Intelligent Machines: From Turing to Deep Blue and Beyond Bart Selman

1
Intelligent Machines From Turing to Deep Blue
and BeyondBart Selman
2
Today's Lecture

• What is Artificial Intelligence (AI)?
• the components of intelligence
• historical perspective
• The current frontier
• recent achievements
• Challenges ahead
• what makes AI problems hard?

3
What is Intelligence?

• Intelligence
• the capacity to learn and solve problems
• (Webster dictionary)
• the ability to act rationally
• Artificial Intelligence
• build and understand intelligent entities
• synergy between
• philosophy, psychology, and cognitive science
• computer science and engineering
• mathematics and physics

4

• philosophy
• e.g., foundational issues (can a machine
  think?), issues of
• knowledge and believe, mutual knowledge
• psychology and cognitive science
• e.g., problem solving skills
• computer science and engineering
• e.g., complexity theory, algorithms, logic and
  inference,
• programming languages, and system building.
• mathematics and physics
• e.g., statistical modeling, continuous
  mathematics, Markov
• models, statistical physics, and complex systems.

5
What's involved in Intelligence?

• A) Ability to interact with the real world
• to perceive, understand, and act
• speech recognition and understanding
• image understanding (computer vision)
• B) Reasoning and Planning
• modelling the external world
• problem solving, planning, and decision making
• ability to deal with unexpected problems,
  uncertainties

6

• C) Learning and Adaptation
• We are continuously learning and adapting.
• We want systems that adapt to us!
• Major part of e.g. Microsoft Research mission.

7
Different Approaches

• I Building exact models of human cognition
• view from psychology and cognitive science
• II Developing methods to match or exceed human
• performance in certain domains, possibly by
• very different means.
• example Deep Blue.
• Our focus is on II (most recent progress).

8
Issue The Hardware

• The brain
• a neuron, or nerve cell, is the basic information
• processing unit (1011 )
• many more synapses (1014) connect the neurons
• cycle time 10(-3) seconds (1 millisecond)
• How complex can we make computers?
• 108 or more transistors per CPU
• supercomputer hundreds of CPUs, 1010 bits of
  RAM
• cycle times order of 10(-9) seconds

9
Computer vs. Brain
10
(No Transcript)
11

• Conclusion
• In near future we can have computers with as many
  processing elements as our brain, but
• far fewer interconnections (wires or synapses)
• much faster updates.
• Fundamentally different hardware may
• require fundamentally different algorithms!
• Very much an open question.
• Neural net research.

12
A Neuron
13
An Artificial Neural Network
Output Unit
Input Units
14

• An artificial neural network is an abstraction
  (well, really, a drastic simplification) of a
  real neural network.
• Start out with random connection weights on the
  links between units. Then train from input
  examples and environment, by changing network
  weights.

15

• Pole Balancing Demo.
• A neural network learning to balance a pole
• In real time. Developed by Dan Hess.

16
Historical Perspective

• Obtaining an understanding of the human mind is
• one of the final frontiers of modern science.
• Founders
• George Boole, Gottlob Frege, and Alfred Tarski
• formalizing the laws of human thought
• Alan Turing, John von Neumann, and Claude Shannon
• thinking as computation
• John McCarthy, Marvin Minsky,
• Herbert Simon, and Allen Newell
• the start of the field of AI (1959)

17
The Current Frontier

• Interesting time for AI
• (May, '97) Deep Blue vs. Kasparov
• First match won against world-champion.
• intelligent creative'' play.
• 200 million board positions per second!
• Kasparov I could feel --- I could smell --- a
• new kind of intelligence across the table.
• ... still understood 99.9 of Deep Blue's moves.
• Intriguing issue How does human cognition deal
• with the search space explosion of chess?
• Or how can humans compete with computers at
• all??

18
Deep Blue

• An outgrowth of work started by early pioneers,
  such as,
• Shannon and McCarthy.
• Matches expert level performance, while doing
  (most likely)
• something very different from the human
  expert.
• Dominant direction in current research on
  intelligent
• machines we're interested in overall
  performance.
• So far, attempts at incorporating more expert
  specific chess
• knowledge to prune the search have failed
  the game
• evolves around the expections to the general
  rules.

