19 replies to this topic

[Yoruichi-san]

First off, I disagree with your definition of definition . I would say a definition is a specification of a set of characteristics that are necessary and/or sufficient to categorize something as that word/phrase. Similarly to in math where a definition could be like "an integer is..."

I do not think removal of information is "lying to ourselves", i.e. when I talk about "an integer" instead of specifying which exact integer it is, I am not lying but rather making my analysis apply to a larger field. Specifying every piece of information and making conclusions that are only true for those exact specifications is not very useful. It's not ignorance, but rather generality which makes the observations (and hence learning and gaining experience in life) actually useful.

And on "sameness", I don't think anyone actually uses sameness in the way you seem to be defining it. The majority of time people don't think or talk about things as "exactly the same PERIOD", but "has the same ______ (color, size, cost, etc)". Its usually to be able to compare things, i.e. there are two boxes of cereal that cost the same but A tastes better than B, so A is obviously the better choice to buy.

I don't think we construct in our minds this idea of things being "the same" the way you are defining it. The "the same" in our minds is a recognition of like characteristics that are correlated with information in our experience that is useful for decision making. I.e. other than having the philosophical debate you specify in the OP, in real life if a captain of a ship thinks of a ship being "the same" he is not thinking it is exactly the same in every way, but instead like thinking whether it will operate in the same way or, like, if he takes shore leave, whether if he returns to the same (as in same location) ship.

[Yoruichi-san]

Secondly, generalizing often leads to the gaining of information rather than the loss of it. Generalizing allows for the specification of what information is necessary and sufficient to draw a correlation. Hence by recognizing that, we gain information about the correlation itself. I.e. when Galileo dropped a wooden ball and a metal ball (or something similar, I don't remember exactly) off a tower and they landed the same time, he gained information about the general principle. By recognizing what was necessary and sufficient for this phenomena of 'sameness' (traveling the same path), he could gain information to come up with a theory to explain the phenomena.

Edited by Yoruichi-san, 21 September 2012 - 07:48 PM.

[Yoruichi-san]

Thirdly, I definitely don't define "sameness" as you. I would say sameness is the sharing of characteristics itself, not the state of sharing all exactly identical characteristics. Hence I would say sameness is a matter of degree rather than black/white or 1/0 (i.e. my DNA has sameness with my mom's to a degree of ~50%) and is inherently context dependent, since it requires a comparison. I think this, or something similar, is what people usually consider when they're applying the abstract principles you mention.

They are not deluding themselves into thinking that, say, one horse is [your definition of sameness] as another, or ignoring the differences or the effects of those differences (well, okay, some people do...but that's called denial ), rather they take in that information (i.e. one horse is brown, the other black, etc) and store that information (not taking into account memory loss...that's a whole different topic) , but they're recognizing that one horse shares the same characteristics that define it as being a horse. Reporting it to someone else as simply "a horse" rather than "a brown horse of exactly X mass...dimensions...history..." etc is not removing information. The person doesn't lose that information, rather he is not passing on that information to a different source. Then we get into the "glass half full or half empty" argument. By generalizing the object as "a horse", it allows an efficient passing on of certain pieces of information while not specifying others. Would that person have passed on that information anyways without the concept of sameness? I.e. if you had to specify exactly what characteristics every object you want to talk about in a conversation, would you talk about that object? If the idea of "sameness" allows information to be passed on that otherwise that would not have been, then I would say that is not a loss. Also, the passing of information is not instantaneous, hence by using the idea of sameness you are improving the efficiency of information passage, i.e. trying to maximize the function of (information passed) per unit time. This allows you to pass more information overall (i.e. if you integrate the function of (information passed) over time, you get a higher value), hence I would say it is increasing information, not decreasing it.

[mmiguel]

First off, I disagree with your definition of definition . I would say a definition is a specification of a set of characteristics that are necessary and/or sufficient to categorize something as that word/phrase. Similarly to in math where a definition could be like "an integer is..."

I do not think removal of information is "lying to ourselves", i.e. when I talk about "an integer" instead of specifying which exact integer it is, I am not lying but rather making my analysis apply to a larger field. Specifying every piece of information and making conclusions that are only true for those exact specifications is not very useful. It's not ignorance, but rather generality which makes the observations (and hence learning and gaining experience in life) actually useful.

