17 A tale of two worlds

It will be bla­tantly obvious by now that the onto­log­ical impli­ca­tions of quantum mechanics go counter to some of our deepest con­vic­tions con­cerning space, time, and matter.

It is safe to say that the fol­lowing idea appears self-​​evident to anyone unini­ti­ated into the mys­teries of the quantum world: the parts of a mate­rial object are defined by the parts of the space it “occu­pies,” and the parts of space are defined by delim­iting sur­faces (bound­aries). Because it says, in effect, that the syn­chronic mul­ti­plicity of the world — the word’s mul­ti­plicity at any one time — rests on sur­faces that carve up space much as cookie cut­ters carve up rolled-​​out pastry, we may refer to this idea as the “Cookie Cutter Par­a­digm” (CCP).

There is con­sid­er­able neu­ropsy­cho­log­ical evi­dence that the CCP is “hard-​​wired”: the way in which the brain processes visual infor­ma­tion guar­an­tees that the result — the visual world — is a world of objects whose shapes are bounding sur­faces. Vision is based on a neural analysis of the visual field (the optical images falling on the retinas in both eyes) that cap­i­tal­izes on con­trast infor­ma­tion. Data arriving from homo­ge­neously col­ored and evenly lit regions of the visual field do not make it into con­scious aware­ness. The cor­re­sponding regions of the phe­nom­enal world are filled in on the basis of con­trast infor­ma­tion that is derived from bound­aries in the visual field.[1–3]

There is, how­ever, a deeper reason why our visual world con­forms to the CCP, for our brain works as it does because our mind works as it does — and not the other way round, as we are wont to think. In the Vedantic scheme of things, the orig­inal cre­ative prin­ciple and dynamic link between UR and the world is a con­scious­ness that, fol­lowing Sri Aurobindo, we may call “super­mind.” The cre­ative action of super­mind is pri­marily qual­i­ta­tive and infi­nite and only sec­on­darily quan­ti­ta­tive and finite. Cos­mo­log­i­cally speaking, mind is the agent of this sec­ondary action lim­iting, defining, dividing, individualizing:

Mind in its essence is a con­scious­ness which mea­sures, limits, cuts out forms of things from the indi­vis­ible whole and con­tains them as if each were a sep­a­rate integer.… It is this essen­tial char­ac­ter­istic of Mind which con­di­tions the work­ings of all its oper­a­tive powers, whether con­cep­tion, per­cep­tion, sen­sa­tion or the deal­ings of cre­ative thought. It con­ceives, per­ceives, senses things as if rigidly cut out from a back­ground or a mass and employs them as fixed units of the mate­rial given to it for cre­ation or pos­ses­sion.[4]

Here we have the reason why, when asked to imagine two exactly sim­ilar objects in dif­ferent places, we balk at the log­ical con­clu­sion that the “two” objects are actu­ally a single object existing, appearing, or man­i­festing itself in dif­ferent places. If we per­ceive things as if rigidly cut out from a back­ground or a mass, then the back­ground or mass from which one thing is cut out dif­fers from the back­ground of mass from which another thing is cut out, even though the two things are cut out from an indi­vis­ible whole.

Let’s con­sider some of the CCP’s impli­ca­tions and how they might lead us up the garden path.

In a world whose syn­chronic mul­ti­plicity rests on sur­faces, spa­tial exten­sion exists in advance of mul­ti­plicity, for only what is extended can be cut up by the three-​​dimensional equiv­a­lents of cookie cut­ters. If, in addi­tion, the parts of mate­rial objects are defined by the parts of space, then the parts of space exist in advance of the parts of mate­rial objects. This is how we come to think of space as a pre-​​existent expanse that is intrin­si­cally divided “all the way down.” But if this is how we think, we cannot con­ceive of fuzzy posi­tions. If parts are defined by geo­met­rical bound­aries, the posi­tions of the parts are as sharply defined as their bound­aries, and there isn’t any­thing fuzzy about the way geo­met­rical bound­aries are defined.

