1. Lucidity, science, and acausality illusions Michael E McIntyre University of Cambridge For more on this, websearch ”lucidity principles”

2. An idea to take seriously (with far-reaching implications): perception works by model-fitting.

3. For more on this, websearch ”lucidity principles” An idea to take seriously (with far-reaching implications): perception works by model-fitting. The unconscious brain actively fits an internal model to the sensory data coming in from the outside world.

4. For more on this, websearch ”lucidity principles” An idea to take seriously (with far-reaching implications): perception works by model-fitting. The unconscious brain actively fits an internal model to the sensory data coming in from the outside world. If the fit is good enough, the internal model becomes the perceived reality.

5. An idea to take seriously (with far-reaching implications): perception works by model-fitting. The unconscious brain actively fits an internal model to the sensory data coming in from the outside world. If the fit is good enough, the internal model becomes the perceived reality. Example: the “walking lights ”: For more on this, websearch ”lucidity principles”

6. What is the perceived reality? A cube rotating? Which way?

7. And what is a model? For more on this, websearch ”lucidity principles”

8. And what is a model? For more on this, websearch ”lucidity principles” (in the sense used here general – a very general sense)

9. And what is a model? Answer: a partial and approximate representation of reality (e.g. of a real person really walking, or of a real wire cube really rotating). For more on this, websearch ”lucidity principles” (in the sense used here general – a very general sense)

10. And what is a model? Answer: a partial and approximate representation of reality (e.g. of a real person really walking, or of a real wire cube really rotating). NB: Science works the same way. For more on this, websearch ”lucidity principles” (in the sense used here general – a very general sense)

11. And what is a model? Answer: a partial and approximate representation of reality (e.g. of a real person really walking, or of a real wire cube really rotating). NB: Science works the same way. For more on this, websearch ”lucidity principles” (in the sense used here general – a very general sense) (e.g Einstein’s Theory of Relativity)

12. And what is a model? Answer: a partial and approximate representation of reality (e.g. of a real person really walking, or of a real wire cube really rotating). NB: Science works the same way. (Implication: science is not about Absolute Truth or Absolute Proof.) For more on this, websearch ”lucidity principles” (in the sense used here general – a very general sense) (e.g Einstein’s Theory of Relativity)

13. And what is a model? Answer: a partial and approximate representation of reality (e.g. of a real person really walking, or of a real wire cube really rotating). NB: Science works the same way. (Implication: science is not about Absolute Truth or Absolute Proof.) (For one thing, we must assume that there’s an outside world…) For more on this, websearch ”lucidity principles” (in the sense used here general – a very general sense) (e.g Einstein’s Theory of Relativity)

14. Models and model-fitting require mathematics For more on this, websearch ”lucidity principles”

15. Models and model-fitting require mathematics (e.g. Euclidean geometry). For more on this, websearch ”lucidity principles”

16. Models and model-fitting require mathematics (e.g. Euclidean geometry). Implication: we all have unconscious mathematics. For more on this, websearch ”lucidity principles”

17. Models and model-fitting require mathematics (e.g. Euclidean geometry). Implication: we all have unconscious mathematics. Another way to say it is: We all have an unconscious power of abstraction For more on this, websearch ”lucidity principles”

18. Models and model-fitting require mathematics (e.g. Euclidean geometry). Implication: we all have unconscious mathematics. Another way to say it is: We all have an unconscious power of abstraction For more on this, websearch ”lucidity principles” – and what is abstraction? Answer: the ability to handle many possibilities at once

19. Models and model-fitting require mathematics (e.g. Euclidean geometry). Implication: we all have unconscious mathematics. Another way to say it is: We all have an unconscious power of abstraction For more on this, websearch ”lucidity principles” – and what is abstraction? Answer: the ability to handle many possibilities at once (even an infinite number of possibilities).