And on "sameness", I don't think anyone actually uses sameness in the way you seem to be defining it. The majority of time people don't think or talk about things as "exactly the same PERIOD", but "has the same ______ (color, size, cost, etc)". Its usually to be able to compare things, i.e. there are two boxes of cereal that cost the same but A tastes better than B, so A is obviously the better choice to buy.

I don't think we construct in our minds this idea of things being "the same" the way you are defining it. The "the same" in our minds is a recognition of like characteristics that are correlated with information in our experience that is useful for decision making. I.e. other than having the philosophical debate you specify in the OP, in real life if a captain of a ship thinks of a ship being "the same" he is not thinking it is exactly the same in every way, but instead like thinking whether it will operate in the same way or, like, if he takes shore leave, whether if he returns to the same (as in same location) ship.

"I would say a definition is a specification of a set of characteristics that are necessary and/or sufficient to categorize something as that word/phrase."
That is the same thing I had in mind, except I wrote it more carelessly, what do you disagree about?

"I do not think removal of information is "lying to ourselves",
I suppose I'm trying to make it seem like there is a contradiction, although I don't really think there is one.

"Specifying every piece of information and making conclusions that are only true for those exact specifications is not very useful. "
I think I said that somewhere. Well I said it's not possible, either way I'm obviously starting from an idealistic case that doesn't make too much sense for practical purposes (ideal case is every characteristic matters), and departing from that back into the everyday world (practical case is only characteristics important to us matter). I'm describing the spectrum of specificity, not saying we should be more specific in everything we do, and less abstract.

"It's not ignorance, but rather generality which makes the observations (and hence learning and gaining experience in life) actually useful."
My point was the realization that the act of generalization itself is equivalent to the act of removing information. Ignorance is lack of information. I thought it was ironic that something good (generalization) arises out of something usually considered bad (removing information).

"And on "sameness", I don't think anyone actually uses sameness in the way you seem to be defining it. The majority of time people don't think or talk about things as "exactly the same PERIOD", but "has the same ______ (color, size, cost, etc)"."
Of course not, there are relative degrees of sameness. A pastrami sandwich might be considered the same as a turkey sandwich since they are both sandwiches (here meat is not an essential characteristic. On a different level of sameness, a pastrami sandwich might be considered the same as a watermelon, since they are both food (here edibility is the only essential characteristic). As the ones creating the thoughts, we are able to choose what degree of sameness we are interested in. What I did, was take this to the most extreme level, where every detail matters. Of course no one does this in their day-to-day life. If anyone did, why would I even post this as something I thought others might find interesting?


"I don't think we construct in our minds this idea of things being "the same" the way you are defining it. The "the same" in our minds is a recognition of like characteristics that are correlated with information in our experience that is useful for decision making."
No, I don't think our brains start with all information and hack it away to get to where we are. Just some information. I think all that information is out there, but we filter out massive quantities of information in order to effectively act on what we find important. This filtering could happen outside of our brain, via our senses, but I think it also happens within our brains.

Consider peripheral vision for example. If you are intensely focusing on something you are watching, you might not even notice the color of something that was lying in your peripheral vision. You don't choose to not notice, it happens, because you only have finite resources for thinking. Behind the scenes, some part of your brain must toss out that sensory information it's receiving from the corners of your eye.

You are talking about recognition: what is recognition any way, let's think. I think it can be well represented with the vocabulary of equivalence classes. You can define an equivalence relation, and say that if two things satisfy this equivalence relation, they belong to the same equivalence class. What we have been discussing relates to the construction of equivalence relations. Assume all objects may be represented as a set of characteristics and values for those characteristics. Let's say an equivalence relation may be defined by selecting certain characteristics to include in an equality comparison. We are free to define whatever equivalence relations we want.
My extreme case is: include everything. In the spectrum of specificity, this is the most specific possible equivalence relation, and the most objective.
The other extreme is: include nothing. In the spectrum of specificity, this is the most abstract possible equivalence relation. Basically, the word "thing" represents the one equivalence class derived from this relation. Anything is a thing. Ideas are things. Cars are things. People are things. Everything is a thing (we even include it in the words everything/anything/nothing). In the most specific case, there is no such thing as sameness. In the most abstract case, everything is the same. Which case do you think is more in tune with reality? I would say the specific case. The more specific things, are the more information is required to represent them. Pure abstraction essentially requires no information at all --- yeah, we'll include it in the class, don't even need to look at it's properties. The fact that the properties exist, the fact that we can even zoom in on them, suggests that all that specific information is out there and real. My conclusion is that abstraction is a product of our finite processing capabilities. Not to say it's a bad thing, but that is what it is.



