Subject: Re: Beware of circles From: Brian Gygi <bgygi@xxxxxxxx> Date: Wed, 24 Mar 2010 23:45:25 +0000 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>----=_vm_0011_W7428020310_11950_1269474325 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Dear Bruno, No wonder they call them "vicious circles." Brian Gygi, Ph.D. Speech and Hearing Research Veterans Affairs Northern California Health Care System 150 Muir Road Martinez, CA 94553 (925) 372-2000 x5653 -----Original Message----- From: Bruno L. Giordano [mailto:bruno.giordano@xxxxxxxx Sent: Wednesday, March 24, 2010 02:46 PM To: AUDITORY@xxxxxxxx Subject: Beware of circles Hello,I can't resist writing a methodological note about circles and whee= ls.In the original posting by Michael, the wheel was conceived as a morph= ing strategy.Stating the obvious, and following up on Richard's note, for= the psychologist the circle can happen to be a concise and visually eleg= ant model of how humans organize a particular sensory/perceptual/cognitiv= e domain. Such a representation is often grounded in the construct of sim= ilarity (objects that are close/far within the representation are similar= /different).Now, my note is about those cases where circular representati= ons are extracted from the multidimensional scaling (MDS) analysis of beh= avioral estimates of similarity. I have seen several of these.What I have= rarely seen pointed out is that popular MDS algorithms under specific bu= t not uncommon circumstances are prone to representing the data as a circ= ular (2D) or spherical (3D) structure, independently of whether a circle/= sphere is there or not. From my understanding, this MDS modeling bias tak= es the name of "annular bias". A similar bias takes the name of "horsesho= e effect".So, circles can be attractive, but there are times when we shou= ld beware of them.=09Bruno~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Bruno L. Gio= rdano, Ph.D.Postdoctoral Research FellowCIRMMT - Schulich School of Music= 555 Sherbrooke Street WestMontr=E9al, QC H3A1E3Canada+1 514 398 4535, Ext= . 00900 (voice)+1 514 398 2962 (fax)http://www.music.mcgill.ca/~brunoRich= ard E Pastore wrote:> What is the reasonable goal of finding an auditory = circle analogy to the > visual color circle?> Although the discussion has= focused on finding an auditory analogue > to the color wheel, the discus= sion really has focused on the wheel. > Color is an artifical system that= represents wavelength, with a > resulting representation of artificial "= nonspectral hues" that do not > correspond to wavelengths in the visible = spectrum. Color space was > defined using color mixing findings. The typi= cal figure from those data > is essentially a triangle with rounded corne= rs. The three primary > colors are at the three corners outside the space= . If 400 and 700 nm > ("blue" and "red") at maximum saturation are along = the abscissa and > roughly 520 nm at the apex of the triangle, the wavele= ngths of the > visible spectrum runs along the outside from the 400 nm co= rner (blue) > through the apex (green) to the 700 nm corner (red). The ab= scissa maps > the non-spectral hues that are an artificial by-product of = mixing the > long and short wavelengths. The space is populated from the = edge to the > non-central region of total desaturation (white) by systema= tic > decreasing saturation or spectral purity. Complimentary colors are = the > opposite ends of any line through "white." This 2-dimensional space= is > actually a cross-section of a 3-D representation, with the 3rd dime= nsion > being intensity or brightness.> The edge from the apex to the lon= g wavelength corner (700 nm) > represents the opponent processing interac= tion between the long (red) > and middle (green) primaries. The space bec= omes populated with the > addition of the opponent processing between the= short wavelength primary > (Blue) and the combined long and middle prima= ries (Yellow =3D Red + > Green). Because of the opponent neural coding th= at is driven by the > breakdown of the light sensitive photopigments, the= afterimages are the > complimentary color of the original.> The "classic= color circle" is a simplified, stylizied version of the > outer edge of = the 2-D cross-section. It is round (a circle) that is > unpopulated and w= ith a gap to represent the non-spectral hue portion of > color space - th= e circle is NOT complete.> Now, back to the original question that prompt= ed the discussion: > What is the "auditory" circle intended to represent = and in what way is > it analogous to the color circle? > > Dick Pastore> = -- > Richard E Pastore> Distinguished Service Professor> Department of Ps= ychology> Binghamton University> Binghamton, NY 13902-6000> Office: (607)= 777-2539 ----=_vm_0011_W7428020310_11950_1269474325 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable <html>Dear Bruno,<br><br>No wonder they call them "vicious circles."