Geezus

( First off, I'd like credit for using the word infinality correctly in a sentence.)
What are your thoughts on knowledge ITSELF? Do you think that one day science and mathematics will create a two varible equation that can be used to explain all things of existence, or do you think that knowledge is infinite and we will coninue discovering until knowledge is beyond comprehension and humans become something abstract?

mandal

Knowledge is most definitely infinite. Just start counting and just from that you'll see that's it's infinite. Also, there's no way mathematics will create a two variable equatin that can be used to explain all things, there aren't even two variable equations for simple things. For example, the position of something in space is already three variables.

Also, I dont believe there's a way to continue discovering utnil knowledge is beyond comprehension, since to me, knowledge implies comprehension. That's why religion and God is not knowledge.

ratiocination

I don't believe that there will ever be an end to the amount of knowledge we can have. The one thing that seems to drive man is his desire to pursue knowledge, and it seems to be innate to a certain degree in all of us. If we could somehow learn all knowledge.. we would be some kind ofa god.

Further more, knowledge of people is still unknown. You may know a lot about how the world functions and a lot about the universal scientific and mathematical truths but you still may not know the true personalities of people.

Eviltree

I disagree that knowlage and comprehension are the same thing, (or that knowlage implies comprehension) Take any (reasonable) mathematical formula. Any idiot can take that formula (knowlage) and plug in numbers to get an answer, it takes someone with comprehension of the subject to (firstoff come up with the formula) understand WHY that happens. With knowlage, you know How, with comprehension you understand the why, and actually grip the entire idea, not just the application of it.

mo42

Knowledge is infinite so long as time continues to march forward, and so long as the universe is changing.

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sandinista

If, as you say, you can plug numbers into an equation, you know how to plug in numbers, but you don't know WHY the equation does what it does, nor why it does it. That was the original posters point - knowledge IS comprehension.

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phukraut

Just a quick note: just because what there is to know is infinite in scope, that doesn't necessarily mean we will keep on discovering. Take mandal's example of the integers. Yes, the set of integers is infinite in size, but we can completely describe them with that set. A curve is similar in the sense that we can think of it as being composed of an infinite number of points, yet we can completely describe (and understand it) with an equation.

Of course, that doesn't mean all things can work like this. There may be things that are infinite in scope AND cannot be completely described: a random sequence for example.

Also, a sufficiently complicated problem may be solvable but not in the lifetime of the universe, say. This is sort of on the same lines as mo42's response.

cybersharp

I beleive that Knowledge is somthing that while can be learned in vaste amounts will not ever be totaly learned of....(That no one individual) will ever learn everything there is to learn..

1. There is simply too much data.
2. It would take a exceedingly large amount of human time.
3. I do beleive that there are ways to learn faster however.
4. Bluntly put...humans will never learn everything because its in there nature to learn more after they have learned a little...this of course can be twisted to say that one day humans will not only be immortal but beings of such power that they would be virtualy to termed God..

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rog1039

Does anyone think that once we build a complete and correct theory on the physics of the universe that we will have discovered everything there is to discover?

Meaning, I think it's a reasonable assumption that everything that occurs in the world is a result of the interactions between molecules, atoms, quarks, strings, etc. I think incredibly complex behavior (in people, meaning someones attitude and why they act a certain way as well as the general behavior of physical objects, such as a leaf falling of a tree) can be broken down into interactions between the most basic objects that make up the universe. I would have to say the argument about counting coming from Mandal doesn't hold here. Mainly for this reason: In a purely physical level (meaning I'm trying to look at this from outside a human perspective), countings and integers don't exist. The universe doesn't count stuff. There is no such thing as counting. Counting and integers are ideas created by us to help us model the universe.

I also think it is unecessary to learn everything there is to know about complex behaviours to be truly knowledgeable. For example, there is a set of numbers known as the Mandelbrot set. This set of numbers is infinite (or at least I'm pretty sure it is), and the graph of the Mandelbrot set, while bounded, is infinitely complex. As such it is known as a fractal, but that is besides the point. It is impossible for a person to know everything there is to know about the Mandelbrot set. We could turn every person on the planet into a mathematician and have everyone study this set of numbers and it would be impossible to know everything about it. However, if one knows how it is created, one can recreate the Mandelbrot set with out difficulty. The differential equations that form the Mandelbrot set are incredibly simple, yet they create something of unimaginable complexity. My point is, I believe something similar may be the case for the universe. A simple set of rules define the interactions between the most basic objects in the universe. And while incredibly complex behaviors may result, those behaviors are still the result of the interactions of the atomic level (or smaller, depending on whatever is the most basic constituent objects are made of).

