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"The more you know, the less you know" Equati

Ren
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1/8/2012 5:30:50 AM
Posted: 4 years ago
So, I was on this other forum I like to hang out at sometimes (INTP Central), and someone came up with an intriguing brain teaser that I wasted so much time on, I decided to capitalize on its (perceived) worth and share it here as well.

The OP was like this:

Hi,

I saw this one forums member which I don't remember who had his signature as "The more you know, the less you know". And since then I kept pondering the implication of it.

This is what I believe it means:
The more (in term of amount) you know, the less (in term of proportion) you know.

I had taken an introduction to logic class, I'd have it proved logically.

This...is an incomplete Syllogism...an enthymeme.
What lacks is that....um, insight.

Premise 1: (If)The more knowledge, (then)the better insight.
Premise 2: (If)The better insight, (then)the lesser proportion of the known.
Conclusion: (If)The more knowledge, (then)the lesser proportion of the known.

Implication: The more you know, the less you know.
Proved.

Perhaps this justifies, perhaps it does not.

--------------------

Now I am more interested whether we can make an equation out of it? From what I know, there might be these factors involved:

A = All knowledge
K = The known (to self)
U = The unknown (to self)
P = The proportion of the known
T = Time

Derived:
# A = K+U
# A(T) //A is a function of T, I believe A increases as time increases
# P = (constant)*1/K

Could anyone help coming up with an equation to explain this? Is it possible?
Feel free to discuss. Cheers.

I had two separate responses, and he had one, so I'll post them below separately.

The last one will be my final conclusion.

Are there any math addicts out there? I know I confined myself to relatively simple mathematical concepts and such, so perhaps some critical analysis can help determine whether I even made sense.
Ren
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1/8/2012 5:31:35 AM
Posted: 4 years ago
I replied:

Okay, okay, let's give it a try.

So, let's see.

First, we have to assign variables.

K will be your overall knowledge. k will be your previous knowledge. Therefore, your increase in knowledge would be [delta]K.

[delta]K = k + -- alright, here, we clearly need something for new knowledge -- n.

[delta]K = k + n.

That will be our statement for learning something new.

However, the more you learn, the less you know overall.

Therefore, n must be negative, first and foremost.

Then, it must increase by a given magnitude. That magnitude, as we agreed, is the amount of new knowledge necessary to fully understand the knowledge you just received. That can acceptably translate as other new "things" that are generally unknown in nature. Each new thing would also compound the amount of new things necessary, meaning that the increase would be exponential. The unknown things, we'll call u.

So, what we have here is:

[delta]K = k - n^(u)

Which translates as, an increase in knowledge causes a negative increase in the amount of knowledge you have overall, due to the amount of unknown knowledge you must have in order to achieve full understanding.
Ren
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1/8/2012 5:32:16 AM
Posted: 4 years ago
He said:

Looks really great, but I don't think this can be negative.

I like the [Delta]K part. Also the n^(u) seems really convincing.

However, I doubt that it's a minus sign in the middle there. Could it be a relationship in some other way that doesn't result [Delta]K in negative.

I believe in this context, we need a change in the proportion of knowledge, not the rate of change([Delta]K). But still [Delta]K could be used as a part of the equation.
Ren
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1/8/2012 5:33:59 AM
Posted: 4 years ago
So, I concluded:

Wow.

This is one hell of a brain teaser.

So, I thought about this and started writing down some notes to keep track of my thoughts and ended up with 4 pages of written notes, perhaps coming to a logical mathematical conclusion that states that perceived knowledge suggests that every time you learn about a subject, you have substantive proof that you do not understand that subject. Therefore, the more you know, the less you know.

I hope that's not retarded. Alright, let me see if I can post these notes. If they're just a bunch of nonsensical ramblings, please don't assume I'm just insane. :\

I'm just going to copy my roughly written notes word-for-word (I'm not sure even I understand them).

x is a Concept

If we assume x is a concept, then y can be one unit of knowledge regarding that concept. This "unit" can be accepted as subsidiary concepts with equal capacity to be understood, and which can be understood within an observer's capacity. z can be how many y's exist in x. Therefore:

x = yz.

Random Potential Aspects

There is a random number of other potential aspects (y) of an unknown concept (x) once it's encountered. However, these aspects are limited by how many aspects (y) a concept comprises (z). Therefore, the number of new y revealed due to an increase in y by 1 is:

1/(x-k)!

Where x is the concept and k is the aggregate aspects of x already known by the observer.

