Scientific publication by bureaucratic ideology – the case of Brain Communications

Science is about curiosity and curiosity itself can often be triggered by a seemingly banal and trivial observation. In neurology, it has often been triggered by observation of the consequences of brain damage in single cases. These observations can appear totally trivial until shown otherwise, sometimes years later. The single case study of Louis Verrey (1888) describing a lesion in a specific part of the visual brain producing an achromatopsia (an inability to see the world in colour) was quickly dismissed with contempt by George MacKay in 1888. Eleven years later MacKay had a Damascene conversion based (you guessed it) on a single case study of his own (MacKay and Dunlop (1899). But even two single cases were seemingly not convincing enough to eminent neurologists like Salomon Henschen (1900) and Gordon Holmes (1918). Henschen dismissed these findings with this powerfully argued scientific statement: “The two cases of achromatopsia published by Verrier [sic] and Machay [sic] do not demonstrate, in my opinion, what these authors want to demonstrate”. Gordon Holmes (1945) was more assertive; he wrote. “My observations tend…tend to show that an isolated loss or dissociation of colour vision is not produced by cerebral lesions” (my emphasis). 

It was only over 70 years later that Verrey’s evidence re-surfaced when it was found that there is indeed a part of the visual brain, located in the area that Verrey had indicated, damage to which leads to cerebral achromatopsia. 

Verrey’s single case study is rather less well know today than the single, and very brief, case study of Pierre Paul Broca. Broca’s single case study revolved around a patient called Tan, who had lost the ability to speak and had been admitted to hospital 10 years before Broca examined him. Tan was only able to utter a single word, Tan; hence the name given to him. Broca started studying him on 12 April 1861, four days before Tan died. At autopsy, the causative lesion was shown to be in the left frontal lobe. Broca did not waste time; he delivered his results and his conclusion to the Société d’Anthroplogie in Paris on the afternoon of the autopsy; he postulated that the third convolution of the left frontal lobe is critical for the production of articulate language and the area is now commonly referred to as Broca’s area. It constitutes a foundational landmark in the study of brain activity as it relates to language and has been described as one that “revolutionized psychiatry” (Scientific American, 2013). But, of course, Broca was fiercely attacked for his single case study, the significance of which became evident much later, retrospectively.

Not much later, in 1889 Hughlings Jackson published a single case study in Brain (of which he was one of the founders). He wrote of a Dr Z who suffered from an unusual type of epilepsy which had, as a consequence, a bewildering amnesia; Z retained consciousness during his seizures and could even examine patients and prescribe the correct medication but had no recollection of having done so later.  CR Butler (2006) wrote in Practical Neurology that similar cases have appeared sporadically since the description of Hughlings Jackson but that they often go unrecognized – a situation which refusal to publish single cases presumably promotes or at least does not help.

Among the more recent, and more extensively studied, single cases, is patient HM, whose memory system was charted extensively by Brenda Milner and her colleagues; HM developed severe memory problems after surgery for epilepsy, which included resection of the hippocampus and adjacent structures. The initial studies on HM were published by Milner and Scoville (1957) and, according to Larry Squires (2009), met with resistance “especially because of the difficulty for many years of demonstrating anything resembling his impairment in the experimental animal”. As with Broca’s study, the importance of this single case became apparent only later, i.e. retrospectively,  and it is now generally agreed that this single case  revolutionized our knowledge of human memory mechanisms. Larry Squire has described patient HM “as probably the best known single patient in the history of neuroscience…Work with him established fundamental principles about how memory functions are organised in the human brain.” 

It would be hard to find an equivalent description of work based on a study of scores of patients, with detailed statistical tables, rather than a single one. And in view of Larry Squire’s view of why Milner and Scoville evidence met with resistance, it is interesting to note here that there is another single case study published (yes, you guessed correctly again) in Brain (1983 and 1991). This is of patient LM who became akinetopsic (lost the ability to perceive objects when in motion) after bilateral cortical lesions affecting the territory of V5, the brain area critical for the perception of visual motion.  Even though the physiology of V5 had been charted extensively in the monkey by then (V5 is perhaps one of the most extensively studied cortical areas), nothing of the same severity and longevity has been described in experimental animals.

