Acrylic Mirror Failures Learning Opportunities

The acrylic mirror samples arrived. I got 3 mirrors about the size of a credit card, but thicker, like a piece of glass.

OBJECTIVE: Create a "trough mirror" that focuses onto a line.

KEY FACT #1: Acrylic mirror softens and bends at around 230-250°F.

KEY FACT #2: A parabola is a mathematically perfect focusing shape, but (a small section of) a circle is plenty fine for my needs.

FIRST ATTEMPT:

I got a big, glass jar with smooth sides. I put it lying down inside the oven. I balanced the mirror on top, shiny side pointing down (and with the protective plastic sheet still on it). I had to tape the mirror in place.

Starting at around 215°F, I slowly heated the oven up until the mirror ends started drooping. After probably an hour of watching it slooooooowly bend, I just reached in with an oven mitt and press-formed it to the glass.

RESULT: Meh. The shape is great and the focusing is accurate but the mirror got all foggy. It looks more like polished metal now. Also the spots where the tape was touching are distorted.

SECOND ATTEMPT:

My theory was that I should have the mirror pointing up, which might make the cloudiness go away and would make using tape unnecessary.

This time I used a regular soup pan tipped on its side. I put the mirror inside so it could form to the inside curve of the pan. Left the protective plastic on. Set the oven to 250°F (that's what I had worked up to from the first attempt) and waited. And waited. And waited.

Once again, I eventually just reached in and press formed it. When I removed the sheet....still cloudy.

THIRD ATTEMPT:

I watched the video again. Oh, I'm supposed to remove the protective plastic. Replay the second attempt, but this time remove the thing first.

After waiting the requisite Long Time, I could see the mirror was already foggy even before I press forming it. Aha! Not the plastic or the form!

WHAT'S PROBABLY GOING ON:

I have small samples, so gravity isn't enough to bend them until they are very soft from being in the oven for 45 minutes or more. In that amount of time, some chemical degradation (or something) is causing the cloudiness. If I rig up some way to put a weight on top of the sample, maybe I could speed that up. Or I could just reach in there earlier and do it by hand.

But now I'm out of samples. I can bend and rebend the cloudy ones just to test out some weighting system and/or get my timing right. But I'll only be able to check if the cloudiness disappears if I buy more mirror. Which I can do, but I hate the shipping charges. Ah well.

Miscellaneous

1. I had a long, long thing here about how following my plan was so easy, but it kept reading like Tighter Buns in 30 Days While Eating Pizza, so let's leave it at this: Down by almost 27 pounds.
2. Way back when, I did some solar experiments. I said I'd come back to that. I'm still working on that. The problem is, the design I came up with is kind of crappy.

   What I want is a parabolic trough mirror focused on a central pipe. I've tried using mylar sheets on various surfaces before, but it didn't come out too well. This time I tried strips of mirror laid in a wooden parabolic form. I haven't tested it yet, but it doesn't look too convincing on the workbench. Lots of gaps, not much total area, not well focused, etc. (No picture, because seriously.)

   While I was wondering what to do about all this, I came across this video. The guy comes across as a little infomercially, but his ideas look pretty good. In particular, I didn't know you could "drape form" plexiglass (aka "acrylic") mirror. That changes everything! Almost zero work and much higher efficiency.

3. Which brings me to the third misc item. WhereTF do you find acrylic mirror at a reasonable price? I've found it as low as $4.50/sqft, but you have to buy at least $50, not to mention shipping. Plenty of ebayers, but the price with shipping never comes out lower than ~$12/sqft and you have to buy several sqft to get that. Lowe's can special order it, but you have to buy 5 48"x96" sheets and it's still $8/sqft. McMaster-Carr, despite their awesome website, doesn't reveal shipping information even if you ask a live human being, which, HELLO.

   This kind of mirror is used in a lot of children's products because it's shatterproof, so I've considered repurposing a baby mirror, but the cost is still pretty high there due to packaging, frames, etc. I've even wandered around Home Depot and Lowe's to see if I could find a bathroom/decorative/whatever acrylic mirror on some other product. The sole success was a really, really crappy medicine cabinet with attached acrylic mirror. The whole unit was $12 and the mirror was 2 sqft.

