First make up some data to test.

library(ggplot2)
age<-10:45
asymptote<-2000
half<-20
coolness<-asymptote*age/(half+age)+rnorm(36,0,20)
d<-data.frame(age,coolness)

Spiral figure

g0 <- ggplot(d, aes(age, coolness)) 
g1<-g0+ geom_line() + theme_bw()
g2<-g1 +  coord_polar(theta = "x")
g2

Line

The more usual way of showing this is as line.

g1