{} {distance}
About {theme} theory

{distance} is a {theme}. The most important single {theme} is {linkage}, < >, which, like other {themes}, plays a fundamental role in the mind's making sense of experience, as well as concepts not originating in experience. For more detailed information about the {themes} and my approach, a study of Introduction to {theme} theory would be very useful (I have to say, indispensable). From the introduction:  

'{theme} theory is completely general and philosophy is only one application-sphere. These illustrative examples are very diverse in subject matter and  in degree of abstraction: for example ethical argument, concrete problems in applied ethics, Nazi atrocities, Stalin, the death penalty, mathematical and philosophical relations, the completion of a  proof, scientific correlation.  There are also marked differences in tone: the tone appropriate to abstract and systematic subject matter but also forthright criticism, for example of Nietzsche, the juxtaposition sometimes of the abstract and  the impassioned.'

'{theme} theory is based upon the conscious, and justifiable, ignoring in many cases of sphere-boundaries, such as the boundaries separating the material sphere, the conceptual sphere, the spheres of the different senses. A mathematician may attack a problem in the mind just as a soldier may attack an all-too-concrete machine-gun post. A scientific model may be material, the model constructed from materials of different kinds, such as wood and plastic, or the model may be purely conceptual, without material expression. Scientific modelling is an activity which can be practised in material or conceptual ways. Linkages may be material, such as a connecting rod in a mechanical system linking mechanical components or non-material, such as the ties of shared history linking, in some cases, nations.'

List of {themes}:

{contrast} ( )
{distance} D
{linkage} < >
{restriction} ==
{separation} //
{substitution} S

In the list, the name of each {theme} is followed by the symbol for the {theme}. Clicking on the {theme} gives access to a page which gives instances of the {theme}. These instances show something of the range of {theme} theory, which addresses the most diverse areas of human experience and knowledge.










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The key system

{distance} and {modulation} in poetry

The unities of drama

Narrative {distance}
Social {distance}: 'du' and 'Sie' in German
Edward Bullough's aesthetic {distance}
Wordsworth's boy at Windermere
The subjunctive and optative in Thucydides
Web design and {distance}
Mathematical {distance}
The law of negligence






As in the case of other themes, {distance} includes seemingly unlinked activities. The claim that the theme links these diverse activities is a radical one. {distance} includes mathematical distance and the distance of literary narrative or narrative in other fields. The theme is applied to time as well as space, to experienced distance as well as empirical, measurable distance. It tends, at greater values, to {remoteness}. The names of themes are nouns but can refer to an activity, in this case the activity 'to distance...' 'to make distant...' and 'to set a distance...'

The datum is the base from which an object or event is distanced. (Compare datum plane, level or line in surveying. From this, heights and depths are calculated.) The datum may be page-home in Large Page Design. The user of the page may go to a point on the page remote from this starting-point, or home as the starting point for journeys in the world. The datum may be the home key of a piece of music. In a development section, remote keys may be used, ones distanced from the datum. Lines in Euclidean geometry can be regarded as having a datum in their construction, a starting point, as also the natural numbers.

A datum can also act as a reference point, but my use of datum differs from one meaning given by Francis D. K. Ching in his 'Architecture: Form, Space and Order:' '...the lines of a musical staff serve as a datum in providing the visual basis for reading notes and the relative pitches of their tones.'

The key system

The circle of fifths

Composers between the later seventeenth century and the earlier nineteenth century who wrote a piece in D major would tend to remain in the tonal region of the keys G and A. The distance between G major and C major is also small. Only one note is changed, F becoming F sharp. D major is more distant from C major. The key C sharp major is remote from C major, in fact the most distant of all. The two keys don't have a note in common, even though the scale is based on the note next to C. (On the piano, there is physical proximity rather than physical remoteness.)

Venturing into the remote tonal region containing the keys of D flat and G flat would be far less likely but there are still many instances of compositions in this period in which a great {distance} is traversed from the home-key datum. For example, the development section of Mozart's Symphony No. 40 in G minor begins in a key at very great {distance} from G minor, F sharp minor. In the development section of the fourth movement, the music reaches the key most remote from G minor, C sharp minor. 'Mozart strains to the limit, if not beyond, the capacity of the listener to retain an awareness of the home key - a capacity on which the proper comprehension of tonal music critically depends.We are, presumably, intended to struggle to avoid losing our bearings altogether. And the next page of the symphony makes it no easier, for the music modulates with such alarming violence and rapidity over eleven bars that it is almost impossible to follow.' Hans Keller writes of the beginning of the development section, ' ... the theme is torn to meaninful shreds, only to be hastily reassembled. The emotional field here explored had not previously been approached by any composer ...' (Essay on Mozart in 'The Symphony,' volume 1, edited by Robert Simpson.) But with the recapitulation, after this tense and baffling but thrilling journey, the recapitulation shows us the way back to home - to the home key of G minor.

Donald Francis Tovey wrote, of tonality, that 'it has much the same place in the classics of music that perspective has in the classics of art ...' ('Musical Form and Matter,' in 'Essays and Lectures on Music.')

{distance} and {modulation} in poetry

{distance} has {/modulation}. A separate page is devoted to {modulation} and the poetry of Jared Carter: From the page, discussing Jared Carter's poem 'The Gleaning:'

'Modulation has, of course, an established use in classical and other music, referring to the transition from one key to another. Modulation is often most striking in the development section of a movement in sonata form. In the development section of a Beethoven symphony, for example, the listener may be taken far from the home key, to ‘remote’ keys, the effect intensified by marked changes of tempo and by other means. In music, ‘modulation’ does not include changes of tempo or dynamics, perhaps from very soft to very loud, but I use the term inclusively, and in my terminology, modulation can even be synonymous with ‘change’ of a certain kind. Although the music exists in time, and is changing from bar to bar, the change which is characteristic of modulation is different from, over and above, if you like, these changes. And it’s the same with modulation in poetry. ’ So, 'The Gleaning' modulates, develops, in very striking ways, and we feel, as we read it, that we have come a long way, far from the starting point, to regions sharply contrasted with the starting point (and each new region can be regarded as a new starting point) so that this comparatively short poem seems a very spacious one, expansive rather than constricted. Modulated poetry gives {distance} from the datum.'

The unities of drama

The unities were codified by neo-classical writers, basing their work on the discussion in Aristotle's 'Poetics.' There are three unities:

(1) Unity of action. A play should have a principal action, without appreciable diversification or digression.
(2) Unity of time. The action should take less than 24 hours, excluding the lapse of days, weeks, months or years.
(3) Unity of place. The play should be within a single space, not represent, in turn, many places.

Using the term from the internet, the established 'home page' and my own 'page-home,' a play which observes the unities employs 'home' action, 'home' time and 'home' place. Re-stating (translating into Theme Theory), a play not observing the unities employs action-distance, temporal distance and spatial distance.

Narrative {distance}

An established term with a range of meanings in the 'theory of narrative.' One reference is to the degree of involvement in a literary work on the part of the reader: closer (as in the case of the characters in a Dickens novel) and more distant (as in the case of a great deal of Joseph Conrad's fiction, according to Jeremy Hawthorn. Literary Theory often neglects evaluation in its survey of a work. The discussion of distance in literary theory has neglected the unintentional distance of a mediocre work, the reader's lack of involvement due to lack of skill on the part of the writer. A reader's lack of involvement may not always be due to lack of skill on the part of the writer. Here, it's necessary to practise diversification: in simple terms, the reader's lack of involvement may be the fault of the writer OR it may not. The reader may be stupid, have a very short attention span, may be out of his or her depth, may not have given enough attention to the text.

Although I accept the usefulness of the established theory of narrative distance, distance here is subject to {restriction}. An adequate theory of distance can include and should include far more than this.

Social {distance}: 'du' and 'Sie' in German

Hammer's German Grammar and Usage (revised by Martin Durrell), entry for 'Pronouns of address:' 'Essentially, the use of du is a token of intimacy, affection and solidarity. People who use du to one another are conscious of belonging to the same group or standing together, whereas Sie signals a certain degree of social distance (rather than 'politeness').

Edward Bullough's aesthetic {distance}

This is well explained in Diané Collinson's essay 'aesthetic experience,' part of 'Philosophical Aesthetics,' edited by Oswald Hanfling. Bullough's account is an aspect of what he calls 'psychical distance.' He explained the ideas in a series of lectures he gave at Cambridge University in 1907. What he calls 'Distance' I assimilate to my concept of {distance}.

I give only a little information here. Diané Collinson writes, 'It seems to be implicit in Bullough's account that 'distancing' is both a phenomenon one may consciously try to produce in order to achieve an aesthetic experience and also one that may just occur without conscious effort. He regards Distance as an aesthetic principle that enables us to distinguish agreeable pleasures which, he says, are non-distanced, from aesthetically valuable experiences that are impossible without the insertion of Distance.

Wordsworth's boy at Windermere

The boy at Windermere imitates the owls (Book 5, lines 364 - 388, 1850 edition)

...and, when a lengthened pause
Of silence came and baffled his best skill,
Then sometimes, in that silence while he hung
Listening, a gentle shock of mild surprise
Has carried far into his heart the voice
Of mountain torrents...