  • CCP: Syn­chronic mul­ti­plicity rests on delim­iting sur­faces.
    QM: Syn­chronic mul­ti­plicity rests on spa­tial relations.
  • CCP: Space is a pre-​​existent and intrin­si­cally divided expanse.
    QM: “Space” has two senses: (i)  an undif­fer­en­ti­ated expanse, (ii) the totality of existing spa­tial relations.
  • CCP: All (rel­a­tive) posi­tions are sharp.
    QM: All (rel­a­tive) posi­tions are fuzzy.
  • CCP: Space is dif­fer­en­ti­ated “all the way down.”
    QM: The spa­tial dif­fer­en­ti­a­tion of the world does not go “all the way down.”

Rigid bodies, as the spe­cial theory of rel­a­tivity has taught us, do not exists. (If they did, they could be used for instant sig­naling, in con­tra­dic­tion of the finite speed limit the theory imposes on the prop­a­ga­tion of sig­nals.) An extended mate­rial object — an object that “occu­pies space” — is nec­es­sarily com­press­ible. What makes it com­press­ible, how­ever, is the elastic forces that act between its com­po­nent parts. Its ulti­mate com­po­nent parts there­fore are nei­ther rigid nor elastic and thus cannot be extended. If we com­bine the exis­tence of par­ti­cles without spa­tial extent with the pre-​​existence of an intrin­si­cally and infi­nitely dif­fer­en­ti­ated spa­tial expanse, we are led on to the notion that such par­ti­cles are pointlike.

  • CCP: A par­ticle without spa­tial extent (or internal struc­ture) is point­like.
    QM: A par­ticle without spa­tial extent (or internal struc­ture) is formless.

Although we readily agree that red, round, or a smile cannot exist without a red or round object or a smiling face (the Cheshire cat notwith­standing), we just as readily believe that posi­tions can exist without being prop­er­ties of mate­rial objects. We are pre­pared to think of mate­rial objects as sub­stances, and we are not pre­pared to think of the prop­er­ties of mate­rial objects as sub­stances — except for one: we tend to think of posi­tions as if they existed by them­selves, whether or not they are pos­sessed. The rea­sons for these dis­parate atti­tudes are to be found, not in the phys­ical world, but in the neu­ro­bi­ology of perception.

In brief, the visual cortex is teeming with fea­ture maps. A fea­ture map is a layer of the cere­bral cortex in which cells map a par­tic­ular phe­nom­enal vari­able (such as hue, bright­ness, shape, motion, or tex­ture) in such a way that adja­cent cells gen­er­ally cor­re­spond to adja­cent loca­tions in the visual field. (In the macaque monkey as many as 32 dis­tinct fea­ture maps have been iden­ti­fied.[5]) Every phe­nom­enal vari­able has a sep­a­rate map (and usu­ally sev­eral ones at dif­ferent levels within the neu­roanatom­ical hier­archy) except loca­tion, which is present in all maps.

If there is a green box here and a red ball there, “green here” and “red there” are sig­naled by neu­rons from one fea­ture map, and “boxy here” and “round there” are sig­naled by neu­rons from another fea­ture map. “Here” and “there” are present in both maps, and this is how we know that green goes with boxy and red goes with round. Posi­tion is the inte­grating factor. In the brain, and con­se­quently in the visual world, posi­tions pre-​​exist — in the brain at the scale of neu­rons, in the visual world at visu­ally acces­sible scales. They exist in advance of phe­nom­enal objects, and this is another reason why we tend to assume that they also exist in advance of phys­ical objects, not only at the scale of neu­rons or at visu­ally acces­sible scales, but also at the scales of atoms and sub­atomic par­ti­cles. (The tran­si­tion from visu­ally acces­sible scales to sub­atomic scales is an unwar­ranted extrap­o­la­tion, but if one pos­tu­lates a pre-​​existent spa­tial expanse that is intrin­si­cally dif­fer­en­ti­ated at some scales, then it is hard to see why it is not intrin­si­cally dif­fer­en­ti­ated at all scales.)