19
ASIDE Using Explicit Knowledge

• Whats the difficulty?
• Example consider tic-tac-toe.
• What next for Black?
• Suggested strategy
• 1) If there is a winning move, make it.
• 2) If opponent can win at a square by next
• move, play that move. (block)
• 3) Taking central square is better than others.
• 4) Taking corners is better than on edges.

20
Strategy looks pretty good right?

• But

1) If there is a winning move, make it. 2) If
opponent can win at a square by next move,
play that move. (block) 3) Taking central
square is better than others. 4) Taking corners
is better than on edges.
Interesting play involves the exceptions to the
general rules!
?
21
How Intelligent is Deep Blue?

• Saying Deep Blue doesn't really think about chess
  is like saying an airplane doesn't really fly
  because it doesn't flap its wings.
• - Drew McDermott

22
On Game 2

• (Game 2 - Deep Blue took an early lead. Kasparov
  resigned, but it turned out he could have forced
  a draw by perpetual check.)
• This was real chess. This was a game any human
  grandmaster would have been proud of.
• Joel Benjamin
• grandmaster, member Deep Blue team

23
Kasparov on Deep Blue

• 1996 Kasparov Beats Deep Blue
• I could feel --- I could smell --- a new kind of
  intelligence across the table.
• 1997 Deep Blue Beats Kasparov
• Deep Blue hasn't proven anything.

24
Game Tree
25
Combinatorics of Chess

• Opening book
• Endgame
• database of all 5 piece endgames exists database
  of all 6 piece games being built
• Middle game
• branching factor of 30 to 40
• 1000(d/2) positions
• 1 move by each player 1,000
• 2 moves by each player 1,000,000
• 3 moves by each player 1,000,000,000

26
Positions with Smart Pruning

• Search Depth Positions
• 2 60
• 4 2,000
• 6 60,000
• 8 2,000,000
• 10 (lt1 second DB) 60,000,000
• 12 2,000,000,000
• 14 (5 minutes DB) 60,000,000,000
• 16 2,000,000,000,000

How many lines of play does a grand master
consider?
Around 5 to 7
27
(No Transcript)
28
Formal Complexity of Chess
How hard is chess?

• Obvious problem standard complexity theory tells
  us nothing about finite games!
• Generalizing chess to NxN board optimal play is
  PSPACE-hard
• What is the smallest Boolean circuit that plays
  optimally on a standard 8x8 board?
• Fisher the smallest circuit for a particular
  128 bit function would require more gates than
  there are atoms in the universe.

29
Game Tree Search

• How to search a game tree was independently
  invented by Shannon (1950) and Turing (1951).
• Technique called MiniMax search.
• Evaluation function combines material position.
• Pruning "bad" nodes doesn't work in practice
• Extend "unstable" nodes (e.g. after captures)
  works well in practice

30
A Note on Minimax

• Minimax obviously correct -- but
• Nau (1982) discovered pathological game trees
• Games where
• evaluation function grows more accurate as it
  nears the leaves
• but performance is worse the deeper you search!

31
Clustering

• Monte Carlo simulations showed clustering is
  important
• if winning or loosing terminal leaves tend to be
  clustered, pathologies do not occur
• in chess a position is strong or weak,
  rarely completely ambiguous!
• But still no completely satisfactory theoretical
  understanding of why minimax is good!

32
History of Search Innovations

• Shannon, Turing Minimax search 1950
• Kotok/McCarthy Alpha-beta pruning 1966
• MacHack Transposition tables 1967
• Chess 3.0 Iterative-deepening 1975
• Belle Special hardware 1978
• Cray Blitz Parallel search 1983
• Hitech Parallel evaluation 1985
• Deep Blue ALL OF THE ABOVE 1997

33
Evaluation Functions

• Primary way knowledge of chess is encoded
• material
• position
• doubled pawns
• how constrained position is
• Must execute quickly - constant time
• parallel evaluation allows more complex
  functions
• tactics patterns to recognitize weak positions
• arbitrarily complicated domain knowledge

34
Learning better evaluation functions

• Deep Blue learns by tuning weights in its board
  evaluation function
• f(p) w1f1(p) w2f2(p) ... wnfn(p)
• Tune weights to find best least-squares fit with
  respect to moves actually choosen by grandmasters
  in 1000 games.
• The key difference between 1996 and 1997 match!
• Note that Kasparov also trained on
• computer chess play.

