TELEMETRY AND JUGGLING

Abstract

One of the beauties of mathematics is its ability to demonstrate the relationship between apparently unrelated subjects. And this is not only an aesthetic attribute. The insight obtained by seeing relations where they are not obvious often leads to elegant solutions to difficult problems. This paper will demonstrate a mathematical relation between telemetry and juggling. Any given pulse code modulation (PCM) format can be mapped onto a juggling pattern. The Inter-Range Instrumentation Group (IRIG) 106 Class I PCM formats are a subset of all juggling patterns while the Class II PCM formats are equivalent to the set of all juggling patterns (within some mathematically precise definitions). There are actually quite a few mathematical results regarding juggling patterns. This paper will also discuss how these topics relate to tessellations, bin packing, PCM format design, and dynamic spectrum allocation. One of the shortcomings of human nature is the tendency to get caught up in a particular topic or viewpoint. This is true of the telemetry community as well. It is hoped that this paper will increase the awareness that there are a variety of areas of theory outside of telemetry that may be applicable to the field.