63 is a centered octahedral number. That means if you build an approximation of an octahedron with cubes, one size of octahedron will have 63 cubes.

In the late 1700’s René Just Haüy developed a theory about how crystals formed: successive layers of fundamental primitives in orderly arrangements. One of those arrangements was stacking cubes together to make an octahedron.

Start with one cube:

Add six more cubes around it, one on each face. Now we have seven:

Add another layer, adding a cube to touch each visible cube, making 25:

One more layer and we have a total of 63:

The remaining numbers in the sequence less than 10,000 are 129, 231, 377, 575, 833, 1159, 1561, 2047, 2625, 3303, 4089, 4991, 6017, 7175, 8473, 9919.

63 also shows up in the Delannoy numbers: the number of ways to traverse a grid from the lower left corner to upper right using only steps north, east, or northeast. Here are the 63 ways of moving on a 3×3 grid:

(Diagram from Wikipedia)

In fact, the number of cubes in a Haüy octahedron with N layers is the same as the number of Delannoy steps on a 3×N grid!

Since the two ideas are both geometric and fairly simple, I would love to find a geometric explanation for the correspondence. The octahedron is three-dimensional, and the Delannoy grids have that tantalizing 3 in them. It seems like there should be a way to convert Haüy coordinates to Delannoy coordinates to show how they relate. But I haven’t found one...

•    •    •

Colophon: I made the octahedron diagrams by asking Claude to write a Python program to do it. It wasn’t a fast process because it took pushing and prodding to get the diagrams to come out the way I liked. But Claude was very competent, and I could think about the results rather than about projections or color spaces. I could dip into it for 10 minutes at a time over a number of days without having to somehow reconstruct a mental context.

This kind of casual hobby programming is perfect for AI assistance. I don’t need the code to be perfect or even good, I just want the diagrams to be nice. I don’t have the focus time to learn how to write the program, so I can leave it to an imperfect assistant.

Today is the 39-year anniversary of my first day working for Digital Equipment Corporation. It was my first real job in the tech world, two years out of college. I wrote about it 19 years ago, but it’s on my mind again.

More and more, I find that people have never heard of Digital (as we called it) or DEC (as they preferred we didn’t call it but everyone did). It’s something I’ve had to get used to. I try to relate a story from that time, and I find that even experienced engineers with deep knowledge of technologies don’t know of the company.

I mention this not in a crabby “kids these days” kind of way. It does surprise me, but I’m taking it as a learning opportunity. If there’s a lesson to learn, it is this:

This too shall pass.

I am now working for Netflix, and one of the great things about it is that everyone has heard of Netflix. I can mention my job to anyone and they are impressed in some way. Techies know it as one of the FAANG companies, and “civilians” know it for the entertainment it produces and delivers.

When I joined Digital in 1986, at least among tech people, it was similar. Everyone knew about Digital and what they had done: the creation of the minicomputer, the genesis of Unix and C, the ubiquitous VT100. Many foundations of the software world flowed directly and famously from Digital.

These days Digital isn’t quite yet a footnote to history, but it is more and more unknown even among the most tech-involved. And the tech world carries on!

My small team at Netflix has a number of young engineers, less than two years out of college, and even an intern still in college. I’m sure they felt incredibly excited to join a company as well-known and influential as Netflix. In 39 years when they tell a story from the early days of their career will they start with, “Have you heard of Netflix?” and have to adjust to the blank stares they get in return?

This too shall pass.

I’m headed to PyCon today, and I’m reminded about how it feels like summer camp, in mostly good ways, but also in a tricky way.

You take some time off from your “real” life, you go somewhere else, you hang out with old friends and meet some new friends. You do different things than in your real life, some are playful, some take real work. These are all good ways it’s like summer camp.

Here’s the tricky thing to watch out for: like summer camp, you can make connections to people or projects that are intense and feel like they could last forever. You make friends at summer camp, or even have semi-romantic crushes on people. You promise to stay in touch, you think it’s the “real thing.” When you get home, you write an email or two, maybe a phone call, but it fades away. The excitement of the summer is overtaken by your autumnal real life again.

PyCon can be the same way, either with people or projects. Not a romance, but the exciting feeling that you want to keep doing the project you started at PyCon, or be a member of some community you hung out with for those days. You want to keep talking about that exciting thing with that person. These are great feelings, but it’s easy to emotionally over-commit to those efforts and then have it fade away once PyCon is over.

How do you know what projects are just crushes, and which are permanent relationships? Maybe it doesn’t matter, and we should just get excited about things.

I know I started at least one effort last year that I thought would be done in a few months, but has since stalled. Now I am headed back to PyCon. Will I become attached to yet more things this time? Is that bad? Should I temper my enthusiasm, or is it fine to light a few fires and accept that some will peter out?

Coverage.py has a large test suite that runs in many environments, which can take a while. But some changes don’t require running the test suite at all. I’ve changed the actions to detect when they need to run based on what files have changed, but there were some twists and turns along the way.

