The amount of terror that lives in a speaker’s stomach when giving a lecture is proportional to the square of the amount he doesn’t know about his audience.
Knuth’s point is about preparation, and it brings to mind the words of Benjamin Franklin, “By failing to prepare, you are preparing to fail”.
It’s essential to find out as much as possible about your audience, not just so that you feel more confident, but also so that what you deliver is appropriate for that audience.
As academics we are used to giving seminars and conference talks for which we know that the audience will be made up of peers, and we usually just need to ascertain where to aim the talk on the axes general researcher–specialist and graduate student–experienced researcher.
For any other talk it is important to go to some effort to find out who will be in the audience, perhaps asking for a list of attendees if the event requires registration. For an after-dinner talk you may want to know whether certain key people who you are thinking of mentioning will be in the audience. For a talk to a general audience you will want to assess the base level of technical knowledge that can be assumed.
Keep these thoughts in mind when that sought-after invitation to give a “TED talk” arrives in your mailbox.
My previous post was about the launch meeting of SIAM Student Chapter at Cardiff, at which I gave the opening talk. My talk was titled Accuracy and Stability of Numerical Algorithms and covered rounding of (floating point) numbers, the interplay between precision and accuracy, higher precision computations, and the effect of tiny relative errors on performance profiles.
Here I describe four examples that I gave where rounding, or the choice of rounding mode, can have interesting or surprising (to some) effects.
In 2006 Justin Gatlin was credited with a new world record of 9.76 seconds for the 100m. Almost a week after the race, the time was changed to 9.77 seconds, meaning that he had merely equalled the existing record held by Asafa Powell. The reason for the change was that his recorded time of 9.766 has incorrectly been rounded down to the nearest hundredth of a second instead of up as the IAAF rules require.
In 2008 the Mail on Sunday got agitated by the possibility that whether or not the UK inflation target of 3% would be exceeded (and it was exactly 3% at the time) could depend on a change of one thousandth of a percent. They realized that since the inflation rate is published to one decimal place, a rate of 3.049 would round down to 3.0% but 3.050 would round up to 3.1% (since ties are rounded up in UK government calculations) and mean the target had been missed.
In 1983 the Vancouver stock exchange found that its index had halved over the year since it had been founded. It turned out that the index had been rounded down after every calculation. When the index was recomputed (presumably with round to nearest, though my reference doesn’t say) it doubled.
My telephone and cable provider, Virgin Media, wrote to me in 2007 with news about pricing. They had decreased the cost of my cable and line rental package. They had also changed the way calls charges are calculated by “rounding up to the next minute” instead of “charging to the nearest second” as before. They gave the example that “a call that lasts 4 minutes 50 seconds will be rounded up to 5 minutes”. What they didn’t mention is that a call that lasts 4 minutes 1 second will also be rounded up to 5 minutes!