In fact the exclusion of single cases, or their absorption into a study of the many because their authors could not bring themselves to believe in the results obtained from outlier, single cases can, and has, seriously compromised results reached from study of groups of patients. A good example is that of the much-revered study by Sir Gordon Holmes, of the effects of lesions in the primary visual cortex (area V1) in humans (Holmes 1918). Among Holmes’ patients was one – a single case – whose condition did not conform to that of the group. This one patient, though also blinded by a lesion in his V1, was nevertheless able to experience visual motion consciously when a moving stimulus was presented to his blind field. Holmes grappled with this one patient – especially in light of a similar discovery (but derived from 5 patients) described a year earlier by George Riddoch (1917) – but Holmes evidently decided against publishing it as a single case; instead, he absorbed this single case into his other cases and lost a great opportunity. His reluctance to isolate this single case was doctrinaire; Holmes cared nothing for any study that showed residual and specialized visual capacities after lesions in V1. In spite of the single case in his own study, Holmes dismissed the findings of Riddoch (and with it his own single case); Riddoch’s study had similarly shown that conscious experience of visual motion in patients otherwise blinded by lesions in V1 is possible. Holmes wrote that Riddoch was “certainly incorrect” because  “…in all my cases the blindness was total” (my emphasis). Had there been a journal in those days that encouraged the publication of single case studies or at least accepted them if only for review, Holmes might have been encouraged to consider his single case more seriously and describe it separately. At any rate, his much revered 1918 paper has, in my view, suffered a serious intellectual setback resulting from not describing a single case that did not conform to the results obtained from examining many cases.

In fact, a study published in Brain in 1993, based on (you guessed it again) a single case showed that Riddoch was right and that patients blinded by lesions in V1 can perceive motion selectively and consciously, thus questioning a doctrine that supposed that such patients, when they see at all, can only “see” unconsciously (the so-called syndrome of blindsight). 

It is now well attested that George Riddoch was right and the phenomenon has indeed been deservedly named after him. 

Note in passing that this single case study of 1993 was published in Brain when its editor was the neurologist Ian MacDonald. Brain currently has the much-misguided policy of strongly discouraging single case studies (see below). 

There is, in brief, a price to be paid for ignoring single cases and a good deal to be said for taking them into account, if only to review them seriously, as with any other scientific study. I have given only a few examples above, but there are many more that can be given.

Imagine therefore my surprise when I received on Monday 27 November 2023 a letter from the Editor of Brain Communications in response to a paper that my colleagues and I had submitted to that journal on Friday 24 November 2023. The paper described the results obtained from examining an unusual single patient who had  what seemed to us very interesting visual disturbances. The nature of these disturbances and their scientific validity is not at issue here. What is interesting is that the paper was returned after spending a weekend on the editor’s desk, with the following comments:

“After careful consideration [during the weekend of Friday November 24 ending on Monday November 27], I regret to inform you that…we do not typically consider case studies as it is difficult to draw robust conclusions about the neurobiology of disease or about the wider implications of the work for other people” (my emphasis), a statement that is evidently based on scientific ideology and policy rather than on the science itself since it is hard to believe that the paper was carefully considered in any other sense than that it was a single case study that did not fit with the journal’s rigid policy. As for not drawing robust conclusions from single case studies, please read above again.

The policy behind such a statement has scientific mediocrity writ large all over it – it does both neurobiology and its practitioners a serious dis-service; it is based on a crass ideology and policy that discourages any neurologist who may come across a patient with an interesting syndrome to pursue their studies, knowing full well that there are out there journals with a pretence to eminence who follow the identical crass policy, with acceptance of articles dictated not by scientific interest but by scientific diktat regarding what scientific papers can and cannot be reviewed, let alone published. It would be totally useless to counter such diktats by saying that a scientific study is either good or not good – good science often does not proceed by following rules established by editors. 

