UCB/UCSD Workshop in cognitive linguistics, January, 1996

Optimality Principles and Conceptual Integration   	
Gilles Fauconnier and Mark Turner

Integration The blend must constitute a tightly integrated scene that can be manipulated as a unit.  More generally, every space in the blend structure should have integration.

Web Manipulating the blend as a unit must maintain the web of appropriate connections to the input spaces easily and without additional surveillance or computation.  

Unpacking The blend alone must enable the understander to unpack the blend to reconstruct the inputs, the cross-space mapping, the generic space, and the network of connections between all these spaces

Topology For any input space and any element in that space projected into the blend, it is optimal for the relations of the element in the blend to match the relations of its counterpart.  

Good reason All things being equal, if an element appears in the blend, there will be pressure to find significance for this element.  Significance will include relevant links to other spaces and relevant functions in running the blend. 

Metonymy projection constraint When an element is projected from an input to the blend and a second element from that input is projected because of its metonymic link to the first, shorten the metonymic distance between them in the blend. 

Pressures

Non-disintegration.  Neutralize projections and topological relations that would dis-integrate the blend.  

Non-displacement   Do not disconnect valuable web connections to inputs.  

Non-interference. Avoid projections from input spaces to the blend that defeat each other in the blend.  

Non-ambiguity Do not create ambiguity in the blend that interferes with the computation.  

Backward projection  As the blend is run and develops emergent structure, avoid backward projection to an input that will disrupt the integration of the input itself.

A taxonomy of blend structures

TO  Structures

TF Structures  

Example boat race,  debate

One-sided TO Structure

Example  boxing business competitors, 'simple' metaphors

Symmetric

Example  Complex numbers, with emergent structure of angles and multiplication;   Desktop interface.

Asymmetric

Example  fighting with Bob Dole in your pocket

Asymmetric with high secondary topology 
Example  boxing Pope

Symmetric with metonymy projection
Printing press smashing car, with projection of intentionality.
Symmetric with metonymy projection and additional frame recruitment
Workers with press and car;  Bertran de Born.

Partially Unfilled TO Structures  (UTO's)

Generic space does not specify 
Direction of Motion/Causality/Sequentiality... 
Intentionality
==>  Inputs may clash at a level lower than TO but higher than TF

	

	TF-UTO
Example  Buddhist monk  -  both directions are projected to the Blend, without clash, because counterparts are not fused.
	
	Two-sided UTO
Example  digging your own grave  -  basic TF_1 comes from Input 1 (graves and death), but Causality, Sequentiality, Intentionality come from Input 2. This clash produces an emergent frame F_B in the Blend and a specific topology TF_B.

Local and global complexity for a TO Structure 
A TO is locally simple for a blend element projected from an input element if the topology of the blend element matches the organizing topology (full TO) of that input element and that input element's counterpart in the other input.  [Example the boxing business competitors.]  
Otherwise, a TO is locally complex, either because the input element has no counterpart in the other input, or because it does have such a counterpart but with an incompatible organizing topology.

Pressures and competition

Non disintegration 
Example  The basic principle of the computer desktop is that everything is on the two-dimensional computer screen.  In the input space of real office work, the trashcan is not on the desktop.  By Topology, the location of the trashcan as not on the desktop would be projected to the computer interface blend; but doing so would destroy the internal integration of the blend, which is why, on the computer screen desktop, the trashcan is on the desktop.  Integration of the blend in this case can only be achieved by relaxing the topology constraint. 

Non displacement
Example  If a user is running five different applications on the desktop and wants to see only one of them, he can click "Hide Others" (conversely, "Show others"); to see a given document partially occluded by another, he need only click anywhere on the desired document.  But in the space of offices, to hide everything on your desk except the one thing you wish to focus on would require complex physical operations.  If these operations were all projected to the blend, it would sever its useful web connections to the input of computer operation.  Function guides competition here. 

Non interference
Example  In the space of office work, we often write "discard" across the top of an outdated version to be discarded.  In the computer desktop, the icon for a file has only one place for a label.  If we projected to the computer desktop the operation of labeling the document "discard" by making a click-command that put that label on the icon, we would lose the title of the file.  So the "title" label and the "discard" label from the space of office work defeat each other if both are projected to the blend.

Non ambiguity
Example  Ejecting floppy disks.  Superposition of  icon a over icon b "means" copying/inserting the contents of a "into" b.  So a plausible interpretation of the disk icon being moved over the trashcan icon is that the contents of the disk is transferred to the trashcan.  But in fact, the meaning in this particular case is entirely different ("eject disk from computer").  This makes the superposition schema in the blend ambiguous.

Backward projection
Example  Under pressure from Integration, the desktop blend places the trashcan on the desktop, but projecting this relation backward to the input of the actual desks would disrupt their efficient use. 

Multiple violation  
Ejecting floppies.
Copy/Paste  The command sequence Select-Copy-Paste on word-processing applications violates Topology.  In the Input where text is actually copied by scribes or xerox machines, copying (after selection) is a one-step operation.  There is no pasting and no clipboard.  Properties specific to the Integration in the blend make it convenient to decompose this operation into two, but they do not map topologically onto corresponding operations in the Input of "real copying."  The labels "Copy" and "Paste" chosen for these two operations in the Blend violate Web, and its corollary, Non-displacement  the Copy operation in the Blend (which actually produces no visible change in the text) does not correspond to the Copy operation in the Input (which does produce visible change); the Paste operation, which does produce change, is closer to "copying" in the Input, but the label "Paste" suggests a counterpart (pasting), which is not even part of the copying process.

The debate with Kant
I claim that reason is a self-developing capacity.  Kant disagrees with me on this point.  He says it's innate, but I answer that that's begging the question, to which he counters, in Critique of Pure Reason, that only innate ideas have power.  But I say to that, what about neuronal group selection?  And he gives no answer.
The Buddhist monk
Riddle of the Buddhist monk and the mountain A Buddhist monk begins at dawn one day walking up a mountain, reaches the top at sunset, mediates at the top for several days until one dawn when he begins to walk back to the foot of the mountain, which he reaches at sunset.  Making no assumptions about his starting or stopping or about his pace during the trips, prove that there is a place on the path which he occupies at the same hour of the day on the two separate journeys.   
Action blends
I'm driving, and someone is sitting in the front passenger seat, talking to me, but I have trouble hearing what they say.  I turn the volume knob on the car radio (which is off, of course).  I've blended the frames for listening to the radio and for conversing with a passenger.  I can't appeal to simple error I am in no way under the misapprehension that the voice is coming from the radio, or that turning knobs will make people speak more loudly.  What I have done, irrelevant, inefficient, and absurd as it may be, is EXTEND my category of controlled sound amplification within a blended space.  
Science
The substance here treated of does not possess any of the properties of ordinary fluids except that of freedom of motion.  It is not even a hypothetical fluid which is introduced to explain actual phenomena.  It is simply a collection of imaginary properties, which may be employed for establishing certain theorems in pure mathematics in a way more intelligible to ordinary minds than that in which algebraic symbols are used.  The use of the word 'Fluid' will not lead us into error if we remember that it simply denotes an imaginary substance with the properties -
[Maxwell 1855 - Electricity, Heat, Magnetism, Galvanism]  (Lansing)

"... several scientists insisted that the term virus is more than a nice metaphor. ... Although computer viruses are not fully alive, they embody many of the characteristics of life, and it is not hard to imagine computer viruses of the future that will be just as alive as biological viruses." 
[N.Y. Times 2/25/90]

Complex numbers  cross-space mapping maps real numbers to one-dimensional space,
maps 'imaginary' numbers to two-dimensional space (Wallis).  In the Blend numbers have number properties (addition, multiplication, square roots, etc.), vector properties (angle, magnitude), and point properties (coordinates). Angles come only from 'spatial' Input.  Multiplication comes only from 'number' input.  In Blend, multiplication includes addition of angles. (emergent structure).
Humor
MENENDEZ BROTHERS VIRUS  Eliminates your files, takes the disk space they previously occupied, and then claims that it was a victim of physical and sexual abuse on the part of the files it erased. (Coulson)

