In the Republic, Plato famously compared ignorant men (those unaware of or unsympathetic to his philosophy) to prisoners chained in a cave in front of a fire, forced to view only the shadows of objects on the cave wall in front of them and hence unable to realize objects as they truly are.

For Plato, this vivid allegory was a representation of our fundamental inability to directly perceive his ideal heavenly forms, which he believed were only possible to intuit through our minds.

To a modern physicist, however, the picture is perhaps even more curious. What if the shadows on the wall somehow represent the "real" objects after all?

For most, the history of physics could be safely regarded as a quest for discovering the ultimate laws governing space, time and matter. But developments in the mid- to late 20th century added a new quantity to this fundamental pantheon: information.

Back in 1948, when the American mathematician Claude Shannon developed a measure of information in terms of bits, he was naturally led to a similar form of mathematical expression that had been developed by Ludwig Botzmann some 75 years earlier in his pioneering work in thermodynamics. This gave rise to the notion that entropy was somehow deeply connected to the concept of information.

While Botzmann defined thermodynamic entropy as the number of individual microscopic arrangements that any given macroscopic system can be in, Shannon defined his entropy as the information required in terms of bits to assemble any given arrangement. Botzmann's entropy depends on the inherent physical makeup of the underlying microscopic level of structure -- what physicists call "degrees of freedom" -- and is ultimately related to our understanding of the fundamental constituents of matter.

The question thus arises as to how much information we could store in a given piece of material. What if we could somehow harness quarks? Superstrings? Or something even deeper, not even contemplated? Is there a limit to how much information we can store and potentially manipulate?

Enter, somewhat shockingly, black holes. These strange cosmic animals, coined as such by American physicist John Wheeler in the late 1960s, are natural consequences of Einstein's theory of general relativity. They represent regions of space-time curvature so extreme that no object, once inside, could ever re-emerge -- even light (hence the name). The boundary of a black hole -- the point of no return, as it were -- is known as the event horizon.

Work by physicists Stephen Hawking, Jacob Bekenstein and others in the 1970s led to a surprising conclusion: consistent thermodynamic understanding of black holes was possible by regarding the entropy of a black hole as directly related to the surface area of the event horizon.

Faced with this understanding of the entropy of black holes, physicists began addressing the question of information limits head on. Building on the work of Bekenstein some 15 years earlier, theorist Leonard Susskind proposed the notion of a holographic bound. Explicitly invoking the notion of black hole entropy, Susskind asserted that the maximum possible entropy of any isolated spherical object that fit inside a square box of length A would be one-quarter of A squared.

The conceptually shocking aspect of this claim is that the maximum possible entropy, and hence maximum possible information, associated with a given object is not related to its volume, as one might naively expect for an object with atoms and subatomic particles jiggling in all three directions, but rather the area of its boundary. In other words, a fundamental feature of a physical object that one would have naturally assumed had to be represented in three dimensions (volume) could in fact be expressed by only two (bounded area).

Never content with making isolated bizarre claims on the nature of reality, physicists have built considerably on these notions to develop a universal holographic framework. The Dutch Nobel Laureate Gerard 't Hooft posited that the holographic bound is really just a natural consequence of a wider holographic principle that states that any physical system in a three-dimensional region of space can be completely described by a physical theory defined only on the two-dimensional boundary of this space.

At present, this holographic principle is a hotly contested notion, with advocates pointing to recent support in isolated cases of higher dimensional field theories, and detractors adamant that there is nothing about our existing universe that can justify such a claim, let alone advancing it to the exalted state of a principle.

Whatever one's sympathies, there is little doubt that the last 30 years have resulted in a vastly increased appreciation of the importance and interdependence of the previously disparate concepts of information, thermodynamics and black holes toward our understanding of fundamental physics.

Meanwhile, some surprising advice can be dispensed to those longtime sufferers chained in the depths of Plato's cave: it might be just as efficient to spend your time studying the shadows on the wall as trying to break free into the sunlight.