Another example is provided by a sister journal to Brain Communications, the journal Brain itself (of which, incidentally, Sir Gordon Holmes was editor between 1922 and 1927). The current, and equally idiotic, policy of this venerable journal, established in the 19^th century and in which many landmark papers in neurology have been published, is as follows: “…single case studies are not considered. More detailed studies of single cases may - in rare instances - be considered as a Report…only when they resolve definitively an important problem in the field or when the data lead to a significant conceptual advance. Studies of single cases that can be readily performed on groups of patients will not be considered.” 

What an extraordinarily unscientific statement: since when has any scientific study resolved definitively an important problem? And the whole point of single case studies is that they cannot readily be performed on groups because naturally occurring lesions in the brain are never perfectly localised to one and the same place. And as to the data leading to a significant conceptual advance, surely that can only be judged retrospectively, after a single case study has been published, as indeed has been the case with the single case studies of Verrey, Broca, Hughlings Jackson and Milner & Scoville – among others. 

But there is of course always the argument based on statistics, generally a good fall back position in attacking single case studies. I will not go into that here because it has been compellingly argued against in a recent study by Nickels et al. in an article entitled Single case studies are a powerful tool for developing, testing and extending theories, published in 2022 in Nature Reviews Psychology. I doubt that it will influence editors who will not consider single case studies although it should because journals have a responsibility to serve their subjects well. 

There are of course many merits to studies that involve scores of patients, and which are acceptable to these editors, in principle. I will not details these merits here but leave it to those journals that proscribe single case studies to do so.

Semir Zeki 

The macro- and micro- worlds in physics and perception

It is well established that there is a contradiction between gravitational physics and quantum mechanics. I shall refer to the former as macro-physics and to the latter as micro-physics. The laws of one do not apply to the laws of the other. The behaviour of particles in the micro-physical world is so unpredictable from the known laws that operate in the macro-physical world that Niels Bohr reputedly said, “Anyone who is not shocked by quantum mechanics has not really understood it”. Schrodinger – a pioneer in quantum mechanics - reputedly said, “I don’t like it and I wish I had had nothing to do with it”.

Ever since the early part of the last century, there have been many attempts to reconcile the two – among them string theory and quantum gravitation. These attempts has so far had no success, which is not to say that they will not be successful in the future.

There is an apparent contradiction in perception which, in some ways, parallels that in physics, although the similarity must not be exaggerated. It is, however, always interesting to draw parallels between remote fields, even if one does not illuminate the other.

As is common knowledge, in ordinary experience different visual attributes such as the colour, form and direction of motion of an object are perceived to be in precise spatial and temporal registration. Let us refer to this as macro-perception, or macro-vision.

One would be forgiven to assume from this common, daily, experience that, likewise, the very earliest visual experience, in what we can refer to as micro-vision – in the first 150 milliseconds after the appearance of a visual stimulus – its attributes of colour, form and motion will also be perceived as being in precise spatial and temporal registration.

But experiments show that this is not necessarily so. Apparently – dependent upon the task – subjects often perceive colours before perceiving the form (orientation) of the stimulus, and before perceiving its direction of motion. The difference in time between perceiving colour and direction of motion is about 80 milliseconds. This is a huge difference in neural terms, given that it takes about 0.5 to 1 milliseconds for the nervous impulse to travel from one nerve cell to the next. And, crucially, this temporal perceptual asynchrony could not have been (and was not) predicted from the apparently synchronous perception of different attributes in the macro-world of perception, just as the properties of the micro-physical world cannot be predicted from the laws governing the macro-physical world.

In general, physicists working in the macro-world are capable of developing their theories without paying much attention to the rules that operate in the micro-world; likewise, those working in micro-physics can ignore the rules that operate in the macro-world, which accounts for the enormous success of quantum mechanics.

Equally, neurobiologists concerned with macro-perception can (and have) generally ignored the rules that govern perception in the micro-world. This is well and good, except that it raises questions about the problem of what is known as “binding”, which refers to the bringing together of separately processed attributes (eg of colour, form and motion) to give us a coherent visual picture, with no trace of the asynchronous operations evident in the micro-world.

A similar dilemma faces physics. While it is possible for one arena of physics to ignore the other, this becomes a problem when things are projected backwards in time – billions of years ago – when the whole of the Universe was contained in a particle of infinite mass but of the size equivalent to a millionth of a millionth of that of an atom (or so physicists now believe). At such a small, micro-level, it is the rules governing the micro-world that must have been in operation. How these rules got transformed into the rules of the macro-world as the Universe began to expand after the “Big Bang” remains a puzzle.

Similarly, how the micro-perceptual, asynchronously operating world is transformed into the synchronous world of macro-perception remains a puzzle. An obvious explanation might be that the responses of cells are somehow ‘bound’ together to give us our unitary perception. But such a supposition brings numerous hurdles, among them that of the physiological mechanisms through which one group of cells in one area “waits” for another group of cells in a separate, specialized area, to terminate its task. This, so far, remains an unaddressed problem and no one has yet managed to clarify successfully how binding occurs.

Dragan Rangelov and I have suggested that the binding process that leads to the macro-world may lie in interactions beyond the perceptive cortex, but this is an idea that is entirely conjectural.

Remote though the worlds of physics and perception may seem, these parallels are worth drawing attention to.

©Semir Zeki

The macro- and micro- worlds in physics and perception

It is well established that there is a contradiction between gravitational physics and quantum mechanics. I shall refer to the former as macro-physics and to the latter as micro-physics. The laws of one do not apply to the laws of the other. The behaviour of particles in the micro-physical world is so unpredictable from the known laws that operate in the macro-physical world that Niels Bohr reputedly said, “Anyone who is not shocked by quantum mechanics has not really understood it”. Schrodinger – a pioneer in quantum mechanics - reputedly said, “I don’t like it and I wish I had had nothing to do with it”.

Ever since the early part of the last century, there have been many attempts to reconcile the two – among them string theory and quantum gravitation. These attempts has so far had no success, which is not to say that they will not be successful in the future.

There is an apparent contradiction in perception which, in some ways, parallels that in physics, although the similarity must not be exaggerated. It is, however, always interesting to draw parallels between remote fields, even if one does not illuminate the other.

As is common knowledge, in ordinary experience different visual attributes such as the colour, form and direction of motion of an object are perceived to be in precise spatial and temporal registration. Let us refer to this as macro-perception, or macro-vision.

One would be forgiven to assume from this common, daily, experience that, likewise, the very earliest visual experience, in what we can refer to as micro-vision – in the first 150 milliseconds after the appearance of a visual stimulus – its attributes of colour, form and motion will also be perceived as being in precise spatial and temporal registration.

But experiments show that this is not necessarily so. Apparently – dependent upon the task – subjects often perceive colours before perceiving the form (orientation) of the stimulus, and before perceiving its direction of motion. The difference in time between perceiving colour and direction of motion is about 80 milliseconds. This is a huge difference in neural terms, given that it takes about 0.5 to 1 milliseconds for the nervous impulse to travel from one nerve cell to the next. And, crucially, this temporal perceptual asynchrony could not have been (and was not) predicted from the apparently synchronous perception of different attributes in the macro-world of perception, just as the properties of the micro-physical world cannot be predicted from the laws governing the macro-physical world.

In general, physicists working in the macro-world are capable of developing their theories without paying much attention to the rules that operate in the micro-world; likewise, those working in micro-physics can ignore the rules that operate in the macro-world, which accounts for the enormous success of quantum mechanics.