Based on that statement, all aspects that relate to x (dividing it into its base parts) is:

x/[1/(x-k)!] = y

Therefore, an aggregate of x can be expressed as:

z[1/(x-k)!]

And the potential number of other aspects of x once x is encountered is:

1/[1/(x-k)!]

Effectively meaning that:

yz = 1/[1/(x-k)!]

Perception of What x Comprises

Now, the perception of x by an observer cannot be x, because yz is unknown. Therefore, yz is undefined in related to the perception of x. Accordingly, the perception of x needs another variable -- we'll call it p.

At first p = 1, because the only concept (y) we know to comprise x is x, and that means that there is only 1 y, making z = 1. Therefore, it would be:

x = 1(1).

However, when we learn something new, z = {1/[1/(x-k)!]}/y

So:

p = {1/[1/(x-k)!]} + k

(as a reminder, "k" is what you already know).

Proportion of "Knowing"

k = what you know

x = yz

yz - k = what you need to know to arrive to x.

Therefore, the statement "the more you know, the less you know" refers to as relationship between what you know and everything there is to know, or:

k and (yz - k)

The more you know (or, the greater k is), the more you need to know (or the greater yz - k is).

However, since yz does not exist in p, neither does yz - k.

The Relationship Between z and Increases in k

y = 1 unit of knowledge
k = the amount of y known
yz - k = what you need to know to arrive to x, but this is undefined in terms of p.

An increase of y by one also increases p by {1/[1/(x-k)!]}, so:

p = {1/[1/(x-k)!]} + k

Learning

Learning is an increase in k.

When k increases p increases by definition.

An increase in p suggests that learning something new about x results in a deviation from p as it draws closer to the constant x.

So, [delta]p is the amount you didn't know about x until you began learning about it, proving that p =/= x.

So, every time you learn something new, you get proof that p =/= x.

So, the more you know, the less you know.

Did any of that make any sense at all?

I think it made sense... :s
Ren
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1/8/2012 5:38:47 AM
Posted: 4 years ago
At 1/8/2012 5:33:59 AM, Ren wrote:

p = {1/[1/(x-k)!]}yz + k

y = 1 unit of knowledge
k = the amount of y known
yz - k = what you need to know to arrive to x, but this is undefined in terms of p.

An increase of y by one also increases p by {1/[1/(x-k)!]}, so:

p = {1/[1/(x-k)!]}yz + k

Fixed.
Stephen_Hawkins
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1/8/2012 5:51:18 AM
Posted: 4 years ago
Maths proves logic valid, not true, unfortunately. It will pinpoint the areas where the logic is axiomatic but not where the general truths are. So the problem is here:

Premise 1: (If)The more knowledge, (then)the better insight.
Premise 2: (If)The better insight, (then)the lesser proportion of the known.
Conclusion: (If)The more knowledge, (then)the lesser proportion of the known.

P1 =/= lead to P2 in all circumstances, where the knowledge is the correction of a previous falsehood.

C1 becomes the problem though, as we can use an absurdum to prove this.

Let Y be a finite positive integer representing the total possible knowledge theoretically achievable on an issue.

Let X be knowledge (meaning [delta]X = new information and X+[delta]X = new stance of knowledge).

For C1 to be true, then Y > X.

However, X = Y in theory, as one may possibly know everything on a specific issue, and all restrictions are ones that may be overcome.

ALSO, false information on an issue, which actually is part of a different issue, is information still but simply false. Therefore X + [delta]x > Y.

This is going to be quite confusing at first, at least, this part. But if we assume the knowledge is with bricklaying, then a bricklayer who knows everything about bricklaying may not know everything about logic, or discerning information from the false information. A scientist, who knows everything about the scientific method, may see merit in Lamarckism where it doesn't exist because he doesn't know enough about discerning information or the empirical evidence against it.

Therefore X > Y in theory.
Give a man a fish, he'll eat for a day. Teach him how to be Gay, he'll positively influence the GDP.

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Ren
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1/8/2012 6:24:22 AM
Posted: 4 years ago
At 1/8/2012 5:51:18 AM, Stephen_Hawkins wrote:
Maths proves logic valid, not true, unfortunately. It will pinpoint the areas where the logic is axiomatic but not where the general truths are. So the problem is here:

Premise 1: (If)The more knowledge, (then)the better insight.
Premise 2: (If)The better insight, (then)the lesser proportion of the known.
Conclusion: (If)The more knowledge, (then)the lesser proportion of the known.

P1 =/= lead to P2 in all circumstances, where the knowledge is the correction of a previous falsehood.

