Sequence-space synesthesia (SSS) involves the habitual visualization of certain sequences (such as months, days, and numbers) as arranged in an ordered spatial configuration. For instance, as one of our participants describes it:
“There are various planes: horizontal, vertical, starting on the left, starting on the right, above waist level, below waist level, and stretching out in front of me. The alphabet is pretty much upright but [the letters are] variable sizes and veers off a bit upwards right, and away from me after QRST.... Months of the year twist a bit and move depending on the starting month I am thinking about… Weeks have several forms starting on a basic Sun-Mon in front of me left to right… All these subjects are in completely separate planes. Nothing shares the same space… I suddenly realize how fixed and definite it all is and am surprised that you don’t know where these things are.” (Ward, 2008)
For some people with SSS, the sequences appear to occupy the peripersonal space outside their body and for others it is on an inner screen (Smilek, Callejas, Merikle, & Dixon, 2006). For some the vantage point with which they view the sequence is fixed but for others they can change perspective or “zoom in” (Jarick, Dixon, Stewart, Maxwell, & Smilek, 2009). For some, the sequences have idiosyncratic visual features such as shading, texture, and font (Gould, Froese, Barrett, Ward, & Seth, 2014). It is generally considered a type of synesthesia and, indeed, these types of visualizations are far more common in people who have synesthetic experiences of color (Sagiv, Simner, Collins, Butterworth, & Ward, 2006; but see Novich, Cheng, & Eagleman, 2011). The first documented case was noted by Hudson (1873) and, soon afterwards, Galton (1880a, 1880b) investigated them extensively in the domain of number, for which he used the term “number form.” Galton’s interest in them stemmed from the wider question of the functional role of mental images in cognitive ability. This approach still resonates in contemporary research in this area (e.g., Price, 2009; Simner, Mayo, & Spiller, 2009). However, before one can determine the precise functionality of SSS, a more basic scientific problem arises in terms of how one can distinguish those who report such forms of synesthetic phenomenology from those who do not report such experiences (but might have intuitive spatial associations; Fias & Fischer, 2005).
For synesthetic color experiences, measures of consistency over time have become a convenient and reliable diagnostic tool. This involves presenting the same stimulus (e.g., a digit) on multiple occasions, measuring the associated color, and then calculating the difference between each attempt. Earlier studies used verbal color descriptions, long test-retest intervals (weeks or months), and measured item consistency in terms of a binary consistent/inconsistent measure (Baron-Cohen, Harrison, Goldstein, & Wyke, 1993). Most contemporary studies use computer-based color selections, involve retests within the same session, and measure distances within color space (Eagleman, Kagan, Nelson, Sagaram, & Sarma, 2007).
Many attempts to establish the authenticity of sequence-space synesthesia have also used measures of consistency in which locations in space are measured. In some studies, synesthetes are asked to imagine a 2D rendering of the spatial form on a computer screen and are then prompted with cues (e.g., “Tuesday”) to localize that stimulus on the screen (Brang, Teuscher, Ramachandran, & Coulson, 2010; Smilek et al., 2006). The cues are presented multiple times and in random orders. In other studies, synesthetes have been asked to point to the location in egocentric space, and angular displacements are used as measures of consistency (Smilek et al., 2006) or synesthetes have been asked to project the locations around a virtual 3D body on a computer display (Eagleman, 2009). Sequence-space synesthetes tend to be more consistent than controls on these measures. However, there has been no suggested diagnostic cut-off point for discriminating between the two samples.
Brang et al. (2010) tested 183 people and noted that as many as 44 % reported a possible spatial form for months of the year. However, when using a test of spatial consistency they classified only 2.2 % (4/183) as having a spatial form. To qualify as a synesthete in their study, a person had to not only report synesthesia but also to fall two standard deviations (SDs) away from the mean of the consistency scores of the normative sample. However, this diagnostic approach makes a strong assumption: namely, that synesthetes’ scores on this test should lie at the extreme tail end of the control distribution of scores. Whilst we would indeed expect synesthetes to be more consistent than controls, it is impossible to know, a priori, the magnitude of that difference.
The approach taken here is different insofar as we attempt to estimate the magnitude of the difference between self-reported synesthetes and controls in order to compute the optimal way of discriminating between them. This uses receiver operating characteristic (ROC) analyses of binary classifications to estimate the sensitivity (probability of classifying a self-reported synesthete as a synesthete) and specificity (probability of classifying a self-reported control as a control) of the measures. For instance, using this general approach we have shown that maximum sensitivity and specificity of tests used to diagnose grapheme-color synesthesia is 90 % and 94 %, respectively (Rothen, Seth, Witzel, & Ward, 2013).