Consciousness

1
Consciousness
2
Inspiration and Invention
3

• Penrose, Emperors New Mind, page 418
• Poincarés experience
• I left Caen, where I was living, to go on a
  geologic excursion under the auspices of the
  School of Mines. The incidents of the travel
  made me forget my mathematical work. Having
  reached Coutances, we entered an omnibus to go to
  some place or other. At the moment when I put my
  foot on the step, the idea came to me, without
  anything in my former thoughts seeming to have
  paved the way for it, that the transformations I
  had used to define the Fuchsian functions were
  identical with those of non-Euclidean geometry.
  I did not verify the idea I should not have had
  time, as upon taking my seat in the omnibus, I
  went on with a conversation already commenced,
  but I felt a perfect certainty. On my return to
  Caen, for convenience sake, I verified the result
  at my leisure.

4

• What is striking about this example (and numerous
  others cited by Hadamard) is that this
  complicated and profound idea apparently came to
  Poincaré in a flash, while his conscious thoughts
  seemed to be quite elsewhere, and that they were
  accompanied by this feeling of certainty that
  they were correct as indeed, later calculation
  proved them to be. It should be made clear that
  the idea itself would not be something at all
  easy to explain in words. I imagine that it
  would have taken him something like an hour-long
  seminar, given to experts, to get the idea
  properly across. Clearly it could enter
  Poincarés consciousness, fully formed, only
  because of the many long previous hours of
  deliberate conscious activity, familiarizing him
  with many different aspects of the problem at
  hand. Yet, in a sense, the idea that Poincaré
  had while boarding the bus was a single idea,
  able to be fully comprehended in one moment!
  Even more remarkable was Poincarés conviction of
  the truth of the idea, so that subsequent
  detailed verification of it seemed almost
  superfluous.

5

• Penrose page 423, speaking of Mozart
• When I feel well and in a good humor, or when I
  am taking a drive or walking after a good meal,
  or in the night when I cannot sleep, thoughts
  crowd into my mind as easily as you could wish.
  Whence and how do they come? I do not know and I
  have nothing to do with it. Those which please
  me I keep in my head and hum them at least
  others have told me that I do so. Once I have my
  theme, another melody comes, linking itself with
  the first one, in accordance with the needs of
  the composition as a whole the counterpoint,
  the part of each instrument and all the melodic
  fragments at last produce the complete work.
  Then my soul is on fire with inspiration. The
  work grows I keep expanding it, conceiving it
  more and more clearly until I have the entire
  composition finished in my head though it may be
  long. Then my mind seizes it as a glance of my
  eye a beautiful picture or a handsome youth. It
  does not come to me successively, with various
  parts worked out in detail, as they will later
  on, but in its entirety that my imagination lets
  me hear it.

6

• Penrose It seems to me that this accords with a
  putting-up/shooting-down scheme of things. The
  putting-up seems to be unconscious (I have
  nothing to do with it) though, no doubt, highly
  selective, while the shooting-down is the
  conscious arbiter of taste (those which please
  me I keep ). The globality of inspirational
  thought is particularly remarkable in Mozarts
  quotation (it does not come to me successively
  but in its entirety) and also in Poincarés (I
  did not verify the idea I should not have had
  time).

7
Non-verbality of thought

• Letter from Einstein The words or the language,
  as they are written or spoken, do not seem to
  play any role in my mechanism of thought. The
  psychical entities which seem to serve as
  elements of thought are certain signs and more or
  less clear images which can be voluntarily
  reproduced and combined. The above mentioned
  elements are, in my case, of visual and some
  muscular type. Conventional words or other signs
  have to be sought for laboriously only in a
  second stage, when the mentioned associative play
  is sufficiently established and can be reproduced
  at will.

8

• Quoting Francis Galton, the geneticist
• It is a serious drawback to me in writing, and
  still more in explaining myself, that I do not
  think as easily in words as otherwise. It often
  happens that after being hard at work, and having
  arrived at results that are perfectly clear and
  satisfactory to myself, when I try to express
  them in language I feel that I must begin by
  putting myself upon quite another intellectual
  plane. I have to translate my thoughts into a
  language that does not run very evenly with them.
  I therefore waste a vast deal of time in seeking
  appropriate words and phrases, and am conscious,
  when required to speak on a sudden, of being
  often very obscure through mere verbal
  maladriotness, and not through want of clearness
  of perception.

9

• Quoting Hadamard
• I insist that words are totally absent from my
  mind when I really think and I shall completely
  align my case with Galtons in the sense that
  even after reading or hearing a question, every
  word disappears the very moment that I am
  beginning to think it over and I fully agree
  with Schopenhauer when he writes, thoughts die
  the moment they are embodied in words.

10
Inspiration in animals

• Lorenz describes a chimpanzee in a room which
  contains a banana suspended from the ceiling just
  out of reach, and a box elsewhere in the room
• The matter gave him no peace, and he returned to
  it again and again. Then suddenly and there is
  no other way to describe it his previously
  gloomy face lit up. His eyes now moved from
  the banana to the empty space beneath it on the
  ground, from this to the box, then back to the
  space, and from there to the banana. The next
  moment he gave a cry of joy, and somersaulted
  over to the box in sheer, high spirits.
  Completely assured of his success, he pushed the
  box below the banana. No man watching him could
  doubt the existence of a genuine Aha experience
  in anthropoid apes.

