DOI: 10.1126/science.1249168
, 1370 (2014);343Science
et al.C. Bushdid
Humans Can Discriminate More than 1 Trillion Olfactory Stimuli
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Humans Can Discriminate More than
1 Trillion Olfactory Stimuli
C. Bushdid,1
* M. O. Magnasco,2
L. B. Vosshall,1,3
A. Keller1
†
Humans can discriminate several million different colors and almost half a million different tones,
but the number of discriminable olfactory stimuli remains unknown. The lay and scientific literature
typically claims that humans can discriminate 10,000 odors, but this number has never been
empirically validated. We determined the resolution of the human sense of smell by testing the capacity
of humans to discriminate odor mixtures with varying numbers of shared components. On the basis
of the results of psychophysical testing, we calculated that humans can discriminate at least 1 trillion
olfactory stimuli. This is far more than previous estimates of distinguishable olfactory stimuli. It
demonstrates that the human olfactory system, with its hundreds of different olfactory receptors, far
outperforms the other senses in the number of physically different stimuli it can discriminate.
T
o determine how many stimuli can be discriminated,
one must know the range and
resolution of the sensory system. Color
stimuli vary in wavelength and intensity. Tones
vary in frequency and loudness. We can therefore
determine the resolution of these modalities
along those axes and then calculate the number
of discriminable tones and colors from the range
and resolution. Humans can detect light with a
wavelength between 390 and 700 nm and tones
in the frequency range between 20 and 20,000 Hz.
Working within this range, researchers carried out
psychophysical experiments with color or tone
discrimination tasks in order to estimate the
average resolution of the visual and auditory
systems. From these experiments, they estimated
that humans can distinguish between 2.3 million
and 7.5 million colors (1, 2) and ~340,000 tones
(3). In the olfactory system, it is more difficult to
estimate the range and resolution because the
dimensions and physical boundaries of the olfactory
stimulus space are not known. Further,
olfactory stimuli are typically mixtures of odor
molecules that differ in their components. Therefore,
the strategies used for other sensory modalities
cannot be applied to the human olfactory
system. In the absence of a straightforward empirical
approach, theoretical considerations have
been used to estimate the number of discriminable
olfactory stimuli. An influential study from
1927 posited four elementary odor sensations
with sufficient resolution along those four dimensions
to allow humans to rate each elementary
sensation on a nine-point scale (4). The number
of discriminable olfactory sensations was therefore
estimated to be 94
or 6561 (4). This number
was later rounded up to 10,000 and is widely
cited in lay and scientific publications (5–7).
Although this number was initially calculated to
reflect how many olfactory stimuli humans can
discriminate, it has also sometimes been used
as the number of different odor molecules that
exist, or the number of odor molecules that humans
can detect. We carried out mixture discrimination
testing to determine a lower limit of the number
of olfactory stimuli that humans can discriminate.
Natural olfactory stimuli are almost always mixtures
of large numbers of diverse components at
different ratios. The characteristic scent of a rose,
for example, is produced by a mixture of 275 components
(8), although typically, only a small percentage
of components contribute to the perceived
smell. We reduced the complexity by investigating
only mixtures of 10, 20, or 30 components drawn
from a collection of 128 odorous molecules (table
S1).These 128 molecules were previously intensitymatched
by Sobel and co-workers, which enabled
us to produce mixtures in which each component
contributes equally to the overall smell of the mix-
1
Laboratory of Neurogenetics and Behavior, The Rockefeller
University, 1230 York Avenue, Box 63, New York, NY 10065,
USA. 2
Laboratory of Mathematical Physics, The Rockefeller
University, 1230 York Avenue, Box 212, New York, NY 10065,
USA. 3
Howard Hughes Medical Institute, 1230 York Avenue,
Post Office Box 63, New York, NY 10065, USA.
*Present address: Université Pierre et Marie Curie, 4 Place
Jussieu, 75005 Paris, France.
†Corresponding author. E-mail: andreas.keller@rockefeller.edu
A B
2.27x1014 possible
mixtures
Component only in
mixture A
Component only in
mixture B
Not used in mixture
Shared component
Mixture of 10
Mixture of 20
Mixture of 30
Not used in mixture
Used in mixture
1.20x1023 possible
mixtures
1.54x1029 possible
mixtures
D
E
No overlap
No overlap
No overlap30% overlap60% overlap90% overlap
95% overlap 75% overlap 50% overlap 25% overlap
96.67% overlap 66.67% overlap 33.33 overlap
Mixture
A
Mixture
B
C
1.34x1017 possible
mixture pairs
1.83x1023 possible
mixture pairs
7.18x1026 possible
mixture pairs
1.10x1028 possible
mixture pairs
1.29x1026 possible
mixture pairs
1.03x1035 possible
mixture pairs
4.28x1042 possible
mixture pairs
8.12x1044 possible
mixture pairs
1.76x1044 possible
mixture pairs
1.10x1054 possible
mixture pairs
7.93x1056 possible
mixture pairs
2.27x1032 possible
mixture pairs
3.24x1049 possible
mixture pairs
Mixturesof10
Mixturesof20Mixturesof30
Fig. 1. Odor mixtures used to test the resolution of the human olfactory
system. (A) Illustration of sample mixtures with exactly 10, 20, or 30 components
(green squares) picked from a collection of 128 odorous molecules (gray squares)
and the number of possible mixtures of each type. (B) Example of one mixture
pair. (C to E) Schematics of each of the 13 types of odor pairs used for discrimination
tests, along with the total number of possible mixture pairs of each type.