20. All this can be seen as a consequence of biological natural selection For more on this, websearch ”lucidity principles”

21. All this can be seen as a consequence of biological natural selection along with certain mathematical facts, especially combinatorial largeness. For more on this, websearch ”lucidity principles”

22. All this can be seen as a consequence of biological natural selection along with certain mathematical facts, especially combinatorial largeness. The unconscious brain must choose the model components to fit to the incoming data from a combinatorially large number of possibilities. For more on this, websearch ”lucidity principles”

23. All this can be seen as a consequence of biological natural selection along with certain mathematical facts, especially combinatorial largeness. The unconscious brain must choose the model components to fit to the incoming data from a combinatorially large number of possibilities. “No organism can afford to be conscious of matters with which it could deal on unconscious levels.” – Gregory Bateson For more on this, websearch ”lucidity principles”

24. How large is combinatorially large?

25. Reminder For more on this, websearch ”lucidity principles” How large is combinatorially large? – Lucidity and Science, Part I 1

26. For more on this, websearch ”lucidity principles” The unconscious brain is especially interested in internal models made of patterns that are as simple as possible “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296.

27. For more on this, websearch ”lucidity principles” The unconscious brain is especially interested in internal models made of patterns that are as simple as possible (Platonic objects – elegance – computational economy) “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296.

28. For more on this, websearch ”lucidity principles” The unconscious brain is especially interested in internal models made of patterns that are as simple as possible (Platonic objects – elegance – computational economy) “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296.

29. For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. The unconscious brain is especially interested in internal models made of patterns that are as simple as possible (Platonic objects – elegance – computational economy) – what we perceive are perfectly smooth curves – mathematically simple !

30. For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. The unconscious brain is especially interested in internal models made of patterns that are as simple as possible (Platonic objects – elegance – computational economy) – what we perceive are perfectly smooth curves – mathematically simple ! (as distinct from what’s actually on the screen!)

31. For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. The unconscious brain is especially interested in internal models made of patterns that are as simple as possible (Platonic objects – elegance – computational economy) – what we perceive are perfectly smooth curves – mathematically simple ! (as distinct from what’s actually on the screen!)

32. – what we perceive are perfectly smooth curves – mathematically simple ! A perfectly straight line is another Platonic object For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. The unconscious brain is especially interested in internal models made of patterns that are as simple as possible (Platonic objects – elegance – computational economy)

33. For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. The unconscious brain is especially interested in internal models made of patterns that are as simple as possible (Platonic objects – elegance – computational economy) – what we perceive are perfectly smooth curves – mathematically simple ! A perfectly straight line is another Platonic object:

34. For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. There are very many Platonic objects. The unconscious brain is especially interested in internal models made of patterns that are as simple as possible (Platonic objects – elegance – computational economy)

35. For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. There are very many Platonic objects. E.g. an infinitely large number of smooth curves. The unconscious brain is especially interested in internal models made of patterns that are as simple as possible (Platonic objects – elegance – computational economy)

36. For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. There are very many Platonic objects. E.g. an infinitely large number of smooth curves. Here’s another smooth curve – can you see it? The unconscious brain is especially interested in internal models made of patterns that are as simple as possible (Platonic objects – elegance – computational economy)

37. For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. There are very many Platonic objects. E.g. an infinitely large number of smooth curves. Here’s another smooth curve – can you see it? (unconscious mathematics again – calculus of variations) The unconscious brain is especially interested in internal models made of patterns that are as simple as possible (Platonic objects – elegance – computational economy)

38. For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. “The illusory contour… is constructed, unconsciously. To wonder at its perfection is to glimpse the Platonic” – Part II, p 296 There are very many Platonic objects. E.g. an infinitely large number of smooth curves. Here’s another smooth curve – can you see it? The unconscious brain is especially interested in internal models made of patterns that are as simple as possible (Platonic objects – elegance – computational economy) Contructivism “versus” Platonism: a false dichotomy : (unconscious mathematics again – calculus of variations)

39. For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. Model-fitting takes place in spacetime. (The walking lights demonstrate it, as does any movie.)

40. For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. Model-fitting takes place in spacetime. (The walking lights demonstrate it, as does any movie.) We perceive continuous motion despite actual discontinuities.

