Poems

1. Ellenborough River

Clear water gushing between rocks,
A floating stick catches, joggles,
Frees itself and rushes on.
My submerged ears hear on the creek bed
The small stones crunch.
Canopy of tall trees meets overhead.
The current catches me and, legs forefending,
Bumps me down by stages
To the deep, black pool.

2 Ladies Rest Room

Feet in elderly shoes
ungainly apart before the pedestal
Seen below the stable door of the Rest Room cubicle.
The mind’s eye completes the picture.
Of skirt pulled up and pants down to knees,
Displaying stocking tops and suspenders
To the outside waiting girl
A sight to appal:
The disdain of youth.

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Predicting the Primes 2.

The Distribution of the Primes

February 2006

Introduction

The distribution of both the composite and the prime numbers in our number system is the essential outcome of a number system constructed of repeated cycles of a sequence of numbers, in our case in decades, that is, as the numbers 1 to 10. The determination of the distribution of the composite numbers is more fundamental than the determination of the distribution of the primes, the primes being those numbers that remain “unchecked” when all the composite numbers in a sequence (whether limited or unlimited) have been determined. The primes are, therefore, essentially negative instances – they are numbers that are not composite.

It will be demonstrated here that the composite numbers in our number system, and in any number system likewise characterized by repeated number sequences, occur lawfully (i.e. they can be predicted) in recurrent cycles whose length is determined by the repetitive character of that system. I will demonstrate this with regard to our number system, which is based on repeated decades, and when this is understood it will be apparent that exactly the same lawful characteristics will apply to any number system built on repeated number sequences. Once the composite numbers have been identified, the primes automatically emerge as, as I have said, negative instances.

Composite Numbers

From the standpoint that composite numbers are created by multiplication rather than characterized by divisibility, if we proceed up the number series in an orderly fashion each number in turn can multiply each other number in the total series (ad infinitum), and each resultant product will be a composite number with its place in the total series. Thus 2 can multiply 1, 2, 3, 4 etc, creating the composite numbers [2], 4, 6, 8 etc, which we know as the even numbers. We also see at once that the composite numbers produced by multiplying by a particular integer can never be consecutive numbers (since multiplication or division by 1 is ruled out by definition).

Similarly 3 can multiply 1, 2, 3, 4 etc to create the composite numbers [3], 6, 9, 12 etc. Some of these numbers are, as it were, redundantly composite as multiples of 3, as they are already composite as products of 2, but 9 is a new addition, divisible by 3 but not by 2. Multiplying by 4, itself a composite number, creates no new composite numbers. As another even number, with 2 as a factor, it merely reproduces the work of multiplying by 2. But multiplying by 5 produces [5], 10, 15, 20 etc and so identifies another new composite number, 15.

The number 2 makes every second number, that is, the even numbers, a composite number. As half of the numbers of each decade are even numbers, being divisible by 2, therefore half of all numbers in the infinite series will necessarily be composite numbers. If we envisage the products, that is the composite numbers, throughout the total series that will be created by the multiplying action of the numbers of the first decade of the series, it is clear that every second number will have been made a composite number by 2, every third by 3, every fifth by 5, and every seventh by 7, while the composite numbers potentially created by 4, 6, 8, 9 and 10 have already been accounted for by 2 and 3.

Readability of the Composite Numbers

Our number system is entirely fortuitously built on repeated decades. This condition exercises quite specific, but also fortuitous, constraints on the patent recognizability of divisibility of numbers, that is, on the immediate readability of their character as either composite or prime numbers.

Only integers that divide evenly into 10 will produce composite numbers that always coincide with the final number in each successive counting decade. Because 2 divides evenly into 10, the composite numbers built on 2 occur always in the same position within a decade – at numbers ending in 2, 4, 6, 8 and 0. 5 is the only other number within the first decade that divides evenly into it, and it creates, like 2, a predictable and recognizable pattern of composite numbers throughout the number system. The number 5 makes every fifth number, that is, ending in 5 or 0, a composite number, that is, two per decade, although the 0-ending numbers have already been accounted for by 2.

The composite numbers built on all other numbers are created in cycles that do not coincide with the decades of our number system.

The Primes

If we look at the role of multiplication by the numbers of the first decade on the numbers from 11 to 20, we find that the effect is that 12, 14, 15, 16, 18 and 20 are all composite in character, but that 11, 13, 17 and 19, missing these operations, can only be divided by themselves or 1, and are therefore what are called primes.

While five of the numbers in the first decade of the number system are primes, because of the increasing number of multipliers involved and hence an increased number of composite numbers, only four are primes in the second decade, 11-20: the number of composite numbers in the second decade has increased from five to six. The proportion of composite numbers will increase as we move up the number series and more successive numbers are included in the multiplicatory process, and in balance the proportion of primes will decrease. However, as in the progress from the first to the second decade, the creation of composite numbers will be increasingly redundant, as a higher percentage of composite numbers will already have been created by multiplication on numbers further back in the number system – not just by 2, 3, 5, and 7, but by 11, 13, 17, and so on. To have any effect, the new numbers must, of course, be primes, which have not already had their composite numbers created for them by lower multipliers.

The Pattern of Composite Numbers

As pointed out earlier, because the early primes 2 and 5 are factors of 10, which is the repeating base of our number system, we can recognize the composite numbers of which they are factors by inspection – numbers ending in 2, 4, 5, 6, 8, or 0 (in an even number) or in 5 – in regular cycles of 10. Thus the majority of the composite numbers are recognizable by inspection. The action of 2 and 5 also determines that all primes beyond the first decade can only end in 1, 3, 7, or 9. Numbers ending in these digits may be primes, but they may also be composite numbers that are the products of numbers other than 2 and 5. Because all numbers other than 2 and 5, whether smaller or greater than 10, are not factors of 10, their character as composite number or not cannot be simply read off the number sequence in terms of their final digit, as is the case with the composite numbers built on 2 and 5.

However, like 2 and 5, each other number in the “total series” determines a regular pattern of composite numbers as it multiplies first itself, and then each number above it. Thus the remaining primes of the first decade – 3 and 7 – although not factors of 10, like 2 and 5 subtend recurring patterns of composite numbers, but unlike those of 2 and 5, these extend beyond the first decade, and, cycling in a manner determined by the decade structure of the number system, also, eventually, return to scratch at the start of a decade. But because they do not divide evenly into 10, they will create differing numbers of composite numbers per decade, and with higher primes, in many decades none at all. However, there is regularity in their creation of composite numbers, as follows:

The rate at which each successive [prime] number creates composite numbers (redundant or otherwise) is 10 per 10n. That is:

2 creates 10 composite numbers in each 2 decades

3 creates 10 composite numbers in each 3 decades

5 creates 10 composite numbers in each 5 decades

7 creates 10 composite numbers in each 7 decades

The composite numbers built on each prime form a cyclical pattern determined by the pace at which one of its products first, and regularly thereafter, coincides with the final term of a standard decade: that is, when a product it creates ends in 0. This only occurs when 10n is reached. Each endlessly repeats this pattern, recommencing at the beginning of the decade after each cycle of 30, 70, 110 etc. The size of these cycles increases as the number series is ascended, and thus composite numbers are added at an ever slower pace.

If we look at the first 50 numbers in the number series, and identify the composite numbers created by 2 only, we find there are 19 (this leaves 31 numbers as potential primes); if ditto by 3, we find 15 (35 remain); if ditto by 5, we find 9 (41 remain); and if ditto by 7, we find 6 (44 remain). However, because some of these composite numbers are the creation of more than one of these four multipliers, the total number of composite numbers is less than the sum of their creations (that is, 49), and is in fact only 34, leaving a potential 16 prime numbers. This is, in fact, the total number of primes in the first 50, as the next prime to multiply itself is 11, whose product, 121, is outside this range. Nor is a greater number of composite numbers added in the next 50 by the primes greater than 7, by 11, 13, 17, 19 etc, because their squares moves into the range 100-400. The prime number 23 will not contribute a new composite number until we encounter its square, 529, and the prime number 37’s first novel composite number is 1369.  The products of their multiplication by composite numbers and primes earlier in the number series than themselves are, of course, already registered as composite numbers in the series.

The large majority of composite numbers continue to be contributed by the primes of the first decade of the number system, by 2, 3, 5 and 7, at roughly a rate of 38-39 per 50 numbers after getting into full gear in the third decade, leaving a potential of 22-24 primes per 100, which will be successively reduced as composite numbers based on the succeeding primes – 11, 13 etc – invade their ranks with ever more sparse regularity.

Distribution of the primes

It can be seen that the distribution of the composite numbers, as expounded above, determines the distribution of the primes by omission, and explains the observed characteristics of their distribution.

The increasing entry of new cycles of composite number creation into the system means that the incidence of primes decreases as the number series advances. However, the increasing length of cycle for each successive composite number cycle that enters the system means that the rate at which the incidence of primes diminishes decelerates as the series advances. An additional factor is that the level of redundancy of the ten new composite numbers per cycle must increase as more cycles enter the system.

A further significant feature of the pattern of composite numbers which is integral to the structure of our decade-based number system is that the eight potential primes (i.e. non-composite numbers) per 30 numbers remaining after the composite numbers based on 2, 3 and 5 are determined (which together account for a large proportion of composite numbers in the system), fall into two clusters in the advancing number series, within each of which potential primes are within 1 to 3 positions of each other, while the two clusters are separated by gaps of 5 numbers. This variation in opportunity underlies the clustering of primes that occurs from time to time throughout the number series, despite their diminishing incidence.

If there were to be a highest prime number, it would occur when sufficient cycles had entered the system to entirely choke out the residual of the potential 8 primes per cycle of 30 when the cycles of 2, 3 and 5 have been accounted for. Whether this can occur (and proofs suggest that it does not) depends on the rate at which composite numbers are generated as against the rate at which new prime numbers occur in the advancing number series.

Generalizability to other Number Systems built on repeated Number Sequences

This understanding of the mechanism of the distribution of the composite numbers in our number system, which is built on the repetition of sequences of 10, is applicable to any number system built on repeated sequences. For example, for a number system built on repeated sequences of 7 digits, the repeating cycle for each number in turn would be that number multiplied by 7 (instead of by 10), so that for 3 in that system there would be a repeating cycle of 21 (though not of course written as 21, but as 30), and 5 in that system would have a repeating cycle of 35 (written as 50); or in a number system based on 12, the cycle for 3 would be 36 (3×12) numbers long (though written as 30) and for 5 it would be 60 (5×12) numbers long (written as 50). The distribution of composite numbers in any such number system would be documentable by the same processes as I have described for the decimal number system – some easily by inspection but others more laboriously by the process of successive multiplication, and with different parameters depending on the particular number base of the system – but in each case resulting in the progressive “sieving out” of the primes.