35
Transposition Tables

• Introduced by Greenblat's Mac Hack (1966)
• Basic idea cacheing
• once a board is evaluated, save in a hash table,
  avoid re-evaluating.
• called transposition tables, because different
  orderings (transpositions) of the same set of
  moves can lead to the same board.

36
Transposition Tables as Learning

• Is a form of root learning (memorization).
• positions generalize sequences of moves
• learning on-the-fly
• don't repeat blunders can't beat the computer
  twice in a row using same moves!
• Deep Blue --- huge transposition tables
  (100,000,000), must be carefully managed.

37
Time vs Space

• Iterative Deepening
• a good idea in chess, as well as almost
  everywhere else!
• Chess 4.x, first to play at Master's level
• trades a little time for a huge reduction in
  space
• lets you do breadth-first search with (more space
  efficient) depth-first search
• anytime good for response-time critical
  applications

38
Special-Purpose and Parallel Hardware

• Belle (Thompson 1978)
• Cray Blitz (1993)
• Hitech (1985)
• Deep Blue (1987-1996)
• Parallel evaluation allows more complicated
  evaluation functions
• Hardest part coordinating parallel search
• Deep Blue never quite plays the same game,
  because of noise in its hardware!

39
Deep Blue

• Hardware
• 32 general processors
• 220 VSLI chess chips
• Overall 200,000,000 positions per second
• 5 minutes depth 14
• Selective extensions - search deeper at unstable
  positions
• down to depth 25 !

40
Evolution of Deep Blue

• From 1987 to 1996
• faster chess processors
• port to IBM base machine from Sun
• Deep Blues non-Chess hardware is actually quite
  slow, in integer performance!
• bigger opening and endgame books
• 1996 differed little from 1997 - fixed bugs and
  tuned evaluation function!
• After its loss in 1996, people underestimated its
  strength!

41
(No Transcript)
42
Tactics into Strategy

• As Deep Blue goes deeper and deeper into a
  position, it displays elements of strategic
  understanding. Somewhere out there mere tactics
  translate into strategy. This is the closet
  thing I've ever seen to computer intelligence.
  It's a very weird form of intelligence, but you
  can feel it. It feels like thinking.
• Frederick Friedel (grandmaster), Newsday, May 9,
  1997

43
Automated reasoning --- the path
1M 5M
Multi-agent systems combining reasoning, uncertai
nty learning
10301,020
0.5M 1M
VLSI Verification
10150,500
Case complexity
100K 450K
Military Logistics
106020
20K 100K
Chess (20 steps deep) Kriegspiel (!)
103010
No. of atoms On earth
10K 50K
Deep space mission control
1047
Seconds until heat death of sun
100 200
Car repair diagnosis
1030
Protein folding Calculation (petaflop-year)
Variables
100
10K
20K
100K
1M
Rules (Constraints)
25M Darpa research program --- 2004-2009
44
Kriegspiel
Pieces hidden from opponent
Interesting combination of reasoning, game
tree search, and uncertainty.
Another chess variant Multiplayer asynchronous
chess.
45

• A few more quotes

46
AI as Sport

• In 1965 the Russian mathematician Alexander
  Kronrod said, "Chess is the Drosophila of
  artificial intelligence." However, computer
  chess has developed as genetics might have if the
  geneticists had concentrated their efforts
  starting in 1910 on breeding racing Drosophilia.
  We would have some science, but mainly we would
  have very fast fruit flies."
• - John McCarthy

47
BUT The Danger of Introspection

• When people express the opinion that human
  grandmasters do not examine 200,000,000 move
  sequences per second, I ask them, How do you
  know?'' The answer is usually that human
  grandmasters are not aware of searching this
  number of positions, or are aware of searching
  many fewer. But almost everything that goes on
  in our minds we are unaware of.
• Drew McDermott

48
Ignoring the Unimportant

• When a superior player defeats an inferior, it
  would be worthwhile to understand why the master
  did not examine presumably! lines of play on
  which the inferior player wasted his time. How to
  avoid wasting time on fruitless lines of
  investigation is important for success in every
  form of computer reasoning.
• John McCarthy

Note we could simply be wrong about did not
examine. Our introspection on what the brain
computes is very limited.
49
Plug

• Kasparov vs. Deep Blue Computer Chess Comes of
  Age
• by Monty Newborn

50
AI Examples, cont.

• (Nov., '96) a creative proof by computer
• 60 year open problem.
• Robbins' problem in finite algebra.
• Qualitative difference from previous results.
• E.g. compare with computer proof of four
• color theorem.
• http//www.mcs.anl.gov/home/mccune/ar/robbins
• Does technique generalize?
• Our own expert Prof. Constable.

