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My main character has access to the entire knowledge of humanity (note: This is year 4000s so they have much more than "our humanity"). He created another consciousness for himself; this new consciousness has limited capacity which is way way smaller than the entire humanities knowledge he has access to, so in the story he compresses this library of knowledge and puts it inside this new consciousness.

For more context he can't expand his capacity with servers or other data storage methods, only the capacity avaible is only that of his new consciousness.

He also doesn't have access to magic.

The main question is, if it is possible to compress knowledge infinitely? If not, what would the roughly smallest ratio you could compress information be?

He can use all science related methods be it digital or material.

Even though I said he is from year 4000s the answer doesn't have to be accessible in 4000s, time period is irrelevant to the question. I just want to know the possibilities.

EDIT - I have looked on my own, they say it's not possible to compress information infinitely, however the limit wasn't found, so I want a rather high estimate which I couldn't find.

My main character has access to the entire knowledge of humanity (note: This is year 4000s so they have much more than "our humanity"). He created another consciousness for himself; this new consciousness has limited capacity which is way way smaller than the entire humanity's knowledge he has access to, so in the story he compresses this library of knowledge and puts it inside this new consciousness.

For more context, he can't expand his capacity with servers or other data storage methods, the only capacity available is that of his new consciousness.

He also doesn't have access to magic.

The main question is: is it is possible to compress knowledge infinitely? If not, what would the roughly smallest ratio you could compress information be?

He can use all science related methods be it digital or material.

Even though I said he is from year 4000s the answer doesn't have to be accessible in 4000s, time period is irrelevant to the question. I just want to know the possibilities.

EDIT - I have looked on my own, they say it's not possible to compress information infinitely, however the limit wasn't found, so I want a rather high estimate which I couldn't find.

I have a MC that has access to the entire knowledge of humanity (note: This is year 4000s so they have much more than "our humanity"). He created another consciousness for himself, this new consciousness has limited capacity which is way way smaller than the entire humanities knowledge he has access to, so in the story he compresses this library of knowledge and puts it inside this new consciousness.

For more context he can't expand his capacity with servers or other data storage methods, only the capacity avaible is only that of his new consciousness.

He also doesn't have access to magic.

The main question is, if it is possible to compress knowledge infinitely? If not, what would the roughly smallest ratio you could compress information be?

He can use all science related methods be it digital or material.

Even though I said he is from year 4000s the answer doesn't have to be accessible in 4000s, time period is irrelevant to the question. I just want to know the possibilities.

EDIT - I have looked on my own, they say it's not possible to compress information infinitely, however the limit wasn't found, so I want a rather high estimate which I couldn't find.

My main character has access to the entire knowledge of humanity (note: This is year 4000s so they have much more than "our humanity"). He created another consciousness for himself; this new consciousness has limited capacity which is way way smaller than the entire humanities knowledge he has access to, so in the story he compresses this library of knowledge and puts it inside this new consciousness.

For more context he can't expand his capacity with servers or other data storage methods, only the capacity avaible is only that of his new consciousness.

He also doesn't have access to magic.

The main question is, if it is possible to compress knowledge infinitely? If not, what would the roughly smallest ratio you could compress information be?

He can use all science related methods be it digital or material.

Even though I said he is from year 4000s the answer doesn't have to be accessible in 4000s, time period is irrelevant to the question. I just want to know the possibilities.

EDIT - I have looked on my own, they say it's not possible to compress information infinitely, however the limit wasn't found, so I want a rather high estimate which I couldn't find.

I have a MC that has access to the entire knowledge of humanity (note: This is year 4000s so they have much more than "our humanity"). He created another consciousness for himself, this new consciousness has limited capacity which is way way smaller than the entire humanities knowledge he has access to, so in the story he compresses this library of knowledge and puts it inside this new consciousness.

For more context he can't expand his capacity with servers or other data storage methods, only the capacity avaible is only that of his new consciousness.

He also doesn't have access to magic.

The main question is, if it is possible to compress knowledge infinitely? If not, what would the roughly smallest ratio you could compress information be?

He can use all science related methods be it digital or material.

Even though I said he is from year 4000s the answer doesn't have to be accessible in 4000s, time period is irrelevant to the question. I just want to know the possibilities.

I have a MC that has access to the entire knowledge of humanity (note: This is year 4000s so they have much more than "our humanity"). He created another consciousness for himself, this new consciousness has limited capacity which is way way smaller than the entire humanities knowledge he has access to, so in the story he compresses this library of knowledge and puts it inside this new consciousness.

For more context he can't expand his capacity with servers or other data storage methods, only the capacity avaible is only that of his new consciousness.

He also doesn't have access to magic.

The main question is, if it is possible to compress knowledge infinitely? If not, what would the roughly smallest ratio you could compress information be?

He can use all science related methods be it digital or material.

Even though I said he is from year 4000s the answer doesn't have to be accessible in 4000s, time period is irrelevant to the question. I just want to know the possibilities.

EDIT - I have looked on my own, they say it's not possible to compress information infinitely, however the limit wasn't found, so I want a rather high estimate which I couldn't find.