So why would the certificate numbers be out of sequence?
There is a very common sense reason as to why certificate numbers of two people born close together could be "out of sequence". It requires an understanding of "HOW" paperwork is processed. My undergraduate degree is in Industrial Technology which includes an area having to do with line queue theory, process control, and motion-and-time studies***.
Two factors (off the top of my head) for the sequence being different from a process standpoint.
1. Human based processing v. Computer based processing.
2. Parallel processing v. Serial Processing
1. Human based processing v. Computer based processing.
Humans tend to process batches of paperwork in what is known as a LIFO Order (Last In, First Out). In contrast to its counter part FIFO (First In, First Out). A clerk sits at a desk and receives batches of work to perform. Unless the process it tightly controlled (and government workers have never been known for tight control of processes) they will by default tend to process paperwork in the most convenient order. (<<-- Note that says "convenient order") The most convenient order may not be the order they were received, more than likely it is taking that which is on top of the "stack" (Last In) to be process (First out). With human processing it is very easy to see an older piece of paper (First In) be processed (Last Out) later. With human processing their is no guaranteed sequence that can be relied on. Unlike modern computer systems that run batches in sequence because they are programmed for FIFO. For example look at the printout of your credit card statement, transactions are processed FIFO down to the fractions of a second, so you better hope the payment gets in before that big charge.
2. Parallel processing v. Serial Processing
The second factor that no one mentions is parallel v. serial processing. Lets say that the government did have tight controls to ensure FIFO v. LIFO in how a clerk processes paperwork (not likely, but lest assume). Another factor is that if ALL birth records from a hospital are shipped to a central location where ONLY ONE clerk processes the data, then you can question sequence. However if transactions are processed at multiple locations and by multiple clerks then you run into sequence being off by parallel processing in two degrees (multiple locations and multiple clerks). Because the same type of paperwork is processed in different locations and by different people there is no way to control the sequence. Even if all the paperwork is processed at a single location, but by multiple clerks then you still cannot control the sequence once the paperwork is routed to the clerks. They may both use the same "log" to assign numbers, but it depends on workload and time of day as to when they get to processing their individuals "stacks". Remember it is very unlikely that the same clerk exclusively issues birth certificates, they may also processes death certificates, marriage certificates, and divorce degrees. Different clerks my work on different functions at different times.
Interesting question, thanks, I haven't had to "think" in those terms in a number of years. I'm a computer/database administrator know and computer batch processing can be quite a bit different. Things tend to get - wonky - when humans get involved.
***If you have watched the 1950's version of the movie "Cheaper by the Dozen", it had to do with Frank Gilbreth who did a lot of work in motion-and-time from a manufacturing standpoint. If you doubt me, Google "Therblig" and see what you get. It's kind of funny really, well in geeky sort of way.
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