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What are the limitations of accumulating or storing knowledge in a binary system? For a more concrete question, can all knowledge information be represented by an infinite sequence of 1's and 0's or is there knowledge information that can't be represented in that way? And if all information is representable in that way does the same apply to knowledge?

Edited to correct some confusion between knowledge and information.

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    It's necessary to distinguish between representing and storing knowledge. I could say the sequence "1101" represents the Gettysburg Address, but it doesn't store anything at all. It might be considered meaningful to me or anyone else who knows that it represents the speech delivered by Lincoln. In the same way, let's agree that "101011" represents all the knowledge acquired by mankind. This illustrates the fact that representing knowledge in this way often fails to capture all the details that one might want to know about what is represented. – user3017 Dec 1 '17 at 14:48
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    That binary sequence adds up to 42...which means so long and thanks for all the fish! – Mozibur Ullah Dec 1 '17 at 14:52
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    I would say that knowledge cannot be represented. What can be represented or communicated is information. In order for our intellect to process information it must take a dualistic form that may be reduced to 1's and 0's. Information situated in this dualistic world is always relative and I suspect always reducible to binary representation. Knowledge is not at all the same thing, however, and may transcend the dualism that allows for a binary representation. in metaphysics a theory may state that 1 = 0, as when 'something-nothing' is taken to be an emergent and conceptual distinction. . – PeterJ Dec 1 '17 at 14:58
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    @PeterJ: 1=0 is also true in the zero ring; that bit of trivia isn't relevant to this question or to your comment but I found it entertaining. – Mozibur Ullah Dec 1 '17 at 15:21
  • Maybe I should have asked about information rather than knowledge. Based on the responses I understand that information is something like a physical representation of a truth and knowledge is something that exists in the mind. Having information is not the same as having knowledge and the inverse is true. But knowledge must be representable otherwise there would be no such thing as information. – Chris Dec 2 '17 at 1:00
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As I understand it, there are 3 parts to your question.
1) The only limitations are those imposed by the physical storage system/medium.
2) To answer the second part, one must distinguish between "internal" (individual) knowledge, and "external" knowledge (information).
All externalized knowledge (information) can be binary encoded, and therefore, can be stored in a binary system.
3) Any "internal" (individual) knowledge can not be accessed, therefore, can not be encoded or stored in a binary system.

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What are the limitations of accumulating or storing knowledge in a binary system?

Ali Ahmad Said Esbar is a Syrian poet who calls himself Adonis as a nod towards his pre-Islamic, pan-Mediterranean muses. I came across a poem of his on the divisions and choices that binary thinking imposes on us.

"Who are you, who do you choose, Mihyar?

Wherever you went, to God or the Devil,

one abyss comes, another goes,

and the world is a choice."

-

"I'll choose neither,

both are walls

both shutter my eyes.

Why would I replace one wall for another

when my sorrow belongs

to the one who brings light,

the sorrow of having known everything."

Of course, this is not the kind of 'binary system' that you are talking about; nevertheless, I think the poem is telling is something quite profound about the way thinking falls into these kinds of traps and why we should deny these traps for thinking (and for thinkers).

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People are probably not answering because this is not quite a redundant question, but the answer has been given many, many times here.

You might want to start from the broader question of whether it is in fact possible to express all knowledge in discrete symbols at all, under any kind of interpretation. Godel's Theorems suggest not.

Starting from the principles of First Order Logic, you can prove that any enumeration of all mathematical truths expressed in discrete symbols, given pretty much any means of interpretation at all, that includes the facts of arithmetic, is either incomplete, or contains contradictory information.

Extending this to higher-order more self-referential symbolism doesn't help. Anything that qualifies has to be either unsound, incomplete or ineffective. Meaning it contradicts itself, it fails to be able to express something true, or you there are reasonable statements about which you cannot determine whether they are true or false.

And that is just math. Many other domains of life reproduce math in its entirety, so none of them can be encoded this way.

It is ambiguous whether you can conquer this with non-discrete symbols. But if you did, you would need a non-discrete version of truth values. So you would surely not be able to represent those with zeroes and ones.

  • Saying something is ambiguous is in no way accepting it – jobermark Dec 2 '17 at 1:25
  • The question outright says binary, so the 1 and 0 it is talking about are discrete. If you mean something else, change the question. – jobermark Dec 2 '17 at 1:26
  • Isn't it easier to accept that there is some 1 that is entirely true? I'm also not convinced that 1 is always discrete. Gödel was concerned about the provability of a sentence, not necessarily its truth. Axiomatic reasoning is under attack from multiples sides though. Axioms are "self-evident truths", such as "heavier objects fall faster than light objects". – Chris Dec 2 '17 at 1:26
  • It may not be his main concern, but it Godel does establish what I said – jobermark Dec 2 '17 at 1:27
  • I agree that axiomatic logic is not most of knowledge, or even most of math, but it is surely a part, and if that part cannot be encoded, the entirety cannot be encoded. – jobermark Dec 2 '17 at 1:28
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Perhaps this question fits better on the math section.

There's no relation between the representation and the actual information.

You are trying to make a direct relationship between information and representation. A representation system approaches data on a different format than the original. So, if you want to represent the number decimal-9 in binary, it is just 1001. The information does not change at all. There are no limitations.

Perhaps your concern is related to the analog-to-digital (ADC) or reverse (DAC) conversion. A philosophical assessment: Theoretically, depending on the approach of your representation (e.g. using a high number of bits) you can get more resolution than reality.

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Knower knows knowledge in the sense that what all is known or is knowable by knower is the meaning of knowledge. Knowing is both by perception and hearsay. Information is the term generally used to denote or connote what is communicated or is communicable, referred to as hearsay or viewsay or audio-visual-say.

For knower to have and hold knowledge, information and communication, clearly it is necessary that the person has a mind, an intellect, a memory and is a 'self aware knower'. In addition the self aware knower needs to identify with a body with its brain and sense organs. But body, brain and sense organs are known similar to objects of knowledge such as of the world. They can be analysed separately from the person. Whereas, the mind, intellect, memory and 'self aware knower' are inseparable integral part of the concept of person. Knowledge, information and communication are also like objects and are analysable separately from the person. But nothing which is separable from person exists without the person who is inseparable from mind, intellect, memory and 'self aware knower.

Separable knowledge and information include what is communicated or is taken in as information by person. They appear only in mind of person, but can be represented by names and forms of objects by apparent separation from the person in the mind of the person. Visual and audible names, and forms that are used for representation of knowledge and information are called languages. They include morse code and binary digital language. Actions to create, communicate and know such languages require predisposition and latent tendencies in persons. Communicated visual forms and sounds of communication develop by habitual actions of body, brain and sense organs. The names and forms held unknown in communication are known only in mind and not outside it on blackboards, computer screens or TV monitors. Communication requires mind, intellect, memory and 'self aware knower' developed by habitual actions of body, brain and sense organs from childhood on. Such actions are generally termed training and education. The training and education needed to create missing predispositions and latent tendencies of the 'self aware knower' may take more than one lifetime to form; even though the self aware knower is unaware of his continuity over many lifetimes.

The question about limits to representation of knowledge and information in binary language cannot be answered in any philosophy lacking a fuller understanding of the person and his or her predispositions and latent tendencies.

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