It has surprised me to discover that some of my best-remembered learning took place at the hands of teachers I did not particularly like. One of these was a professor who introduced me, via outside reading assignments, to books by Lillian R. Lieber (1886-1986). Her free-verse-style lines in Infinity: Beyond the Beyond the Beyond gave me insights into the calculus I had recently completed as well as the set theory of my current course. (Lieber wrote not just as a mathematician but also as a human being, as a wonderfully informed and openly opinionated person. For this, too, I treasure her work.)
About her poetic-stanza-style of putting words on the page, Lieber said:
This is not intended to be
Writing each phrase on a separate line
facilitates rapid reading,
is in a hurry
Alas, the current edition of Lieber's Infinity lacks some of those chapters that were important to me in my college days. However, at sites such as abebooks.com, the early editions are available. Here, in tribute to Lieber, I offer the opening lines of Chapter 1 (formerly Chapter 2), "Infinity in the Physical World."
Of course you know that
is a subject which
has always been of the deepest interest
to all people --
to the religious,
as well as to
(The Celebrated Man-in-the-Street)
and to his mate,
And it probably interests you,
or you would not be reading this book
Now some people
make the MISTAKE of thinking that
Infinity is merely
something VERY LARGE!
But of course
what is "VERY LARGE" to one person
may seem quite small to another.
there are some peoples,
untrained in these matters,
in whose language
there is no word for
a number greater than 2 (or 3) --
after that they merely say "many" --
one, two, many!
And perhaps they think that 3 is
Others think that
the number of stars is infinite --
and yet . . .
Still others believe that
the number of grains of sand on a beach
is infinite --
and yet if one estimates
the number of grains in a small sample,
and then estimates the dimensions of the beach,
the TOTAL number of grains of sand
on any beach
turns out to be again a LARGE number
but NOT INFINITY!
. . .
Other books by Lieber are listed here in Wikipedia.