51
(No Transcript)
52
Playing Chess vs. Proving Theorems (I)

• Deep Blue is enormously faster than any other
  modern reasoning engine by any measure
• nodes expanded
• backtracks
• Yet search depth similar to that needed to solve
  interesting math problems
• EQP's Robbins proof 15 steps in 8 days
• Deep Blue depth 15 in 30 minutes

EQP is name of thm. prover used for Robbins conj.
53
Playing Chess vs. Proving Theorems (II)

• Deep Blue does much more search than any theorem
  prover
• EQP 2,000,000 rewrites
• Deep Blue 100,000,000,000 board evals.
• Can we make a theorem prover that powerful?

54
Applying Chess Techniques to Automated Reasoning
(I)

• Iterative deepening
• Hash-table learning
• like a stripped down, efficient version of
  chunking or EBL
• Constant-time meta-control
• don't think too long at internal nodes
• compare alpha-beta pruning
• forget about forward-checking, etc
• special hardware?
• but recall the ill-fated 5th Generation Prolog
  machines (Japan) ...

55
Applying Chess Techniques to Automated Reasoning
(II)

• Parallel search
• hard to parallelize FO theorem proving
• more success with propositional
• systematic divide and conquer
• stochastic
• can reduce variance
• no speedup on average time?
• Is there an equivalent to an opening or closing
  book?
• endgame database of short resolution proofs?

56
So, what about forward pruning?

• 1996 -- Kotok/McCarthy program beat by ITEP
  (Adelson-Velsky, et al., Moscow)
• Kotok/McCarthy - Shannon type B, pruning, depth 4
  plies
• ITEP - Shannon type A, no pruning, depth 5 plies
• Brute-force beats pruning
• "Pruning threw away the baby with the bath-water"
• Yet... is quickly identifying relevent lines of
  inference actually the key to intelligence?

57
The Compute Intensive Hypothesis

• It is necessary to do an exponential amount of
  work to successfully search an exponentially-large
  solution space. WASTE IS NECESSARY.
• None the less, it is feasible to do this for
  useful commonsense and scientific reasoning
  tasks.
• Issues
• How can we make this hypothesis precise and
  testable?
• How can AI researchers study it in the context of
  games?

Related field Meta reasoning, when/how do you
decide not to think (search/inference) about
something?!
58
Studying General AI in the Context of Games

• The questions behind the compute intensive
  hypothesis
• When can/must you use search in place of
  knowledge?
• the compute intensive approach
• When can/must you use knowledge in place of
  search?
• the knowledge intensive (expert systems) approach

59
Suggested Problems The Limits of Knowledge

• For what games can you prove that no fast optimal
  evaluation function exists?
• Equivalently can you compile an optimal
  evaluation function into a small Boolean circuit?
• If you cannot, then you MUST search!
• When can an evaluation function be approximately
  so accurately that pruning can be made to work?
• Can we develop a better way of pruning?

60
Suggested Problems The Limits of Search

• Exactly what is the tradeoff between the quality
  of the evaluation function (knowledge) and the
  amount of search performed?
• How bad can an evaluation function be, and still
  be useful?
• Can we extend work by Nau and Pearl on
  pathological game trees to understand why minimax
  search WORKS as well as it does?

61
The Role of Knowledge in Compute Intensive
Programs

• Deep Blues strength lies in brute force
• But - the improved evaluation function from 1966
  to 1977 pushed it from impressing the world
  champion to beating the champion
• Traditional expert systems a little search on
  top of a lot of knowledge
• Compute intensive programs a little knowledge on
  top of a lot of search

62
Things that Havent Work (so far)

• The applicability and limits of many AI
  techniques can be studied by understanding why
  they do NOT work for chess
• Forward pruning
• Pattern recognition (Michalski Negri 1977)
• Analogical reasoning (de Groot 1965, Levinson
  1989)
• Partitioning
• Is it time to revisit these techniques in the
  context of game playing?

