Things a few calculations tell us

Let's take the bridge, to start.

This is the GK Gokhale bridge in the northern Mumbai suburb of Andheri—a vital east-west connector across the railway tracks. In 2022, recognizing that it was old and dilapidated, the municipal corporation demolished it and promised to build a new bridge.

The months since have been a nightmare for commuters in the area. Without that bridge, getting across the railway has meant a long detour. Naturally, everyone has been waiting eagerly for the new bridge to be completed. It was, a few weeks ago. Or really, as these things go these days, one part of it was completed and "inaugurated" for public use. And that's when we found something remarkable about this new bridge.

Connecting to the old bridge was a ramp from what's known as the Barfiwala flyover. Traffic that needed to go to where this flyover led would simply shift onto the ramp. With the new bridge, though, there's a problem stemming from a particular design decision: the new bridge is about 2m higher than the old bridge. Thus the Barfiwala flyover does not connect to the new roadway. As things stand, as I write this, the BMC is searching for a remedy.

“What led to this?" and “Why?" are good questions that have their answers. But I'm interested here in the BMC's explanation for this disconnect ("Clarification regarding comments/reels appeared in social media and newspapers", BMC notification No ChE/16082/Bridges of 28 February 2024).

The problem, says the BMC, is that a connector between the Barfiwala flyover and the new Gokhale bridge would need to have a "vertical gradient" of 7.25%. This, claims the BMC, would cause engine noise and trouble, discomfort to passengers, and more.

What is a 7.25% gradient? It means that for every 100m length that such a road slopes upwards, it ascends 7.25m. This is steep, but not excessively so, not unknown. In Mumbai's Bandra, for example, you'll find Zig Zag Road. Over its 100 metres, it ascends about 13m to Pali Hill, meaning its gradient is 13%. On the other side of the same hill, a 200m stretch of road to the sea sees a descent of 15m: a 7.5% gradient. Admittedly neither road is like a major flyover, but both stretches see plenty of traffic in both directions without any particular engine trouble or passenger discomfort. Besides, the possible Gokhale-Barfiwala connector will be, as best as I can tell from maps, about 20m long. And that's if another, less sloped solution isn't found. So, is the BMC seriously warning us about passenger discomfort and the like, over a stretch that's just 20m long?

Then there's the State Bank of India. When the Supreme Court ruled electoral bonds unconstitutional in mid-February, the judges also asked SBI—the sole vendor of these bonds—to submit details of all bonds so far sold by 6 March. Two days before that deadline, SBI told the Court that this was a near-impossible task, and asked for an extension until 30 June. Just incidentally, of course, 30 June is after the upcoming Lok Sabha elections.

What was SBI's reasoning underlying its demand for a delay? There were some 22,500 bonds sold, they claimed, and there was something about how the records of these bond purchases were stored in two different places. The actual details are not as important as this apparently daunting number: There are effectively 45,000 records to consider, collect, collate, correlate, and whatever else is required to be done to submit the information to the Court. This gargantuan effort, said SBI, would take till 30 June.

Numbers again. Just as I was mulling them over, just as I was about to make some tentative calculations to gauge how weighty this task really is, I got a message from my friend Shailesh Gandhi, the former Central Information Commissioner. For he had just attempted the same calculation.

Here's how we thought about it:

Again, SBI claims there are about 45,000 transactions. Let's assume all these records have to be copied from paper onto a computer. A competent data-entry operator, let's also assume, would take three minutes over each transaction. That means she should be able to enter 120 transactions in a six-hour day; no point pushing her to work longer on this stultifying job. This means we will need 375 person-days to finish all 45,000 entries.

Not that weighty, really. Put 30 SBI employees on the job and they will be done on day 13. If they had got going on the day of the original Supreme Court ruling, 15 February, the job would have been complete by the end of February. That would have left a clear week more to package all the data elegantly and, for good measure, even tie a virtual ribbon around it.

Of course, when the Supreme Court refused to allow an extension till 30 June, SBI submitted the records within two days. Clearly they were far more diligent than our back-of-the-envelope calculations above suggest.

Sticking with Shailesh Gandhi: Another of his calculations involves case backlogs in our courts. The numbers seem staggering: The backlog across all our courts amounts to some 50 million cases—a clear world record. What is the hope that we will ever catch up?

Gandhi points out that this enormous backlog "has often been ascribed to the fact that there are not [an] adequate number of judges". The Supreme Court suggests that we must have 50 judges per million population, which means about 70,000 altogether. Compare with a currently-sanctioned strength of 23,000, though across our courts about 21% of those positions are vacant. Do we need to triple or quadruple the number of judges we have, to address the backlog?

This prompted Gandhi to "try and figure out how many judges would be required to ensure that the pendency would reduce". He did this by analyzing publicly-available data for the years 2006-17 on the Supreme Court website. That told him that that "the average increase in pendency was less than 3% per year."

Think of that. If we can simply fill the 21% vacancies, the pendency will automatically stop increasing. (Gandhi's calculations are a little, but only a little, more intricate.) In fact, we will start eating into that 50 million backlog.

The things a few calculations can tell us.

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun.