The Shaky Foundations of Science: The Theory of Falling Toothbrushes

I've been reading Classic Feynman, which has gotten me thinking about physics again, and science in general.

There are some problems you encounter when you try to figure how stuff works in the real world. Some of them are very clear to me; they're problems, but I understand them. There are other problems that aren't very clear to me, and hang around in the back of my mind like little nagging doubts. Let me explain.

This morning I was brushing my teeth and imagined that I knew nothing about physics and was trying to figure out what happens when you drop a toothbrush. That's all science is after all: you see stuff happen and try to understand it better and explain it.

So what would I do?

I'd start dropping the toothbrush and watching it. I'd watch it again and again. Soon I'd probably notice that it starts out slow and speeds up as it falls. Maybe I'd get a video camera and videotape the toothbrush falling and watch the tape frame by frame, and figure out exactly how fast it's falling. I'd notice that it falls at almost the exact same way every time. Sooner or later I'd come up with the Theory of Falling Toothbrushes, which might be stated as follows:

Toothbrushes fall at a constant acceleration: 9.8m/s²

So, is this a good theory? It has some things in it's favour, principally that it predicts the position of the falling toothbrush at a given time to within the error tolerance of most experimental setups you might imagine.

This theory is as good as a scientific theory can be. It has some problems, but, as far as I can tell, these problems are fundamental to scientific theories; that is, these problems exist for every scientific theory that could be invented.

Here are the problems I can see with this:

Category 1: Problems I Understand
These problems are not particularly interesting. They're just occupational annoyances that scientists face. I'll explain them here to distinguish them from the interesting questions.

Problem #1: Almost every physical process you can observe is very very complicated. For instance, when you drop a toothbrush, it bangs into air molecules, and starts out with a small bit of angular momentum since you can't drop it straight down. These will make your experiment come out a bit different every time, and the the complications they introduce will be incalculable. This is not news: The Theory of Falling Toothbrushes actually describes what would happen if you dropped a toothbrush from a perfect dropping machine that imparts no "twist" or "push" as it drops, in a perfect vacuum. If this was the only objection to the theory, it would still describe exactly how toothbrushes fall in a vacuum.

Problem #2: Theories are always doomed to remain theories. I haven't dropped my toothbrush in every possible location at every possible time to ensure that the theory accurately describes toothbrushes falling everywhere at every time. Therefore, my theory will forever remain a theory: I have pretty good confidence that this is how it works, but it's impossible to be sure. No matter how many ways I drop a toothbrush, I might be surprised one time to discover things don't go the way I expect. Sure enough I would. I would discover that at higher altitudes (in a vacuum), the toothbrush would fall slightly slower since I'm farther away from the center of mass of the Earch. If I dropped it from a great enough height, I'd see it gain mass and slow down as it approached the speed of light, according to relativity. If I dropped it from a great height not in a vacuum, I'd see it hit terminal velocity as the air particles bumping into it faster and faster offset the effects of gravity. This is fine too; I understand that a theory is a description of how I think things work from my experience, and I always might be wrong.

Category 2: Problems I Don't Understand
These problems I don't understand the implications of. Clearly they are not serious objections to science, since science has accomplished so much in spite of them. I don't know if they are fundamental issues with the underpinnings of science, or if I'm just confused and need to get straightened out.

Problem 3: At some point you have to jump from abstract to concrete, and I don't really understand the details of the jump.

When I think about a toothbrush falling, I'm working in the abstract math world. I'm assuming that actual physical "space" works exactly like mathematical 3-d space: there are infinite numbers of continuous points, and matter within that space exists within a closed surface with a certain density. That's a mathematical abstraction though that just kinda seems to work like reality, but they're only related by this foggy "I think it works a bit like that" feeling that I have no confidence in. So my description of how toothbrushes fall is really a set of rules for my toothbrush abstraction (my closed curve in math 3-d space with a density function within the surface). What do I really mean when I use that abstraction to describe the real world that actually has molecules and atoms and quarks, etc... etc... and is not an actual density function in math space? I don't know. I have kind of a foggy idea that you could make a set of rules that map your math model to predictions about what your measurement tools will read with various experiments. Kind of a real-world to math-model interface definition. I'm not really happy with my understanding of this yet though.

