Things that we can't "know" directly

Haven’t had much board time recently, so my replies are slow.

Well, I agree that we need a better definition of complexity. From the link you posted, it appears that model theorists think so, too. Now if only one of them would stumble by this thread and give us one . . . :wink:

I appreciate the compliment (though I can’t remember the last time I was a pure anything, much less a mathematician). I am not sure I agree with the distinction you are drawing, though. Yes, I gave an example of derived “complexity” [sub]wish I knew what that really meant[/sub] and you are talking about building a model to predict the behavior of an existing system. But the result that arl argued for, and which you seemed to agree with as far as systems of “infinite complexity” go, implied not only a one-to-one mapping between model and system, it declared identity between them.

Now, when I think of the relationship between models and systems I generally consider it to e a many-to-one mapping. We can model plane figures in cartesian equations, polar equations, or with methods of Euclidean construction. We can model the positron with dirac’s equations or Feynman diagrams. I don’t see any compelling reason why modeling an infinite system will necessarily restrict us to a single construction.

Furthermore, even if that reduction holds, and only a single model of arbitrary accuracy is possible for an infinitely complex system, I cannot see any means of making the leap from that single model to identity with the system itself.

Actually, I take that back. I can see one means – if the reduction is not to a single case but to 0. If it is not possible to construct a model of arbitrary precision without replicating in exact detail all facets of the original and it is not possible to build that model as a separate but identical “copy”.

For instance, if we had to build a “miniature universe” to model teh Universe, and if we had to build it in the Universe. Then, of course, we would have to build a miniature model of the part of the Universe which held our model, which would have to contain a miniature model of the miniature model . . . ad infinitum. BANG! Then we hit the quantum wall and cannot miniaturize any further. Our model thus is not arbitrarily precise. The only “model” for the Universe is the original.

That seems a far cry, though, from the types of mathematical models which intiated this discussion. I wish I had a friend who was a model theorist, so I could go beat on him until he gave me a straight answer to the implications of complexity. [sub]Okay – I just wish I had a friend. We all have our wounds. Thanks so much for seasoning mine.[/sub]

We need an expert. Maybe I should ask Stephanie Seymour what she thinks.

No argument there, but I still don’t see how this takes us to identity of model and system. If we take our dynamic equations and set them in the middle of a hurricane, I doubt we will learn much of interest (though the idea has a certain visceral appeal). Likewise, the output of tose equations, no matter how copious the data we pass into them as parameters, will not drop water on farmer Brown’s fields.

I write that and fear I have engaged in reductio ad absurdum, but I really think not. I think, rather, for any finite model the identification is absurd. And I don’t see whatever line of reasoning would convince you that the absurdity necessarily vanishes for a system of infinite complexity.

This sounds like you are arguing for the reductive case I argued above: only a physical replication is fit to model the Universe and that replication cannot be achieved. QED the Universe can be modeled only by itself. (OR: the Universe has no model, which says the same thing.)

I am not sure how you would generalize this argument to any system of infinite complexity, though.

That squishy sound you hear is my brain leaking out of my ears. And I’m still on Page One.

See y’all again after I get to the end.

If I make it…! I’m gonna need a sharper machete…

Spiritus - I can’t find much to argue with in that.

I guess that I am suggesting that (as you said), yes, the only way to model the universe in its entirity is to build a mini-universe, but since that is contained within our universe the model must also be the universe.

I suppose that one could say instead that the universe has no model. Either way is fine by me.

This:

I have no quarrel with. I merely note that an infinite system is not the same thing as the universe itself. I’m quite happy that one can construct models of inifinite systems that are not identical to the system. But an arbitrarily predictive model of the whole universe would be the mother of all models.

My support of arl was only to the extent that the system being modelled was the actual universe. I said:

Firstly I must hold my hands up: the infiniteness of the universe is not really my point, more its completeness (for lack of a better word). That may have led us down the wrong path - I’m sorry. An analysis of whether this statement is true or not would probably be better focused on whether reality is synonymous with universe. That was the key assumption and I’m not sure in retrospect whether or not it is true. I’m not sure that it’s not true either mind you.

NB please note that in the same post I also said

which I think is the point you were reiterating with your last post.

Incidentally - “implied” and “derived” complexity were concepts I made up. I did this to try to get across the different angles we were coming from. I think that you understood me well enough, so our language bottomed out OK :slight_smile: I wouldn’t want you to go away thinking that you should research “derived complexity” though.

pan

No worries. I knew what you meant. I even had a tangent semi-composed to address the issue. Then my better nature [sub]okay, pure laziness[/sub] kicked in.

I still want to find a model theorist to grill, though. :wink:

[sub]or matbe broil. I need to watch my fat intake.[/sub]

OK, models and reality.

Both spiritus and kabbes:
OK. I think we can resolve something here, at least using the same arguments that have been presented to me already; but I still have more questions.
Firstly, [if] the model is never the equivalent of what is being modeled. When this is the case, we find that we may point to the model and point to what is being modeled. ie- a car, a model car, a Hot Wheels car. The complexity of the model varies along with how well and on what points it corresponds. What seems to be the problem here is distinguishing information gained from the model from information gained from the thing-being-modeled. We have, for example, the car body only in a wind tunnel to model aerodynamics. We don’t need a functional engine, etc.
The problem here isn’t that the model isn’t the thing…it still is. It truly is the model of aerodynamics…it IS the aerodymamics. What we know we gleam from the model. Our ability to seperate the actual model from the actual thing is interesting for discussion, but that’s about where it ends.

The problem here, of course, is that our models are incomplete. They do not offer 100% correlation with empirical data. Thus, we do know on some level that our models are NOT the thing being modeled.

We have a mathematical theory (model) of meteorological events. We form weather predictions. These predictions are wrong, or at least “near misses”. Now, when faced with such a situation, what can we say?
[li]We know about the weather from our model[/li][li]We know about the weather from our data[/li][li]We can combine our model with our data[/li][li]When we combine our model with our data we may form a more accurate model[/li][li]At some point, we stop due to kabbes’s point of diminishing returns: the complexity of our model increases at a rate faster than the accuracy improvement (whether or not this is completely asymptotic is interesting, though lets assume it is).[/li]Conclusion? It seems to me that all models, when taking into account all factors, are infinitely complex. If this is the case, then we are faced with some sort of dilemma: what is the difference between our finite complex models and the empirical data we gather?

It is one thing to point at today’s rain and say, “This is real,” then point to the incorrect(inaccurate) prediction and say “this is the model.” It is another entirely to assume that we haven’t already based this conclusion on another model, namely of course what this whole thread has been about: epistemology. A model of knowledge itself.

My problem here seems to stem from the incompleteness of models. We know they are wrong, and yet what we know is through the models. We know that epistemologies (here) cannot validate themselves, and yet this is through a model for logic.

Again I am faced with a language/turtle/typical-arl problem: bottoming out. (pauses for extended sighs from the peanut gallery)

If I were asked to write a summary of this thread so far, it would be this:

I don’t know what’s more circular, the topics this thread covers or my ideas about this thread. Er, wait…are they the same thing? :stuck_out_tongue:

Problem?

The purpose of a model is to generate information that for one reason or another we cannot gain from the original.

The shell in the windtunnel is not the car on the street. the model (shell in windtunnel) is used to generate information that we can use to predict the behavior of the car on the street.

We are not “modeling” the behavior of the shell in the wind tunnel. We are measuring it. What we know about the behavior of the shell, we have measured (or perhaps gleaned from other models). What we know about the behavior of the car on the street we have learned from the shell-in-windtunnel model.

No.

Our ability to separate the model from the actual thing is inherent in the concept “model”.

We know our models are not the thing being modeled because they are models. If our modles were arbitrarily accurate, that would not change. Models are not guaranteed to “approach” the original as they become more accurate. Relativistic equations are not “more like” the arc of a cannonball than Newtonian mechanics.

I think you may have written this without thinking it through carefully. Would you like to reconsider it?

I agree. But this “fact” implies no particular conclusions about the identification of any particular model with its referent.

Some things don’t bottom out. You just have to put your foot down. :wink:

Indeed. And since accounting for empirical data is a shifting target, it is an open question wehther a general epistemological “model” of reality is an achievable goal. I know of no rigorous arguments one way or the other.

Actually, I do not think this is correct. Some models do not predict with 100% accuracy. That does not imply that all models show this disparity. For instance, as you read this thread your monitor will model the order of keystrokes that my fingers made as I typed this post. If I have not gone back and corrected any typos (or revised any sentences) then the model could well be 100% accurate.

The key, really, is to understand what the model is and what is being modeled (both of which are determined by us). Just as many models can be constructed for one system, one model may be used to represent many systems (order of keystrokes, visual display on my scren, communicative intent, etc.)

