The Nature of Energy: A Philosophical Perspective

[quantumcarl]

After having my "What Is Energy Made Of?" thread running in the Quantum Physics section I learned.. after the some great replies.. that energy is more of an abstract concept that explains interactions, transfers and potentials or storage... many times the analogy of money was used.

With this in mind I have decided that the Philosophy section might be a better proving ground for the study of the concept of energy so...

Where does energy come from?

What is energy?

Is energy anything at all? (aprez David Letterman)

Is energy information?

All replys are appreciated. Thank you.

 

[loseyourname]

While I will say upfront that I do not think the philosophy section is the best place to host this discussion, I will let it go anyway. I must ask, though, that you clarify the questions, otherwise we're bound to lose focus very quickly or simply never have any to begin with.

When you ask what energy is, what exactly do you mean by that? It has a fairly precise definition within its usage as a physical quantity, so are you asking what the referrent of this quantity is? How do you propose one goes about answering that?

With respect to the title of your thread, what is the definition of "information" that you are working with? There are mathematical definitions for the term, of which I frankly have no expertise whatsoever, but what do you mean when you use the word?

 

[quantumcarl]

While I will say upfront that I do not think the philosophy section is the best place to host this discussion, I will let it go anyway. I must ask, though, that you clarify the questions, otherwise we're bound to lose focus very quickly or simply never have any to begin with.

When you ask what energy is, what exactly do you mean by that? It has a fairly precise definition within its usage as a physical quantity, so are you asking what the referrent of this quantity is? How do you propose one goes about answering that?

With respect to the title of your thread, what is the definition of "information" that you are working with? There are mathematical definitions for the term, of which I frankly have no expertise whatsoever, but what do you mean when you use the word?

Thanks for letting this thread go a bit longer.

Pehaps I should only ask one question... "is energy information?"

To define "information" I'll use this:

a message received and understood

Now, this is the philosophical part of it because we'll have to define "received" and "understood" to continue from here.

"received":

S: (n) Earth-received time, ERT (the coordinated universal time when an event is received on Earth)

I'm using this example because it does not simply pertain to a human receiving statistical information (math, literature, imagery etc...). It refers to receiving the influence of a force or event by an object not just an aware organism.

"understood":

"the understood conditions of troop withdrawal were clear"

I chose this example because it describes a condition that is reached or about to be reached (received) and this, without specific reference to an aware organism experiencing an understanding of the condition.

This is what I'd like to try to narrow down

The electromagnetic waves (information) generated by the sun are received by the Earth and the result (interpretation) is that a variety of forms of life are supported by this event/condition. Is it the information carried by the sun's em waves that sets other processes into play?

When a hammer hits a nail into a board the information (or energy) of the motion and mass of the hammer is transferred and translated by the nail's motion through the substance of a piece of wood.

The information that was transferred from the hammer and its motion is now in the form of a nail embedded in wood... splintered wood and a bond between two boards. Of couse the nail holds information (energy) of its own... and so does the wood.

All of these types of information (energy) interact to arrive at a nail in some wood which may result in the formation (or information) of a structure of some kind.

So what I'm asking is: "is it information that is contained in the mass and the motion of em waves, hammers, neruotransmitters, electrons etc... that is transferred from form to form... but we call it energy... not information... or is this too simplistic of a recipe for energy"?!

Dictonary definition:

The capacity for doing work. Forms of energy include thermal, mechanical, electrical, and chemical. Energy may be transformed from one form into another.

www.eere.energy.gov/financing/glossary.html[/URL]

 

[sd01g]

.

Pehaps I should only ask one question... "is energy information?"



[/url]

Energy is a mysterious force that causes things to move. Energy is not information but it is required to transfer information. Energy can exist without information, but information cannot exist or be transferred without energy.

 

[sneez]

Maybe we are having difficulty with energy =information due to our usage of language. To even describe energy, one needs information , to process, and store that information we realize we need energy.

So I am sorry to ask question here, but , is information existent if no one(cognitive being), nothing(biological being) is existent who could make a "meaning"/"understanding" of the information? [ i guess this will depend on definition of information we agree on]

i feel we should agree for this thread sake on definition of information we all will understand in this context.

if i may take a shot at it: information= any pattern that can be expected/used as input and that is used to stimuli or propel transformation.

 

[Hurkyl]

quantumcarl is probably referring to the classical observation that to "forget information", you have to produce heat.