63
AI Examples, cont.

• NASA Autonomous Intelligent Systems.
• Engine control next generation spacecrafts.
• Automatic planning and execution model.
• Fast real-time, on-line performance.
• Compiled into 2,000 variable logical reasoning
  problem.
• Contrast current approach customized software
  with
• ground control team. (E.g., Mars mission 50
  million.)

64

• Decision theory and statistical user-models.
• Microsoft Office '97 / Office assistant. ?
• General probabilistic reasoning system.
• Also, restricted natural language parsing.
• Key issue attempt to adapt to individual user.
• Configuration systems and expert-system style
• fault diagnosis and monitoring of telephone
• switching networks (ATT).

65

• Machine Learning
• In 95, TD-Gammon.
• World-champion level play by Neural Network
• that learned from scratch by playing millions
  and
• millions of games against itself! (about 4
  months
• of training.)
• Has changed human play.

66
GAMES

• Chess
• deterministic
• key technique game-tree search
• matches world-class human performance 1996
• Backgammon
• game of chance
• key technique reinforcement learning
• matches world-class human performance 1991

67
Challenges ahead

• Note that the examples we discussed so far all
• involve quite specific tasks.
• The systems lack a level of generality and
• adaptability. They can't easily (if at all)
• switch context.
• Current work on intelligent agents
• --- integrates various functions (planning,
  reasoning, learning etc.) in one module
• --- goal to build more flexible / general
  systems.

68
A Key Issue

• The knowledge-acquisition bottleneck
• Lack of general commonsense knowledge.
• CYC project (Doug Lenat et al.).
• Attempt to encode millions of facts.
• Reasoning, planning, learning can compensate
• to some extent for lack of background
  knowledge
• by deriving information from first-principles.
• But, presumably, there is a limit to how
• far one can take this. (open question)

69

70
Summary

• Discussed characteristics of intelligent
  systems.
• Gave series of example systems, involving e.g.
• game playing, automated reasoning
• and diagnosis, decision theory, and learning.
• Computers are getting smarter!

71

• THE END

72
On Game 2

• (Game 2 - Deep Blue took an early lead. Kasparov
  resigned, but it turned out he could have forced
  a draw by perpetual check.)
• This was real chess. This was a game any human
  grandmaster would have been proud of.
• Joel Benjamin
• grandmaster, member Deep Blue team

73
Clustering

• Monte Carlo simulations showed clustering is
  important
• if winning or loosing terminal leaves tend to be
  clustered, pathologies do not occur
• in chess a position is strong or weak,
  rarely completely ambiguous!
• But still no completely satisfactory theoretical
  understanding of why minimax is good!

74
Time vs Space

• Iterative Deepening
• a good idea in chess, as well as almost
  everywhere else!
• Chess 4.x, first to play at Master's level
• trades a little time for a huge reduction in
  space
• lets you do breadth-first search with (more space
  efficient) depth-first search
• anytime good for response-time critical
  applications

75
Special-Purpose and Parallel Hardware

• Belle (Thompson 1978)
• Cray Blitz (1993)
• Hitech (1985)
• Deep Blue (1987-1996)
• Parallel evaluation allows more complicated
  evaluation functions
• Hardest part coordinating parallel search

76
Deep Blue

• Hardware
• 32 general processors
• 220 VSLI chess chips
• Overall 200,000,000 positions per second
• 5 minutes depth 14
• Selective extensions - search deeper at unstable
  positions
• down to depth 25 !

77
Evolution of Deep Blue

• From 1987 to 1996
• faster chess processors
• port to IBM base machine from Sun
• Deep Blues non-Chess hardware is actually quite
  slow, in integer performance!
• bigger opening and endgame books
• 1996 differed little from 1997 - fixed bugs and
  tuned evaluation function!
• After its loss in 1996, people underestimated its
  strength!

78
(No Transcript)
79
Playing Chess vs. Proving Theorems (I)

• Deep Blue is enormously faster than any other
  modern reasoning engine by any measure
• nodes expanded
• backtracks
• Yet search depth similar to that needed to solve
  interesting math problems
• EQP's Robbins proof 15 steps in 8 days
• Deep Blue depth 15 in 30 minutes

80
Playing Chess vs. Proving Theorems (II)

• Deep Blue does much more search than any theorem
  prover
• EQP 2,000,000 rewrites
• Deep Blue 100,000,000,000 evaluations
• Can we make a theorem prover that powerful?

