point of a lander. I mean, you start 120 miles up. You have to realize it doesn't change much, so can be approximated as a constant. But you've been exposed to that in physics class, so maybe you just assume it's a constant.

- How the hell does thrust work as a function of burn rate? Is the exhaust velocity higher when you burn more? In other words, considering 100 lbs/sec vs 200 lbs/sec, when you double the flow of fuel into the engine, and then you burn it, it turns into twice as much fuel in the same volume. Wouldn't it be forced out at twice the speed? Or at least a higher speed? Maybe you think of the universal gas law, PV=nRT. The volume is constant (the volume of the engine), n is doubled, R is a universal constant. So that means P or T changes, or both. Why is T, which is a function of the velocity of the molecules, constant why P is doubled? Why don't both change?

- So you talk to your Dad, who happens to be a physicist. Most high school students, even those getting an A in physics, don't have a physicist for a father who can look up the properties of rocket engines and find the Tsiolkovsky rocket equation. So a high school senior finding the rocket equation is impressive to me.

- To go from velocity to position, you need to integrate. I'm not sure your average A physics senior would think of replace the FLOG() call with a Taylor series and integrating it term by term.

- How many terms of the Taylor series do you need? Does it even converge for you? If he thought of these subtleties, that's impressive. But it's possible that young Jim didn't realize these issues and just uses 5 terms because that seemed like a lot of terms.

- So now you can simulate it in near the moon. Cool! But how do you detect when it hits the ground? You could try to solve for altitude equals zero, and see if there are zero or more solutions. But even if there are solutions, they might be in the past or the future. So instead you decide to look where the velocity is zero, since you know this happens exactly once during the turn. I think that shows some ingenuity there, although I don't know if that was 18 year old Jim's thought process.

- So you try to invert the rocket equation: given a desired delta-V, how much fuel do you need to burn to achieve it? If you try this with pencil and paper and high school math, including Calculus, you keep getting stuck. You don't have the tools to show that it's actually impossible and needs you to introduce a new function, the Lambert W.

- So maybe you give up, or maybe your physicist Dad helps you again. Using your Taylor series, you now have to solve a 5th degree polynomial. So you decide to scrap the 3rd, 4th and 5th term to get yourself a quadratic. Why is it ok to scrap these now, when it wasn't ok when computing the regular dynamics? I'm impressed that he realized he can use different levels of approximation in different circumstances, without it generating some inconsistencies or other problems.

- You somehow figure out how to use the alternate form of the quadratic equation, which means you didn't just look it up and type it in. Possibly impressive.

I was in high school in 1969, knew some calculus, and was very interesting in programming. In a good size city with a major engineering university and a large high school the main barrier was access to computers. Our school had teletypes connected to a remote mainframe. My friends and I found a few computers at the university we could use at night, but most had card readers and line printers, and none had graphics terminals of any kind. I think the particular combination of skills, interest, and access would have been pretty rare at the time.

Automobiles are more (wear-)efficient at braking when they use the engine to brake, not the brakes, so that would probably be a better approach to automate

I often wonder the same thing about my bicycle.

For regenerative braking, a similar question would be how best to break to recover as much energy as possible.

That's awesome

I just wanted to add, there's also mechanical lander games that pre-date lunar lander

I can't find a picture. IIRC the machine was something like this

https://content.invisioncic.com/r322239/monthly_10_2015/post...

Except it had terrain and pits. A pit would light up and you needed to land in the pit (your ship landing would depress the button in the center of the pit). If you didn't aim well your ship would hit the edge of the pit, tilt, and you'd fail. If you did hit the button then the light would go off and a different pit would light up.

-- update --

now that I think about it, maybe the controls were more like UFO catcher where you'd align at the top and then press "land".

Anyway, it used to be at Disneyland at the Main Street Arcade.

I'm honored to be included in this article--I wrote Lander (1990) originally for Windows 2.x.

When I applied for a job to work on Lotus Notes (back in 1989), I showed the interviewer (Tim Halvorsen) my Lander game. He said, "That's pretty cool--let's try running it on Windows 3."

At first, I thought, cool! I get to see Windows 3 (which had not yet been released). But then he said, "Windows 3 runs everything in protected mode, so if you have any out-of-bounds pointer access, it will crash instantly. Let's see how you did."

