Henry J. Kelley (1960). Gradient Theory of Optimal Flight Paths.
[1] https://claude.ai/public/artifacts/8e1dfe2b-69b0-4f2c-88f5-0...
I am still going through it, but the latter is quite interesting!
So sad to see the current state. Hopefully we can turn it around.
AIAA 65‑701 (1965) “optimum thrust programming” for lunar transfers via steepest descent (Apollo‑era) https://arc.aiaa.org/doi/abs/10.2514/6.1965-701
Meditch 1964 (optimal thrust programming for lunar landing) https://openmdao.github.io/dymos/examples/moon_landing/moon_...
Smith 1967 & Colunga 1970 (explicit Apollo‑type trajectory/re‑entry optimization using adjoint gradients) https://ntrs.nasa.gov/citations/19670015714
One thing AI has been great for, recently, has been search for obscure or indirect references like this, that might be one step removed from any specific thing you're searching for, or if you have a tip-of-the-tongue search where you might have forgotten a phrase, or know you're using the wrong wording.
It's cool that you can trace the work of these rocket scientists all the way to the state of the art AI.
I think "its" refers to control theory, not backpropagation.
- Henry J. Kelley (1960), “Gradient Theory of Optimal Flight Paths,” ARS Journal.
- A.E. Bryson & W.F. Denham (1962), “A Steepest-Ascent Method for Solving Optimum Programming Problems,” Journal of Applied Mechanics.
- B.G. Junkin (1971), “Application of the Steepest-Ascent Method to an Apollo Three-Dimensional Reentry Optimization Problem,” NASA/MSFC report.
I pasted the output so a ton of people wouldn't repeat the same question to ChatGPT and burn a ton of CO2 to get the same answer.
I didn't paste the query since I didn't find it interesting.
And I didn't fact check because I didn't have the time. I was walking and had a few seconds to just do this on my phone.
Not sure how this was rude, I certainly didn't intend it to be...
It's a weird thing to wonder after so many people expressed their dislike of the upthread low-effort comment with a down vote (and then another voiced a more explicit opinion). The point is that a reader may want to know that the text they're reading is something a human took the time to write themselves. That fact is what makes it valuable.
> pncnmnp seems happy
They just haven't commented. There is no reason to attribute this specific motive to that fact.
The reader may also simply want information that helps them.
> They just haven't commented.
Yes, they did.
The reader will generally want at least a cursory verification that it is information that helps, which dataflow didn't try to do.
Especially when you're looking for specific documents and you don't check if the documents are real. (dataflow's third one doesn't appear to be.)
Directly posting the random text generated by the LLM is more annoying. I mean, they didn’t even vouch or it or verify that it was right.
Also, I quite love it when people clearly demarcate which part of their content came from an LLM, and specifies which model.
The little citation carries a huge amount of useful information.
The folks who don't like AI should like it too, as they can easily filter the content.
The Minimum-Time Thrust-Vector Control Law in the Apollo Lunar-Module Autopilot (1970)
https://www.sciencedirect.com/science/article/pii/S147466701...
> "Since his first work on the subject, the author has found that A. Bryson and Y.-C. Ho [Bryson and Ho, 1969] described the backpropagation algorithm using Lagrange formalism. Although their description was, of course, within the framework of optimal control rather than machine learning, the resulting procedure is identical to backpropagation."
I remember reading this book enthusiastically back in the mid 90s. I don't recall struggling with the proof, it was fairly straightforward. (I was in senior high school year at the time.)
In it, he stated the following:
> Indeed, the famous “backpropagation” algorithm that was rediscovered by David Rumelhart in the early 1980s, and which is now viewed as being at the core of the so-called “AI revolution,” first arose in the field of control theory in the 1950s and 1960s. One of its early applications was to optimize the thrusts of the Apollo spaceships as they headed towards the moon.
I was wondering whether anyone could point me to the paper or piece of work he was referring to. There are many citations in Schmidhuber’s piece, and in my previous attempts I've gotten lost in papers.