Is knowledge infinite?

[darkrobe]

Im not sure what is being argued here. but it sounds interesting so im going to post.

[EmeraldTiger]

My answer is: For most people knowledge is or seems infinite. Those that have the means to explore and expand what they know, may think there is and end to knowledge, and will attempt to achieve that end.

I think for myself though and say, I do not have enough information to make an assumption either way.

[maverixk]

Well , this depends on what you mean by knowledge...in numbers, yes there is an infinite number of numbers, or concepts.
At the universal level, there is a finite, while very, very large, set of information describing each and every particle, which changes every moment.

[ralouf]

Infinite obviously and even more for a human with his very little capacity (short life, bad memory etc..)

[Zeru]

Infinite obviously and even more for a human with his very little capacity (short life, bad memory etc..)

We are not talking about "a lot", we are not talking about "more than we can ever possibly learn". We are talking about an actual infinity.

Let's look at History for example.
The Earth has existed for a limited time and it will exist for a limited time. It also has limited space. So the total number of possible historical facts is finite.
Of course it's a lot. Perhaps it's more than we could ever learn (assuming we would even want to keep track of all possible events and somehow learn about the events that we already missed). But still, History of Earth is finite

If something in this thread is obvious, it's obvious that you are not correct.

This is a really cool question. 5 stars for the thread from me

[Zeru]

Heh, refuting my own argument.

History is a bad example. I forgot just how incredibly dense both time and space are. Allow me to explain. I will make a couple of methods of collecting data and then count just how much data we will have.
Let's begin with:

We write down the most important fact from the history of the planet in a single year. That way we receive: 1*1=1 historical fact per year.
1 is less than infinity, let's do a little more work.

The most important event from a continent in a single month. That way we get: 7*12= 84 hf/y
Closer, but still not infinity.

How about 1 event for each country per day? Well. The amount of countries vary over time (the amount of continents vary over time as well), so the model is pretty inaccurate, but let's just go on with it for simple calculations.

~200 * 365 = 73 000 hf/y

Still far from infinity.

Each state per hour? Each city per minute?

Even if we were to write down the most important event of each centimetre^2 each second, it would still not be infinity.

However.

Let's write down the most important event from each infinitely small amount of space per infinitely small amount of time.

Bingo. We don't even need both of them to be infinitely small at the same time. Even one of them is enough. Infinity * a = Infinity, if a>0.
This fact got through my mind when I wrote the post above but I quickly discarded it with a "We won't be able to do that". But then I wondered "How do I know that?". So in conclusion my example is bad.


This is why I like this thread so much. You can just think about it deeper and deeper. I would like to add an additional question to the opening post.
Is there a field of study that, for 100% certainty we can say, is finite?

[OldTrees]

Is there a field of study that, for 100% certainty we can say, is finite?

Probably depends on how small a topic still counts as a field. Does the game theory of RPS or the Prisoner's dilemma count as a field?

Even those sub fields can be infinite in the case of repeated games.

[Pineapple]

Refuting Zeru's most recent post...
"infinity" * A ≠ "infinity", because infinity is a concept and not a discrete number that is bound by the rules of algebra.

As a counter-example, assume "infinity1" is the number of elements in the set of all positive odd integers, i.e. "1, 3, 5, 7, ...", and "A" is the constant "2".
Now, let's assume "infinity2" is the number of elements in the set of all positive integers, i.e. "1, 2, 3, 4, 5, 6, 7, 8, ...".

"infinity1" * A ≠ "infinity1"
However
"infinity1" * A = "infinity2"

The fatal assumption you make in your argument is that knowledge can be measured by this unit called "facts" and consequently that the proposition "knowledge is infinite" is true if and only if the number of "facts" is infinite.

However, think about this:
It takes me exactly 24 hours to walk a distance of 60 km, for a total of 60km.
That means that it takes me 2 twelve-hour parts of 30 km, for a total of 60km.
And 3 eight-hour parts of 20 km, for a total of 60km.
And 4 six-hour parts of 10 km, for a total of 60km.
...
And an infinite number of infinitesimally short parts of infinitesimally small lengths, for a ... total time of 24 hours and a total length of 60km.

Although the number of parts may change, the total does not.
With your reasoning, our existence is infinite. Sure, we are existing at an infinite number of points on the line that is our life, but the time that we spend here, the thing that we actually want to measure, is a finite, discrete value.

As for my own answer, I raise Determinism: There can only one [knowledge] and, if that fails, Logical Positivism: We're just screwing up our English.

[OldTrees]

1) The infinite set of the positive even integers is the exact same size as the infinite set of positive integers. I can match 1:1 every member N of the first set with a member N/2 of the second set and vice versa.

2) Zeru was not arguing that our lives had infinite duration. Rather he was arguing that our finite lives were composed of infinite events/moments all of infinitesimal duration.

3) Even if Determinism is the case there will still be an infinite amount of infinitesimal moments.

[Pineapple]

1) The infinite set of the positive even integers is the exact same size as the infinite set of positive integers. I can match 1:1 every member N of the first set with a member N/2 of the second set and vice versa.

2) Zeru was not arguing that our lives had infinite duration. Rather he was arguing that our finite lives were composed of infinite events/moments all of infinitesimal duration.

3) Even if Determinism is the case there will still be an infinite amount of infinitesimal moments.

1) rawr.

2) Yet my point still stands. Zeru had yet to prove that the "number of events/moments" in the analogy was what we should be measuring. It's just as likely that what should be measured is the "duration". Number of facts and amount of knowledge, respectively.

3) Building from my point above, knowledge never changes. There has always been and will always be one pool of knowledge whose properties cannot be modified. Who is it to decide whether a puddle of water is made up of one puddle of water or millions of raindrops of water?

[Zeru]

1) Isn't math fun?
2) No I don't. I took a very specific field of study - History. And your analogies completely fail. The more details you have, the more accurate is your History.
Compare method (1) and (2).
In (1) you have 1 event per year. In (2) you have 84 events per year.

By your reasoning, those 84 events have the same significance as that 1 event from (1). But that is obviously flawed. "The most important event from the world" belongs to the set of 84 events. If an event is "the most important in the world", it is also "the most important in it's continent". So the effect of using method (2) is equal to the effect of (1) + 83 completely new events.

Seriously. How could you think that making almost no records whatsoever is equivalent to making incredibly precise ones?

3) Achilles paradox does not work here. I have over 2000 years advantage over their Maths. I thought out the second post a lot more carefully than the previous one.
And well.. a puddle is both a puddle and and a combination of many atoms. In the same way 1 kg = 1000 g. History does not work like that. The more effort you put to record facts, the better is your History.

4) I had a conversation on this topic with someone. Try to think about Biology or Music. Are they finite?

[ralouf]

Maths are very fun indeed I really enjoy it.

Too lazy to read the rest and this discussion is annoying for me