BBeyond information: A bit of meaning.
Olaf DREYER Dipartimento di Fisica, Universit`a di Roma “La Sapienza”and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma, Italy
Is our world just information? We argue that our current notion of informationhas one serious shortcoming: It is quite literally meaningless. We suggest a mean-ingful extension of the notion of information that is dynamic, internal, approximate,contains an element of randomness, and is layered. This new notion of informationderives from the interactions of material objects. Our answer to the essay questionthen is Bit from It or, more appropriately, Bit ++ from It. We discuss how our newnotion of information sheds light on the measurement problem in quantum mechanicsand how it can be applied in philosophy and computer science. Contents
I. Sphingidae can suck it II. A simple example III. The six characteristics of meaning IV. A Gedankenexperiment V. It from bit or Bit from it? References a r X i v : . [ qu a n t - ph ] N ov I. SPHINGIDAE CAN SUCK IT
I have just received such a Box full from Mr Bateman with the astoundingAngrcum sesquipedalia with a nectary a foot long – Good Heavens what insectcan suck it [. . . ]
Letter from C. R. Darwin to J. D. Hooker, 25. January 1862[1]
In 1862 Darwin was sent a box containing samples of angraecum sesquipedale, an orchidthat possesses a spur that is over 30 cm long. This spur is a part of the flower that grows be-hind the head of the flower and contains the nectar at its bottom (see figure 1). Immediatelyafter seeing the orchid Darwin conjectured that there should be an insect with a proboscis that is long enough to reach the bottom of the orchid’s spur . The insect in question wasnot found until 1903. It is the sphinx moth, or sphingidae, from Madagascar and it doesindeed have an elongated proboscis that can reach the bottom of the sphinx orchid.Without ever having seen the moth Darwin was able to infer its existence by looking atthe orchid. The orchid is able to do this through its shape. Anything that wants to get atthe nectar at the bottom of the spur has to be very particular. If the tool for extractingthe nectar is too short it can’t reach the nectar. If it is too wide it can’t enter the spur. Itis the way the spur interacts with other objects like it that allowed Darwin to infer detailsabout the sphinx moth. The orchid is a representation of the sphinx moth because of howit interacts with other objects like it (proboscises, beaks, ... ).This is the first and most important characteristic of our new notion of information. Theorchid is a representation of the moth. The orchid acquires this meaning by the way itinteracts with other objects. This is a form of information that includes meaning throughinteraction.Let us remark on two other characteristics of this kind of information. The first thingis that the representation is approximate. It captures some qualities of the moth but notothers. The shape of the orchid gives no indication of the color of the moth for example.The other important characteristic is that the representation of the moth by the orchidis completely internal to the orchid. Nothing else other than the orchid is needed to inferthe moth. A proboscis is the elongated snout of an insect that allows it to reach parts deep inside a flower. Wallace went further and suggested that the insect in question was in fact a moth.
FIG. 1: Angraecum sesquipedale, or Darwin’s orchid. The remarkable feature of this orchid is itsvery long spur which extends from behind the flower and grows to a length of over 30 cm. Thenectar is found on the bottom of this spur. Both Darwin and Wallace predicted that there shouldbe an insect with a proboscis that is long enough so that it can get to the nectar. The Sphinxmoth was found in 1903 in Madagaskar. [2]
II. A SIMPLE EXAMPLE
We are so accustomed to this rigidity property that we do not accept its almostmiraculous nature, that it is an “emergent property” not contained in the simplelaws of physics, although it is a consequence of them.
P. W. Anderson
Basic notions of condensed matter physics[3].I refute it thus.
S. Johnson Let us look at an easier example of this kind of information. Possibly the simplest exampleis that of a solid representing a position. If we want to represent a position we can just puta solid at the position that we want to represent. In the introduction we have seen threecharacteristics of the kind of information that we are talking about here: meaning arisesthrough interaction, it is dynamic, and it is internal. We can immediately see all thesethree characteristics in this simple example. The solid represents a position by being at theposition. The way to infer the position is to take another solid and probe the space. If onebumps into the solid one has found the position. This process is dynamic because it requiresthe interaction of the two solids. It is also internal. This representation of a position doesnot require an external dictionary that tells us what the representation means. The meaningof the solid comes from how it interacts with other solids. An external representation wouldlook like this: ( x, y, z ) (1)This representation is external because the three numbers alone do not tell us enough aboutthe position that we want to describe. What are the axis? What are the units? But thingsare even worse than that. The three numbers could represent many other things other thana position. They could be the Euler angles of a rotation, the GDP figures of Great Britainin the last three years, etc. To properly understand the three numbers additional, external,information needs to be given. This is not the case with the representation of the positionby a solid. The solid is all that is needed to infer the position. To refute Bishop Berkeley’s idealism Samuel Johnson kicked a stone while exclaiming “I refute it thus”(for more details see [4]).
