Today I went to a tracking page for Ikea’s delivery company and saw that the shipment weight was said to be “248.678880000 lbs.” This is, of course, impossible. The alert reader will perhaps already know where I am going with this. Why is this impossible? It is impossible because no commercially available scale is able to weigh things to a precision of eight significant digits. Expressed in colloquial terms, there is no scale that you or I could ever conveniently be in the same room with that would be able to distinguish between something that weighs 248.67888 pounds or 248.67889 pounds or 248.67887 pounds.
The chemistry laboratory triple-beam balance that we all used in our analytical chemistry class in college had a precision of, at best, maybe one part in one million, or at most six significant digits. So it is completely illusory for this delivery company to give the impression that it knows the weight of the Ikea shipment to eight significant digits.
Indeed the presence of the four trailing zeroes on the number might be interpreted as a representation to the reader that the value is actually known to twelve significant digits, which is laughably past being merely illusory.
It’s one thing to get this kind of thing wrong if you are a web site designer but it’s quite another if you are a patent practitioner. From time to time I run into issued patents where similar missteps have been made. See for example US patent number 6325012 which talks about an undersea habitation bubble 19 connected via a passage 20 to a mainland outside location 22. (Yes, the surface of the water is shown in this figure as sloping, which would never happen in real life.) At column 4 the practitioner says:
The air going out through the air-discharge tube is pushed out by means of the condensation unit fan by using the pressure difference between the bubble (202.650 kPa) and outside pressure (101.325 kPa) and using this parameter and the required flow, the return tube (air-discharge to main land) diameter has been calculated by using Muller’s formula.
Here the practitioner refers to the pressure at each of the two locations using six significant digits. The practitioner showed a bit of cluelessness given that most commercial gas or liquid pressure measurement sensors have a precision of no better than about 0.1% or at most about four significant digits. So it is illusory for the practitioner to suggest that the pressure in the bubble might be known to six significant digits and that the pressure outside might likewise be known to that precision. (Imagine the poor impression that this might make for a better-informed patent examiner!)
In the case of this US patent, it is very easy to work out the source of the blunder. The source document from the inventor surely referred to the air pressure at sea level as “1 atmosphere” and then somewhat arbitrarily assumed that the bubble might be at a depth of around two atmospheres. (Such a depth is around twenty meters or around sixty feet.) What probably happened next is that the patent practitioner decided that “one atmosphere” and “two atmospheres” somehow did not sound fancy enough or scientific enough. Or maybe the patent practitioner had heard in some CLE presentation that it is a good idea to use metric units when you are writing a patent application. Or maybe the patent practitioner realized that to justify the bill that was going to get sent to the client, the patent application as filed desperately needed to look different from the original disclosure document from the inventor. Anyway, for one or more of these reasons, the patent practitioner then looked up somewhere to find out the ten-dollar-word way to say “one atmosphere”, and read that this is 101.325 kiloPascals. In which case two atmospheres would be 202.650 kiloPascals. And that is what got stuffed into the patent application.
The original numbers from the inventor were at best a single significant digit, if that. But the patent practitioner gave a completely false impression that the pressures were being measured to six significant digits.
How do you feel about significant digits? What do you recall from your first-year physics class about the difference between accuracy and precision? What fond memories of your analytical chemistry class remain with you today, that you might like to share? Please post a comment below.