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'''Ordinal-linguistic personification''' ('''OLP''', or '''personification''' for short) is a form of [[synesthesia]] in which ordered sequences, such as [[ordinal number]]s, [[week-day names|days]], [[months]] and [[Letter (alphabet)|letters]] are associated with personalities and/or genders ({{Harvnb|Simner|Hubbard|2006}}). Although this form of synesthesia was documented as early as the 1890s ({{Harvnb|Flournoy|1893}}; {{Harvnb|Calkins|1893}}), researchers have, until recently, paid little attention to this form (see [[History of synesthesia research]]).
'''Ordinal-linguistic personification''' ('''OLP''', or '''personification''' for short) is a form of [[synesthesia]] in which ordered sequences, such as [[ordinal number]]s, [[week-day names|days]], [[months]] and [[Letter (alphabet)|letters]] are associated with personalities or genders.<ref name=Simner2006>{{cite journal|last= Simner |first= J. |last2= Hubbard |first2= E. M.|year = 2006 |title = Variants of synaesthesia interact in cognitive tasks: Evidence for implicit associations and late connectivity in cross-talk theories |journal=Neuroscience |issue=3 |volume=143 |pages=805–814 |pmid=16996695 |doi=10.1016/j.neuroscience.2006.08.018}}</ref> Although this form of synesthesia was documented as early as the 1890s,<ref name=Flournoy1893>{{cite book|last=Flournoy|first=T.|year=1893|title=Des Phénomènes de Synopsie|place=Geneva and Paris|publisher=Alcan}}</ref><ref name=Calkins1893>{{cite book|last=Calkins|first=M. W.|author-link=Mary Whiton Calkins|year=1893|title=A Statistical Study of Pseudo-chromesthesia and of Mental-forms|journal=American Journal of Psychology|issue=4|volume=5|pages= 439–464|doi=10.2307/1411912|jstor=1411912}}</ref> researchers have, until recently, paid little attention to this form (see [[History of synesthesia research]]).


==Experiences and Reports==
==Experiences and reports==
In Flournoy's 1893 reports on OLP, one synesthete identified as Mme L. reports that "1, 2, 3 are children without fixed personalities; they play together. 4 is a good peaceful woman, absorbed by down-to-earth occupations and who takes pleasure in them. 5 is a young man, ordinary and common in his tastes and appearance, but extravagant and self-centered. 6 is a young man of 16 or 17, very well brought up, polite, gentle, agreeable in appearance, and with upstanding tastes; average intelligence; orphan. 7 is a bad sort, although brought up well; spiritual, extravagant, likable; capable of very good actions on occasion; very generous. 8 is a very dignified lady, who acts appropriately, and who is linked with 7 and has much influence on him. She is the wife of 9. 9 is the husband of 8. He is self-centered, maniacal, selfish, thinks only about himself, is grumpy, endlessly reproaching his wife for one thing or another; telling her, for example, that he would have been better to have married a 9 since between them they would have made 18 – as opposed to only 17 with her… 10, and the other remaining numerals, have no personifications" {{Harv|Flournoy|1893|pp=219–220}}.
In Flournoy's 1893 reports on OLP, one synesthete identified as Mme L. reports that "1, 2, 3 are children without fixed personalities; they play together. 4 is a good peaceful woman, absorbed by down-to-earth occupations and who takes pleasure in them. 5 is a young man, ordinary and common in his tastes and appearance, but extravagant and self-centered. 6 is a young man of 16 or 17, very well brought up, polite, gentle, agreeable in appearance, and with upstanding tastes; average intelligence; orphan. 7 is a bad sort, although brought up well; spiritual, extravagant, likable; capable of very good actions on occasion; very generous. 8 is a very dignified lady, who acts appropriately, and who is linked with 7 and has much influence on him. She is the wife of 9. 9 is the husband of 8. He is self-centered, maniacal, selfish, thinks only about himself, is grumpy, endlessly reproaching his wife for one thing or another; telling her, for example, that he would have been better to have married a 9 since between them they would have made 18 – as opposed to only 17 with her… 10, and the other remaining numerals, have no personifications."<ref name=Flournoy1893/>{{rp|219–220}}


