Why do your legs only get wet when you walk? A guide to rain physics and geometry:

So, I was out for my morning walk today, and it started to rain. Luckily, I had planned ahead and brought my umbrella. I opened it up, and was standing there, enjoying the rain…and then I started to walk, and my legs started to get wet. I stopped, my legs stopped getting wet, I started walking, my legs got wet again.

The question is why?

I narrowed the problem down to the following variables:
– Height of the person (technically, the height of the edge of the umbrella)
– Walking speed and wind speed (I’m putting these together for reasons you’ll see later)
– Size and shape of rain droplets (this is to measure terminal velocity)
– S also added ‘size of umbrella’, but I’ll address that in the assumptions section

This is a lot of variables, so let’s make some assumptions:
– The human in question is about 2m tall (accurate within 5%)
– The edge of the umbrella is about 2m from the ground (accurate within 10-15%)
– The edge of the umbrella is about 25-50cm from the front of the leg horizontally
– We count the leg as getting wet as when the rain hits the front of the leg just above the ground
– Raindrop terminal velocity is about 20m/s, as per this graph:

– Wind-speed is negligible, as per this chart from Environment Canada, showing that wind at the time in question (9am) was about 2km/h, from the North:

Now on to the math!

We can easily show that with negligible wind, rain falling straight down will not hit the legs.

But assuming 90-degrees from ground vertical legs, what wind-speed would be necessary to rain on them?

At 20m/s, the rain would need to travel 0.25m or 0.5m horizontally as it traveled 2m vertically, or a horizontal wind of about 20m/s * 0.25m/2m = 2.5m/s or 9km/h for 25cm of umbrella overhang to 18km/h for 50cm of umbrella overhang.

So it turns out that the wind-speed was actually really important, as you can see that at other points today, it alone would have made the difference.

Now, what happens when we start walking? There are two factors at play here:
– Walking speed
– Extension of the leg forward out of the protection of the umbrella as you take a step

So we have to add some more assumptions:
– Assuming an average walking speed of about 5.4km/h or 1.5m/s
– Assuming that the toe to toe per step distance is 0.8m (from above), assume that at maximum extension, the tip of the leg is 40cm ahead of the body

Using the wind-speed calculation above, we can see that 1.5m/s of forward motion would only counteract about 1.5m/s / 20m/s * 2m = 15cm of umbrella cover, not enough to make your legs wet.

However, if your leg is 40cm ahead of your body, that would be enough if your umbrella was any reasonable amount off ‘exactly centered’ over the front of your body, and if your leg is 40cm ahead, and your walking speed adds another 15cm, that is enough to counteract even perfect vertical umbrella placement (40cm + 15cm > 50cm).

My experience this morning suggests that either the rain was falling more slowly than 20m/s, I was walking slightly faster than 1.5m/s, or I was resting the umbrella diagonally over my shoulder (most likely). This would have given me the approx. 25cm protection above, and caused my legs to be wet only while I was walking.

How would you calculate this? What would your assumptions be? Have you experienced this? Are you going to test this the next time it rains? Are you as surprised as I am that leg placement and step length are much more important than walking speed (as long as you’re only walking)?

Let me know what you think in the comments!

On the Importance of Encouraging People to ask (Sincere) Questions

Recently, a couple of friends of mine shared the following meme:

On the face of it, it may seem harmless, poking some fun at people who not only know less than you, but who know less than you consider reasonable (or perhaps even ‘possible’!)[1].

However, this laughing at others can lead to contempt, and a reluctance in the willingness of others to ask questions, due to the loss of psychological safety.

So, why might people laugh at those who know less about a topic than they?

Some describe surprise as a necessary component of laughter. You can be surprised that others know not just less than you know, but even less than you think is possible to know. This cognitive bias causing this surprise is a subset of the ‘Curse of Knowledge‘, perhaps best summed up by this drawing from Rajesh Mathur:

Sometimes, however, the laughter is not just about surprise, but also comes from a place of insecurity, the desire (conscious or not) to place one’s self above others. This could also be a trauma response, perhaps to experiences with ‘Sealioning‘, where people will repeatedly throw bad-faith questions into a debate or forum instead of engaging with the argument directly.