Of course we could try to analyze why I put off doing my homework in favor of responding to threads on this board. I'm sure we could get a physcologist in here and he could learn about my life and my behavior and build complex theories any why I procrastinate all the time. Or a physicist, with knowledge of the true physical laws of the universe could just tell it in less human terms. "He procrastinates because these chemicals in his brain fire in this manner which is caused by the interactions of this neuron with this neuron, which is further caused by the chemical attraction of this molecule to this one, which is futher caused.....on and on until we reach the most basic objects that make up the universe.

End point is this: If everything in this universe is caused by the interactions between the most basic objects in the universe and are goverened by a set of laws, then once we discover these rules, what is left to discover?

Karkaboosh1

IF knowlage = awareness
AND awareness - mental capacity != x, where x is anything and/or everything (awareness is DNE without mental capacity)
AND mental capacity != infinite
THEN knowlage = limited
limited != infinite
and finality != limit

good job if you udnerstood the above. basicly, since everyone has a limited mental capacity, ie no one has an infinitly sized mind, you cant know everything.

Zeraph

Your only problem Karkaboosh1 is that there has been no definitive evidence yet that our mind is limited

If the universe is infinite, and we are the universe then our knowledge is infinite. But the two questions that remain, is anything infinite? And we are apart of the universe, so how do we want to define ourselves?

doncalypso

From what I've read throughout my lifetime (and from my personal experience thanks to the School of Hard Knocks) I've come to the conclusion that the more knowledge one acquires the more one realizes that there is so much more to learn out there and that one cannot possibly acquire all the knowledge that there is to be found.

Hell.... I wouldn't want to be omniscient even if I could because omniscience without omnipotence would be a burden, not a blessing, and it would cause one to go crazy.

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Yakk

Actually, we can't.

See Gödel's incompleteness theorem. We can't describe the integers completely, consistantly and decideably. The integers cannot be described.

Even if you had a simple equation describing the universe, look at gravity. The three body problem can't be solved analytically -- yet, gravity is a rather simple mathematical equation.

It is quite possible that there are games which are inheritly complex. Even if we knew the laws of physics, it wouldn't help us figure out how to play chess. If humankind runs out of things 'in the universe' to play with, we can play with things that are not. Or so I suspect.

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phukraut

I think you may be talking about number theory. I'm not. I'm simply saying that the integers can be described by a set in such a way as there is no confusion about them. We can describe an object such as the set of integers without needing to describe every possible relation of the integers to each other. The former is describing the integers. The latter is number theory.

Yakk

Actually, I want to describe the integers and plus and times.

I can't. You can't. You can try, but what you are describing isn't the integers. It contains both things that are the integers and things that are not, under one interpritation.

When you go and say the word 'set', are you talking set theory? If so, you run into the same problem as you do when describing the integers.

Now, you can play fast-and-loose, wave your hands, and pretend their is no confusion. "The integers are {..., -3, -2, -1, 0, 1, 2, 3, ...}", and gloss over the problems. But all GIC is is a set of questions about a description of the integers, and a proof you cannot answer them.

Is 'infinity' in your integers? Are you sure? I'm not.

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phukraut

If you are talking about arithmetic (I'm not sure what you are doing there by including the two operations, unless you mean the ring of integers), then I can only point to <a href="http://mathworld.wolfram.com/GoedelsIncompletenessTheorem.html">MathWorld</a>, which contains the following quotation.

I am not talking about arithmetic though---Peano or otherwise, nor set theory. It is enough, in my opinion, to assume naive set theory to wave my hands and pretend in order to create my particular set.

However, you know more about Godel's work than I do I think, and it seems you are seeing something I am not, so I will defer the point. You are right that my approach is fast and loose.