Calkins (1893) describes a case for whom “T’s are generally crabbed, ungenerous creatures. U is a soulless sort of thing. 4 is honest, but… 3 I cannot trust… 9 is dark, a gentleman, tall and graceful, but politic under his suavity” {{Harv|Calkins|1893|p=454}}.
Calkins (1893) describes a case for whom "T's are generally crabbed, ungenerous creatures. U is a soulless sort of thing. 4 is honest, but… 3 I cannot trust… 9 is dark, a gentleman, tall and graceful, but politic under his suavity".<ref name=Calkins1893/>{{rp|454}}


For synesthete MT, “I [is] a bit of a worrier at times, although easy-going; J [is] male; appearing jocular, but with strength of character; K [is] female; quiet, responsible…” {{Harv|Cytowic|2002|p=298}}.
For synesthete MT, "I [is] a bit of a worrier at times, although easy-going; J [is] male; appearing jocular, but with strength of character; K [is] female; quiet, responsible…"<ref>{{cite journal|last=Cytowic|first=R. E.|year=2002|title=Synesthesia: A Union of the Senses, 2nd ed|place=Cambridge, MA|publisher=MIT Press|isbn=0-262-03296-1|url=http://cytowic.net/_Books/_books.html}}</ref>{{rp|298}}


Simner and Holstein report an OLP case in which the synesthete perceived February as “an introverted female”, while F is a [male] dodgy geezer”. Similarly, May is reported to be “soft-spoken” and “girly” while M is an “old lady [who] natter[s] a lot”, and while August is “a boy among girls”, A is a female “mother type” ({{Harvnb|Simner|Holenstein|2007}}; {{Harvnb|Simner|Hubbard|2006}}).
Simner and Holstein report an OLP case in which the synesthete perceived February as "an introverted female", while F is a "[male] dodgy geezer". Similarly, May is reported to be "soft-spoken" and "girly" while M is an "old lady [who] natter[s] a lot", and while August is "a boy among girls", A is a female "mother type".<ref name=Simner2006/><ref name=Simner2007>{{cite journal|last=Simner|first=J.|last2=Holenstein|first2=E.|year=2007|title=Ordinal linguistic personification as a variant of synesthesia|journal=Journal of Cognitive Neuroscience|issue=4|volume=19|pages=694–703|pmid=17381259|doi=10.1162/jocn.2007.19.4.694}}</ref>


==Experimental Studies==
==Experimental studies==
Personifications tend to co-occur with [[grapheme-color synesthesia]] and share many of the characteristics that are definitional of synesthesia, such as being consistent over considerable time intervals and generating concurrents automatically {{Harv|Simner|Holenstein|2007}}. To demonstrate that personifications are automatically evoked, Simner and Holenstein used a modified [[Stroop effect|Stroop]] paradigm, in which a mismatch between the evoked personality and the gender leads to slower [[reaction time]]s. To test this, synesthete AP was asked to report whether common names, like Brian or Betsy were male or female names. Because ‘b’ is a male letter for AP, she was faster to identify Brian as being a male name, and slower to identify Betsy as being a female name. These results demonstrate that personifications are automatically evoked, as are other forms of synesthesia. In a slightly different task, in which letters that evoke either male or female personifications are arranged into a stick figure of either a boy or a girl, reactions times are slower when the letters do not match the figure than when they do, again demonstrating the automaticity of this form of synesthesia {{Harv|Sagiv|Amin|Olu-Lafe|Ward|2005}}.
Personifications tend to co-occur with [[grapheme-color synesthesia]] and share many of the characteristics that are definitional of synesthesia, such as being consistent over considerable time intervals and generating concurrents automatically.<ref name=Simner2007/> To demonstrate that personifications are automatically evoked, Simner and Holenstein used a modified [[Stroop effect|Stroop]] paradigm, in which a mismatch between the evoked personality and the gender leads to slower [[reaction time]]s. To test this, synesthete AP was asked to report whether common names, like Brian or Betsy were male or female names. Because 'b' is a male letter for AP, she was faster to identify Brian as being a male name, and slower to identify Betsy as being a female name. These results demonstrate that personifications are automatically evoked, as are other forms of synesthesia. In a slightly different task, in which letters that evoke either male or female personifications are arranged into a stick figure of either a boy or a girl, reactions times are slower when the letters do not match the figure than when they do, again demonstrating the automaticity of this form of synesthesia.<ref>{{cite journal|last=Sagiv|first=N.|last2=Amin|first2=M.|last3=Olu-Lafe| first3=O.|last4=Ward|first4=J.|year=2005|title= Beyond Colour: Further Varieties of Synaesthetic Experience|journal= 14th European Society for Cognitive Psychology Meeting, Aug 31 - Sep 3, Leiden, the Netherlands|url=http://www.psychologie.leidenuniv.nl/cog/content_docs/ESCoP2005/proceedingsweb2.pdf#page=34}}</ref>