   I would just go with that, but the fact that it's attached to something else only proves that I should be able to get the mirror alone for cheaper. Also, I hate to buy something specifically so I can throw it away. In the mean time, I ordered a set of these to experiment with. With the shipping, even amortized over several other items in my order, the price per sqft comes out at lalalaicanthearyou.

Tic Tac Lego

The building where I work has several "closed areas" where cellphones aren't allowed in. But of course people still bring their cells to work, plus there are visitors, random construction workers, etc and these people need a place to put their phones while they are inside. So they recently installed a cellphone cubby outside the door to the closed area. The cubby isn't just outside the door, it is also directly across from the main stairwell door that leads to it. It has a very prominent placement, is what I'm saying.

The cubby is a 3x3 array of squares. Every single time I pass it I think of tic-tac-toe. Surely I can't be the only one that thinks of this, so I thought it would be funny to put Xs and Os in there for everyone else to enjoy. But how to make them? Eventually my officemate thought of Lego. Of course!

We actually went through a few designs that were rejected because of strength issues or ugliness or size. Finally I hit on a pretty strong design for both pieces that, if I do say so myself, looks very nice.

Don't these look great? They look like very font-like, I think. Or maybe I'm overthinking it. Anyway, they are exactly the same height and width, which is also exactly the right size to fit the cubbies.

Unfortunately, cameras are even less allowed than cellphones, so I can't take a picture in situ. However, I'm posting this a while after putting it up, so here's a sample of coworker reactions:

• nothing
• small, confused smile
• swapping of X for O to change outcome of illustrated game (happened many times)
• "Niiiiiice" (in a Korean cleaning lady accent)
• "Are you the LegoMeister? Nicely done."
• From my boss's boss: something whispered about tic tac toe I guess he was trying to keep my identity secret?
• I've noticed many games in progress, with one move played by each passer-by. Also, I've heard reports of some people just standing in front of the cubbies to play a whole game.

Tornado in a Box

1: Cut a hole in a box
2: Put your.....no

1: Make a large, square(ish), cardboard tube. Mine is about a meter high and maybe .25 m x .25 m at the base. This is actually two boxes taped together. They aren't even the same size--I just blocked the holes with cardboard and duct tape.

2: On each side, make a slit near the right edge. Or the left edge. But the same for all 4 sides. It doesn't matter which you pick, since you can reverse it by flipping the tube end for end.

The exact width and distance from the edge don't matter too much and you can see I wandered all over the place. Hey, cutting cardboard is kind of hard!

3: Boil some water inside. I went to WalMart for a hotplate but the cheapest one was $20. I tried it on the stove, but that's dangerous and it was hard to see. Then I thought of the bottom of the rice steamer.

Position the tornado box under a light to maximize the reflection from the droplets.

We found that when the steamer was going full....steam, there was too much steam in there swirling around (steam steam steam). So if you turn it on and off every few minutes it might work better. Also, we tried using a steam humidifier but we got nothing at all. I think the steam jet might be coming out too fast and hot. (An ultrasonic humidifier probably has better visibility, but since it isn't hot you'd be missing another vital ingredient.)

The payoff at the end: I asked the Numbers, now that they'd seen a tornado being made, when and where would hurricanes be most likely? In the winter at the North Pole or in the summer at the equator. Ooooooooh, I get it! they said.

Pumpkin

Every single year I think "I'd like to do something different than the usual triangle eyes and so forth" and every single year I fail to find a pumpkin carving kit. This year, Number Two (6 years old) was pretty excited about the idea of weird designs and we escalated awesome ideas up and up to the point that I knew I had to do something.

I had some jigsaw blades lying around. I cut the end off (diagonally, to leave a sharp point) with a wire cutter. Then I sandwiched it between two sticks of wood to make a handle and wrapped it up with duct tape. It works really well. Surprisingly well, actually. There's only two problems, one of which is fixable.

1. The saw blade isn't long enough. I was able to cut all the way through the pumpkins in most places, but some spots I had to go back over with a knife. A longer blade shouldn't be too hard, though too much longer and it will have to be thicker, which makes fine cuts harder.
2. Pumpkin shavings are emitted, which collect on the surface, obscuring (or even erasing) the lines drawn there. That said, none of the three of us had any major problems with it. In my case, I just worked in a consistent pattern so that I wasn't dropping goop on places I'd need to see later.

This year's pumpkins were tests of the method and of how well the pumpkin holds up with so much material removed. Here's the result:

OK, this isn't my personal pumpkin--it's a collaboration between Number Two and I. But it shows we tried.

Pumpkin PI, get it? PI (=PIE)??

You don't get it.

What Price A Stamp?

So stamp prices are going up again. And by "going" I mean "went, like 5 months ago". The wheels of Project Potpourri grind slowly, but they grind exceedingly fine.

Now they have a Forever Stamp. You buy it today and it will be good until the end of time regardless of future price increases. Sounds like a great way to save literally hundreds of cents, right? My wife (or maybe it was me--these human details are so much dross) posed this question: If I buy a 41 cent Forever Stamp in 2007, am I really saving money vs a 53 cent stamp in 2020 or does it come out in the inflationary wash?

IIRC, inflation is something like 3% per year, but of course we don't have the information on what future stamp prices are going to be. What about history? How closely have stamp prices tracked inflation in the past? Using a history of stamp prices and relative dollar values since 1913 I was able to answer this question. (Notes: All this is based on the first ounce only. I didn't try to go back farther than 1913. For each year, I only use the average dollar value for the year, I didn't break it down by month. For years with more than one price increase, I only report the last one. Since 2007 isn't over yet, I used the last dollar value available, which is September.)

Year	Apparent price that year	Stamp price in 2007 dollars	% diff relative to today
1917	0.03	0.49	16
1919	0.02	0.24	-70
1932	0.03	0.46	10
1958	0.04	0.29	-42
1963	0.05	0.34	-20
1968	0.06	0.36	-14
1971	0.08	0.41	0
1974	0.10	0.42	3
1975	0.13	0.50	18
1978	0.15	0.48	14
1981	0.20	0.46	10
1985	0.22	0.43	3
1988	0.25	0.44	6
1991	0.29	0.44	7
1995	0.32	0.44	6
1999	0.33	0.41	0
2001	0.34	0.40	-2
2002	0.37	0.43	4
2006	0.39	0.40	-1
2007	0.41	0.41	0

It used to fluctuate quite a bit, but for almost the last 30 years, they've been within a few percents of the same price. And given that even a 10% difference is only $.04, I'd call it fairly constant over the last 100 years (except for a few years).

How To: Lose Weight (And I Don't Even Mention Lettuce!)

First of all, let's define our terms. There's "losing weight" and there's "getting healthy". For the latter, you need to eat carrots and exercise. I'm not too interested in carrots and, while I don't mind incidental exercise, I don't have the time or inclination to run around for no direct reason. This post is solely about making the number on the scale be smaller. That in itself is a great step towards "getting healthy", though, as long as you aren't too stupid about it (i.e. no starvation).

The mantra in diet books is "don't diet--change your lifestyle". Partly this is just a good idea. They don't want you going on a crash diet and then fattening back up. But partly this is making a virtue of necessity. The reason they want you to change your lifestyle is that a non-starvation diet doesn't change your weight fast enough to notice it unless you try it over the long term. That is, if you only drop .4 lbs in a week, are you really going to notice it adding up even over the course of a month, if you last that long? Who is going to remember, to the tenth of a pound, what they weighed 2 weeks ago? The first secret of losing weight: You need to keep a history of your progress to refer back to.

But if you are only losing .4 lbs/week, there's another problem: Noise. The key to controlling a variable to to be able to measure it accurately. Otherwise how do you know if what you are trying is working? But diet books also tell you not to weigh yourself very often. The reason they give for this is that your weight can vary because of non-fat variables. A large meal only partially digested, extra water, etc.

That's really terrible advice, though. For instance, children's test scores vary a lot from child to child, so should you just choose one random child from each school to measure performance? Of course not! If anything, taking fewer measurements increases the noise problem. The way to fix noisy data is to remove the noise. The second secret of losing weight: Noise reduction.

One simple way to remove noise from data is via averaging. Particularly, a "moving average". Let's say I take the following daily measurements:

Mon: 201
Tue: 201
Wed: 202
Thu: 201
Fri: 201
Sat: 202
Sun: 200
Mon: 201
Tue: 200
Wed: 200
Thu: 199
Fri: 200
Sat: 201

Nothing is happening! This diet sucks!!!

But wait, let's try doing a moving average. For each day, we'll average in with the previous two days (which means we have to skip the first two since there aren't two days before them).

Mon: 201 (no avg)
Tue: 201 (no avg)
Wed: 202 (201.3)
Thu: 201 (201.3)
Fri: 201 (201.3)
Sat: 202 (201.3)
Sun: 200 (201)
Mon: 201 (201)
Tue: 200 (200.3)
Wed: 200 (200.3)
Thu: 199 (199.6)
Fri: 200 (199.6)
Sat: 201 (200)

In fact, I lost a pound to 1.3 pounds, depending on where you count from. (There are many ways to doing a moving average, including ways to weight the average more heavily towards more recent measurements. Don't worry about the specific method here.)

The difference between raw and averaged (aka "smoothed") data is even more dramatic if you look at a graph. The circles are (fictitious-but-realistic) readings from the scale. The line is the smoothed average. Some of those weigh-ins differ by as much as 2 pounds in a single day. If you wake up a day after "being good" on your diet and see you weigh 2 pounds more than yesterday, doesn't that make you want to give up? But after you smooth the data, the problem may not be so bad.

In fact, it might not be a problem at all. Say the 3 days you were averaging yesterday were 205,202,201 (202.6). All you ate yesterday was carrots, but today you got 203. The weighted average is still 202, which is down from yesterday's average. How awesome is that!

Answer: Very awesome. But not so awesome we need to make things harder for ourselves. For instance, try to weigh yourself under the same circumstances every time: Same time of day, same state of undress, same fullness of stomach and bladder, etc. Also, I have gotten into the habit of "unofficially" weighing myself at various times throughout the day and I've gotten to know exactly how much to subtract for my clothing, how much water I'll lose via respiration overnight, etc. If I weigh X when I got to bed, I will weigh between X-3.5 and X-3 in the morning, rock-solid. An unofficial weigh-in the evening before can help prevent sticker shock in the morning and will also tell you if you can afford a bowl of ice cream. (That might not work for you.)

But who wants to juggle a bunch of numbers?! That's worse than being fat! Don't worry, you don't have to do a thing. Just head on over to PhysicsDiet. Create a free account, give it some info like your starting weight (you can ignore all the stuff about percent bodyfat and exercise) and away you go. The site handles the moving average and plots pretty charts and everything.

Since I started in late March I've only been losing an average of .44 lbs/wk. That's slow enough that I would have given up after a couple weeks, especially since it's also far less than the noisiness of the data (particularly since my scale only weighs in .5 lb increments). But with the two secrets of losing weight, historical progress and noise reduction, I've managed to lose over 15 lbs so far. Also, there are 3500 calories to a pound of fat, so that's just an average of 220 calories per day, which I barely even notice missing from my plate, let alone do I have to eat carrots and rice cakes. It's like I'm not even dieting (almost).

Christmas Present Idea

Long have I pined for a mechanical watch where you could actually see the gears and springs and whatnot flying around. I've seen things like this with the "Fossil" brand attached, but they are always less than what I really wanted. I tried googling for "mechanical watch with visible gears" but that wasn't too helpful.

Today I discovered the magic word: Skeleton. A "skeleton" watch is one where it is purposely made to be see-through. "Full skeleton" means that even things that you'd kind of like to have on a watch, like numbers and hands, are as tiny and hard to use as possible so you can see the full glory of the gears.

Feast your image display software on THIS:

I gather it is possible to spend up to and including ONE MILLION DOLLARS on a watch like this, but, I further gather, Chinese imports can be had for under $100. Even well under $100. For instance.

I wouldn't have many requirements on such a gift. It should be as visible as possible and be actually mechanical, no hidden battery doing the work.

A New Recipe for π

I've been working on a Difference Engine in Lego. A little derivative perhaps, but still a big challenge. For one thing, there's not that much construction detail at that site. For another, what little there is I'm ignoring. I want to try to solve this on my own.

