Tensors and Love
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I found unexpected wisdom in World Scientific’s attempt to define what a tensor is:
(https://www.worldscientific.com › doi › pdf)
Chapter 1 Confusions: What Are Tensors Exactly?
Chapter 1 starts by posing this profound question:
“What do love and tensor have in common?” and then proceeds by trying to find answers to the question “What is love?”
Apparently equating the depth of the reader’s ignorance about tensors with the degree of innocence that children have about the meaning of Love, we are first treated to a priceless collection of definitions from kids in pre- and elementary school:
“Love is when a girl puts on perfume and a boy
puts on shaving cologne and they go out and smell each
other.” (age 5)
“Love is when you tell a guy you like his shirt, then
he wears it every day.” (age 7)
“If you want to learn to love better, you should start
with a friend who you hate.” (age 6)
“Love is when mommy sees daddy smelly and sweaty
and still says he is handsomer than Robert Redford.”
(age 8)
“Love is when your puppy licks your face even after
you left him alone all day.” (age 4)
“Love is when you kiss all the time. Then when you
get tired of kissing, you still want to be together and you
talk more.” (age 8)
“I know my older sister loves me because she gives
me all her old clothes and has to go out and buy new
ones.” (age 4)
“I let my big sister pick on me because my mom says
she only picks on me because she loves me. So I pick on
my baby sister because I love her.” (age 4)
and then the author elaborates on the equivalence of the two problems:
“Each of these answers certainly tells some aspect of the truth.
What do love and tensor have in common? Is the love between sisters
the same as that between mom and dad, dating teenagers, and dogs and
humans? Compare with the question: is the tensor in machine learning
the same as those in mathematics and physics?
The concept of love is abstract and complex, and it has never been
rigorously defined. The tensor is also abstract and complex. It was
poorly defined in the past. There are rigorous modern definitions, but
at a cost of being more abstract and less intuitive. So the old-fashioned
definition is hard to understand because it is not rigorous; the modern
definition is hard to understand because it is rigorous. It is the goal of
this book to explain the rigorous definitions of tensor in an intuitive way,
so that students no longer have to recite those definitions like a parrot.”
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❤️