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Riemann hypothesis should be next... Which paper on the linked website is this exactly?

hmmm, last year at the AIAA conference in Toronto I presented a continuation approach to design a DRO (three-body problem). Nothing new here unfortunately. I know the work of Caillau, although interesting what is presented was solved 10 years ago by others. The interest of his work is not in the applications (CR3BP), but in the research of particular regularity conditions that unfortunately make the problem limited practically. Look also at the work of Mingotti, Russel, Topputo and other for the (C)RTBP. Smart-One inspired a bunch of researchers :)

Topputo and some of the others 'inspired' researchers you mention are actually here at the conference and they are all quite depressed :) Caillau really solves the problem: as a one single phase transfer, no tricks, no misconvergence, in general and using none of the usual cheats. What was produced so far by other were only local solutions valid for the particular case considered. In any case I will give him your paper, so that he knows he is working on already solved stuff :)

Answer to Marek: the paper you may look at is: Discrete and differential homotopy in circular restricted three-body control

Ah! with one single phase and a first order method then it is amazing (but it is still just the very particular CRTBP case). The trick is however the homotopy map he selected! Why this one? Any conjugate point? Did I misunderstood the title ? I solved in one phase with second order methods for the less restrictive problem RTBP or simply 3-body... but as a strict answer to your title the problem has been solved before. Nota: In "Russell, R. P., "Primer Vector Theory Applied to Global Low-Thrust Trade Studies," JGCD, Vol. 30, No. 2", he does solve the RTBP with a first order method in one phase.

I think what is interesting is not what he solved, but how he solved the problem. But, are means more important than end ... I dunno

I also loved his method, and it looked to me that is far more general than the CRTBP. As for the title of this post, OK maybe it is an exageration as it suggests that no solution was ever given before, on the other end, as Marek would say "come on guys!!!!!"

The generality has to be checked. Don't you think his choice of mapping is too specific? he doesn't really demonstrate it works better than other. In addition, the minimum time choice make the problem very regular (i guess you've experienced that solving min time is much easier than mass max, optimality-wise). There is still a long way before maximum mass+RTBP, Topputo et al should be re-assured :p Did you give him my paper, he may find it interesting since I mention the homotopy on mu but for max mass:)

Joris, that is the point I was excited abut, at the conference HE DID present solutions to the maximum mass problem!! One phase, from LEO to an orbit around the moon .. amazing :) You will find his presentation on line.... (according to the organizers) I gave him the reference to you paper anyway, but no pdf though as you did not upload it on our web pages and I could not find it in the web. So I gave him some bibliography I had with be from the russians, and from Russell, Petropoulos and Howell, As far as I know these are the only ones that can hope to compete with this guy!!

for info only, my phd, in one phase: http://pdf.aiaa.org/preview/CDReadyMAST08_1856/PV2008_7363.pdf I prefered Mars than the dead rock Moon though!

If you send me the pdf I can give it to the guy .. the link you gave contains only the first page ... (I have no access till monday to the AIAA thingy)

this is why I like this Diigo thingy so much more than delicious ...

What do you mean by this comment, Leopold? ;-) Jokes apart: I am following the Diigo thingy with Google Reader (rss). Obviously, I am getting the new postings. But if someone later on adds a comment to a post, then I can miss it, because the rss doesn't get updated. Not that it's a big problem, but do you guys have a better solution for this? How are you following these comments? (I know that if you have commented an entry, then you get the later updates in email.) (For example, in google reader I can see only the first 5 comments in this entry.)

"Kurzweilians"... LOL. Still not sold on embodiment, btw.

The biggest problem with embodiment is that, since the passive walkers (with which it all started), it hasn't delivered anything really interesting...

The problem with embodiment is that it's done wrong. Embodiment needs to be treated like big data. More sensors, more data, more processing. Just putting a computer in a robot with a camera and microphone is not embodiment.