No consistent epistemology will detect errors within itself. How can it?

This is no more dogmatic than any other consistency.

I think I am pushing the model thing to far, perhaps, but I’m still having hard time seeing how we seperate them from reality. In a similar vein to my language-construction argument earlier, I posit the following.
“So, as you can see, this car is very aerodynamic.”
~“In a wind tunnel.”
“Well, to be sure. But the wind tunnel isolates effects which we are studying to ensure our data is accurate.”
~“In a wind tunnel.”
“But that’s how we explain the workings of the wind world outside the tunnel. The data we gather is an approximation of the real world. It is not the same thing.”
~“So tell me about some aerodynamic effects.”
“Well, as you can see here–” turns on wind tunnel and smoke streamers “–The shape of the body works to keep some downward pressure on the vehicle for better road handling.”
~“But you don’t even have a road there!”

sigh It seems trivial, I know, but we know the real world through our models. I am not prepared to say that should we remove the models we remove the real world, but if we explain and understand the real world through our models then our models are the real world, at least so far as we can explain, teach, and understand.

I guess I should say, instead, that the sum of our different models is the real world. I do not like the ease with which you seperate the models from reality… I think that is a very flimsy line when we probe deep enough. Although you seem to be focusing more on the realist view of the models (words on paper, physical size, etc) whereas I’m looking at the understanding and application of them in comparison to perception of the real world.

No more than the neural firings in my brain are the words in this post. If you remain huddled in nihilism, then the distinctin between real world and model disappears (along with the real world). If you make the leap required to function under an epistemology that accepts an objective referent for experienced stimuli, then the distincion is clear and inescapable.

Models are epistemological tools. They are not the objective referent.

The sum of our models is a proper subset of our epistemology. That subset is no more our objective referent than any particular member.

I do not understand your unease. Truly. The line is basic at any level of probing.

ARL and SM agree that rationalistic epistemology is putting Descartes before the horse.

They agree that in principle a more scientific approach should give them a Locke on it, but cannot refine this well enough to take it Hume.

A critique of pure epistemology Kant be done.

Attempts to model such an epistemology result in poor replicas of the ideal done in Play-Doh.

Attempting to bring in Chinese philosophy leads to Lao-Tse results.

Pragmaticism is no avail to Peirse the problems.

Existentialism leads only to unSartreainty.

(Excuse me, I need to go pick this Whitehead.)

I have read this entire thread, and I am sorry, but arguing whether you know something is quite pointless. Arguing whether what we know is real or not is pointless. But since no one has brought it up the entire thread I will show you true knowledge.

Are you ready?

I know the future of myself and every person who reads or replies to this thread.

Get set?

Here it comes…

I am going to die. You are going to die. We are all going to die.

If you do not know this, then you do not understand death. The day that you really know this, and the day will come, life will be easier. Fear will become insubstantial. And you will begin to realize that you have to make of it the best you can. This, you will know.

SM
We teach from models. We learn from models. What do we know, the models or what the models represent?
Epistemology is a model for knowledge. Do we know what the epistemology represents or do we know the epistemology? The automobile’s shell acts as a model for the automobile in a wind tunnel. Do we know about aerodymics itself from this or only about the model?

In other words, what do we know about the real world that we don’t gain from our models?

Now, I do see what you are saying. I believe in an external reality, seperate from my own senses. I’m having a hard time formulating an explanation for this, though.

polycarp
Excellent. :smiley:

sojourn
You sound like my roommate, who often likes to say, “Shit happens, you can’t control anything, and you’re gonna die.” Fantastic.

:rolleyes: So this knowledge is automatic, and if I don’t have it I’m screwed? No use debating the validity of such knowledge?

Thanks for your contribution.

So let me guess, you think you are going to live forever or you have not accepted the fact that you are going to die some day. Am I right? Was this thread not about what we really know compared to what we might know? And did I say that you were screwed? You pretty much came up w/ that on your own, and if you think that way, well sorry, have a nice life.

So tell me then how you cannot know that you are going to die. How is this not sure knowledge? Do you know someone who death will never come for? I never said that the knowledge was automatic, and knowing one day that you are going to die is not going to screw you for life, unless you cannot handle the fact. You can go on the rest of your life not knowing this, but in the end, reality will catch up with you.

So if you are finished debating on if what we really know is real, then I will prove this to you. One day, you are going to die. And the day that death comes knocking at your door, then you will really learn what reality is. And at that time, you will know that I was right.

