One of the most treasured defining characteristics of information is its huge range of forms. During processes its form can change, e.g. during transportation, storage, and direction of actions. This is common knowledge in today's era of personal computing devices. It's accurate too for older forms of information such as telegrams and letters, of course.
In any form handled by any process, people would certainly prefer to not lose their valued information along the way. They wish to get/reconstruct the information that went through the process(es). Acceptable forms and processes are reversible. There should be a method to access the information by inverting the processes and forms—not necessarily into the original form but into a form that holds the same information.
Reversibility in turn is restricted by the amusingly named pigeonhole principle: whenever someone is placing mail into the numerous compartments of an old-fashioned desk, at least one compartment must have two or more letters whenever there are more letters than compartments. This principle is more general and useful than it seems because the difference in quantity is the sole condition. It applies to all kinds of sets and set members. When set B has fewer members than set A, then a one-way relationship directed from each member of A to one member of B requires that two or more members of A have the relationship to a member of B. (Note that sets A and B can be uncounted as long as someone knows that B's count is less than A's; mathematicians can exploit this principle on two infinite sets like the sets of integers and irrational numbers.)
The restriction on reversibility becomes immediately apparent by picking an element of B and asking which single element of A has the one-way relationship to it. The pigeonhole principle decrees that depending on the element of B someone happens to pick, there could be at least two possible answers. That information is gone. Strictly speaking the one-way relationship isn't reversible. An English letter substitution cipher conceals a message (poorly) by substituting a different letter for each. It's a one-way relationship between the letters of the source's plain alphabet to the letters in a jumbled "cipher alphabet". This relationship is rapidly reversible by the message's recipient: if plain E goes to cipher J, then cipher J goes to plain E.
But if the cipher alphabet has 18 letters—the sender has to type on a keyboard with missing keys?—then the recipient would have more trouble despite having the key. Then the pigeonhole principle guarantees that a letter in the cipher alphabet was substituted for more than one letter in the plain alphabet. After enciphering the message "the quick brown fox jumps over the lazy dog", one cipher letter might occur five times in the sent message. Maybe A and B and C and H are all substituted by I. Or maybe T and U and W are all substituted by F. The recipient might still be able to use context and trial and error to deduce the plain message, but the cipher is less reversible. Information of the distinctions between A/B/C/H or T/U/W has been lost. If the information were a picture instead, perhaps it would be smudged or have fewer shades of color. If it were a song, perhaps there would be a smaller gap between its quiet and loud sections.
The inescapable upshot is that anything that processes information without losing distinctions needs to have the relevant capacity, i.e. the minimum number of representative states. Yet this need doesn't demand that one object has all the states. For instance, one object of 255 states can be replaced with eight cooperative objects which have two states, named "0" and "1". The first state can be the sequence 00000001, the second 00000010, the third 00000011, and on and on. This is equivalent to numbering each input state in binary numbers. The individual binary digits are the familiar bits. Objects with few states, but massively connected together, can successfully absorb and emit a multitude of informative distinctions. People weren't the first to notice this. DNA is a famously excellent form of information built from sequences of four bases, A, C, G, T.
None of the preceding is controversial. Everybody admits that the information capacity of a year old SD card can be different than a 10 years old SD card with identical dimensions. The increase in the number of bits isn't magic. The one year old card's innards in total have more states available than the 10 years old card, probably thanks to the continuing miniaturization of components.
The endless conflicts begin when people transfer these analyses to the most prized conduit of information of all: the human brain. This topic has a perennially popular alternative that could be labeled the bottomless pocket of bits. In this alternative, it's assumed that the brain isn't capable of managing the bits passed to it. So the bits "really" go in and out of an incorporeal bottomless pocket, which is assumed to augment the brain's memory and abilities by inscrutable mechanisms.
The image of a bottomless pocket has made countless appearances in fiction. Animated characters have pulled object after object from their pockets, as if the objects expand and contract on command. Because the object pulled out is frequently a big mallet, the internet word for where these objects come and go is "hammerspace". Games containing puzzles about acquiring and using items have expansive "inventory lists", which hold more items of more sizes and weights than the character in the game could hold in their pockets. The handy convenience is undeniable. There is at least one equally well known detrimental example of an infinitesimal hiding place: wherever the missing socks go when the clothes dryer finishes running.
A justification for the idea of bottomless pocket of bits might be the assumption that some of the stuff in the brain can't be bits like the rest. So this inexpressible stuff resides in the pocket. That is to say, bits come in, divert to the pocket where this inexpressible stuff does some advanced work, and then the product bits come out in some form like changed behavior. The suggestion is that although the information coming from the senses is a believable stream of unremarkable bits, "deep" phenomena, such as abstract principles and words and hunches and wishes and empathy and kinesthetic skills and pattern observations, etc., etc., just cannot be translatable into normal boring bits. The hope is that existence in the super-special bottomless pocket permits different rules.
