For the case of two taps to the skin, the Bayesian model perceives the length between taps, l* , to be a function of the actual length, l , and the elapsed time, t : This is the perceptual length contraction formula, so-named in analogy with the physical length contraction described in the theory of relativity. Note that, just as observed in rabbit illusion experiments, the formula shows that l* underestimates l to a greater extent when t is made smaller; as t becomes large, l* approaches l and the illusion disappears. The model's parameter, tau ( τ ), is a time constant for tactile space perception; the value of tau determines how rapidly the perceived length approaches the actual length as the time between stimuli, t , is increased. The perceived length equals one-third the actual length when t=τ , and two-thirds the actual length when t=2τ . Goldreich and Tong (2013) showed that tau is the ratio of the observer's low-speed expectation and tactile spatial acuity; they estimated the value of tau to be approximately 0.1 s on the forearm. A novel prediction of the Bayesian model, pointed out by Goldreich and Tong (2013), is that the amount of length contraction experienced will depend on the intensity of a tactile stimulus: lighter taps, which are more difficult to localize, should produce larger tau values and therefore more length contraction. Tong et al  (2016) confirmed this prediction experimentally.
For the case of two taps to the skin, the Bayesian model perceives the length between taps, , to be a function of the actual length, , and the elapsed time, : This is the perceptual length contraction formula, so-named in analogy with the physical length contraction described in the theory of relativity. Note that, just as observed in rabbit illusion experiments, the formula shows that underestimates to a greater extent when is made smaller; as becomes large, approaches and the illusion disappears. The model's parameter, tau ( ), is a time constant for tactile space perception; the value of tau determines how rapidly the perceived length approaches the actual length as the time between stimuli, , is increased. The perceived length equals one-third the actual length when , and two-thirds the actual length when . Goldreich and Tong (2013) showed that tau is the ratio of the observer's low-speed expectation and tactile spatial acuity; they estimated the value of tau to be approximately 0.1 s on the forearm. A novel prediction of the Bayesian model, pointed out by Goldreich and Tong (2013), is that the amount of length contraction experienced will depend on the intensity of a tactile stimulus: lighter taps, which are more difficult to localize, should produce larger tau values and therefore more length contraction. Tong et al . (2016) confirmed this prediction experimentally.
D
l*
D
l
D
t
R
l* underestimates l
underestimates
D
t
D
t
R
l* approaches l
approaches
D
τ
D
t
D
t=τ
D
t=2τ
A
.