Measurement Problems in Ancient Greece – IAS Fellows Public Lecture

Yesterday there was an IAS Fellows Public Lecture hosted at St John’s college, Durham. The Speaker was Dr Barbara Sattler of the University of St Andrews. Her theme was to peel back some of the concepts we now take for granted to show some of the elements which had to be constructed from scratch, as it were, to enable the development of the concepts of time and speed.

It was a relatively short lecture with time for a Q&A session at the end.

She started by pointing out that at the time of Aristotle there were conversations happening about scale but that before we get to these complex comparative concepts the ancient Greeks needed to develop the basic components.

To illustrate this idea of measurements pre-scale she pointed out that we would all instinctively understand her if she said she drove to Durham from Newcastle at 60mph. We can see this from our speedometers – which are much more impressive than we often recognise!

60 mph is speed.

This is made up of the components of distance and time placed in relationship to each other. Mile per hour. Here we divide, but there are other concepts where we multiply. The important thing is the relationship.

Dr Sattler then turned to  time and distance.

In Aristotle’s ‘Physics’ Time is a measure of motion and being moved. It wasn’t bound to the idea of distance.

She then described how they had no real way to compare ships with one another. To do this they needed to figure out how to put two magnitudes together in relation with each other. So Dr Sattler gave three scenarios which built on one another to build the complexity of speed.

As we are in Durham rather than Athens, and given the strength of the female amateur rowing team here in Durham, these scenarios were  a variety of boat races on the river Wear between various bridges in Durham.

The first ‘race’ was between two boats starting at the same time from one bridge and racing to the next bridge. The winner is clear, we can see who gets to the next bridge first (obviously that would be St John’s!).

The second ‘race’ covered the same stretch but this time with a staggered start. So the St. John’s boat starts and then 20 seconds later the St. Chad’s boat starts. Is it now as easy to say that when the St John’s boat reaches the end first, that they do so faster than St Chad’s? We can’t tell just from observation.

The third ‘race’ involves each boat covering a different part of the river, with different distances to travel. How can we tell who is faster?

We need both time and distance.

Boat A does 300m in 75 seconds.
Boat B does 100m in 40 seconds.

Which is faster?

Without knowing the measurements all we can say is:

Boat B takes less time.
Boat A covers more distance.

When we know the separate magnitudes we can put them in relation to discover the speed.
Boat A  goes at 4m per second.
Boat B goes at  2.5m per second.

So, Boat A is faster

These scenario’s show us that speed is complex.

Dr Sattler suggests that Aristotle has everything he needs to develop this but doesn’t do it.

She then steps back to look at time.

In Ancient Greece there was:

1. No unified calendar
2. No unified temporal framework

If we were to say that yesterday there was this lecture, and there was a film on in the cinema and that it was someone’s birthday we wouldn’t have a problem because we assume a shared calendar. Each of these things happened on February 16th 2017.  Even if there’s no causal relation they have a temporal relation by being able to be put in the same calendar.

The Greeks, though, had different calendars in different places and even when in one place there would often be more than one calendar. Athens, for example, is known to have had three calendars.

There was one for festivals based on the lunar cycle with 12 months.
There was a political one based on the solar cycle of ten months.
Then there was the agricultural, seasonal calendar based on the movements of the stars.

One of the results of this is that it is often quite hard to distinguish which year an event happened in. Events were not identified numerically but in relation to who ever was in power.

This works great for identifying events which have happened but makes the future intangible. You can’t identify the future when you don’t know who will be in charge.

To further complicate things, the calendars were not rigid systems but were used to serve the purposes of the people. This means that they would adjust them to serve their purposes. Occasionally they would repeat a month to help hold the calendars closer together in sync.

This lack of a unified calendar leads us to consider their lack of a unified temporal framework.

Relationship between past present and future are not Connected in the linear way that we understand them now. However the future and the past were related in a way in that they are both not the present.

Dr Sattler identified five different senses of ‘time language’

Measurable time

Chronos, a Greek word for time, was used to indicate a particular time.

The use of  words such as before and after. Interestingly these words often qualified objects and people rather than time per se.

Measurable time:
Concepts such as Day, Month, and Year. These concepts were only connected with the word chronos in the 5th Century BCE which gives chronos it’s more linear conception that we might be more familiar with.  There’s still a difference between the way that they conceived of these concepts. They were not just used as quantitative words but also with a qualitative dimension as well.

There was the Greek word kairos which was used to signify the right or critical time for an event or action. Apparently this was especially important in the medical language used in the Hippocratic Corpus with regards to treatments and so on.

The last aspect of time that Dr Sattler looked at was the concept of tenses. She described these as acting much more with the ‘arrow’ or directional nature of time. One of the interesting aspects which comes with the present tense is the idea of what I would refer to as ‘objective’ truths, or that which has been and will remain true – it is.

These different elements of the concept of time show that for the Ancient Greeks time was something which was experienced. More so than for us, their experience was anchored in the present moment and from that moment they would look back at the past and then look forward to the future. It sounds similar to our linear perspective of time where we tend to assume a sense of progression and trajectory from the past into the future but actually the idea of having a perspective rooted in the moment and looking from there, both forwards and backwards, is not a linear conception of time.

Dr Sattler concluded by observing that ‘the future’ was a relatively late concept to be developed in Ancient Greek thought.

There were then some interesting questions which followed.

She was asked about the Simultaneous in Greek thought.

She responded that Homer seems to have struggled with indicating concurrent events but to mistake this for an idea of bilocation would be to shift from the complex ideas involved thinking about time to the equally complex ideas surrounding the philosophical development of the concept of place.

There was a question about the relationship between the idea of telos or purpose and time.

She responded that Plato seems to be aware of it but laments that it wasn’t a part of the metaphysical frameworks which were passed down by the philosophers.

There was another question which picked up on the objective truths element and wondered if there were any examples she would offer.

In fairness to her the idea of universal truths tends to be a more moral question and so she left it at the acknowledgement that it’s hard to find a general consensus on what those truths might be.

Overall this was an interesting lecture. It would be easy to say that we didn’t learn anything “new” about time, however that would be to miss the point. The point is that we operate instinctively with complex and sophisticated concepts of time and speed, rarely acknowledging the significance of the conceptual work that was required to bring us to the point where we can nonchalantly book in a date for a wedding next summer in our calendars on our phones or adjust our speed to match the limits on different roads.

That’s a fun idea to think about next time you see your speedometer or check your calendar.


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