We didn't model dynamics in the way your diagram / paper shows it, but Maya does allow the connection of properties between nodes in a graph, and the nodes themselves perform operations ranging from trivial to very complex, and all of those had to be emulated with the instruction set we arrived at for the VM. Most of it was relationships - like, over the range of motion of your elbow, how does the shape of the bicep change? Or, given a target location and an "interest level", move the upper body, head, and eyes to follow the target by an appropriate amount. Given a "smile" amount, move all the joints and vertices in this specific character to make him smile. So, more direct than what you're talking about, but still compiling code from a visual graph.
You remind me that what is in the diagram is not a DAG. John Baez introduces loops feeding back from top to bottom so it is cyclic. That is not like the acyclic thing I was talking about in the Lucol language. BUT those wires turn around at the bottom and top are not just connecting wires in his system the are actual elements "cup" and "cap" on the same footing as "add", "multiply" etc. So when it comes to implementation the loops can be broken on "cap". The input to cap being saved and used on the next iteration as it's output. This brings the thing back to the purely Functional Programming style of Lucol.
@Jascon,
Sounds like you are describing a complex reverse kinematics problem. A lot more complex than I'd like to be tackling !
But will Lucol, Simulink, LabVIEW, Maya, etc. automatically solve equations for the right variables for you before simulating them? Yes, feedback loops obviously have to be broken somewhere, but Lucol and Labview at least (I know almost nothing about the other two) will not do this for you automatically, Let's say you want to understand a complex system. With my program, you'd just type in the equations modelling your system, solved for whatever variable you found them in, and it would solve them for the desired variables for you. You can instantly switch from have it simulate variable A in terms of B and C to having it simulate variable B in terms of A and C, without needing to first take a break to solve re-solve your system for B and then re-enter that into the program. The algebra solver doesn't need to be great, at least for preliminary simulation visualization purposes - it only needs to be fast enough to run on a modern computer. It can cheat using things like the Newton-Rhapson Method for equations that it can't solve and Runge-Kutta integration for integrals it can't find closed forms for, while, in the background, possibly continuing to look for closed-form solutions.
No idea about the others but Lucol is just a good old fashioned programming language, with some restrictions and features that make it possible to create code that is easy to test thoroughly, and easy to analyse and verify it does not exceed it's execution time budget.
All that equation solving business is another world. Way above my pay grade
I have sort of a different take on this. To me, category theory is intended to allow the comparisons of mathematical treatments, which superficially appear to use different constructs... by categorizing the constructs in a general way. It is "object oriented" math.
I think it is interesting to see that mathematicians, with such profound skills, promote their work, by quoting the 2014 report of the IPCC ... without comment, except to say that their work should be useful to anyone studying such complex systems as those, which seem so perfectly understood by the IPCC.
No doubt the Nobel committee already has these guys on their short list.
By the way, I use programmable semicolons all the time. You probably do to. Maybe we should write a paper, which no-one actually understands, and then say that global survival depends upon using our method. That's what they are doing.
These guys are to mathematics what Piaget was to epistemology.
From time to time I have a little read of these Functional Programming ideas or watch some presentation on the YouTubes. My brain soon freezes over and I still have no idea what they are talking about. All this talk of monads and category theory makes my head spin.
Sometimes I get the impression that they have invented some programming language that is incomprehensible, Haskell, and then show how smart they are by describing ways to actually do something useful with it!
From time to time I come away with perhaps a useful concept: Creating your code from stateless functions that have no side effects will make it a whole lot easier to reason about, test and debug. Or mapping a function over a collection might be better than writing yet another "for" loop.
As you say, we probably do some of this naturally.
John Baez is a brilliant mathematician who has turned is attention to the effects of humans on the environment. Who knows where that will lead? But typically when mathematicians roll their sleeves up and get that hands dirty with real world problems magic things happen. Like pretty much all of the technological landscape we live in!
Note: There is no Noble prize in mathematics. If you are a mathematician and want a Noble prize you are going to have to sneak in under the guise of something else e.g. economics in the case of John Nash.
Still, I like that paper if only for the gloriously simple signal flow diagrams and the rigorous definitions of all the symbols.
These guys are to mathematics what Piaget was to epistemology.
Note: There is no Noble prize in mathematics. If you are a mathematician and want a Noble prize you are going to have to sneak in under the guise of something else e.g. economics in the case of John Nash.
And even that isn't a Nobel (note spelling..). Nobel never created a prize for economics. It's just a prize by the Swedish Central Bank, and given at the same time. "The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel"
Another interesting PID demo featured on Hackaday. Interesting idea for sure. Could be a good demo with a nice front panel to tune things and a plot of angle and set point over time.
Is that a sardine can he has built the thing into?
Looks like it. I was just about to say, "DUH, your sardine can is unstable and wobbling, you have to fix that before you can stand a chance of tuning that ramshackle rig..."
And then the PID kicked in and all the wobbling stopped. Magical.
A sad tale of miscontrol, miscommunication and mismanagement. Jump to 17:00 to see an aircraft control system in distress. Don't blame P, I, or D here, blame all these people blaming the system. Not one word from the pilot, interestingly. A beautiful airplane, the vector thrust nozzle has only 3 flaps. Reminds me of 3 omniwheel bot.
Fortunately the remaining X31 redeemed itself at the Paris Airshow, watch to the end. Fabulous maneuvers.
I didn't watch the whole video, but the aircrafts fuselage to wing ratio looks out of balance. I'm definitely no expert on anything involved, less wing, less control. It just seems like a design that you wouldn't push to any limits. No airspeed, no lift, no control.
The pilot-less plane recovers a couple of times before the crash.