<br><= br><div><font face=3D"Verdana" size=3D"2"> </font></div> Brian Gygi, Ph.D. <br> Speech and Hearing Research <br> Veterans Affairs Northern California Health Care System <br> 150 Muir Road <br> Martinez, CA 94553 <br> (925) 372-2000 x5653<div><font color=3D"#0000ff" face=3D"Verdana" size=3D= "2"></font> </div> <blockquote style=3D"border-left: 2px solid rgb(0, 0, 255); padding-left:= 5px; margin-left: 5px; margin-right: 0px;"><font face=3D"Tahoma" size=3D= "2">-----Original Message-----<br><b>From:</b> Bruno L. Giordano [mailto:= bruno.giordano@xxxxxxxx<br><b>Sent:</b> Wednesday, March 24, 2010= 02:46 PM<br><b>To:</b> AUDITORY@xxxxxxxx<br><b>Subject:</b> Bewar= e of circles<br><br></font>Hello, I can't resist writing a methodological note about circles and wheels. In the original posting by Michael, the wheel was conceived as a morphing strategy. Stating the obvious, and following up on Richard's note, for the psychologist the circle can happen to be a concise and visually elegant model of how humans organize a particular sensory/perceptual/cognitive domain. Such a representation is often grounded in the construct of similarity (objects that are close/far within the representation are similar/different). Now, my note is about those cases where circular representations are extracted from the multidimensional scaling (MDS) analysis of behavioral = estimates of similarity. I have seen several of these. What I have rarely seen pointed out is that popular MDS algorithms under = specific but not uncommon circumstances are prone to representing the data as a circular (2D) or spherical (3D) structure, independently of whether a circle/sphere is there or not. From my understanding, this MDS = modeling bias takes the name of "annular bias". A similar bias takes the = name of "horseshoe effect". So, circles can be attractive, but there are times when we should beware = of them. =09Bruno ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Bruno L. Giordano, Ph.D. Postdoctoral Research Fellow CIRMMT - Schulich School of Music 555 Sherbrooke Street West Montr=E9al, QC H3A1E3 Canada +1 514 398 4535, Ext. 00900 (voice) +1 514 398 2962 (fax) http://www.music.mcgill.ca/~bruno Richard E Pastore wrote: > What is the reasonable goal of finding an auditory circle analogy to= the > visual color circle? > Although the discussion has focused on finding an auditory analog= ue > to the color wheel, the discussion really has focused on the wheel. = > Color is an artifical system that represents wavelength, with a > resulting representation of artificial "nonspectral hues" that do no= t > correspond to wavelengths in the visible spectrum. Color space was = > defined using color mixing findings. The typical figure from those = data > is essentially a triangle with rounded corners. The three primary > colors are at the three corners outside the space. If 400 and 700 n= m > ("blue" and "red") at maximum saturation are along the abscissa and = > roughly 520 nm at the apex of the triangle, the wavelengths of the > visible spectrum runs along the outside from the 400 nm corner (blue= ) > through the apex (green) to the 700 nm corner (red). The abscissa = maps > the non-spectral hues that are an artificial by-product of mixing th= e > long and short wavelengths. The space is populated from the edge to= the > non-central region of total desaturation (white) by systematic > decreasing saturation or spectral purity. Complimentary colors are = the > opposite ends of any line through "white." This 2-dimensional space= is > actually a cross-section of a 3-D representation, with the 3rd dimen= sion > being intensity or brightness. > The edge from the apex to the long wavelength corner (700 nm) > represents the opponent processing interaction between the long (red= ) > and middle (green) primaries. The space becomes populated with the= > addition of the opponent processing between the short wavelength pri= mary > (Blue) and the combined long and middle primaries (Yellow =3D Red + = > Green). Because of the opponent neural coding that is driven by the= > breakdown of the light sensitive photopigments, the afterimages are = the > complimentary color of the original. > The "classic color circle" is a simplified, stylizied version of = the > outer edge of the 2-D cross-section. It is round (a circle) that is= > unpopulated and with a gap to represent the non-spectral hue portion= of > color space - the circle is NOT complete. > Now, back to the original question that prompted the discussion: = > What is the "auditory" circle intended to represent and in what way = is > it analogous to the color circle? > > Dick Pastore > -- > Richard E Pastore > Distinguished Service Professor > Department of Psychology > Binghamton University > Binghamton, NY 13902-6000 > Office: (607) 777-2539 </blockquote></html> ----=_vm_0011_W7428020310_11950_1269474325--