Dead Root briar is a subject that has been beaten, if you’ll pardon me, to death. Some insist the legends are true, while others (especially briar cutters, who really ought to know, and many pipe makers who laugh when they hear the term) tell me that once the shrub dies, the burls are almost instantly attacked by decomposers (molds and fungi, beetles, bacteria), and within a very short period, are rendered unsuitable for pipe making. In fact, at least today, they don’t even harvest these because of the considerable effort involved, and the low probability of any useable wood being found within them.
The term most likely found its way into use in the early part of the Twentieth Century through the marketing genius of Alfred Dunhill when he sought a way to differentiate exceptionally grained pipes from the rest. At the time, grain was not as highly valued as it is today, so making this distinction allowed him to sell these pipes for premium prices. The term stuck, and the legend has been promulgated by a few others since to differentiate their best pipes from the run of the mill.
The one thing we can be sure of is that by the time a block of wood is crafted into a pipe, it is most certainly and surely dead; in effect, all pipes are made from dead root.
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There are a great many myths present in the lore of pipe smoking, including the smoking characteristics of briar of different provenance, the magical qualities of the rare (in fact, non-existent) "Dead Root" briar, the effects of arcane incantations over the wood by some makers, and so on. But, that lore, those myths are part of the romance, and romance, at least to me, is a very important part of the overall experience.
Myth or Fact is of little import, really. What matters is that we enjoy what we smoke, and smoke what we enjoy. If it gives a fellow pleasure to imagine the burl from which is pipe was made struggling in the hot Algerian sun for centuries before finally being captured, and brought to life in the form of the pipe, then so be it.