In each system a certain stable number of composite numbers would be created in the cycle based on each prime number in turn, although the number would differ depending on the sequence base – i.e. it would not in every case be 10. Further, one cannot expect the same presence of “readable” composites in all number systems. In number systems built on odd numbers such as 5 and 7, in the example above, there would be no readable composites in that no number within the repeated sequence would divide evenly into the basic span (as 2 and 5 divide into 10).

Why describe the Distribution of the Primes?

In that the distribution of the composite numbers, rather than the distribution of the primes, is the primary phenomenon, with the primes emerging by default, is it not, perhaps, perverse to concentrate on this remainder, rather than on the essential multiplicatory patterning in the creation of composite numbers, when describing this feature of number systems? Indeed, some number systems may have no primes.

 

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Predicting the Primes 1.

A Reasoned Exposition of the Distribution of the Composite Numbers

Abstract

A large part of the distribution of the composite numbers can be identified simply by inspection. All numbers ending in an even number or 5 can be simply read off the number series as composite numbers. This is because they are products of 2 or 5, both primes which are factors of 10, which is the cyclical basis of our number system. The distribution of the remaining composite numbers is not simply readable, but is equally predictable because it is created by similar cycles of multiplication on each of the primes that is not a factor of 10 (that is, other than 2 and 5). The distribution of the primes is, of course, determined by the distribution of the composite numbers.

 

Our number system is, entirely fortuitously, built on repeated decades. This exercises quite specific, but also fortuitous, constraints on the patency of divisibility of numbers, that is, on their character as composite or prime numbers.

Half of the numbers of each decade are divisible by 2. These are the even numbers and represent half of all numbers. The only other number within the first decade that divides evenly into it is 5, creating, like 2, a predictable and recognizable pattern of composite numbers throughout the number system. Thus:

The number 2 makes every second number, that is, the even numbers, a composite number.

The number 5 makes every fifth number, that is, ending in 5 or 0, a composite number, although the 0-ending numbers have already been accounted for by 2.

Because the primes 2 and 5 are factors of 10, which is the repeating base of our number system, we can recognize the composite numbers of which they are factors by inspection – numbers ending in 2, 4, 5, 6, 8, or 0. Thus the majority of the composite numbers are recognizable by inspection, and we also know that all other primes can only end in 1, 3, 7, or 9. All numbers ending in these digits are either primes or the products of primes other than 2 and 5.

Like 2 and 5, each other number in the “total series” will determine a regular pattern of composite numbers as it multiplies first itself, and then each number above it. Numbers that are built on the two primes that are factors of 10 (e.g. 4, 25) continue to be immediately detectable on the basis of their final digit – an even number or 5. Those based on a prime which is not a factor of 10 cannot be so simply identified. They will end in 1, 3, 7, or 9, but numbers with these as final digits may be either primes or composite numbers. What is it, as an innate characteristic of out number system, that determines their individual status as prime or composite numbers?

The remaining primes of the first decade – 3 and 7 – although not factors of 10, nevertheless also subtend recurring patterns of composite numbers, which extend beyond the first decade, and which, cycling in a manner determined by the decade structure of the number system, also, eventually, return to scratch at the start of a decade. The composite numbers built on each – its products, whether primes, composite numbers or a combination of the two – will form, and be recognizable in, a cyclical pattern determined by the pace (length of number series) at which one of its products first, and regularly thereafter, coincides with a root of the decade: that is, when a product it creates ends in 0, and this will only occur when 10x is reached. Thus its pattern will only begin to repeat beyond 10x, and thereafter at 20x, 30x, 40x … and so on.

This is initially, and most easily, seen in the repeating pattern of composite numbers built on the prime 3, in a cycle 30 (i.e. 1 – 30, 31 – 60, 61 – 90 etc), but similarly occurs, forming a different pattern, for those deriving from the prime 7, which cycle between 1 and 70 (71 – 140, 141 – 210 etc). 10x is always the first point at which a number, and for our purposes a prime number (e.g. 3, 7, 11), reassumes the initial position in a decade, and from that point the pattern of its creation of composite numbers will recur until the next sequence is completed. This is an essential concept, permitting us to see the products of each prime number as recurring patterns within our number system based on 10.

Applying the above: the prime number 3 does not divide evenly into 10, but it, like 2 and 5, determines a regular pattern of divisibility in the numbers which follow it, and its regular cycle extends over not one, but three decades; that is, the cycle is from 1 to 30. Unlike those deriving from 2 and 5, however, the composite numbers built on it are not identifiable by simple inspection. The number series 1 – 89 (three cycles), showing only numbers ending in 1, 3, 7, and 9 (since all others end in even numbers or 5 and so are already identified as composite), is set out below and the pattern of composite numbers built on 3, that is, when 3 is multiplied first by itself and then by each following number which is neither even nor 5 (which products can be simply read as composites), is shown in bold:

1          3          7          9

11        13        17        19

21        23        27        29

 

31        33        37        39

41        43        47        49

51        53        57        59

 

61        63        67        69

71        73        77        79

81        83        87        89

It can be seen that the pattern repeats over each successive set of 30 numbers. It will recur ad infinitum, as 3 is successively multiplied by each number ending in 1, 3, 7, and 9. It is immediately recognizable that the potential primes remaining after removing even numbers and numbers ending in 5, are, after the identification of the composite numbers based on 3, reduced by a further 4 per 3 decades; that is, from 12 (all numbers ending in 1, 3, 7, 9) to 8. In every successive 30 numbers, a maximum of 8 can now be prime, due to the multiplicative outcomes of the prime numbers 2, 3, and 5.

Similarly, for the prime number 7 we have the following repeating pattern over cycles of 70 numbers:

1          3          7           9         11        13        17        19        21        23         27       29

31        33        37        39        41        43        47        49        51        53        57        59

61        63        67    69

 

71        73        77        79        81        83        87        89        91        93        97        99

101      103      107      109      111      113      117      119      121      123      127      129

131      133      137      139

(The numbers in bold italics are those already identified as composite numbers for the cycle of 3.)

It will be noticed that all the numbers ending in 1, 3, 7, and 9 not identified as composite numbers in the recurring cycles of 3 and 7 are primes (with the exception of 121, which will be identified in the next cycle, based on 11). Each of these primes in turn will create its own cyclic pattern of composite numbers, so determining the complete (within any set of limits) distribution of composite numbers; and as above, those numbers left out of the distribution form the next in the series of primes, and will be the bases of further cycles of the non-readable composite numbers.

That is, every succeeding prime number creates, by its multiplicative action, a regular pattern of composite numbers within its cycle of 1 to 10x, and will, reliably according to its pattern, create/identify composite numbers among the numbers left as potential primes after the extraction of the products of all lower primes

Moving up the primes, beyond the first decade, a repeating cycle will occur for 11 over 11 decades (1 – 110, and thereafter), and for 13 over 13 decades (1 – 130 and thereafter).

Thus for the prime number 11 we have the following repeated pattern in a cycle of 110:

1          3          7           9         11        13        17        19        21        23         27       29

31        33        37        39        41        43        47        49        51        53        57        59

61        63        67        69        71        73        77        79        81        83        87        89

91        93        97        99        101      103      107      109

 

111      113      117      119      121      123      127      129      131      133     137      139

141      143      147      149      151      153      157      159      161      163      167      169

171      173      177      179      181      183      187      189      191      193      197      199

201      203      207      209      211      213      217      219

 

(Again, the numbers in bold italics have already occurred as composite numbers in the cycles of  the two lower primes, 3 and 7.)

It will be observed that in each cycle, whether of 30, 70 or 110, four numbers are taken out as composite numbers by the given base number, deriving from the four numbers ending in 1, 3, 7, and 9 by which the prime is multiplied before the end of the cycle is reached.

Each successive prime number creates a regular but different pattern of composite numbers as this process proceeds up the scale, with each cycle and pattern repeating itself ad infinitum. As the base number increases in size, so does its cycle size, but each of these cycles, regardless of its length, introduces four non-readable composite numbers (see tables above), although varying numbers of these are novel (that is, not already created/identified as composite numbers, by a lower prime).

If we superimpose all such cycles, with their differing patterns of composite numbers, on one another (having already eliminated all even numbers and numbers ending in 5), we will have as remainder the distribution of primes in the total number series. That is, those numbers in the total series that do not occur as products (that is, as composite numbers) in this successive process are the prime numbers. The distribution of the primes is thus determined by the distribution of the composite numbers.

The following table shows this process of superimposition for the cycles of 3, 7, and 11 to the end of the second cycle of 11 (the composite numbers deriving from 2 and 5 are again omitted as entirely immediately recognizable), The numbers shown in bold are those which occur as products in the cycles of 3, 7, and 11; that is, they are all composite numbers:

 

1          3          7           9         11        13        17        19        21        23         27       29

31        33        37        39        41        43        47        49        51        53        57        59

61        63        67        69        71        73        77        79        81        83        87        89

91        93        97        99        101      103      107      109      111      113      117      119

121      123      127      129      131      133     137       139      141      143      147      149

151      153      157      159      161      163      167      169*    171      173      177      179

181      183      187      189      191      193      197      199      201      203      207      209

211      213      217      219

*the first non-redundant appearance of 13

 

It can be seen that all the remaining numbers, after the composite numbers identified by the five number cycles (2, 3, 5, 7, 11) are eliminated, are prime numbers. (The first of the autonomous cycle of 13 occurs within this range and is also identified as a composite number).

 

The cyclic patterns of composite numbers built on primes, in the range 1 to 2000

The full complement of composite numbers in fact represents the successive multiplication of each number >1 in the “total series” by each other number in turn, thus: 2 x 2, 2 x 3, 2 x 4 etc., then 3 x 2, 3 x 3, 3 x 4 etc., then 4 x 2, 4 x 3, 4 x 4 etc., and so on. These calculations are, however, redundant for any number lower than the multiplier, as that lower number will already have contributed the same composite when it took its turn as multiplier. Thus the autonomous 5 series begins at 25, as 2, 3, and 4 as multipliers have already disposed of 10, 15, and 20.  5 then takes on this role for higher number multipliers – 6, 7 etc. Therefore, in what follows, the table begins with the square of the number concerned. Further to avoid redundancy, as already explained, only primes are included as base numbers, and only numbers ending in 1, 3, 7, and 9 are used as multipliers.

As a larger demonstration, the following tables, and their later superimposition, cover the number series from 0 to 2000, and show the composite numbers derived from all primes up to 43; the next prime, 47, squared is 2209, and so falls outside the range 0 – 2000. Composite numbers derived from 2 and 5, identifiable by simple inspection, are not shown, and composite numbers created by 3 as well as by the table multiplier are in italics.