The problem is that this suggestion fails confirmation. These deep phenomena are observed to be too similar to other information in the brain. They're either instinctive or gradually learned and may be disrupted by various ailments. Some people are born without them or have a lot of difficulty developing them. They're heavily customized by the lifelong environmental, cultural settings of the person. The power to "feel" the right answer in a domain of expertise grows after the expert has been shaped by years of experiences.
Introducing the bottomless pocket of bits is a solution to a dilemma that isn't proven to exist. The brain's own capacity is unquestionably large because of its flexible high connectivity. It's a vast coordinated population. And the number of cells is dwarfed by the number of byzantine connections, which act as the forms and processes of information. A complete listing of all the connections would contain substantially more than a trillion items. This presents an astounding surface to etch information into, albeit with two cautions: not all the connections would be valuable (in fact a lot of pruning happens), and it's too naive and reductive to equate every one of these connections to one bit of information.
Like some of the examples from earlier, in the brain a whole complex chain of simple objects mirrors the information. When connections to subgroup 3 are active, subgroups 1 and 2 might be embodying slightly different "bits" than when connections from 1 and 2 to subgroup 8 are active. The collective is the unit of significance. This strategy comes with the distressing tendency to go too far in connecting dots and filling in missing data points. People can believe that they know more than the information realistically shows.
On the positive side, losing one cell doesn't lose one episode of memory. The total impressions evoked by new information persist more than the tiny details. Changes proceed in stages, not like flipping switches. The path to conclusions resembles a loud committee "voice vote" more closely than a neat dictate trickling out of a bottomless pocket. The structure matches the expectation for an information processor that's adaptable, economical, and bending not breaking after injury. Through changed connections, old pieces of information can be recruited and reused in novel remixes; the thinker can manipulate Y as a lightly modified version of a past X. Creativity is possible without an exotic auxiliary.
Having a better informed perspective on the human brain's roominess for information gives a basis for distrusting claims about information encased in cruder things. By referring to the same considerations as before, and appending the sensible rule that consciousness about things involves the minimal level of information handling, a dust mote can't have a consciousness akin to a human's. It can't be having thoughts because no states are changing in it. In a human brain, as everyone is aware from the innumerable fMRI studies, changes happen when thoughts happen. The brain performs mental tasks without a bottomless pocket; the dust mote can't.
This also leads to inferences about the type of ideas that could be in the hypothetical consciousness. Whether it's animal, vegetable, or mineral, without a human-like grasp of the variations of a type of idea, it can't be said to have comparable types of ideas in its consciousness. For example, a thing without the resources for assimilating elaborate visual information can't be having images in its "inner world". Human color vision is sophisticated. But how could something that doesn't even have separate information pathways for different colors be having dreams or daydreams in color?
In reality, a portable internet-ready device is a more fitting approximation of the bottomless pocket of bits. Its reliance on its internet connection acts like the pocket, so its own design can potentially be relatively primitive. It might not permanently keep any of the flowing data bits after it promptly produces a video or audio signal, shows a message, takes a picture, activates a circuit, etc. The bulk of its "intelligence" might not be within itself either. It might function as a specialized input/output "face" for some high-performing cluster of computers somewhere else on the other side of the internet. Deprived of the internet, its capabilities drop.
Moreover, the unmiraculous work underlying this real-world version reiterates the hand-waving incompleteness of the abstract versions. Sending bits is a lengthy procedure. The device breaks the bits into standardized chunks or packets with address and identification information. It transfers the packet into speedy adjustments of its electromagnetic connection medium (wire or wireless), compensating for interference of course. The packet joins larger channels. It's delivered via intermediary stops or hops to the destination address, this time compensating for temporary outages at any point in the journey. Then the receiving computer does the reverse to extract the bits out of the packet. It reassembles the chunks of bits and asks for missing chunks to be retransmitted. Finally it writes the bits for later retrieval; space isn't infinite but it's fairly cheap when it's bought in humungous quantities and usable for many purposes.
Every part of this procedure arose through the diligent efforts of inventors and maintainers. Initial techniques were improved. Miles of cables were laid. It turns out that feasibly accomplishing something like the bottomless pocket of bits is a marvel...of engineering. The luxury of ignoring constraints of volume, time, energy, entropy, and so forth is a feature of fantasized ideas.
Some less radical interpretations of a brain pocket do comply with the physical universe. In these the brain hoards information in dramatically exotic or miniscule matter: at the scale of DNA base pairs or at the extreme quantum scale of elementary particles/fields. (It's an inspiring technological goal. When people succeed at shrinking their information that far, the density will be staggering.) Nevertheless, the shortcomings remain. There must be enough cumulative states with enough organization, and there must be dependable, reversible processes to read and write the states. The smaller the scale, the less plausible those prerequisites are. It's easy to argue that there're a lot of intriguing niches that the brain could use. It's less easy to argue how the brain could ever so delicately cram bits into the niches, trust that the niches don't succumb to literally random fluctuations, and draw out the desired bits in the future without clearing the rest.
Drawing out the recognizable bits is the impressive phase. A hypothetical pocket accepting item after item could be bottomless in a very misleading sense. It might have a hole at the other end.