The two-stream hypothesis of visual perception (^{Goodale & Milner, 1992; Goodale, Jakobson, & Keillor, 1994; Hu & Goodale, 2000; Milner & Goodale, 1995}) suggests that certain illusions will not affect motor responses since they are mediated by the dorsal stream, which operates via egocentric (absolute) metrics. In contrast, the allocentric (relative) metrics used for perception by the ventral stream are systematically biased by such illusions. Experimental studies have revealed dissociations consistent with this hypothesis, whereby subjects make accurate motor responses to illusory stimuli despite perceptual responses that are biased in accordance with the illusion (^{Aglioti, DeSouza, & Goodale, 1995; Haffenden & Goodale, 1998; Haffenden, Schiff, & Goodale, 2001; Mack, Heuer, Villardi, & Chambers, 1985; Servos, Carnahan, & Fedwick, 2000; Westwood, Chapman, & Roy, 2000; Westwood, Heath, & Roy, 2000}). However, there are also reports of motor and perceptual responses being affected approximately equally by visual illusions (^{Daprati & Gentilucci, 1997; de Grave, Brenner, & Smeets, 2004; Elliott & Lee, 1995; Franz, 2003; Franz, B?lthoff, & Fahle, 2003; Franz, Fahle, Bulthoff, & Gegenfurtner, 2001; Gentilucci, Chieffi, Deprati, Saetti, & Toni, 1996; Meegan et al., 2004; Predebon, 2004; van Donkelaar, 1999}), which have been used to argue in favour of a single representation of space for perceptual and motor responses (^{Franz et al., 2003}).

One explanation for the latter findings is that the illusions used may generate biases early in the visual system, before the ventral and dorsal stream split, so that they are inherited by both streams (^{Milner & Dyde, 2003}). ^{Dyde and Milner (2002)} explored this possibility by setting two illusions against each other to null overall bias. The simultaneous tilt illusion operates over short distances and is presumed to arise early in the visual system, perhaps from inhibitory connections between cortical columns in V1. In contrast, the rod-and-frame tilt illusion operates over much greater distances, thus putatively originating from higher visual cortical areas?presumably in the ventral stream. As a result, the simultaneous tilt illusion is inherited by both ventral and dorsal streams affecting both perceptual and motor responses, whilst the rod-and-frame illusion only affects perceptual responses. Consequently, when these two illusions were combined ? by placing a tilted frame around a simultaneous tilt illusion stimulus ? and set in opposite directions, the net effect on perceptual responses was nulled whilst motor responses remained biased in the direction specified by the simultaneous tilt illusion.

With notable exceptions, such as the above experiment, studies exploring potential dissociations between motor and perceptual biases have drawn heavily upon a small range of illusions. Most commonly used are the M?ller?Lyer illusion, and size-contrast illusions such as the Ebbinghaus/Titchener. Other types of illusion are greatly under-represented in the literature. For example, the Poggendorff effect is a robust illusion of extrapolation misalignment quite distinct from size-contrast illusions. Despite extensive exploration of its perceptual effect, the only study we are aware of that compared this with motor responses reported an approximately equal impact of the Poggendorff illusion upon both response modes (^{Predebon, 2004}). However, the motor response in this experiment was not a natural ballistic pointing movement but a form of manual estimation, whereby subjects gripped a rod which was positioned below the stimulus and slid it along a track to indicate their response. Such non-ballistic manual estimation tasks may actually be mediated by perceptual mechanisms (^{Franz, 2003; Haffenden & Goodale, 1998}), and are unlikely to engage real-time visuo-motor dorsal stream processing. We wished to study responses to a Poggendorff figure using a rapid naturalistic pointing movement, conditions that are most suited to engaging dorsal stream mechanisms.

Experimental conditions were the same as in Experiment 2, except for the use of a horizontal rather than a vertical configuration (see Fig. 4). The purpose was to see whether part of the motor bias was due to an under-reach in the unknown dimension of the target. Pointing to the extrapolated target location requires that subjects move their fingertip from the start position at the distal end of the oblique pointer along a particular trajectory to an extrapolated position on the landing line. Subjects always knew the approximate direction of the movement (down-right for a top-left start position and upright for a bottom-left start position), but they had to choose the magnitude of this movement. Since the landing line explicitly informs subjects how far they must move their finger horizontally across the screen, their decision centres around the vertical component of the movement vector, so that the motor bias may be thought of as an error in placing their finger in the (unknown) vertical dimension. Specifically, Fig. 2 shows that they do not move far enough in the vertical dimension from their start position. Thus, the motor bias can be considered an ?under-reach? in this unknown dimension of movement. However, an alternative conception is that in an extrapolation task, the vertical component of the movement is in general decreased relative to the horizontal. To distinguish between these possibilities, we presented stimuli in a horizontal configuration. This kept finger start positions and pointing directions the same, but the unknown dimension of movement was now the horizontal, since the landing line now explicitly indicated how far subjects must move their finger in the vertical domain. As shown in Fig. 5, the results were consistent with the first hypothesis: subjects now under-reached in the (unknown) horizontal dimension. As before, whilst both the perception and action systems were subject to the full Poggendorff illusion, with mean net inversion effects being significantly greater for motor than perceptual responses [F_(1,8)?=?7.97, p?<?0.05], the landing line bias in the pointer-only conditions was predominantly seen only in motor responses.

