Lesson 34.  Thinking and Calculating

 Thinking refers to a wide range of activities, from rational thought deployed in reflection and reasoning to perception, sensations of pleasure and pain, souvenirs, thought associations, aesthetic experience and imagination.  At first sight it would seem then that we cannot reduce thinking to a logical operation of calculation that reason would perform by means of ideas.

And yet as soon as we want to reach a goal, make a prediction, solve a problem, then thinking comes very near to being a calculation.  It would therefore be tempting to think that there is on the one hand rational thought, which is a form of calculation, and on the other hand irrational thought, which is immediate and of lesser importance.

When the mind reflects upon ideas can one say that it is calculation? Is thinking the same as calculating?  

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A  The concept of calculation

 A calculation is the activation of one of the aptitudes characteristic of the mind, an operation that the mind performs in many fields.

1.  It is first of all a mathematical operation performed with variables, numbers or constants, and which supposes the application of rules.  Adding, subtracting, multiplying, extracting the square root are all calculations.  The numbers are the elements.  Addition is a rule of performance for the calculation stating how to relate the variables used.

   A calculation is an operation done in order to find a result that conforms to the application of a rule.  An equation is a formula that combines variables, constants and rules of performance in order to establish an identity between two entities.

2)  A calculation can also be merely logical.  If we give to the proposition A the truth value T (true), and if B = F (false) and C = T, then we have elements that can be studied such as they appear in combination inside a chain of reasoning.   Logic can decide if a form of reasoning is valid or not, if a conclusion is correct or not.  Propositional logic and the calculation of predicates are forms of logical calculation founded on binary values T/F, present in the dualising thinking of ordinary vigilance.

 3)  But the notion of calculation is wider.  A calculation can be economical.  Economy is the science of exchange in which quantifiable evaluations take place.  The man with shares on the stock market makes calculations for his placements to bring the highest possible returns.  The CEO of a company manages benefits to augment the profits of his business. 

4) Calculations can be political.  Machiavelli teaches that a skilful politician is first of all a dexterous politician able to make timely decisions and foresee their consequences (when to hold elections, when to debate a bill in Parliament and so on).

5) A calculation can be military.  We call strategy the art of calculating how to make the enemy yield to one’s own troops.  Wars are a matter of strategy and therefore of calculation in order to win a battle.  The kind of thinking involved in chess is also of this nature, the player seeks to checkmate the king of his adversary in order to win the game.

6) There is calculation involved in any field in which measurements are required.  The surveyor measures a piece of land, a grocer at the market weighs the fruit.  In statistics we find combinations of measurements.

7) More generally there is calculation where there is a rigorous arrangement of means to an end, where a project is being worked out.  To calculate is to correctly arrange means with an end in view.  The sports commentator says that it was “bad calculation” to change tyres in the Formule 1 race.  As soon as we set a practical goal, then it would seem that the manner in which the mind is mobilised in order to reach it is some form of calculation.

Hence a calculating mind is not the privilege of the mathematician.  It is a characteristic of the reasoning mind.  A calculating mind is a mind the operations of which appear strictly confined to calculations in view of a result.  What it wants is the result, whatever the consequences.  That is why we say that the calculating mind is cold, cunning, cynical and implacable.  When sheer profit is wanted at the cost of degrading labour conditions we speak of economic cynicism.  The man who makes decisions with only economy in mind is more than ready to eliminate whatever he looks upon as unnecessary costs, especially salaries, and replace men by machines, and he will not mind catastrophes due to pollution, as that would have meant more expenses.  He may also ignore moral values if this is profitable.  The financial shark is not concerned with values other than money.  Political cynicism is another expression of the calculating mind.  It turns the politician into a manipulator who sole aim is to keep the power.  Choosing the date of elections, of promoting a public figure, of dissolving Parliament: everything can be a matter of calculation.  The word to use here is ‘strategy’, a strategy used to obtain victory and keep the power.  This shows us that from politics to military force there is but one step.  Clausewitz said that war is the continuation of politics by other means.   A cold and calculating mind could not care less about how people fare and feel.  It has figures and results in view, the rest is immaterial.  It is implacable because it is focussed on a single end, which it tenaciously pursues, and because this end does not allow for any possibility of moderation or change of course.  Whence the constant appeal to cunning.  All that matters is how to obtain a result, means justifying the end.  The means may be immoral when only the result is important, yet since immorality cannot be defended, the calculating mind artfully hides his questionable practice in order to achieve his end.  Machiavelli teaches that the Prince must be a good calculator, able to manage opportunistic situations in such a way as to turn them as much as is possible to his own advantage.

What seems odd is that thinking can then be thought of some sort of strategy game, a soulless mechanism.  A calculating mind is similar to a machine whose function it is to combine means in view of an end, a mental machine that abstains from any form of reflection on its own goal and therefore ends up with no other aim than results.  Is this an ill-intended use of the mind’s faculties or is the mind naturally calculating?  Is the mind mechanical by nature?

  B. Logical Mechanics

   Is this to say that thinking would consist in a dexterous arrangement of means in view of a mechanical end?  If so, it could be the task of a machine, a computer.  This question is acutely relevant inside the framework of today’s computerised workplace.

Can one say that a computer thinks?  No one contests that it performs brilliant calculations, it is an excellent calculator able to perform a great number of operations in a very short time.  Is it possible to think of all the operations of thinking as a form of calculation?  If this is the case then the computer can think.

Here is a joke told by computer scientists: ask a computer, how do you chose between a broken watch that has stopped at three o’clock and one that is late by another five minutes every day?  The reply obtained by computer calculation is:  take the broken watch because it shows the correct time twice a day!  While the watch that is slow will give the exact time only every x days, where x is a very big number, something in the range of 685,785 days.  But human common sense does not hesitate to choose the watch that is late: this one will be of use to us since at least it is working.  Hence the logic of calculation does not always coincide with common sense!  A calculation is not sufficient to uncover the reasons for preferring a watch that is working albeit approximately.  Common sense appears more intelligent than strict calculation, which is exact but its vision is extremely restricted.  A computer performs an operation that is launched by the input it is given.  The operator dials 8*5 and launches the operation, the machine returns 40.  Strictly speaking it is a little as if the input were a stimulus triggering off a response.  Pavlov’s dog is conditioned to salivate at the sight of red light.  The computer is conditioned to yield results when given data on which it can operate.  It executes all the mechanical operations of thinking fast and correctly.

On the other hand the data is not thought by the machine.  The data has no meaning other than as a chain of signs.  A single gap or wrong connection is enough for the machine to be unable to operate.  If the word balance is associated with an order, writing balacne blocks the calculation.  The human operator will immediately understand and correct the error as it relates to context (for instance accountancy).  This can make programming exasperating because a single typing mistake might block the machine.  Whence one’s irritation with these stupid machines that are unable to understand what any human would think of straight away!  The relation between stimulus and response is not thought of by the machine, but established by the programmer who has specified what the machine must do when fed this kind of data.  If the machine is made to yield nonsense, then the output will be nonsense.  This is to say that it is the programmer who is intelligent, not the machine.  He is the one who knows that this relation between A and B is correct, that other one is nonsense.

For a computer to think, it must be able to intuitively apprehend meaning.  Yet machines know only discursive thinking, not intuitive thinking.  The manipulation of significant elements would require that meaning could be entirely formalised into propositions of language.  It would also require that natural language be formalised into logical language.  But is this possible?  It would require the prodigious act of converting all the operations of human thinking into a form of calculation that the machine could interpret, that is translating all the statements of natural language into logical language.  But in fact the machine does not even operate at a logical level.  What it requires is that one transforms the logical code into binary language, which is the only one that the machine is able to “understand », because computers use memories that only have two states, the 0 and 1 of Boolean algebra.

  The passage from natural to logical language is extremely difficult.  Understanding three pages of Proust is easy for a human reader.  The formalisation of all the statements they contain is an enormous labour for the logician. Indeed one finds statements that are very difficult to formalise: aesthetic judgements, moral judgements, subjective appreciation of feeling, dreams, metaphorical statements, propositions about probabilities, suppositions and so on.  Of course research into artificial intelligence is moving forward very rapidly.  One has already managed to construe efficient grammatical correctors, although they keep stumbling over some rather comical mistakes, which common sense immediately perceives.  A sharp intelligence easily detects mistakes that logical mechanics does not find.  

 The fundamental question is: can any thought boil down to the finite logic useful to the machine? The idea that one might transcribe the statements of all the articles of an encyclopaedia in order to constitute logical and coherent knowledge is a fascinating one.  This would make it possible to ask the computer a question using natural language and obtain a structured answer, and this not only in an interrogative mode, which is rather simple.  It would be enough then to distribute knowledge in a database.  In this case the computer plays a very basic part, that of a memory arranged in directories.  This is a prowess performed by small calculators, that contain a translation dictionary.