Cheers.

flstf

Infinite knowledge will probably require an infinite amount of time. But then I don't really understand infinity or time. To me asking if there is a finite amount of knowledge to be acquired is like asking if there is a finite amount of space in the universe. It seems like if either one ends there must be something after that.

fckm

What is knowledge?

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fckm

Just because you know the rules, doesn't mean you have any predictive power. Somebody already said it. The three body probelm in classical mechanics:
You have three equally massed objects in space.
They are governed by gravity.
Given initial conditions, solve the differential equation which describes their motion.

You can't. It's impossible.

In fact, if anything in physics tells us how limited our "knowledge" is, it would be quantum mechanics. QM says that the best you can do is to determine the probability of events, you never know for certain what will happen.

The Universe is Non-deterministic. The only way to know for sure, is to measure.

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1010011010

Even if we did develop an all encompassing theory of everything and reduced it down to a single relatively simple equation...

Well, there is an infinite set of numbers to plug into the equation, isn't there?

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Drayab

Sure you can. Get a computer. Have it crunch out the differential equations with some good code. You will find that certain initial conditions give unstable solutions, but it can be done. Next imagine a computer that can solve the problem to an accuracy less than the uncertainty principle. Now you've got something that is operationaly as good as (perhaps arguably better than) an analytical solution. If that seems like an ad hoc solution to the problem consider that the analytical solutions to physics problems are almost always had at the expense of making some simplifying assumptions.

Still, just because you've got the ultimate equation (think: unification of physics) that doesn't mean it's the end of the story. When Maxwell wrote down his famous equations it was not the end of learning about electromagnetic theory; there was a lot of work to be done in understanding all the applications/implications of the new theory. Besides, there is also the issue of emergent properties of many body systems which do not lend themselves well to understanding with the fundamental equations. Just think about thermodynamics. On some level all that we measure is governed by the microphysics (electromagnetic interactions) but instead we talk about things like entropy, pressure, and the like. Thermodynamics stands as knowledge apart from any ultimate theory of reality.

I had an idea while I was reading the posts here. People have noticed that all information has a certain amount of energy associated with it. To prove this to yourself, imagine discovering some new knowledge without expending some energy in the process or try to imagine conveying some information to somebody else without expending energy. If you can buy that, then I bet that information and knowledge are fundamentally limited by the amount of energy available in the universe. There are reasons to believe that the amount of energy in the universe is finite. I can't think of the exact reasons right off the top of my head unfortunately, but I think it is tied to the size and expansion of the universe somehow. Anyway, if the energy is finite and the information is proportional to the energy then the information must also be finite!

On a happier note, there is so much energy out there that I bet we will destroy ourselves with our knowledge before we exhaust our supply.

Yakk

If you are solving the problem to an accuracy less than the uncertainty principle, threshold you better be doing wave equations. =)

Hmm. So, you want the answer within epsilon, so you measure your location within f(epsilon), and use a massive massive massive computer to do the simulation in such a way that the end error will be less than epsilon.

Reminds me of the constructive reals. =)

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biznatch

No variables, nothing to understand... 1=1...isn't simplicity the answer to everything? Humans have the arrogance to think they one day find the answer...
Is there an answer? Is there a "reason" for "everything"...Do we have to look further than our own lives and what's actually happening in them...family, work, routine...stuff like that? I don't see other animals looking for the "answer"..
There just might not be an answer...Who knows? "knowledge" is invented by humanity...we invented mathematic as something that works to better understand the world around it and make the abstract concrete.
I don't know. I just don't think there is an answer...And if there is one, I think man is not going to find it, because of his arrogance. Maybe if humanity united for knowledge, to find what knowledge really is.

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mushroommike

What you call arrogance I see as the pride, drive, and ambition that has driven all humans to succeed. There is no 'reason for everything' as you put it, there must be a concrete question to answer in the first place. I'm assuming you are referring to the reason of existence then...but this is something that is for the most part self-defined by each individual.

biznatch

What you see as pride, drive and ambition can be seen as man being arrogant ..
but without this pride (or arrogance) I wouldnt be typing on this keyboard right now...because there wouldnt be computers.
But can we see man's gain of knowledge as a good thing?...so much knowledge is used for destruction...or to prevent others from gaining knowledge..
Some have taken their intelligence to the point they think they are superior to the rest...we're only a scracth on a tiny bit of rock (the earth) compared to the infinity of the universe and the infinity of time.
we're dust.

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mushroommike

There are no doubt some negative consequences where the more knowledgeable and powerful have taken advantage of people in ways that I do not morally support, but for the most part you cannot deny the overwhelming positive effects of increased knowledge on humankind overall. As for our significance...tt's just the way you look at it I suppose...as a glass half-full or half-empty. When you compare humans with 'the infinity of universe and time', it's easy to get lost in how much knowledge we have failed to discover thus far...but if you really consider how far we have come from being cavemen...by mastering our surroundings with the power of the mind, the power of individuality, the human race has much to be proud of.

Philangicality

Knowledge is infinite. As humans we develop knowledge as we interact with our environment. As long as we continue to live, knowledge will never cease to exist, so it is impossible to know everything.

You only know as much as you know you don't know

Hain

There is a difference between knowing an understanding. To know something means only that you recognize that it is. To understand something is to realize why it is.

AND CURSE YOU FCKM!!!!! I was going to talk about how you can't know everything about something instantly because of quantum mechanics. Kudos to you.

I believe if people aquired understanding of the universe gradually, beyond the where petty human emotions such as pride to horde that knowledge or misuse disappear, then there wouldn't be a problem to searching for that infinite amount of knowledge. You'd always have something to do.

And who's to say that once you know enough you can't just accurately "guess" the next step, make sure it's true, and keep going. Optimistic but not happening within my life time (Unless Yakk brings up quantum immortality then YES I will live to see it, somewhere, maybe even here. )

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Yakk

Yes, but we are some badass dust.

It has been said, that if the universe exists for humankind, that's an awful waste of space.

Whoever said that doesn't understand exponential growth.

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Hain

But isn't there a finite amount of matter? So technically... it's a logistic growth... than afterwards it becomes a logistic decay . So is that a bell curve?

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nickynicole

Apparently knowledge = math.

Having had way too much exposure to sociology, I tend to think of knowledge as relative. Throughout history, knowledge, especially about the environment, has changed, and will continue to change.

As I recall from highschool chemistry, the atomic structure I was taught (and this wasn't too long ago) wasn't correct, it was just easier to comprehend.

I would offer that there may be an infinite number (or at least multiples) of ways to interpret information. Add that to the continuously growing field of information, and knowledge is most certainly infinite, or at the very least, we don't have enough time to reach the finality of knowledge. Unless, of course, matter is finite and time/human existence is infinite.

I am talking out of my ass. I think.

Yakk

*nod*, exponential growth runs into barriers.

But first whatever was growing exponentially gets big.

The old bit of math: if there are 1 trillion stars per galaxy and 1 trillion galaxies, and it takes a star system 1 million years, after being settled, to colonize another star system... It will take 80 million years to colonize the universe. This is riduculous, as relatively (speed of light barrier) gets in the way.

Life is star dust. But it is exponential star dust. Rarr.

This doesn't answer 'can we know everything', but it does remind people that 'just star dust' doesn't mean we are nothing.

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Hain

And I'd like to say that for star dust you people have come a long way, and hopefully go a long way.
... I mean WE'VE COME ALONG WAY... yeah...

But seriously...

I figure if we are star dust, then even if we leave this Earth to find another, we never are really leaving home. It's all around us, every bit in the universe. To reach out further to to understand more of our own origins. To understand more is to put us in touch with which are eternally kin to.

As Bill said in in his and Ted's Excellent Adventure, "Let's reach out and touch someone."

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HoundstoothHero

Many epistemological arguments involve certainty in justification, and a prevailing view is that knowledge requires certainty to be absolute. Any doubt (or chance of doubt) necessarily prohibits knowledge.

My own view regarding knowledge gravitates toward what is referred to as the 'fallibilist' approach: it is impossible for us to achieve absolute certainty, and therefore any such high-standards approach to knowledge results in skepticism. What we as humans 'know' does not rely on absolute certainty, but rather on good enough reasons for believing a (necessarily true) proposition. G.E. Moore's response to skepticism also appeals to me: it is more reasonable to believe we at least know some things than to believe we know nothing.

That being said, there is a low ceiling on what we can 'know' and comprehend. Humans and their faculties are decidedly finite.

biznatch

I hear you HoundstoothHero. If we're talking about "human knowledge"...It won't get much further than where it is now. We're not a perfect species..(far from it) and our gray matter can't be the container of these universal truths...If this "knowledge" is discovered, it won't be done by us.

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Livia Regina

If we live in a finite universe, then theoretically, there is a point where all that can be known, is. However, I think the universe is so big that the human race will be extinct before it can all be studied.
And what if there is more to reality than is in our universe?
I think knowledge must be infinite.

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shesus

I agree with you that knowledge is different than comprehension. Bloom's taxonomy is a chart that states the different levels of learning. The bottom level is knowledge. The levels are knowledge, comprehension, application, analysis, synthesis, and evaluation. With these steps, however, eviltree's assumption that any idiot can plug numbers into a math problem does not work. The concept of Bloom's is that you cannot jump a step. Therefore, you cannot know a formula and then apply it without comprehending it first.
But back to the original question, I think that knowledge is infinite. First of all there are many things about the earth that we do not know. Supernatural, mathematical, scientific, psychological, medical...There are still species of animals and plants being discovered everyday. Only about 10% of the ocean has been explored, so there is a lot more to learn there. And who knows how much of the universe needs to be explored.
Even if we did find answers to all the ideas that we know we don't know, there will still be a lot of things that we don't even know we don't know. (If that makes sense)
When I was reading this question, I thought of Adams' Hitchhiker's Guide to the Universe, when they create the machine to find the answer to the universe and it was 42. Yet, they didn't even know the question. I think that knowledge will always be like that. Even when we find an answer, there will still be questions present.

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Hain

That is why the romantics had the right idea about natures. You can view a stunnnig painting by Frederick in my signiture, or if I've changed it: http://www.runegild.org/wanderer.jpg
Can you honostly tell me that when you gaze at this scene you do not feel something of the infinite grazing your conscience, almost tugging it to something more?

I believe though that the romantic idea of leaving everything else up to nature is silly. But I do like simplicity. However our society cannot change overnight. To understand is to evolve, their ideas of simplity are so very elegant and beautiful but lack the need to evolve. So I say this:

"The Romantics where half right: nature is the greatest teacher of simplicity. However, complexity is what with we apreciate and gain simplicity... As one understands complexity to simplicity, there is purity."

When I get my paper back from my English Prof, I will post the saying I finished my Romantic Period Essay with.

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pennywise121

[QUOTE=HoundstoothHero]Many epistemological arguments involve certainty in justification, and a prevailing view is that knowledge requires certainty to be absolute. Any doubt (or chance of doubt) necessarily prohibits knowledge.

My own view regarding knowledge gravitates toward what is referred to as the 'fallibilist' approach: it is impossible for us to achieve absolute certainty, and therefore any such high-standards approach to knowledge results in skepticism. What we as humans 'know' does not rely on absolute certainty, but rather on good enough reasons for believing a (necessarily true) proposition. G.E. Moore's response to skepticism also appeals to me: it is more reasonable to believe we at least know some things than to believe we know nothing./QUOTE]

You are talking about JTB principle truth. I have a belief that i can justify which turns out to be true. Can we truly call this knowledge? Moreover, we are looking at this whole thing in a very specific manner. From today's viewpoint, we would like to require certainty for knowledge, but none of us can even say why we do the things we do. If we say we know anything, it would seem to make sense that it would be about ourselves, but even that is questionable (see Festinger's work on misatribution of aroused states or Schacthter's work on conformity in group settings).

archpaladin

I think there are a lot of good statements going around here so I won't say much, except to offer a brief thought:

I think the available knowledge, in terms of facts, laws, systems of nature, and the like, are indeed finite. There are only so many things (albeit MANY things) to know. Even non-deterministic things can have their probabilities determined. However, the interpretation and application of said knowledge I believe is infinite. For humanity, there will always be a new way of looking at things and a new way of applying knowledge to a problem. I believe to say that interpretation of knowledge is finite implies that whoever is interpreting the knowledge is outside the realm of time, and is effectively God.