Haven't quite been following this thread, but closed form solutions are generally only good if you can describe a system in one equation. For Tuco's problem, once you get the right vector to your end point, you can stop turning and then you end up with a piecewise solution. Here's how I would simulate it, but I don't have MATLAB on this computer, so I can't actually test it.
Science!! Fucking magnets, how do they work?
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Mist
REEEEeyore
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Inertia?
EDIT: Rather, the underlying forces that govern inertia. Velocity attempting to remain constant is a property of the massiness of an object, and the more massy it is, the more inertia it has. Another way to say that is the more mass something has the more 'information' about it's velocity it can store, and that information is has some built in resistance to change which we call inertia.
If the universe were a data simulation, inertia would be a mechanism built in to make sure that more massive objects have more consistent velocities requiring the data simulation to update their velocities less frequently, saving on the computational resources that would be taken up by very massy objects.
Tuco
I got Tuco'd!
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Sorry, I didn't do a sanity check on it so I don't know if 10 meters is too close. If so then make it 30 meters
Szlia
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If the target on the Y axis is not the closest that the car can reach, there will be an infinite number of possible trajectories, making it difficult (maybe even impossible) to answer the questions properly.
That said, my tired self does not even know what is the radius of the circle the car travels on given a set steering angle.
Ambiturner
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Inertia is another one of those quantities that intuitively seem simple until physicists get their hands on it.
http://www.calphysics.org/inertia.html
Ah, are you saying that a position tracking model doesn't need to run at discrete units in time ex, update every millisecond, but can instead be run from an arbitrary starting point to an arbitrary endpoint with a complete equation?
If so then yeah, I agree. Some of my vehicle modeling code does propagation by moving the systems many times at discrete time steps to achieve a given time propogation which I guess is very common but I've always wanted to replace it with a single propagation but have never seriously looked into it. I've also had problems modeling ackermann vehicles that have a steering angle and a steering angle rate of change.
Since this is a science thread, I'll pose this quandary and see if anyone wants to walk me through it!!
Because I'm a big nerd, updated my code and made a plot. Green = turning, black = straight
It does, but my sim is missing a key part of your problem: steering angle vs velocity. I made the assumption that you're always moving towards where the car is pointing, which isn't strictly true. Turning the wheel turns the body of the vehicle, which imparts a force which changes your velocity.
So basically, I never used the 'max steering angle of 30 deg' because in my sim max steering angle is always 0 deg.
To bring it back to the greater conversation, if I wanted to 'simulate the world', I wouldn't do so at the velocity level, I'd do it through accelerations. Each cell has a position and a mass and will expand/contract when a force is exerted on them or can exert their own force through chemical reactions.
So basically, I never used the 'max steering angle of 30 deg' because in my sim max steering angle is always 0 deg.
To bring it back to the greater conversation, if I wanted to 'simulate the world', I wouldn't do so at the velocity level, I'd do it through accelerations. Each cell has a position and a mass and will expand/contract when a force is exerted on them or can exert their own force through chemical reactions.
And this is where I always see people with new models get this shit wrong. It's always the small stuff that trips them up.
Drakurii
Golden Baron of the Realm
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This Guy Beat Googlet Easy | WIRED
Andrej Karpathy knows what it's like to compete with artificial intelligence.
He first went head-to-head with an artificial intelligence algorithm in 2011. A team of Stanford University researchers had just built the world's most effective image-recognition software, and he wanted to see how well his very real brain stacked up against their digital creation on what was, at the time, a standard image recognition test.
The Stanford software analyzed a pool of about 50,000 images, slotting each into one of 10 categories, such as "dogs," "horses," and "trucks." It was right about 80 percent of the time. Karpathy took the same test and completely smoked the AI code, scoring 94 percent. Karpathy, himself a graduate student at Stanford, thought humans would beat machines on this type of test for a long time. "t will be hard to go above 80 percent," he wrote in a blog post, referring to AI algorithms, "but I suspect improvements might be possible up to range of about 85-90 percent."
Boy, was he wrong.