Genuinely intelligent knowledge would be one containing relations that the machine would be able to create by itself, without any human operator having done it before.  Indeed what is an intelligent mind ?  It is a mind that perceives relations, a mind immediately able to establish connections.  To see a relation is much more than being able to calculate with operating elements.  It is imagining that which is not immediately given, seeing what cannot be flatly observed.   There is quit a leap between this sort of intelligence and the logical mechanism of calculation.  These are two different forms of thinking.  By the way, this is something any teacher of Mathematics will have experienced.  There are pupils who succeed through repeating the same exercises again and again until the mechanism has been acquired and who are lost at the slightest variation in the presentation of the question.  There are other pupils who immediately understand the relations, in other words, who understand.  These are more creative and intelligent and for them, the mechanics of calculation is of secondary importance.  This is to say that the former have laboriously acquired the discursive aspect of calculation, while the latter have an intuitive feeling for Mathematics.

C. Complexity of thinking


We must proceed to distinguish forms of thinking.  In its verb form, thinking designates an act, the act of executing thought.  The word thought has a wider meaning.  1) Thought is both the mental activity in all the forms in which it produces ideas, and this also includes the imagination, as well as delirium or hallucination.  In this sense dreams are thoughts.  The dreamer is « thinking » and thinking a lot, and yet he is unconscious in his bed.  When someone is sunk in his own world we offer a penny for his thoughts.  Maybe these are just associations of ideas, vague reveries.  Thinking is not necessarily rational.  2) Thinking also designates the rigorous conduct of reasoning, discursive thinking, the procedure of development of an intuition, intuitive thinking.  Here we could not say that the dreamer “thinks”, because he has no logic.  Common sense does not think either, it repeats common place and received opinions.

Calculating thinking is one kind of discursive thinking, that is, of reasoning.  There are other forms of reasoning than calculation.  In science one can reason theoretically in order to draw the consequences of an accepted theory and compare it with other theories.  One can reason in a purely philosophical manner to solve problems in science that are not technical but of a more general nature.  Discursive thinking is of course intentional.  But intention does not mean calculation   Truth is an aim sufficient for reasoning.  Phenomenological description for instance is a form of thinking that unfolds from something originally given in the intuition.

To the theoretical research in science a technical goal can be added, such as is the case when one is seeking to improve the tools; then the mind has to follow a path that will yield results.  Since our scientific knowledge is closely connected to technology, this means that research is often related to possible applications, in such a way that research is the fruit of calculation.  Much of rational thinking is effectively a calculation.  Yet this is not the whole of rational thought.  Intuitive thinking goes beyond mere calculation.

                                                                                        Also, rational thinking includes a dimension which is not rational and this in two meanings :

1) infra rational thinking, the one at work in unconscious phenomena.  Freud has shown that the preconscious rationalisations of the mind may well dissimulate unconscious tendencies, in such as way that he who pretends to master rational thinking in his discourse may be unaware that infra rational thinking is also at work in his reasoning.

2) supra rational thinking which is at work in the artistic creation, in the work of the writer, in poetry, in the imagination of the painter and the musician.  Here we also find the spiritual intuition of the mystic.  There is inside artistic genius a flux of inspiration that is different from the slow and gradual path of rational thought.  Even the most rigorous rational thought often proceeds via flashes of intuition, rather than via the mere means of Logic.

It is possible that much of mental functioning is mechanical in nature.  This is the case if thinking is ruled by memory, if it is a mere reaction to stimulus. In this case thinking reproduces a conditioning that it is not able to go beyond. D. Bohm uses the analogy of a program written on a floppy disk.  Memory then contains a succession of programmed reactions and most of the time all I do is draw from memory in order to analyse a situation or an experience.  Yet genuine Intelligence consists essentially in seeing, not in remembering.  It is this intuitive intelligence that one must awaken in man for thinking to get out of its mechanical limits. Thus David Bohm  writes in For a Revolution of Consciousness that: “Thinking appears to possess a certain inertness, a tendency to proceed in the direction in which it has been thrown.  It appears to need that we sustain it. ».   

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 When we asking if thinking is calculating, then what we want to know is 1) if thinking, as mental activity, can be reduced to some form or other of a calculation or if 2) if the act of thinking is, in its essence, nothing other than a calculation.  If this is not the case we will have to show why thinking in both 1 and 2 are more than a form of calculation.  

When calculating, thinking creates nothing, imagines nothing, it only combines elements that were there before.  Thinking depends on memory.  In a passive or receptive sense, one cannot say that thinking boils down to calculation.  However the mind is very clearly calculating.  The real question we must ask is whether it is possible for us to make an intuitive leap that would give thinking the all-embracing character of a vision beyond calculation.


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