in Riegler, A. & Peschl, M. (eds.) Understanding Representation in the Cognitive Sciences. New York: Plenum Press. 127-134.

Response Selectivity, Neuron Doctrine,and Mach's Principle in Perception.
Ken Mogi
Physiological Laboratory
University of Cambridge
Downing Street
CB2 3EG U.K.
Present Address
Sony Computer Science Laboratory Inc.
Takanawa Muse Bldg.
3-14-13, Higashigotanda
Shinagawa-ku, Tokyo, 141-0022 Japan
Tel +81-3-5448-4380
Fax +81-3-5448-4273

Abstract
I discuss the principle that bridges neural firingand perception. I start from the assumption that inorder to understand perception, the state of neuralfiring in the brain is necessary and sufficient (theneuron doctrine in perception). I argue that theconcept of response selectivity, currently the defacto central dogma in explaining the relation
between neural firing and the brain, is
incompatible with the neuron doctrine. I suggestthat we start instead from Mach's principle asapplied to the neural correlates of perception. I
propose to define a percept as an interactionconnected firings of neurons, not as a single (or an
ensemble of) neuron(s) which selectively
respond(s) to a particular set of stimulus, as is
assumed under the paradigm of response
selectivity. This definition ofpercept bynecessity leads to an interesting argument about
the neural basis of psychological time, namely theprinciple of interaction simultaneity. Finally, I
discuss the relevance of the twistor formalism tothe foundations of neuropsychology.

1. Introduction
Perception can be approached from two points of view.
One perspective is concerned with the subjective natureof perception, including ultimately such question as
qualia (Chalmers 1995). In another, perception can be
regarded as the computational process in the brain. For
example, the currently much debated "binding
problem" (e.g. Singer & Gray 1995) can be approachedalternatively as a problem of the subjective integrity ofperception, or as one of the computational process

which integrates information represented in the various
areas of the cortex. In order to study perception as anempirical science, the computational viewpoint is
crucial. On the other hand, our ultimate interest inperception is propelled by its subjective nature, whichlies at the core of the so-called mind-body problem.
In this paper, I suggest that the two approaches toperception can be successfully integrated byconsidering the following question; what is the natural
framework for describing the dynamics of the neuralnetwork in the brain? Here, by "natural framework" Imean one in terms of which the dynamical evolution of
the neural network can be described in a causal
manner. The construction of the space-time structurethat describes the dynamics of the neural network in a
causal manner is a non-trivial problem. I criticallyreview the idea of response selectivity as is applied toneuropsychology. I suggest to adopt "Mach's principle
in perception" as the basic principle that bridges neuralfiring and perception. I then go on to suggest how theneural correlate of a percept (element of perception)
should be defined. This definition will lead to aninteresting relation between perceptual time and the
dynamics of neural network. Finally, I put forward theconjecture that the perceptual space-time actuallycorresponds to a twistor-like space constructed fromthe causal relation between neural firings.

2. The Neuron Doctrine in Perception
Barlow (1972) applied the neuron doctrine (e.g.
Sherrington 1941) to the problem of perception, andproposed the neuron doctrine in perception. His
proposal consisted of 5 dogmas. Of special interest
here is the first and fourth dogma. Namely, thata description of that activity of a single nerve cellwhich is transmitted to and influences other nerve
cells, and of a nerve cell's response to such influencesfrom other cells, is a complete enough description forfunctional understanding of the nervous systemand thatjust as physical stimuli directly cause receptors toinitiate neural activity, so the active high-level neurons
directly and simply cause the elements of ourperception.
Barlow's neuron doctrine has often been associatedwith the idea of a "grandmother" cell, especially in thecontext of the fourth dogma. Recent evidence of"sparse coding" in, for example, the temporal cortex ofmonkeys (Rolls & Tovee 1995) has been cited as anargument against the "grandmother" cell idea.
However, the neuron doctrine itself does notnecessarily imply a grandmother cell type coding. I
propose to reformulate the neuron doctrine as follows.

