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Can Cognitive Science Survive Hypercomputation?
Selmer BringsjordProfessor of Logic, Philosophy, Cognitive Science, and Computer Science
with...
Marc DestefanoClinical Assistant Professor of Game Studies
Rensselaer AI & Reasoning (RAIR) Laboratory
Department of Cognitive Science
Department of Computer Science
Rensselaer Polytechnic Institute (RPI)
Troy NY 12180 USA
Cognitive Science Society Online Lecture [email protected] http://www.rpi.edu/~brings
Cognitive Science and artificial intelligence (AI) assume that
cognition is computation.
Newell’s “20 Questions” Paper
• The study of the mind is painfully fragmentary, but at any rate...
• Man is a computer.
Pinker’s How the Mind Works
• “The mind is a system of organs of computation designed by natural selection to solve problems faced by our evolutionary ancestors in their foraging way of life.”
Anderson’s Recent “Newell Test” Paper in BBS
• The study of the mind is less fragmentary now, and certainly...
• Humans are computers.
Are Newell & Simon & Co. correct?Are human persons computers?
No. They’re wrong. And they can be wrong...even if we are fundamentally information processors.
R1 R2 R3
If R5 is non-empty, take a bead away.,,,
If they’re right, this is what, at bottom, we are!
R4 R5 R6 R7 R8 R9
“Humble” Circle of Computation
Turing machines
Abaci
Register machines(modern high-speeddigital computers)
Recursive functions
“Humble” Circle of Computation
Turing machines
Abaci
Register machines(modern high-speeddigital computers)
Recursive functions
-calculus
“Humble” Circle of Computation
Turing machines
Abaci
Register machines(modern high-speeddigital computers)
Recursive functions
-calculus
programming languages(Lisp, C++, ...)
“Humble” Circle of Computation
Turing machines
Abaci
Register machines(modern high-speeddigital computers)
Recursive functions
-calculusprogramming languages(Lisp, C++, ...)
logic programming(in first-order logic)
But we’re not mere carbon-basedcreatures somewhere in this circle
(of mere animal life)!
The Mathematical Landscape
Space of all information processes
The “Turing Limit”
Turing machines, abaci, programs, …
Hypercomputation, now exploding with activity revolutionizing computer science, mathematics, physics, etc.
Analog Chaotic Neural Networks, Zeus Machines, Weyl Machines, P/Poly Machines, …
} Cognitive Science & AI
What are we?
“TuringLimit”
Turing machines, abaci, programs, …
Analog Chaotic Neural Networks, Zeus Machines, Weyl Machines, P/Poly Machines, …
Superminds!Phenomena not capturable in any third-person scheme.
e.g., phenomenal consciousness (e.g., that which it feels like to carve ski turns at 40mph)
So what are these hypercomputers you’re talking
about?We know what computers are.
What’s a hypercomputer?
Bertrand Russell (1936):“Ambrose says it is logically impossible [for a man] to run throughthe whole expansion of . I should have said it was medically impossible. ... Might not a man's skill increase so fast that he performed each operation in half the time required for its predecessor?In that case, the whole infinite series would take only twice as long as the first operation.”
A Hypercomputer: Zeus Machine
7th Grade Math Problem, Anticipating Elementary Calculus
€
limn →∞
1
4n= 0
John Anderson: “But Godel shot down Hilbert’s Program
with a proof! You’re just claiming.”
Ok, fair enough.I have proofs, or at least formal
arguments. Seventeen of them, in fact.Today, one intuitive, one precise
(synopsis only, of course).
The Mountaineering “Argument”Imagine a race of creatures:ipas (ih-pah-s). Ipas areinformation-processingcreatures. They live on the HighPeaks of Hypercomputation, and are capable of phenomenal feats of information processing (suchas cracking the halting problem).We know this because some humansare able to climb the mountainsand study the ipas. In fact, thesehumans have proved all kindsof things about the capability ofipas, and in general know whatthe essence of ipa cognition is.
And yet it is said that no humansare capable of ipa mentation, but are forever limited to living in theValley of Turing Machines.
