It is also useful. In your digital systems class you were designing finite sate automata. It seems to me to be really useful to know what sort of things you can make such a thing do. When you start asking these questions you are doing automata theory.
Regular expressions are a nice way to represent a language accepted by a finite state machine. they are used for pattern matching and parsing text (this is useful whnever you want to search for anything
if you combine regular languages with more powerful systems you can do neat things like code generation, write compilers, and (try) to make systems that understand natural language.
The theory is useful when you want to know what your machine can do.
Two rocks collide in the cold vacuum of space and instantly freeze (no rebound, no transfer of kinetic energy, etc...)
I would say that the 'vacuum' wasn't really a vacuum. (currently) Unobservable objects carried away the energy of the two rocks when they met.
If I interpreted it this way, I would then of course have to start a new research project to find these unobservables and make them fit into my current theories. Unless I am omniscient I can't be sure that these unobservables don't exist, and unless I have a better theory (something that explains more than what was previously explained) I won't give up this law.
Where to draw the line between a good scientific reluctance to give up useful theories, and a nonscientific faith in past results is not apparent
Yes it is but it's at the individual level. If you claim that you have found a refutation for one of Newton's laws, and you outline the experiment, I can attempt to reproduce the experiment. If I reproduce it correctly and observe something different than what you claimed, I would discard your claim. If I reproduce it correctly and observe the same thing, I move toward revising current theory. The *act* of Science can be considered the largest distributed computation of all time.
The problem is there is no algorithm to determine what the right interpretation of an experiment is. You can clearly draw the line between the scientific and the unscientific at the individual level but whether or not your methodology for doing so is sound is an open question.
"The universe is governed by 'God,' who lives in a place called heaven (which we won't find until we die) and cannot be contacted by mortal man." -- this is an empty assertion (it can't be disproven.)
"For every action there is an equal and opposite reaction." -- this assertion can be disproven.
What exactly counts as disproving this statement?
If you say that it is experimentation, then I challenge you to show me an experiment with results that can be used to clearly refute this law. I can easily say that the results that refute this statement are due to experimental error; and if I don't want to do that then I can always say that the problem was in the definition of the terms equal and oposite.
This sort of thing is done quite often in natural science. Scientists are happy to postualate the existence of unobservables to hold on to their theories. This is also not necesarily a bad thing, sometimes the problem really is an experimental error, and terms usually aren't wll defined until they are tested by apparently contradicting evidence.
Where to draw the line between a good scientific reluctance to give up useful theories, and a nonscientific faith in past results is not apparent.
Slashdot Mirror
Automata theory is fun.
It is also useful. In your digital systems class you were designing finite sate automata. It seems to me to be really useful to know what sort of things you can make such a thing do. When you start asking these questions you are doing automata theory.
Regular expressions are a nice way to represent a language accepted by a finite state machine. they are used for pattern matching and parsing text (this is useful whnever you want to search for anything
if you combine regular languages with more powerful systems you can do neat things like code generation, write compilers, and (try) to make systems that understand natural language.
The theory is useful when you want to know what your machine can do.
Two rocks collide in the cold vacuum of space and instantly freeze (no rebound, no transfer of kinetic energy, etc...)
I would say that the 'vacuum' wasn't really a vacuum. (currently) Unobservable objects carried away the energy of the two rocks when they met.
If I interpreted it this way, I would then of course have to start a new research project to find these unobservables and make them fit into my current theories. Unless I am omniscient I can't be sure that these unobservables don't exist, and unless I have a better theory (something that explains more than what was previously explained) I won't give up this law.
Yes it is but it's at the individual level. If you claim that you have found a refutation for one of Newton's laws, and you outline the experiment, I can attempt to reproduce the experiment. If I reproduce it correctly and observe something different than what you claimed, I would discard your claim. If I reproduce it correctly and observe the same thing, I move toward revising current theory. The *act* of Science can be considered the largest distributed computation of all time.
The problem is there is no algorithm to determine what the right interpretation of an experiment is. You can clearly draw the line between the scientific and the unscientific at the individual level but whether or not your methodology for doing so is sound is an open question.
"The universe is governed by 'God,' who lives in a place called heaven (which we won't find until we die) and cannot be contacted by mortal man." -- this is an empty assertion (it can't be disproven.)
"For every action there is an equal and opposite reaction." -- this assertion can be disproven.
What exactly counts as disproving this statement?
If you say that it is experimentation, then I challenge you to show me an experiment with results that can be used to clearly refute this law. I can easily say that the results that refute this statement are due to experimental error; and if I don't want to do that then I can always say that the problem was in the definition of the terms equal and oposite.
This sort of thing is done quite often in natural science. Scientists are happy to postualate the existence of unobservables to hold on to their theories. This is also not necesarily a bad thing, sometimes the problem really is an experimental error, and terms usually aren't wll defined until they are tested by apparently contradicting evidence.
Where to draw the line between a good scientific reluctance to give up useful theories, and a nonscientific faith in past results is not apparent.