(Hubel & Wiesel 1962) (Fig.1(a)). In areas MT, V4,
IT, we find neurons that respond to motion, color (inthe context of "color constancy" see Land (1983)), andform, respectively (Newsome et al. 1989, Zeki 1980,
Tanaka 1993). As we go to the higher visual areas,
we find neurons with more complex response
selectivities, and larger receptive fields. One idea thatemerges is the assumption that when a neuron with a
response selectivity to a particular visual feature fires,the perception of that feature occurs. For example,
when a neuron selectively responsive to a bar slantedby 45 degrees to the right fires, the perception of theslanted bar would be invoked. When a neuron
selectively responsive to a "face" fires in area IT, theperception of a "face" is invoked, and so on.
There is, however, a fundamental flaw in this line ofargument, which becomes apparent when one tries toanswer the following question. "When a neuron

Our perception is directly invoked by the neuralfirings in the brain. A non-firing neuron is as good as
non-existent as far as perception is concerned. The
characteristics of our perception should be explainedby the nature of neural firings only.
The neuron doctrine, when phrased in this form,
appears to be a reasonable starting point forneuropsychology at present. There are ideas, forexample, that the molecular level processing at the
microtubules participate in the conscious process (e.g.
Hammerof and Penrose 1996). However, the available
data, especially those from single unit recordings (e.g.
Newsome et al. 1989) seems to be compatible with theidea that neural firings are necessary and sufficient toinvoke perception, and the cellular processes, such as
the release and binding of neurotransmitters at thesynaptic cleft and the subsequent postsynaptic flow ofions across membranes, influence perception only as
far as they affect the neural firing.
Although the neuron doctrine as rephrased above
does seem to give a correct starting point forneuropsychology today, the most profound question,
namely why the neural firing plays such a special rolein our perception, and indeed our consciousness,remains unanswered. From the dynamical point ofview, the non-linearity and the all-or-none character
involved in the action potential generation is likely to
be at the basis of the crucial importance of neural firingin perception. In this view, it is of interest to note that
there is no sub-neural processes known at present
which demonstrates the same degree of non-linearity or
all-or-none character as the action potential generation.

3.

Response Selectivity"Response selectivity" is a concept of a central
importance in neurophysiology today. For example, inthe primary visual cortex (V1), we find neurons that
selectively respond to a bar with a certain orientation

selectively responsive to a feature A fires, how does
the brain (or the subject) know that it is selectively
responsive to feature A?" The visual feature space isvast and complex. The fact that a neuron fires
vigorously to a particular feature A does notnecessarily mean that the neuron has the response
selectivity to feature A only. In fact, in order toestablish the response selectivity of a neuron, every
possible visual feature should, in principle, bepresented to the neuron. Of course, this is impossible
both in practicality and in principle. Moreover, theneuron doctrine dictates that our perception isconstructed based on the neural firings at a particularpsychological moment. It is impossible, just based on
the firing of the neurons at a particular time, to2

establish the response selectivity of a particular neuron.
The reason for this being that response selectivity isbased on the idea of an statistical "ensemble", the setof all possible stimulus-response relations. If ourperception is based on response selectivity, the brain
must somehow have an instantaneous access to every
element within the ensemble when only a sample from
it is presented as stimulus. Such an assumption seems
to be implausible.
In general, as we go higher up the visual system, themore difficult it becomes to define the response
selectivity of a particular neuron in an operationalmanner (see Tanaka 1993 for example). Even if aneuron seems to fire rigorously only when a frog ispresented, for example, it is virtually impossible toestablish that the neuron is selective to a frog only, as
the visual stimulus space is vast and complex(Fig.1(b)). This is in contradiction with the idea that theneurons in the higher visual areas play a crucial role inour perception through their response selectivity. Evenin the case that our perception is evoked by the
successive neural firings from the lower visual areas tothe higher visual areas, the significance of the neurons
in higher visual areas becomes obscure, if indeed the
response selectivity plays an essential role inperception.
From these considerations, I conclude that response
selectivity cannot be the foundation for the relation
between neural firing and perception. Some otherbridging principle(s) should come into the picture.

