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wherever
Those signs are older than you are, and some date back to before the trail was upgraded
I wouldn't bet on it. I may not be old, but I've been young for a very long time.
I found some info here that says those steel signs with burned-through lettering date back to the 1950s:
http://www.yosemite.ca.us/library/yosemite_resources/recent_years.html#page_771Quote
Another sign type in the war years [1940s] involved routing white-painted letters on 1-1/2-inch-thick redwood planks about four feet above the trail, but these also fell prey to bears, perhaps attracted to the oil used, as well as to hikers for campfires, souvenirs, or simply as acts of vandalism. A last resort in the 1950s involved burning lettering into iron plates and cementing the signposts into place.31
[31. Bert Sault to Jim Snyder, 9 July 1975, in Separates File, Yosemite-Trails, Y-46, #42, Yosemite Research Library and Records Center. Evidently Landscape Architect Thomas Vint was not favorably impressed with the new iron signs for aesthetic reasons, but agreed that they were necessary to solve the problem of signage in the backcountry. Notes taken by Carl P. Russell, “Conference July 30, 1952,” in Box 78, Box A—NPS files, 1938-1953, Development Part XII, Yosemite Research Library and Records Center. The metal sign program in Yosemite was initiated with designs by signmaker Lee Buzzini and welder Bill Kirk. Douglas H. Hubbard, “Yosemite Bears Chip Teeth,” Yosemite Nature Notes 34, no. 3 (March 1955).]
So "Big Red" must be an example of the first kind of sign. I wonder if it's actually the original from the 1940s or if NPS has replaced it with another one of the same kind. For whatever reason, it seems to have survived unburned, unvandalized, and ungnawed.