let's start with a definition of i,

The square root of -1 is a special number we call i and it is a member of a set of numbers called the imaginary numbers.  The imaginary numbers are the set of all numbers that are the square root of negative numbers.
- The Math Forum

Q: why bother with such a seemingly frivolous and useless abstraction as i?
A: albeit abstract, i is neither frivolous nor useless, as is demonstrated below,

For most human tasks, real numbers (or even rational numbers) offer an adequate description of data. Fractions such as 2/3 and 1/8  are meaningless to a person counting stones, but essential to a person comparing the sizes of different collections of stones.

Negative numbers such as -3 and -5 are meaningless when weighing the mass of an object, but essential when keeping track of monetary debits and credits.

Similarly, imaginary numbers have essential concrete applications in a variety of sciences and related areas such as signal processing, control theory, electromagnetism, quantum mechanics, cartography, and many others.
-wikipedia

yet despite their utility, it is the highly abstract nature of
imaginary numbers that we tend to struggle with, to resist

for most of us this level of abstraction represents a barrier
that separates us from the world of higher mathematics

while for others, as shown in the video below, the abstraction
of imaginary numbers is "cool"

and it represents the first real and welcome challenge on the
road to a career in mathematics, and more importantly, to
a glimpse at truths that few can comprehend



the soundtrack of the above is an excerpt from a
BBC Radio 4 5 Numbers podcast

Related Posts:
- The World’s Most Mysterious Number
- The Fibonacci Sequence and Nature’s Number
- The Most Important Number In the Universe
- A Hierarchy of Infinities

"infinity" refers to,

several distinct concepts (usually linked to the idea of
"without end") which arise in philosophy, mathematics,
and theology.

In mathematics, "infinity" is often used in contexts where
it is treated as if it were a number (i.e., it counts or measures
things: "an infinite number of terms") but it is a different
type of "number" from the real numbers.
- wikipedia

now given that infinity is not a real number, as is 2, 6.8, pi,
it seems reasonable, if not understandable, that there is
no single infinity -

but rather, there are multiple infinities, with some larger
than others -

a hierarchy of infinites, as proposed in the video below



the soundtrack of the above is an excerpt from a BBC Radio 4
5 Numbers podcast

Related Posts:
- The World’s Most Mysterious Number
- The Fibonacci Sequence and Nature’s Number
- The Most Important Number In the Universe

what was the time of the greatest generation gap ever?

many would argue it was the mid-1960s, when such diverse
acts as the Beatles and TV bandmaster Lawrence Welk
were massively popular in America

despite their popularity, the Beatles and Welk shared
very few fans; those who favored one, generally scoffed
at others' tastes and life styles

the great majority of those who favored the Beatles
were below the age of 30, while those who favored
Welk tended to be above (often well above) that
generational dividing line

the video below features a '60s radio broadcast of
The Jean Shepherd Show

Shepherd's parody reflects how the younger generation
viewed Lawrence Welk and his fans

back in 1965, a young Bob Dylan was hailed as an
"artistic genius"

given this reputation, it is not surprising that
a reporter once asked Dylan whether he foresaw
a time when he would paint or sculpt

check out the video below for the "modern day
Michelangelo's" response



throughout his autobiography, Chronicles: Volume 1
Dylan complains of the projections and expectations
thrust upon him

he was labled, and expected to act like, a "genius",
"poet", "politician", "spokesman for a generation" . . .

and when he would contend that he "was only a musician",
there'd be a price to pay

the video below describes conditions at the center
of a black hole;

it relates these to conditions those that existed
just prior to the Big Bang;

and it points out the relevance of studying the former
to understand the latter



the above video consists of excerpts from
Stephen Hawking's Universe (1997)