That vectored thrust nozzle was a game-changer for maneuverability, so a lot of the old wing/fuselage/stabilator rules didn't apply. I worked for Pratt & Whitney in 1982-83 on the F-15 & F-16 engine, the F-100. Pratt was working on a 2D nozzle, just four butted titanium honeycomb plates making a square nozzle, like the F22's shown below. Only the top & bottom plates moved, and that was a bear to develop. The three small moving flaps on the X-31 are much simpler mechanically and clearly they work well enough to vector the thrust. I'm guessing there's a circular nozzle inside the engine too. And probably no augmentor (afterburner).
Gets my motor running every time. Jump to 3:00 for some sweet test stand nozzle/afterburner shots.
This would make a nice garage heater, and would keep the Starlings and Grackles away at the same time. But I can't even stand the noise of my bullet heater for very long.
as far as the design of modern miltary aircraft, they need a steep glide slope in case of total engine failure. I guess it is safer to bail, than to try land.
like the Space Shuttle, you have one chance to do it right.
as far as the design of modern miltary aircraft, they need a steep glide slope in case of total engine failure. I guess it is safer to bail, than to try land.
Wow, for all the PID nerds out there: I just came across a paper by our hero James Clerk Maxwell in the Proceedings of the Royal Society of London in 1868 in which he is discussing speed governors for steam engines.
This is perhaps the first discussion of PID control. Maxwell is asking the mathematicians of the day to apply their minds to the problem of stability.
On a quick glance it seems a one Prof, J. Thomson had invented an integral control mechanism for steam engine speed regulation. You know, the Thomson that discovered the electron that we all know and love.
Comments
Ha, does look a bit like a chemical plant.
You remind me that what is in the diagram is not a DAG. John Baez introduces loops feeding back from top to bottom so it is cyclic. That is not like the acyclic thing I was talking about in the Lucol language. BUT those wires turn around at the bottom and top are not just connecting wires in his system the are actual elements "cup" and "cap" on the same footing as "add", "multiply" etc. So when it comes to implementation the loops can be broken on "cap". The input to cap being saved and used on the next iteration as it's output. This brings the thing back to the purely Functional Programming style of Lucol.
@Jascon,
Sounds like you are describing a complex reverse kinematics problem. A lot more complex than I'd like to be tackling !
All that equation solving business is another world. Way above my pay grade
A monad is a programmable semicolon.
I have sort of a different take on this. To me, category theory is intended to allow the comparisons of mathematical treatments, which superficially appear to use different constructs... by categorizing the constructs in a general way. It is "object oriented" math.
I think it is interesting to see that mathematicians, with such profound skills, promote their work, by quoting the 2014 report of the IPCC ... without comment, except to say that their work should be useful to anyone studying such complex systems as those, which seem so perfectly understood by the IPCC.
No doubt the Nobel committee already has these guys on their short list.
By the way, I use programmable semicolons all the time. You probably do to. Maybe we should write a paper, which no-one actually understands, and then say that global survival depends upon using our method. That's what they are doing.
These guys are to mathematics what Piaget was to epistemology.
From time to time I have a little read of these Functional Programming ideas or watch some presentation on the YouTubes. My brain soon freezes over and I still have no idea what they are talking about. All this talk of monads and category theory makes my head spin.
Sometimes I get the impression that they have invented some programming language that is incomprehensible, Haskell, and then show how smart they are by describing ways to actually do something useful with it!
From time to time I come away with perhaps a useful concept: Creating your code from stateless functions that have no side effects will make it a whole lot easier to reason about, test and debug. Or mapping a function over a collection might be better than writing yet another "for" loop.
As you say, we probably do some of this naturally.
John Baez is a brilliant mathematician who has turned is attention to the effects of humans on the environment. Who knows where that will lead? But typically when mathematicians roll their sleeves up and get that hands dirty with real world problems magic things happen. Like pretty much all of the technological landscape we live in!
Note: There is no Noble prize in mathematics. If you are a mathematician and want a Noble prize you are going to have to sneak in under the guise of something else e.g. economics in the case of John Nash.
Still, I like that paper if only for the gloriously simple signal flow diagrams and the rigorous definitions of all the symbols. Do wha'. Is that good or bad
Oops..well spotted. I nobbled my own post. No prizes for me.
Looks like it. I was just about to say, "DUH, your sardine can is unstable and wobbling, you have to fix that before you can stand a chance of tuning that ramshackle rig..."
And then the PID kicked in and all the wobbling stopped. Magical.
You need to wash the can, are you actually working on a robot? something smells a little fishy.
Fortunately the remaining X31 redeemed itself at the Paris Airshow, watch to the end. Fabulous maneuvers.
The pilot-less plane recovers a couple of times before the crash.
This would make a nice garage heater, and would keep the Starlings and Grackles away at the same time. But I can't even stand the noise of my bullet heater for very long.
as far as the design of modern miltary aircraft, they need a steep glide slope in case of total engine failure. I guess it is safer to bail, than to try land.
like the Space Shuttle, you have one chance to do it right.
Some planes land themselves! Otto Pilot?
This is perhaps the first discussion of PID control. Maxwell is asking the mathematicians of the day to apply their minds to the problem of stability.
http://rspl.royalsocietypublishing.org/content/16/270
On a quick glance it seems a one Prof, J. Thomson had invented an integral control mechanism for steam engine speed regulation. You know, the Thomson that discovered the electron that we all know and love.
Edit: Also, perhaps a slightly more readable version here: https://upload.wikimedia.org/wikipedia/commons/b/b1/On_Governors.pdf
Amazing story, thanks for posting.
This guy doesn't have the whiny voice that hurts my ears.
It's the Aussie total lack of political correctness.
The Aussie slang is poetry.
EEVBlog Dave is a bit whiny. It does not hurt anymore than the Yankee "wha wha wha" that annoys me on TV everyday.