I like how he attacks Moore's Law. It always looks a bit naive to me if people start to (ab)use it to make their point. No strong opinion about embodiment.

@Paul: How would embodiment be done RIGHT?

Embodiment has some obvious advantages. For example, in the vision domain many hard problems become easy when you have a body with which you can take actions (like looking at an object you don't immediately recognize from a different angle) - a point already made by researchers such as Aloimonos.and Ballard in the end 80s / beginning 90s. However, embodiment goes further than gathering information and "mental" recognition. In this respect, the evolutionary robotics work by for example Beer is interesting, where an agent discriminates between diamonds and circles by avoiding one and catching the other, without there being a clear "moment" in which the recognition takes place. "Recognition" is a behavioral property there, for which embodiment is obviously important. With embodiment the effort for recognizing an object behaviorally can be divided between the brain and the body, resulting in less computation for the brain. Also the article "Behavioural Categorisation: Behaviour makes up for bad vision" is interesting in this respect. In the field of embodied cognitive science, some say that recognition is constituted by the activation of sensorimotor correlations. I wonder to which extent this is true, and if it is valid for extremely simple creatures to more advanced ones, but it is an interesting idea nonetheless. This being said, if "embodiment" implies having a physical body, then I would argue that it is not a necessary requirement for intelligence. "Situatedness", being able to take (virtual or real) "actions" that influence the "inputs", may be.

@Paul While I completely agree about the "embodiment done wrong" (or at least "not exactly correct") part, what you say goes exactly against one of the major claims which are connected with the notion of embodiment (google for "representational bottleneck"). The fact is your brain does *not* have resources to deal with big data. The idea therefore is that it is the body what helps to deal with what to a computer scientist appears like "big data". Understanding how this happens is key. Whether it is the problem of scale or of actually understanding what happens should be quite conclusively shown by the outcomes of the Blue Brain project.

Wouldn't one expect that to produce consciousness (even in a lower form) an approach resembling that of nature would be essential? All animals grow from a very simple initial state (just a few cells) and have only a very limited number of sensors AND processing units. This would allow for a fairly simple way to create simple neural networks and to start up stable neural excitation patterns. Over time as complexity of the body (sensors, processors, actuators) increases the system should be able to adapt in a continuous manner and increase its degree of self-awareness and consciousness. On the other hand, building a simulated brain that resembles (parts of) the human one in its final state seems to me like taking a person who is just dead and trying to restart the brain by means of electric shocks.

Actually on a neuronal level all information gets processed. Not all of it makes it into "conscious" processing or attention. Whatever makes it into conscious processing is a highly reduced representation of the data you get. However that doesn't get lost. Basic, low processed data forms the basis of proprioception and reflexes. Every step you take is a macro command your brain issues to the intricate sensory-motor system that puts your legs in motion by actuating every muscle and correcting every step deviation from its desired trajectory using the complicated system of nerve endings and motor commands. Reflexes which were build over the years, as those massive amounts of data slowly get integrated into the nervous system and the the incipient parts of the brain. But without all those sensors scattered throughout the body, all the little inputs in massive amounts that slowly get filtered through, you would not be able to experience your body, and experience the world. Every concept that you conjure up from your mind is a sort of loose association of your sensorimotor input. How can a robot understand the concept of a strawberry if all it can perceive of it is its shape and color and maybe the sound that it makes as it gets squished? How can you understand the "abstract" notion of strawberry without the incredibly sensible tactile feel, without the act of ripping off the stem, without the motor action of taking it to our mouths, without its texture and taste? When we as humans summon the strawberry thought, all of these concepts and ideas converge (distributed throughout the neurons in our minds) to form this abstract concept formed out of all of these many many correlations. A robot with no touch, no taste, no delicate articulate motions, no "serious" way to interact with and perceive its environment, no massive flow of information from which to chose and and reduce, will never attain human level intelligence. That's point 1. Point 2 is that mere pattern recogn