The dorny/paths-filter action can check which files have changed for pull requests or branches. I added it to my tests action like this:

jobs:

  changed:
    name: "Check what files changed"
    outputs:
      python: ${{ steps.filter.outputs.python }}
    steps:
      - name: "Check out the repo"
        uses: actions/checkout

      - name: "Examine changed files"
        uses: dorny/paths-filter
        id: filter
        with:
          filters: |
            python:
              - "**.py"

  tests:
    # Don't run tests if the branch name includes "-notests".
    # Only run tests if Python files changed.
    needs: changed
    if: ${{ !contains(github.ref, '-notests') && needs.changed.outputs.python == 'true' }}

The “changed” jobs checks what files have changed, then the “tests” job examines its output to decide whether to run at all.

It’s a little awkward having an output for the “changed” job as an intermediary, but this did what I wanted: if any .py file changed, run the tests, otherwise don’t run them. I left in an old condition: if the branch name includes “-notests”, then don’t run the tests.

This worked, but I realized I needed to run the tests on other conditions also. What if no Python file changed, but the GitHub action file itself had changed? So I added that as a condition. The if-expression was getting long, so I made it a multi-line string:

jobs:

  changed:
    name: "Check what files changed"
    outputs:
      python: ${{ steps.filter.outputs.python }}
      workflow: ${{ steps.filter.outputs.workflow }}
    steps:
      - name: "Check out the repo"
        uses: actions/checkout

      - name: "Examine changed files"
        uses: dorny/paths-filter
        id: filter
        with:
          filters: |
            python:
              - "**.py"
            workflow:
              - ".github/workflows/testsuite.yml"

  tests:
    # Don't run tests if the branch name includes "-notests".
    # Only run tests if Python files or this workflow changed.
    needs: changed
    if: |
      ${{
        !contains(github.ref, '-notests')
        && (
          needs.changed.outputs.python == 'true'
          || needs.changed.outputs.workflow == 'true'
        )
      }}

This seemed to work, but it has a bug that I will get to in a bit.

Thinking about it more, I realized there are other files that could affect the test results: requirements files, test output files, and the tox.ini. Rather than add them as three more conditions, I combined them all into one:

jobs:

  changed:
    name: "Check what files changed"
    outputs:
      run_tests: ${{ steps.filter.outputs.run_tests }}
    steps:
      - name: "Check out the repo"
        uses: actions/checkout

      - name: "Examine changed files"
        uses: dorny/paths-filter
        id: filter
        with:
          filters: |
            run_tests:
              - "**.py"
              - ".github/workflows/testsuite.yml"
              - "tox.ini"
              - "requirements/*.pip"
              - "tests/gold/**"

  tests:
    # Don't run tests if the branch name includes "-notests".
    # Only run tests if files that affect tests have changed.
    needs: changed
    if: |
      ${{
        needs.changed.outputs.run_tests == 'true'
        && !contains(github.ref, '-notests')
      }}

BTW: these commits also update the quality checks workflow which has other kinds of mix-and-match conditions to deal with that you might be interested in.

All seemed good! Then I made a commit that only changed my Makefile, and the tests ran! Why!? The Makefile isn’t one of the checked files. The paths-filter action helpfully includes debug output that showed that only the Makefile was considered changed, and that the “run_test” output was false.

I took a guess that GitHub actions don’t like expressions with newlines in them. Using the trusty YAML multi-line string cheat sheet, I tried changing from the literal block style (with a pipe) to the folded style (with a greater-than):

if: >
  ${{
    needs.changed.outputs.run_tests == 'true'
    && !contains(github.ref, '-notests')
  }}

The literal form includes all newlines, the folded style turns newlines into spaces. To check that I had it right, I tried parsing the YAML files: to my surprise, both forms included all the newlines, there was no difference at all. It turns out that YAML “helpfully” notices changes in indentation, and includes newlines for indented lines. My expression is nicely indented, so it has newlines no matter what syntax I use.

The GitHub actions docs don’t mention it, but it seems that newlines do break expression evaluation. Sigh. My expressions are not as long now as they had gotten during this exploration, so I changed them all back to one line, and now it all works as I wanted.

There are some other things I’d like to tweak: when the tests are skipped, the final status is “success”, but I’m wondering if there’s a way to make it “skipped”. I’m also torn about whether every change to master should run all the workflows or if they should also filter based on the changed files. Currently they are filtered.

Continuous integration and GitHub workflows are great, but they always seem to involve this kind of fiddling in environments that are difficult to debug. Maybe I’ve saved you some grief.

Python regexes have a number of features that bring new power to text manipulation. I’m not talking about fancy matching features like negative look-behinds, but ways you can construct and use regexes. As a demonstration, I’ll show you some real code from a real project.

Coverage.py will expand environment variables in values read from its configuration files. It does this with a function called substitute_variables:

def substitute_variables(
    text: str,
    variables: dict[str, str],
) -> str:
    """
    Substitute ``${VAR}`` variables in `text`.