"Secondly, generalizing often leads to the gaining of information rather than the loss of it. Generalizing allows for the specification of what information is necessary and sufficient to draw a correlation"
I argue that it never does, although it allows us to focus on components of information that are more important to us.
You could draw 100,000 useless correlations if you generalized as little as possible... but you wouldn't care.
It is filtering out useless information (removing information), that allows us to do great things and draw correlations we care about.
How useful information is to me, or to you though only matters within our own heads.


"Hence by recognizing that, we gain information about the correlation itself. I.e. when Galileo dropped a wooden ball and a metal ball (or something similar, I don't remember exactly) off a tower and they landed the same time, he gained information about the general principle. By recognizing what was necessary and sufficient for this phenomena of 'sameness' (traveling the same path), he could gain information to come up with a theory to explain the phenomena. "
He made a conclusion that is important to mankind.
If he spent 200 days examining the intricacies in the shape of the wooden ball as compared to the metal ball, he would have gotten a lot more information than the rule above ---- it's just worthless information to him and everyone else.

"Hence I would say sameness is a matter of degree rather than black/white or 1/0 (i.e. my DNA has sameness with my mom's to a degree of ~50%) and is inherently context dependent, since it requires a comparison"

Your fuzzy depiction of sameness can by represented by dividing whatever objects you are comparing into subcomponents and discretely evaluating sameness.
How could you even get a number such as 50% ---- (i know you did this by assuming you are half your mom and half your dad), but maybe a more rigorous approach is to compare your nucleotides, position by position to your mother's. For each nucleotide, you make a hard comparison (use the equivalence relation to include only chemical structure, removing other non-important information). Say for example, you count X that match, out of Y total. You could then say that your DNA is roughly X/Y of your moms.... much more than 50%.... somewhere I heard human vs. chimp is like 99% or something. Anyway, I think it is possible that every fuzzy comparison can be represented as the aggregation of other hard comparisons....



"They are not deluding themselves into thinking that, say, one horse is [your definition of sameness] as another, or ignoring the differences or the effects of those differences (well, okay, some people do...but that's called denial ), rather they take in that information (i.e. one horse is brown, the other black, etc) and store that information (not taking into account memory loss...that's a whole different topic) , but they're recognizing that one horse shares the same characteristics that define it as being a horse."
Agree, I'm not saying their sensory information disappears. I'm saying they generate the concept of "horse" (or more likely have had it previously generated at some point in their life), and use that concept instead of their actual sensory information for any practical purpose involving the horse thereafter. This abstract, generated concept of a horse, requires less information than, the real specific horse. A real, specific horse has all the properties contained in the concept definition, and way way more. It has color, hair patterns, and tons of other stuff too, which would be impractical to store. By retaining and using this abstract concept, which has less information, the person is building a model of they're observed experiences which has less information than the true source of the experience itself. This is no surprise, but it is something that most people probably don't think about. I think that understanding this spectrum of specificity is the key to understanding how things like recognition work.


"By generalizing the object as "a horse", it allows an efficient passing on of certain pieces of information while not specifying others. Would that person have passed on that information anyways without the concept of sameness? I.e. if you had to specify exactly what characteristics every object you want to talk about in a conversation, would you talk about that object? If the idea of "sameness" allows information to be passed on that otherwise that would not have been, then I would say that is not a loss. Also, the passing of information is not instantaneous, hence by using the idea of sameness you are improving the efficiency of information passage, i.e. trying to maximize the function of (information passed) per unit time. This allows you to pass more information overall (i.e. if you integrate the function of (information passed) over time, you get a higher value), hence I would say it is increasing information, not decreasing it. "

Information = Useful Information + Useless Information
You are saying by getting rid of useless, information, we increase information. What you really mean is we increase the potential to transfer useful information. This is absolutely true. But if you remove the boundary between useful and useless, and just consider information in general... outside of any subjective perspective... it is the loss of information.