Specifically, any isothermic interaction is reversible... whatever "information" was contained in the system is still there after an isothermic intereaction, and can, in principle, be recovered by reversing the interaction.

So, to actually "forget" information: that is, to undero an interaction that cannot be reversed to recover the original "information", you have to produce heat.



So, now that I've stated what we want to prove, our goal is to find definitions of all the words so that it's true. :Smile:

 

[-Job-]

I'm not sure why we would call it information, is it just a semantics issue or something more? Information is not independent of how it is interpreted. Depending on how you interpret a sequence of electrical signals the information you'll retrieve will vary. In fact, for each possible block of information there is a way to interpret that information such that your interpreter will produce every possible value.
I don't disagree with calling it information, because it is that, just that this information doesn't have an actual value, the value will vary depending on how we choose to read it.

 

[Hurkyl]

Depending on how you interpret a sequence of electrical signals the information you'll retrieve will vary.

Then do away with the interpretation -- the sequence of electrical signals itself would be information!

 

[-Job-]

Ok. I thought it was being proposed that this information encoded something some higher level message, for some reason.

 

[Rade]

Now, since a thing may be open to energy, but closed to information, the two may not have the same identity as relates to a thing. For example the electron, as a fundamental thing that exists it is open to energy but closed to information. Thus the answer to the OP would seem to be no, energy and information may represent distinct aspects of any thing that exists.

 

[disturbed1]

id like to think of information and matter as the same thing. one could derive that information holds a kinda potential energy because it can be reproduced. since the universe is full of matter information is everywhere. think of it traveling all around us. it appears unique when it stabilizes in matter and even more unique when it developes the ability to reproduce. information is made of a signal and a receiver in any medium. the signal could be any form of energy, wave, mater moving through space time. It is a controling force. it seems to almost always have a goal. It is mutated easily when reproduced for some reason. we measure information to get values of dimensions and interpret reality. it is quite unique in my eyes.

 

[Hurkyl]

For example the electron, as a fundamental thing that exists it is open to energy but closed to information.

What do you mean by "open" and "closed"? Can you propose a definition of energy and information that would agree with this statement?

one could derive that information holds a kinda potential energy because it can be reproduced.

You can't derive that it has potential energy unless you show that information is involved in a conservation of energy law.

Why do you say that information can be reproduced? If I xerox a sheet of paper, have I really reproduced information? Might I not have the same amount of information I had originally? Or even lost some information in the process?

information is made of a signal and a receiver in any medium. the signal could be any form of energy, wave, mater moving through space time.

This sounds more like you're talking about how information is transferred. But maybe that's the same thing!

 

[disturbed1]

You can't derive that it has potential energy unless you show that information is involved in a conservation of energy law.

...lol...I think it would be the reproduction of it that would increase its potential energy. this would have to be measured over time. some loss of its real value is almost always assured because of time.

Why do you say that information can be reproduced? If I xerox a sheet of paper, have I really reproduced information? Might I not have the same amount of information I had originally? Or even lost some information in the process?

the xerox had a beginning value which is hard to maintain. technology of the last century has focused on reproducing information while maintaining its integrity. a machine. but information travels without machines and technology, affecting everything around it. its potential, clearly unmeasured. obviously the xerox has doubled your real paper while maintaining most of its info value. now your new paper will influence its receiver to release energy to your mutual goal. this might be as simple as reading the paper or developing some new more complex strategy that would require a lot of energy release. the information itself being the limiting factor.



This sounds more like you're talking about how information is transferred. But maybe that's the same thing![/QUOTE]

ITs like the old saying, believe nothing you hear and half of what you see.

lets say that there is only so much information in the universe. a potential of what it can accomplish. we are just unlocking it in small intervals.

 

[jim mcnamara]

Hurkyl - what about entropy and your isothermic reaction example?

In plain English an isothermic process occurs at the same temperature.

The First law of Thermodynmics says that 'You can't create or destroy energy'. The Second Law says 'Energy in equals energy out plus entropy' (from a chemical reaction in this example).

So, assuming these Laws are correct your example defies Law #2. IFF I understand your point.

Here's why. Since we can't lose energy, it must mean that in any transformation (like the isothermic example you gave) the output side must have lost something. Other than energy. Whatever it lost went to entropy. Since we can't lose energy we must have lost information.