C1 becomes the problem though, as we can use an absurdum to prove this.

Let Y be a finite positive integer representing the total possible knowledge theoretically achievable on an issue.

Let X be knowledge (meaning [delta]X = new information and X+[delta]X = new stance of knowledge).

For C1 to be true, then Y > X.

However, X = Y in theory, as one may possibly know everything on a specific issue, and all restrictions are ones that may be overcome.

ALSO, false information on an issue, which actually is part of a different issue, is information still but simply false. Therefore X + [delta]x > Y.

This is going to be quite confusing at first, at least, this part. But if we assume the knowledge is with bricklaying, then a bricklayer who knows everything about bricklaying may not know everything about logic, or discerning information from the false information. A scientist, who knows everything about the scientific method, may see merit in Lamarckism where it doesn't exist because he doesn't know enough about discerning information or the empirical evidence against it.

Therefore X > Y in theory.

You mentioned something brilliant that I completely forgot to consider -- false information. I must think on this further.

How would one say false information is delivered? Could we apply a Planck's Constant to information -- say, the natural constant rate at which information is delivered -- and use this as a basis? Then, how would false information behave? Would you say that false information is due to persuasion and thus, has a greater intensity than true information? Although, some false information is happenstance. One way or another, this could prove that, using the y variable from my example, and f as false information,

f > y

We would just need to figure out the proportion to which f is greater and apply that (say, persuasion and happenstance considered, it's .67 times stronger than y), then we could just assume that f = .67y by definition. This way, it can fit into the equation. ^_^
Ren
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1/8/2012 6:36:53 AM
Posted: 4 years ago
Going over it, I noticed I screwed up a bit of the math.

The actual final equation is:

p = {1/[1/(x-k)!](z[1/(x-k)!])}yz + k;

or

{1/[1/(x-k)!](z[1/(x-k)!])}^2 + k
Oryus
Posts: 8,280
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1/17/2012 3:28:03 PM
Posted: 4 years ago
Not to rain on your math/logic parade, I'm super into it, but the statement seems to mean to me that perhaps the more knowledge you have, the more you know that the breadth of possible knowledge is WIDE- so wide that you realize how very little you actually know and how very little you can possibly know in the grand scheme of things.

You know?

That seems pretty similar to what you're saying.
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Ren
Posts: 7,102
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1/17/2012 6:42:24 PM
Posted: 4 years ago
At 1/17/2012 3:28:03 PM, Oryus wrote:
Not to rain on your math/logic parade, I'm super into it, but the statement seems to mean to me that perhaps the more knowledge you have, the more you know that the breadth of possible knowledge is WIDE- so wide that you realize how very little you actually know and how very little you can possibly know in the grand scheme of things.

You know?

That seems pretty similar to what you're saying.

Rain?

Looks like sunshine to me.

Very interesting -- so, it made sense to you???
Ren
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1/17/2012 6:59:20 PM
Posted: 4 years ago
And yes, I consider your interpretation rather accurate, and more effectively communicated than when I attempted to. :P
Ren
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1/18/2012 8:26:33 AM
Posted: 4 years ago
At 1/17/2012 6:42:24 PM, Ren wrote:

Very interesting -- so, it made sense to you???

By the way, when I asked this question, it wasn't because I'd be surprised at any sort of mathematical aptitude; it was more that I wasn't sure (and still am not) whether what I wrote was sensible.

Just thought I'd make that clear. ^_^
Oryus
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1/18/2012 11:20:28 AM
Posted: 4 years ago
At 1/17/2012 6:42:24 PM, Ren wrote:
At 1/17/2012 3:28:03 PM, Oryus wrote:
Not to rain on your math/logic parade, I'm super into it, but the statement seems to mean to me that perhaps the more knowledge you have, the more you know that the breadth of possible knowledge is WIDE- so wide that you realize how very little you actually know and how very little you can possibly know in the grand scheme of things.

You know?

That seems pretty similar to what you're saying.

Rain?

Looks like sunshine to me.

Very interesting -- so, it made sense to you???

haha well... unless it just means something way out of left field, I'm guessing that's what it is. Or maybe it is a koan- meant to incite an otherworldly moment of, "uh... what?"
: : :Tulle: The fool, I purposely don't engage with you because you don't have proper command of the English language.
: :
: : The Fool: It's my English writing. Either way It's okay have a larger vocabulary then you, and a better grasp of language, and you're a woman.
:
: I'm just going to leave this precious struggle nugget right here.