Ipas
Humans
Argument from Infinitary Reasoning(from Superminds)
Proof. Assume that all human reasoning is at or beneaththe Turing Limit. Then all chains of human reasoning(e.g., proofs) are identical to some chain of reasoningexpressed in first-order logic. But there are many chainsof human reasoning in infinitary logics, and we know that such chains in infinitary logic cannot possibly beexpressed in first-order logic. Contradiction! So, byindirect proof, the starting assumption (which has led toabsurdity) is false. I.e., it’s not true that all human reasoningis at or beneath the Turing Limit. QED
If we are superminds, then, by the way, the received view
concerning our origins explodes...
A Proof that People Didn’t Evolve
(1) If people are the product of evolution, they were produced by an algorithmic process (= by a process at or below the Turing Limit).
(2) Theorem Ã: No algorithmic process can produce a device capable of hypercomputation.
(3) People are capable of hypercomputation.(4) People were not produced by an algorithmic
process. (from 3 and 4)(5) People aren’t the product of evolution.(from 4 and 1)
If we are superminds, how then should we proceed, in concrete
terms?
Next-Generation “Weak” Logic-based CogSci/AI
• Isolate and dissect human ingenuity.(psychology of reasoning)
• Mathematize a weak correlate to this ingenuity courtesy of advanced logical systems.• Implement this correlate in working programs.• Augment the correlate with machine-specific power.
The Rensselaer AI & Reasoning Lab(The RAIR Lab)
A while back,RPI StrategicInvestment
Cracking Project; “Superteaching”
Slate (IntelligenceAnalysis)
Item generation(theorem proving-basedgeneration)
synthetic characters/psychological time
Wargaming
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
hypothesis generation; AI in support of IA
PERI(Psychometric Experimental Robotic Intelligence)
http://www.cs.rpi.edu/~schimb/peri/
• Scorbot-ER IX
• Sony B&W XC55 Video Camera
• Cognex MVS-8100M Frame Grabber
• Dragon Naturally Speaking Software
• NL (CARMEL & RealPro?)
• BH8-260 BarrettHand Dexterous 3-Finger Grasper System
RAIR Lab’s Push Against the Turing Limithttp://www.cs.rpi.edu/~kelleo/busybeaver/
For Further Reading...
For Further ReadingForthcoming New Proof (one of the seventeen) that Minds Hypercompute: Forthcoming New Proof (one of the seventeen) that Minds Hypercompute:
Bringsjord, S. & Arkoudas, K. (forthcoming) “The Modal Argument for Bringsjord, S. & Arkoudas, K. (forthcoming) “The Modal Argument for Hypercomputing Minds” Hypercomputing Minds” Theoretical Computer ScienceTheoretical Computer Science..
Argument #1 Against Pinkerian View that We are Evolved ComputersArgument #1 Against Pinkerian View that We are Evolved Computers: : Bringsjord, S. (2001) Bringsjord, S. (2001) “Are We Evolved Computers? A Critical Review of Steven Pinker’s How the Mind Works” Philosophical Psychology 14.2:227-243.
Paper Exhibiting Human Infinitary ReasoningPaper Exhibiting Human Infinitary Reasoning: Bringsjord, S. & van Heuveln, B. : Bringsjord, S. & van Heuveln, B. (2003) “(2003) “The Mental Eye Defense of an Infinitized Version of Yablo’s Paradox,” Analysis 63.1: 61-70.
Book Explaining and Defending View That We’re “Superminds”: Bringsjord, S. & Zenzen, M. (2003) Superminds (Dordrecht, The Netherlands: Kluwer Academic Publishers).
Anderson’s “Newell Test” paper: Anderson, J. & Lebiere, C. (2003) “The Newell Test for a Theory of Cognition,” Behavioral and Brain Sciences 26: 587-601.
Zeus Machines Introduced and Contextualized, and the Humble Circle Fully Explained: Boolos, G. & Jeffrey, R. (1989) Computability and Logic (Cambridge, UK: Cambridge University Press).
Phenomenal Consciousness and Cognitive Science: Block, N. (1995) “On a Confusion About a Function of Consciousness,” Behavioral and Brain Sciences 18: 227-247.
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