Last year, a system built by researchers at Google aced another, more complex, image recognition test, called ImageNet, scoring 93.4 percent accuracy (you can see how Google's software performed on the test here). Again, Karpathy, with some colleagues at Stanford, went head-to-head with the system. But this time, they bombed what was a much more complex test, initially scoring about an 85 percent accuracy rate. Comparing the ImageNet test to the 2011 test software isn't exactly an apples-to-apples comparison, but here's the point: Humans were easily beating AI software in 2011; now that's not the case. Not by a long shot.
Andrej Karpathy knows what it's like to compete with artificial intelligence.
He first went head-to-head with an artificial intelligence algorithm in 2011. A team of Stanford University researchers had just built the world's most effective image-recognition software, and he wanted to see how well his very real brain stacked up against their digital creation on what was, at the time, a standard image recognition test.
The Stanford software analyzed a pool of about 50,000 images, slotting each into one of 10 categories, such as "dogs," "horses," and "trucks." It was right about 80 percent of the time. Karpathy took the same test and completely smoked the AI code, scoring 94 percent. Karpathy, himself a graduate student at Stanford, thought humans would beat machines on this type of test for a long time. "t will be hard to go above 80 percent," he wrote in a blog post, referring to AI algorithms, "but I suspect improvements might be possible up to range of about 85-90 percent."
Boy, was he wrong.
Last year, a system built by researchers at Google aced another, more complex, image recognition test, called ImageNet, scoring 93.4 percent accuracy (you can see how Google's software performed on the test here). Again, Karpathy, with some colleagues at Stanford, went head-to-head with the system. But this time, they bombed what was a much more complex test, initially scoring about an 85 percent accuracy rate. Comparing the ImageNet test to the 2011 test software isn't exactly an apples-to-apples comparison, but here's the point: Humans were easily beating AI software in 2011; now that's not the case. Not by a long shot.
Tuco
I got Tuco'd!
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Important piece:
If you a person a set of 100 small images, 50 of which have dogs and 50 of which don't, and the dogs in those images are generally difficult to discern, it would be tremendously difficult for the AI to win. But they changed the rules.
When you instead present a classification algorithm that uses input like:
http://people.csail.mit.edu/khosla/papers/fgvc2011.pdf
It's a very different problem that has to do with relational databases rather than machine vision. Outperforming a human on any CV task is cool and impressive and not to take away their victory here, but when it's generally easy to extract, "large ears", "droopy ears", "brown", "short hair" "spots" it's just a matter of feeding that into a classification system to fit a database.
The other part to this is that it's trivial for a human to detect when picture of a dog is actually a cartoon, or a picture of a human in a dog suit, but these corner cases can be difficult with CV.
The challenge with computer vision often isn't how precise or how many objects can be classified, but how well it handles corner cases of occluded, shadowed, reflective or otherwise degraded images.article_sl said:
If you a person a set of 100 small images, 50 of which have dogs and 50 of which don't, and the dogs in those images are generally difficult to discern, it would be tremendously difficult for the AI to win. But they changed the rules.
When you instead present a classification algorithm that uses input like:
http://people.csail.mit.edu/khosla/papers/fgvc2011.pdf
It's a very different problem that has to do with relational databases rather than machine vision. Outperforming a human on any CV task is cool and impressive and not to take away their victory here, but when it's generally easy to extract, "large ears", "droopy ears", "brown", "short hair" "spots" it's just a matter of feeding that into a classification system to fit a database.
The other part to this is that it's trivial for a human to detect when picture of a dog is actually a cartoon, or a picture of a human in a dog suit, but these corner cases can be difficult with CV.
iannis
Musty Nester
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I have an engineering textbook that my grandfather gave me from the early 40's. It's part mechanics, part sociology, part history. About 1/4 of that book devoted to exploring what the author calls, "The emerging Cult of Machine" interlaced with a brief history of the Industrial Revolution. And then in the other half there's all these formulas and tables and mixes of different types of math, all tools for the design of different sorts of structures. That talk reminded me very much of Machine Cult.
They don't make textbooks like that anymore. They should!
They don't make textbooks like that anymore. They should!
Sheldrake is full of shit and should be listened to byno one.
TEDx talks completely discredited: Rupert Sheldrake speaks, argues that speed of light is dropping! Why Evolution Is True
iannis
Musty Nester
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Y u mad tho? That's not what he said. I mean I dunno, I haven't read his book. Maybe he does go on to put way too fine a point on it in his book. But I didn't hear that in those 18 minutes.
That talk itself was skirting right to the edge of mysticism, granted, but not stepping over. If you review his observation of scientific dogma you'll find them hard to refute directly. There are dogmas. Of course there are. There have to be. And they remain useful for exactly so long as they are useful. His concept of mind I don't think is remotely scientific. But I don't think he's asserting that it is, either. What he is saying is that perhaps there is use in continual examination of them. And that is almost always true to the point of nearly being a platitude.
But take that specific complaint. Current wisdom is that light, being assumed and observed massless, travels at c. c is axiomatic. But perhaps light = c is not. And perhaps it is. Point is that's a guess, no matter how educated. He's not saying that light slowed down for 10 years. He is saying that we don't even check.
I don't think particle physicists would be thrilled to learn that light speed is variable. I think they'd doubt the veracity of their instruments. And I think that's a fine and reasonable doubt to have. But it is dogmatic, and it is possible to become a self-limiting sort of dogma.
What he's really arguing is the limits of science as a process, and he seems to want to expand that limit. And you do that by allowing for creative thought, even if it sounds kooky. But now extraordinary claims and all that...
That talk itself was skirting right to the edge of mysticism, granted, but not stepping over. If you review his observation of scientific dogma you'll find them hard to refute directly. There are dogmas. Of course there are. There have to be. And they remain useful for exactly so long as they are useful. His concept of mind I don't think is remotely scientific. But I don't think he's asserting that it is, either. What he is saying is that perhaps there is use in continual examination of them. And that is almost always true to the point of nearly being a platitude.
But take that specific complaint. Current wisdom is that light, being assumed and observed massless, travels at c. c is axiomatic. But perhaps light = c is not. And perhaps it is. Point is that's a guess, no matter how educated. He's not saying that light slowed down for 10 years. He is saying that we don't even check.
I don't think particle physicists would be thrilled to learn that light speed is variable. I think they'd doubt the veracity of their instruments. And I think that's a fine and reasonable doubt to have. But it is dogmatic, and it is possible to become a self-limiting sort of dogma.
What he's really arguing is the limits of science as a process, and he seems to want to expand that limit. And you do that by allowing for creative thought, even if it sounds kooky. But now extraordinary claims and all that...
Furry
🌭🍔🇺🇦✌️SLAVA UKRAINI!✌️🇺🇦🍔🌭
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I agree complete with him in the faults of scientific dogma. What I disagree with him on is his claims on what science could be. Its fine and dandy shitting on the way science is done in the modern day, because there is a lot of whichcraft to it. But presenting ideas like people can sense stare rape from behind? Don't bring that shit to a scientific discussion without some science behind it. You're even worse than the problem then.
Valishar
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They would be THRILLED, the speed of light being a variable changes literally everything. The way we measure distance is all wrong. Einstien's metric tensor is wrong. Maxwell's equations of electromagnetism are wrong. If c was still c, but light traveled at less than c, it means relativity is wrong. It also means particle physics, also probably wrong.
One of the problems is that light has no rest mass, it has no choice but to travel at the max speed of the universe. The second problem is by Maxwell's equations the value of the strength of the electric force is different for each differing value of the speed of an electromagnetic wave. Since the structure of matter and chemical reactions haven't really changed over the course of human history it would mean those equations need to be changed.
So basically yeah, you'd probably get a Nobel at least if you found that out.
Rupert Sheldrake isn't a physicist though, so he wouldn't know anything about this. I heard him on Rogan and basically had to shut off the podcast an hour or so in, he seems like he has a bit of a taste of something interesting, and then jumps right into the deep end without and real analysis. You've got to take what he says with like a bathtub's worth of salt.