[Yoruichi-san]

1) What about theories? How do you classify them in your depiction of information? I.e. no many how many times you drop a ball it will not give you the theory of gravity as information unless you generalize and make the correlation and come up with the theory. Then the theory allows you to draw further conclusions etc, giving you information about the world. Rather than dropping 200 balls and gaining useless information, if I drop 2 and come up with the theory of gravity I would say that is overall more information.

2) Stop not taking account my symbols, please . I said ~50% (as in approximately), it's just an example of how sameness comes in degrees. My sameness is not any less valid than yours and I think is more common.

3) We disagree on the way we think people think, I think . The difference in our definition of definition comes in that you think the characteristics are an average of the traits of, say, a horse, where I think there are the specification of necessary and sufficient traits. Hence by your definition of definition, information is lost, since information is always lost in averaging. In my definition, information is not lost, it is recognized that there are things (color, mass, dimensions, etc) that are not specified in the definition and that those things could be anything. The information is not lost, rather, it is left open-ended.

I.e. if we pretend 'horse' is a described by the variables W,X,Y,Z, where W and X are the necessary and sufficient biological classification, and Y and Z are the things that can differ and still allow the object to be classified as a horse, and let's pretend the mean of Y is 5 and Z is 6, then you would say people mentally use horse = (W,X,5,6), and I would say people mentally use horse=(W,X,y,z), where they recognize that y and z are variable and differ from each horse. No information is lost, it is only not specified when thinking of the general concept of horse. Sure, a lot of times if you say 'horse' people will visualize a horse and they'll visualize the average, but they recognize conceptually that that is only an imaginary average and understand that those traits are actually variable in real horses. The general concept of 'horse' and the mental visualization of 'horse' are not the same thing.

4) I still do not see how information is necessarily lost, especially using my above definition of definition. I don't think something can be lost that would never have been given in the first place. If I see a horse and it is brown and I tell my friend and do not tell him it is brown, is that loss of information? I still know the horse is brown, and the horse does not cease being brown, the only thing is that the information was not propagated. However, if I was not allowed to generalize, and was required to describe the horse as "a four-legged mammal with brown fur, with mass ______ , length from head to tail _____, height from ground ______, etc..." I very well might not choose to convey the information that I saw the animal, in which case, net information was increased by allowing for generalizations.

Also, maybe, instead of saying "I saw a horse, it was brown", I say "I saw a horse, I also saw a donkey", which takes about the same time and effort. I pass on more information, since the 'donkey' contains more information as a generalization than specifying the color of a horse. Some information might be excluded, i.e. the color of the horse, but there is a net increase in the information gained by my friend in me using the second than the first.

5) How is information being lost outside a subjective perspective? The horse does not cease having its properties if I do not specify them, it does not cease to exist. The only difference in information is what is inside the heads of people, how is that not subjective?

Edited by Yoruichi-san, 22 September 2012 - 06:51 AM.

[mmiguel]

1) What about theories? How do you classify them in your depiction of information? I.e. no many how many times you drop a ball it will not give you the theory of gravity as information unless you generalize and make the correlation and come up with the theory. Then the theory allows you to draw further conclusions etc, giving you information about the world. Rather than dropping 200 balls and gaining useless information, if I drop 2 and come up with the theory of gravity I would say that is overall more information.

2) Stop not taking account my symbols, please . I said ~50% (as in approximately), it's just an example of how sameness comes in degrees. My sameness is not any less valid than yours and I think is more common.

3) We disagree on the way we think people think, I think . The difference in our definition of definition comes in that you think the characteristics are an average of the traits of, say, a horse, where I think there are the specification of necessary and sufficient traits. Hence by your definition of definition, information is lost, since information is always lost in averaging. In my definition, information is not lost, it is recognized that there are things (color, mass, dimensions, etc) that are not specified in the definition and that those things could be anything. The information is not lost, rather, it is left open-ended.

