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Victor Miller's avatar

Wow, did you program in LOGO? One of my jobs, many years ago, was to be the official maintainer for the PDP-10. I still have a printout listing.

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Ben Recht's avatar

When I was a kid, logo was used in an educational context. we had it on Apple IIs in elementary school. It was always cool the things you could draw with the few silly pen up, pen down, move procedures. Ah memories.

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Maxim Raginsky's avatar

It's also very cool that Seymour Papert was involved in the design of Logo and of educational methodologies based on Logo and on Piaget's theories.

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Cosma's avatar

I think there's supposed to be a figure where you have "Xxx picture" (just before the sentence "Affine transformations are a modestly more complex mixture of these two primitives."). Or perhaps the "Xxx" version of affine transforms was too racy for Substack...

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Ben Recht's avatar

haha, forgot to delete that one. Thanks!

Turns out my ability to draw something helpful in keynote while I'm drinking coffee is... um... limited.

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Austin's avatar

Just to clarify, when you write the Cartesian product C1 x C2 and get [x, z] for all x in C1 and z in C2, is [x, z] a row vector or a column vector?

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Ben Recht's avatar

my apologies., I'm trying to play a little fast and loose with notation in these blogs.

The shape of [x,z] is whatever shape you started out with. If x and z are column vectors, [x,z] is a column vector. Similarly, if x and z are row vectors, [x,z] is a row vector. If x is a column vector and z is a row vector, then you have to transpose one of them for the Cartesian product to make sense.

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