FIG. 2: The lattice is an emergent property of a solid. A consequence of the lattice is the rigidityof the solid: when you push the solid it pushes back in an attempt to maintain the lattice. Thelattice also breaks the symmetry of space. The molecules that make up the solid are at certain non-random positions. This breaking of the symmetry introduces an inevitable element of randomnessin the process of creating the solid.
The example of the position allows us to give two more characteristics of our kind ofrepresentation: The existence of layers and the appearance of randomness.In our representation of the position it is important that one solid prevents another solidfrom moving any further when it bumps into it. This rigidity is such a common feature ofour world that we hardly ever pause to consider how remarkable it is. It is a consequenceof the lattice of molecules that make up the solid. The solid wants to maintain this lattice.This means that a force on one molecule will move the whole lattice. It is this resistance thatwe feel when we bump into a solid and it is a feature that the solid has but the moleculesdo not. We can repeatedly bump into a solid to check its position while we can not do thesame with a molecule. One bump and the position of the molecule will have changed somuch that we can not use the molecule to represent that position.The lattice and the resulting rigidity are true emergent properties of a very large numberof molecules. There are thus two layers of objects with different properties: the layer ofsolids and the layer of molecules. The layer of solids has objects that have the propertyof rigidity that allows them to represent positions. The layer of molecules does not haveobjects with this property.When a solid together with its lattice forms a remarkable thing happens: a particularposition for the lattice gets chosen. If we take a cubic lattice as an example we need justtwo things to describe the whole lattice, the position of one molecule and the three vectorsthat give the edges of one basic cell. We can built the whole lattice by putting moleculesat the ends of the vectors that are obtained by adding all possible multiples of the basicvectors. Before the solid is formed the system is completely symmetric. There is no specialposition in space. After the solid has formed the lattice is breaking this symmetry. Theposition of the one molecule is special. The choice of this particular position depends onsmall random fluctuations that are present when the solid forms. There is an inevitableelement of randomness involved when one goes from one level to the next.
III. THE SIX CHARACTERISTICS OF MEANING
Let us gather the different characteristics of information that we have seen so far. Themost important aspect is that the meaning of an object arises from the way it interacts withsimilar objects. The physical restrictions of the orchid imply the moth and the rigidity ofthe solid gives its position. An important corollary of this is that meaning is dynamic andnot static.The meaning is also internal. No external encyclopedia is needed to tell us that theorchid represents the sphinx moth or that the solid represents a certain position. Thephysical properties of the orchid and the solid tell us that.
Interaction
Meaning arises from the interactionof objects of the same kind.
Dynamic
Meaning is dynamic and not static.
Internal
Meaning is internal and not external.
Approximate
Meaning is approximate.
Random
The process of emergenceincludes elements of chance.
Layered
Meaning arises in layers.TABLE I: The six characteristics of our new notion of information.
Furthermore meaning that arises in this way is necessarily approximate. We have seenthis in the example of the orchid. The form of the orchid gives information about theproboscis of the moth but not about its color.The example of the solid gave us two more characteristics: randomness and layers. Thesolid acquires its meaning through its rigidity which goes back to the lattice of moleculesthat is making up the solid. Randomness enters the picture because the lattice breaks thetranslational symmetry of space. When the solid is formed one choice for the position of thelattice has to be made. This choice is determined by random fluctuations of the environmentin the moment of creation. Another example of this kind is given by the ground state of alarge number of interacting spins. In the ground state all spins point in the same direction.This direction breaks the rotational symmetry of space and is again chosen by randomfluctuations during the formation of the ground state .The rigidity that is so important for our new notion of information appears only on the Just like in the case of the solid the spins want to maintain this direction. In the case of the spins thistendency to resist change is called generalized rigidity (see [3, 5] for more details). level of solids and not on the level of the molecules that make up the solid. Furthermore, themeaning of the solid only arises from interactions with other solids not with molecules. Wethus have a natural layered structure to our notion of information. The layers are relatedto each other through a process of emergence. Table I summerizes these six characteristicsof information.
IV. A GEDANKENEXPERIMENT
I, at any rate, am convinced that He does not throw dice.
A. Einstein , Letter to Max Born[6].We are now in the position to ask an interesting question. One of the characteristicsof our new notion of information is that it is layered. The meaning of objects arises fromtheir interaction with objects in the same layer and different layers are related to each otherthrough a process of emergence. Now imagine the following situation: Imagine that whatwe thought of as the lowest, most basic, layer turns out not to be the lowest layer. Instead,what we thought were the most basic objects turn out to be emergent from objects on aneven lower layer (figure 3 depicts this situation). How would that look to us?The first thing that we will note is that these more basic objects (layer 0 objects, seefigure 3) will lack properties that we think of as fundamental. Because they are not on thesame level as the objects we thought were the most basic objects (layer 1 objects) they donot have the same set of properties. Trying to interact with them as we do with other level1 objects will lead to inconsistent and confusing results.We will try to assign to level 0 objects the same properties that we assign to level 1objects. We will do this by devising methods to create level 1 objects whose propertieswe can easily verify. As we have seen in the previous sections this process introduces anirreducible element of randomness. We will thus be faced with a situation where chanceenters our description of nature in a fundamental way.Is this just an academic Gedankenexperiment? The quote at the beginning of this sectionindicates that we think it is not. In fact we think that this is exactly what happened to usin the beginning of the last century when we discovered quantum mechanics. We discoveredobjects that do not seem to have such fundamental properties as position. We devised waysto create level 1 objects (like bubbles in a cloud chamber) that allowed us to assign (ormeasure) properties of these level 0 objects and we discovered randomness in the process.We propose that some of the puzzling features of quantum mechanics can be understoodwith our new view of information.
FIG. 3: The tower of layers. The arrows indicate the direction of emergence. We pose the followingquestion: How does layer 0 look like to someone who’s lowest level meaningful objects are fromlayer 1? V. IT FROM BIT OR BIT FROM IT? Douglas Adams , The hitchhiker’s guide to the galaxy.Frequently the messages have meaning ; that is they refer to or are correlatedaccording to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem .The significant aspect is that the actual message is one selected from a set ofpossible messages.
C. E. Shannon , A Mathematical Theory of Communication [7] (emphasis added)The birth of information theory came with its ruthless sacrifice of meaning – thevery quality that gives information its value and its purpose.
J. Gleick , The Information [8]If we have to decide between ”It from bit” and ”Bit from it” it is clear that we comedown on the latter: Bit from it. What we have spent most of this essay on though is ourconviction that the bit-part needs to be improved. A bit is usually seen as the basic unitof information. The question ”It from bit” or ”Bit from it” is then the question aboutwhat is more fundamental, information or matter? A number of people have suggested thatinformation should be seen as the basis of our description of the world [9, 10]. Our analysisshows that there is something fundamentally wrong with this suggestion. Naked bits requirea dictionary that gives them meaning. Such a dictionary is necessarily external to the bitsthemselves and a description of the world that focuses solely on the bits will be incomplete.We have shown that meaning can be internal but it requires us to give up the idea that ourworld is pure information.The narrow view of information that was introduced by Shannon served us well duringthe fast evolution of computer technology in the last fifty years but we think that we arenow running up against its limitations. We have already hinted at how our new view ofinformation can be used to see the measurement problem in quantum mechanics in a newlight. Other possible applications include philosophy and computer science itself.One of the perennial problems in philosophy is the problem of consciousness. One reasonconsciousness is puzzling is that there seems to be an infinite regression present. It feels like1there is someone observing the thoughts inside our head but then what about the thoughtsof that someone? D. Dennett called this view of consciousness the Cartesian Theatre[11].Our view of information might be able to break this infinite loop because the meaning of ourobjects is internal. There is no outside observer required. The thoughts acquire meaningthrough the way they interact with other thoughts.Our view of information suggests that there should be a new paradigm of computationthat we might call emergent computation. This computation will consists of the dynamicevolution of emergent objects. The six characteristics that we have outlined in section III willbe present here. In particular the computation will by necessity include random elementsand be approximate. Two properties not shared with our current model of computation.The most important aspect of emergent computation will be that the meaning of the objectsin the computation is completely internal.
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