Equally, neurobiologists concerned with macro-perception can (and have) generally ignored the rules that govern perception in the micro-world. This is well and good, except that it raises questions about the problem of what is known as “binding”, which refers to the bringing together of separately processed attributes (eg of colour, form and motion) to give us a coherent visual picture, with no trace of the asynchronous operations evident in the micro-world.

A similar dilemma faces physics. While it is possible for one arena of physics to ignore the other, this becomes a problem when things are projected backwards in time – billions of years ago – when the whole of the Universe was contained in a particle of infinite mass but of the size equivalent to a millionth of a millionth of that of an atom (or so physicists now believe). At such a small, micro-level, it is the rules governing the micro-world that must have been in operation. How these rules got transformed into the rules of the macro-world as the Universe began to expand after the “Big Bang” remains a puzzle.

Similarly, how the micro-perceptual, asynchronously operating world is transformed into the synchronous world of macro-perception remains a puzzle. An obvious explanation might be that the responses of cells are somehow ‘bound’ together to give us our unitary perception. But such a supposition brings numerous hurdles, among them that of the physiological mechanisms through which one group of cells in one area “waits” for another group of cells in a separate, specialized area, to terminate its task. This, so far, remains an unaddressed problem and no one has yet managed to clarify successfully how binding occurs.

Dragan Rangelov and I have suggested that the binding process that leads to the macro-world may lie in interactions beyond the perceptive cortex, but this is an idea that is entirely conjectural.

Remote though the worlds of physics and perception may seem, these parallels are worth drawing attention to.

The myth of "interdisciplinarity"

The great buzz word in research applications is “interdisciplinarity”.  Often research councils frame their invitations to applicants in terms which make it seem that they favour interdisciplinary research. And of course there is much that speaks in favour of such research. In a way, it has been happening slowly and almost imperceptibly at universities. Departments have changed their names and their structures as well to reflect this fact, or so they believe.

In truth, interdisciplinarity is just a word used to soothe the conscience of funding bodies that they are “with it” in the world of modern research. In fact, a recent report from Australia shows that the chances of being funded for an inter-disciplinary project are significantly less than that in mono-disciplines. Interdisciplinarity, it seems, often means nothing more than combining neuroanatomy with neuropathology, or neurochemistry with neuropharmacology, or parallel studies in English and German Romantic literature.

But try to combine science with the humanities (e.g. neurobiology with mathematics, or physics with philosophy) and you will end up against a brick wall.

In fact the British Academy has set up an investigation into interdisciplinarity in higher education and research, a sure sign that the buzz word  has not had much effect.

The reason for this is to be sought, so we are told, in the structure of the committees that oversee funding and there is no doubt that this is partly true. When applying for a grant, the applicant must choose a panel that will decide the fate of the application, but the panels are often composed of people who are highly specialized in their fields. There are some examples when the funding agencies seek to cross the border and seek opinion from the “other” field. But this is somewhat rare. Hence, interdisciplinary applications commonly fail, with utterly banal "feed-back" to the applicants, such as “you have not convinced the committee that this is transformative research” or “you have not made a case for incorporating humanities into your work”. Often the work is thus dismissed through the “triage” system overseen by those who have little understanding of the "other" discipline, without going to referees for a full appraisal.

The dearth of genuine inter-disciplinary research is also reflected in the dearth of journals which publish articles that genuinely cross disciplines.

There is another, and unacknowledged, factor that impedes interdisciplinarity -  territoriality.  Many, especially in the humanities, are consciously or unconsciously resentful of the incursion of sciences into what they regard to be their discipline; they fear being relegated into second-class participants. Scientists, on the other hand, have a general tendency to dismiss research in the humanities as not having the high standards of proof that they claim for their own fields.