Fig. 6 shows mean net inversion effects for each condition. The pattern of results is exactly the same as for Experiments 1 and 2, although the effects are generally weaker with these horizontal stimuli than for the corresponding vertical conditions of Experiment 2, which is consistent with previous findings on perceptual responses to the Poggendorff illusion. Net inversion effects for the full Poggendorff stimulus were +5.8? and +7.4? for the perceptual and motor biases, respectively, whilst for the landing line bias in the pointer-only conditions net inversion effect were +1.1? and +2.4?, respectively. A two-factor (response mode, inducers) ANOVA again confirmed significant effects of the Poggendorff inducing line ? with greater biases when the inducing line was present compared to pointer-only conditions [F_(1,8)?=?48.1, p?<?0.001] ? and once again of response mode, with motor bias being greater than perceptual bias [F_(1,8)?=?7.97, p?<?0.05]. The idea that the effect of the inducer and of the response mode are additive factors was further supported by the absence of any interaction between response mode and stimulus type in the ANOVA [F_(1,8)?=?0.12, n.s.].

Our initial aim was to determine whether rapid pointing responses would be affected by the Poggendorff illusion. We confirmed that they were. Although motor response biases to other visual illusions have been used to argue against the duplex theory of vision, our result does not necessarily contradict the two streams hypothesis for perception and action. ^{Milner and Dyde (2003)} proposed that if an illusion manifests itself early in the visual system then both the dorsal and ventral streams will inherit the bias. Such a shared inheritance could explain an equal bias of both motor and perceptual responses. Since the Poggendorff illusion is presumed to manifest itself early, perhaps due to expansion of the acute angle due to lateral inhibition of orientation detectors (^{Blakemore, Carpenter, & Georgeson, 1970}); ?bowing? of the transversal pointer (^{Wenderoth, 1980}), or blurring of second stage filters in V2 (^{Morgan, 1999}), our results do not contradict Milner and Dyde's proposal. Thus, the common bias of the Poggendorff effect upon perception and action, which added a consistent 2?3^o of bias on top of whatever landing line bias was already present in the pointer-only condition (Fig. 2), is consistent with the notion that angular illusions of this type arise before the division into dorsal and ventral processing streams, possibly in V1 or V2.

Another possibility, which is also consistent with our findings, is that all motor responses will show the same illusory biases as perceptual judgements, subject to procedural differences. ^{Franz, Hesse, and Collath (2008)} argued recently that recorded motor biases may often be smaller than recorded perceptual biases because motor responses can be modified on-line by visual feedback, thereby reducing the magnitude of the initially programmed response bias. Franz's hypothesis would predict a strong illusion in our pointing conditions since unlike size illusions where visual feedback about the accuracy of grip size can be obtained in flight, the observer in our Poggendorff task has no explicit target to correct their motor response during the trajectory.