==Neural and Developmental Basis==
==Neural and developmental basis==
One study in 2016 led by Prof. Julia Simner showed subtle differences in the white matter structure in the brains of people with OLP, compared with control subjects. These harmless differences were in five clusters, in the pre-postcentral gyrus/ dorsal corticospinal tract, left superior corona radiata, and the genu, body and left side of the corpus callosum. A number of these regions play a role in social responsiveness (Simner et al., 2016<ref>{{cite journal|last1=Simner|first1=J.|last2=Rehme|first2=M.K.|last3=Carmichael|first3=D.A.|last4=Bastin|first4=M.E.|last5=Sprooten|first5=E.|last6=McIntosh|first6=A.M.|last7=Lawrie|first7=S.M.|last8=Zedler|first8=M.|title=Social responsiveness to inanimate entities: Altered white matter in a 'social synaesthesia'|journal=Neuropsychologia|date=October 2016|volume=91|pages=282–289|doi=10.1016/j.neuropsychologia.2016.08.020|pmid=27553270|url=http://sro.sussex.ac.uk/64745/1/Simner_etal_DTI_Neuropsychologia.pdf}}</ref>).
One study in 2016 led by Prof. Julia Simner showed subtle differences in the white matter structure in the brains of people with OLP, compared with control subjects. These harmless differences were in five clusters, in the pre-postcentral gyrus, dorsal corticospinal tract, left superior corona radiata, and the genu, body and left side of the corpus callosum. A number of these regions play a role in social responsiveness.<ref>{{cite journal|last1=Simner|first1=J.|last2=Rehme|first2=M.K.|last3=Carmichael|first3=D.A.|last4=Bastin|first4=M.E.|last5=Sprooten|first5=E.|last6=McIntosh|first6=A.M.|last7=Lawrie|first7=S.M.|last8=Zedler|first8=M.|title=Social responsiveness to inanimate entities: Altered white matter in a 'social synaesthesia'|journal=Neuropsychologia|date=October 2016|volume=91|pages=282–289|doi=10.1016/j.neuropsychologia.2016.08.020|pmid=27553270|url=http://sro.sussex.ac.uk/64745/1/Simner_etal_DTI_Neuropsychologia.pdf}}</ref>


Number personification in children is typically considered a different phenomenon than OLP; though, like OLP, number personifications in children are typically temporally consistent and assignments of personalities to numbers is idiosyncratic, number personification is highly prevalent among children while OLP is uncommon among adults {{Harv|Matsuda|Okazaki|Asano|Yokosawa|2018}}. This is consistent with the pruning hypothesis, which states that synesthesia is common in early childhood but diminishes throughout development through [[synaptic pruning]].
Number personification in children is typically considered a different phenomenon than OLP; though, like OLP, number personifications in children are typically temporally consistent and assignments of personalities to numbers is idiosyncratic, number personification is highly prevalent among children while OLP is uncommon among adults.<ref>{{cite journal|last1=Matsuda |first1=Eiko|last2=Okazaki|first2=Yoshihiro|last3=Asano|first3=Michiko|last4=Yokosawa|year=2018|title=Developmental Changes in Number Personification by Elementary School Children|journal=Frontiers in Psychology|doi=10.3389/fpsyg.2018.02214|doi-access=free}}</ref> This is consistent with the pruning hypothesis, which states that synesthesia is common in early childhood but diminishes throughout development through [[synaptic pruning]].
==Among the Pythagoreans==
The [[Pythagoreans]], an ancient Greek cult of natural philosophers notable for their interest in [[numerology]], personified the natural numbers by assigning gender to them; the odd numbers were male and the even female {{Harv|Rucker|1988}}. However, given the prevalence of synesthesia (1 in 23, see the main [[Synesthesia#Prevalence|synesthesia]] entry), and that this is consistent among the Pythagoreans, this is unlikely to be synesthesia, but rather a form of learned association.


