Re: Modification of what I said

[Ross Street <ross.street@mq.edu.au>]

Permit me to perturb this modification further in the Whitney direction.

As a grad student I knew about Hassler Whitney in connection with homological algebra and cohomology.
These are very categorical subjects! In 1980 André Joyal was visiting Sydney. He was lecturing us in our
Seminar on using toposes for differential geometry.
[André's night job then was writing ``Une théorie combinatoire des séries formelles, Adv. Math. 42 (1981)''.]
In connection with smooth functions \phi on the reals satisfying \phi(-x) = \phi(x), André quoted a result of Whitney.
I was not conscious of Whitney's work on manifolds before that.

In any case, around that time, Hassler Whitney appeared in our staff common room.
[In those days, people met in the ``tea room'' for lunch as a matter of course.]
Whitney was not there because of math research, he was visiting our Numeracy Centre.
When I was at Wesleyan University in 1976-77, I learnt about the ``Math Anxiety Clinic'',
a concept which, I believe, started there. We had a need for such a centre at Macquarie
because a math course was mandatory for students planning to teach primary school and
many of them, through no fault of their own, were terrified of that.

I took an immediate liking to Whitney. He had grandchildren and I had two children.
Whitney had taken a keen interest in Math Anxiety and in teaching math to the young.
He pointed out that, when his grandchild was setting the table for supper, they would not say
there are 6 people, so I need 6 forks. They would say: one fork for Mommy, one for Daddy,
one for sister, one for brother, one for me, and so on. A bijection!

My point is that we have heard in this forum about Whitney's categorical thinking in his
early career. I am claiming that he was still at it throughout his interesting life.

[By the way, our Numeracy Centre is still in demand and thriving under the leadership of Carolyn Kennett.]

Ross

> On 19 Dec 2023, at 4:44 pm, Dusko Pavlovic <duskgoo@gmail.com> wrote:
>
> The nice thing about this reference to Whitney is that it explains why Eilenberg and MacLane's Kantian naming taste was applied to *categories* and *functors* but abandoned when it came to 'natural transformations'. I was always wondering why we have been deprived of the pleasure of talking about, say, *transcendental* transformations all these years...



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