81
Applying Chess Techniques to Automated Reasoning
(I)

• Iterative deepening
• Hash-table learning
• like a stripped down, efficient version of
  chunking or EBL
• Constant-time meta-control
• don't think too long at internal nodes
• compare alpha-beta pruning
• forget about forward-checking, etc
• special hardware?
• but recall the ill-fated 5th Generation Prolog
  machines...

82
Applying Chess Techniques to Automated Reasoning
(II)

• Parallel search
• hard to parallelize FO theorem proving
• more success with propositional
• systematic divide and conquer
• stochastic
• can reduce variance
• no speedup on average time?
• Is there an equivalent to an opening or closing
  book?
• endgame database of short resolution proofs?

83
Monty Newborn's TGTP (The Great Theorem Prover)

• Resolution theorem-prover built on chess
  technology!
• Main techniques
• iterative-deepening search
• transposition (hash) tables
• Debut at CADE-97 - bakeoff between 6 provers
• TGTP took early lead
• Worse near end, took 4th place overall
• winning strategy 7 different algorithms run in
  parallel

84
So, what about forward pruning?

• 1996 -- Kotok/McCarthy program beat by ITEP
  (Adelson-Velsky, et al., Moscow)
• Kotok/McCarthy - Shannon type B, pruning, depth 4
  plies
• ITEP - Shannon type A, no pruning, depth 5 plies
• Brute-force beats pruning
• "Pruning threw away the baby with the bath-water"
• Yet... is quickly identifying relevent lines of
  inference actually the key to intelligence?

85
Ignoring the Unimportant

• When a superior player defeats an inferior, it
  would be worthwhile to understand why the master
  did not examine lines of play on which the
  inferior player wasted his time. How to avoid
  wasting time on fruitless lines of investigation
  is important for success in every form of
  computer reasoning.
• John McCarthy

86
The Danger of Introspection

• When people express the opinion that human
  grandmasters do not examine 200,000,000 move
  sequences per second, I ask them, How do you
  know?'' The answer is usually that human
  grandmasters are not aware of searching this
  number of positions, or are aware of searching
  many fewer. But almost everything that goes on
  in our minds we are unaware of.
• Drew McDermott

87
The Compute Intensive Hypothesis

• It is necessary to do an exponential amount of
  work to successfully search an exponentially-large
  solution space. WASTE IS NECESSARY.
• None the less, it is feasible to do this for
  useful commonsense and scientific reasoning
  tasks.
• Issues
• How can we make this hypothesis precise and
  testable?
• How can AI researchers study it in the context of
  games?

88
Studying General AI in the Context of Games

• The questions behind the compute intensive
  hypothesis
• When can/must you use search in place of
  knowledge?
• the compute intensive approach
• When can/must you use knowledge in place of
  search?
• the knowledge intensive (expert systems) approach

89
Suggested Problems The Limits of Knowledge

• For what games can you prove that no fast optimal
  evaluation function exists?
• Equivalently can you compile an optimal
  evaluation function into a small Boolean circuit?
• If you cannot, then you MUST search!
• When can an evaluation function be approximately
  so accurately that pruning can be made to work?
• Can we develop a better way of pruning?

90
Suggested Problems The Limits of Search

• Exactly what is the tradeoff between the quality
  of the evaluation function (knowledge) and the
  amount of search performed?
• How bad can an evaluation function be, and still
  be useful?
• Can we extend work by Nau and Pearl on
  pathological game trees to understand why minimax
  search WORKS as well as it does?

91
The Role of Knowledge in Compute Intensive
Programs

• Deep Blues strength lies in brute force
• But - the improved evaluation function from 1966
  to 1977 pushed it from impressing the world
  champion to beating the champion
• Traditional expert systems a little search on
  top of a lot of knowledge
• Compute intensive programs a little knowledge on
  top of a lot of search

92
Things that Don't Work

• The applicability and limits of many AI
  techniques can be studied by understanding why
  they do NOT work for chess
• Forward pruning
• Pattern recognition (Michalski Negri 1977)
• Analogical reasoning (de Groot 1965, Levinson
  1989)
• Partitioning
• Is it time to revisit these techniques in the
  context of game playing?