It can be seen that, in every case, each row (showing the 4 composite numbers created in each cycle) exhibits the same recurring pattern, which can be simply written down, ascending the cycles, without the need for calculation, just as one can write down the composite numbers based on 2 – 2,4,6,8,10 / 12,14,16,18,20 – ascending the number series, without calculation.

 

Composite numbers deriving from 7

7 – 2000 :  29 cycles of 70                                                                               7 squared = 49

successive multipliers ending in

1                      3                      7                      9

0-69                                                                             49                    63

70-139                         77 (7×11)         91(7×13)          119(7×19)        133(7×19)

140-209                       147(7×21)        161(7×23)        189(7×27)        203(7×29)

210 etc                         217 (etc)          231                  259                  273

280                              287                  301                  329                  343

350                              357                  371                  399                  413

420                              427                  441                  469                  483

490                              497                  511                  539                  553

560                              567                  581                  609                  623

630                              637                  651                  679                  693

700                              707                  721                  749                  763

770                              777                  791                  819                  833

840                              847                  861                  889                  903

910                              917                  931                  959                  973

980                              987                  1001                1029                1043

1050                            1057                1071                1099                1113

1120                            1127                1141                1169                1183

1190                            1197                1211                1239                1253

1260                            1267                1281                1309                1323

1330                            1337                1351                1379                1393

1400                            1407                1421                1449                1463

1470                            1477                1491                1519                1533

1540                            1547                1561                1589                1603

1610                            1617                1631                1659                1673

1680                            1687                1701                1729                1743

1750                            1757                1771                1799                1813

1820                            1827                1841                1869                1883

1890                            1897                1911                1939                1953

1960                            1967                1981

 

Composite numbers deriving from 11

11 – 2000 :  19 cycles of 110                                                                           11 squared = 121

successive multipliers ending in

1                      3                      7                      9

0

110                              121                  143                  187                  209

220                              231                  253                  297                  319

330                              341                  363                  407                  429

440                              451                  473                  517                  539

550                              561                  583                  627                  649

660                              671                  693                  737                  759

770                              781                  803                  847*                869

880                              891                  913                  957                  979

990                              1001                1023                1067                1089

1100                            1111                1133                1177                1199

1210                            1221                1243                1287                1309*

1320                            1331                1353                1397                1419

1430                            1441                1463*              1507                1529

1540                            1551                1573                1617                1639

1650                            1661                1683                1727                1749

1760                            1771*              1793                1837                1859

1870                            1881                1903                1947                1969

1980                            1991

 

*composite numbers based on 7 also in italics

 

Composite numbers deriving from 13

13 – 2000 :  16 cycles of 130                                                                           13 squared = 169

successive multipliers ending in

1                      3                      7                      9

0

130                                                      169                  221                  247

260                              273                  299                  351                  377

390                              403                  429                  481                  507

520                              533                  559                  611                  637*

650                              633                  689                  741                  767

780                              793                  819                  871                  897

910                              923                  949                  1001*              1027

1040                            1053                1079                1131                1157

1170                            1183*              1209                1261                1287

1300                            1313                1339                1391                1417

1430                            1443                1469                1521                1547*

1560                            1573#              1599                1651                1677

1690                            1703                1729*              1781                1807

1820                            1833                1859                1911                1937

1950                            1963                1989

 

#composite numbers based on 11 also in italics

 

Composite numbers deriving from 17

17 – 2000 :  12 cycles of 170                                                                           17 squared = 289

successive multipliers ending in

1                      3                      7                      9

0

170                                                                              289                  323

340                              357                  391                  457                  493

570                              527                  561                  629                  663

680                              697                  731                  799                  833*

850                              867                  901                  969                  1003

1020                            1037                1071                1139                1173

1190                            1207                1241                1309*              1343

1360                            1377                1411                1479                1513

1530                            1547*              1581                1649                1683

1700                            1717                1751                1819                1853

1870                            1887                1921                1989

 

Composite numbers deriving from 19

19 – 2000 :  11 cycles of 190                                                                           19 squared = 361

successive multipliers ending in

1                      3                      7                      9

0

190                                                                                                      361

380                              399                  437                  513                  551

570                              589                  627                  703                  741

760                              779                  817                  893                  931*

950                              969                  1007                1083                1121

1140                            1159                1197                1273                1311

1330                            1349                1387                1463*              1501

1520                            1539                1577                1653                1691

1710                            1729*              1767                1843                1881

1900                            1919                1957

 

Composite numbers deriving from 23

23 – 2000 :  9 cycles of 230                                                                             23 squared = 529

successive multipliers ending in

1                      3                      7                      9

0

230

460                                                      529                  621                  667

690                              713                  759                  851                  897

920                              943                  989                  1081                1127*

1150                            1173                1219                1311                1357

1380                            1403                1449                1541                1587

1610                            1633                1679                1771*              1817

1840                            1863                1909                                       

 

Composite numbers deriving from 29

29 – 2000 :  7 cycles of 290                                                                             29 squared = 841

successive multipliers ending in

1                      3                      7                      9

0

290

580                                                                                                      841

870                              899                  957                  1073                1131

1160                            1189                1247                1363                1421*

1450                            1479                1537                1653                1711

1740                            1769                1827                1943

Composite numbers deriving from 31

31 – 2000 :  7 cycles of 310                                                                             31 squared = 961

successive multipliers ending in

1                      3                      7                      9

0

310

620

930                              961                  1023                1147                1209

1240                            1271                1333                1457                1519*

1550                            1581                1643                1767                1829

1860                            1891                1953

 

Composite numbers deriving from 37

37 – 2000 :  6 cycles of 370                                                                             37 squared = 1369

successive multipliers ending in

1                      3                      7                      9

0

370

740

1110                                                                            1369                1443

1480                            1517                1591                1739                1813*

1850                            1887                1961

Composite numbers deriving from 41

41 – 2000 :  5 cycles of 410                                                                             41 squared = 1681

successive multipliers ending in

1                      3                      7                      9

0

410

820

1230

1640                            1681                1763                1927

Composite numbers deriving from 43

43 – 2000 :  5 cycles of 430                                                                             43 squared = 1849

successive multipliers ending in

1                      3                      7                      9

0

430

860

1290

1720                                                    1849

 

47 squared goes beyond the matrix.

 

Superimposition of distributions of composite numbers based on primes 3 and 7 – 43

When all 11 series are superimposed we get the matrix of composite numbers shown in the following table in which all composite numbers are shown in bold.  It can be seen that the remaining (non-bold) numbers are the primes.

Distribution of Composite Numbers (in bold) and Primes in the Number Series 1 to 2000 (not including composite numbers based on 2 and 5)

3                      7                     9

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

100                  01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

200                  01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

300                  01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

400                  01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

500                  01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

600                  01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

700                  01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

800                  01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

900                  01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

1000                01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

1100                01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

1200                01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

1300                01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

1400                01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

1500                01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

1600                01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

1700                01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

1800                01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99

1900                01                    03                    07                    09

11                    13                    17                    19

21                    23                    27                    29

31                    33                    37                    39

41                    43                    47                    49

51                    53                    57                    59

61                    63                    67                    69

71                    73                    77                    79

81                    83                    87                    89

91                    93                    97                    99                    2000

           

Distribution of the primes

It can be seen that the distribution of the composite numbers, as expounded above, determines the distribution of the primes.

The increasing entry of new cycles into the system means that the incidence of primes decreases as the number series advances. However, the increasing length of cycle for each successive number matrix that enters the system means that the rate at which the incidence of primes diminishes decelerates as the series advances. An additional factor is that the level of redundancy of the four new composite numbers per cycle must increase as more cycles enter the system.

The fact that 5 of the 8 potential primes per 30 numbers remaining after the extraction of the multiples of 2, 3, and 5 are consecutive predicts the clustering of primes that occurs from time to time, despite a diminishing incidence.

If there were to be a highest prime number, it would occur when sufficient cycles had entered the system to entirely choke out the residual of the potential 8 primes per cycle of 30 when the cycles of 2, 3 and 5 have been accounted for. Whether this can occur (and proofs suggest that it does not) depends on the rate at which composite numbers are generated as against the rate at which new numbers enter the system.

Using this approach, the primes do not have to be identified post hoc, as it were, but will automatically emerge from increasing the extension of the matrix of composite numbers which is created by pursuing the cycling of the products of the successive primes.

 

November  2003

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Consciousness 2.

Memory is Consciousness, Consciousness is Memory

My proposition is that memory and consciousness are one and the same.

There can be no memory without consciousness – that is, we cannot remember events that occurred while we were unconscious, whether asleep, anaesthetized, or comatose. Nor can we remember vents of which we were “unconscious”, even though we were awake and “conscious” at the time.

Equally, we do not remember memories when we are unconscious. Memory and consciousness are simply alternative names for the same condition of mental activity. Merely, we allocate these two equivalent terms differently on the basis of the temporal character (present or past) and stimulatory source (exteroceptive or interoceptive)  of the events thus mentally recorded – consciousness for present exteroceptively referred events and memory for past interoceptively referred events.

That both are equally covered by the concept of consciousness is apparent in that one can be in a state of virtually complete perceptual deprivation and still be fully conscious in that one’s mental activity as memory does not cease in these conditions – it may contain elements of present awareness, but there is no exteroceptive perception; but one cannot be conscious, that is, awake to present stimuli, without the laying down of memory, however short-lived – one’s consciousness cannot be divorced from memory.

Although the investigation of consciousness has more or less halted at the starting post, considerable progress has been made, since the initiation of the study of cognitive processes in psychology in the 1950s, in the mechanisms of memory. What we have learned of the progressive processes of memory supports this identification.

Cognitive psychologists have identified three phases in the laying down of memory. Most ephemeral is sensory memory (“echoic” and “iconic” for sight and sound, respectively) of the multitude of stimuli impinging on us, from which a subset is selected (attended to) and further processed immediately, but which retains the vestiges of unattended sensation, which make their presence felt if, for some reason, Attention (processing) is switched to their fast-fading traces. Sensory memory has an accessible life of only a few seconds, and will disappear without trace unless subjected to further processing in the second phase of mental record keeping. Proximal consciousness, that is, consciousness of the world around us, is no other than sensory memory. This first imprint of sensory memory serves to give us the sense of continuity or stability of exteroceptive consciousness without the necessity of permanent storage or the vast mass of information with which we are constantly bombarded and which we necessarily monitor to maintain, mentally, our locational and temporal position in the world.

In the next stage of processing, the exteroceptive stimulus begins its progress into short term memory (STM, sometimes called working memory), selects from and succeeds sensory memory. It is essentially the memory we function on in our proximally conscious lives, interpreted by recycling of our permanent long term memories (LTM). Like sensory memory it records proximal stimuli but unlike sensory memory, it subjects the selected stimuli to a much “higher” level of processing, thereby providing them with a future in distal or recycled consciousness.

