The Sand-Heap Paradox is an ancient Greek
paradox, which considers the failure of
induction. Imagine a heap of sand from which
one grain is removed. Surely what is left
is a heap of sand. But if we repeat this
process long enough, we are left with a
single grain of sand, which is not a heap.
Many of us have lived with Moore’s
Law for all of our professional lives. We
knew that Moore’s Law—the doubling
of the number of transistors on a chip
every couple of years—cannot continue
forever, but the end of Moore’s Law always seemed to be beyond the horizon.
No more. It is now becoming clear that
we are witnessing the denouement of
an extraordinary technical saga.
In fact, this denouement has been
going on for the past decade. As I
wrote in “Is Moore’s Party Over?” (Nov.
2011), Dennard Scaling, described by
IBM’s Robert Dennard in 1974, which
asserted that as transistors got smaller, power density stays constant, already broke down about 10 years ago.
As I wrote then, that meant increased
transistor density no longer automatically leads to improved computer performance. While the semiconductor
industry has been able to continue innovating, reducing transistor size, and
increasing transistor density, there are
more and more signs that Moore’s Law
is in a serious trouble.
To start, the terminology used by
the industry to describe its ongoing
march to the drumbeat of Moore’s Law
has turned from physics to marketing.
Back in the days of 0.35-micrometer
chips, the number referred to transis-
tor gate lengths. But today, as Intel
starts production of 14-nanometer
chips, it is not clear at all what this
number means other than a suggestive
reference to the continuing increase in
While the industry has been struggling to harness transistor density to
deliver performance, it is also being
challenged from the business side.
After all, the real point of Moore’s Law
was not merely delivering improved
performance, but delivering improved
cost-performance, which meant we
got improved performance at a fixed
and even reduced cost. No more. The
Linley Group, a semiconductor consultancy, pointed out last year that
while in 2012 one could buy 20M
28-nanometer transistors per dollar,
the forecast for 2015 is 19M 16-nano-
meter transistors per dollar. Such a
rise in the cost of transistors is simply
Finally, at the current rate of progress we will reach the five-nanometer
milestone within 10–15 years, and
there are strong technical arguments
why CMOS, the semiconductor technology that served us well for decades,
cannot be scaled down further. Indeed, Robert Colwell, currently at
DARPA and previously chief IA- 32
architect at Intel, recently declared
publicly that he expects Moore’s
Law to die around 2020. In a recent
analysis, Andrew A. Chien and Vi-jay Karamcheti argued that when it
comes to flash memories Moore’s
Law has already ended and increases
in capacity will be accompanied by
reduced reliability and performance.
While there are numerous alternatives
to CMOS technology, it is doubtful any
one of them will be mature enough to
become the workhorse of the semiconductor industry in 10 years.
So the real question is not when precisely Moore’s Law will die; one can say
it is already a walking dead. The real
question is what happens now, when
the force that has been driving our field
for the past 50 years is dissipating. In
fact, Moore’s Law has shaped much of
the modern world we see around us. A
recent McKinsey study ascribed “up to
40% of the global productivity growth
achieved during the last two decades to
the expansion of information and communication technologies made possible by semiconductor performance
and cost improvements.” Indeed, the
demise of Moore’s Law is one reason
some economists predict a “great stagnation” (see my Sept. 2013 column).
“Predictions are difficult,” it is
said, “especially about the future.”
The only safe bet is that the next 20
years will be “interesting times.” On
one hand, since Moore’s Law will not
be handing us improved performance
on a silver platter, we will have to deliver performance the hard way, by
improved algorithms and systems.
This is a great opportunity for computing research. On the other hand,
it is possible that the industry would
experience technological commoditi-zation, leading to reduced profitability. Without healthy profit margins to
plow into research and development,
innovation may slow down and the
transition to the post-CMOS world
may be long, slow, and agonizing.
However things unfold, we must
accept that Moore’s Law is dying, and
we are heading into an uncharted
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Moshe Y. Vardi, EDITOR-IN-CHIEF
Copyright held by Author.
Moore’s Law and
the Sand-Heap Paradox
DOI: 10.1145/2600347 Moshe Y. Vardi