I've made some progress, but my (borrowed) video camera is being cranky so I've been unable to record and post it. (Aside to person I borrowed it from: I'm just getting a black screen in record mode. Also a little red flashing light that I think is the button battery so I thought that was it. However recording suddenly started work despite that, but only for a few minutes. ???) Thus this post isn't about that.

When the Difference Engine actually is running, I thought it would be fun to have it calculate π. NO WAIT, LET ME FINISH!!! I know π is transcendental, meaning there is no polynomial for which π is the solution.

The point of the Difference Engine is that as you crank the handle, you calculate the value of the polynomial for higher and higher values of x. What I'd like is a polynomial such that for higher and higher x, the value is closer and closer to π.

So I just google for a polynomial that does that, right? I mean, there must be hundreds of them by now. No. There are none that I can find.

There are plenty of series approximations, however. For instance:

π = ¹/₁ - ¹/₃ + ¹/₅ - ¹/₇ + ¹/₉ - ¹/₁₁ +....

And with some series...es, it's possible to come up with an expression that the series sums to up to any given point. For instance, the sum of the first n odd numbers:

1 + 3 + 5 + 7 + .... 2n-1 = n²

So maybe one of the series approximations of π can be manipulated into a polynomial. Then I can use the Lego Difference Engine on that polynomial and crank out 2 or 3 digits.

However, I'm having a great deal of trouble with this (not that that indicates anything other than the fact that I'm really not that great at math). For one thing, I've concentrated my efforts on the simple-to-remember 1/1 - 1/3 + 1/5 approach. But I just realized this morning that this series alternately overshoots and undershoots the target, meaning it has an infinite number of humps and valleys. A polynomial of degree n can have a maximum of n-1 humps and valleys, AFAIK, so that series is out.

If I'm going to start from a series, I need one that's always more or less than π and never the other. Or an entirely different idea. I can think of plenty of iterative methods, but that's basically just a series. I need a single step where the accuracy is chosen by the value of x I input. Since I haven't been able to find any reference to such a thing, I'm thinking it hasn't ever been done. Is that because it's impossible?

You Program My Back, I'll Program Yours

If you are a math/science/computer nerd and you have a child, you have undoubtedly wondered how you can teach your child programming. I googled for such a thing more than once and found the usual suspects: BASIC, LOGO, etc, etc. The free ones were all half-finished or too hard, the good ones were all expensive or geared towards classrooms.

I tried teaching Number One Son (8 years old) some pseudo-codey stuff to do simple math problems and learn about loops. He enjoyed that, but we didn't get very far and I always had to be the virtual machine to check if his program ran.

However, MIT has recently come up with something that absolutely rules--Scratch. And it's free!

Scratch is graphical. You drag the little components around to assemble a program. For instance, to make a loop, you drag your components into a loop widget, which wraps around it like a vice. If you want to construct a conditional, you get out the "if" widget and drag and drop logical/mathematical conditions in from the toolbox. Just fill in the blanks and go.

The GUI isn't just for show, either. You don't feel like you are using the mouse to write a program, you feel like you are literally assembling a physical object. And it eliminates syntax errors, which is a major deal in the under-13 crowd. Furthermore, the graphical programming language ties right in to the very graphics-oriented programs Scratch is targeted towards and children love. Creating and animating sprites takes just a few clicks. Object collision is just a matter of checking if two colors are touching. And this is all clearly presented enough that an 8 year old can (and has) figured most of it out himself.

I think he learned more about programming in 2 days with Scratch than he did in all the previous years of my bumbling explanations. He goes off and works on a program for a while and then will come to me with a question about how to do something. And they are pretty sophisticated problems (considering his age), such as how to cycle through sprite costumes and wraparound at the end or how to keep various sprites in sync. With the concrete example of his non-working program providing the motivation, the explanations of modular arithmetic or semaphores stick much better.

So far he's created programs that simulate a robot in a maze, animate a rocket flying to the moon, teach the alphabet to his two-year-old sibling and even one generic drawing program with adjustable pen size and color. All 100% on his own.

Windows and Mac only, but:

1. They claim they'll have a Linux version out "before the end of 2007".
2. The usefulness, fun and polish of Scratch is more than worth setting up an old PC with Windows.

It's possible to upload your program to share with other kids, but we haven't tried that yet. Videos of Scratch in action..