The Beginning of Infinity: Explanations That Transform the World (21 page)

Natural numbers
   The whole numbers 1, 2, 3 and so on.

Reductionism
    The misconception that science must or should always explain things by analysing them into components (and hence that higher-level explanations cannot be fundamental).

Holism
    The misconception that all significant explanations are of components in terms of wholes rather than vice versa.

Moral philosophy
    Addresses the problem of what sort of life to want.

– The existence of emergent phenomena, and the fact that they can encode knowledge about other emergent phenomena.

– The existence of levels of approximation to true explanations.

– The ability to understand explanations.

– The ability of explanation to escape from parochialism by ‘letting our theories die in our place’.

Reductionism and holism are both mistakes. In reality, explanations do not form a hierarchy with the lowest level being the most fundamental. Rather, explanations at any level of emergence can be fundamental. Abstract entities are real, and can play a role in causing physical phenomena. Causation is itself such an abstraction.

The earliest writing systems used stylized pictures – ‘pictograms’ – to represent words or concepts. So a symbol like ‘
’ might stand for ‘sun’, and ‘
’ for ‘tree’. But no system ever came close to having a pictogram for
every
word in its spoken language. Why not?

Originally, there was no intention to do so. Writing was for specialized applications such as inventories and tax records. Later, new applications would require larger vocabularies, but by then scribes would increasingly have found it easier to add new
rules
to their writing system rather than new pictograms. For example, in some systems, if a word sounded like two or more other words in sequence, it could be represented by the pictograms for those words. If English were written in pictograms, that would allow us to write the word ‘treason’ as ‘
’. This would not represent the sound of the word precisely (nor does its actual spelling, for that matter), but it would approximate it well enough for any reader who spoke the language and was aware of the rule.

Following that innovation, there would have been less incentive to coin new pictograms – say ‘
’ for ‘treason’. Coining one would always have been tedious, not so much because designing memorable pictograms is hard – though it is – but because, before one could use it, one would somehow have to inform all intended readers of its meaning. That is hard to do: if it had been easy, there would have been much less need for writing in the first place. In cases where the rule could be applied instead, it was more efficient: any scribe could write ‘
’ and be understood even by a reader who had never seen the word written before.

However, the rule could not be applied in all cases: it could not
represent any new single-syllable words, nor many other words. It seems clumsy and inadequate compared to modern writing systems. Yet there was already something significant about it which no purely pictographic system could achieve: it brought words into the writing system that no one had explicitly added. That means that it had reach. And reach always has an explanation. Just as in science a simple formula may summarize a mass of facts, so a simple, easily remembered rule can bring many additional words into a writing system, but only if it reflects an underlying regularity. The regularity in this case is that all the words in any given language are built out of only a few dozen ‘elementary sounds’, with each language using a different set chosen from the enormous range of sounds that the human voice can produce. Why? I shall come to that below.

As the rules of a writing system were improved, a significant threshold could be crossed: the system could become
universal
for that language – capable of representing every word in it. For example, consider the following variant of the rule that I have just described: instead of building words out of other words, build them out of the
initial sounds
of other words. So, if English were written in pictograms, the new rule would allow ‘treason’ to be spelled with the pictograms for ‘
T
ent’, ‘
R
ock’, ‘
EA
gle’, ‘
Z
ebra’, ‘
N
ose’. That tiny change in the rules would make the system universal. It is thought that the earliest alphabets evolved from rules like that.

Universality achieved through rules has a different character from that of a completed list (such as the hypothetical complete set of pictograms). One difference is that the rules can be much simpler than the list. The individual symbols can be simpler too, because there are fewer of them. But there is more to it than that. Since a rule works by exploiting regularities in the language, it implicitly encodes those regularities, and so contains more knowledge than the list. An alphabet, for instance, contains knowledge of what words sound like. That allows it to be used by a foreigner to learn to
speak
the language, while pictograms could at most be used to learn to write it. Rules can also accommodate inflections such as prefixes and suffixes without adding complexity to the writing system, thus allowing written texts to encode more of the grammar of sentences. Also, a writing system based on an alphabet can cover not only every word but every
possible
word in its language, so that words that
have yet to be coined already have a place in it. Then, instead of each new word temporarily breaking the system, the system can itself be used to coin new words, in an easy and decentralized way.

Or, at least, it could have been. It would be nice to think that the unknown scribe who created the first alphabet knew that he was making one of the greatest discoveries of all time. But he may not have. If he did, he certainly failed to pass his enthusiasm on to many others. For, in the event, the power of universality that I have just described was rarely used in ancient times, even when it was available. Although pictographic writing systems were invented in many societies, and universal alphabets did sometimes evolve from them in the way I have just described, the ‘obvious’ next step – namely to use the alphabet universally and to drop the pictograms – was almost never taken. Alphabets were confined to special purposes such as writing rare words or transliterating foreign names. Some historians believe that the idea of an alphabet-
based
writing system was conceived only once in human history – by some unknown predecessors of the Phoenicians, who then spread it throughout the Mediterranean – so that every alphabet-based writing system that has ever existed is either descended from or inspired by that Phoenician one. But even the Phoenician system had no vowels, which diminished some of the advantages I have mentioned. The Greeks added vowels.

It is sometimes suggested that scribes deliberately limited the use of alphabets for fear that their livelihoods would be threatened by a system that was too easy to learn. But perhaps that is forcing too modern an interpretation on them. I suspect that neither the opportunities nor the pitfalls of universality ever occurred to anyone until much later in history. Those ancient innovators only ever cared about the specific problems they were confronting – to write particular words – and, in order to do that, one of them invented a rule that happened to be universal. Such an attitude may seem implausibly parochial. But things
were
parochial in those days.