What is ‘amount of information’ ? If I do not know if coin is heads or tails, then I have 0 bits of information about state of the coin, if I open my eyes and see it is heads, I have 1 bit. The information is in narrowing of the possibilities. That is conventional meaning. edit: though of course the information is not increased until next perception—perhaps that is what you meant? edit: still, there is a counter example—you can have axially magnetized coin, and electromagnet that can make the coin flip to heads up when its powered. You initially don’t know which way the coin is up, but if the action is to magnetize the electromagnet, you will have the coin be heads up. (Of course the overall entropy of world still did go up, but mostly in form of heat). One could say that it doesn’t increase knowledge of environment, but decreases the entropy in environment.
You are expressing a number of misconceptions here. I may address some in future posts, but in short:
By information I mean the Shannon information (see also links in OP). Your example is correct.
By the action of powering the electromagnet you are not increasing your information on the state of the world. You are increasing your information on the state of the coin, but through making it dependent on the state of the electromagnet which you already knew. This point is clearly worth a future post.
There is no “entropy in environment”. Entropy is subjective to the viewer.
I think it is mostly a matter of definitions. I am not familiar with your terminology. Also, if I have an atom that is in unknown alignment, and I align it using magnetic field, then take away the resulting heat, then the entropy (number of states) of that subsystem decreases, and this is used to attain extremely low temperatures. I am more familiar with the physical notion of entropy.
edit: Also, after powering electromagnet, I know that the direction of coin and direction of electromagnet relate in a particular way, which I did not know before. At the same time, I have physically restricted the number of states that the environment can be in—the coin can not now be other way around. It’s in this sense that entropy of environment (as seen on large scale) decreases . (and it is of course subjective, that the number of states that environment can be in, decreases. It does not decrease according to agent that already knows which way the coin is)
What is ‘amount of information’ ? If I do not know if coin is heads or tails, then I have 0 bits of information about state of the coin, if I open my eyes and see it is heads, I have 1 bit. The information is in narrowing of the possibilities. That is conventional meaning. edit: though of course the information is not increased until next perception—perhaps that is what you meant? edit: still, there is a counter example—you can have axially magnetized coin, and electromagnet that can make the coin flip to heads up when its powered. You initially don’t know which way the coin is up, but if the action is to magnetize the electromagnet, you will have the coin be heads up. (Of course the overall entropy of world still did go up, but mostly in form of heat). One could say that it doesn’t increase knowledge of environment, but decreases the entropy in environment.
You are expressing a number of misconceptions here. I may address some in future posts, but in short:
By information I mean the Shannon information (see also links in OP). Your example is correct.
By the action of powering the electromagnet you are not increasing your information on the state of the world. You are increasing your information on the state of the coin, but through making it dependent on the state of the electromagnet which you already knew. This point is clearly worth a future post.
There is no “entropy in environment”. Entropy is subjective to the viewer.
I think it is mostly a matter of definitions. I am not familiar with your terminology. Also, if I have an atom that is in unknown alignment, and I align it using magnetic field, then take away the resulting heat, then the entropy (number of states) of that subsystem decreases, and this is used to attain extremely low temperatures. I am more familiar with the physical notion of entropy.
edit: Also, after powering electromagnet, I know that the direction of coin and direction of electromagnet relate in a particular way, which I did not know before. At the same time, I have physically restricted the number of states that the environment can be in—the coin can not now be other way around. It’s in this sense that entropy of environment (as seen on large scale) decreases . (and it is of course subjective, that the number of states that environment can be in, decreases. It does not decrease according to agent that already knows which way the coin is)