11
Consciousness and Language

• Penrose 383-4
• Many philosophers and psychologists seem to take
  the view that human consciousness is very much
  bound up with human language. Accordingly, it is
  only by virtue of our linguistic abilities that
  we can attain a subtlety of thinking that is the
  very hallmark of our humanity ... From this
  viewpoint, our language is taken to be the key
  ingredient of our possession of consciousness.

12

• Now we must recall that our language centres are
  (in the vast majority of people) just on the
  left-hand sides of our brains The viewpoint
  just expressed would seem to imply that
  consciousness is something to be associated only
  with the left cerebral cortex and not with the
  right! Indeed, this appears to be the opinion of
  a number of neurophysiologists.

13

• Penrose, page 425 It should be clear to the
  reader why I find that viewpoint totally
  unacceptable. there can be no doubt of the high
  level of consciousness required for mathematical
  thought. Whereas analytical thinking seems to be
  mainly the province of the left side of the
  brain, geometrical thinking is often argued to be
  the right sides, so it is a very reasonable
  guess that a good deal of conscious mathematical
  activity actually does take place on the right!

14
Split Brain Experiments

• Penrose, p. 384 In relation to this, I should
  mention a remarkable collection of observations
  concerning human subjects (and animals) who have
  had their corpus callosums completely severed, so
  that the left and right hemispheres of the
  cerebral cortex are unable to communicate with
  one another.

15

• Penrose, p. 385 What is most striking about
  these split-brain subjects is that the two sides
  seem to behave as virtually independent
  individuals, each of which may be communicated
  with separately by the experimenter although
  communication is more difficult, and on a more
  primitive level, with the right hemisphere than
  with the left, owing to the rights lack of
  verbal ability.

16

• One is tempted to raise the issue do we have two
  separately conscious individuals both inhabiting
  the same body? This question has been the
  subject of much controversy. Donald Wilson and
  his coworkers examined a split-brain subject,
  referred to as P.S.. After the splitting
  operation, only the left hemisphere could speak
  but both hemispheres could comprehend speech
  later the right hemisphere learned to speak also!
  Evidently both hemispheres were conscious.
  Moreover, they appeared to be separately
  conscious, because they had different likes and
  desires. For example, the left hemisphere
  described that its wish was to be a draughtsman
  and the right, a racing driver!

17

• Pages 385-386 I, myself, simply cannot believe
  the common claim that ordinary human language is
  necessary for thought or for consciousness. I
  therefore side with those who believe, generally,
  that the two halves of a split-brain subject can
  be independently conscious.
• Presumably, before the operation each split-brain
  subject possessed only a single consciousness
  but afterwards there are two! In some way, the
  original single consciousness has bifurcated.
• The puzzle would be further exacerbated if
  somehow the two consciousnesses could later be
  brought together again.

18
Consciousness and Time

• Penrose pp. 439-442 A number of human subjects
  volunteered to have electrical signals recorded
  at a point on their heads, and they were asked to
  flex the index fingers of their right hands
  suddenly at various times entirely of their own
  choosing. there is a gradual build-up of
  recorded electric potential for a full second, or
  perhaps even up to a second and a half, before
  the finger is actually flexed. This seems to
  indicate that the conscious decision process
  takes over a second in order to act!

19

• This may be contrasted with the much shorter time
  that it takes to respond to an external signal if
  the mode of response has been laid down
  beforehand. For example, instead of it being
  freely willed, the finger flexing might be in
  response to the flash of a light signal. In that
  case a reaction time of about one-fifth of a
  second is normal, which is about five times
  faster than the willed action .

20

• In the second experiment, Benjamin Libet with
  Bertram Feinstein tested subjects who had to
  have brain surgery for some reason unconnected
  with the experiment and who consented to having
  electrodes placed at points in the brain .
  When a stimulus was applied to the skin of these
  patients, it took about half a second before they
  were consciously aware of that stimulus, despite
  the fact that the brain itself would have
  received the signal of the stimulus in only about
  a hundredth of a second, and a pre-programmed
  reflex response to such a stimulus could be
  achieved by the brain in about a tenth of a
  second. Moreover, there would be the
  subjective impression by the patients themselves
  that no delay had taken place at all in their
  becoming aware of the stimulus!

21

• See also Science 20 February 2004 vol. 303 page
  1144, The Where and When of Intention.

22

• Conscious perception of a stimulus can be masked
  by an event about a quarter of a second later.
• However, one does not seem to be aware of such
  a long time-delay in ones perceptions.
  Perhaps the time of all ones perceptions is
  actually delayed by about a half a second from
  the actual time . The subject does appear to
  refer the perception of the skin touching
  backwards in time by about half a second. The
  cortical stimulation seems not to be referred
  back in this way.

23

• The apparent implication of these two experiments
  taken together is that consciousness cannot even
  be called into play at all in response to an
  external event, if that response is to take place
  within a couple of seconds or so!
• we appear to be driven to the conclusion that
  we act entirely as automatons when we carry out
  any action that would take less than a second or
  two in which to modify a response.

24

• Page 443 I suggest that we may actually be
  going badly wrong when we apply the usual
  physical rules for time when we consider
  consciousness!
• Page 445 Suppose that there is even something
  vaguely teleological about the effects of
  consciousness, so that a future impression might
  affect a past action.
• Recall my proposal that consciousness, in
  essence, is the seeing of a necessary truth
  and that it may represent some kind of actual
  contact with Platos world of ideal mathematical
  concepts.