What I mean by this is the following:
-know what the inside of a closed shape (defined by an equation) is
-recognize objects in a picture (2d plane?) using parameters
-know the relations of a certain variable in a group
-a system in which the input changes the output but at the same time changes the input
-a system in which the input changes the output but at the same time changes the input
consider a differential eqn describing a rocket. it starts with a certain mass but through burning becomes lighter. the input affects the output and the output affects the input ie less fuel less mass.
#3
petormojer
15
0
@jedishrfu
Can you please explain it mathematically?
What I mean by this is the following:
-know what the inside of a closed shape (defined by an equation) is
-recognize objects in a picture (2d plane?) using parameters
-know the relations of a certain variable in a group
-a system in which the input changes the output but at the same time changes the input
Petor, it is great that you are starting to use the PhysicsForums to learn more about science and mathematics and technology! But it will help us a lot to answer your questions if you can tell us your technical background and eductation. And when you post questions like this, please post links to what you have been reading so far on the Internet and in textbooks and journals. Your question as stated in the quote is hard to interpret and answer well. Please post some examples or links to help us help you learn. Thank you.
Tell us more about your background and why the interest in problems not solvable by math.
There's an analogue in computer science with games that we that can't implemented well with computers. The one comes to is drawing arcs on a piece of paper where the end points of the arcs are at the midpoint of other arcs and no arc can cross over any other arc.
#6
petormojer
15
0
@berkeman
I am a high school student, so I don't know much mathematics as you guys do.
I learned algebra, trigonometry, discrete mathematics and single variable calculus.
I don't know anything else unfortunately.
I've been looking up on science documentaries where one of the shows had a stanford team that made a computer program that uses a camera to detect objects (dishes, computers, pencils, people, and etc.) so I would guess that they definitely used some sort of mathematical algorithm in their computer system.program.
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#7
petormojer
15
0
@jedishrfu My interest in problems not solvable in math is because mathematics is a useful tool to know solutions to problems that are hard to solve without mathematics.
But the real reason is that I want to use it to make a computer program that uses these as applications for artificial intelligence.
Those are noble goals. One thing though is that computers follow the Turing model and as such will always be limited in the kinds of problems they can solve in a finite amount of time. The Turing model is a mathematical representation of a computer.
Read about it and other models of computation so you can better understand what a computer can and can't do.
The object recognition in an image has a long and venerable history too. Matlab even provides the filtering tools to adjust an image and pick out shapes. Again, the computer has limits of what it can and can't do. It might see a circle but not know its a ball because the shading isn't there or because it's not using stereoscopic hardware.
Cornell Univ developed an interesting program that can extract the equation from a large set of data. They tested with a double pendulum which has very complex motion and it correctly pulled out the equation without knowing physics from the data.
http://creativemachines.cornell.edu/natural_laws
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#9
petormojer
15
0
@jedishrfu do you know the link to the algorithm for the creative machine program? It sounds very interesting.
#10
ellipsis
158
24
There are certain problems which become intractable with classical computers on a sufficient input size (NP, or Non-polynomial problems, like Traveling Salesman, Bin-packing, optimization problems) and there are problems which are downright impossible.
The biggest example of something you cannot do with computers (and therefore cannot do with math, or anything, ever) is, using a single algorithm, determine if a program of arbitrary size eventually stops or not.
Sure, there are examples of programs where it's very easy to see the behavior. If it was impossible to determine whether a program would do X, how would we programmers operate? But, still, the more complex a program is, the more complex of an algorithm it takes to determine its behavior.
Following from that, you could, practically, build a huge, monolithic program that determines the halting behavior of other programs. But it would not work on itself, or anything more complex than itself. There's always a program more complex, that requires a halting-analyzer even more complex.
And looking at size, and run-time won't work. You may think: "Why don't I build a program to count the size of input program P, run P, and see how long it runs? If it's pretty short and it runs over (size)^10 seconds, then I can say with certainty it will never halt"
Unfortunately, there exist tiny programs (less than 20 characters) which halt eventually (after a few billion years). The halting problem is one of the most fascinating problems in computer science / mathematics.
An open question: Quantum computers have been shown to address a larger set of problems than classical computers. Is there a "quantum mathematics" somewhere in the platonic realm, that address problems that current mathematics cannot?
PS: It follows from the Halting Problem that there are programs which a human programmer can never grok, for the algorithm he mentally implements in his brain is simply not strong enough. Is an algorithm capable of building a more complex/capable copy of itself? This is the question of artificial intelligence, and IMO, the fate of our race.
There are certain problems which become intractable with classical computers on a sufficient input size (NP, or Non-polynomial problems, like Traveling Salesman, Bin-packing, optimization problems) and there are problems which are downright impossible.
The biggest example of something you cannot do with computers (and therefore cannot do with math, or anything, ever) is, using a single algorithm, determine if a program of arbitrary size eventually stops or not.
Sure, there are examples of programs where it's very easy to see the behavior. If it was impossible to determine whether a program would do X, how would we programmers operate? But, still, the more complex a program is, the more complex of an algorithm it takes to determine its behavior.
Following from that, you could, practically, build a huge, monolithic program that determines the halting behavior of other programs. But it would not work on itself, or anything more complex than itself. There's always a program more complex, that requires a halting-analyzer even more complex.
And looking at size, and run-time won't work. You may think: "Why don't I build a program to count the size of input program P, run P, and see how long it runs? If it's pretty short and it runs over (size)^10 seconds, then I can say with certainty it will never halt"
Unfortunately, there exist tiny programs (less than 20 characters) which halt eventually (after a few billion years). The halting problem is one of the most fascinating problems in computer science / mathematics.
An open question: Quantum computers have been shown to address a larger set of problems than classical computers. Is there a "quantum mathematics" somewhere in the platonic realm, that address problems that current mathematics cannot?
PS: It follows from the Halting Problem that there are programs which a human programmer can never grok, for the algorithm he mentally implements in his brain is simply not strong enough. Is an algorithm capable of building a more complex/capable copy of itself? This is the question of artificial intelligence, and IMO, the fate of our race.
Code:
for (i = 0; i < 10^10^10^10^10; i++) {;}
Dear ... I like your post but not your chosen name here. How do I reference you as a poster without confusing someone when I use the ... To extend my own sentences.
Should I refer to you as three little dots or as 3dot or 3... To avoid confusion. Notice how the spell corrector capitalizes the next word... See what I mean?
It s never good to have someone think of ways to subvert your clever screen name.
Look what happened to Why aka Why the Lucky Stiff when some jerks nitpicked his code as some programmers will do.
@jedishrfu do you know the link to the algorithm for the creative machine program? It sounds very interesting.
There should be enough info in the article I posted for you to find more info on their work. Try to use google to search for it.
#13
ellipsis
158
24
Call me ellipsis. I enjoy subverting username systems. My preferred choice is an empty string if I can convince web forms to accept it. Or the unicode control characters, hah. (I wonder if they've locked down the registration system since we've migrated to Xenforo... hmm...)
Call me ellipsis. I enjoy subverting username systems. My preferred choice is an empty string if I can convince web forms to accept it. Or the unicode control characters, hah. (I wonder if they've locked down the registration system since we've migrated to Xenforo... hmm...)
@...
Have you checked your PMs? You have been asked by the Mentors to pick a new username so we can change it. Please do a forum search to be sure it hasn't been used already.