In other words, the starting arrangement of molecules in a system doesn't reform exactly the way it originally existed after an "isothermic" transformation. ... if we care to posit that such structure is information.

People use this argument all the time to say that the 2nd Law dictates "Time's Arrow" or, to argue that systems lose information (Shannon's H) under any transformation. Because of the "deduction" imposed by entropy. Since information is usually deemed to be the opposite of randomness, the argument goes that entropy increases randomness in a closed system.

YMMV.

 

[Rade]

For example the electron, as a fundamental thing that exists it is open to energy but closed to information.

What do you mean by "open" and "closed"? Can you propose a definition of energy and information that would agree with this statement?

A thing is "open" if an operation on the thing results in a transformation to a new thing, "closed" if no transformation results (e.g., the thing remains the same). Now, consider a single electron (e-). It can be acted on by energy in the form of positron (e+) and a transformation results. Thus the (e-) is "open" to energy. However, the information of the single electron as a fundamental existent is 1.0 (e.g., the electron is the electron) and thus no additional information can be added to it--it is "closed" to information. So, a general statement may be--energy transforms things, information transforms sets of things. The single electron being thus a "thing", and not a "set of things", is open to energy and closed to information. If my logic errors, please correct.

 

[disturbed1]

ok, If any transformation occurs, you add time and see that its information has obviously changed. any information being a 1 is the hardest to crack. use time to see its changes. information changes as it moves. it is moving all around us. because of time, it is always stored in a medium------->everything!

 

[quantumcarl]

What do you mean by "open" and "closed"? Can you propose a definition of energy and information that would agree with this statement?



You can't derive that it has potential energy unless you show that information is involved in a conservation of energy law.

Why do you say that information can be reproduced? If I xerox a sheet of paper, have I really reproduced information? Might I not have the same amount of information I had originally? Or even lost some information in the process?



This sounds more like you're talking about how information is transferred. But maybe that's the same thing!

Wow. I didnt think the thread would last over night...!... and here you guys are going at it like it was fun!

Anyway... thanks for the input. Hurkyl and one other person figures we'd better find a place for "information" in the conservation of energy law. Where could we find that... hmmmmm.

What I'm seeing is that the law itself is a form of information. All events are governed by that law... and by the information contained in the law.

If anyone could help me be wrong or right about that please feel free!

 

[disturbed1]

You can't derive that it has potential energy unless you show that information is involved in a conservation of energy law.

The Law of Conservation of Energy states that energy cannot be created or destroyed, but can change its form.

as energy changes form over time its information has changed also

 

[quantumcarl]

You can't derive that it has potential energy unless you show that information is involved in a conservation of energy law.

The Law of Conservation of Energy states that energy cannot be created or destroyed, but can change its form.

as energy changes form over time its information has changed also

The fact that information changes over time does not exclude it from being "information".

Also... I realize now, after a few minutes of thinking about it, the conservation law is about "energy" and I'm trying to equate "energy" with "information".

So, how would the "conservation of information" law look!? (discarding government cover ups etc... )

It would look like this... the conservation of information is a necessary law because if the amount of information contained in any and I mean any event would be catastrophic if it were unleashed in a single moment. Not only would it be catastrophic... it would be very confusing and there would be no structure (or "formation") that would result. There'd just be a mass of squiggley stuff that would be gone as soon as it happened.

PS. I'm sorry but I can't find who thought this thread was about "higher information" being beamed down from some celestial grand poobah. I have to categorically say that this thread is about energy and what the heck it is. That's all... eh!

 

[-Job-]

Sometimes i prefer to think of energy as the curvature of space in a given region. I don't know how valid this interpretation is, but sometimes it's helpful.

 

[Hurkyl]

So, how would the "conservation of information" law look!? (discarding government cover ups etc... )

Unitary evolution. Everything is a reversible process! (at least in principle)

 

[disturbed1]

information=potential energy

 

[GiZeHy]

energy=information?
let me show you my view on this topic.

in physics energy is defined as: stored work or stored power, the potential for activity.
information is basically knowledge which is purpose orientated. there are many definitions but i refer to that one which comes to everybodys mind intuitivly.
a simple example for the first definition is to bend a clip, you all know that one...
but science shows us that energy is more than that, it shows us that everything that exists IS energy, appearing in different states. matter, sound, anything you receive thru your senses or you can even imagine is energy which presents itself in different forms ( frequencies ).
based upon that, see the world you go thru, the reality you experience, as a bunch of energy which is formed to what it appears like.
because everything results from energy there is nothing in our physical universe ( except 'beyond' ) which is not energy.