I was on pins and needles the entire time.

But fortunately, Lander didn't crash, and Tim was happy. I ended up getting the job, which forever changed my career.

dude,that's awesome!

Lunar Lander was one of the early games I tried to make a copy of as I was learning programming in high school: (Java applet!) https://github.com/celwell/space-landing

Wow, that is a great article. Incredible research and depth. Thanks for the contribution.

The nature of the bug is that it has trouble finding when the lander has touched the surface. You need to have an altitude of less than zero for around 0.05 seconds for the game to notice that you've landed. If your thrust during that time is 200 or 199, to have an altitude < 0 for that long, then you need to have a speed greater than 1 MPH when your altitude is zero.

Even when the bug is fixed, the code is still only approximating the lowest point. Also, even when it detects that you've landed, now it needs to compute the time when you land, i.e. when the altitude is zero, not velocity. It also uses an approximation for that.

So the times will be a little off. If you're burning 200 or 199 during that last time step, you have a high acceleration so even a small amount of time turns into a large amount of velocity. Instead, if you're burning say 10 lbs/sec, then being off by say 0.08 sec won't change your velocity much.

There wasn't any graphical output or any frame rate to speak of in the sense you are thinking. The output would appear printed, like this:

https://www.cs.brandeis.edu/~storer/LunarLander/LunarLander/...

Only updating the mass/acceleration at ten-second intervals would be wildly incorrect!

OP here (of this blog post, not the original game). The naive way is what I expected too, and described as the Euler method in the post.

In terms of physical accuracy, especially when you get near the surface, the mass does change significantly if you have a high rate of fuel burn. But in terms of how challenging/fun it would be, and what strategies you use as a player, I doubt it would make much difference. In fact, there are other lunar lander simulations in the BASIC computer games book, I think one of them does use the naive approach.

If 10 seconds is too long, you could still leave that as the turn in the UI, but internally break each turn into a bunch of smaller time steps, e.g. 10 time steps of 1 second each. Actually, the existing game does that in certain places, which is why his physics simulation takes in an arbitrary time S rather than always the full 10 seconds.

Oy vey, "no chance" is putting it lightly.

A lot of this BASIC code had roots in the 1960's-70's. Back then, editors ruled the roost of print magazines where this code often showed up within, and in books of collections of code they especially ruled with an iron fist. There was little notion that source code had to be dropped in verbatim with absolutely zero changes, so editors would make "judicious" changes in the source code. They thought they were "helping" with "obvious" typographical and editorial decisions.

This lesson was slowly, painfully learned until material improvements across the industry started to take hold starting in the 1980's and realization that source code shouldn't be touched in print really began to permeate the print industry. Though sometimes I wonder if this dynamic spurred the rise of BBS' and helped loosen the stranglehold print media had upon source code distribution, and what an alternative timeline might have looked like if the ones in power in print media were more open to "outsiders" having absolute control over some portion of "their" content.

I learned all the above decades later after I first started playing around with coding as a child, from talking with a much older friend who rose up from within the print media world and saw what happened. When I was a child, with zero adult guidance, and only a handful of books from the school and community library about programming, it was a wonder I stuck with coding at all with the countless programs I typed in by hand from print media that were similarly riddled with errors, so your reminiscing brought back powerful memories.

Probably copy/paste errors (in editorial) mixed with deadlines mixed with no QA.

That was an enjoyable read. I, too, when I was a child sometimes thought the same thing about my C64 “magically” being able to load some game-related images with just a few lines of code that are… just somewhere inside it? A super bizarre thought, but as a child you’re still prone to a lot of magical thinking.

and the convoluted logic "440 IF <condition> GOTO 450“

To expand a little bit on that, while some instances in the code of your book could indeed use some cleanup (line 440 is especially egregious), the code in the book was likely written for the common BASICs of home computers of the time, which only operated on line numbers and had very limited branching statements?

The BASIC you use seems to be “structured”, which was extremely unusual for home computers of the time. I just recently saw that a C64 magazine from 1984 spent at least 3 issues of the magazine on a lengthy article series that introduced the readers to the wonders of structured programming!