Fig.1 Response Selectivity

4. Mach's Principle in Perception
Ernst Mach (1838-1916) was a physicist, philosopher,
psychologist who had a major influence on Albert
Einstein in his development of the theory of relativity.
"Mach's principle" states that the mass of a particle isdetermined by its relation to all the other particles in
the universe (Fig.2 (a)). If there was only one particle
in the universe, it is meaningless to question how large
its mass is. In a nutshell, the idea behind Mach's
principle is that the properties of an individual isdetermined by its relation to other individuals in thesystem.
A similar line of thought is relevant when we
consider the neural correlates of perception. Namely, aneural firing plays a particular role in our perception,
not because it is selectively responsive to a visualfeature (the idea behind the neuropsychologicalapplication of response selectivity), but because theneural firing is related to other neural firings in thebrain in such a way that the particular role inperception is endowed on the neural firing in question.
Namely, I propose to formulate the following principle.
In perception, the significance of a firing neuron isdetermined by its relation to other firing neurons at thatpsychological moment.
We shall call this idea "Mach's principle inperception" (Fig.2 (b)). For example, suppose a neuron
in area IT fired, and a perception of "rose" is invokedin our mind. In this case, the perception of "rose" isinvoked not because the neuron selectively responds tothe presentation of a rose, but because the neural firingin question is endowed with the property of "rose"through its relation to other neural firings in the brain.
Specifically, the cluster of neural firings connected bymass M(a) Mach's Principle(b) Mach's Principle in
Perception

Fig.2 Mach's principle andMach's principle in Perception
interaction through action potentials that is initiated inarea V1 and leads up to the neural firing in area IT
codes the perception of "rose". It is meaningless toconsider a single neural firing in isolation and ask its
significance in perception, even if the response
selectivity of that neuron could be establishedunequivocally.
Under the scheme that I have put forward above, a
percept is coded not by a single neural firing, but by acluster of interaction-connected neural firings. This isthe bridging principle that is consistent with the neuron
doctrine in perception, and Mach's principle inperception. Namely, a percept is coded non-locally.
Neural firings in spatially distant areas of the brain are
integrated into a cluster through their mutualinteractions, and form a percept.
That a percept is defined not as a single (or an
ensemble of) neuron(s) which selectively respond(s) toa particular set of stimulus, but as a cluster ofinteraction-connected neural firings, has an immediate
impact on some important issues in perception, such as
the binding problem (Damasio 1989;Gray et al.
1989;Malsburg 1981;Singer & Gray 1995). The
various visual features are represented by the neuralfirings in spatially separate areas of the brain. For
example, color is coded in area V4, motion in area MT,form in area IT, and so on. However, our visual3perception is not a collection of fragmentary features,
but a coherent world view. The binding problem
questions how the brain integrates the visual features
into a coherent picture of the world.

texture
color

form

percept. However, inhibitory connections are notincluded explicitly in the cluster of neural firings that
forms a percept.
In order to see the intuitive meaning of thisarrangement, consider a white bar in a black surround.
In order that the white bar is a bar, it is necessary thatthe area surrounding the bar is black, rather than white.
If the surround was white, then the bar would not be abar (Fig.4(a)). So the surround contributes to theformation of a white bar by not being white. However,the black surround does not constitute an explicit partof the percept "white bar" (Fig.4(b)).
The idea that excitatory connections and inhibitory
connections contribute differently in the formation of apercept should be grounded in the mathematicaldescription of the dynamics of the neural network, as isoutlined in section 6.

Visual field as given by V1
Fig.3 The Binding Problem
The binding problem arises from the view thatperception is coded locally, by the firing of a neuron(s)that respond(s) selectively to a particular subset offeatures. As the features is coded locally, it becomes
necessary then to question how the brain integrates the
locally coded representation of features.
Under the view that a percept is coded non-locally,
as a cluster of neural firings arising in area V1 andleading up to higher cortical areas such as V4, MT, andIT, the binding problem is not such an acute one any
more. What is likely to be happening is that the neuralfirings in V1 function as a kind of "address" for thevisual features to be integrated (Fig.3). As the percepts
now have "tags" of interaction-connected neural firings
originating from area V1, they are embedded with thenecessary information to be organized into thebasically retinotopic visual field, which functions as
the frame of reference for our coherent world view.
Although the details are still to be worked out, and thebinding problem does remain a difficult one, it isimportant that the very formulation of the binding
problem assumes a local coding, which for reasons
discussed above seems not to be the case.
The distinction between the excitatory (e.g.
glutamate) and inhibitory (e.g. GABA) connections
now becomes important. Specifically, it appears that
only excitatory connections are included explicitly inthe cluster of neural firings that forms a percept.
Inhibitory connections affect the formation of percepts
only indirectly. For example, in the color constancy
mechanism (e.g. Land 1983), inhibitory inputs fromsurrounds will lead to a non-formation of a percept of acolor in the center. Inhibitory connections havesignificance in that they can "veto" the formation of a

Fig.4 White Bar in a Black Surround

5. Principle of Interaction Simultaneity
The definition of the neural correlate of a percept in
the previous section lead to an interesting relation
between the dynamics of neural networks and the timein our perception.
Albert Einstein, in his first paper of relativity theory
published in 1905, stated thus.
One thing should be remarked here. Such amathematical description is physically meaninglessunless the way we construct time is made clear. All ourjudgements about time is one about events that occur
simultaneously.
We see below that the argument that led us to thedefinition of a percept as an interaction-connectedcluster of neural firings leads to an operational
definition of simultaneity in perception, namely thepsychological "now".
Let us start from the neuron doctrine in perception.
Namely, we assume that knowledge about the firing
neurons is necessary and sufficient to determine thecontent of perception. The concept of "interaction
simultaneity" dictates how to determine the nature of
psychological time in a way consistent with the neuron
doctrine. Under the principle of interaction

4

simultaneity, when a neural firing and another neuralfiring are connected by interaction (i.e., action potential
propagation and subsequent synaptic interaction), these
are considered to be simultaneous events (Fig.5). It
takes a finite length of time (say 5 milliseconds) for theeffect of a neural firing to propagate to a postsynaptic
neuron. However, under the principle of interaction
simultaneity, these firing events should be regarded as"simultaneous". We call the time parameter thus
constructed "proper time" and write it as t . When thepresynaptic neuron fires at time t, and the postsynaptic
neuron fires at time t + Dt (as a result in part of the
EPSP caused by the presynaptic firing), we assign thesame proper time t to the pre- and postsynaptic
events.

action potential
veloci t y c

time

dt=0

B A

Ne uron A a xon
le ngt h Lt

t =t +Lc

Ne uron B
B A

B A

t+

L

c

B A

space

B A

=t

B A

Fig. 5 Principle of Interaction
Simultaneity in a Neural Network.
Interaction simultaneity is derived from a more
fundamental principle, that of "causality". Here,"causality" is taken to mean that given the state of thesystem at proper time t , we are able to derive the stateof the system at a slightly later time t + Dt .
Schematically,W(t ) ÆW(t + Dt )where W(t ) is the state of the neural system at proper
time t . We need to use the proper time t in order todescribe the dynamical evolution of the neural network
in a causal way. Note that a system described by adifferential equation in time satisfies the above
definition of causality. Also, this concept of causality
encompasses both the deterministic (e.g. Newtonian)and stochastic (e.g. quantum mechanical) dynamics.

