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Simpson’s paradox

“A common example of Simpson’s Paradox involves the batting averages of players in professional baseball. It is possible for one player to hit for a higher batting average than another player during a given year, and to do so again during the next year, but to have a lower batting average when the two years are combined.”

Napkin Analysis of the Sand Flea Jumping Robot

I shared this video1 with Peter, who then asked:

I saw that a couple days ago. Awesome! And has some cool practical applications. I [couldn’t] quite tell if the pitch of the robot was adjustable by the user, or of it always jumped in the same direction. Did you get a sense for that?

It was a good question and one I didn’t have an immediate answer to.

I would actually guess that I don’t have immediate answers2 to at least 50% of questions people ask me3. I have to do some amount of thinking, and sometimes even some research. I think people tend to think I know the answer off the top of my head, I assure you: I am not that smart.

I do have an inquisitive mind, I do know where to look, and I do know how to ask the right question.

Extended Mind
https://xkcd.com/903/

I decided to remedy this question though by talking it through, instead of just giving an answer. This is basically my thought processes as it occurred. Except that I got Sin and Cos mixed up and didn’t realize it until I had finished my conclusion. So I had to redo my entire analysis, and that’s what you see here. Please note this is still really just a paper napkin answer:

As far as angle, I’m not sure. I suspect there would be some angle change.

Elevation angle can affect two things, how high it goes and how far it goes forward, and these two things are intrinsically linked through SohCahToa. Height and forward distance can also be affected by the force applied (ceteris paribus4). This gives a problem with two independent input variables (angle and power) and two dependent output variables (height and forward distance/range).

Since my primary goal is to jump, I’m going to put most of my energy into that. If I want to jump higher, I can either apply more force or make my elevation angle higher (as long as it’s < 90°). As the elevation angle nears 90° [latex]\left (\frac{\pi}{2} \right )[/latex], more of my energy goes into going up than going forward. The proportion of energy applied to going up is defined by Sin and the proportion of energy applied to going forward is defined by Cos. Also worth remembering is that the Sin[x] + Cos[x] is not a straight line, it's another parabola that peaks at 45 degrees. The biggest bang for your average buck is to angle yourself at 45 degrees and shoot. Additionally, Cos (forward) angles that are near 90° have a high rate of change (i.e. going from 80° to 81° has more of a difference than going from 10° to 11°), thus little changes in elevation angles near 90° have relatively larger impacts on how far forward I go. Conversely, Sin (height) angles that are near 90° have very low rates of change. The cross over point for rates of change between Sin and Cos is - you guessed it - at 45° . Since the goal of the robot is to jump high (not far), it would make sense to only use high angles (above 45° ). To vary height significantly though, you are going to have vary power. Going from 46° to 90° only increases height by ~93% if the force remains the same. In comparison, going from 1 degree to 45 degrees increases height by 164,000%. Math is great, but if you can't implement it, it doesn't matter so let's turn to what's practical: One of the underlying assumptions is if the robot can vary the force it uses and if it could accurately set it's elevation angle. Setting the angle is pretty easy using encoders, and accelerometers to determine which way is down (if you were jumping from an angled surface, for instance). We've also already seen that the jumping leg can move, so adding functionality for precision angle measurements (within a degree, let's say) is pretty trivial. The real question, I think, is how does it jump? Delivering energy quickly has always been a problem. Delivering a measured amount of energy quickly even more so. Based on jumping from the ground to the loading dock (1.5 meters in height at most) and then from the loading dock to the roof (probably at least 4 meters), that's about a 166% increase in height, which is not quite enough as could be accomplished by just varying the angle from 46° to 90°. Since you can't gain that height just by altering the angle alone, it makes sense to assume that the jump force setting can be altered. However, if you change the jump force setting, what does that do to the forward movement (we know it will make the robot jump higher)? It will, of course, move the robot forward even more. How much more? I don't know exactly, but probably enough to make some minor angle tweakage worth it. We would have to sit down and work on the math to verify the exact amount. I think it involves something with squaring the derivative of the force divided by the mass. Squaring always make numbers bigger, so I tend to think it would be significant. Suffice it to say, if you don't want to proportionally more forward when you jump significantly higher, you would have to adjust your jump elevation angle. Thus I would assume there may be small changes in angle elevation, but that's hard to estimate given the view-point the videos were shot at. It's also pretty easy to solve for power required and angle needed to reach a particular height while moving forward only a certain amount (once you figure out what the maths are), so at least the implementation factor is pretty easy from a computing standpoint. And I've spent way to much time on that answer.5 As always, please check my work.

  1. found via the always interesting Kottke ↩

  2. answers that only involving recalling a specific outcome ↩

  3. I just made that number up, really ↩

  4. all other things being equal or held constant ↩

  5. One of the reasons I decided to blog about it, the work was pretty much a sunk cost ↩

Dreaming About Tomorrow

Generally, I try to be content with how things are. This has been a challenging mix of rejecting the status quo when I believe it is required but also not getting sucked in by Shinny Object Syndrome (rushing off to the next latest and greatest thing, what I think George Leonard would call “The Dabbler”1). This has been a careful mix because I feel like I’ve spent much of life “moving on” from one thing to the next, always trying to reach some je ne sais quoi.

Since I graduated from college, I’ve been trying to use my time for good, being involved in things that I think are important and extending my network of connections. Over the last year though, I’ve had to trim this back as I’ve simply got too many things going on. I even had to come up with form letter to send out because of all the awesome opportunities I got:

Unfortunately I’m at capacity (actually probably a bit over capacity) for doing things right now and I’m going to have to decline your invitation to help with the INSERT_EVENT_NAME_HERE. This year I’ve had a lot to manage and be involved in, which is a good sign: I’m gaining responsibility and learning a lot! But when push comes to shove, I tend to eliminate the “me time” first because that’s, unfortunately, the easiest thing to eliminate. I’ve slowly but surely been pushing back on that, reclaiming the time I need in order to function in the rest of the areas of my life.

Ultimately, that results in me having to say no to a lot of great opportunities. At some point in the future I may be at a point where my other responsibilities have dropped to a point where I can take on new projects. The time isn’t now though.

This has been a season of saying “no” for me and it’s been heart breaking. You haven’t been the first person or group that I’ve had to say no to and you won’t be the last. The thing that gives me hope is that it means that I’m on to something. It means that I’m cultivating a “thing” that is valuable and people want. I just need to figure out how to clone myself now.

Until we get the cloning thing perfected, I respectfully must decline your invitation to be involved with the INSERT_EVENT_NAME_HERE. Thank you for the consideration though, it does mean a lot that you thought of me.

Sincerely,
Andrew

I was talking with some friends a few nights ago and got some solid honest feedback about what I do really well that I may not know about. A lot it seemed to revolve around this “thing” I’ve been spending my time cultivating: being honest, willing to tackle tough questions, childlike curiosity.

I’ve also had some really awesome comments from friends over the last few months about my passion for engineering, technology, and even my job.

I feel like I’m brewing something amazing, but I don’t know what it is yet. And yet I’m afraid that this thing I’m brewing won’t come and one day I’ll wake up and find that I’ve stopped dreaming, in part because I’ve tried to slow down and all the time I’ve put into it will have been wasted.

I’ve been following Neil deGrasse Tyson for about a year now — ever since I saw him give a lecture, Adventures of an Astrophysicist, at the University of Washington. I may not agree with everything Neil says, but I have the utmost respect and admiration for him. In my books, he is a champion of honesty, curiosity, and willingness. He has spent time enlightening everyone from Congress2 to the Internet at large by doing a questions and answers session on Reddit.

When asked what he would do if he were President by the New York Times, Neil answered:

From www.haydenplanetarium.org:

The question, “If I were President I’d…” implies that if you swap out one leader, put in another, then all will be well with America – as though our leaders are the cause of all ailments.

That must be why we’ve created a tradition of rampant attacks on our politicians. Are they too conservative for you? Too liberal? Too religious? Too atheist? Too gay? Too anti-gay? Too rich? Too dumb? Too smart? Too ethnic? Too philanderous? Curious behavior, given that we elect 88% of Congress every two years.

A second tradition-in-progress is the expectation that everyone else in our culturally pluralistic land should hold exactly your own outlook, on all issues.

When you’re scientifically literate, the world looks different to you. It’s a particular way of questioning what you see and hear. When empowered by this state of mind, objective realities matter. These are the truths of the world that exist outside of whatever your belief system tells you.

One objective reality is that our government doesn’t work, not because we have dysfunctional politicians, but because we have dysfunctional voters. As a scientist and educator, my goal, then, is not to become President and lead a dysfunctional electorate, but to enlighten the electorate so they might choose the right leaders in the first place.

Neil gets it, he rejects the status quo as insufficient. Neil dreams and he doesn’t get sucked in to Shinny Object Syndrome. Neil has a Big Hairy Audacious Goal (BHAG).

Sometimes I worry that I don’t have a long-term BHAG. I worry that I’m not ultimately working towards something that is clear to me.

Short term dreams — zero to two years — I love. I can manipulate those short-term dreams in my mind and they feel tangible (which is not necessarily the same as feeling achievable), but how do they link up? How do I take my somewhat disparate dreams and make them into something worthwhile and awesome? I worry that when I dream about my future in the long-term, my dreams are fuzzy; and it’s not because I don’t have ideas — I do. Still, I wonder what is it that I’m ultimately working toward? Am I spending my time wisely?

Exploring the Solution Space (Source: http://blog.intercom.io/criticism-and-two-way-streets/)

I’ve been spending a lot of time doing Exploration, and I love it. But what about Refinement? Sometimes I feel like I’m not spending enough time on the refinement aspects because of Shinny Object Syndrome. At what point do I decide to switch from Exploration to Refinement?

So that’s some of the things I’ve been thinking about lately: How do I spend my time? What is my BHAG? How do I do all of this in as a Christian? How do I know if I’m doing God’s plan?

  1. Mastery: The Keys to Success and Long-Term Fulfillment by George Leonard ↩

  2. Priorities, Plans, and Progress of the Nation’s Space Program, Senate Commerce Committee ↩

Age of Ignorance

I feel like this quote does a good job of capturing my feelings behind why I have no kill switch on awesome:

From www.nybooks.com:

Widespread ignorance bordering on idiocy is our new national goal. It’s no use pretending otherwise and telling us, as Thomas Friedman did in the Times a few days ago, that educated people are the nation’s most valuable resources. Sure, they are, but do we still want them? It doesn’t look to me as if we do. The ideal citizen of a politically corrupt state, such as the one we now have, is a gullible dolt unable to tell truth from bullshit.

I’m just one person though. And my sphere of influence is only so big and so powerful. This makes me feel very sad about what our country has become. Is it too late for us to make things better? How do we make intelligence desirable?

An Atkins Wedding!

During all my travels last year, I did get to do many fun things, such as attending the awesome wedding of Lance and Nicole! I’ve known Lance for several years and he’s one of the most interesting and funny guys I know. He’s also done some amazingly cool things like going on a mission trip to Africa for two months to help fly airplanes, start his own business making computer cases, and marrying Nicole. Nicole is really awesome too, and very sweet. And together, they through a pretty awesome party, as evidenced below:

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As always, there are more pictures over on Flickr: An Atkins Wedding!

Tornadic Supercell Thunderstorms

I spent some significant amount of time (significant for me at least) in Oklahoma last May. I also survived some major weather phenomenon again:

From www.srh.noaa.gov:

Several tornadic supercell thunderstorms developed over parts of western and and [sic] much of central Oklahoma on May 24, 2011, with extensive damage occurring over many areas of central Oklahoma.

Highlights included:

From www.srh.noaa.gov:

  • Twelve tornadoes were confirmed.
  • One tornado has been rated EF-5. Two tornadoes were rated EF-4. Two tornadoes were rated EF-3, two EF-2, two EF-1, and three EF-0.
  • In addition to the damaging tornadoes, hail sizes reached at least 3″ in diameter.

I made the best of it by tweeting, taking pictures, and foraging for food after it was all clear.

From twitter.com:

It’s a mixture of tornado sirens, thunder, and lightening. Insane.

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Men Who Stare At Goats on Quandary Peak

One of the three times I went back to Colorado last year was to hang out with the old clan from college, specifically roommates and associated friends from that era. Ben planned it all and we had awesome time hiking, playing paintball, putt-putt golf, have some drinks, and watching movies — basically, just like old times but not.

For whatever reason, we did hiked the 14er on our first day of activities. I’m not in the greatest shape, but I’m couch potato either, so I was prepared to tackle the mountain. What I didn’t take into account was the 14,000 foot elevation gain I was making in just about 12 hours. I started in Seattle (177 feet ASL1) on Thursday night and summited Quandary Peak (14,265 feet ASL) at 10am the next day. It took a bit for the symptoms to set in, but I had a migraine, felt very nauseous, and not really like my self — perhaps even slightly confused. Fortunately, it wore off pretty quick — within a couple of hours — after descending back below 6,000 feet.

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  1. Above Sea Level ↩