It’s storage is thought to be electrical and therefore subject to permanent loss if its electrical retention is interrupted before it can be transferred into its final and stable form. Its transfer is thought to take up to half an hour before it is completed. Evidence for this comes, for example, in the loss of memory for the half hour of so prior to a severe blow to the head. The lead up to the blow, and the blow itself cannot be recalled – are lost to memory – as if the person had been unconscious at the time, which was definitely not the case.

Permanent storage occurs in the third stage of memory formation, long term memory (LTM), which is laid down chemically in the brain via the electrical recycling of STM. It is thought possible that all stimuli (information) that have completed their transformation in STM are permanently stored in LTM, even if we have lost the paths of access for resurrecting them into consciousness.

Whether we retain their paths of access seems to depend on whether we recycle them into consciousness before they are moved into some hinterland of the brain, whence it may be they can have unconscious (conditioned) but not conscious influence on our behaviour. The role of review in keeping LTMs accessible is seen in the tactics of deliberate memorization, such as students used in preparation for exams in the past – dwelling on individual items of information and testing recall, or reading a text three times, after which it is well retained, while one or two readings are inadequate for comprehensive recall – indeed some degree of conscious review may be necessary to bring the STM process of transformation to completion.

As we have seen, “Attention” determines what stimuli will move from sensory to short term memory. Its significance for understanding the identity of memory and consciousness lies in what its investigation has revealed of the brain’s limited capacity as regards information processing, conceptualized as “central processing capacity”. The study of Attention amply demonstrates that we can only conscious of what we process, and that only what we process can enter memory. A limited central processing capacity means that we can only be conscious of a subset of all the potential information impinging on us at any one time.

The role of Attention in memory is limited to the primary element of consciousness, of being “awake”, of present exteroceptive processing. To fully comprehend consciousness, memory of what has been attended to in the past, that is, its interoceptive content must also be accounted for. Memory in its conscious form is the recycling of past processed information, that is, of the contents of earlier primary consciousness. This is at its simplest. But human consciousness consists also in recycling the contents of secondary consciousness, of what has been remembered previously, and of reconstruction its memories in what we call thought, and in recycling (bringing to consciousness again) the product of these reconstructions for further elaboration. Further, and most peculiarly human, consciousness as thought can reconstruct what has never been processed exteroceptively, but exists only as the memorial transcripts of language.

A cockroach when running about is conscious in the first sense (sensory processing of exteroceptive data), but we would be reluctant to admit it has consciousness in the second sense  (the recycling of remembered sensory data). The psychological concept of conditioning attempts to explain the functioning of such creatures without invoking consciousness in the form we consider most essential to its human manifestation, namely its memory contents.

In what we call consciousness, recycled memory createsa new present out of its record of the past, which can function almost alone, or in synchrony with the on-going newly created record of the exteroceptive present.

Most people over 50 are aware that as their memory file has grown larger, just as with a paper file, locating the required memory can become much less immediate than in youth (when the file contents was smaller); and most will be familiar with the weird experience of trying to recall a name without success, only to have it suddenly arrive in consciousness several hours later, as if one had set an automatic search in motion which has finally come up with the answer when one’s thoughts were on quite another matter.

How we file our memories, how we “tag” them, for recycling in consciousness, whether they fade (chemically) or lose their access routes over time due to interference by memories laid down later in time – these are all matters that have been investigated in the experimental science of cognitive processes, and probably belong to “memory” rather than the more general field of “consciousness”. No doubt, too, there are neurological answers to these questions as well as phenomenological ones, if neurologists care to take them on.

Thus my original proposition that consciousness is coterminous with memory should be expanded to declare that consciousness is information processing plus memory in a continuous self-integrating loop of mental activity.. The characteristics of “Attention”, and “Memory” already uncovered in cognitive psychology are the characteristics of consciousness also – limited processing capacity, three neurophysiological forms or manifestations (the three stages of transfer) exhibiting successive loss of exteroceptive information, interference, interference of similar in the process of storage, the greater ease of “recognition” over “recall” in reactivating memory (stored information) into consciousness, and so on.

The last of this list indicates a need to distinguish in terminology between memory in its inactive (unconscious) and its active (conscious) modes. The terms memory and consciousness alone will not do, as we need to distinguish terminologically the exteroceptive and interoceptive (from LTM) contents of consciousness.

Work relating IQ and central capacity makes it a plausible hypothesis that there is a limited central processing capacity available to consciousness such that the greater the amount at any time devoted to the processing of new exteroceptive information (attendion), the less is available for recycling stored interoceptive interoceptive information (memory), and vice versa – hence the advantage of quiet (i.e. to eliminate exteroceptive stimuli as far as possible) or a familiar environment (familiar stimuli make less call on processing capacity) when engaged in deep thought or other creative production which is the restructuring of already stored information (memory), and a parallel need to be free from the distractions of memory and other cognitive tasks when executing environmentally interactive tasks demanding of attention to exteroceptive stimuli (e.g. playing tennis, doing a jigsaw).

Thus while a large part of our consciousness is forced on us by our current material environment, a large part also is constructed by ourselves from our stored memories of our past material environments – by our own peculiar, and to a large extent chosedn, system of memories, developed over time from what, among the multitude of impressions the world provides, we have recycled sufficiently to maintain accessibly in LTM.

Against this, it is also clear that the brain plans and executes many essential survival (including metabolic) functions without the monitoring interposition of consciousness, such that there is also some other allocation of its processing capacity devoted to enabling the organism’s preservation of homeostasis and intactness in a constantly changing external environment.

 

In implicit acknowledgement of the identity of memory and consciousness, the French use the word “rapelle!” – “recall” (remember) – as a road sign in dangerous spots, meaning, in fact,  “concentrate” (attend, be conscious).

 

Nature from time to time publishes articles on consciousness which take neurological science as their starting point and in which the study of consciousness is conceived as a new departure in the field of the study of mind. It does not seem to be realized that consciousness has already been extensively studied phenomenologically under other names in the field of cognitive psychology. In neglecting these findings, neuroscientists deprive themselves of what might be useful points of departure and guidelines to direct their own investigations.

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Consciousness 1.

Consciousness is Memory

My proposition is that memory and consciousness are one and the same. There can be no memory without consciousness – that is, we cannot remember events that occurred while we were unconscious, whether asleep, anaesthetized, or comatose. Nor can we remember events of which we were “unconscious”, even though we were awake and “conscious” at the time. Equally, in a normal state of unconsciousness, memory does not accrue. .

Memory and consciousness are simply alternative names for the same condition of mental activity. We (in general) allocate these two equivalent terms differently on the basis of the temporal character (present or past) and stimulatory source (exteroceptive or interoceptive) of the contents of consciousness – “consciousness” for present exteroceptively sourced events and “memory” for past interoceptively sourced events. This is not a rigorous categorization, as we shall see. .

That memory should be subsumed under the concept of consciousness is apparent in that one can be in a state of virtually complete perceptual deprivation and still be fully conscious. One’s mental activity does not cease under this condition – it persists as memory recycled into consciousness (working memory). There is present awareness, but exteroceptive perception is minimal. Similarly, one cannot be conscious, that is, awake to present stimuli, without laying down memory, however short-lived; one’s consciousness cannot be divorced from memory.

Although the investigation of consciousness has more or less halted at the starting post, considerable progress has been made, in the field of cognitive psychology since the 1960s, in delineating the characteristics and mechanisms of memory. What we have learned of the nature of memory can be legitimately applied to consciousness. Three phases have been identified in the laying down of memory. Initially, and most ephemeral, there is Sensory Memory (“echoic” and “iconic” for sight and sound, respectively) which records the multitude of stimuli impinging on us. A subset from this record is selected for further processing immediately, while sensory memory retains briefly the vestiges of unattended sensations. Their brief retention persistence is revealed if, for some reason, processing (now called “attention”) is switched back to their fast-fading traces. Sensory memory has an accessible life of only a few seconds (longer for echoic than iconic), and will disappear without trace unless subjected to the further processing which characterizes the second phase of mental record keeping which constitutes memory.

The brief imprint of sensory memory serves to give us continuity or stability of exteroceptive consciousness without the necessity of permanent storage of the vast mass of information with which we are constantly bombarded. Consciousness of the world around us is thus no other than sensory memory.

In the next stage of processing, a subset of the impinging exteroceptive stimuli in sensory memory begin their progress into Short Term Memory (STM, sometimes called working memory). The process of their selection and entry is called Attention in cognitive psychology. STM is essentially the memory we function on in our conscious lives. Like sensory memory, STM records exteroceptive proximal stimuli but it subjects the selected stimuli to a much “higher” level of processing, retrieving the more detailed information from them that is required for their full delineation, for current purposeful activity. (Under the more encompassing definition of working memory it has afurther function in recalling already stored memories, as we shall see.)

Storage in STM is thought to be electrical, for (like sensory memory) it is subject to permanent loss if its electrical substrate is prematurely interrupted. STM processing takes up to half an hour before it is completed. Evidence for this is, for example, the loss of memory that occurs for the half hour or so prior to a severe blow to the head. The lead up to the blow, and the blow itself cannot be recalled, as if the person had been unconscious at the time.

Permanent storage occurs in the thirdphase of memory formation, Long Term Memory (LTM) when the electrical storage of STM has been transformed into chemical storage in the brain. It is thought possible that all stimuli (information) that have completed their time in STM are permanently stored in LTM, even if we have lost the paths of access for resurrecting them in memory.

As we have seen, attention is the term given to the process of selecting some exteroceptive stimuli from the full contents of sensory memory for further processing in STM. What has been learned of its characteristics supports the proposition that consciousness and memory are essentially the same mental phenomenon. Its investigation has revealed the need for a selection from the full array of exteroceptive stimuli for admission into full consciousness due to the brain’s limited capacity for information processing, conceptualized as “central processing capacity”. It has been demonstrated that we can only remember later what we have processed in STM to the degree to which we have processed it, whether to a lower or a higher level in a “hierarchy of tests”, from the purely sensory to word recognition. STM and consciousness cannot be differentiated at this stage. A limited central processing capacity means that we can only be conscious above the level of sensory memory of a subset of all the potential information impinging on us at any one time.

“Attention” in cognitive psychology refers only to the processing of present exteroceptive stimuli in STM. To fully describe consciousness, it must also be recognised that what has been attended to in the past, that is, long-term memories are part of its contents – its interoceptive component. In its conscious form, LTM is the recycling into consciousness of past processed information, that is, of earlier STM contents. If the initial processing of exteroceptive stimuli is primary consciousness, we might call the return to consciousness of its products from LTM, secondary consciousness. But human consciousness consists also, in the recyclings of secondary consciousness, of the reconstruction of memories into new relationships in what we call thought, and still further in recycling (bringing to consciousness again) the product of these reconstructions for further elaboration.