time

W(t+dt)W(t)Fig. 6 Causality
Interaction simultaneity is based on the idea that if
we are to derive the properties of our perception fromneural firings, we should not adopt the position where
we "observe" the neural firings from "outside thebrain". If we observe the brain from the outside, we candescribe the dynamical evolution of the neural networkwith any desired temporal accuracy. We may, forexample,describe the release and diffusion ofneurotransmitters at synapses with submillisecond
temporal resolution. However, under the neuron
doctrine in perception, only the neural firing enter
explicitly in our perception. Therefore, properties ofour perception should be described without resorting to
the idea of an outside observer. Thus, the adoption of
the principle of interaction simultaneity is justified.
Note that interaction simultaneity is necessary inorder for the definition of a percept as an interactionconnected cluster of neural firings, as is required by
Mach's principle, to remain consistent. Suppose that apercept, for example that of a "rose" is formed by thecluster of interaction-connected neural firings fromarea V1 up to area IT. As it takes a finite length of time
for the presynaptic activity of neuron to be transmitted
to the postsynaptic activity of neuron and result in its
firing, there is a time delay (referred to as latency in theliterature) involved. However, we subjectively assign apercept to a particular psychological moment. There isno inherent passage of psychological time involved in
the percept of a "rose". If we consider the percept of acolor (e.g. red), which is invoked by neural activities
leading up to area V4, the assignment of that percept toa psychological moment, in other words the absence ofany necessary passage of time per se, becomes moreevident. The proper time t constructed from theprinciple of interaction simultaneity fits such temporalcharacteristics of the percepts well. Namely, there is no
passage of proper time, and therefore of psychologicaltime, accompanying the formation of clusters of neuralfirings within the brain which underlie our perception(Fig.7)5dt=0 dt=0

dt=0
dt=0

dt=0
dt=0 dt=0

physicaltimetSuch a picture of time seems to coincide with thesubjective "feeling" of time flow.. Lockwood (1989)
refers to a similar model of psychological time. It is ofinterest that Libet (1985) reports that in order thatneural activities enter consciousness, they need to be
maintained at least 500 milliseconds. At present it is
not possible to make detailed arguments about theneural basis of psychological time, but I believe thatthe idea of interaction simultaneity is to play asignificant role in the construction of future models.

6. Causality and Twistor formalism

propertimetFig.7 Element of Perception

We can obtain some interesting conclusions about
the nature of psychological time. Firstly, thepsychological "present" has a finite duration, whenmeasured by the physical time t. The duration
corresponds to the transmission delay present when thecluster of interaction-connected neural firings isformed. This would be of the order of ~ 50 ms. This
time gives the measure of transmission delay necessary
for neural excitation to travel across the cluster ofneurons involved in the formation of a percept. In otherwords, there would be a minimum "unit" of thepsychological time, with a duration of ~50ms. Despite
the existence of such a finite duration of thepsychological "moment", the flow of psychologicaltime is shown to be smooth. Specifically, thedisplacement between the adjacent "moment" can bemade arbitrarily small. This in turn means that there isan "overlap" between adjacent psychological moments.
A particular neural firing is shared by the neighboring
sp acet-dt t t+ dt
h

dt

ti me

moments. Schematically, we can summarize theproperty of the neural system parametrized by theproper time t as follows (Fig.8).

( t - t ¢ < h)"e > 0,"t $ t ¢ s.t.( t - t ¢ <e )W(t ) «W(t ¢) ≠ ∅Interaction simultaneity is concerned with theconstruction of the psychological time. This in turn ispart of a more general problem, namely, how ourperceptual space-time structure emerges from theneural firings in our brain. "Causality" is conjectured to
be a leading principle in the construction of theperceptual space-time. Note that the perceptual spacetime does not necessarily coincide with the physicalspace-time in which the neurons are embedded, as isevident from the marked difference in space-time
structure of different sensory modalities.
The construction of the space-time in perception is a
two-sided problem. One aspect is the nature of thespace-time structure in our perception from asubjective point of view. The other is concerned withhow to construct our perceptual space-time structure insuch a way that within that framework, it becomes
possible to describe the dynamical evolution of theneural network in a causal way. The principle ofinteraction simultaneity gives such a construction
scheme.
What then is the mathematical language that weshould adapt to describe the neural network dynamics
in a causal way? It should be noted that to construct asystem of variables and space-time structure thatsatisfies causality is a highly non-trivial problem,
especially when we consider that (1) there is a finite
delay in the transmission of signals between theneurons (2) only the neural firing are to enter explicitly
in the description of the dynamics. For example, there
is an ambiguity in the meaning of the state of a neuron
at proper time t . If the firings of mutually connected
neurons A and B at the physical time t reaches thepostsynaptic neurons at the time t + Dt , the state of
the two neurons A( t + Dt) and B( t + Dt) are
simultaneous to the states A( t) and B( t) by theprinciple of interaction simultaneity. (Recall interaction
simultaneity was a consequence of causality).
Therefore, schematically we construct(A( t) ,B( t) ,A( t + Dt) ,B( t + Dt)) Æ ( A(t ) ,B(t ))Fig.8 Nature of Time under Interaction Simultaneity

