Numbers and brains
C. R. Gallistel
Published online: 14 April 2017
Psychonomic Society, Inc. 2017
Summary The representation of discrete and continuous quan-
tities appears to be ancient and pervasive in animal brains.
Because numbers are the natural carriers of these representations,
we may discover that in brains, it’s numbers all the way down.
Cuttlefish assess prey number and prey size before deciding
where and when to attack (Yang & Chiao, 2016). Bees have
cognitive maps on which they represent distances and directions
(Degen et al., 2016). Mice represent the number of lever presses
they have made and the duration of an elapsing interval, and
they also represent their uncertainty about those numbers and
those durations (Berkay, Cavdaroglu, & Balcı, 2016;Kheifets,
Freestone, & Gallistel in press). The capacity of animal brains to
represent in memory such abstract quantities as number, dis-
tance, direction, duration, rate, and probability appears to be
evolutionarily ancient and extremely widespread. This poses
the question, What carries these representations? How are they
coded in neural tissue? That is, how are they stored in memory?
make it retrievable for later use in behavior.
Most treatments of memory are domain specific: spatial
memory, associative memory, emotional memory, declarative
memory, procedural memory, episodic memory, and so on. To
be sure, the processes that extract information from experience
and those that use it later are domain specific, because predicting
what will happen next is not the same computational problem as
computing the range and bearing of another location from one’s
current location. Both computations presuppose memory, be-
cause both rely on information acquired piecemeal from expe-
riences distributed over long stretches of the past. But building a
cognitive map from scraps in memory is a different enterprise
from building a good model of what events predict what other
events at what latencies, and using a stochastic model to antic-
ipate the next event requires different computations than those
required when using a cognitive map for route finding.
Domain-specific treatments of memory focus on how
memories are created and how they are utilized, not on mem-
ory itself. Memory is the medium through which the past
communicates with the future. Its function is to convey infor-
mation extracted from past experience forward in time in a
manner that makes this information accessible to computation
whenever it is needed to inform behavior.
A key insight at the foundation of information theory and
modern information technology is this: When it comes to in-
formation conveyance, what the information is about is irrel-
evant. In the article that laid the foundations of information
theory, Shannon (1948, p. 379, emphasis in original) wrote:
Frequently the messages [conveyed] have meaning;that
is they refer to or are correlated according to some system
with certain physical or conceptual entities. These seman-
tic aspects of communication are irrelevant to the engi-
neering problem. The significant aspect is that the actual
message is one selected from a set of possible messages.
The system must be designed to operate for each possible
selection, not just the one which will actually be chosen
since this is unknown at the time of design.
Target publication Yang, T. I., & Chiao, C.-C. (2016). Number sense
and state-dependent valuation in cuttlefish. Proceedings of the Royal
Society: Series B, 283, 20161379. doi:10.1098/rspb.2016.1379
* C. R. Gallistel
Rutgers Center for Cognitive Science, Rutgers University, 158
Frelinghuysen Road, Piscataway, NJ 08854, USA
Learn Behav (2017) 45:327–328