LDC is the new project of my team. It combines a digital slip box (Zettelkasten) for your personal collection of ideas, notes and internet-links with a safe exchangebility of personally selected zettels (cards).
As a surplus we have added a novel deliniation of logic, especially convenient for the dynamics in reflections and discussions.
LDC is freeware and publicly available at ld-cards.com. Thank you for your interest.
The bit is the basis of IT
Our information technology is based on the bit. Everything that happens in our computers is based on this smallest basic element of information. If someone asks you what a single bit means, you may well answer that the bit can assume two states, of which one means 0 and the other means 1. As is generally known, this enables us to write numbers of any size; all we have to do is to line up a sufficient number of bits.
But is this really true? Does the one state in the bit really mean 0 and the other 1? Can these two states not also assume completely different meanings?
A bit can be attributed arbitrary meanings
In fact, the two states of the bit can assume any meaning. Besides 0/1, true/false, yes/no and positive/negative are also popular; but in principle and in practice, a bit can be attributed any meanings from the outside. Of course, inversions are also possible, i.e. 0/1 and 1/0.
The attribution of the meaning of the bit comes from the outside
Whether the specific bit in the computer programme means 0/1 or 1/0 or something else, does of course play a crucial part. However, the meaning is not in the bit itself, for the bit is a most radical abstraction. It only says that two states exist and which is currently active. What the two mean, however, is a completely different story, which goes far beyond the single bit. In a computer program, it can be declared, for instance, that the bit corresponds to the TRUE/FALSE pair of values; but the same bit, together with another bit, can also be interpreted as part of a number or a letter code – very different meanings, then, depending on the program context.
Digital and analogue context
The software program is the digital context, and of course it consists of further bits. The bits from the surroundings can be used to determine the meaning of a bit. Let’s assume that our bit and other bits are involved in defining the letter ‘f’. Our program is also organised in such a manner that this letter will appear in a table, in a column which is headed ‘Gender’. All this is clearly set out in the software. Now, does the software determine the meaning of the bit? You will doubtless not be surprised if the ‘f’ means ‘female” and the table probably lists various people who can be male (m) or female (f). But what do male and female mean? It is only in the analogue world that these expressions receive a meaning.
The bit, the perfect abstraction
In fact, the bit represents the final point of a radical abstraction of information. In a single bit, information is reduced to what is absolutely elementary in that the information about the meaning has been completely removed from the bit. The bit merely says that two states exist that have been described outside it and which of the two is active at a specific point in time.
This radical abstraction is intentional and makes a great deal of sense in a software, for in this way, the same physical bit in the chip of the computer can be put to a new use again and again, once as a TRUE/FALSE pair, once as 0/1, once as YES/NO, etc. This is very practical and enables the computer to solve any task whatsoever. The perfect abstraction that has thus been achieved, however, simultaneously deprives the single bit of its individual meaning, which can and must be attributed to it anew for every application.
The endless regress
When the meaning of the bit is given from the outside, then of course other bits can take on this task and define the meaning of a bit. For this purpose, however, these outside bits must have the necessary effective power, which of course they cannot have without their own meaning. And naturally, the meanings of the bits of this outer circle are not in these bits themselves – for the same reason as above – but have to be given from the outside, i.e. by a further circle of bits. The bits of this second outer circle must be explained in a further circle, and the meanings of the bits of this further circle in another outer circle… Of course this process of attributing meanings never reaches an end in a world of bits: the regress is endless.
The endless regress only ends in the analogue world
Only when we step out of the program into the real world are we really able to attribute a meaning to the information from the computer.
Selective and descriptive information content
If we recapitulate the above, we can make the following distinction in the bit:
The descriptive information content says what the bit means; it describes the two states of the bit but does not say which state has currently been selected. The selective information content says which of the two states is currently active but does not know anything about the properties of the two states and thus about their individual meanings.
The distinction between the selective and descriptive information content was coined by the British radar pioneer and information scientist Donald McKay in the 1940s, practically at the same time as the first mention and description of the classic bit by the American Shannon. McKay also clearly recognised that Shannon’s bit only carries a selective information content and that the descriptive information content must be given from the outside.
Surprisingly, this insight of McKay’s has almost fallen into oblivion today.
Conclusion:
When you hear a melody, it is based on a musical scale. The scale consist of the small number of tones which are allowed and may occur in the melody. In a linear sequence, these tones constitute the musical scale. Most melodies that can be heard in our cultural area can be traced back to one single scale, the Ionian or major scale, which is made up of seven notes in very specific scale steps.
However, there are thousands of different scales. Presumably you are familiar with the minor as well as with major scale and may have heard something about pentatonic scales or about whole tone scales, Lydian and Phrygian scales, Indian ragas, Japanese and African scales. All these scales differ from each other.
As we will see, however, they have some astounding similarities. Why should people all over the world, in all cultures and with all their differences, comply voluntarily and strictly with these similarities? The reasons for this are easy to explain if we don’t merely look at one world (‘world’ in the sense of Penrose), but at the interaction of all three worlds.
Scales are part of our reality, no matter how we define reality – unless we define reality as that which we call matter. In that case, the scales are not part of matter. They may manifest themselves in the physical world, for instance if a human being sings or plays them, but they have an identity which is independent of the individual way they are performed. In this sense, scales are non-local, as is typically the case with entities of the Platonic world. Between the scale and its performance, there is thus the relationship of an abstract, i.e. Platonic pattern with its material instance. This is always a 1/n relationship, for the pattern is unique but can be the source of any number of instances.
As a pattern, scales are part of the Platonic world, even though they manifest themselves in the material world. Mathematics, in particular, has much to do with the form of scales, which can be demonstrated easily, yet you don’t need to know anything at all about this kind of mathematics in order to recognise the scales correctly or to sing them. Your mental world in which you experience these scales has no need of figures and formulae.
Scales thus exist in all three worlds:
Platonic world: here, a scale exists as an entity, i.e. as a unity and as a whole. Here, every scale exists only once.
Physical world: here, a scale exists as any number of occurrences – whenever melodies are produced on the basis of it.
Mental world: here, i.e. in your head, you recognise the melodies and the scales.
Of course, each world is organised in its very own way. Now, how do the three worlds interact?
This is a text in the series about the theory of the three worlds.
Translation: Tony Häfliger and Vivien Blandford