Jay Leno on Sidney Biddle Barrows' new job as "expert" commentator for the Heidi Fleiss trial at one of the cable channels
Instead of hiring a legal expert, they got a woman who made her name as a madam.  They figured it's a few bucks cheaper, and she essentially does the same thing.
The boat race
As we went to press, Rich Wilson and Bill Biewenga were barely maintaining a 4.5 day lead over the ghost of the clipper Northern Light, whose record run from San Francisco to Boston they're trying to beat.  In 1853, the clipper made the passage in 76 days, 8 hours.  —"Great America II," Latitude 38, volume 190, April 1993, page 100.

At this point, Great America II is 4.5 days ahead of Northern Light.  

Metaphor

Boxing business competitors  Rupert Murdoch knocked out Iacocca.

Printing press smashing a car with glee represents the same situation. (cartoon)

George Bush was born on third base and thinks he hit a triple.

Dan Quayle was born on third base and thinks he kicked a field goal.

The stork dropped George Bush on third base with a silver spoon in his mouth.

Max is digging his own grave.

He's driving his mother into her grave. ( Lakoff )

The U.S. is in a position to exhume itself from the shallow grave that we've dug for ourselves. [ The UCSD Guardian ]  ( Coulson )

Elmer was so angry, the smoke was coming out of his ears.

Bertran de Born
[Context In the Inferno (canto 28, lines 139-142), Dante presents Bertran de Born, who while living had instigated strife between the King of England and the king's son.  In hell, Bertran carries his head in his hand, and says]

Perch'io parti' così giunte persone,	Because I parted people so joined,
partito porto il meo cerebro, lasso!	I carry my brain, alas, separated
dal suo principio ch'è in questo toncone.	from its root, which is in this trunk.
Così s'osserva in me lo contrapasso.	Thus is to be seen in me the retribution.

"So foul a sky clears not without a storm. / Pour down thy weather." 
[Context King John speaks to a troubled-looking (and perhaps tongue-tied) messenger who appears before him.  Shakespeare, King John Act 4, scene 2, lines 108-109.]

"I have a feeling that if you walked through Huffington's deepest thoughts, you wouldn't get your feet wet."

Analogical counterfactuals
In France, Watergate would not have harmed Nixon.
"Why punish me for the sins of my father?" ( Coulson )
"If I were his wife, I would have been his widow long ago." ( Mandelblit )
If Churchill had been prime minister in 1938, WW II would have been averted.
If I were you, I wouldn't get pregnant.

Multiple Blends

 "What President Clinton did, bravely and brilliantly, I think, was to gamble that the repertory actors of the health care industry have frightened Americans so badly that we are willing to accept anything, including higher taxes, rather than to continue being extras in a medical melodrama that resembles nothing so much as an endless "Dracula" movie where the count always wins, right up to the last drop."  [Written by Richard Reeves, in a Los Angeles Times article titled "Best Performance by a Politician."  Example discovered by Bill Gleim]

  "The Dracula crowd will scream 'socialized medicine' and moan that you won't be able to pick your own doctor."   [Reeves.]

Why God won't get tenure

1. Only published one book.				9. When one experiment went awry, He tried to 							cover it up by drowning all the subjects.
2. It was in Hebrew.					10. When sample subjects do not behave as 							predicted, He deletes the whole sample.
3. It had no references.					11. He rarely comes to class-just tells His 							students to read the Book.
4. He did not publish it in referenced journals.			12. It is rumored that He sometimes lets His 							Son teach the class.
5. Some doubt He even wrote it Himself.			13. Although He only has 10 requirements, His 							students often fail His tests.
6. He is not known for His cooperative work.			14. He expelled His first two students for 							learning.
7. Sure, He created the world, but what has He done lately?	15. His office hours were infrequent and usually 
8. He did not get permission from any review board to work 	held on a mountain top.
with human subjects.