41. For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. Model-fitting takes place in spacetime. (The walking lights demonstrate it, as does any movie.) We perceive continuous motion despite actual discontinuities. Musical example: Mozart’s “flowing oil” – a feeling of continuous motion evoked by discontinuous sounds (from the K545 piano sonata).

42. For more on this, websearch ”lucidity principles” “Platonic” versus “constructivist” – another of our false dichotomies! Again see Lucidity and Science Part II, p. 296. Model-fitting takes place in spacetime. (The walking lights demonstrate it, as does any movie.) We perceive continuous motion despite actual discontinuities. Musical example: Mozart’s “flowing oil” – a feeling of continuous motion evoked by discontinuous sounds (from the K545 piano sonata). The outer indistinct, ragged “contour” reminds us of the playing of a pianist less skilled than Mozart:

43. For more on this, websearch ”lucidity principles” Music takes us deeper still.

44. For more on this, websearch ”lucidity principles” Music takes us deeper still. Natural selection again: auditory scene analysis.

45. For more on this, websearch ”lucidity principles” Music takes us deeper still. Natural selection again: auditory scene analysis. An implication is that the harmonic series is another Platonic object, part of the brain’s model-building repertoire:

46. For more on this, websearch ”lucidity principles” Music takes us deeper still. Natural selection again: auditory scene analysis. An implication is that the harmonic series is another Platonic object, part of the brain’s model-building repertoire: Ravel trio: ↑ ↑ ↑ ↑

47. Indeed, this is evolutionarily ancient. It’s not just our brains that make use of the harmonic series: For more on this, websearch ”lucidity principles”

48. Indeed, this is evolutionarily ancient. It’s not just our brains that make use of the harmonic series: “And somewhere, out in that blue and green splendour, something was singing: a small voice, high up, starting and ceasing, incredibly sweet. What was it? A little, sweet, wild voice, a music in mid-air. He listened, and his breath caught in his throat.” – Ursula Le Guin, The Dispossessed For more on this, websearch ”lucidity principles”

49. Indeed, this is evolutionarily ancient. It’s not just our brains that make use of the harmonic series: “And somewhere, out in that blue and green splendour, something was singing: a small voice, high up, starting and ceasing, incredibly sweet. What was it? A little, sweet, wild voice, a music in mid-air. He listened, and his breath caught in his throat.” – Ursula Le Guin, The Dispossessed Examples: New Zealand tui and kokako : For more on this, websearch ”lucidity principles”

50. Tui song recorded in Invercargill, New Zealand): Recording by Les McPherson > For more on this, websearch ”lucidity principles” actual half speed

51. Kokako song

52. Two further points about the “walking lights” example: For more on this, websearch ”lucidity principles” 1. The model favoured by the unconscious brain isn’t any old linkage: it‘s a particular 3-dimensional linked structure, with unchanging distances between pairs of links – to good approximation. (Re “favoured”, see my website’s “On thinking probabilistically”.)

53. Two further points about the “walking lights” example: For more on this, websearch ”lucidity principles” 2. The example illustrates another basic point about our perceptual and cognitive processes : the organic-change principle. Thanks to natural selection we favour – are perceptually sensitive to – patterns in which some things change slightly, while others stay the same 1. The model favoured by the unconscious brain isn’t any old linkage: it‘s a particular 3-dimensional linked structure, with unchanging distances between pairs of links – to good approximation. (Re “favoured”, see my website’s “On thinking probabilistically”.)

54. Two further points about the “walking lights” example: For more on this, websearch ”lucidity principles” 2. The example illustrates another basic point about our perceptual and cognitive processes : the organic-change principle. Thanks to natural selection we favour – are perceptually sensitive to – patterns in which some things change slightly, while others stay the same (another abstract concept – and it points straight toward the deepest connections between music and mathematics – e.g.“invariance theorems”..) 1. The model favoured by the unconscious brain isn’t any old linkage: it‘s a particular 3-dimensional linked structure, with unchanging distances between pairs of links – to good approximation. (Re “favoured”, see my website’s “On thinking probabilistically”.)

