Could there ever be an end to knowledge?

[geordief]

Is knowledge merely ''knowing'' information, or is it actually understanding it enough to be able to teach someone else about it

You can memorize a fact but as soon as you memorize the context (you do this by arranging the fact and related facts in your head so that they "make sense") you have ,by my definition "understood" the fact.

Note that this does not mean you have correctly understood the fact ; if the context you place this fact in is somehow flawed to an outside observer(or to yourself at a later time) , then it will appear that you have misunderstood the fact.

This is why ,I imagine you are advised to read a text more than once if you are taking an exam on it. The first time is to line up the "facts" in the memory and subsequent readings are to make an ordered sense of them -after which time the facts are remembered in different ways and contexts.

When I was a more prolific reader I well remember reading whole pages only to realize I had taken nothing of consequence in. I had simply read the passages by rote.

 

[Yazata]

Can math solve for uncertainty, though?

Math and cognate subjects like logic and statistics are certainly trying. Reasoning in conditions of uncertainty is an active area of research, with many practical applications.

Probability and statistics address uncertainty. So does fuzzy thinking, in the mathematical sense.

In conventional logic every meaningful proposition is either true or false. In fuzzy logic, every meaningful proposition has a numerical value between one and zero, that can easily be interpreted as degree of certainty, likelihood or plausibility.

Fuzzy set theory does the same thing. In the case of regular sets, membership in a set is a bivalent property: member of the set/not a member of the set. In fuzzy sets, each element has a numerical degree of membership, which once again can be interpreted as certainty or likelihood

Of course finding a formal way to assign initial numerical weights might be a problem.

Another way to address similar ideas is evidence theory. This is an extension of Bayesian statistics applied to what it calls 'belief functions'.

https://en.wikipedia.org/wiki/Dempster–Shafer_theory

https://en.wikipedia.org/wiki/Bayesian_probability

 

[geordief]

Fuzzy logic is no help in quantum mechanics,is it?

 

[Dywyddyr]

I doubt that there could be an end: Heisenberg (for one) puts limits on what can be known - that suggests that there will be things that can't be. So at best all we could do is know everything that could be known, rather a come down from "knowing everything".

 

[geordief]

If we restrict the area to be known , is there an area small enough so that we can say that we know everything about it . We can restrict the time involved too . Say my teacup for the next 5 minutes . Will we ever run out of observations that can be made with respect to it?

 

[Yazata]

Fuzzy logic is no help in quantum mechanics,is it?

I can certainly imagine using probabilities squeezed out of the Schroedinger equation as a way of assigning weights in a fuzzy logic scheme.

That's above my pay-grade though. (I'm just a layman in physics and math.)

For one thing, I'm not sure how logical contradiction works in fuzzy logic. It seems at first glance that propositions that would seem to contradict in conventional logic might be able to coexist in fuzzy logic, if each one has a likelihood of less than one. (The cat being alive, the cat being dead.)

 

[Yazata]

If we restrict the area to be known , is there an are small enough so that we can say that we know everything about it . We can restrict the time involved too . Say my teacup for the next 5 minutes . Will we ever run out of observations that can be made with respect to it?

You would have to limit how closely you look at your teacup too. If matter is infinitely divisible, with more and more detail the deeper we penetrate into the microscale, then even a speck of dust might turn out to be infinitely complex like a Mandlebrot set if we had an infinite microscope.

Quantum mechanics may or may not place limits on that kind of microscale detail, I guess.

 

[C C]

If we restrict the area to be known , is there an area small enough so that we can say that we know everything about it . We can restrict the time involved too . Say my teacup for the next 5 minutes . Will we ever run out of observations that can be made with respect to it?

The natural occurring version of ambiguous information presents the possibility of conceiving non-uniform patterns in multiple ways. Everyday examples (in a purely visual context and also rubbing shoulders with pareidolia) would be the rival perceptions of what a set of clouds can look like or what objects and scenes can be discerned on the random surfaces of certain types of old ceiling and floor tiles. Such sensory perspectives themselves become less relevant in systematic enterprises where measurements, device detections, and abstract accounts come into play.

However, there's probably a human cognitive limit to how many interpretations both the macroscopic and microphysical content of a teacup could have. Not to mention the narrower degree of what a particular science discipline's pre-established standards would accept or define as "knowledge" interesting to it; as well as the selective-ness and functional boundaries of what can be measured by the investigative instruments employed.

Even if the teacup content had an endless sequence of nested domains, the Planck level is where meaningful territory supposedly ceases for human apprehension / intellect.

