Prime Numbers

Quantity and Quality

Prime numbers, are the fundamental building blocks of the natural number system. A prime number has no factors other than itself and 1. So, for example, 7 is a prime number, as it has no other factors other than 7 and 1.

Now, bearing in mind that in dynamic terms numbers have dual aspects both as quantities and qualities, we will define prime numbers in a likewise manner.

Thus we can list on a horizontal scale the set of prime numbers 2, 3, 5, 7, 11 ..... ,

and also on a vertical scale the same set 2, 3, 5, 7, 11 ..... .

The first set represents numbers as quantities, all defined within the same dimension (i.e. number as quality). This is always taken - where not otherwise stated - as the 1st dimension.

Strictly speaking this first (quantitative) set should be listed as 21, 31, 51, 71, 111.....

Here the focus is on prime numbers as quantities (within the given number quality or dimension "1").

The second set represents numbers as qualities, with the same number (as quantity), raised to different prime powers or dimensions. Again - unless otherwise stated - the given number is again 1.

Again, strictly speaking this second (qualitative) set should be listed as 12, 13, 15, 17, 111 ..... .

Here the focus is on the prime numbers as qualities or dimensions (to which the given number quantity "1" is raised).

In the former case, the inclusion of the dimensional characteristic (i.e. the 1st) does not affect the quantitative interpretation of the number. For example 21 = 2. Therefore in quantitative terms, reducing the combined quantitative-qualitative expression of 21 to the merely quantitative expression of 2 apparently makes no difference.

In the latter case, the inclusion of the quantitative characteristic (i.e. the number "1"), this time does not affect the qualitative interpretation of the number. 12 = 2 (i.e. the dimensional characteristic here "2" remains unchanged regardless of the number quantity used).

Therefore in qualitative terms, again reducing the combined qualitative-quantitative expression of 12 to 2, apparently makes no difference.

However, because both sets - in reduced terms - are now formally identical, the misleading step is then made of reducing the second qualitative set of numbers in turn to the first quantitative set.

Thus conventionally, numbers in mathematics instead of signifying dynamic two way relationships (with complementary aspects), are treated one way as static entities.

Psychological Dimensions

Now, this might all seem far removed from psychological development, but in fact there is a fascinating direct connection.

The first instictive stage of infant development can be referred to as primitive. The very word "primitive" bears direct comparison with "prime" where the basic building blocks of experience emerge.

Now this stage emerges from a state, where both conscious and unconscious minds are totally undifferentiated. This leads - and I am deliberating using language that is suggestive of the mathematical connections - to complete confusion as between objects and dimensions.

The child is not yet able to place objects in an environment of space and time, but rather confuses both in an immediate and fleeting experience. Indeed, this always remains the basis of instinctive response, where the quantitative experience (i.e. what is projected objectively) is so spontaneous and immediate, that it eludes separate qualitative control. Subjective emotion directly attaches to the object so that both literally are confused.

Thus the emerging infant, initially greatly confuses quantitative impersonal with qualitative personal experience. Constancy of phenomena is not possible, because this requires placing them in a dimensional environment of space and time, whereas for now, phenomena are directly experienced as dimensions so that there is the confusion of whole with part.

When we link up the primitive structures (psychological), with the prime strtuctures (mathematical), we can cee clearly the complementary relationship.

With the primitive structures, there is total confusion as between quantitative and qualitative experience. Phenomena in experience cannot be yet separated from the dimensions of space and time.

With prime numbers - in complementary fashion - there is total separation of quantitative (i.e. reduced numerical value) and qualitative (i.e. dimensional) characteristics.

Once again prime numbers as (mathematical) quantities have an indirect interpretation as (psychological) qualities; prime numbers as (psychological) qualities (or dimensions) have an indirect interpretation as (mathematical) quantities. In conventional mathematical only prime number quantities (direct and indirect) are recognised.