I.e. if we pretend 'horse' is a described by the variables W,X,Y,Z, where W and X are the necessary and sufficient biological classification, and Y and Z are the things that can differ and still allow the object to be classified as a horse, and let's pretend the mean of Y is 5 and Z is 6, then you would say people mentally use horse = (W,X,5,6), and I would say people mentally use horse=(W,X,y,z), where they recognize that y and z are variable and differ from each horse. No information is lost, it is only not specified when thinking of the general concept of horse. Sure, a lot of times if you say 'horse' people will visualize a horse and they'll visualize the average, but they recognize conceptually that that is only an imaginary average and understand that those traits are actually variable in real horses. The general concept of 'horse' and the mental visualization of 'horse' are not the same thing.

4) I still do not see how information is necessarily lost, especially using my above definition of definition. I don't think something can be lost that would never have been given in the first place. If I see a horse and it is brown and I tell my friend and do not tell him it is brown, is that loss of information? I still know the horse is brown, and the horse does not cease being brown, the only thing is that the information was not propagated. However, if I was not allowed to generalize, and was required to describe the horse as "a four-legged mammal with brown fur, with mass ______ , length from head to tail _____, height from ground ______, etc..." I very well might not choose to convey the information that I saw the animal, in which case, net information was increased by allowing for generalizations.

Also, maybe, instead of saying "I saw a horse, it was brown", I say "I saw a horse, I also saw a donkey", which takes about the same time and effort. I pass on more information, since the 'donkey' contains more information as a generalization than specifying the color of a horse. Some information might be excluded, i.e. the color of the horse, but there is a net increase in the information gained by my friend in me using the second than the first.

5) How is information being lost outside a subjective perspective? The horse does not cease having its properties if I do not specify them, it does not cease to exist. The only difference in information is what is inside the heads of people, how is that not subjective?

The word theory refers to different things in different contexts. There are things like mathematical theories which logically deduce from axioms, and other, observations theories which are logical inferences to observations, for which we are more confident in than a hypothesis.
I basically provided two definitions just now, which could be parsed out as a set of constraints on essential characteristics
Our definition of definition (meta-definition if you will): is that a definition is a list of constraints on characteristics.
I stated it slightly different before, but you formulate a constraint as a true-false statement, you can treat the truth of such a statement as a characteristic itself, and use the true or false value of each such constraint within an equivalence relation as I stated before. Our (meta-) definitions are consistent, and the concept of theory can fit into both of our frameworks.



"Rather than dropping 200 balls and gaining useless information, if I drop 2 and come up with the theory of gravity I would say that is overall more information."
You misunderstand me, and I am not arguing what you are implying I am arguing. You are saying a general result that can be applied to many things in the world, contains in it more information than a specific result that only really applies to one thing. What I am saying has nothing to do with comparing multiple observations to few. Let's say he only drops 2. I'm saying there are many characteristics he *could* choose to remember about both of these observations, and tons of information in just those 2. He could choose to observe, analyze, and remember minute variations in the trajectory (assume he has perfect vision and memory---which obviously isn't realistic). He could choose to remember a lot, but he only focuses on and remembers the properties of the observations associated with constant acceleration of the objects. He filters out all that other garbage, which is valid information, it's just not important information. Having a wider sphere of applicability does not require more information, if that were the case, every law of physics, which are believed to have practically the widest spheres of applicability compare to anything else, should be require volumes of words to represent (more information means more intricacies, i.e. more bits are needed to represent more aspects). The fact that most can be elegantly and simply stated hint that they have less information, but more usefulness per bit than do other things.

2) Ok, sorry, wasn't trying to put your def down, was just trying to show that fuzziness can be simulated with what I was saying.