Death comes to us all, even those who do not believe or run from it. At the time that you face death you will have what everyone calls “your life flashing before your eyes”. Do you know why this occurs? Because at the moment of death, you will look back on your life and see if you lived it to the furthest. This is the end for you, there will be no further in life. For those who are fortunate enough to escape death’s clutches, then that knowledge will be known, and at that time, you will be better prepared to live your life to it’s furthest and know that when the day comes again when death comes to take you, you will be satisfied w/ what you have done. But you will never escape death.

More than likely you and everyone else will read this post, roll your eyes and go on about with your arguements. At this point, I will know, and so will all others who understand what I am talking about, will realize that you have the toughest lesson yet to learn in your life. This does not mean that you are screwed, this does not mean to belittle you for not knowing. It is nothing more but a way to, hopefully, let you know of what is to come before you before you lose the chance to do anything about. Because like I said, one way or the other, you will know, whether you want to or not.

No. What you mention is a piece of knowledge. We are discussing the root of knowledge and what we use to verify such knowledge as true. Thus, your resistence to this thread made me wonder if the knowledge you profess is automatic; otherwise this entire thread applies to what you are telling me (us).

No.

Did you read what I said? I said that IF I didn’t have this automatic piece of knowledge (that is, irrefutable in any way and in any thought structure) I would be screwed by your line of thought since this was the most important fact to know.

I am aware of my own mortality. In fact, the awareness I have of my mortality is part of the reason I enjoy exploring my life which consists, in no small part, of thinking.

Did you just watch Fight Club? Sheesh. I thought I liked that movie, but you’re killing me here. I don’t think that I’m finished debating if what we know is real, but I can handle more than one conversation at a time.

I should mention, however, as a warning–I already know I will die, so your task isn’t that difficult. :slight_smile:

Thanks Moses. You have a custom Magic 8-Ball there?

I take it you’ve died before, and that you are speaking from experience?

[QUOTE]
*Originally posted by aynrandlover *
**

If you are saying that I watched Fight Club to come to this realization, then yes I did. That is of course if Fight Club was in the movie theatres 15 years ago.

Just another example that those with no wisdom mock what they do not understand.

Yes and no. Yes I have experience in escaping death. No I have not died, but I have spoken to people who have been clinically dead and was revived. Have you?

Go ahead and head back to your philosophical debate on is indirect knowledge real. I heard that the Atlantic ocean was really beautiful this time of year, so I’ll just go and find out for myself while you still talk it out.

That depends entirely upon our epistemology, doesn’t it? :wink:

Our ability to “know” anything external to our minds is dependent upon our epistemology.

Epistemology is not a model for knowledge. It is a method of eveluating/constructing/describing knowledge. Unless your knowledge exists as an external objective referent, of course.

The subset of an epistemology which addresses teh “real world” is a class of models, of course. But some epistemologies lack any models whatsoever. (Of course, they are not particularly useful.)

Nothing.

That does not mean that the model is the referent, though.

sojourn
You have both entirely misunderstood the nature of this conversation and demonstrated a depth and clarity of thought that I haven’t witnessed since I was kicked out of metaphysics 211. It is astounding that you have come so far a mere fifteen years after realizing that you were going to die.

Thanks for the memories.
polycard
You will be punished.

Yes. Shit. :slight_smile:

Yes. Damn it. :slight_smile:

I have truly gone too far with the model=reality thing.


I was thinking this weekend about self-referentiality when I asked my friend, “Do you think I am aware of myself?” What a strange phrase, you know, in terms of an RToT styled epistemology.

Now, our system of thought would not allow for the system to use itself ON itself, but would that invalidate all forms of self-referentiality everywhere? I’m unsure about the implications of that. Could I know that I am aware of myself under an RToT styled epistemology?

No, but it is interesting that you tell me it is absolutely certain that death is unescapable, then follow that up with a post stating that you’ve escaped death and known people who have died then come back to life.

At least, that has been the case so far…

Not sure what the problem is. Yes, self-reference is out. Why should you know that you are aware of yourself? You can take objective reality as an axiom, but it isn’t provable as you well know. Forget “I think therefore I am” - the solipsism has descended into “I know I am”.

pan

Waitaminute… you’re saying that I can’t know anything about myself? This cannot be a strong point of epistemology, can it?

No - I’m saying that you can’t know that you know anything about yourself.

Just remember the cliched brain-in-a-jar example and all will be well.

pan