Also, a situation of "infinite amount" that was also declared a simultaneous and completed condition would be a contradiction. By being completed it is actually a finite amount (no matter how staggeringly vast the count of its individual distinctions is). To be endless in quantity such must be perpetually incomplete and either constantly or intermittently "adding more" or "dividing into more". In turn, the latter would seem to have the consequence of a universe with loose ends -- it wouldn't be an internally coherent and closed system where relationships wrap themselves neatly up at some point or feed back into other, existing ones. Always futilely waiting on "more" via change or the future to resolve its dangling issues in a non-finite context (which the latter by its character wouldn't allow).

 

[Magical Realist]

"If the doors of perception were cleansed everything would appear to man as it is, infinite."--William Blake

 

[exchemist]

I agree about the 3 -body solution. I thought (=assumed ) it had been solved in decent if complicated formula. I was obviously mistaken.

Sorry I thought FOR was a common abbreviation for Frame of Reference.

Is the concept of an FOR used or potentially usable in QM ? (I know you are not an expert in QM but you know more than me)

Ah yes, thanks. It could be, but probably used mostly in relativity, about which I know very little indeed. I know a bit about atomic and molecular QM, having read chemistry, but don't claim to know as much about it as a physicist, obviously.

I think there are number-crunching approximations for the 3 body problem that work quite well, but you may be right about it. I'd need to look it up. I do recall the difficulty theoretical chemists have in modelling exactly any molecule more complex than the hydrogen molecule ion, (i.e. H2+ : 2 protons and one electron, so 3 bodies).

In chemistry one almost always deals with approximations, because real live atoms and molecules are inconveniently complicated for applying the rules that the physicists use. This may be why I view this topic in the way I do.

 

[exchemist]

lol I suppose so.

So, back to the original question, could there ever be an end to knowledge? If we go with merely knowing ''of'' things, then probably not, but knowing things enough to explain them to others, then yes. Or we could have a hypothetical scenario where every human being alive right now has the learning capacity and IQ to ''understand'' all possible things, there still could be an end to knowledge, because as the universe evolves and changes, new things will be discovered about it and thus even the brightest person, couldn't 'know it all.' Not even you, Dywyddr lol

Exactly. The existence of change seems to me to preclude an end to knowledge.

I am reminded of Wowbagger the Infinitely Prolonged, whose self-imposed mission is to insult every creature in the universe - even though it is logically impossible.

 

[Write4U]

Mathematics cannot solve for uncertainty in all cases. The Uncertainty Principle in Quantum Mechanics is not the only example. Chaos Theory is another (the one about the butterfly's wing leading to a tropical storm, etc etc). The "Three Body Problem" is a third. No doubt there are many other examples.

It seems that the behaviour of the physical world cannot, even in theory, be exactly determined by mathematical calculation.

Could it be that apart from *constants* the ever changing dynamical nature of spacetime actually prevents us from mathematically predicting the future with 100% accuracy?

I still believe that everything works by mathematical functions, but the sheer number of interactions makes it impossible to *account* for all the mathematical functions that may be *in play* at any given time.

Terms Used in Equations,

Here are the terms used in equations for addition, subtraction, multiplication, and division. These terms include augend, addend, sum, subtrahend, minuend, difference, multiplicand, multiplier, product, factors, dividend, divisor, quotient, and remainder.

are all components of the universal mathematical functions under different dynamical conditions.

Weather, rivers, oceans, and the Pilot Wave function itself, all have so many dynamical variables that it is impossible to predict their *state* at any given moment. All we can ever measure with high confidence are the results of the dynamical functions.

 

[wegs]

You can memorize a fact but as soon as you memorize the context (you do this by arranging the fact and related facts in your head so that they "make sense") you have ,by my definition "understood" the fact.

Note that this does not mean you have correctly understood the fact ; if the context you place this fact in is somehow flawed to an outside observer(or to yourself at a later time) , then it will appear that you have misunderstood the fact.

This is why ,I imagine you are advised to read a text more than once if you are taking an exam on it. The first time is to line up the "facts" in the memory and subsequent readings are to make an ordered sense of them -after which time the facts are remembered in different ways and contexts.

When I was a more prolific reader I well remember reading whole pages only to realize I had taken nothing of consequence in. I had simply read the passages by rote.

Back in college, I had short term memory, strictly memorizing for the sake of test taking. When it comes to math for example, a subject I really struggled to do well in, I didn't retain one thing. Well, maybe ONE thing. But, it simply didn't matter to me, I wasn't naturally cut out to understand math (some people are, I believe this), and therefore, I needed to do well on my tests, so I just studied to understand it for the short term. So, did I really understand it? I received B's in math mostly through high school and college, but if one doesn't retain the knowledge, does that even count? lol

History, Science, English...all of those subjects were much more interesting and therefore, I've retained that knowledge.