21 MARCH 2014 VOL 343 SCIENCE www.sciencemag.org1370
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ture (9). The 128 molecules cover much of the
perceptual and physicochemical diversity of odorous
molecules (10–12) because the collection contains
most of a collection of 86 odorous molecules
that were selected to be well distributed in both perceptual
and physicochemical stimulus space (9).
To generate each mixture, we combined these
components together at equal ratios. The 128
components can be combined into 2.27 × 1014
different mixtures of exactly 10, 1.20 × 1023
different
mixtures of exactly 20, and 1.54 × 1029
different mixtures of exactly 30 (Fig. 1A). The
most salient difference between two mixtures
with the same number of components is the percentage
of components in which they differ.
We therefore performed psychophysical testing
to determine the resolution of the human olfactory
system along this axis. We asked by what
percentage two mixtures must differ on average
so that they can be discriminated by the average
human nose. This percentage difference in components
is the resolution of the olfactory system.
Subjects performed forced-choice discrimination
tests to determine the discriminability of pairs
of mixtures (referred to here as “mixture A” and
“mixture B”) that varied in the percentage of shared
components (Fig. 1B). In double-blind experiments,
subjects were presented with three odor vials, two
of which contained the same mixture, whereas the
third contained a different mixture. The testing procedure
was computerized by using a custom-written
application in which subjects were instructed to
identify the odd odor vial on the basis of odor quality.
Each subject completed the same 264 discrimination
tests. The order of the tests was randomized.
For each of 13 types of stimulus pairs (Figs. 1, C
to E, and 2A), 20 different stimuli pairs were tested,
for a total of 260 mixture discrimination tests. In
addition, four control discrimination tests comprising
individual odor molecules were interleaved
across the mixture discrimination tests so as to
measure general olfactory acuity and subject compliance.
Because we wished to ensure that discrimination
was based on odor quality differences and
not small intensity differences, one of the three
stimuli in a test was diluted in propylene glycol at
a 1:2 ratio, the other at a 1:4 ratio, and the third was
not diluted. The dilutions were assigned to the
stimuli at random. The components and dilutions of
all stimuli used in this study are given in table S2.
Twenty-eight subjects completed the study,
but two were excluded from the analysis because
they failed to correctly identify the odd odor in
at least three of the four control tests. Data from
26 subjects [17 female; median age 30 (range of
20 to 48); 14 Caucasian, 5 African-American, 5
Asian, 2 Other; 4 Hispanic] are included in the
analysis presented here.
Pairs of mixtures are more difficult to distinguish
the more they overlap. At least half of
the tested subjects could discriminate mixture
pairs that overlapped by less than 75% of their
components. Some could also discriminate mixture
pairs that overlapped by 75 and 90%, but
none could discriminate mixture pairs with more
than 90% overlap (Fig. 2B). In this evaluation,
the results of 20 mixture pairs of a certain type (for
example, mixtures of 20 components that overlap
by 75%) are pooled. Specific mixture interactions
that are known to occur in odor mixtures, such as
synergy and masking, are averaged out. To assess
whether this biased our results, we also analyzed
the results for each individual mixture pair, averaged
across the 26 subjects (Fig. 2C). The results
of this analysis were very similar. Of the 260 pairs
of mixtures that were tested for discriminability,
subjects performed above chance level for 227. For
148 of those, 14 or more of the 26 subjects (54%)
chose the correct vial, resulting in a statistically
significant difference from chance (Fig. 2C).
The resolution (or difference limen) of the visual
and auditory system is defined as the difference in
frequency between two stimuli that is required for
reliable discrimination. In the olfactory system,
resolution can be defined as the highest percentage
overlap in components between two mixtures at
which those mixtures can be distinguished. The
resolution of the olfactory system is not uniform
across the olfactory stimulus space. For example,
half of the mixtures of 20 components with 50%
overlap could be discriminated, whereas the other
half were indiscriminable (Fig. 2C, middle). Nonuniform
resolution across stimulus spaces is also
found in other sensory systems. In hearing, for
example, frequency resolution is much better at
low than at high frequencies (3). In vision, wavelength
discrimination is best near 560 nm, at which
a difference in wavelength of 0.2 nm can be discriminated
under optimal conditions (13).
