Mark Reed

Ah, cool. I was wondering about envars in general. Why is return value output suppressed on `2⎕NQ '.' 'GetEnvironment' 'whatever'?

Is there a way to query the WS size from inside Dyalog?

Thanks, @Adám. Didn't know about ATO; nice to see some updates to the tio.run idea. Though the APL versions at TIO are honestly new enough for anything I've tried there so far, and it has no problems with i/o from a dfn. I mainly fired up tryapl.org because it groks the Dyalog key sequences, so I can build short snippets right in the browser instead of copying and pasting from RIDE.

How come you can't do ⎕← inside a dfn on tryapl.org? It says "NOT PERMITTED: Illegal token". Does it not present the browser as an I/O stream? I can't read from quad even outside an fn, though writing to it does work there.

It's biorhythms. They operate at the level of whole days. Any attempt to generalize to sub-day resolution will require providing time of birth (with time zone, or preconverted to UTC), and no matter how you approach it, you have a different and more complicated problem. Lacking such data, the only way you can be sure if two day counts are on the same day is if they are in fact the same number.

At least, that's what I got when I added the 379.5 to my list of moduli. The details of the rounding don't matter, just the fact that you still only count criticals on exact multiples of the co-period, even when that includes a fraction.

So there's no double critical on day 182 because 181.5 ≠ 182. But since both cycles meet at exactly 379.5, there is a double critical on day 380.

@AidenChow No, you still only count a double critical day when both cycles hit exactly the same number – even if that number is something .5 instead of a whole number. The rounding only kicks in when reporting the date of the crossover: if it's halfway between days, you count it as the later day.

I think it works, though. If you just use the numbers as given the result is that you are assumed to have downward critical days on the day after the between-day crossing in the odd cycles. So day 115 isn't a double because the intellectual critical on 115.5 rounds to 116, but day 380 is a double because both cycles cross at 379.5.

@AidenChow You're not crazy... at least this doesn't indicate so, if you are. :) I think the 379.5 is there because they tried to keep the calculation of the pairwise periods relatively straightforward, but introducing the fraction does rather muddle up the whole problem statement.

@Adám well, the thing is, when considering biorhythms at the granularity of whole days, only the emotional cycle ever crosses downward on any day. The other two cycles only cross downward between days, and thus never contribute to a critical day when crossing in that direction. So the only critical days excluded by the original problem code are thet ones with the emotional cycle crossing downward at the same time as one of the other cycles is crossing upward.

that leaves the definition of "critical day" unchanged from the general understanding while still having "double critical" defined to match the code/examples.

@Adám You could change the definition of "double critical" day to read "A "double critical day" occurs when two of the three cycles cross the x-axis on the same day in the same direction"

tomayto, tomahto

and wouldn't require any code changes.

A note like "to simplify the problem we only consider critical days to occur on upward crossings" would be plenty.

3:30!

I'm in the NY time zone myself, but got hit with a bit of insomnia tonight.

Thanks for passing it along!

yeah, because it's lcm(23,33), the combination of odd cycles. Which matters because they cross the axis going downward in between days, so you get two almost-critical days on either side of the crossing rather than one critical day on it like you get with the emotional cycle's even period.

After 644 days, you're back to day.0 on both the physical and emotional cycles. That's where that number comes from, and likewise for the other pairs and the triple. But after just 322 days you're on day 0 of the physical and day 14 of the emotional, which is also a double-critical day for those two cycles.

which, again, is the usual definition as well

based on the definition of critical day at the top of the problem page

it's "when do two cycles both cross the x axis"

because the problem isn't "when do two cycles both go back to day 0"

all three values that include the 28-day cycle

because, as it says in the problem statement, a critical day happens when it crosses the x axis in either direction

but every 28-day cycle contains two critical days, not one

Yes, 644 days is a whole number of 23-day and 28-day cycles

yup.

I'm sure it's too late to change the problem. But it might be worth a note on the page.

Assuming a 28-day periodicity means critical days happen every 28 days.

It's a simple derivation error

I'm quite sure they did not intend some alternate-universe version of biorhythms.

oh, whups, wrong year. :)

That's what I've been saying. :)

During which it crosses the x axis twice

Yes. The period is 28 days.

I haven't gotten my solution to a submittable form yet. I'm curious to see which way the tests go...

it's not something invented for this task. they were very big in the 70s, rivaling astrology for a while as the in-vogue pseudoscience :) Finding your biorhythms was a popular task in Things to Do With Your Calculator books and introductory BASIC programming problems.

The emotional biorhythm cycle is a 28-day cycle. That's the whole sine curve in the math sense, and has been since the things were invented. it starts at 0, peaks at 7, crosses the axis at 14 ,bottoms out at 21, and comes back to the start at 28.

Your earlier statement is accurate - the 644, 924, and 21252 numbers should be halved

the issue is the opposite of what you're describing

No. They say that's what they're talking about, but the numbers they give miss half the crossings.

it says "in either direction" right there in the task description.

""Critical days" are days when a cycle crosses the x-axis in either direction and are purported to be accompanied by unstable conditions in the corresponding area. A "double critical day" occurs when two of the three cycles cross the x-axis on the same day. The periodicity of double critical days is the least common multiple of periodicities of the two involved cycles"

A note would be good. It's just odd that they explicitly say that a critical day happens when it crosses in either direction, and then derive numbers that only find the ones where it crosses in one specific direction.

Since the physical and intellectual cycles are odd, their downward cross is between days anyway; it either doesn't create a critical day or creates two of them, depending on interpretation. So ignoring those is probably fine. But the emotional cycle is even and crosses the axis every 14 days instead of every 28, so the periods given that involve it are all too long by a factor of two.