shoo

> Running the suite in CI on every build would have caught a lot of this

yeah, provided:

  1. test cases are being designed to cover functionality
  2. test cases are implemented correctly - i.e. they actually fail if the implementation is defective
  3. the tests aren't all commented out
  4. the test suite fails if a test fails
  5. CI actually detects test suite failure
  6. failing tests block changes from being merged (apart from initial triage to stabilise the suite)

Presumably a few of these things weren't being done -- I'd bet 1 & 2 were skipped or implemented so poorly that they were worse than having no tests at all -- checking nothing but giving a false illusion that some kind of testing had happened.

Five years ago, outsourcing your software development (including QA) to the lowest bidder might have gotten you results like this -- if you didn't explicitly require automated tests as a deliverable, you wouldn't get any, or if you got some they'd be vacuous and not test anything.

> how this was allowed to be tested

I can see it happening if they genuinely had no idea of how defective / non-existent their internal QA & testing processes were.

If the US were to follow this excellent idea to raise revenue, it could completely solve the federal budget deficit.

A modest download tax of USD $2.07 per GB suffices.

Estimate:

  - 134 million households
  - approx 80% of households subscribe to home broadband
  - approx 750 GB download per month per household
  - $2 trillion annual deficit
  - assumes no change in household behaviour in response to the new tax

It's possible for both a new technology to be hugely beneficial in the long run & for early investors to lose a lot of money funding it (if they over-invested / over-paid).

Yep! Or for a slightly generalised example, if we pick our sublinear function of n to be n^(1-epsilon) for some small epsilon > 0

then 2^(n^(1-epsilon)) belongs to 2^o(n)

Suppose p(n) is some polyonomial in n, our polynomial reduction. Let's make it a monomial for simplicity, p(n) = n^a

Does 2^(p(n)^(1-epsilon)) necessary belong to 2^o(n)?

No, that only holds if (n^a)^(1-epsilon) = n^(a (1-epsilon) ) < n^1 . So, it fails for p(n) = n^a for any a such that a >= 1/(1-epsilon)

Paul, cheers for your thoughtful reply -- all the best with PressAudit

Here's a few related ideas:

1) rejection sampling - this is the name to the general technique used in the first example, to estimate pi by sampling from a uniform distribution over a unit square (easy) and then rejecting the samples that fall outside of the distribution you're actually interested in (unit disk).

Another simple example of rejection sampling is if you want to randomly pick between 5 ordered options and only have a d6. Roll the d6. If you roll a 6, reject the roll & re-roll. If you roll 1-5, that's your choice.

2) the Metropolis-Hastings algorithm -- this is a Markov chain Monte Carlo algorithm. It can be useful in some applications to sample from a distribution that is difficult to sample from.

Suppose you have some system described by a state vector x & you know that the probability of the system being in state x, p(x), is proportional to q(x), where q is some function you can compute. If you could integrate q over x, to give Z := integral_{x in X} q(x) dx then you'd have p(x) = Z^-1 q(x)

For a concrete example, x might be a state vector of a physical system -- say a bunch of molecules in a box, where you can compute the energy of any given state u(x) and know the probability of x, p(x), is proportional to exp(-u(x)).

Metropolis-Hastings is neat as it gives you a way to sample from p even if you cannot compute Z or sample from q --- you just need to have some way to sample a proposed a new candidate state x' from x (this proposal distribution doesn't need to have any relationship to the distributions p & q you're actually interested in). Can often think of the proposed candidate state x' as some kind of local mutation of x. Provided you can compute q(x') / q(x), you can use that ratio as a probability of accepting the move to replace x with candidate x'.

By the algorithm depending on the ratio of probabilities of two different states p(x') / p(x) = q(x') / q(x), it lets you sample from p even if you can't compute Z or have any direct way to sample from p or q. *

Metropolis-Hastings & Markov Chain Monte Carlo methods are definitely in the territory of clever 'what to do if you don't know what to do' methods --- if there's some other more direct & practical way of computing the thing you're trying to compute, use that instead! But if there's not, & you have some gnarly problem, maybe MCMC might be the best option available.

* caveat caveat caveat: provided you let the sampler run long enough for it to 'burn in', & perhaps restart it a few times from different initial states x_0 to reduce the chance of it getting trapped in some unrepresentative local optima

be the change you want to see in the world

When you say pointer heavy, just how heavy is that pointer?

In traditional brainfuck, a single < suffices to move The Pointer one cell to the left.

For a dialect of brainfuck where The Pointer is 3x as heavy as is traditional, you'd have to apply 3x the effort, i.e. <<<, in order to move one cell to the left.

Cursed bogocomputing idea of the day: a variant of brainfuck where The Pointer is physically simulated, with mass & momentum. < & > apply impulses. The Pointer continues to move across The Array with momentum after you apply an impulse.