We extrapolated functions that relate the percentage
mixture overlap to mixture discriminability
fromour data. The function that relates the percentage
mixture overlap (x) with the percentage of subjects
that can discriminate the mixtures (y) is y =
–0.81x + 91.45 (Fig. 3A). The function that relates
the percentage mixture overlap (x) with the percentage
of discriminable pairs (y) is y = –0.77x +
94.22 (Fig. 3B). According to these formulae, most
subjects can discriminate mixture pairs that overlap
by less than 51.17%. Most pairs that overlap
by less than 57.43% can be discriminated.
To calculate a lower limit of how many discriminable
mixtures there are, the number of possible
mixtures and the difference between two mixtures
that renders them indistinguishable have to be
known. There are 2.27 × 1014
possible mixtures of
exactly 10 (out of 128), 1.20 × 1023
possible mixtures
of exactly 20, and 1.54 × 1029
possible mixtures
of exactly30.Usingthe numbersfromour data,
a lower limit of how many discriminable mixtures
there are can be calculated. Mathematically, this
%correct
20
40
60
80
100
Chance
Component only in A
Component only in B
Component in A and B
Discriminable mixture
Non-discriminable mixture
Mixture
A
Mixture
B
C
Median
% mixture
overlap
90 60 30 0 75 50 25 0 96.67 66.67 33.33 095
Subjects who can discriminate
Subjects who cannot discriminate
Median
%correct
20
40
60
80
100B
Chance
A
10 components 20 components 30 components
Fig. 2. An empirical investigation of the resolution of the human olfactory system. (A) Schematicofthe
discrimination tests carried out for mixtures of 10, 20, or 30 odorous molecules. (B and C) Results of discrimination
testswith26subjectsaskedtodiscriminatemixturesof10(left),20(middle),or30(right)componentswithdecreasing
overlap from left to right. The dotted line represents the chance detection level (33.3%). For (B), dots represent
performance of individual subjects across 20 mixture pairs. For (C), dots represent average performance of all 26
subjectsforagivenmixturepair.Statisticallysignificantdiscriminability(reddots)wasassessedwithac2
test;P<0.05.
www.sciencemag.org SCIENCE VOL 343 21 MARCH 2014 1371
REPORTS
presents a coding problem that can be formulated in
information theory as a problem of packing spheres
in multidimensional space (14). The solution to this
problem (details are available in the supplementary
materials, materials and methods) shows that a
resolution of 51.17% overlap results in 9.37 × 107
distinguishable mixtures of exactly 10, 1.12 × 1011
mixtures of exactly 20, and 1.72 × 1012
mixtures of
exactly 30 (Fig. 3C). A resolution of 57.43% overlap
results in 4.01 × 108
, 1.55 × 1012
, and 5.58 ×
1013
discriminable mixtures, respectively (Fig. 3D).
Mixtures that overlap by less than 51.17% can
be discriminated by the majority of subjects, which
means that humans can, on average, discriminate
more than 1 trillion mixtures of 30 components.
However, there are large differences between
subjects. The number of discriminable mixtures
with 30 components in one subject of this study is
1.03 × 1028
, whereas it is only 7.84 × 107
in another
subject (fig. S1).
One can calculate the number of mixtures that
can be discriminated by either using the discrimination
capacity of subjects or by the discriminability
of stimulus pairs. Depending on what criteria are
used, our results showthat humans can discriminate
1.72×1012
or5.58×1013
mixturesof30components
outofthe collectionof128 odorousmolecules.1.72×
1012
may seem like an astonishingly large number.
However, there are 1.54 × 1029
possible mixtures of
30 from the 128 components used here. Therefore, if
there are 1.72 × 1012
discriminable stimuli, this means
that for each mixture tested there will be 8.95 × 1016
other mixtures that cannot be discriminated from it.
Our results show that there are several orders
of magnitude more discriminable olfactory stimuli
than colors (1, 2) or tones (3) (Fig. 3E). Colors
are spatially arranged to create a large number
of visual objects that are the building blocks of
visual experiences, and tones can be combined to
form a large number of chords that form auditory
objects. The number of visual and auditory objects
is much larger than the number of colors
and tones, but it is unknown how many of these
objects humans can discriminate. However, the
difference between the number of discriminable
olfactory stimuli and colors or tones is even larger
if one considers that the number of discernible
tones and colors includes stimuli that differ in
loudness or brightness. We focused here only on
stimulus quality and ruled out intensity-based
discrimination. Thus, our estimate of 1.72 × 1012
is a conservative one yet is still several orders of
magnitude higher than previous estimates of the
number of discriminable olfactory stimuli (5–7).
The actual number of distinguishable olfactory
stimuli is likely to be even higher than 1.72 × 1012
for three reasons. First, it is currently not known
how many odorous molecules there are or how
many of them can be discriminated from the
others. However, there are considerably more possible
odorous molecules than the 128 different
components that we used. Second, components can
be combined in mixtures of more than 30 components.
Third, even mixtures with the same components
can be distinguished if the components are
mixed at different ratios (15). Our results therefore
establish only a lower limit of the number of discriminable
olfactory stimuli. Although this lower
limit of greater than 1 trillion is several orders of
magnitude more than distinguishable colors or
tones, it is presumably dramatically lower than the
actual number of discriminable olfactory stimuli.
References and Notes
1. M. R. Pointer, G. G. Attridge, Color Res. Appl. 23, 52–54 (1998).
2. D. Nickerson, S. M. Newhall, J. Opt. Soc. Am. 33,
419–422 (1943).
3. S. S. Stevens, H. Davis, Hearing, Its Psychology and
Physiology (Wiley, New York, 1938), pp. 152–154.
4. E. C. Crocker, L. F. Henderson, Am. Perfum. Essent.
Oil Rev. 22, 325 (1927).
5. A. N. Gilbert, What the Nose Knows (Crown Publishers,
New York, 2008), pp. 1–5.
6. J. A. Gottfried, in Taste and Smell: An Update, T. Hummel,
A. Welge-Lüssen, Eds. (Karger, Basel, 2006), p. 46.
7. E. R. Kandel, J. H. Schwartz, T. M. Jessell, S. A. Siegelbaum,
A. J. Hudspeth, Principles of Neural Science (McGraw-Hill
Companies, ed. 5, 2013).
8. G. Ohloff, Scent and Fragrances: The Fascination of
Odors and Their Chemical Perspectives [W. Pickenhagen,
B. M. Lawrence, Transl. (Springer-Verlag, Berlin, 1994)].
9. T. Weiss et al., Proc. Natl. Acad. Sci. U.S.A. 109,
19959–19964 (2012).
10. R. Haddad et al., Nat. Methods 5, 425–429 (2008).
11. K. Snitz et al., PLOS Comput. Biol. 9, e1003184
(2013).
12. R. M. Khan et al., J. Neurosci. 27, 10015–10023
(2007).
13. R. L. Hilz, G. Huppmann, C. R. Cavonius, J. Opt. Soc. Am.
64, 763–766 (1974).
14. J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices and
Groups (Grundlehren der mathematischen Wissenschaften)
(Springer, ed. 3, Berlin, 1999).
15. E. Le Berre et al., Chem. Senses 33, 389–395 (2008).
Acknowledgments: We thank A. N. Gilbert, J. D. Mainland,
and members of the Vosshall Lab for discussion and comments
on the manuscript. We also thank M. Hempstead for support
with data collection. A.K. was supported by a Branco Weiss
Science in Society Fellowship and a NARSAD Young Investigator
Award. L.B.V. is an investigator of the Howard Hughes Medical
Institute. This study was supported in part by grant UL1
TR000043 from the National Center for Advancing Translational
Sciences [NCATS, National Institutes of Health (NIH)] Clinical
and Translational Science Award (CTSA) program.
Supplementary Materials
www.sciencemag.org/content/343/6177/1370/suppl/DC1
Materials and Methods
Fig. S1
Tables S1 and S2
2 December 2013; accepted 19 February 2014
10.1126/science.1249168
Discriminable sensory qualities
106
104
108
1010
Smells
Mixtures of 10
Mixtures of 20
Mixtures of 30
Tones
Colors
A C
0
50
100
020406080100
%subjectsthatcan
discriminatemixtures
% mixture overlap
Mixtures of 10
Mixtures of 20
Mixtures of 30
%mixturepairs
discriminable
% mixture overlap
B
Mixtures of 10
Mixtures of 20
Mixtures of 30
D
0
50
100
020406080100
E
0 20 40 60 80 100
100
1010
1020
1030
#discriminable
mixtures
% mixture overlap
allowing discrimination
0 20 40 60 80 100
100
1010
1020
1030
#discriminablemixtures
% mixture overlap
allowing discrimination
Mixtures of 10
Mixtures of 20
Mixtures of 30
Mixtures of 10
Mixtures of 20
Mixtures of 30
1012
1014
Previous estimates
Fig. 3. The number of discriminable olfactory stimuli. (A) Discrimination
capacity of subjects according to percentage of mixture overlap. (B) Discriminability
of mixture pairs according to percentage of mixture overlap. (C)
Extrapolation of the number of discriminable mixtures derived from (A). (D)
Extrapolation of the number of discriminable mixtures derived from (B). (E)
Summary of discriminable sensory stimuli across sensory modalities. Data are
curated from the following sources: smells (previous estimates) (5–7), tones
(3), and colors (1, 2).
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