==In fiction==
==Cultural perceptions==
The [[Pythagoreans]], an ancient Greek cult of natural philosophers notable for their interest in [[numerology]], personified the natural numbers by assigning gender to them; the odd numbers were male and the even female.<ref>{{cite book|last=Rucker|first=R.|year=1995|title=Infinity and the Mind|publisher=Princeton University Press|isbn=978-0-691-00172-2}}</ref> However, given the prevalence of synesthesia (1 in 23, see the main [[Synesthesia#Prevalence|synesthesia]] entry), and that this is consistent among the Pythagoreans, this is unlikely to be synesthesia, but rather a form of learned association.

===In popular culture===
In ''[[A Tree Grows in Brooklyn (novel)|A Tree Grows in Brooklyn]]'', Francie gives numbers personalities while learning basic math operations. She gives X and Y personalities as well.
In ''[[A Tree Grows in Brooklyn (novel)|A Tree Grows in Brooklyn]]'', Francie gives numbers personalities while learning basic math operations. She gives X and Y personalities as well.


In "[https://www.loc.gov/poetry/180/051.html A Primer of the Daily Round]," poet [[Howard Nemerov]] assigns actions to personified letters of the alphabet.
In "A Primer of the Daily Round," poet [[Howard Nemerov]] assigns actions to personified letters of the alphabet.<ref>{{cite web|last1=Nemerov |first1=Howard |title=A Little Girl Tugs at the Tablecloth |url=https://www.loc.gov/poetry/180/051.html |website=Library of Congress, Washington, D.C. 20540 USA}}</ref>


On the first episode of season thirty-one of ''[[Jeopardy!]]'', show champion Elizabeth Williams spoke of her experience with ordinal linguistic personification during the contestant interview portion of the show. She reported to host [[Alex Trebek]] that nine "has a mustache, like you."<ref>{{cite news|last=Heil|first=Emily|url=https://www.washingtonpost.com/news/reliable-source/wp/2014/09/16/d-c-jeopardy-contestants-riveting-take-on-alex-trebeks-mustache/|title=D.C. 'Jeopardy!' contestant's riveting take on Alex Trebek's mustache|work=The Washington Post|date=16 September 2014|access-date=1 July 2016}}</ref>
==On television==
On the first episode of season thirty-one of ''[[Jeopardy!]]'', Jeopardy! Champion Elizabeth Williams spoke of her experience with ordinal linguistic personification during the contestant interview portion of the show. She reported to host [[Alex Trebek]] that nine "has a mustache, like you."<ref>{{cite web | url=https://www.washingtonpost.com/news/reliable-source/wp/2014/09/16/d-c-jeopardy-contestants-riveting-take-on-alex-trebeks-mustache/ | title=D.C. 'Jeopardy!' contestant's riveting take on Alex Trebek's mustache | work=The Washington Post | date=September 16, 2014 | access-date=July 1, 2016 | author=Heil, Emily}}</ref>


==See also==
==See also==
* [[Synesthesia]]
* [[Ideasthesia]]
* [[Ideasthesia]]
* [[Synesthesia]]


==References==
==References==
{{reflist}}
{{reflist}}
{{refbegin}}
* {{Citation
| last= Calkins | first= M. W. | author-link=Mary Whiton Calkins
| year= 1893
| title= A Statistical Study of Pseudo-chromesthesia and of Mental-forms
| journal= American Journal of Psychology
| issue= 4| volume= 5 | pages= 439–464
| doi=10.2307/1411912| jstor= 1411912 }}
* {{Citation
| last= Cytowic | first= R. E.
| year=2002
| title= Synesthesia: A Union of the Senses, 2nd ed
| place= Cambridge, MA | publisher= MIT Press
| isbn=0-262-03296-1
| url= http://cytowic.net/_Books/_books.html}}
* {{Citation
| last= Flournoy | first= T.
| year= 1893
| title= Des Phénomènes de Synopsie
| place= Geneva and Paris | publisher= Alcan
}}
* {{Citation
| last1=Matsuda | first1=Eiko | last2=Okazaki | first2=Yoshihiro | last3=Asano | first3=Michiko | last4=Yokosawa
| year= 2018
| title= Developmental Changes in Number Personification by Elementary School Children
| journal = Frontiers in Psychology
| doi = 10.3389/fpsyg.2018.02214
| doi-access=free }}
* {{Citation
| last= Sagiv | first= N. | last2= Amin | first2= M.
| last3= Olu-Lafe | first3= O. | last4= Ward | first4= J.
| year=2005
| title= Beyond Colour: Further Varieties of Synaesthetic Experience
| journal= 14th European Society for Cognitive Psychology Meeting, Aug 31 - Sep 3, Leiden, the Netherlands
| url= http://www.psychologie.leidenuniv.nl/cog/content_docs/ESCoP2005/proceedingsweb2.pdf#page=34}}
* {{Citation
| last= Simner | first= J. | last2= Holenstein | first2= E.
| year = 2007
| title = Ordinal linguistic personification as a variant of synesthesia
| journal= Journal of Cognitive Neuroscience
| issue=4 | volume=19 | pages=694–703
| pmid=17381259
| doi=10.1162/jocn.2007.19.4.694}}
* {{Citation
| last= Simner | first= J. | last2= Hubbard | first2= E. M.
| year = 2006
| title = Variants of synaesthesia interact in cognitive tasks: Evidence for implicit associations and late connectivity in cross-talk theories
| journal= Neuroscience
| issue=3 | volume=143 | pages=805–814
| pmid=16996695
| doi=10.1016/j.neuroscience.2006.08.018}}
* {{Citation
| last= Rucker | first= R.
| year= 1995
| title = Infinity and the Mind
| publisher = Princeton University Press
| isbn = 978-0-691-00172-2}}

{{refend}}


[[Category:Synesthesia]]
[[Category:Synesthesia]]

Revision as of 18:11, 12 May 2023

Ordinal-linguistic personification (OLP, or personification for short) is a form of synesthesia in which ordered sequences, such as ordinal numbers, days, months and letters are associated with personalities or genders.[1] Although this form of synesthesia was documented as early as the 1890s,[2][3] researchers have, until recently, paid little attention to this form (see History of synesthesia research).

Experiences and reports

In Flournoy's 1893 reports on OLP, one synesthete identified as Mme L. reports that "1, 2, 3 are children without fixed personalities; they play together. 4 is a good peaceful woman, absorbed by down-to-earth occupations and who takes pleasure in them. 5 is a young man, ordinary and common in his tastes and appearance, but extravagant and self-centered. 6 is a young man of 16 or 17, very well brought up, polite, gentle, agreeable in appearance, and with upstanding tastes; average intelligence; orphan. 7 is a bad sort, although brought up well; spiritual, extravagant, likable; capable of very good actions on occasion; very generous. 8 is a very dignified lady, who acts appropriately, and who is linked with 7 and has much influence on him. She is the wife of 9. 9 is the husband of 8. He is self-centered, maniacal, selfish, thinks only about himself, is grumpy, endlessly reproaching his wife for one thing or another; telling her, for example, that he would have been better to have married a 9 since between them they would have made 18 – as opposed to only 17 with her… 10, and the other remaining numerals, have no personifications."[2]: 219–220 

Calkins (1893) describes a case for whom "T's are generally crabbed, ungenerous creatures. U is a soulless sort of thing. 4 is honest, but… 3 I cannot trust… 9 is dark, a gentleman, tall and graceful, but politic under his suavity".[3]: 454 

For synesthete MT, "I [is] a bit of a worrier at times, although easy-going; J [is] male; appearing jocular, but with strength of character; K [is] female; quiet, responsible…"[4]: 298 

Simner and Holstein report an OLP case in which the synesthete perceived February as "an introverted female", while F is a "[male] dodgy geezer". Similarly, May is reported to be "soft-spoken" and "girly" while M is an "old lady [who] natter[s] a lot", and while August is "a boy among girls", A is a female "mother type".[1][5]

Experimental studies

Personifications tend to co-occur with grapheme-color synesthesia and share many of the characteristics that are definitional of synesthesia, such as being consistent over considerable time intervals and generating concurrents automatically.[5] To demonstrate that personifications are automatically evoked, Simner and Holenstein used a modified Stroop paradigm, in which a mismatch between the evoked personality and the gender leads to slower reaction times. To test this, synesthete AP was asked to report whether common names, like Brian or Betsy were male or female names. Because 'b' is a male letter for AP, she was faster to identify Brian as being a male name, and slower to identify Betsy as being a female name. These results demonstrate that personifications are automatically evoked, as are other forms of synesthesia. In a slightly different task, in which letters that evoke either male or female personifications are arranged into a stick figure of either a boy or a girl, reactions times are slower when the letters do not match the figure than when they do, again demonstrating the automaticity of this form of synesthesia.[6]

Neural and developmental basis

One study in 2016 led by Prof. Julia Simner showed subtle differences in the white matter structure in the brains of people with OLP, compared with control subjects. These harmless differences were in five clusters, in the pre-postcentral gyrus, dorsal corticospinal tract, left superior corona radiata, and the genu, body and left side of the corpus callosum. A number of these regions play a role in social responsiveness.[7]

Number personification in children is typically considered a different phenomenon than OLP; though, like OLP, number personifications in children are typically temporally consistent and assignments of personalities to numbers is idiosyncratic, number personification is highly prevalent among children while OLP is uncommon among adults.[8] This is consistent with the pruning hypothesis, which states that synesthesia is common in early childhood but diminishes throughout development through synaptic pruning.

Cultural perceptions

The Pythagoreans, an ancient Greek cult of natural philosophers notable for their interest in numerology, personified the natural numbers by assigning gender to them; the odd numbers were male and the even female.[9] However, given the prevalence of synesthesia (1 in 23, see the main synesthesia entry), and that this is consistent among the Pythagoreans, this is unlikely to be synesthesia, but rather a form of learned association.

In popular culture

In A Tree Grows in Brooklyn, Francie gives numbers personalities while learning basic math operations. She gives X and Y personalities as well.

In "A Primer of the Daily Round," poet Howard Nemerov assigns actions to personified letters of the alphabet.[10]

On the first episode of season thirty-one of Jeopardy!, show champion Elizabeth Williams spoke of her experience with ordinal linguistic personification during the contestant interview portion of the show. She reported to host Alex Trebek that nine "has a mustache, like you."[11]

See also

References

  1. ^ a b Simner, J.; Hubbard, E. M. (2006). "Variants of synaesthesia interact in cognitive tasks: Evidence for implicit associations and late connectivity in cross-talk theories". Neuroscience. 143 (3): 805–814. doi:10.1016/j.neuroscience.2006.08.018. PMID 16996695.
  2. ^ a b Flournoy, T. (1893). Des Phénomènes de Synopsie. Geneva and Paris: Alcan.
  3. ^ a b Calkins, M. W. (1893). A Statistical Study of Pseudo-chromesthesia and of Mental-forms. Vol. 5. pp. 439–464. doi:10.2307/1411912. JSTOR 1411912. {{cite book}}: |journal= ignored (help)
  4. ^ Cytowic, R. E. (2002). "Synesthesia: A Union of the Senses, 2nd ed". Cambridge, MA: MIT Press. ISBN 0-262-03296-1. {{cite journal}}: Cite journal requires |journal= (help)
  5. ^ a b Simner, J.; Holenstein, E. (2007). "Ordinal linguistic personification as a variant of synesthesia". Journal of Cognitive Neuroscience. 19 (4): 694–703. doi:10.1162/jocn.2007.19.4.694. PMID 17381259.
  6. ^ Sagiv, N.; Amin, M.; Olu-Lafe, O.; Ward, J. (2005). "Beyond Colour: Further Varieties of Synaesthetic Experience" (PDF). 14th European Society for Cognitive Psychology Meeting, Aug 31 - Sep 3, Leiden, the Netherlands.
  7. ^ Simner, J.; Rehme, M.K.; Carmichael, D.A.; Bastin, M.E.; Sprooten, E.; McIntosh, A.M.; Lawrie, S.M.; Zedler, M. (October 2016). "Social responsiveness to inanimate entities: Altered white matter in a 'social synaesthesia'" (PDF). Neuropsychologia. 91: 282–289. doi:10.1016/j.neuropsychologia.2016.08.020. PMID 27553270.
  8. ^ Matsuda, Eiko; Okazaki, Yoshihiro; Asano, Michiko; Yokosawa (2018). "Developmental Changes in Number Personification by Elementary School Children". Frontiers in Psychology. doi:10.3389/fpsyg.2018.02214.
  9. ^ Rucker, R. (1995). Infinity and the Mind. Princeton University Press. ISBN 978-0-691-00172-2.
  10. ^ Nemerov, Howard. "A Little Girl Tugs at the Tablecloth". Library of Congress, Washington, D.C. 20540 USA.
  11. ^ Heil, Emily (16 September 2014). "D.C. 'Jeopardy!' contestant's riveting take on Alex Trebek's mustache". The Washington Post. Retrieved 1 July 2016.