There is little experimental precedent for a motor response bias being greater than the corresponding perceptual response bias to a given stimuli (e.g., ^{Bruno, Bernardis, & Gentilucci, 2008}) other than when deliberately manipulated (e.g., ^{Dyde & Milner, 2002}) or when the tasks may be mis-matched (^{Franz et al., 2001}). Interestingly though, one example of a greater motor bias from ^{Bruno and Bernardis (2003)}, occurred when mental extrapolation was required, as is also required in the Poggendorff task. We found larger motor response biases to the full Poggendorff stimulus because of the presence of a motor-specific bias to the landing line alone ? despite near-veridical perceptual responses ? which added to the shared inherited bias of the Poggendorff inducing line. The motor bias can be thought of as a consistent ?under-reach? in the unknown dimension of hand movement. This may not represent an illusion, but could simply reflect a deliberate strategy. Accurate reaching or pointing movements are presumed to require on-line corrections to an initial motor programme (^{Glover & Dixon, 2001}), which predominantly occur late in the movement (^{Grant, Melmoth, Morgan, & Finlay, 2007; Melmoth & Grant, 2006; Melmoth, Storoni, Todd, Finlay, & Grant, 2007}). Under sub-optimal viewing conditions subjects adopt a conservative strategy for prehension movements, which includes under-reaching (^{Bradshaw & Watt, 2002; Elliott, Carson, Goodman, & Chua, 1991; Elliott & Lee, 1995; Grant et al., 2007; Melmoth & Grant, 2006; Melmoth et al., 2007; Watt & Bradshaw, 2000}) and subsequent correction. In our current task, there is a region of uncertainty within which the true extrapolated target position is located. A conceivably efficient evolved motor strategy for reaching would be to take the effector (in this case the finger) to the nearest boundary of the region of uncertainty and then make any additional corrections if necessary. Since, in our experiments, no additional feedback is available by which to make any further correction, no such adjustments are made and the initial under-reach remains. One difference between the response modes was that on half of the motor response trials the true location of the extrapolated intersection was explicitly shown, with subjects required to point to it. This was necessary due to the recording set-up, which required that we measure baseline performance to subtract the discrepancy between the location of the reflective marker (placed on the finger nail) and the fingertip placed on the screen. However, if anything, this would be expected to improve motor response accuracy, relative to perceptual responses, so cannot account for the greater motor bias.

Another difference between response modes was the duration over which they took place since ballistic pointing movements are, by their nature, quicker than an iterative adjustment task. Pointing movements in our experiment took approximately 1200?ms to complete (500?ms to initiate movement and 700?ms to execute), whilst perceptual responses were unconstrained and took much longer. Accordingly, response time for the perceptual task could have been constrained to match the natural durations of pointing movements?for example, via a ?one-shot? perceptual task, or a 2AFC. However, ^{Franz (2003)} reports that using 2AFC method-of-constant-stimuli to test perceptual biases to illusions with time constraints down to 800?ms produced the same results as using time-unconstrained method of adjustment. Likewise, if the Poggendorff illusion manifests early (e.g., in V1) then it is unclear what theoretical framework exists for supposing that allowing multiple eye movements in our perceptual task reduced the strength of the illusion. Nevertheless, we are currently investigating time-constrained perceptual responses since the possibility remains that the additional bias found in the motor responses is not specifically inherent to the motor (dorsal) system, but rather reflects a difference in the speed/duration of response and that by suitably constraining perceptual response conditions a similar bias could become manifest. A confound of this is that eye movements are, in themselves, a motor response and we have preliminary evidence that they too are subject to the motor-specific landing line bias. If these saccadic movements are used as the basis of a ?perceptual? judgement, then we may indeed expect them to affect perceptual response biases.

Future experiments will also test motor responses when the motor response does not have the same vector as the extrapolated line, i.e. when the reaching movement does not follow the trajectory of the pointer. For example, when pointing direction is orthogonal to the extrapolated line, if the concept of an under-reach holds angular bias would occur in the opposite direction to those reported here.

That the additional motor landing line bias is separate from any bias arising from the Poggendorff illusion is apparent both from the fact that it occurs in the absence of the inducing line, and that when the landing line and inducing line are set orthogonally the two biases oppose each other, reducing overall bias. A remaining question is why perceptual biases with these ?opposing? configurations in Experiment 4, were reduced compared to Experiment 1. The finding is not unprecedented. For example, ^{Weintraub and Krantz (1971)} found that the Poggendorff effect was weaker without a second parallel. It is also known that the full Poggendorff stimulus consists of numerous compounded visual illusions such as the vertical?horizontal extent, Wundt, Zehender and Obonai illusions to mention just a few (e.g., ^{Day, 1973; Goldstein & Weintraub, 1972; Hotopf, 1981; Hotopf & Hibberd, 1989; Pressey & Swinney, 1969; Tibber et al., 2008; Weintraub & Krantz, 1971}). These interacting effects are mediated by different component elements of the full Poggendorff stimulus so it is no surprise that the net perceptual bias is affected by changing the stimulus configuration. It should also be remembered that this reduction was significantly smaller than for the corresponding motor responses.

We have found that the acute angle version of the Poggendorff illusion affects perceptual (adjustment) and motor (rapid pointing) tasks equally, supporting the notion of a shared inheritance of this bias. However, in addition, there is a motor effect without a perceptual counterpart, when the acute angle is absent, resulting in larger total motor bias to the full Poggendorff stimulus. The motor effect appears as an under-reach in the unknown component of the pointing vector, which could be explained by a strategy to reduce effort. Finally, the dynamics of pointing to an extrapolated target position are the same as those for pointing at an explicit target, once the difference in path lengths are accounted for.

Supported by a grant from the Wellcome Trust (no. 079766)