when we define information we face the word knowledge. to understand information we must understand the word knowledge by which we come to a small problem:
one part of definition: knowledge causes the ability to expediently and consciously react to certain stimulus in a system. we can understand that. but it is hard to find a correct definition because the definition of knowledge changes knowledge itself because the definition is part of the knowledge. sounds weird but it is comprehensible for anybody who is into philosophic thinking. therefore we can only create a description of the effect of knowledge.

when you slam a nail with a hammer it is not the information which causes the nail to go down, it is energy affecting energy. information is the data which enhances your knowledge, for example in this case making you know what happens.

the big question is: what was first, energy or information?
or are they correlated. i believe it is not the same. when 'energy affects energy' ( cause and effect ) can happen without information something must have started this chain of events. this something, whether made up of energy itself or not, must have contained knowledge. in this universe where every cause and effect seems so perfectly 'designed' there is no space for chance.

this is a very difficult topic. because humankind did not find the true essence and functionality of energy and information ( knowledge) yet, it is impossible to answer this question in a definite way.

read arthur shopenhauer concerning objectivation of will. maybe youll find more in there...

 

[quantumcarl]

Unitary evolution. Everything is a reversible process! (at least in principle)

You're touching on something I asked in another thread to do with:

"did life evolve an (electromagnetic) awareness at the same time as the universe or is life immitating an (electromagnetic) awareness of the universe?

A unitary evolution would suggest that all events evolve along one "simultaneous" sequence. A kind of synchronized and synergistic mechanism that is the result of the law of conservation. Without this mechanism events would not occur... or, at the most, would not happen for long because they'd overload then flatten out. No duration. No moxy!

This would include everything like strings and parallel universes and anti-matter etc... it would all be evolving simultaneously with every other event in a Unitarily Evolving universe.

And it would be and it is a lot of information.

Thank you GiZeHy for your contribution. That's all stuff I agree with actually.

One thing you have to be clear about is that "information" is really just another physical occurance... as in an "event". It is as motivating and mobilizing as gasoline. It is stored as electromagnetic events at a molecular scale yet one of these events holds the potential to produce a sun or destroy a planet.

Information. I equate it with the term "energy" because energy is a term of measurement, nothing more.

Information is the resulting event of a measurement and so, seems more likely a candidate for the position that energy holds as the great motivator!

 

[quantumcarl]

Are we measuring the information of an event?

Or are we interpreting the event as information?

 

[GiZeHy]

hi again
let me bring in some other aspect. maybe you already thought about it.

It is stored as electromagnetic events at a molecular scale yet one of these events holds the potential to produce a sun or destroy a planet.

now, where do these stored electromagnetic events come from? basically we talk about natural forces. objects have a certain behavior and only because they are perfectly 'created' it is possible to calculate coming up events. concerning the big bang theory they came into being at one point of time. because chance has no place in our universe, otherwise anything would collapse immediatly, these forces had to come from any kind of knowledge, whether at the big bang or not. in schopenhauers works he he shows us the idea of reducing all appearing forces to will.
beside that i want to add something. i believe that time and space have no beginning and end. maybe we would define it like that by our point of interpretation. when i think about mind itself our thoughts and the reality we see infront of our 'minds eye' equals the reality that we experience normally but it is not bound on time/space. we can switch wherever and however we want to. i want to come to a certain point. is information reduced to 'measuring' and accordingly 'interpretation'? when you want to create something you first build it up in your mind. maybe you need basic data to actually start this process but you are able to create new information by your own will. i don't mean linking existing information to build new information but creating absolut new.
now, is information 'only' a physical occurance or does it maybe stand above physical occurances?

It is as motivating and mobilizing as gasoline.

what i mean is: what causes our reality to behave as it is behaving? energy is the 'medium' in which manifestations occur. what is causing energy to behave in certain ways? information...?

let me throw in one last thought in this post. the last mentioned information ( cause ) which is directing energy thru frequencies to build up a universe like ours, is it mind?

 

[disturbed1]

quote
by gizehy
when you want to create something you first build it up in your mind. maybe you need basic data to actually start this process but you are able to create new information by your own will. i don't mean linking existing information to build new information but creating absolut new.

