## Monday, 25 May 2009

### Probabilities

In his little book, Insight, Lonergan has this wonderful remark about the relative probabilities of an unconnected aggregate of events, and a connected set of events that he calls 'scheme of recurrence.' The probability of the former, he points out, is the product of the individual probabilities, while the probability of the latter is the sum of the individual probabilities.

Since probabilities can be written in terms of fractions, it is easy to see that the product of a set of fractions is far smaller than the sum of the same set of fractions.

Which means that the probability of an event occurring jumps when it forms part of a scheme of recurrence.

Some months ago I had a wait-listed ticket from Thivim to Dadar which eventually became RAC. That meant I could board the train, but it also meant that I had only a seat: I had to share a berth with someone else. Now if you have ever shared a berth on an Indian train, you will know what that means. But my point here is different: the point is that, despite the fact that I had a rather good wait-list number (I think it was in single digits), all I got was an RAC seat, and not a proper berth. I discovered the reason for that in the train: there was a huge college tour group on the train that day. The TC pointed out that such groups do not easily change their reservations. If there was no such group, he said, I would have stood a better chance of getting a berth for myself.

Now here is an interesting situation: a group, vs a set of unconnected people. The probability of my getting a berth would have been higher in the latter case.

How would that compare with Lonergan's remarks? I am still trying to work that one out... Any help?

1. Dear Ivo

I had a similar problem doing doctroal research on Insight.
I now think what Lonergan meant was that a scheme of recurrence privileges certain types of events to re-occur, therefore their probablility is increased or added together, while probable events outside any scheme of recurrence increase the improbability of those events that are dependent on them, and therefore their improbablity is increased, or multiplied together.

Does that make sense?
Do you think that is what Lonergan meant?
Kind regard
David Legg
St Peter's College, Auckland, New Zealand.
By the way I have tried (unsuccessfully) to contact you. Do you have an email I can use to contact you personally?
My emails are:
legg.nye@ihug.co.nz (home)
dlegg@st-peters.school.nz (work)

2. Dear David,
I think you are absolutely right.
I have no problem about understanding that schemes of recurrence (SR) have a much higher probability than mere aggregates of events, and that the probability of the former is given by the sum of the individual probabilities of the events, while that of the latter is given by the product...
My problem was trying to apply this to my concrete situation!

Will be good to be in touch. My email is ivo.coelho@gmail.com

I will be attending the Lonergan Workshop later this month... Am busy preparing a paper, always hard work.

3. Dear Ivo

It's good to hear from you, I will send an email to your personal address.

Re: The train ticket problem.
If a person (say you) is considered a random individual, in relation to a situation where beneficial but probable outcomes can be gained, however, in that same situation a scheme of recurrence operates, then the members within the recurring scheme will have a higher probalility of getting the benefits, then you.

What do you think?
Can that analysis be applied to the operation of class privilege?

Cheers
David Legg
New Zealand

legg.nye@ihug.co.nz
dlegg@st-peters.school.nz