where t is the proper time. Here,A(t ) couldA( t) or A( t + Dt) .

The same

either mean

6

ambiguity exists for B(t ) One way to avoid thisambiguity is to adopt a convention such that in the
product A(t ) B(t ) , the term on the right side specifies
the state at the time t, and the left term specifies thestate at the time t + Dt Namely, in general we haveA(t ) B(t ) - B(t ) A(t ) ≠ 0
There are further complications owing to the fact thatthe time required for the transmission of signals
between neurons varies depending on the length anddiameter of axons, the duration of synaptic anddendritic delays, and the fact there are excitatory,
inhibitory, and modulatory synapses. Specifically, if
we look at the post synaptic potential f BA exerted byneuron B on neuron A, the rise time ta , decay time
tm , synaptic delay ts , dendritic delay td , and thel BA, where l BA isc BA
the length of the axon of neuron A, and c BA is theaction potential transmission timetransmission velocity, should all be taken into account(Fig.9). These parameters typically take the values

ts <ª1ms
td <ª1 ~ 2ms
ta <ª1ms
tm ª 10ms
l BA
ª 1ms
c BA

Although the idea of interaction simultaneity strikes
some similarity with the relativity theory, care should
be taken as the parallelism is sometimes misleading.
For example, in relativity theory the constancy of thevelocity of light is one of the starting assumptions,
indeed an axiom. In the case of neural networks the
conduction velocity varies, as do other time parametersthat describe the synaptic interaction between neurons.
It is customary in relativity to define the "simultaneity"
between events by the co-ordinate time t. Here, we
defined the simultaneity by the proper time t . So there
is no "relativity of simultaneity" involved in the present
scheme. In addition, there is no mathematical structure
corresponding to the Lorentz transformation in the caseof neural networks. Despite these differences, therelation between causality and proper time is basicallythe same in relativity theory and interaction
simultaneity, and this could lead to some interesting
consequences.
In order to develop the model of neural basis ofperception put forward above any further, we need tohave a solid mathematical background. At present, one
is yet to be found. Penrose's "twistor" is a hint for themathematical structure to be developed from such an
approach. Penrose constructs a "twistor space"
separately from the physical space-time. We consider aspinor field W which satisfies the twistor equation—A ¢ ( W ) = 0
AB

W can be written in terms of some other spinor field
p and a constant spinor w as

The variables parametrized by the proper time t ,and the space-time structure constructed upon them,should reflect all these properties.

f BA(t)WA = w A - ix AA ¢p A ¢where x represents the Minkowski coordinates.
Twistor is then expressed by a pair of spinors()

Za = w A ,p A ¢ ;a = 0,1,2,3
decay time tm

rise time t a 10l
t s + t d + BA
c BA

tB - tA

Fig.9 Time Constants in Interaction Simultaneity

A spinor, in turn, is a geometrical object closely
related to the metric of the space-time. A spinor canbe returned to itself only when it is rotated by 4p . A
rotation of 2p sends a spinor into its negative. In
relativistic picture, the trajectory of light (null vector)
is represented as a straight line in physical space-time(assuming it is a Minkowski, i.e. flat space-time). In
twistor space, it is mapped to a point. This can beinterpreted in terms of causality structure as follows.
The trajectory of light represents the world-line along
which causal interaction propagates. In twistor space,
the set of points in physical space-time that areconnected by the interaction (which is represented by
the trajectory of light) is mapped into a point.
Therefore, twistor space can be considered to be basedon the causal relations between world points inphysical space-time (Fig.10 above).

7

In a nutshell, the idea behind the twistor formalism isto regard the causal connection between points inphysical space-time as more fundamental than thespace-time itself. The twistor space is in a sense a more
fundamental framework for natural law than physicalspace-time itself. Penrose writes in Penrose & Rindler(1984)We should think of twistor space as the space interms of which we should describe physics.
We cannot apply the twistor formalism directly toneural network. However, the basic idea of the twistor
approach, namely to regard the causal relation between
the individuals as more fundamental than theindividuals
themselves,
corresponds
toourarrangement of regarding the cluster of interactionconnected neural firings as the percept, that is, theelementary unit in perception. The nature of ourperception is ultimately determined by the dynamics ofthe neural network. Accordingly, the cluster ofinteraction-connected neural firings functions not only
as an element of perception, but also as an element in
the dynamics of neural network. In order to describesuch a dynamics, we would need a mathematicalstructure similar to that of twistor space.
An intriguing possibility is that a twistor-like spacecan be constructed to describe the dynamics of a neuralnetwork, and the space thus constructed corresponds toour perceptual space-time (Fig.10 below)). The
differential contributions of the excitatory andinhibitory connections in the formation of a percept is
expected to be of importance here. If such a picture isfound to be the case, our mind would inhabit thetwistor-like space that describes the dynamics of neuralnetworks in the brain. Of course, at present this ismerely a conjecture.

Fig.10Twistor space and Perceptual space-time

7. Conclusion
The concept of response selectivity plays animportant role in neuroscience today. For example, theobjective of the single unit recording experiment is toestablish the response selectivity of the particular
neuron under study. I have argued that response
selectivity cannot be the foundation for the neuralcorrelates of perception, as it is based on the idea of an
ensemble, and therefore incompatible with the neuron
doctrine in perception. However, this does not exclude
the practical applicability of response selectivity inanalyzing the experimental data such as those fromsingle unit recordings. Mach's principle should be theultimate starting point in explaining the relation
between neural firing and perception. However, atpresent, it is not easy to come up with an observablemeasure of neural activity from Mach's principle. Thisis mainly due to the lack of detailed knowledge about
the synaptic connections between the cortical neurons
that contribute to the formation of a percept. Whensufficient data on the chemical anatomy of the corticalneural network is accumulated, and a rigorous
mathematical framework is obtained to describe thedynamics of a neural network, we can construct anobservable measure of the neural activities that
underlie perception. Until such time, the concept of
response selectivity will continue to play an importantrole in understanding the relation between neural firingand perception. Moreover, it may be the case that there
is some intrinsic relation between response selectivity
and Mach' principle in perception.

The main idea behind this paper has been thatthe set of variables and space-time structurethat successfully describes the dynamics ofthe neural network in a causal way will findthe corresponding counterparts in our
perception. The idea of interaction
simultaneity, and the possible applicability ofthe twistor formalism, are derived from such a
concept. Namely, I have argued that themechanisms underlying our perception,
whatever its exact nature, should be regarded
as a part of the natural laws in that its
framework is derived from causality, the mostfundamental Merkmal of the natural laws..
There is no ad hoc ambiguity involved here.
8When the neurons in the brain fire in a certain
way, a certain perception is invoked in our
mind. It is this one-to-one correspondence
that is central to the question of the neuralcorrelates of perception, and that can bestudied from the point of view of causality.
Acknowledgements

Sherrington (1941) in Man on his nature. Cambridge
University Press.
Singer, W. & Gray, C.M. Visual feature integration andthe temporal correlation hypothesis. (1995) Annu. Rev.
Neurosci. 18, 555-588.
Tanaka, K. (1993) Neuronal mechanisms of object
recognition. Science 262, 685-688.
Zeki, S. (1980) The representation of colours in the
cerebral cortex. Nature 284, 412-418.

I thank Horace Barlow and Yoshihide Tamori for
helpful discussions. This work was supported in part by
Human Frontiers Long Term Fellowship to K.M.

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