Another variant of this occurs often in teachers (and oddly enough, IT professionals), where if you’re continually hearing the same question from many different people, it can feel like ‘they just don’t learn'[2], because each year (or semester or day), you get a new person who hasn’t asked that question yet.

So, why might people be asking questions like this?
– They genuinely don’t know: As shown in the diagram above, the variability in knowledge between humans is vast. Even though you know about Oppenheimer because you’ve read multiple books on the subject[3], others might only have a passing knowledge, or even none, despite his pivotal involvement with the start of the Atomic Age.

– They might be mostly sure, but their experience with the thing made them doubt, or they heard a rumor….and the consequence[4] of their assumption being wrong is so large, the ‘importance x likelihood'[5] equation pushes them to ask the question, humans being loss-averse.

– They’re asking a slightly different question: ‘Is Oppenheimer based on a true story’ could mean a lot of different things. There’s a wide range between how much the movie ‘300‘[6] is based on a true story and how much ‘Oppenheimer‘ is. The question could easily be a rephrasing of “how close is the movie ‘Oppenheimer’ to a ‘true story’?”

– They may have difficulties expressing the specific question they want answered: I think it’s worth mentioning that the ability to ask specific targeted questions into a search engine is a (mostly learned) skill, and like all skills, is subject to privilege and ableist gatekeeping. In fact, one could argue that a large part of the uptake of GPT-like software is their ability to answer peoples’ questions when they are not phrased precisely, helping those who are less able to quickly articulate precise thoughts in written form.
– The search engine could be condensing or de-duplicating the wording of questions asked: On a purely technical note, the search engine has a limited amount of space on the page, and it would make sense that they would condense similar questions into perhaps the simplest and clearest version, making it look like people were very commonly asking a simple question.

Thanks for joining me on this wandering journey. I want to learn (and help others learn) to treat others with more kindness, and it’s important to me to deconstruct all of the reasons behind why I (or others) might be doing this. Thanks for reading!

[1] Having done a bunch of teaching, I was aware of the importance of teaching to different styles of learning, and also to different levels of knowledge, but I remember first hearing about this specific subset of this bias relatively recently, probably in a meme, where an expert in a field says ‘how can they not know about this ?’

[3] Most of my knowledge and understanding of Oppenheimer is from Feynman.

[4] This consequence can be social, such as ‘why didn’t you know about this?’, or personal, such as ‘I don’t want to change the way I think about this unless I have to’, amongst others.

[5] Humans are generally bad at judging the overall expected value of ‘Low-Probability, High-Impact’ events, which is probably why insurance is a thing, although the reduction in distraction/open-loops is probably worth it.

[6] Yes, I know ‘300’ is based on a graphic novel, that’s part of the point I’m trying to make. I’m specifically mentioning 300 because of the large number of known historical inaccuracies and general problematic-ness. There’s also a huge conversation about ‘The Western Canon’ that is out of scope.

Meetings & Mystics: Some RPG-inspired ideas for Meetings

What if meetings had a ‘hit points bar’, that showed how healthy they are?

Yesterday, S & I were talking about unhealthy & pointless meetings, and S had the following idea:

What if, every time that someone didn’t show up for a meeting[1], that meeting would ‘lose hit points’?

Each meeting has a number of hitpoints, its initial value related to:
– The length of the meeting[2]
– The number of participants
– The ‘importance’ of the meeting organizer or participants[3]

Those hit points change when:
– Each time someone forwards, ‘accepts’, or attends a meeting, the meeting is healed and soothed
– Whenever someone ‘declines’ a meeting, or perhaps worse, no-shows, the meeting is attacked and takes damage
– Whenever someone participates in a meeting, the meeting is bolstered[4]

When hit points decrease below various thresholds:
– The time allocated to the meeting decreases
– The number of people able to attend decreases[5]
– The meeting timeslot moves to a less desirable time[6]
– The meeting becomes less frequent[7]