The severe restrictions of the IF statement made assembly-language style conditional branches (using GOTO) extremely common and necessary.

You definitely could not nest IFs (as done in your code), so if you wanted to combine IFs together, you had to jump over the ones not taken. Commodore/C64’s BASIC (effectively Microsoft BASIC) did not even have ELSE, so usually ELSE had to be implemented with a negated condition and jumping over what would be the “ELSE” branch.

C64 BASIC did however have the interesting quirk that any other statement on the same line would belong to the THEN, e.g.

   10 IF A=1 THEN PRINT “FOO” : PRINT “BAR”

A lot of the convenience and rigor we take as granted today wasn’t there. C64 BASIC seemed especially “dirty” to me, having lots of bizarre quirks that are more the result of its implementation. (Another random instance: Every function had to have an argument, whether it was required or not, so you had to write something like “?FRE(123)” to print the amount of free memory, where the 123 did not matter at all.)

Given the simplistic nature of the game, I'm not convinced.

The game is tiny. It does not even have any graphics. It would be an impressive feat to fit even 10 bugs in there, and still have it seem like a functioning game.

Why? This is from a time when there weren't any "other games". Heck, there were no computer games, period: there were only applications that could be described as "a sort of game on the computer" but only in the sense that you were asked to perform a task, tell the application what you though the task parameters should be, and then the application told you whether you were right.

Applications were also still measured in bytes (the idea of the average program being so large that everything needed to be described in kilobytes was still in its infancy). So you literally didn't have enough space to hide 100 bugs that would linger unnoticed for 55 years: 100 bugs would be your entire source code. In fact, here's the source code for the game in the article: https://www.cs.brandeis.edu/~storer/LunarLander/LunarLander/... - it's 2027 bytes. If it had 100 bugs, or even 5, it either wouldn't run, or it would be obviously wrong.

And that source code also illustrates the kind of "game" this is: it's just a text prompt to get you to fill in the values that set up the flight, and then it runs a simulation with your parameters and spits out the result. That was enough to constitute a game people would play religiously, back in the day.

Things changed a lot since then =D

I also remember this lunar lander game running on a couple terminals at the Lawrence Hall of Science in Berkeley, California, also in the mid 1970s.

I recall lunar lander being available on, IIRC, ADM-3 terminals at Lawrence in early 1973, usually surrounded by a cluster of male teens. One "feature" of the kiosk mode for games was that a carefully-timed Ctrl-C would escape kiosk mode, and allow the user to play other games. Happenstance, or catnip for proto-hackers?

OP here. True, I oversimplified. What I meant was, there are two parts to the dynamics, the rocket equation and gravity. They add linearly, so any extra velocity that comes from gravity needs to be eliminated by increasing the delta V from the rocket equation. The gravity delta V is just acceleration of gravity times time, so you want to minimize the time. Surprisingly (to me), in the rocket equation, it doesn't matter how long it takes, or what sequence of burns you use, or whether you burn at a constant rate all the way through vs short strong bursts, etc. So to land with zero velocity using the least fuel, you just need to land in the shortest amount of time.

Internet Archive or Computer History Museum? Ask @textfiles for recommendations for places that might be interested.

...what? The game was made by a teenager. The only reason they're now old is because 55 years have passed.

I played it on a hp97/hp67.

Memory hazy, but I think I used the inbuilt calculus features of the calculator to get a perfect landing with a burn of 45 (about half the fuel) on say turn 12.

I had no prior expectation of what the optimum burn was and certainly had not heard of a 'suicide burn'.

Agreed. It's a numerical error that only affects accuracy, but not a serious glitch, like the Pac-man Kill Screen Bug, not exploitable (to cheat/get resources/lives, like reaching 990,000 points in Defender), and not an Easter egg.

See e.g. Glitchipedia: https://errors.fandom.com/wiki/Glitchipedia:About

OP here. Cool! I was born in 1969, less than a month before Neil Armstrong walked on the moon, and was only a few months old when this game was written. I too learned BASIC, then spent hours pouring over the book "BASIC Computer Games", before I even had a computer of my own. Fond memories, as you say.

When I made the proposal to restore the CHM's pdp-1, the reason was "Spacewar!"