Here, 'far into his heart' is an instance of {distance}.

The subjunctive and optative in Thucydides, 'The Peloponnesian War' iii, 22

The subjunctive and optative forms of the verbs are used here to express degrees of {distance}, less and more remote:

' ... the subjunctive form often expresses the more immediate or more certain contingency, and the optative form the more remote or more uncertain contingency' and 'the historians, especially Thucydides, seem often to have thrown themselves so completely into the past events which they recorded that those events became as present to them, and hence a form of the subjunctive group follows a historic tense. Sometimes indeed forms from both groups occur in a clause dependent on the same historical sense ...' (Clyde, 'Greek Syntax, section 40, obs. 2, quoted in the edition of Thucydides Book IV, edited with notes by C E Graves.)

In 'The Peloponnesian War,' iii, 22:

ὅπως ἀσαφῆ τὰ σημεῖα τῆς φρυκτωρίας τοῖς πολεμίοις  καὶ μὴ βοηθοῖεν,

[ After Thucydides has written that the Plataeans displayed fire signals ] 'so as to make the enemy's signals unclear and to prevent help from coming.' (My translation.) Here, making the enemy's signals unclear was the more immediate objective, preventing help from coming had more remote {distance}.

Nietzsche wrote of Thucydides - a writer I revere - 'One must turn him over line by line ...' ('Twilight of the Idols,' Section 2.)

Web design and {distance}

In the form which I've devised called 'Large Page Design,' page-home is the starting point for Page Travel. The traveller in the page may be brought a long way from page-home and the psychological feeling of remoteness may cause disquiet, as often the experience of being in a country very distant from home. In the case of page travel, the feeling of remoteness can be lessened or eliminated by the provision of simple ways of returning to page-home, rails and dual-purpose text and images.

Mathematical {distance}

This has various meanings. In Euclidean space, for example, the distance is 'the length of the shortest line segment joining the given points, measured as the square root of the sums of the squares of the differences between the coordinates of the two points.' (The 'Dictionary of Mathematics' of E. J. Borowski and J. M. Borwein.)

The Peano axioms for the integers can be regarded as having a datum: the first term 1 of the set N of integers. By use of successors, integers become progressively distanced from the datum.

The law of negligence

In the law of negligence in this country, if a breach of duty has been established, then the claimant is required to show that the breach has resulted in damage or injury ('causation') and that the damage or injury isn't only distantly linked with the breach ('remoteness,' which can be interpreted as an instance of {distance}.)


One theme can have another theme as its application-sphere. {distance} has as a sphere of application {distortion}. R. D. Laing made claims for 'the sanity of psychotics,' (not his own phrase), but it would be generally agreed that although non-psychotics may have a severely distorted view of reality, the view of psychotics is far more severely distorted, and to that extent it has much greater {distance} from the datum.

Amongst non-psychotics, particular interpretations and responses may be very distorted. A particular concern, preoccupation, interest can lead to distortion. I would claim that religions and ideologies are major sources of distortion. These are discussed on a number of other pages. A very concise treatment is on the page aphorisms.

Physics and related fields provide many instances of {distortion}. A very poor microscope or telescope will give a much more distorted view than a very good microscope or telescope, one with a much greater distance from the datum. Poor electronic apparatus will amplify a pure waveform with far more distortion than good apparatus, with greater distance from the datum. Here, the datum refers to the undistorted wave and {distance} has no reference to physical distance. The datum is not the line from which the amplitude of a wave form is measured. It may be that poor, distorting apparatus gives a wave form which is less distant measured from the physical line than the good, less distorting apparatus.

{distortion} has {/empirical distortion} and {/distortion by weighting}. {empirical distortion} is to do with the extent to which a system reproduces the characteristics of its input in its output and includes as instances distortion in electronic amplifiers and distortion in optical systems. {Weighting} has {/defensible weighting} and {/indefensible/erroneous weighting}, which is {/distortion by weighting}.


{/temporal distance} and {/spatial distance} are para-sub-themes of {distance}: {/spatial distance} is not to be regarded as more fundamental.


A common assumption in ethics is that this linkage holds:
[greater distance from the moral agent] < > [{reduction} in moral obligation] 

The assumption is that there is a greater moral obligation to near relatives than to distant relatives, people have a greater moral obligation to other people than to apes. There may be moral conflicts, resolved for the agent, if not for the moral theorist, by a weighting. Someone may well give greater weighting to the welfare of a pet dog than to a person who is (geographically) very distant.