I don't see anyway to create or build real information. Its already here.
we interpret things around us to create ideas and such, which is information, but a different form. one must say there are different kinds of information. that which governs reality and that which makes us function everyday. one could imagine irrelavant information, which is very common. but in truth, there are rules that govern the universe and this would be real information and only so much real information here. how much potential does it have? we could view information itself as kinetic and potential. where an idea has potential in future, and kinetic being the acting out of the informations gain. it seems to me that all information has a natural ability to reproduce. could this be viewed as a real source of energy, perhaps measureable? I don't know. very interesting.

quote
by gizehy

in physics energy is defined as: stored work or stored power, the potential for activity.

information is directly relevant here. not only does information travel in energy but also in matter. It can be stored in both places, and once unlocked, you could call it stored power, perhaps be reproduced to gain potential.


quote
by quantumcarl

One thing you have to be clear about is that "information" is really just another physical occurance... ... as in an "event"

information is more than that. I like to view it as a measurement of everything in reality(present), and a controling force of the energy around it. Its fairly weak on the grand scale of things.

quote
by gizehy

when you slam a nail with a hammer it is not the information which causes the nail to go down, it is energy affecting energy. information is the data which enhances your knowledge, for example in this case making you know what happens

information is more here than just the present measure of reality. let's first define a hammer and nail. they are tools, developed from organized information, applied to matter. matter and information cannot be seperated. now, all the information from the process has control of the future energy of the process. meaning, you project the nail can hold weight for a given amount of time.

 

[quantumcarl]

quote
by gizehy
when you want to create something you first build it up in your mind. maybe you need basic data to actually start this process but you are able to create new information by your own will. i don't mean linking existing information to build new information but creating absolut new.

I don't see anyway to create or build real information. Its already here.
we interpret things around us to create ideas and such, which is information, but a different form. one must say there are different kinds of information. that which governs reality and that which makes us function everyday. one could imagine irrelavant information, which is very common. but in truth, there are rules that govern the universe and this would be real information and only so much real information here. how much potential does it have? we could view information itself as kinetic and potential. where an idea has potential in future, and kinetic being the acting out of the informations gain. it seems to me that all information has a natural ability to reproduce. could this be viewed as a real source of energy, perhaps measureable? I don't know. very interesting.

quote
by gizehy

in physics energy is defined as: stored work or stored power, the potential for activity.

information is directly relevant here. not only does information travel in energy but also in matter. It can be stored in both places, and once unlocked, you could call it stored power, perhaps be reproduced to gain potential. quote
by quantumcarl

One thing you have to be clear about is that "information" is really just another physical occurance... ... as in an "event"

information is more than that. I like to view it as a measurement of everything in reality(present), and a controling force of the energy around it. Its fairly weak on the grand scale of things.

quote
by gizehy

when you slam a nail with a hammer it is not the information which causes the nail to go down, it is energy affecting energy. information is the data which enhances your knowledge, for example in this case making you know what happens

information is more here than just the present measure of reality. let's first define a hammer and nail. they are tools, developed from organized information, applied to matter. matter and information cannot be seperated. now, all the information from the process has control of the future energy of the process. meaning, you project the nail can hold weight for a given amount of time.

Thanks to both GiZeHy and Disturbed 1.

First of all, Gizehy, the mind is a brain and the electromagnetic waves it produces. It is an event.

If the brain is interpreting an event as "information" then information is part of a closed system... belonging only to the realm of a brain. An analogy would be like when a leaf interprets light as a catalys in the production of sugar. That is its bias in how it experiences light.

Beyond this biased, structured view humans have of events (ie: information in the form of measurments) everything is simply an event... even the "mind" or brain is an event.

Matter is an event. Light is an event. EM Radiation is an event. Space is an event. Individual events and combinations of events are events.

This sort of basic way of looking at what I've proposed has led me to understand... once again... that our languages and our expressions are simple interpretations of events.

What we say about an event does not describe an event... it only describes how we perceive an event.

So, there you go. I shot myself down in my own thread.