I naturally do not want to tar all scientists and humanists with the same brush. There are many, many honourable exceptions in both camps; but they remain exceptions.

This territoriality, I suggest, is perhaps an even more important factor in impeding the progress of inter-disciplinarity. It is also much more difficult to combat because it operates silently. After all, no member of any panel is going to declare publicly that “this application is trespassing into my field”

Hence, research councils must protect themselves against that but it is not an easy task.

Of course, any changes to the structural and administrative organization of funding councils will take years. Meanwhile, for those increasing number of young researchers who are enthusiastic about research that crosses boundaries, because in the world of knowledge there are no such artifical boundaries, there is this word of advice – don’t waste your time applying to the research councils for big cross-disciplinary research. Try instead some other source  – for example big companies which see a commercial return from funding such research.Better still, identify a wise and enlightened benefactor - a sort of modern Lorenzo de' Medici, if you can find one.

It may be cynical to say so; it is certainly sad.

But it is also true, and will remain true until such time as the research councils wake up and realise that research aspirations have changed beyond recognition while they were snoozing.

Unconscious intuition and its conscious resolution

Contributed by Mikhail Filippov, Varun Prasad and Semir Zeki

Ever since the description of the neural correlates of the experience of mathematical beauty, we have been wondering to what extent mathematical beauty falls into the category of biological beauty.

This has led us to enquire further into the extent to which mathematics itself constitutes a study of the brain’s logical architecture; in other words, the extent to which the study of mathematics also belongs in a branch of biology and more specifically neurobiology.

We start by enquiring into the processes which led one of the most interesting mathematicians of the last century, namely Srinivasa Ramanujan, to his conclusions. 

They are commonly referred to as INTUITION.

But what is intuition?

The term is commonly used to signify that a significant insight or conclusion has been reached without thinking and without reasoning. This is true in all languages to which we (the writers of this post) have access. One would no doubt find definitions which are more sophisticated but, as the quotations below show, the absence of logical process in having an intuition is the most common definition and reflects, in fact, what the lay person usually means by it. 

The term has been much written about recently, especially since the publication of a book about Ramanujan by Robert Kanigel entitled The Man who Knew Infinity, recently made into a film.

Consider the following definitions of intuition, which exclude any reasoning process:

“Direct perception of truth, fact, etc., independent of any reasoning process, immediate apprehension”

“An immediate cognition of an object not inferred or determined by previous cognition of the same object”                                                                                                                                                       (from Dictionary.com)

“The immediate apprehension of an object by the mind without the intervention of any reasoning process; a particular act of such apprehension.”                                                                                                     (from Oxford English Dictionary)

The French definitions given in Larousse are even more explicit in this regard:

“Connaissance directe, immédiate de la vérité, sans recours au raisonnement, à l'expérience.”


“Sentiment irraisonné, non vérifiable qu'un événement va se produire, que quelque chose existe”

One Italian dictionary defines intuition as follows:

“Intuizione: Conoscenza diretta e immediata di una verità, che si manifesta allo spirito senza bisogno di ricorrere al ragionamento, considerata talora come forma privilegiata di conoscenza che consente, superando gli schemi dell’intelletto, una più vera e profonda comprensione”

while its Spanish counterpart states:

“Percepción clara e inmediata de una idea o situación, sin necesidad de razonamiento lógico”

Nor are such definitions restricted to Western European languages. Much the same definition appears in Japanese.

"直感" = to capture things by feeling rather than reasoning or discussion.

Or

"直観" is to directly understand the essence of things without relying on reasoning.

We give these definitions in different languages only to show that much the same applies to all. Central to most (but not all) definitions is the absence of reasoning or logical thinking during the intuitive process or its result. Hence, the dictionary definitions given do indeed reflect the way in which the term is commonly understood.

Other definitions come closer to the arguments we give below; they make no reference to the absence of reasoning logic, but only to the absence of proof or evidence.

For example, the Merriam-Webster and the Free Dictionary define intuition as follows, respectively:

“A natural ability or power that makes it possible to know something without any proof or evidence: a feeling that guides a person to act a certain way without fully understanding why” 

“Something that is known or understood without proof or evidence”                                                                                                (from Merriam Webster)

“The faculty of knowing or understanding something without reasoning or proof”

(from Free Dictionary )

which is not dis-similar to the definition given in the Great Soviet Encyclopaedia

“ИНТУИЦИЯ(позднелат. intuitio, от лат. intueor - пристально смотрю), способность постижения истины путём прямого её усмотрения без обоснования с помощью доказательства.”

(Intuition is an ability to comprehend the truth through direct discovery without its justification with the proof)

We propose below an alternative definition that may be obvious to some but is not to many and therefore worth giving:

An intuition is an unconscious logical brain process with an outcome or conclusion in the form of a  statement or proposition. But whether the outcome of the intuitive process is “right” or “wrong”, or “correct” or “incorrect”,  can only be determined by a conscious logical process.

The closest dictionary definition to this that we know of is to be found in the Russian Dictionary of Psychology, which of course targets a more specialized audience: 

“Интуиция (от лат. intueri – пристально, внимательно смотреть) - мыслительный процесс, состоящий в практически моментальном нахождении решения задачи при недостаточной осознанности логических связей.”

(Intuition - thought process allowing almost instant finding of the solutions to the problem with the lack of awareness of logical connections.)

Mathematics is a subject in which intuition is often invoked. 

But the end result of the unconscious logical process that is intuition can only be “right” or “wrong” (correct or incorrect) when consciously scrutinized.

As examples of “right” and “wrong” mathematical intuitions consider the following:

A right (correct) intuition: Pick a point at random on the Earth (assume that the Earth is a sphere). The probability that the point picked lies in the northern hemisphere is 50%.

Most students of mathematics (i.e. those who have enough knowledge to understand the above statements, but who do not know if they are right or wrong) would intuitively guess this statement to be true and it is.

A wrong (incorrect) intuition: Pick a real number randomly. The probability that the real number picked is rational is zero.

Most mathematics students would intuitively guess this statement to be false (you can obviously pick a rational number!). However, it is correct.

But the conclusion that they are correct or incorrect can only be reached through a conscious logical process.

Ramanujan was reluctant to submit his intuitions to the conscious process of deductive logic, until Hardy brought him to England and forced him to do so – i.e., to provide proofs for his intuitions – a conscious process.

The absence of any logical process or reasoning in the intuitive process is not the only weakness of the definitions of intuition; some also exclude the role of experience in reaching conclusions through intuition, as in the Larousse Dictionary or the Dictionary.com definitions given above.

We believe, however, that to have an intuition in any area, one must have experience of that area or knowledge of it, to provide a conclusion or statement, whether correct or incorrect.

Since we suspect that there is only a limited set of deductive logical processes in the brain, it follows that the same logical processes must be used to derive intuitions in different domains; what distinguishes intuitions in different domains, and the logical processes that lead to them, is past experience and knowledge in the relevant domain.

The result of this unconscious logical process (the intuition) depends on initial conditions or inputs, which are based on previous (conscious) knowledge, consciously or unconsciously obtained.

Our proposed definition raises interesting and important issues and leads to the suggestion that

a.     There are many (but a limited number of) logical processes, which operate in the unconscious state.

b.     These processes are undisciplined and unruly but still obey some sort of brain logical process.

c.      They become disciplined and eliminated by revisiting them, and the conclusions to which they lead, in the conscious state.

d.     The latter eliminates many of the undisciplined and vagrant unconscious logical processing possibilities, thus stabilizing the logical processing systems of the brain.

The study of intuition in mathematics thus belongs as well to neurobiology. Or, put another way, mathematicians are also covert neurobiologists. 

© Mikhail Filippov, Varun Prasad and Semir Zeki