3) "Hence by your definition of definition, information is lost, since information is always lost in averaging."
More like filtering vs. averaging. Averaging doesn't make sense in many cases for aggregating properties. Filtering is essentially removing any specification from those properties.
"The information is not lost, rather, it is left open-ended."
As far as the information content required to represent a concept, leaving something open-ended is exactly the same as not allocating any bits of information to represent a specification. This is what I have been saying all along. Don't even mention color when talking about horses, and don't store a specification for color along with your concept of horse. This makes your concept of horse contain less information, and rightly so, since color typically has nothing to do with using a horse for transportation or companionship whatever else people find them useful for. The concept contains less information, because we filtered out things like color. Adding specifications on characteristics require storing additional information as part of the concept.
"I.e. if we pretend 'horse' is a described by the variables W,X,Y,Z, where W and X are the necessary and sufficient biological classification, and Y and Z are the things that can differ and still allow the object to be classified as a horse, and let's pretend the mean of Y is 5 and Z is 6, then you would say people mentally use horse = (W,X,5,6), and I would say people mentally use horse=(W,X,y,z), where they recognize that y and z are variable and differ from each horse."
Actually, I would say that people would mentally use (W,X). They remove all information associated with Y,Z, from the generic definition of horse, unless it becomes pertinent at some point to consider that for a specific horse. This may vary from person to person. Say for example Y = color. As part of some people's definition, they might include a specification on the range of color (e.g. should be "natural" looking colors). If they saw a really strange, bright green horse, they might think it is something other than a horse. Anyway, they would have (W is True for this object, X is true for this object, and Y is in range of natural colors [defined based on what i have previously observed]). For practical purposes, it would make no difference if they add the Y constraint or not, although I suspect most people would not.... they would rather continue to classify it as a horse, but note that maybe it was spray-painted or something (poor horse).
With the (W,X) definition above, this a necessity for making sense out of the world. You chose 4 possible attributes, but is there really a limit to the amount of attributes you can apply to an object? We would run out of letters long before we ran out of possible attributes if we tried to add as many as possible to some observation we might have right now. One of my points is that this filtering prevents us from having that problem. This filtering is the same as abstraction, the same as generalization, and is the result of taking massive amounts of information and removing pieces of it, leaving only what is important to us as humans. It is a simple form of lossy information compression. This is not all done within our brains, but a neat thing is that we do have influence and power over the final result. We can choose to define a new concept by selecting new attributes, and as we see and observe new things, we build a library of these concepts (ontology if you will).

4) " I still do not see how information is necessarily lost, especially using my above definition of definition. I don't think something can be lost that would never have been given in the first place. If I see a horse and it is brown and I tell my friend and do not tell him it is brown, is that loss of information? I still know the horse is brown, and the horse does not cease being brown, the only thing is that the information was not propagated."
We are cutting fine hairs now. An analogy to your case above might be (your eyes in this analogy = you from above, and your brain in this analogy = your friend from above). In that case, does suddenly going blind, or having a bright light being shined in your eyes correspond to a loss of information in what you might be trying to see at the time? This is a semantics argument, and one could argue either way. In both my analogy and your example, we are talking about data flow. If the information content of the data decreases as it flows from one place to another, do we consider that loss of information in the flow? I would say so.

I think you think I am trying to say something other than what I am trying to say, and that for the most part, if we understand what the other is actually meaning, we probably mostly agree.

5) I was not being clear. I was essentially referring to the same concept of data flow that I mentioned above. The part where I mentioned subjectivity refers to saying that the way we choose attributes in our ontologies is subjective - there is no objective rationale for defining a horse the way we do. We define horse the way we do because we have subjectively determined that it is a useful definition to have. If we try to make ourselves more objective, we suddenly have less and less rationale to define anything the way we currently do, since the concept of "importance" vanishes as you become more and more objective.
For example, say in my mind, I define favorite food = pizza. As I attempt to make myself less subjective, all the reasons for which I currently like pizza become less and less important -- I need to be able to have this more objective concept account for people who hate pizza. I would probably end up in the end with the definition of favorite food being identical to the definition of food in general.

As you become less subjective, the boundary between useful and useless information disappears, and it all just becomes information.
Now from our currently, "objective" perspective where all information is equally useful (or useless, depending on how you look at it), say for example we observe a data flow such as your example above, or my analogy. If we, as our objective observer selves, were to judge whether or not information is being lost in such a data flow, we would conclude that the information is not entirely flowing through. It is getting filtered.

That's all I was saying there. I wasn't saying that the actual, objective properties of the horse vanish in real life or anything.


I think what I am saying is not as radical as you think it is.

Edited by mmiguel, 22 September 2012 - 12:39 PM.

[mmiguel]

Just had a duh! moment. Theory is only second definition, theorem is first. This is why I need sleep. Commencing hibernation in t minus .....