 

[disturbed1]

quote by quantumcarl

Beyond this biased, structured view humans have of events (ie: information in the form of measurments) everything is simply an event... even the "mind" or brain is an event

because of the smallest unit of time is moving, each frame of reality, chained together, is a real event. our perception of this is limited to our understanding of the real information extracted from each frame of reality.

lets focus on the subject of the thread... is information=energy?

lets say that humans are a form of information. we are made up of genes and dna that are complex codes of information that know how to reproduce. we have energy. what is its source? would you say that our sun can only produce so much energy? what if we escape it to populate another solar system. has the energy that was given off by the sun gained some new potential, or is it simply regular physics explaining interactions of matter and energy. for one, the amount of energy released from the sun would be higher than the amount projected over its life span. but did its reproduction of life add energy to the universe? or is it simply matter and energy reformed. what about its hidden value? can it be found in a conservation of energy law? I don't know...lol...help!

 

[Rade]

lets focus on the subject of the thread... is information=energy?

Suppose you have five fundamental units, A to E and each unit has identical energy content. Now, suppose a system like this {A,A,A,A,A}. How much "information" does this system have ? Next, suppose a system {A,B,C,A,D}. Clearly the second system has more information than the first, yet identical amount of energy. Thus, information content of a system does not = energy content of a system.

 

[disturbed1]

quote by rade

Suppose you have five fundamental units, A to E and each unit has identical energy content. Now, suppose a system like this {A,A,A,A,A}. How much "information" does this system have ? Next, suppose a system {A,B,C,A,D}. Clearly the second system has more information than the first, yet identical amount of energy. Thus, information content of a system does not = energy content of a system.


not really rade. where as its pattern of energy can be potential in itself.

 

[Hurkyl]

Now, suppose a system like this {A,A,A,A,A}. How much "information" does this system have ? Next, suppose a system {A,B,C,A,D}. Clearly the second system has more information than the first, yet identical amount of energy.

Why is that clear? This strikes me as the sort of reasoning that leads people to believe that having 1, 2, 3, 4, 5, 6 as the lotto numbers is somehow less likely to happen than 3, 14, 17, 29, 36, 45.

 

[quantumcarl]

Suppose you have five fundamental units, A to E and each unit has identical energy content. Now, suppose a system like this {A,A,A,A,A}. How much "information" does this system have ? Next, suppose a system {A,B,C,A,D}. Clearly the second system has more information than the first, yet identical amount of energy. Thus, information content of a system does not = energy content of a system.

If you look at the information content of "A" and the information content of "E" you will see that there is more energy contained in the "E" than the "A". Why? Because the "A" has fewer lines than the "E". Also, the "E" is pronounced useing more energy than the "A" ("A" is pronounced in a slack jawed manner where "E" is pronounced using more muscle and energy).

The number of lines in the "E" take more energy to produce (in writing and in binary code).

The number of lines in the "A" take less energy to produce. This should be a clue that there is more energy encapsulated in the production of an "E" than that of an "A" and therefore the actual letter "E" represents a higher measurment of energy than the letter "A"

When we get to the Compound Curves of letters like "S" and "C" I have a feeling the energy content and the energy expended in producing these letters is considerably more that the rectilinear letters.

 

[quantumcarl]

Why is that clear? This strikes me as the sort of reasoning that leads people to believe that having 1, 2, 3, 4, 5, 6 as the lotto numbers is somehow less likely to happen than 3, 14, 17, 29, 36, 45.

Everytime the numbers are in sequence I go nuts and become convinced the whole thing is rigged!.

 

[Rade]

Why is that clear? This strikes me as the sort of reasoning that leads people to believe that having 1, 2, 3, 4, 5, 6 as the lotto numbers is somehow less likely to happen than 3, 14, 17, 29, 36, 45.

I am not talking about individual events, but "sets" of events. The "set" {A,A,A,A,A} has less "variety" (thus information) than the "set" {A,B,C,A,D}. The first set has variety of one element, the second set has variety of four elements. The two sets thus have different information content, yet the same energy, because it was given in my example that all possible elements (A to E) of any set of five elements have identical "energy. Thus the first set has total energy of five elements, and likewise the second set has total energy of five elements.

If you look at the information content of "A" and the information content of "E" you will see that there is more energy contained in the "E" than the "A". Why? Because the "A" has fewer lines than the "E"...

OK, but if you read the premise of my example, you see that A - E have identical energy--this was a given. Think of billiard balls, each can be assumed to have identical energy. So, if I put together into one set five billiard balls such that they number {1,1,1,1,1}, this set has less variety (thus information) than the set {1, 4, 6, 1, 9}. In this way, the two sets have identical energy content yet they convey different amounts of information. Thus the reason for my comment that energy may not always = information, for "sets" of things.