According to the history books the Arabic numeral 'zero' was invented as a 'place holder', i.e. to indicate the absence of a positive integer in the number base being used; in the decimal system this occurs at 0, 10, 20, ...through 100, 110, 120 etc..
However, the 'full' zero is the number that is the average between +1 and -1.
The full zero is supposed to represent nothing. The absence of anything. This is the same nothing that (Western Humanist?) physicists tell us must have existed prior to the beginning of the Universe and what will exist, when it ceases to exist.
But from a (Buddhist or) psychological perspective, the idea that nothing exists beyond our conscious experience of it seems absurd. You must exist even if I have never met you, after all.
The materialist assumption (that Western Humanism often makes) is that consciousness is coterminous with the experience of material existence. But this is only true if you believe that consciousness is a property of the brain rather than the mind.
This philosophical difference is, I guess, reflected in the popularity of different beliefs regarding Life after Death: either the 'nothingness' of Western materialist humanism or some form of 'reincarnation', 'rebirth' or 'renewel' espoused by various forms of Organised Religion and their associated spiritualities.
So I would like to propose that the full zero does not equate to 'nothing', if it did, it would not exist, because by definition, 'nothing' does not exist.
This seems like a logical contradiction and indeed it is. We often think of 'nothing' as being what is left outside of the boundary if we could enclose 'everything' within a set. There is a polarity here between everything and nothing. If it is not everything it must be nothing. However, as someone who works in mental health I have been taught to be suspicious of such 'black and white', 'dichotomous', 'either/or' or 'binary' thinking.
Bertrand Russell realised there could not be a Set of Everything, because if there was it would have to include itself. If it included itself there would be something outside of it, itself. Thus, Set Theory hit a road block that it could not get passed. In the folklore of science we are told that Russell fell off his bike on the cobbled streets of the University when he realised this. Such is mathematics.
Black and white thinking tends to lie behind the sort of thinking that leads to anxiety and depression: "If I do not get an A grade at A-level then I must be a failure". This creates a cognitive distortion that leads to catastrophizing and the emotional symptoms of hopelessness and helplessness; possibly including some forms of suicidal ideation.
In psychotherapy the solution to these problems is to try and find some 'middle way' or 'gap' between the two opposing poles. Then build some graded alternatives, as a cognitive-affective bridge between them. For instance, "If I can do as well as I am possibly able to in my A-level exams then I will have achieved a success".
So my contention is that if zero cannot signify nothing, because logically nothing does not exist, it must signify the absence of something, and in its place, the presence of something else.
According to this view, even though the 'something else' may indeed be thin air, it is something, it is always something else, never nothing!
This idea is however very unpopular with people who seek to repress or deny parts of their own thinking or being. It creates the possibility that we are more than what we consider the boundary of our living selves to be; because even our absence is the presence of our absence. The moment of our existence can never cease to exist.
Mathematicians argue about this stuff all the time and would require me to prove this assumption using the same rules of logic that they do. I am not a trained mathematician but here is an attempt at a logical proof:
However, the 'full' zero is the number that is the average between +1 and -1.
The full zero is supposed to represent nothing. The absence of anything. This is the same nothing that (Western Humanist?) physicists tell us must have existed prior to the beginning of the Universe and what will exist, when it ceases to exist.
But from a (Buddhist or) psychological perspective, the idea that nothing exists beyond our conscious experience of it seems absurd. You must exist even if I have never met you, after all.
The materialist assumption (that Western Humanism often makes) is that consciousness is coterminous with the experience of material existence. But this is only true if you believe that consciousness is a property of the brain rather than the mind.
This philosophical difference is, I guess, reflected in the popularity of different beliefs regarding Life after Death: either the 'nothingness' of Western materialist humanism or some form of 'reincarnation', 'rebirth' or 'renewel' espoused by various forms of Organised Religion and their associated spiritualities.
So I would like to propose that the full zero does not equate to 'nothing', if it did, it would not exist, because by definition, 'nothing' does not exist.
This seems like a logical contradiction and indeed it is. We often think of 'nothing' as being what is left outside of the boundary if we could enclose 'everything' within a set. There is a polarity here between everything and nothing. If it is not everything it must be nothing. However, as someone who works in mental health I have been taught to be suspicious of such 'black and white', 'dichotomous', 'either/or' or 'binary' thinking.
Bertrand Russell realised there could not be a Set of Everything, because if there was it would have to include itself. If it included itself there would be something outside of it, itself. Thus, Set Theory hit a road block that it could not get passed. In the folklore of science we are told that Russell fell off his bike on the cobbled streets of the University when he realised this. Such is mathematics.
Black and white thinking tends to lie behind the sort of thinking that leads to anxiety and depression: "If I do not get an A grade at A-level then I must be a failure". This creates a cognitive distortion that leads to catastrophizing and the emotional symptoms of hopelessness and helplessness; possibly including some forms of suicidal ideation.