[Yoruichi-san]

0) Okay I use examples that are often gross oversimplifications/idealizations to try to better explain my point, like using the idea of an 'ideal gas' to try to explain how gases work, or modeling a particle in an infinite box to model potential. Please don't get too caught up in the example itself, the point is the point .

1) No, you misunderstand me, I am not implying what you think I am implying you are saying . My original statement was that generalization can lead to more information being, not that it in itself provides more information. I.e. the theory of gravity allows us (humankind) to gain a lot of information. If I don't generalize I can't propose the theory of gravity, since it (and all other theory/theorems) are generalizations themselves. Sure there is information that I did not gain by not looking at specifics, but generalizing in this case leads to more information overall.

2) It's alright, my point in pointing out the differences in our definitions is that I think mine is a more accurate description of how people typically use the concept of sameness.

3)

As far as the information content required to represent a concept, leaving something open-ended is exactly the same as not allocating any bits of information to represent a specification.

I disagree. By leaving open-ended I mean, like, allocate a variable to it, which is allocating a bit if I understand the computer terminology correctly. That's why I included the example, I was not saying that a horse can be defined by four aspects, but I was grossly simplifying to simply try to demonstrate the difference between how we think people think. The difference is that you think they use a specific value that is some kind of average or mode or last-seen or something for the things that differ from horse to horse, where as I think they leave it as a variable, i.e." the horse could be any of brown or white or tan or black or red or...but cannot be blue or purple or green..." or "the horses in the north of the state are usually brown, but the horses in the south are usually white, but they could also be..." this is information, just not specific information, that they attach to 'horse'. Or they could have, like, something akin to a probability density function relating, say, the breed of horse and where it would be found.

4) I don't think you can lose something you never had. I think what you mean is that there is a loss of the opportunity to have gained information, which I will agree with. However, an opportunity is just that: an opportunity, a chance. That information might have been gained had the person not generalized, but it also might not have, if the person wouldn't have gone through the effort if he had not been allowed to generalize. So to evaluate the expected information difference from generalizing and not generalizing on a particular thing, then you have to consider (amount of information not gained by generalizing)*(probability information would have been sought out if not generalizing). To evaluate the overall (net) expected change in information in the system, you also have to consider (information gained by time/effort saved by generalizing so that it could be spent elsewhere). I argue that generalizing gives a net increase.

5) I see. But again I argue the difference between data flow and possible data flow. The information had by people in the world will never be one continuous data flow, it is actually physically impossible for every piece of information to be passed on continuously, since data transfer is not instantaneous, human lives are finite, and so are resources (bandwidth, pencils, etc). I would agree with you that some specific pieces of data are dropped from the data flow, but it allows for more new pieces of data to enter into the flow. And I would argue that the process of generalization allows for more efficient data flow, allowing more data to flow per unit time/effort.


So to answer your general question, I would say, making exception for those cases where generalizing is abused, that generalizing is good thing, that recognizing what characteristics are the same in things is useful to allow us to compare and contrast things as well as to make correlations that allow us to understand the workings of the world better, and pining for an ideal world in which data flow was instantaneous, took zero effort, and could be continuous is kinda pointless ;P.

[Yodell]

Wow , you two make it really hard for another to follow your conversation .. not to mention your points...

Miguel, in my opinion there are no two things/objects... what ever you want to think of .. equal (as in "the same") .. but in order to distinguish between two "of the above" that LOOK the same/equal one would have to be all-knowing... to be, in a word, "God"

I agree with Y-san, "sameness" as you two call it is a concept that appeared out of necessity : to learn, to generalize, to be able to share at least the part of the information that one knows and wants to share.. Most people learn best and understood things by comparison to a familiar thing/object.

To use your example :If you say "pony" is the same as a "horse" but with a smaller caliber/height , does this mean that ponies are 99.99% equal to a horse, except height ? NO, because not event two horses are not equal..not by a long shot... you cannot have two identical things/objects, but they might be enough alike to be recognized by most as belonging to a "same" something (class, order, etc..).

[~andy~]

Remember 'only fools and horses' ?
Trigger was proud of using the same broom for 14 years, replacing the head eight times and the handle six times

Is it the same broom? I don't think so