Note that if any of the above go to zero, the meeting is cancelled

More outlandish ideas
– Meetings can fall asleep (meeting doesn’t happen this week)
– Meetings can be poisoned (meeting loses ‘hit points’ over time)
– Meetings can catch diseases (meeting is at half-length or half bandwidth until ‘healed’), etc…
– People could be given tools or ‘potions’ to heal or harm[8] meetings
– Meetings could be automated and given tools to sort it out amongst themselves, a la ‘Doom as a tool for System Administration’.[9] This logically would lead to:
– Meetings can have ‘classes’ such as ‘tank’ (absorbs damage meant for associated meetings) or ‘healer’ (actively heal associated meetings) or ‘DPS’ (strike back at competing meetings[10]

Some possible wrinkles:
– Some meetings might only ever have a small number attending out of those invited (such as a large Scrum of Scrums), but might be very useful for those who attend, and not a significant distraction for those who do not. We want to retain that usefulness while removing or reducing meetings that don’t have that usefulness…a ‘meeting budget’ [11] might be a way around that
– How does this work with 1:1s? They are generally acknowledged to be vitally important, but how do they fit in? Can one make a personal sacrifice to move ‘hitpoints’ from a 1:1 to a larger meeting when it’s really important?

Closing thoughts, some choice quotes by S:
—S: “Each meeting has a ‘power level’, which determines how many of its attendees it can hold on to….if it loses power, they can peel away & escape?”
—S: “It just occurred to me that the meeting is a monster, not a friend….why is the manager trying to heal the monster?”

[1] (if they weren’t on PTO). Also, when I say ‘meeting’ here, I generally mean ‘meeting series’, as the measurement of the health of a meeting while it is in progress, while very interesting, is a separate topic and out of scope

[2] Longer or larger meetings are not necessarily better, but they might take more effort to completely eliminate, having built up some inertia over time. One could get around this by assigning more ‘hit points’ to the first half hour of a meeting, with progressively fewer per unit of time as it gets longer. Similarly, with the number of attendees; A meeting with 1,000 people might be 500 times more costly than a 1:1, but is it 500 times more important?

[3] The importance of the meeting participants can go either way. If the people who want the meeting are ‘important’, that could be an argument for keeping the meeting. If they show up and don’t participate[4], that could be a clear signal that they should be removed or the meeting is not that important.

[4] Here, ‘participate’ is tricky….If you have a regular meeting where people of ‘importance’ get very useful information by listening, how do you measure that? Scientific talks or status updates between departments might be good examples of this. Also, ‘vigorous participation’ can be difficult to measure, and as ‘engagement’ metrics show, difficult to measure without encouraging loud arguments….One could also use whether video is turned on or not as a sign of engagement, but different organizations may have different cultural norms around this, and there may also be equity issues with this.

This could also lead to meetings being squeezed; When the ‘energy’/’usefulness’ of a meeting (perhaps measured by when people leave or enter) is consistently high all the way through, there is no change….when this decreases for marked sections of the meeting, the meeting ‘health’ decreases until the length of the meeting makes it so that the meeting has a consistently high energy all the way through

[5] IRL, this could be done by reassigning meeting rooms, virtually by restricting the number of simultaneous attendees.
—S: “Each meeting has a ‘power level’, which determines how many of its attendees it can hold on to….if it loses power, they can peel away & escape?”

[6] cf. Star Trek TOS Season 3. Note that this can be complicated by time zone issues

[7] E.g. from every day to 3 times a week, from once a week to once a month. This is already done in an ad hoc way for many types of meetings, for example when a team decides to go from daily to 3/week ‘standups’.

[8] Being able to harm other meetings feels like a very bad idea, but it might lead to fun stories 10 years later

[9] This is where a programmer famously modified the Doom sourcecode to create a world where all the processes on a Linux system would exist as monsters, fighting with the SysAdmin (and each other) through the Doom GUICached link (Sadly the UNM CS server seems to be down right now.) Original Link

[10] If you assign classes and automate meetings ‘interacting’ with each other, you might be able to clear your calendar (or everyone else’s calendar) very quickly….Also, we went back and forth about what each ‘class’ each type of meeting might be, for example, depending on the importance of the meeting, or how reliably it is important (regularly somewhat important like a status meeting, or rarely very important like a ‘these are the code changes going out around the organization’ meeting)

[11] A ‘meeting budget’ might make more explicit the opportunity/social capital cost people incur when arranging meetings (and help alleviate the issue of junior folks not wanting to ‘waste the time’ of senior folks to bring up issues early).