Further, and most peculiarly human, consciousness as thought can reconstruct what has never been processed exteroceptively, but exists only as the memorial transcripts of language. Recycled memory, as consciousness, creates a new present out of its record of the past, and this can function almost alone, and/or in synchrony with the on-going memorial creation of the exteroceptive present. This we might call tertiary consciousness.

Work relating IQ and central capacity makes it a plausible hypothesis that the limited central processing capacity available to consciousness means that the greater the amount of capacity at any time devoted to the processing of new exteroceptive information (attention), the less is available for recycling stored interoceptive information (memory), and vice versa – hence the advantage of quiet (i.e. to eliminate exteroceptive stimuli as far as possible) or a familiar environment (familiar stimuli make less call on processing capacity) when engaged in deep thought or other creative production, which is the restructuring of already stored information (memory); and a parallel need to be free from the distractions of memory and other cognitive tasks when executing environmentally interactive tasks demanding close attention to (advanced processing of) exteroceptive stimuli (e.g. playing tennis, doing a jigsaw).

Whether we retain access to our long-term memories or not seems to depend on whether and how frequently we recycle them into consciousness. If neglected, they are moved into some hinterland of the brain, whence it may be that they can have unconscious (conditioned) but not conscious influence on our behaviour. The role of review in establishing long-term memories is demonstrated in the tactics of deliberate memorization, such as students used in preparation for exams in the past – dwelling on individual items of information and testing recall, or reading a text several times. Indeed, some degree of conscious review may be necessary to bring the STM process of transformation into LTM to completion.

Thus while a large part of our consciousness is forced on us by our current material environment, a large part also is constructed by ourselves from our stored memories of our past exteroceptive encounters – by our own peculiar, and to a large extent chosen, system of memories, developed over time from what, among the multitude of impressions the world provides, we have recycled sufficiently to maintain accessibly in LTM.

Most people over 50 are aware that as their memory file has grown larger, locating the required memory can become much less immediate than in youth when the file contents was smaller (just as with a paper file); and most will be familiar with the weird experience of trying to recall a name without success, only to have it suddenly arrive in consciousness several hours later, as if one had set an automatic search in motion which has finally come up with the answer when one’s thoughts were on quite another matter.

How we file our memories, how we “tag” them, for recycling into working memory consciousness, whether they actually fade chemically or merely lose their access routes over time, perhaps due to interference from memories laid down later in time, the greater performance ease of “recognition” over “recall” in reactivating stored information into consciousness, and so on.  – these are all matters that have been investigated in the experimental science of cognitive processes, and probably belong to “memory” rather than the more general field of “consciousness”. No doubt, too, there are neurological answers to these questions as well as phenomenological ones, if neurologists care to take them on.

Against this, it is also clear that the brain plans and executes many essential survival (including metabolic) functions without the monitoring interposition of consciousness, such that there is also some other allocation of its processing capacity devoted to enabling the organism’s preservation of homeostasis and intactness in a constantly changing external environment.

A cockroach when running about has primary consciousness in the sense of processing of exteroceptive data, but we might have doubts as to its capacity for secondary consciousness, and we would be most reluctant to admit its capacity for tertiary consciousness, as above. The psychological concept of conditioning in animal learning attempts to explain the functioning of such creatures without invoking consciousness in the form we consider most essential to its human manifestation, namely its memory contents.

In summary and conclusion, my original proposition that consciousness is coterminous with memory should be elaborated to declare that consciousness is information processing plus memory in a continuous self-integrating loop of mental activity. The characteristics of “Attention”, and “Memory” already uncovered in cognitive psychology are the characteristics of consciousness also. This coalescence creates the need to distinguish in terminology between memory in its inactive (unconscious) and its active (conscious) modes. The terms consciousness and memory alone will not do, as we need to distinguish terminologically the exteroceptive and interoceptive contents of consciousness.

It is true that none of the information about the structure and functioning of memory related here is new, but I believe that putting it in the context of consciousness and positing its relevance for what we conceive of as consciousness is.

In implicit acknowledgement of the identity of memory and consciousness, the French use the word “rapelle!” – “recall” (remember) – as a road sign in dangerous spots, meaning, in fact,  “concentrate” (attend, be conscious).

 

Nature from time to time publishes articles on consciousness which take neurological science as their starting point and in which the study of consciousness is conceived as a new departure in the field of the study of mind. It does not seem to be realized that consciousness has already been extensively studied phenomenologically under other names in the field of cognitive psychology. In neglecting these findings, neuroscientists deprive themselves of what might be useful points of departure and guidelines to direct their own investigatios.

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Federation Peak Diary 1962

                Diary

                                                                                                          HangingLake

                                                                                                             Federation.

                                                                                                     Sunday 28th January, 1962

 

            The first thing I really liked on the trip was when we came to NorthLake. It was very cold and we were battling through the mist and rain. I was admiring the pretty pink flowers growing round about in the coarse moor grass and suddenly there it was through the mist, just the near shore its flat water and a few rocks. A few yards further on the view broadened out and it looked bleak, windswept and exciting. There were no rocks anywhere else. Just the coarse moor grass down to the edge. It was just after that that we got lost for the first time.

            I’m writing this in my sleeping bag in our yellow tent at night, by the light of a candle set in a tin filled with wet earth – wet because all the ground here on the edge of the lake is sodden. Don is going to sleep beside me. The others are reading by a candle in their tent and I can just see the golden-orange glow it makes through their door flap when I look back through the opening of out tent. Our door flaps are slightly open and the tapes are hanging down. We’ve got our rucksacks up at the end of the tent and also the two air-drop tins full of food. I’ve again got sticking plaster all over my hands, covering the wounds I got probably from rock and scoparia. They don’t seem to heal quickly on their own. I’m wearing Father’s Oxford Blue athletics jumper over my blue and green striped one. It’s a yellowy-white now, with blue letters and wreath on the front. I like to think it’s being used again now, in such a different way, and I’m Father’s daughter.

            The second thing I really loved was coming down Blandfordia Ridge in the evening.

                                                                                    Monday morning, 29th Jan.

Just while it was dusk and peaceful we were walking through fields of white flowers which seemed to glow and blossom in the half-light. The ridge was broad there on both sides of the path so that they seemed to spread away all around us. The views on both sides were beautiful, soft in the evening, all the colours half-turned to grey. On  the right were wooded mountains and valleys with great streaks of grey-white dead trees across them, the trees killed by bushfire. But what I loved most was walking through the flowers, knee and shoulder high, sometimes seeing a bush so thickly clustered with flowers that it seemed to leap out, white and vital, ecstatic, from the darkened vegetation.                       The next day was spent walking across button-grass plain and over a few hills, between the Cracroft and Pass Creek. It was quite heavy going because the grass grows in hard clumps and you have to step between and the ground is often marshy. The views were lovely, peaceful and pretty, of the surrounding mountains. Somehow the yellowy colour of the button grass seems to set off the view very well. Towards evening we climbed over a little ridge and made our camp just above a little creek that ran behind it. Although the view was blocked the sky looked a beautiful blue against the yellow grass ridge and pure white clouds, wispy and thick, sailed across, sometimes half below the ridge. Luckman’s Lead stretched up behind. I had a little time, being lazy while the boys collected wood, to appreciate the evening there. Lately I have come to love the evening. Towards the end of my day at the Ringroks I sat out on the grass every evening I could and watched the sunset and its close, at about 7 o’clock. This is one of the happiest times of my life. And the song I sang to myself and the beauty of the landscape and mountains, and the evening, I keep now for these times.

            This morning I am up by myself in the saddle just before the southern traverse of Federation sitting on a rock and I can see the view over the Eastern Arthurs, which we traversed to get here, and the Western Arthurs, further away and bluer. On the other side there are mountains too, but not so rocky and impressive. The white brittle daisies are scattered over the mixture of immature vegetable sheep and moor grass on the ground. It is cold and I shall have to go soon. My legs keep getting pins and needles. It’s before breakfast.

            Yesterday afternoon I sat up on the top of the rocky ridge on the western edge of HangingLake, by myself with a view for the first time and looked back over the massive Federation group and I loved it. I read poems from “The Knapsack” and liked Elliot for the first time, in a few landscape poems. Blake has been impressing me again lately – in “Auguries of Innocence” saying that man is made for joy and sorrow and it is right that it should be so.  And last night in my tent I read and was impressed by his “Proverbs of Hell”. The one saying that we should think in the morning, act at noon, eat in the evening, and sleep at night has stuck in my mind and I have inclinations to apply myself to it, though of course I can’t and won’t entirely. But I’d like to think along those lines.

            Yesterday afternoon, sitting on the ridge, I also read “Illumination”, an extract from possibly the diary of possibly an Austrian soldier, about the sickness and death of the kitten and the reactions of those around it, written with a sensitivity and feeling for small events and a quality of reflection on them which I liked to find in someone else, carried to an extreme which I would probably never allow myself to express. Ken and Gordon had gone off rock-climbing. After a while I saw two tiny figures coming down the mountainside opposite. They walked together, then separated, waited a while, then came together again. One wandered down off the hillside to the left for a bit, then came back. All the time I could hear their voices very clearly and almost distinguish phrases here and there, although they were so far away. Gordon was singing “Run Around Sue” and “Walking Back to Happiness” as they walked up the edge and to the camp site and it came up to me as loud and clear as day. For a while I wondered if it was really them for the singing seemed better and fancier than Gordon usually is, and they wandered about in a way I didn’t expect of those two, but by the way they went into the campsite I knew it was them. It gave me a nice feeling to sit and watch those two little figures moving about far below. It was a friendly feeling to see two other people about although they didn’t know I was there. Later they wandered up Jeeves Bluff and I called out to them and went round the rock ridge to meet them and we sat on top and ate boiled lollies. Then we wandered down. They played about a bit throwing rocks over the overhang on the left on the way down. When we got to the campsite I’d done a complete traverse of the edges of the lake.

            It always fascinates me the way flowers tremble in the wind, ever since I noticed it in the beginning of “One Summer of Happiness”.

            I had lots of worrying dreams last night. Plum dreamed that he had murdered someone and was condemned in court to be executed and he and I were walking off hand in hand singing happily, towards his execution.

             The part perhaps I loved best to see of the trip in a happy joyful way was walking up to the beginning of Thwaites Plateau. All the moor grass was shining a rich yellow in the sunlight, with grey chunky rocks sticking high out here and there and smaller bits too scattered about and the sky was blue against the yellow. It was late afternoon. It reminded me of something, I can’t think what. Perhaps something prehistoric and in England, perhaps Stonehenge. I never really liked to look at Federation when we saw it on the way in. It looked rather silly. But soon after this we saw it close up. It is a whitish grey rock and from this angle had a couple of gendarmes at the side. It is sheer rock without vegetation. I looked at it unimpressed and then suddenly saw its beauty. There was a sort of purity about it that I’d never seen before. I took a picture of it.

            Last night round the fire we talked and talked for almost the first time on the trip – mostly about our childhood and the fights we used to have. We started off about poetry. Plum likes humorous verse and Browning. Gordon loves Coleridge and seems to have good taste in poetry, because of a good English teacher at school. This morning we talked about films. Don doesn’t care about poetry and is tone deaf.

                                                                                                            StillHangingLake

                                                                                                                  Tues 30th Jan.

            Walking back from Federation with Gordon today in the rain the alpine daisies were all closed up into tight round little buds with pink round the bottom of the outside petals. Closed up against the inclement weather, it seemed.

            I shall be sorry to leave here.

            There are white stiff alpine daisies and yellow ones the same. There are also irises. I don’t remember noticing any of the lovely pink flowers which grow in a raceme about here. They were at Goon Moor at least. The irises are very pretty, white with blue (purple?) yellow and black markings. I think at one place on the southern traverse there is a great clump of them. The soft daisies are nice the way they grow in clumps in green nooks. There is one minute square “sunken valley” with several yellow ones growing beautifully in it near the foot of the climbing gully. The alpine daisies grow in more open spots on the ridges and moors. They are tough. They are nice to see scattered about.

 

                                                                                                            Tues. 6th Feb 1962

                                                                                                                        NorthLake

            We’re almost out. I’m writing in my sleeping bag in the morning before getting up for the last walk out through country which will no longer be the Federation type. Yesterday we walked from Quartz Knob, almost at the bottom of the Pictons. It was a gorgeous day, the first really fine one since the weather set in a week ago, and there were lovely blue views to both sides of the range. The sky was a beautiful blue with white clouds again against the yellowy mountain-top vegetation.

            The day before was all cloud although little rain, and we could see even in the evening Federation still up among the mists. We saw some clear sky far down on the S.E. horizon which Don thought presaged fine weather. At night we were talking. We said how clear it was from Federation the last morning we were up there.

                                    “And then the rain came.”

                                    “And it hasn’t gone yet.

                                      But we have.”

            That evening there was a beautiful view from Wilsmicro Lead back down the CraycroftValley and a valley to the left and of the three mountain masses which contained them, Hopeton on the right and two others. The colour had a hidden luminescence and glow which was subdued yet almost dazzling at the same time. There was the khaki of the button-grass stretching ½ way up the mountains then the dark of the trees both coloured by a purplish tone. There was grey dead timber among the trees near the bottom of Hopeton. And the end ridge of the centre mountain had a beautiful curve to it. I sat out and watched for a while. In the morning there was a cloud sea and Federation came out of the clouds at times looking massive and rather sublime. It seems so much bigger from that angle for all the lower level slopes become part of it.

            We moved round to Bechervaise on the second afternoon of the rain, and the wind there was terrific. Ken and I were in his tent and it was quite frightening at times the way it flapped up and down and bellied in and out in the wind. The wind drove the rain right through in a fine spray and through the second night made us quite wet in our sleeping bags. The wind kept up all the second day reaching a peak late in the afternoon just at about the time the Victorians arrived. The tent probably looked worse from inside than out. Sometimes it made me quite scared and I was sure it must suddenly be snatched from over us and blown away. I began to feel a need for such Catholic expressions requesting succour as “Holy Mary pray for us now in the time of our need” which I inwardly muttered, calling on God and the angels. Strange that these expressions come to one. One needs to call for help where there is nothing and religion provides the formula. Perhaps it is another example of substituting words for action, as we learnt in Linguistics the swearing at a kicked table was. Next morning when we looked out there was snow everywhere, piled along the edges of the tents and scattered all over the ground. It snowed more, really sleet, and it was very coarse snow, and we walked on it a bit, My toes felt like blocks of ice in my sandshoes. It was snowing still in the morning and later we had hail, but the wind had dropped quite a bit. During the worst of the wind Ken and I had been unable to cook in our tent for the wet and the walls blowing right in almost on to us. We lay on our backs in our tents for two days and they went amazingly fast. Every movement takes so long in a tent that I expect this helps to fill out the time. Twice every day I went for a walk about outside, needing to get out for a while, doing the washing up and just wandering about, usually in gaps in the rain. The first afternoon I was out in the driving wind and rain in just my red thing and sandshoes. I wandered over a bit out of the wind and when I came back there were people clustered round our tent, packs on their backs. It was the Victorians, just arrived. They scattered to look for a campsite. I stayed out for a while and it was sweet and funny to watch them running through the mist and rain, hurrying for the cold. They were all little black figures, black parkers, gaiters and boots. They ran with long steps, hands in their pockets, as if trying to avoid the rain and wind, which of course was impossible. They looked somehow very sweet, rather quaint, moving to and fro, small, a short distance off, not seen too clearly through the mist and rain. Three of them had beards and I talked to two for a while as they sheltered behind the rocky bushy mound near our tents. That was sweet too, the way they sheltered sitting against it, though I had done it too the previous day before we had the tents ready.

I read, talked, drew, and sang and slept for those two days, and was never bored and it was always later than I thought. As dark came down it reminded me of being sick in bed at home and I thought of my lovely check blankets on my bed.

            The third morning we packed up in the mist and occasional fine rain and set off down Moss Ridge.

            The last few days we have been constantly saying what day it is, probably because we have to get out at the right time, but it doesn’t mean anything as it normally does. We know the name of the day but it doesn’t seem to sink in any further than that. It has lost its connection with life, with our life in here.

            I heard the bird sounds coming up from down below again this year as I sat on Quartz Knob. It gives a feeling of peace and detached isolation, and also appreciation of the beauty below.

            As we came down round and off Hewardia Ridge yesterday afternoon the broad panoramic view of blue ranges, one mountain after another, disappeared. I looked back and saw the last glimpse of Federation before it was hidden by the shoulder of a mountain, but it had already lost its special position and beauty and was just a funny shaped block of rock sticking up higher than the rest. However the scene was beautiful and I looked at it and remembered what it was like when one is actually there, amongst all its size.

            The bushes on the hillside twinkled with bright shining spots all among the green leaves. The leaves sparkled as brightly as the sun because they were so clean after all the rain and there is no dust. These sparkles were all over the mountainside as one looked back towards the sun.

            The white trunks of dead eucalypts on Wilsmicro Lead rose up above the view from near our campsite there. They threw up their few writhing spare branches with a sort of distortion and wildness and also a helplessness and vulnerability.

 

                                                                                                            Sydney  20th February

            Perhaps the thing that assumed most importance for us while we were in there, quite differently from when living at home, was the weather. As time went on we came to feel our happiness or misery more and more dependent only on it. Specially after the first day or two of the bad weather at Bechervaise you can’t imagine with what trust in its decree for our happiness we looked out each morning at the sky, and the disappointment when always it was misty. We watched the weather with such care for the mist lifting and coming down again and I heard with frustrated jealousy the news that sun could be seen in the Craycroft valley. On Moss Ridge when for a moment or two we stood in sunlight it cheered us up tremendously, unconsciously almost, although we also openly rejoiced, and we went on our way singing loudly. It was wonderful to have really fine weather on the Pictons.

            It was strange in Canberra to be alienated from the weather. I tried to keep up an interest in it but it was no longer the legislator for my happiness and now I no longer notice it much, or somehow not with the intense reality I did before. Before it was an important thing in my life, now it is just an interesting thing to notice. It was strange but good, I loved it more than anything, to have all these physical  things – weather, rest, food – the important things in one’s life. These were what made up my life in Federation. Rest and food assumed an enormous positive value. The scenery and poetry were my joys. I like this allotting of elements.

            On the days when we were confined to our tents, as night came on we used to get tired and subside and try to sleep for a while as it got dark, and then after a while we’d rouse ourselves in the dark and light the candles and primuses and cook tea. On the last evening at Bechervaise while Ken was sunk into this half-sleep I was half-dozing with my eyes shut singing softly to myself all the lullabies I knew. When I’d finished I announced “That’s all the lullabies I know.” Ken said to go on. He’d liked it. That was all my lullabies so he asked me to sing the Elizabethan songs, which I’d been singing the other day. He must have liked them, and I was pleased because he usually only likes funny things. So I sang them but not so well as the lullabies because I was singing to someone and conscious of my voice. I felt very tender towards him in doing it. When I’d finished, the others called out and we cooked dinner. It was dark.

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Frenchman’s Cap 1961

                                                     Diary                                                           12/1/61

            I’m sitting in my sleeping-bag with my back against the back wall of the Frenchman’s Cap Hut and my notebook on my knees and my torch shining up at it from my lap. It just lights up my hands and makes them a lovely warm brown colour because they’re so sunburnt and there are shadows round my thumbs. There is crumpled pink elastoplast on my left thumb because I tripped over in Barron’s Pass while running to get my rucksack for lunch and gouged a deep cut into it. It throbs a bit. The light is falling on a part of the black knitted cuff of my anarak and on a little bit of the green sleeve of my left hand. The light falls finally on the roof at the other end of the hut. Elizabeth is on my right sitting the same way writing, and Noela is on my left lying on her stomach writing. Judy is in the other corner sitting on her sleeping bag writing to her mother and father and Anne is reading lying on her stomach on her sleeping bag.

            It is a gorgeous hut. It seems as if somebody loves it, some club perhaps, who built it, because such a lot has been done for it. There are little carved signs everywhere and a wonderful door latch carved of wood which opens when you pull a string outside. There is a boomerang over the door with the words “for the monster only” carved on it. There is a mountain lake (Tahune) only a few yards from the hut. When Elizabeth and I swam in Crater Lake we were afraid of a monster and didn’t like to swim far out.

            The hut and lake are just below Frenchmans, which rises up a huge yellowy-white tower far above. The scenery here is magnificent and grand. We have had wonderful views today.

We met Judy and Ann at the Franklin river turn-off the night before last. We got a hitch there with two boys who were a scream. They talked all the time in terrible accents and were very interested, and enthusiastic, about everything they’d seen in Tasmania. They were from Sydney. One of them was a saw-doctor and a lot of his fingers were cut off. They were probably younger than us.

            Not much happened the first day. There were long flat stretches and one steep pull. It rained on and off. I’ve been wearing sandshoes. LakeVera was hidden. We sat on a slope and decided that it must be in the valley below although it seemed impossible, and when we went suddenly it flattened out and there was the lake and a cleared mucky camping ground and a sort of shelter full of rubbish in the drizzling rain. I lit a fire with the help of solid fuel (there was lots of chopped wood piled out in the rain) insisting loudly that no-one should touch it except me. It was a long time before we could cook properly and I felt a bit miserable and lonely. After a while the rain stopped and we dried our clothes and they smelt of smoke. It was lovely when we went to bed. Noela and I had overlapped our tents and there was lots of room. It was lovely because Elizabeth and I lay and read for a little while in our sleeping bags and read by our torches.

