et al.

BOOKS ET AL.
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senting hundreds of millions of pages such as
the full text of Wikipedia. Yet except for these
restricted special domains, AI remains a long
way from its human variant.
Kurzweil introduces the reader to one of
AI’s signature mathematical techniques that
he himself used to build speech recognition
systems: hierarchical, hidden Markov models
(HHMMs). These are trainable algorithms
well matched to deal with the many levels of
human language, from phonemes to words
to sentences and beyond. For certain types
of simple problems, HHMMs can be trained
fairly automatically and are easy to implement
in “units” that are connected by ascending
and descending links.
It is here that Kurzweil leaves the solid
ground of his expertise to wade into the muddier
waters of biology and psychology. For
he now categorically asserts that HHMMs
provide a powerful and universal model of
neocortical computation, with 300 million
pattern recognizers distributed across the
cortical sheet.
Kurzweil introspects into his own mind’s
capabilities and the nature of perception and
memory, without bothering to refer to the
massive literature on these topics. One of the
most basic lessons of psychology is that we
have little idea of what goes on in our minds,
as evolution has not given us access to most
parts of the brain (explaining why so much
philosophy of mind has been barren when all
it could rely on was introspecting philoso-
BROWSINGS
phers). He then moves on to the brain, describing
its anatomy in terms of the “new” brain,
higher-order regions of the neocortex, and the
“old” brain (everything else). According to
Kurzweil, the new brain is clever, learns fl exibly,
and controls the primitive impulses of
the old brain relating to food, sex, and aggression.
His understanding of neuroanatomy is
about as sophisticated as U.S. Secretary of
Defense Donald Rumsfeld’s understanding
of international politics when he articulated
his belief of a division of Europe into an Old
and a New one during the run-up to the second
Gulf War in 2003.
Kurzweil’s knowledge of neuroscience is
simply inadequate to the task at hand. From the
tens of thousands of studies published annually,
he selectively cites a handful of papers
that buttress his points, without giving any
context. He mistakes the striatum for cortex
and apical dendrites for axons, belies the cognitive
contributions of the basal ganglia, and
denies higher mental abilities to insects, cephalopods,
and birds that don’t have a neocortex.
Yet he has the unerring belief of the prophet
(or the fool): “I maintain that the model I have
presented is the only possible model that satisfi
es all of the constraints that the research and
our thought experiments have established.”
Scientists trying to simulate the mindbrain
fall along a continuum, ranging from
extreme biological chauvinism (the need to
consider every ionic channel, action potential,
and neuron to fully do justice to the
Mathematical Excursions to the World’s Great Buildings. Alexander J. Hahn. Princeton University
Press, Princeton, NJ. 2012. 344 pp. $49.50, £34.95. ISBN 9780691145204.
While touring examples of western architecture
from the great pyramids of Giza
to Frank Gehry’s Bilbao Guggenheim
Museum, mathematician Hahn intertwines
two historical narratives: The architectural
focuses on aspects of appearance (shapes,
symmetry, and proportion) and mechanics
(loads, compressions, tensions, and
thrusts). The mathematical progresses from
Euclidean geometry and trigonometry to
basic calculus. His discussions reveal how
mathematics provides insights into the
design and construction of the buildings
and how the buildings incarnate the math.
[Carefully composed using circles and squares, Leon Battista Alberti’s 15th-century facade (above)
for the medieval church Santa Maria Novella in Florence was a source of inspiration to a number of
Renaissance architects.] As Hahn notes, his two strands are linked topically rather than chronologically,
because the actual builders generally lacked the mathematics that clarifi es understanding of their
constructions. Readers wishing to shore up their own understanding of that mathematics can work
through the chapter-end problem sets and discussions.
15 FEBRUARY 2013 VOL 339 SCIENCE www.sciencemag.org
Published by AAAS
baroque complexity of the brain’s circuits) to
the austerity of a purely algorithmic approach
of replicating the mind in software (the mind
is not wet, after all). Mathematicians and
engineers naturally belong to the later camp,
convinced that one algorithm rules them
all. Previous favorites include logical calculus,
neural networks, cellular automata, selfreferential
programs, and, yes, hidden
Markov models [as proposed a few years earlier
by fellow entrepreneur and inventor of the
PalmPilot Jeff Hawkins ( 1)].
Kurzweil correctly points out that the
pace at which biologists accumulate data
has increased dramatically over the years
(although I only wish that his claim that “the
spatial resolution of brain scanning … [is]
doubling every year” were true). From this
he infers that a complete understanding of the
brain and the mind can’t be far away.
Paradoxically, the endless data fields
make it ever more diffi cult to distinguish the
signal from the noise. Indeed, the torrent of
data begets the illusion of progress. While
data about the brain accumulate exponentially,
our understanding increases sublinearly.
Basic questions about cortical circuitry
posed by future Nobel laureates David Hubel
and Torsten Wiesel in a celebrated publication
in 1962 ( 2) remain unanswered 50 years
later. Functional human brain imaging has
yet to affect standard medical practice (the
upcoming fi fth edition of the Diagnostic and
Statistical Manual of Mental Disorders does
not even mention any functional magnetic
resonance imaging diagnostic criteria). And
even the lowly roundworm Caenorhabditis
elegans, a creature no bigger than the letter
l and with exactly 302 nerve cells, is for now
beyond the ability of computational neuroscience
to comprehend. Kurzweil’s claim that
we will soon fi gure out how the 100 billion
neurons of the human brain function on the
basis of designed HHMMs is complete bosh.
One thing is certain. Biology knows nothing
of simplicity. Brains are not assembled
out of billons of identical LEGO blocks but
out of hundreds of distinct nerve cell types.
Each cell type has its own idiosyncratic morphology,
signaling, and active genes. And
they are interconnected with elaborate wiring
rules that we only discern darkly. To paraphrase
Winston Churchill, neuroscience is
(perhaps) at the end of the beginning of the
quest to understand our brain and mind.
References
1. J. Hawkins, S Blakeslee, On Intelligence (Times Books,
New York, 2005).
2. D. H. Hubel, T. N. Wiesel, J. Physiol. 160, 106 (1962).
10.1126/science.1233813
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