my notes
Combinatorial Explosion
 Diagram is misleading because by God’s eye view, but in life we’re not out there, we’re at the initial state  ignorant
 Problem solving method is any method finding the sequence while obeying the path constraints
 Diagram not complete
 Can calculate number of pathways by calculating F^D
 F = number of operators I’m applying at any stage
 D = number of stages
 Ex: chess:
 on any turn number of operations is 30 on any turn
 On average 60 turns
 Combinatorial explosion
 Vast number 4.29 X 10^88
 Incomprehensibly large
 Have about 10^10 neurons
 Have 5 x 10^15 neuronal paths
 Greater than the number of particles estimated to exist in the universe
 So can’t search the whole space
 Since can’t search the whole space  what we do is zero in on a small subspace, and often find a solution. Zero in on the relevant information.
 How do we do that?
 Issue of avoiding combinatorial explosion is a central way of understanding intelligence
 Experience in two ways:

 generation of obviousness: what we have to explain

 how things are salient to us, how they stand out to us, grab our attention
 That process isn’t static, sometimes one is more than the other
 Dynamically selforganize what we find relevant and salient
 Newell and Simon realized have to deal with combinatorial explosion
 Proposed: heuristic and algorithm
Algorithm
 Problem solving technique guaranteed to find a solution or prove one can’t be found
 Standard of certainty
 So have to search the whole problem space to guarantee certainty
 Cognitive suicide if want certainty because space is combinatorially explosive
 That’s why Descartes doomed
 Deductive logic is certainty
 Logic and math operate algorithmically  we can’t be comprehensively logical
 Therefore rationalinity =/ being logical
Rationality
 Being rational means knowing when, where, how much, and what degree to be logical in order to overcome selfdeception and optimally achieve the goals that we want to achieve
 Not just logic or consistency
Heuristic
 Problem solving method not guaranteed to find a solution, reliable for increasing chances of achieving your goal
 Can’t play chess algorithmically, can play chess heuristically
 Get queen out early
 Control board
 castle
 Try to prespcifiy where you should search for the relevant info: limits the space searching
 Prejudge what is going to be relevant
 Heuristic = bias
 Bias where we’re paying attention
 No free lunch: have to use heuristics to avoid combinatorial explosion, price you pay is you fall prey to bias.
(This makes a point that I’ve made a lot: bias is not inherently bad. It is part of the human condition. It is often useful.there’s just too much information to take into account. But it has limits and can lead us astray.)
 Bias is adaptive: very thing that makes us adaptive makes us prone to selfdeception
 Ex: representative and availability heuristics: can’t calculate exactly so how many plane crashes can I remember
Newell and Simon
 V respects NandS:
 What makes us intelligent is our ability to use heuristics
 Necessary part: powerful work. Add one more dimension to what it is to do good cognitive science.
 All the great changes that make the scientific way possible is exemplified by them:
 Analyzing, taking complex phenomena breaking it down
 Like Descartes trying to formalize it: graphical mathematical
 Trying to mechanize: I’ve got this right if I can make a machine to carry out my formal analysis
 Trying to explain the mind often fall into a particular fallacy:
 See a triangle, light comes off of it, goes into eye. Into the space (working memory), projected inner screen, homunculus (little man) says triangle
 Sounds like giving mechanical explanation but how does the little man see  well inside his head, etc.
 Gets an infinite regress. Doesn’t explain anything
 Using vision to explain vision
 Circular
 N+S taking a mental term trying to formalize using nonmental terms.
 Naturalistic imperative: try to explain things naturalistically
 Doing this to try and avoid circular explanations of intelligence
 Scientific revolution seems to explain everything except for how I generate scientific explanations  consciousness
 Hole in the naturalistic worldview that’s why many zero in on our capacity to make meaning have consciousness as the thing that’s not being explained
 Right to do that, but wrong to conclude it legitimates other worldviews
 Need to show this project is failing, that not making progress on it.
 Can’t defeat a scientific program by showing problems  what have to do is point to fact that not making any progress in coming up with explanation
 Hard to say we’re not making progress in explaining intelligence by trying to analyze, formalize, mechanize it
 Critique:
 N+S notion of heuristic while necessary is insufficient.
 Didn’t pay attention to other ways we constrain the problem space and zero in on relevant information
 Didn’t notice that they had an assumption in their attempt to come up with a theoretical construct for problem solving. Assumed all problem solving the sam
 Heuristic of essentialism:
 Essentialism: when group a bunch of things with a term, they must all share some core property (essence)
 Some things fall into that (ex: triangles), but not all
 Not everything we group together has an essence
 Ex: call many things games: what set of necessary conditions meet all games  won’t find a definition that meets all and only games
 Science discovers things that have an essence
 Treat any category as if has an essence (heuristic), but many categories don’t have essences
 We look for essences because it allows us to generalize. We can overgeneralize, but also undergeneralize  also a mistake
 N+S thought that problems had an essence, that all problems essentially the same, so to make a general problem solver need one essential problem solving strategy
 essentialism is not a bad thing, we need it
 Fundamentally different kinds of problems:
Well defined vs. ill defined problems
 Welldefined problem: good meaning and effective guiding representation of the initial state and goal state
 Psychotechnologies make welldefined problems for us
(how has this been scientifically established?)
 Can get blinded that that’s how most problems are like
 Most problems illdefined: don’t know what the relevant information about the initial stat or goal state are, or relevant operators, or even path constraints
 Problem: take good notes.
 Initial state;Don’t have good notes
 Pay attention to relevant information
 But how? How make a machine to do that?
 Operations: write stuff down: do you? What stuff write down? Everyone’s notes look different
 What does the goal state look like? What do good notes look like?
 What’s missing in an illdefined problem is how to formulate the problem: Zero in on the relevant information constrain the problem to solve it
 Good problem formulation
 If they had noted this, they would have realized that the important work being done by problem formulation
 Following a conversation is an illdefined problem, go on a successful first date
 Need to be able to deal with illdefined problems to be considered intelligent
Mutilated Chessboard Problems
 If have dominos, covers 2 squares, need 32
 Now mutilate chessboard, remove a couple squares
 Now, can cover without overlap
 Many find it a hard problem because formulate it as a covering problem. Trying to imagine the chessboard and possible configurations of dominos
 Covering strategy, try and imagine it.
 Combinatorially explosive
 Two squares taken off are the same colour, but not standing out in a way that makes the solution obvious.
 If put piece down always covering one black and one white, no way to put it on the board without covering a black and white square. To cover the whole board need an equal number of  there isn’t an equal number of black and white squares
 Can prove that it is impossible.
 Parity strategy  now solution is obvious, covering strategy combinatorially impossible
 This is why flow and higher states of consciousness so relevant. Capacity to come up with good problem solving formulation  that’s insight
 Insight in addition to logic is central to rationality
 In addition to logical techniques to improve inference, need to have other kinds of psychotechnologies to improve capacity for insight.
(Bam! Brought it home!)
 Involves mindfulness  gives ability to restructure your salience landscape
 Starting to see how problem formulation and relevance realization central to being a real world problem solver, avoiding combinatorial explosions, avoiding ill definedness