            Insects are making funny little noises outside. The hut is all dark except for the little spots of torch-light and the clothes and bags of food that can be just made out hanging from the ceiling.

            There was a row of notches cut in one post of the shelter at LakeVera and I said that perhaps there was a wild man living nearby who killed sleeping campers and cut a notch for each. Judy said. “Then there’ll be five more notches tomorrow.” We didn’t eat all our apples and left the billy on the ground with the lid on it. In the night I woke up and heard something at the billy. It was rattling away. I couldn’t help thinking of the wild man. I knew it must be an animal but there was a heavy thumping sound now and then which sounded too heavy for a small bush animal. Then I thought of a wallaby and should have stopped worrying but I couldn’t quite disbelieve in the wild man. Noela woke up and made a few noises to scare it. She went to sleep and it came back, clinking and tinkling away. I didn’t like to look because it would have been too terrible if I had seen a wild hairy man. It would have been so terrible that I couldn’t take the risk of looking even though it was impossible. It would have been too frightening to bear. I went to sleep and Elizabeth said that when she woke up there was a lovely little wallaby in the entrance to the tent and it had such a pretty face. I told her that I had thought it might be a monster in the night and had thought that it might accept the apples as an offering instead of us. Our apples were nearly all gone.

            Today was the most beautiful day for scenery and we were terribly terribly lucky that it was fine most of the time and we could see what was around us. I’ll write about it when I write again. It’s quite cold and I’m going to get down into my sleeping bag and read for a little while before I go to sleep. Elizabeth is reading now and the others are going to sleep. Just two little torch lights.

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Windsor Girl 2000

            It was my morning on duty at the local history museum in Windsor, and I had taken my chair onto the verandah looking onto Thompson Square to read in the sunshine while things remained quiet. I noticed a man, in about his forties, hovering on the footpath and looking across to the other side of the Square. He walked forward a few steps, then back, then forward again, as if keeping his eye on a moving target or trying to gain a better view. I followed his line of sight, and with my short-sighted gaze saw, unclearly, a small figure on the ground near one of the seats on the far side. I thought perhaps it was his child, playing up while he kept his eye on it from a distance. Soon he went on up the footpath towards the Macquarie Arms, and I returned to my book.

            But I was soon distracted from my reading by the arrival of, I at first thought, a very young girl of fifteen or so, who I later decided was probably in her mid-twenties. She cast herself onto the front step, near my feet. “I bet you thought I was dead,” she said. She was wearing a checkered flannelette shirt and had her hair in bunches (hence her youthful appearance), the former unpressed and the latter uncombed, although she was perfectly clean. In fact, I hadn’t been thinking anything about her at all — she had appeared out of nowhere — but I soon surmised that it had been she who was lying on the ground in the park, putting on a performance I had entirely failed to appreciate.

            Drawing my attention to the roar of the trucks as they ground up the cutting from the bridge to the roundabout, just beyond where she had been lying, she complained that the drivers did it just to annoy her. The absurdity of this notion – they couldn’t possibly have known she was there – was a first indication to me of what seemed to be some slippage in her grasp of reality, aggrandising her significance to other people. I said I thought it was just through having to change gears to get up the hill, but she was unconvinced. She then boasted that when a man had come over to ask her if she was all right, she told him to mind his own business. I was not favourably impressed by this repulse of an offer of kindness, particularly when, as I judged, her behaviour been designed to attract just such attention

She stayed with me, holding forth, for probably two hours, during which time I supplied both of us with a cup of tea from the Museum kitchen, until I was relieved by the person on duty for the afternoon. Her talk was mostly rational, but verging on the deluded from time to time, although in these days of common reference to psychics and astrology, one is hard put to it to know when the threshold from sanity has been crossed.

Did I believe in ghosts? she asked. I said no, but she went on just the same. About a year ago she’d been told that her husband had died, but only a couple of weeks back she was sitting in a car outside a house in which all her friends were using drugs, she was out there getting away from them, when his face appeared at the car window. He spoke to her, then he disappeared. Perhaps he hadn’t really died, I suggested, but she thought not.

Her friends, she said, were always putting her down, criticizing her because she’s cleverer than they are and won’t do the low things they do. All her friends used drugs, she said, but she didn’t. Taking drugs was wrong. She used this word, not harmful, or dangerous. She used to think it didn’t matter, she said, but now she knew it was wrong. Cynically, I wondered if this was a ploy to win my approval.

            She spent some time telling stories of her naughtiness at school, and what she saw as her cleverness in provoking the teachers. When the class were told to take out their books, she held hers on her lap under the desk. She was sitting at the front of the class and the teacher fixed his eyes on her because her book wasn’t on the desk. After a bit she demanded provocatively of him, “What are you staring at?”

            “I said, get out your book!”

            “I have!”

            “I can’t see it!”

And so on, with the teacher, of course, getting the worst of it. The repartee she reported was characterized by a capacity to exercise an insolence that stays just inside the line of the insupportable, and this was what seemed to define her conception of her cleverness — her smart answers which her friends could not equal. Eventually I became a little tired of listening to the tales of her superiority to all comers and ventured to suggest that a little more modesty and appreciation of others might be in order, but this was not accepted; indeed, I doubt she got the point.

Mostly, there was something not quite genuine about her tales told against the powers of society that oppressed her, the welfare authorities in particular, which her cleverness, in her view, outwitted. I assumed that she was homeless, or semi-homeless, and subsisting on welfare, but I noticed that she spoke with an educated or middle-class accent, and her speech, to me at least, was free of the uncontrolled use of expletives that is characteristic of the welfare wanderers of Windsor. I wondered what her background might be, and how she came to be as she was; but she would not admit to any parents, positively avoiding answering my probing in that direction. She did, however, speak of relatives on a large property in western or north-western New South Wales, and I gained the impression that she had grown up in the country.

On just two occasions did a true, and appealing, voice come through the monologue of self-aggrandisment. She spoke with a real ring of pleasure about the birds and bush on a western station she knew (perhaps, in fact, her home). And again, she suddenly interrupted her talk and lifted her head and said, “Smell that!” I, too, lifted my head in interrogation, but before I could identity it, “Sheep!” she said, with real warmth and feeling. “I love that smell.” It’s a strong odour that not everyone would enthuse over, though with a certain appealing country fragrance. And that was what it was. A large truck carrying livestock rolled up through the cutting from the bridge across the Hawkesbury, no doubt having come from the north via the isolated Putty Road.

At some stage, she told me she had had four children, but they had all been taken from her, and these days of course such a thing is possible. It added another dimension of tragedy. I was prepared to believe this but again I suspected a wavering of reality when she said that when she arrived at the hospital to have her last baby, they injected her with drugs, and then after the birth they took out all her own blood and replaced it with a blood transfusion. This, she said, was so that no one could tell that they had drugged her, and this was in some way a plot to ensure she could not keep her baby. Her description could have been a misinterpretation of the sorts of things often done to women giving birth, without explanation. But what became of the baby? Does this sort of thing happen?

Near the end of our talk, another, unexpected facet of her circumstances was revealed. It seemed that she had to report to the police every day, and again a note of genuineness, but this time one of frustration, almost of desperation, came into her voice. “I’m just so tied up,” she said, “I can’t move.” Yes, I thought, I can just see why. It’s because of your insolence, your smartness, towards authority – police and social welfare workers now, instead of teachers. What you congratulate yourself on as your cleverness is what is causing all your problems. If you could just act politely and submissively, you would get away with everything, with your nice speech and manners.

When my afternoon substitute arrived, she immediately departed, apparently not inclined to award her sociability to the newcomer. In a way, throughout I had sensed that there was an unspoken bait, to me as an older woman, to offer my personal help to her; but I declined the lure, because I sensed the professional. Later I described the encounter to my friend, Jean, who is usually a good source of local information, and she suggested that the girl was one that several women in Windsor had responded to, had tried to help, but in the end got nowhere. She was thought to come from “a good family”, but nothing more specific than that. I have seen her twice since, once on the platform at Windsor station, and once walking along The Terrace away from the river, but not to speak to and with no sign of recognition.

Windsor had responded to, had tried to help, but in the end got nowhere. She was thought to come from “a good family”, but nothing more specific than that. I have seen her twice since, once on the platform at Windsor station, and once walking along The Terrace away from the river, but not to speak to and with no sign of recognition.

 Postscript

            A year or two elapsed between the above account and Jean mentioning that a girl, one of the welfare crowd, had hanged herself from a tree along the riverbank. Jean’s house looks out onto the river and the riverbank park, at the point where The Terrace turns away from the river and the park continues along the river, hidden behind the houses built on the rising levee bank. There, out of sight from the road, the local derelicts, the River Rats as they are called by the Museum volunteers, sometimes gather and the homeless camp. Early in the morning, she had noticed ambulances and police passing along the track below her house, and she later heard that two of the girl’s druggie friends had found her, and were fighting under the tree about whose fault it was that she’d killed herself when the police came. It reminded me of Hamlet and Laertes fighting in Ophelia’s grave over who had loved her most.

            The husband or son-in-law of a friend of Jean’s, who is in the local police, said that, really, the dead girl had done herself a kindness, because she was so tied up with drugs and alcohol that she was going nowhere. Those words, the being tied up and going nowhere, recalled to me, with a pang, the words of my girl at the Museum, so that I felt it must be her.

            A week later, in the late afternoon, I called on Jean and happened to enquire about the progress of a new development, a huge house being built overlooking the riverbank park. She suggested we walk round to view the monstrosity, already nicknamed the RSL, but not so very bad, I thought, when I saw it. This took us along the riverbank where the girl had died, unavoidably raising the mental query as to which was the tree. Beside the new bicycle path we saw that a tree had been sawn off, a double trunk, the remaining stump only a few inches above the ground. Leaning against it was a bunch of dead flowers wrapped in paper with a note attached — “We miss you  From Sarah and Michael”. All of the tree had been removed, no trunk lay on the ground, nor were branches strewn about.

If this was the tree on which the girl hanged herself, who had cut it down, I wondered? Surely not the Council. Her friends would be unlikely to have a chain saw or to be either competent or tidy. Could there be some archaic tradition of cutting down the suicide tree, unknown in my academic world, to which authority, in the form of Councils, silently conforms? Or perhaps there might be a tradition specific to Windsor and the other MacquarieTowns, along with some other surprising survivals, transported from eighteenth century England but never taking root in later settlements in Australia – the baffled sociologist can hypothesize many possibilities. Perhaps her family (with tree-felling skills) came from the country and took it, someone suggested, when I recounted our discovery.

Carol, in an old Windsor family solicitors office, who has many official and semi-official contacts, was the person to ask.  She was fascinated and said she would find out. Within a few hours she was back to me. No, it wasn’t the Druids, she said. The tree had been cut down by Council at the request of several elderly ladies whose houses look out onto that stretch of the river. They had been distressed by the events there, and didn’t want to be reminded by the tree. This at first sounds straightforward enough, but the willingness of a Council to comply so unprogrammatically is redolent of persisting strains of traditional uneasiness in the face of suicide. The tree was half dead anyway, it was said in justification.

            Of course my girl at the Museum may not have been the girl at the centre of this tragedy. I will be watching out for her around the streets of Windsor from now on, because I know that any number of negative instances does not afford a certainty.

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Tobacco Stringing, Dalbeg, North Queensland – December 1961

            My boy is called Dino Poley. He is Italian but born in Australia. The Ringroks and Keniffs are terrific matchmakers and are now longing to get Lister a date with some girl or other. They just about push you into the most eligible boys’ arms. Elizabeth was amazed. Of course I’ve seen them in action before. Elizabeth’s boy is called Bill Leacey. Dino looks very kind and has a lovely smile but I don’t think he’s very interesting. He is very quiet but when you speak to him he sort of lights up. Bill is ordinary but quite nice. In one way they provide an interest but it is a bit of a bore and disturbs the peace one tends to settle into here, and which is so pleasant as a change from university life. The Keniffs and Ringroks seem to think that if you have a boy you must be happy, it doesn’t matter much who. I think they think we’re a bit queer, needing so much pushing. You couldn’t imagine how much they organize things without seeing it.

            We went into Ayr the Saturday night before Christmas and it was awful. We went to a hotel where there was a sort of beer garden with a floor for dancing and an incredible band. A great fat woman who played the piano and stared out constantly at the people with a completely dead-pan expression, a guitarist and singer who never changed his expression, and a mad elderly drummer who flirted with us and got madder and madder as the night went on and he got drunker. The people were a motley collection – a lot of Italian men, some men and women with children and an assorted lot of Australians, mostly pretty draggish. The families mainly just sat there, never moving for hours, while the children wandered round picking up peanuts from the floor. We were provided with whistles to blow. The floor was quite large and mostly crowded, but what was so awful was that there was no joy anywhere. All these people were supposed to be enjoying themselves and probably were as much as they ever had. They didn’t know what joy is. The only consolation was jiving because, no matter who you’re dancing with, if they can do it you enjoy it, and you get so wrapped up in the movement that you don’t notice what’s going on round about. Later we went to another hotel, at Brandon, a small town about 5 miles from Ayr. This was really dreadful. The other place was passable but this was tough and dreadful. There was much the same set-up, but far fewer people. It somehow had a vulgarity the other place missed. It gave the impression that there must be hundreds of similar places in little towns in Australia where people enjoy themselves. This was horrible to think of. I met a man there who was liberal in the way most people are Communist – dogmatic, belligerent, and arrogant. I really would have guessed he was Communist. We had quite an irritable argument and his great over-riding reason for being liberal seemed to be that they will win. He was one of those dreadful people to argue with who concede you points and then say the opposite, say they understand but don’t at all. I rather hated him. He said to write to him in ten years and tell him if I was still labour. He betted I wouldn’t be. I couldn’t find out what his job was but he seemed not to work at all. He lived in a hotel. He was Scotch and about 40, thin with glasses. He jived with little tarty girls, stamping his feet about but quite good.

            One thing I liked was two funny skinny old men who danced with an oldish woman in an exaggeratedly professional way. One moved about with great long sweeping strides, bending the woman over backwards, made particularly funny by his knobby old knees and skinny calves. The other did a sort of cave man jive, bending down low, gaping, and clapping.

            Tonight we’re going to the New Year’s Eve dance at Dalbeg.

            There is a Greek on this farm who left Cyprus because they were after his life, something political. He reads a German philosopher called Fabricius? He often plays Greek records and it’s nice when you’re sitting outside to hear the raving and mournful wavering on the note that the Greeks have in common with the Indians in their singing.

            I’m reading the Communist Manifesto and I’ve never come across so many unjustified assumptions in my life. You have to keep thinking up your own explanations for its quite unqualified assumptions about economic development and its influence in other fields and about the place of the bourgeoisie in historic development. Although you can usually find them it makes it seem all very arbitrary because you feel you could just as well have found justifications for quite a different theory. It seems so much a one-sided interpretation. I was amused and surprised at its sentimentality concerning lordship and vassalage.        

Dino has a brother called Sag (Sergio) with a beard and red mouth showing through it in the way Roy Churcher’s does. He looks rather wild and scares me a bit but Elizabeth is made of sterner stuff and thinks he is gorgeous. He’s always supposed to be reading – comics and westerns.

            When I first came here I was awfully alert and felt keen-minded after the exams, but now I’m sinking down towards the beasts of the fields. Apparently you can’t keep a body and mind working at the same time.

            We live in a grading room upstairs, with unpainted orangey plywood walls. The branches of a rain-tree just reach above the window sills and at night I can see the stars and clouds from my bed, and I enjoy this. But in the day if I’m resting, trying to have a sleep, sometimes the room gives me a dreadful empty feeling that I’m wasting my life lying there. There seems to be nothing in that room to live for. And sometimes when I’m half-asleep and my mind’s empty and defenceless a realization of death flashes in on me. I’m not afraid of it and don’t care really when I die except that I would like to have done something I’m made for before I do, but it seems dreadful and incomprehensible that death should be. I feel this personally as well as generally. It makes me think that minds are out of place in this transient world. Death and change should occur, not be known.

            I was having a great rage against my mind one day, out in the paddock, because my mind seems to leave me, myself, out of account. My mind seems to tie me to my emotions, just as emotionally I am forced to think, and tire me out. You and John Fowler and others are lucky in that either you can identify yourselves with your intellect or else the gap between your intellectual thinking and your feelings is great enough so that there is no constant tension between them. I feel at the mercy of my mind and yet I couldn’t give it up, having got it. Elizabeth feels much like me in this. It is dreadful when thinking is tied to feeling. Purely intellectual thinking is wonderful and exhilarating.

Sometimes I get so tired of feeling for people. In this way I am tied to the Ringroks. After having known them as I did in the first year I was here I could never give them up, even if our friendship went quite sour. At the moment we are getting on very well. We cook for ourselves now, and this seems to have relieved all the tensions. Mrs Ringrok is very bossy towards her husband and I feel very sad about the way it is affecting him. He usually gives in, and is getting an almost saintlike expression at times, and there is often pain in his eyes when you wouldn’t expect it. He gives in not because he is weak, but because she never would. She just doesn’t see that she is bossy, and so can’t try to regulate her bossiness.

            Elizabeth says she isn’t at all pantheistic in her beliefs now. She is not Christian. She believes in God and an after life, but can’t explain to me how, so that I can understand. Probably because I can’t believe in anything, not even the clouds on Mt Coot-tha, we can’t communicate on that subject.

            I’ve got very brown from working in the sun. And I must be getting awfully strong from lifting the heavy tobacco bales. I hate to think what I’ll be like when I get back from Tasmania.

            I wrote to Ellen and Rob at length about my thesis topic. I’ve decided that I should get a terrific kick out of writing about Walter Raleigh and the Elizabethans if I don’t work with first class honours in mind, but just for what interests me. Ellen has a new job which sounds awfully interesting. This is what she says – “I am now being a clerk in Collets Book Shop in the Export Subscription department. We are concerned with sending banned publications of all sorts into Russia and the other Communist countries. There is another department which arranges for Russian publications to come here. The place is staffed mainly with Communists but they are quite unlike what I would imagine. They treat the party as though it was their local church group; They make things for Bazaars and say things like “He’s supposed to be a responsible Party member and yet he does childish things like that.” About the magazines they send – “Some of the little ones like “Laundryman’s Journal” refuse for Patriotic reasons to send to Russia (so the bookshop orders them in its own name and posts them off) but the Government printers send off the reports on Atomic Energy Research without any worry.” They are becoming mixed up in CND.

            Tonight we are sitting out listening to the Greek music playing in the workers’ quarters and I was thinking how sad all primitive music is and how different from Western music. And yet basically it echoes something in us. It makes one wonder whether primitive man expresses man most truthfully and whether more developed types of music are just accretions invented by man to distract himself from a fundamental sadness. And man is, as the music seems to express, lost in the world.

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Richmond Line 2000: 18. Public Living

            I wasn’t immediately aware of the small family which chose seats at the end of the carriage forward of where I was sitting on a late morning train. But soon a persistent high level of activity caused me to look up and register their presence. The volume of sound came from the mother who was still on her feet in the space between the facing seats, apparently rooting about in a bag. The children were not visible above the back of the seat, and the man was slumped low beside the window, only the back of his head in view.

            The woman’s hair was an artificial hard, bright yellow, and she had one of those rather pinched, unwomanly faces which today seem to say “welfare class”, where once it would have been “working class”. She eventually retrieved a small container and, still on her feet, began lifting her T-shirt and spraying under her arms with extreme vigour. She then got to work on the man, pullling up his slightly resisting arms to do the deodorizing job. Their whole little area seemed to be filled with spray. Her next grooming job was her hair, and this was also publicly and expansively performed, with no effort at privacy or discreetness.

Meanwhile, she kept up a constant flow of instruction and admonition of man and children. He had little or no interaction with the children, so I assumed he was her partner but not their father. Her tone of voice, her accent, was peculiarly graceless, ugly, mainly as a result of a total flatness of affect. ‘What sub-culture of deprivation does that way of speech come from?’ I wondered. It seemed scarcely possible that it could be a natural accent of any functioning social group. By contrast, and one wondered how it could happen, the children seemed to speak quite nicely, with a proper human intonation. Later it occurred to me that her speech might be the chronic version of that slowed-down flatness one hears in teenage boys who are using marijuana heavily. Perhaps she had been a sufficiently heavy drug-user in the past for her nervous system to have failed to recover.

            When the man turned his head, I saw he was a rather comely, masculine Aboriginal. She grumbled at him persistently, and quite aggressively, but was quick to let him know that his words in self-defence offended her. Counselling on assertiveness has had its greatest success among the least amenable sections of society, and aggressive attack, imputing offence, is used to pre-empt objections to one’s own offensive or “inappropriate” behaviour. Her disfavour increased, and eventually she grasped his hair and began forcing his head down sideways. I became alarmed that domestic grooming in public would be replaced by domestic violence in public, but the man, despite his powerful features, remained entirely mild and submissive, and there was no further escalation.

            With their considerable collection of bags, they seemed to be on a family expedition for the day. They left the train before we reached the city, a busy little group — having provided me with a small glimpse of domestic peace somehow surviving the ministrations of a woman who was obviously deeply concerned with her little family group, but whose behaviour offended against all the normal niceties that one sees as essential to oiling the wheels of harmony.

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