Fea­tures present in the same place thus get inte­grated into a single object, while fea­tures present in dif­ferent places get inte­grated into dif­ferent objects (or dif­ferent parts of the same object). This is why we are con­vinced by default that one and the same object cannot be in dif­ferent places, and that dif­ferent objects cannot be in the same place. It is also why we are baf­fled by the apparent ability of a single elec­tron to be simul­ta­ne­ously in dif­ferent places, and by the ability of two or more par­ti­cles to be in pos­ses­sion of exactly the same (fuzzy) posi­tion. (Helium illus­trates this nicely. In the ground state of a helium atom, the posi­tions of the two elec­trons rel­a­tive to the nucleus are exactly iden­tical. And in a bottle of super­fluid helium, the posi­tions of the atoms rel­a­tive to the bottle are exactly identical.)

  • CCP: Two objects cannot be in the same place simul­ta­ne­ously.
    QM: Two par­ti­cles or atoms can simul­ta­ne­ously pos­sess the same (fuzzy) position.
  • CCP: The same object cannot be in two places at once.
    QM: A par­ticle, atom, or mol­e­cule can be simul­ta­ne­ously in (what we tend to think of as) dif­ferent positions.

Yet another reason why we tend to think of posi­tions as sub­stances is this: the role that posi­tion plays in per­cep­tion is anal­o­gous to the role that sub­stance plays in con­cep­tion. Among the ideas that philoso­phers have asso­ci­ated with the word “sub­stance,” the fol­lowing is rel­e­vant here: while a prop­erty is that in the world which cor­re­sponds to the pred­i­cate in a sen­tence com­posed of a sub­ject and a pred­i­cate, a sub­stance is that in the world which cor­re­sponds to the sub­ject. It objec­ti­fies the manner in which a con­junc­tion of pred­ica­tive sen­tences with the same sub­ject term bun­dles pred­i­cates. While sub­stance thus serves as the “con­cep­tual glue” that binds an object’s prop­er­ties, posi­tion serves as the “per­cep­tual glue” that binds an object’s phe­nom­enal features.

Ein­stein[6] believed that “things claim an exis­tence inde­pen­dent of one another” when­ever they “lie in dif­ferent parts of space.” It is ironic that Ein­stein based this belief on the demand that things be inde­pen­dent of the per­ceiving sub­ject, for it is pre­cisely the ille­git­i­mate pro­jec­tion of the struc­ture of the visual world into the phys­ical world that under­lies it. It is because our minds and/​or brains process visual infor­ma­tion in con­for­mity with the CCP that we tend to think of space as a pre-​​existent and intrin­si­cally dif­fer­en­ti­ated expanse, in which objects are sep­a­rated by “empty space.”

Fact is that the three spins, which may be light years apart, are not inde­pen­dent of one another. Fic­tion is that they lie in dif­ferent parts of space. Space is not some­thing that has parts. Nor is there such a thing as empty space — not because space is “filled with vacuum fluc­tu­a­tions” as the dumbed-​​down lit­er­a­ture has it, but because in the phys­ical world there is no such thing as an unoc­cu­pied loca­tion or an unpos­sessed posi­tion. Space is the totality of existing (=pos­sessed) spa­tial rela­tions. Where there is nothing (no thing) there is no “there.” (In another sense, space is an undif­fer­en­ti­ated expanse. Instead of dividing things, it unites them by its utter lack of parts.) If we add to this that all existing rela­tions are self-​​relations — rela­tions between UR and UR — we find that there is nei­ther a struc­tural nor a sub­stan­tial basis on which phys­ical things could “claim an exis­tence inde­pen­dent of one another.”

1. [↑] Hubel, D.H. (1995). Eye, Brain, and Vision, Sci­en­tific Amer­ican Library.

2. [↑] Hoffman, D.D. (2000). Visual Intel­li­gence: How We Create What We See, W.W. Norton and Company.

3. [↑] Enns, J.T. (2004). The Thinking Eye, the Seeing Brain: Explo­rations in Visual Cog­ni­tion, W.W. Norton and Company.

4. [↑] Sri Aurobindo (2005). The Life Divine, Sri Aurobindo Ashram Pub­li­ca­tion Depart­ment, pp. 173–174. Emphases added.

5. [↑] Clark, A. (2000). A Theory of Sen­tience, Oxford Uni­ver­sity Press.

6. [↑] Ein­stein, A. (1948). Quan­ten­mechanik und Wirk­lichkeit. Dialec­tica 2, pp. 320–324.