55. For more on this, websearch ”lucidity principles” Music consists of organically-changing sound patterns. The existence of music – as well as mathematics – is direct evidence of our unconscious power of (and interest in) abstraction.

56. For more on this, websearch ”lucidity principles” E.g. the way harmony works (websearch “musical hyperspace”) :

57. For more on this, websearch ”lucidity principles” E.g. the way harmony works (websearch “musical hyperspace”) : Powerful, continuous harmonic motion uses organic change – some things changing slightly while others stay the same – where in this case “slightly” can mean either of the two kinds of perceptual proximity, "melodic" or "harmonic“.

58. For more on this, websearch ”lucidity principles” E.g. the way harmony works (websearch “musical hyperspace”) : Powerful, continuous harmonic motion uses organic change – some things changing slightly while others stay the same – where in this case “slightly” can mean either of the two kinds of perceptual proximity, "melodic" or "harmonic“. (And powerful chords are made of harmonic-series subsets. Debussy was the first great composer to recognize all this (Peter Platt, Debussy and the Harmonic Series) – in fact Western music has two templates in slight conflict. That conflict is a rich artistic resource exploited by musicians with fine-tuning skills.)

59. For more on this, websearch ”lucidity principles” One last point: Hearing music and making sense of it reminds us, again, that the brain’s unconscious model-fitting takes place in time as well as space

60. For more on this, websearch ”lucidity principles” One last point: Hearing music and making sense of it reminds us, again, that the brain’s unconscious model-fitting takes place in time as well as space (or rather, in this case, musical hyperspace).

61. For more on this, websearch ”lucidity principles” One last point: Hearing music and making sense of it reminds us, again, that the brain’s unconscious model-fitting takes place in time as well as space (or rather, in this case, musical hyperspace). Therefore, subjective time can differ from objective (outside-world) time.

62. For more on this, websearch ”lucidity principles” Subjective, i.e., perceived, time is an internal-model property.

63. For more on this, websearch ”lucidity principles” Subjective, i.e., perceived, time is an internal-model property. (So it needn’t obey the usual laws of physics regarding causality.)

64. Example: acausality illusions The perceived time of an event can precede the arrival of sensory data defining the event. For more on this, websearch ”lucidity principles” Subjective, i.e., perceived, time is an internal-model property. (So it needn’t obey the usual laws of physics regarding causality.)

65. Example: acausality illusions The perceived time of an event can precede the arrival of sensory data defining the event. Basic to Western music are events called harmony changes: For more on this, websearch ”lucidity principles” Subjective, i.e., perceived, time is an internal-model property. (So it needn’t obey the usual laws of physics regarding causality.)

66. For more on this, websearch ”lucidity principles” Mozart K 545 again: Example: acausality illusions The perceived time of an event can precede the arrival of sensory data defining the event. Basic to Western music are events called harmony changes: Subjective, i.e., perceived, time is an internal-model property. (So it needn’t obey the usual laws of physics regarding causality.)

67. Any composer asked to provide a straightforward orchestral accompaniment would put the harmony change at the time of the arrow:

68. Finally: the central idea or hypothesis that perception works by model-fitting deserves to be taken seriously for other reasons too, e.g., For more on this, websearch ”lucidity principles” ”V. S. Ramachandran” ● The nature of “self ”: the brain is committee-like, yet has a single internal “self-model” – continuously being fitted to the incoming data (visual, auditory, tactile, and proprioceptive). ● Acausality illusions include the perceived (subjective) times of making decisions (e.g. experiments by Grey Walter and Libet – cf. free-will debate). (… “perceived times of internal decisions must be later than, and perceived times of outside-world events earlier than… physical events in the nervous system. Only thus can the brain… represent both sets of times in its internal model of the self in its surroundings at the… accuracies needed for survival.” )

69. (No time for the following slides:)

70. Mozart K 545: Not quite Mozart K 545: