Developing Intelligence

New research from Wharton and the Carlson School shows that a methodologically-appealing measure of impulsivity – hyperbolic discounting rate – may actually reflect a systematic “skew” in the way people perceive time.

Previous work has shown that people tend to decreasingly discount the usefulness or appeal of a reward with increasing delays; that is, a reward provided now is more appealing than a reward provided 1 week or 1 month from now, but that change in appeal is nonlinear (hyperbolic) across time. In other words, people prefer to behave impatiently now, but prefer to act more and more patiently in the future – suggesting that this “hyperbolic discounting rate” might be related to impulsivity.

Neuroimaging research has shown that hyperbolic discounting rate can be decomposed into two overlapping exponential functions, one which governs behavior in the immediate future (related to activations of subcortical brain regions), and a second which governs behavior in the distant future (related to activations of the prefrontal cortex). This framework epitomizes the view that hyperbolic discounting rate reflects the degree to which we can exert prefrontal “cognitive control” over the immediate, primitive appeal of “the now”, governed by suitably primitive regions of the brain.

However, it’s possible that such apparent impulsivity might not reflect failures of cognitive control so much as differences in the way time is perceived. In other words, if time is not represented linearly by the mind, perhaps it is that peculiarity which generates impulsivity, rather than a failure of control!

Until recently I considered this just an outlandish hypothesis (although I do have some ongoing work focused on testing it) – but Zauberman, Kim, Malkoc & Bettman beat me to the punch. Their forthcoming paper in the Journal of Marketing Research demonstrates conclusively that the hyperbolic function that characterizes discounting rate does indeed reflect nonlinearities in time perception.

In a first experiment, 57 subjects completed a standard intertemporal choice experiment (how much would you have to be paid to wait 1 month, 1 year, or 3 years to use a $75 gift certificate which is valid today), and then to estimate on a time-line their subjective experience of the duration between today and another day 3 months, 1 year, or 3 years in the future. While the intertemporal choice paradigm revealed a hyperbolic discounting rate in terms of objective time, the discounting rate appeared linear when calculated against subjective time (which was itself markedly nonlinear, as determined through analysis of the time line results). A second experiment replicated these findings (with reversed task order, using months as the consistent unit of time, and with 36 subjects in a within-subjects design), as did a third experiment (with blocked, randomized time-line estimates, the use of 12 different imagined durations, and the fitting of hyperbolic and linear models to the data of each of 106 individual subjects).

Two final experiments demonstrated that hyperbolic discounting is sensitive to attention to time. The authors asked subjects to either estimate the duration of a variety of activities (what they called “supraliminal priming”) or estimate the number of calories in various foods (a control condition). Subjects in the priming condition showed a reduction in the nonlinearity of their discounting rates, but this was not subsequently replicated (in the right direction numerically, but it was not statistically significant).

Thus the authors have conclusively demonstrated that nonlinearities in the perception of time are sufficient to explain the tendency for subjects to prefer to act impatiently now but more patiently in the future. Instead of reflecting a lack of cognitive control, this apparent impulsivity appears to be related to our perception of time itself.

Of course, time perception is probably mediated by the same prefrontal networks which are involved in controlling behavior. However, it is no longer sufficient to argue simply that hyperbolic discounting reflects only a failure to inhibit impulsive tendencies, given that it is directly related to time estimation tasks without an obvious inhibitory component, and given that it can be influenced by simply encouraging subjects to actively attend to duration.

Related Posts:
Surprise! You just distorted time.
Spacetime and Linguistic Relativity
Lacking More than Foresight: do Children Even Comprehend Time?
Reversing Time by Crossing Your Hands
Discovering the Future: Development of the Mind’s Time Machine
Time Distortion Due to Visual Flicker
Does IQ Reflect Temporal Acuity?
Reversing Time: Temporal Illusions


  1. #1 Jim Tobias
    May 21, 2008

    Could this non-linearity have something to do with one of the key ways our ancestors perceived time, as the size of an object (esp. prey/predator) coming closer to us? That size grows as the square of the speed of closing, and those scenarios require fast judgment and action.

  2. #2 daedalus2u
    May 21, 2008

    I have had some thoughts along these lines too, but I think the discount rate is much more variable, and that it is used as a control parameter in the context of extreme and life threatening metabolic stress. My hypothesis is that under such stress the “discount rate” becomes higher, and in the limit becomes infinite. This occurs during things such as being chased by a bear where to be caught is certain death. With an infinite discount rate, any injury can be tolerated if it allows for survival for the next few minutes, no matter what the “cost” in the future.

    I think this is what occurs during stimulant abuse. The discount rate is infinite, avoiding future adverse effects is of zero value compared to being high the next few moments. This is why deterrence cannot work to prevent drug abuse. If fear of death from HIV doesn’t stop drug abuse, why would fear of prison? Sure enough, deterrence doesn’t work to prevent drug abuse.

    I have an extensive write up of it on my blog.

    The write-up is more in the context of how extreme metabolic stress induces acute psychosis, but it does touch on the discount rate aspects of it too.

  3. #3 joek
    May 22, 2008

    It’s unsurprising, if you take into account the problem of time in biology. Biological systems care about the decrease in predictability over time, or in other words the entropy production. With fairly stable entropy production, what you have is at least a parabolic growth in information required to predict the future as time increases – so biological systems would not use mechanical time, but thermodynamic time.

    It’s not primarily a predator/prey thing like Jim Tobias suggests, but a much deeper and more general problem of time measurement. Biology got it right, while economics gets it wrong. Of course, the parabolic function is just a loose approximation, since there are attractors in the system decreasing the growth of the time metric, and the environment also has periods of perturbation (as suggested by daedalus2u) increasing the growth of the time metric.

  4. #4 Gabriel Kent
    July 20, 2008

    Interesting idea… though I think mortality and opportunity costs have larger roles to play in this than is given credit here.

    Carpe diem ;)

    @joek, how do you mean ‘biology got it right, economics got it wrong’? Is not one reducible to the other? The message to decode in this abstract (URL below) seems familiar to our discussion here.

  5. What exactly is the purpose of “Impulsivity Due to Distortions in Time: Hyperbolic Discounting and Logarithmic Time Perception : Developing Intelligence” ?