In psychotherapy the solution to these problems is to try and find some 'middle way' or 'gap' between the two opposing poles. Then build some graded alternatives, as a cognitive-affective bridge between them. For instance, "If I can do as well as I am possibly able to in my A-level exams then I will have achieved a success".
So my contention is that if zero cannot signify nothing, because logically nothing does not exist, it must signify the absence of something, and in its place, the presence of something else.
According to this view, even though the 'something else' may indeed be thin air, it is something, it is always something else, never nothing!
This idea is however very unpopular with people who seek to repress or deny parts of their own thinking or being. It creates the possibility that we are more than what we consider the boundary of our living selves to be; because even our absence is the presence of our absence. The moment of our existence can never cease to exist.
Mathematicians argue about this stuff all the time and would require me to prove this assumption using the same rules of logic that they do. I am not a trained mathematician but here is an attempt at a logical proof:
- If every integer can be a positive or negative number and if 0 is an integer, then, arguably, it is possible to have a +0 and -0.
- This can create an 'optical illusion' so that when I ask "which is closer to +1, is it -0 or +0?" the sign value fools some part of our minds into suggesting that +0 must be closer to +1 than -0, at least if we think about all three numbers lined up beside each other on a single line or dimension.
- However, this cannot be the case because, according to the laws of mathematics and our rational minds, both +0 and -0 remain one unit of distance from +1, i.e.: +1 - +0 = +1; and +1 - -0 = +1.
- Thus, the sign cannot increase the distance between 0 and 1. If it is possible to increase the polarity of 0, this must occur along some other unseen dimension that is 'superimposed' on the integer system.
- So many people will say 0 cannot be a -0 or a +0; 0 is not an integer like every other integer, it has special rules applied to it that say it cannot carry a positive or negative value to it, only in this way can the general laws of mathematics be maintained.
- Thus, I say, what we have proved is that 0 is defined as the absence of something, in this case by the absence of any positive or negative value. This does not require any appeal to any external source which is outside the laws of mathematics in the same way that the Set of Nothing appears to be.
- I surmise, nothing does not exist, what exists is (on any line or dimension) a point at which there is an absence of any positive or negative sign value.
These suggestions are based on the overlap between the empirical sciences of neurology and phenomenology. They are based on the assumption that the brain and associated neural structures encode the value of an electrochemical signal and communicate that value, or series of values in the form of a coded message, to its nearest neighbours.
Ultimately the brain, and every neuron within it, must have a resting potential, the homeostatic equilibrium, to which the neuron must return. This 'resting potential' need not be 'zero potential' although it may appear in our minds to be 'nothing' due to the absence of firing; and it may not be the same resting potential for all neurons, although I have never tested this hypothesis.
Thus, at the level of the neuron we find language. We do not really understand that language at the moment. However, it could be argued that the polarity of the positive and negative signs that are attached to the 'phenomenological experiencing of things' at the neural level is, at least partially replicated in the adjectives of our interpersonal languages, e.g.: good/bad; strong/weak; active/passive. These antonymic adjectives have been described by Osgood's 'Semantic Differential' and used to differentiate the relativity of phenomenological experience in various cultures.
In theory, the Semantic Differential is the basis of all the objective measurable qualities of objects, according to which objects can be compared with each other. You can conceive of all objects as being coded according to their location (in space and time) and their affective value; so that either the location or emotional state of the subject would be enough to recall the object from memory.
Mathematically this might look something like the following equation: It states that the subjective probability of noticing an object (X) at a specific time (t) and place (p) is equal to the sum of the probabilities that it is coded positively (X +ve) or negatively (X -ve) at the same time (t) and place (p) by the subject.
This does not sound like big news. But what it doesn't tell you is that the actual (or objective) probability of the object being in that time and place (p (X t.p)) is indeterminate because it is impossible to predict the probability of an object's existence in the Universe without knowing how many other objects exist in the Universe at that time and place.
Thus, p (X t.p) is subjective in the sense that it is a prediction, or expectation of the subject about the presence, or absence of the object at a certain time or place. It remains an inductive estimate based on a calculation of the affective values (X+ve and X-ve) that an object has for us, or had for us in the past; the inductive estimate can also be based on previous encounters with the object (by changing the equation on the right or left slightly to denote 't' as 't+1' or 't-1', respectively) and has to be constantly updated when new information becomes available about other objects in our Universe.
To fit this in with the previous discussion regarding mental health: In Klienian Object Analysis the encoding of social objects during the development of the child is then said to progress from a dichotomous 'paranoid-schizoid' position (where the world is painted in black and white terms) towards a 'depressive' position (where the world is much less powerfully determined by the affective extremes).
This still means there can be multiple dimensions (of +ve and -ve values) that can be attached to objects that can then be compared with each other according to the same basic integer system. It's just that all such measurement ceases to be 'objective'; because all such measurement is relative to the position of the subject in the Universe; or 'the Subject's developmental trajectory within the developmental trajectory of the Universe' if you like. And the sum of all those values may, or may not, sum to zero.
Sociologists argue about this sort of stuff too. However, for a Sociologist 'the Universe' is the relative confines of the culture they inhabit. For instance, one major battle-front of the feminist movement was that this system of binary oppositions was used to exploit the differences between men and women. The argument was that all powerful or positive adjectives are attached to 'masculine' objects; the subjucation of the 'feminine' objects was seen as a social injustice. Similar arguments were raised within the US Civil Rights movement regarding the negativisation of the word 'black'; other social movements followed.
All these movements made the case for the isomorphism of language and culture; through their struggles they made this isomorphism a social and political fact. As political movements they armed a generation with the intellectual tools to fight oppression. That struggle still continues.
Coincidentally, the 'zero sum' position of critical analysis is also the basis of scientific objectivity; science must maintain the absence of emotional subjectivity to justify the validity of its 'theology'. Arabic numerals underpinning Western thoughts: There is a strange irony about that. It is not nothing. Nothing, by definition, does not exist. I wonder what else is not nothing?
Ultimately the brain, and every neuron within it, must have a resting potential, the homeostatic equilibrium, to which the neuron must return. This 'resting potential' need not be 'zero potential' although it may appear in our minds to be 'nothing' due to the absence of firing; and it may not be the same resting potential for all neurons, although I have never tested this hypothesis.
Thus, at the level of the neuron we find language. We do not really understand that language at the moment. However, it could be argued that the polarity of the positive and negative signs that are attached to the 'phenomenological experiencing of things' at the neural level is, at least partially replicated in the adjectives of our interpersonal languages, e.g.: good/bad; strong/weak; active/passive. These antonymic adjectives have been described by Osgood's 'Semantic Differential' and used to differentiate the relativity of phenomenological experience in various cultures.
In theory, the Semantic Differential is the basis of all the objective measurable qualities of objects, according to which objects can be compared with each other. You can conceive of all objects as being coded according to their location (in space and time) and their affective value; so that either the location or emotional state of the subject would be enough to recall the object from memory.
Mathematically this might look something like the following equation: It states that the subjective probability of noticing an object (X) at a specific time (t) and place (p) is equal to the sum of the probabilities that it is coded positively (X +ve) or negatively (X -ve) at the same time (t) and place (p) by the subject.
p (X t.p) = p (X+ve t.p) + p (X-ve t.p)
This does not sound like big news. But what it doesn't tell you is that the actual (or objective) probability of the object being in that time and place (p (X t.p)) is indeterminate because it is impossible to predict the probability of an object's existence in the Universe without knowing how many other objects exist in the Universe at that time and place.
Thus, p (X t.p) is subjective in the sense that it is a prediction, or expectation of the subject about the presence, or absence of the object at a certain time or place. It remains an inductive estimate based on a calculation of the affective values (X+ve and X-ve) that an object has for us, or had for us in the past; the inductive estimate can also be based on previous encounters with the object (by changing the equation on the right or left slightly to denote 't' as 't+1' or 't-1', respectively) and has to be constantly updated when new information becomes available about other objects in our Universe.
To fit this in with the previous discussion regarding mental health: In Klienian Object Analysis the encoding of social objects during the development of the child is then said to progress from a dichotomous 'paranoid-schizoid' position (where the world is painted in black and white terms) towards a 'depressive' position (where the world is much less powerfully determined by the affective extremes).
This still means there can be multiple dimensions (of +ve and -ve values) that can be attached to objects that can then be compared with each other according to the same basic integer system. It's just that all such measurement ceases to be 'objective'; because all such measurement is relative to the position of the subject in the Universe; or 'the Subject's developmental trajectory within the developmental trajectory of the Universe' if you like. And the sum of all those values may, or may not, sum to zero.
Sociologists argue about this sort of stuff too. However, for a Sociologist 'the Universe' is the relative confines of the culture they inhabit. For instance, one major battle-front of the feminist movement was that this system of binary oppositions was used to exploit the differences between men and women. The argument was that all powerful or positive adjectives are attached to 'masculine' objects; the subjucation of the 'feminine' objects was seen as a social injustice. Similar arguments were raised within the US Civil Rights movement regarding the negativisation of the word 'black'; other social movements followed.
All these movements made the case for the isomorphism of language and culture; through their struggles they made this isomorphism a social and political fact. As political movements they armed a generation with the intellectual tools to fight oppression. That struggle still continues.
Coincidentally, the 'zero sum' position of critical analysis is also the basis of scientific objectivity; science must maintain the absence of emotional subjectivity to justify the validity of its 'theology'. Arabic numerals underpinning Western thoughts: There is a strange irony about that. It is not nothing. Nothing, by definition, does not exist. I wonder what else is not nothing?