Problem 4: What the heck is this reality we're describing anyway? How do I know about toothbrushes in the first place? My rods and cones are stimulated to make a mental image of the toothbrush, and the sensors in my hands and mouth seem to tell me something is there. And I could taste it, smell it and hear it too. But that's all I've got! Who knows what it's like out there! Is there some kind of reality outside of my head? Seems to be that way; I think The Superhero exists and we seem to agree on what's out there. Does it make sense to talk about "out there"? All I know is what's in my head. Chris Langan addresses some of these issues in CTMU.

I think the way it works is that there's 2 separate problems: the mental to real-world (or math-model to real-world) mapping is one problem, and that's the one that's fuzzy for me. Then science sits on top of that and uses it, and has the problems in Category 1, which I've got under control.

That's all I've got for now; I'll report back when I figure it out!

The Crazy Curve

I have a theory about kids and the wacky stuff they say. When kids start to talk, they can't say much, so when something comes out, it's just one out of a few words they know. When you get to be a teenager, you can construct sentences to say anything you want, but you're smart enough by then to know which are the truly ridiculous things and keep them in. There's kind of a sweet spot in the middle, somewhere between 5 and 8, where kids think up all kinds of weird stuff, and they don't know it's ridiculous, and they can articulate it.

In my head, it looks like this:
My kids (ages 1/3/4/4) are just getting into the zone these days, especially the twins. When I watch them and The Superhero is off doing something else, I like to write down the funny things they say so she can read them later. Today I'll share them with the rest of you too.

This afternoon I was helping them with a video game and told Twin A how he had to move something. To which he started to sing:

Twin A: "I like to move it move it, I like to move it move it."
Number 3: "I like to MOVE it too!"

Just now I went upstairs and heard a ruckus going on in the 3 older kids' room so I went in to tell them to quiet down and go to sleep.

Me: "Everyone, I have two things to say: 1) That's a very nice pepperoni song you're singing, and 2) It's time for everyone to find a pillow and a bed."
Twin A: "The soup is all over me!"
Me: "Excuse me?"
Twin A: "The soup is all over me! I'm wet!"
Twin B: "This is our Jumping Bed!" (as he scurries off to the other bed which is presumably the Sleeping Bed).
Number 3: "Can I sleep in the bucket?" (They have a large Rubbermaid bucket in their room that they've emptied of toys).
Me: "Yes, you may sleep in the bucket." (Number 3 proceeds to put his pillow into the bucket and curl up in it).

They'd better start sliding down the other side of the crazy curve before they start looking for a woman to marry. Or date. Or even talk to. That is all I have to say.

What Should I Do?

There are a few things that I learnt in school that have really stuck in my head - where I've been so excited to learn about them that they went straight into long term memory.

A lot of the stuff in Psychology 101 is like that for me. When I went to university I knew nothing about psychology, but I thought it would be the coolest thing to learn about. Imagine, finding out how people think, feel, remember, behave, and so on! I ended up taking the course twice, since The Superhero took it first, and I tagged along to the lectures, and then I took it myself later.

Anyhow, a whole bunch of the stuff we learnt in that class stayed with me, and one of them is the hierarchy of needs. The idea is that there are different levels of needs, from very basic (shelter, food) to more sophisticated (sense of belonging, purpose), and you don't care about the upper levels until you've satisfied the lower ones.

There's something to this theory: if you ever hear people talking about times when they didn't have enough to eat, all they can talk about is wanting food. They don't care about anything else. Same thing whenever you go through a major life transition; you don't really care about anything else until your life is back in order.

I find myself recently with the weird difficulty of struggling with the needs at the top of the pyramid. I can recall the second-to-last semester of university in which we had baby twins to care for and The Superhero and I were both in school full time; we were totally focused on the everyday demands of life and getting through the term without failing a course of losing a baby. But now, as we ease out of the super-hard work section of our life, I feel a weird kind of emptiness that comes from getting exactly what you asked for.

The Superhero and I basically have it figured out. The bills get paid. We're healthy. Our family is happy. We have friends. We have hobbies. We have no "real problems". In fact it's typical for The Superhero or I to catch the other complaining about something relatively unimportant and say "Please talk to me when you have a Real Problem.".

So I find myself with this funny kind of life-optimization problem. I think to myself "Ok, so now what?". I'm 27 now. I'm going to die when I'm 80 or so. That's a lot of time in the middle! Today I have extra time and energy over and above what I need to keep the basics of life flowing smoothly. As time goes on, I'll have only more... the kids will get more independent and eventually leave, The Superhero and I will have more spare money, etc.

So what should I do? What will my future 80-year old self wish I had done? I have a bunch of disconnected thoughts on this, but most of it is probably wrong, and I don't know anything about how it fits together. Nonetheless, here are my thoughts on how to improve my life, in no particular order:

• The key to happiness seems to be improvement. It doesn't matter where you are, happiness seems to be all about how quickly things are getting better. I don't know what this means in terms of a plan, but there you have it.


• It makes me really happy to start to learn about something new, or start learning a new skill or hobby. So I think I should do that a lot.


• As the kids get older, I can teach them everything. I've learnt most of the easy stuff, but they don't even know how to add yet! So I can teach them stuff, both academic and life-skill-wise.


• I think I'm missing out on a bunch of life by not being open to people. Meeting people exposes you a whole lot of randomness and different points of view that you wouldn't otherwise think of. For instance I'm reading a book called Classic Feynman, which is a collection of talks that Richard Feynman gave, and I've learnt from him to translate complicated things into things that I understand very clearly before thinking further.


• I think I should learn about everything. The library is full of books about everything you could ever think of! I believe there's a limitless source of books I'd be really excited to read, so there's no excuse for being bored when there's a public library where I'm living.


• One of my favourite things to do is have fun with The Superhero. So I'll always do a lot of that too.

As you can see I really have no idea what I'm doing here. A bunch of swirling ideas, but nothing concrete. So, blogworld of limitless wisdom, what should I do? I've been put in charge of this healthy 27-year old body, in an affluent democratic country in a wonderful family. I don't have any of the problems that most people in the world have (y'know, like getting food). So what's next?

Me and My Time

Disclaimer: This post will only be of interest for the truly dorky-at-heart. I will accept no liability for any wasted time or annoyance this may cause. You will not get this time back.

I have some good news and some bad news: I am continuing to get to work on time, but that in no way guarantees that I get anything more useful done than if I had stayed in bed.

I'm working on a project now that I have to get done roughly for the end of the month. I find some days that I end up doing everything else at work and not the main project I'm supposed to be doing, and other days I get lots done on the project. Until a few days ago, I had a bunch of nagging questions that I had no way to answer, like:

• How many more hours of work do I have left?
• Can I finish my project on time?
• Am I spending enough time on my main work in comparison to other tasks that come up?
• Am I actually getting anything useful done at work?

Now I can answer these questions, by using the geek's equivalent of real men's duct tape: the spreadsheet.

Throughout the day, every time I switch tasks, I enter what I did and how long I did it for. I also enter how much I now estimate I have left on that task before it's done. For example, if I have a 4-hour task, and I work on it for 2 hours, hopefully I think there's 2 hours left. But maybe I ran into a snag and now I think there's 3 hours left still, so although I put in 2 hours, I only got 1 hour's worth of "estimated" work done.

The output of spreadsheet is, among a couple of other things, 3 numbers.

1. Work efficiency: This is the time I spend doing productive things divided by the total number of hours in the office.
2. Focus efficiency: This is the time I spend working on the stuff I'm "supposed" to be working on compared to random things that come up (e-mail, meetings, etc.).
3. Estimation efficiency: This is the estimated hours I've gotten through (that is, what I estimate remains for all my tasks at the beginning of the day, minus the same thing at the end of the day), divided by the actual hours I put in on those tasks.

The product of these 3 numbers is my efficiency at turning in-the-office hours into estimated hours that can be taken off the books.

The results? Dismal. Problem number one is that I spend hardly any time on the stuff I should be doing. Focus efficiency has been less than 50%. Work efficiency has been ok; I've been spending about 80%-90% of my time in the office actually doing something useful. When I actually sit my butt down and work on what I should be working on, I'm getting it done faster than expected. My estimation efficiency is more than 100%.

To get this project done, I need to clear 5 estimated hours per day for the rest of the month. I've barely done this over the last two days, and I wasn't coming close before I started measuring.

So there you have it: this is how I spend my productive hours, working like a computer, at a computer, programming computers.

Human Spectrophotometry

The Superhero and I have a running metaphor called human spectrophotometry.

Spectrophotometry
is a way of determining the constituent substances in a solution. The idea is to send varying frequencies of light through a solution and see which frequencies are absorbed and which pass through. Every constituent substance has a "signature" of light it absorbs, and if, for instance, you see 3 spikes in the spectrophotometry graph (see left), you can say that you have 3 different chemicals mixed together, and you can tell what they are from where the spikes show up.

The idea of "human" spectrophotometry is that people have a variety of different constituent properties and you could plot a graph describing what any given person is like. For instance, I have a very spiky spectrophotometry: I have areas in which I'm very strong (logical thinking, for instance) and areas in which I'm very weak (dealing with people). The Superhero's spectrophotometry is very even and very high: she's well-rounded and talented across the board.

The Twins are just like me; they're spectrophotometry is also very spiky, and spiky in the same spots. While I'm sure they'll have lifelong difficulties making friends and decoding women, they're great when it comes to learning letters, numbers, days of the week, and the like. I still recall the day when they demonstrated that they could count to 10 in Spanish, sans parental instruction. Their parents may have been taking refuge with Dora the Babysitter Explorer around that time. Hard to say.

In any case, up until this past weekend, the Twins have had a weird blind spot for understanding the differences between the different meals. Breakfast, Lunch, and Dinner were interchangeable synonyms until I decided to make this:


Ever since, we've been crystal clear. We have to read through all the characteristics of the various meals every time we sit down to eat. Is it morning, afternoon or night? How many meals have we had today?

There are some very nice changes as the kids are getting older. They don't scream in the night, and I get to teach them stuff! I love to explain stuff to people! Even if they won't need math help as much as I'd like, there are all kinds of holes in what the school system teaches. Like how to have a nice marriage, or how to make a budget, or how to delegate, or the importance of exercise. One day, we can even sit down and draw our very own spectrophomometry graphs!

Habits and the Clear Path to Success

I have a crazy weekday schedule. I get to work around 6:30 in the morning and leave around 3:30.

A few weeks back, I was getting to work at more like 6:40-6:50. The main problem was that I was getting lazy at night and leaving stuff to do in the morning, and also procrastinating leaving in the morning, since running 6 1/2 km in double-digit sub-zero temperatures takes more energy than I tend to have at 5:30 in the morning.

Anyhow, missing 10-20 minutes of work is not the end of the world, but it bothered, me, mainly because I wasn't able to take control of it.

This is the kind of problem in which my father-in-law would say there is a "clear path to success". There's all kinds of problems which are actually complicated and require complicated solutions, but there are a whole class of problems in which the solution is painfully obvious, and yet oddly elusive. I know exactly how to solve this problem. Get my shit together the night before. Leave promptly in the morning. Don't be a lazy ass. And yet I didn't do it; day after day I was showing up late.

I have some opinions about this. I'm sure I'm wrong (here's why), but nonetheless it's a working theory:

1. There are some "clear path to success" problems that some people will never have. I will never have problems with overspending and debt. I hate debt and I rarely have the impulse to buy anything. I don't try hard to stay out of debt, it's just who I am. It's not a matter of will power or zen, I just don't want to buy stuff. The Superhero really loves to run. She'll never be out of shape because she really likes to exercise. It's just who she is.


2. Everyone has some "clear path to success" problems that they struggle with. Punctuality is one of mine. My instinct to leave for scheduled events is not strong enough to get me there on time.


3. "Will power" is an unreliable way to solve these problems. The best way I've found is to get creative and find a strategy other than will power to make myself behave properly. For instance, in my early days of running, I ran with my brother-in-law, which forced me to get up in the morning. Now running is my transportation to work, which is often my only way to get there.
   


4. Sometimes the only way fix the issue is suck it up and change my habits. This is trickier than it sounds! I've read that it takes about 3 months to make new habit. The "new kick" motivation wears off after a week or 2. That's a long 2.5 month gap in there to stick with a new behaviour before the "habit pain" of doing something out of the ordinary wears off.
   

I took approach #3 to solve my work-arrival time issue. Before reading on, take a minute and think: How you would solve this?

It took me a couple of days to figure out what to do, but the moment I thought of the New Plan, I knew it would be successful. And it has been; my work start time now varies a bit, but the average start time is 6:30. Exactly 6:30.

My scheme is this:

Day 1: Get up whenever the hell I want. Try to get to work on time.
Day 2: Adjust my alarm by whatever would have been needed to get to work on time. E.g. if I set the alarm for 5:30 on day one and got to work 20 minutes late, set it for 5:10 the next day.
Day 3 (and so on): repeat Day 2.

Now, if I'm slow one day, I pay for it the next day. Getting to work on time was never good enough motivation to hustle in the morning, but getting to sleep more the next night sure is!

On that note, I'm off to bed... wake-up time is 5:04 tomorrow!

Thank You For Screaming, Part II

I have some bad news for you today. I'm very sorry to be the one who has to break the news to you, but here it is: You're wrong about most things.

Oh, I know, there's a big category of stuff you're not wrong about. Like what city you live in. And where the grocery stores are near your house. And what your kids' name are. You've got that stuff under control.

But there's a whole collection of stuff in which you don't know your ass from your elbow. Like political views, religious views, moral views, opinions on how to parent, teach, be a good friend, and manage your life. I'm really very sorry, but you just don't know nearly as much as you think you do on these topics. I don't either.

I've learnt something over the last couple of years, mainly from studying chess and in my job programming computers, and that is the importance of testing. When you're trying to figure out how something will work, most things are just really, really complicated. You're not going to figure them out just by thinking; you're only going to figure them out by testing.

I slowly became convinced of this as I went through software project after software project and observed two things:

• The project always takes way more time than you estimate.
• The problems that arise during the project are never the ones you predict.

Similarly, as I studied chess positions, I noticed that the solutions given by the author almost always include new wrinkles that I hadn't anticipated.

I became quite impressed with the intrinsic complexity of these types of problems, and how invariably the failures of the project planning or the chess position-solving could only be uncovered by watching the systems fail and observing where the problems were, and never by just "thinking it through".

Intrigued, I observed everyday life and observed the same types of things:

• People tend to be right about stuff that gets regularly tested.
• People tend to be wrong about stuff that they just think through, without either the opportunity or interest in testing whether it's right or not.

So when you think you know what city you live in, you're right. You test it all the time. If you were wrong, you'd find out right away when you couldn't find your house.

But questions of the philosophical sort are typically untestable, and I'm convinced we're generally wrong about the things we tend to believe. For instance:

• Is it a good idea to try to cure cancer? To donate money to starving countries? Yes! Of course! Or, maybe, do we risk overpopulation by doing so? What's the risk to the environment? What kind of crazy socio-policital chain reactions could we be setting off? I have no idea.
• Is it a good idea to have freedom of speech? Sounds like a good idea. Who knows what the consequences are? Are the countries with fewer civil liberties happier? They have lower suicide rates. I have no idea.

I haven't tested it. I just don't know. And if you haven't done extensive research, you don't either. Even if you have, you still don't know. You have a slightly better guess.

Anyhow, all this comes to one final example; something that gets tested everyday, and has totally the opposite answer to what you'd expect.

When The Superhero gets mad and yells at me, how does it affect the interaction? Our day? Our marriage?

Totally for the better, on all counts. Who would have thought? Not me.

It diffuses the fight; beforehand it's resentment in The Superhero's head. The yelling lets it out. And it makes me laugh. I have no explanation for this. It's complicated! That's why you must test stuff! The laughter diffused the situation. The Superhero feels loved, relaxed, and much better off than before.

The unexpected laughter is not short-lived. If I was grumpy before, it cheers me up. My day gets brigher. Totally unexpected. But true.

Furthermore, it has a wonderful effect on our marriage. I never have to worry that I'm walking on The Superhero and she isn't telling me. I know if she's upset she'll let me know and stand up for herself. No long-term resentment.

Overall the yelling is a great thing, and nobody would have guessed.

This, in addition to the unexpected benefits of Twin B's shrieking? Mind-boggling, but true.

Where would I be if I didn't have such a charming family full of people to yell at me?