    Variables in the text can take a number of
    shell-inspired forms::

        $VAR
        ${VAR}
        ${VAR?}         strict: an error if no VAR.
        ${VAR-miss}     defaulted: "miss" if no VAR.
        $$              just a dollar sign.

    `variables` is a dictionary of variable values.

    Returns the resulting text with values substituted.

    """

Call it with a string and a dictionary, and it makes the substitutions:

>>> substitute_variables(
...     text="Look: $FOO ${BAR-default} $$",
...     variables={'FOO': 'Xyzzy'},
... )

'Look: Xyzzy default $'

We use a regex to pick apart the text:

dollar_pattern = r"""(?x)   # Verbose regex syntax
    \$                      # A dollar sign,
    (?:                     # then
        (?P<dollar> \$ ) |      # a dollar sign, or
        (?P<word1> \w+ ) |      # a plain word, or
        \{                      # a {-wrapped
            (?P<word2> \w+ )        # word,
            (?:                         # either
                (?P<strict> \? ) |      # strict or
                -(?P<defval> [^}]* )    # defaulted
            )?                      # maybe
        }
    )
    """

This isn’t a super-fancy regex: it doesn’t use advanced pattern matching. But there are some useful regex features at work here:

• The (?x) flag at the beginning turns on “verbose” regex syntax. In this mode, all white space is ignored so the regex can be multi-line and we can indent to help see the structure, and comments are allowed at the ends of lines.
• Named groups like (?P<word1> … ) are used to capture parts of the text that we can retrieve later by name.
• There are also two groups used to get the precedence of operators right, but we don’t want to capture those values separately, so I use the non-capturing group syntax for them: (?: … ). In this code, we only ever access groups by name, so I could have left them as regular capturing groups, but I think it’s clearer to indicate up-front that we won’t be using them.

The verbose syntax in particular makes it easier to understand the regex. Compare to what it would look like in one line:

r"\$(?:(?P<dollar>\$)|(?P<word1>\w+)|\{(?P<word2>\w+)(?:(?P<strict>\?)|-(?P<defval>[^}]*))?})"

Once we have the regex, we can use re.sub() to replace the variables with their values:

re.sub(dollar_pattern, dollar_replace, text)

But we’re going to use another power feature of Python regexes: dollar_replace here isn’t a string, it’s a function! Each fragment the regex matches will be passed as a match object to our dollar_replace function. It returns a string which re.sub() uses as the replacement in the text:

def dollar_replace(match: re.Match[str]) -> str:
    """Called for each $replacement."""
    # Get the one group that matched.
    groups = match.group('dollar', 'word1', 'word2')
    word = next(g for g in groups if g)

    if word == "$":
        return "$"
    elif word in variables:
        return variables[word]
    elif match["strict"]:
        msg = f"Variable {word} is undefined: {text!r}"
        raise NameError(msg)
    else:
        return match["defval"]

First we use match.group(). Called with a number of names, it returns a tuple of what those named groups matched. They could be the matched text, or None if the group didn’t match anything.

The way our regex is written only one of those three groups will match, so the tuple will have one string and two None’s. To get the matched string, we use next() to find it. If the built-in any() returned the first true thing it found this code could be simpler, but it doesn’t so we have to do it this way.

Now we can check the value to decide on the replacement:

• If the match was a dollar sign, we return a dollar sign.
• If the word is one of our defined variables, we return the value of the variable.
• Since the word isn’t a defined variable, we check if the “strict” marker was found, and if so, raise an exception.
• Otherwise we return the default value provided.

The final piece of the implementation is to use re.sub() and return the result:

return re.sub(dollar_pattern, dollar_replace, text)

Regexes are often criticized for being too opaque and esoteric. But done right, they can be very powerful and don’t have to be a burden. What we’ve done here is used simple pattern matching paired with useful API features to compactly write a useful transformation.

BTW, if you are interested, the real code is in coverage.py.

A parenting story from almost 30 years ago.

My wife told me about something her dad did when she was young: in the car, knowing they were approaching an exit on the highway, he’d say to himself, but loud enough for his daughters in the back to hear, “If only I could find exit 10...” The girls would look out the window and soon spot the very sign he needed! “There it is Dad, we found it!” I liked it, it was clever and sweet.

When my son Max was six or so, we were headed into Boston to visit the big FAO Schwarz toy store that used to be on Boylston St. They had a large bronze statue of a teddy bear on the corner in front of the store. It must have been 10 or 12 feet tall. I wanted to try my father-in-law’s technique with it.

Max had always been observant, competent and confident. The kind of kid who could quickly tell you if a piece was missing from a Lego kit. I figured he’d be the perfect target for this.

We got off the T (the subway if you aren’t from Boston), and had to walk a bit. When we were a half block from the store, I could clearly see the bear up ahead. I said, “If only I could find that bear statue...”

Max responded, “Oh Dad, I knew you didn’t know where it was!”

•    •    •

The store closed in 2004 and the bear was removed. I thought it was gone for good. But on a walk a few weeks ago, I happened upon it outside the Tufts Children’s Hospital.

Now I definitely know where it is: