Serious Zane

2011-09-13T18:16:00.001-07:00

I thought I would try a new thing. A fresh writing style. Not so much effort into making sure that punctuation is correct, and meaningful! And pictures, lots of pictures. With lots of cool pictures (it doesn't even matter as much what I say.)

The other day we had art time as a family. I have always thought that the artsy stuff that my nieces, nephews, brothers, and sisters have don

e is pretty cool. However, I've often been reticent during these kind of things. Anyway, Katherine and I kind-of got onto an alien theme while drawing things.

Mr. T kept asking what it was I was drawing. However, I found myself less than willing to identify what each scratch and line on my paper was supposed to be.

In fact, I think this that comes around to my desire to simply not follow directions during these kind of activities. I'm wasn't doing anything specific and I wanted to keep it that way.

At work I am trying to learn as much as I can. However, I often feel the pressures and confusions associated with the corporate environment. But, still

I'm trying to still learn. The other day I was somewhat discouraged and on of my coworkers must have sensed this because he told me that if I'm trying to live right then nothing that happens at work can hurt me. That was pretty comforting.

Anyway, I think it is almost time for another picture. Here is a diagram of a mosfet transistor cross-section. This is what all the fuss is about. What fuss you say? You know, all the moors-law hababaloo, and all that fancy computer and electronics and modern life junk we deal with every day. Well, this simple and surprisingly complicated little thing called a transistor is what makes all this possible.

It has three terminals (actually four if you count the one that's not shown in the picture). A voltage on the gate makes the source to drain area conductive. And somehow that works and somehow that makes all the cool technology possible!

Spotting a crank in his natural environment

2011-02-16T16:41:00.000-08:00

It is hard to define what a crank is. But, I found evidence of one while browsing through the wild Internet.

The other day I was just poking around looking for some information on the Internet and I ran across a funny conversation between a person who dubbed himself the "Diode Array Inventor" and another fella who was trying to reason with him. In the conversation, a little after Diode Array Inventor said that he was sidestepping the second law of thermodynamics, he said this:

Another quick concept test method is to see if
a C nanotube or LaB6 needle field emitter array cathode produces useful
electrical output when placed close to a smooth anode of high work function
conductor separated by a thin porous spacer in a vacuum in the dark. The anode
should become negative. This device consists of many cold cathode vacuum diodes.

How do I upload images from my computer?

This text just struck me funny because in the middle of the supposedly brilliant techno jargon is a super basic question (not a dumb question, just a basic one).

But, the Diode Array Inventor is clearly a crank. First, the ideas in the text are a crazy mixture of ideas that don't fit together in a very meaningful way. Second, it sounds like he is trying to get energy for free, which doesn't happen.

But, I hope I'm not being mean in my judgment because I am liable to be a crank in the same sort of way, although I try not to be.

What cranks do is take their imaginative ideas and to obsess over them until they believe they are real, they believe that they are geniuses, they believe that any ideas contrary to their own are wrong, and they will argue about them until they turn green. Often cranks will focus on disproving something that is firmly held to be true by the intellectual community, like that free energy is impossible.

Another Question

2011-01-30T15:25:00.001-08:00

For the moment I am sick. I’ve heard about some crazy rhino cold virus (rhino sounds tough, doesn’t it) and I don’t think I have it, but I still feel rotten. In fact, both Katherine and I are sick, and Emma seems to be sick too. The upshot of this is that I haven’t been sleeping well these past couple of days, and sometimes when I lie awake for inordinate amounts of time I start to think. It’s a dangerous pastime, I know.

One sleeping tick I’ve been trying lately is to count while trying to visualize what the number looks like. I told Katherine about this and she asked if I was trying to visualize a certain number of things or just the number as it was written down. I was doing the number as it is written.

Since she asked I tried it the other way. The idea of trying to visualize some number of things was interesting, and unfortunately, I’ve found that I can only really keep track of 4 things in my mind without everything getting really fuzzy. However, I did develop an interesting question in the process of trying to visualize things. That is where I’m trying to go with this.

I was trying to visualize dots, and as things go, you can arrange dots in many ways. They can all placed on a line, or they can be bunched into a square or rectangle. It was interesting to think that if you have a prime number amount of dots that no matter how you shuffle them they will not all fit into any sort of rectangle.

And so the question came, given some number of dots, how many different ways are there to arrange them? For this exercise, I was keeping the dots all equally spaced like on grid paper, and I was keeping the dots close together so they were touching, but they didn’t have to lie flat.

So, one dot. How many ways to arrange it? Easy piesy! There is only one way to arrange one dot.

Two dots. How many ways? It seems that there is only one unique way. They lie on a line touching.

Three dots? Well, it seems there are two unique ways to arrange three dots. But, a picture would be best at this point.

So, did I miss any arrangements? And, how many are there for 5? Or 6, or 1000? Is there an easy trick to know, or do you just have to sit there and count ways without ever being sure you didn’t miss any?

And, if I were to write down the sequence of numbers (1 1 2 4 …), would I find that it corresponds to a sequence already known, or would it be brand new and how would I be sure they are really the same? Also, how quickly does the sequence grow? Does it get really big, really fast? Or does it hang back and not grow fast at all?

Also, each arrangement of dots correspond to an arithmetic expression (or they at least seem to). For example, in the case of three dots, if we were to count the number of dots in the figure we could write 3*1 = 3 because there is one row of three. Also, we could write 2+1 = 3 for the other figure. Does the number of different ways of arranging the three dots correspond to the number of “unique” arithmetic expressions that equal three? If so, what does “unique” mean?

Anyway, I had better go before I convince the world that I’m a big crank. But, these are real questions with real answers, I just don’t know the answers at the moment.

The case when n=2 (part 2)

2010-11-26T17:50:00.000-08:00

On the last post I was getting close to putting together the solution to the case where n=2.

I’ll just have to give the answer because I don’t think I’m in the mood for a long, drawn out explanation.

For n =2, the deal is this: P = 1 - (L – ε)^2/L^2

I don’t think I have the energy to go into it right now, but I that is the probability that the average of two points picked out of the constant distribution bounded by +/- L will be less than ε.

Now, I wanted to do n=3, but the idea of doing that scared me somewhat. For n=1 we were talking about a line with length 2L. For n=2 we were talking about a square of each side having length 2L. For n=3 we start working with a cube, and n=4 we start working with a hypercube, etc. etc.. It all just gets nasty really quick.

I thought it would be best to change direction and start thinking about the Gaussian distribution which isn’t bounded on either side (no worrying about crazy many dimensional boundaries).

While working on that for a few days I had some neat ideas and made some good progress until I dribbled up a nasty equation that would work for any n, but that was indeed nasty. I didn’t know how to calculate the answer until I found a neat theorem in the back of an old statistics book I got from a dejunking book sale by the university library.

That theorem promised to make the solution for any number of points really simple and easy to calculate. However, it didn’t quite fit right, and I haven’t investigated it since. I just haven’t really thought about why the theorem works and so I can’t tell if I can use it in my situation. I’ve just been too busy with life, ya know.

So there is the ten thousand foot view of my work on this problem. Perhaps later I can throw down the equations with an explanation of where they came from, and maybe I can even decide if I have a workable answer or not.

The case when n=2 (part 1)

2010-11-21T15:59:00.001-08:00

The problem:

What is the probability that the mean of n points picked randomly according to a distribution σ(x) will be within |ε| of the mean of σ(x)?

Last time I did the case when n=1 and σ(x) = 1/2L. The probability P in that case is equal to ε/L.

Another solution:

Letting n=2 means that we are figuring out what the probability that two random points will have a mean a certain distance from the mean of the probability distribution. We thus have a new equation to work with, the definition of the mean of two numbers:

Since we are looking for when x_bar is going to be less than |ε|, we can use the definition of the mean to express that condition is crisp mathematical language:

But, before I run too long with this equation, there is another problem that must be dealt with, and that is how we are going to deal with σ(x). The problem is that we have two points and this distribution only describes the likelihood of picking one point. There is a probability rule that states that when there are two independent events (that is, one event doesn’t effect the likelihood of the other) then the probability of both of them happening is the product of the each individual probability. I’m going to go out on a limb here and say that you can play the same game with the distributions. (I think I can show it, but I just haven’t gotten around to it.) So, I think we can use σ(x) to create a new distribution with two inputs σ(x0,x1) (forgive me for using the same symbol twice), and that the it should look like this:

But, this is a bit different from the last distribution. In the last one the area underneath the curve represented the probability. However, this distribution is a function of two variables. That means that this represents a surface (in this case a plane), not a curve. Without a curve, there is no area underneath the curve to measure. But, just for fun (and it works too) lets just say that the volume underneath the surface represents probability.

Notice σ(x0,x1) is bound by a square with each side length 2L. It is expected that the probability of finding a random point (x0, x1) somewhere is the square is 1. So, what is the total volume underneath the surface bound by the square? The volume of a cube is length*width*height. The height is a constant 1/4L^2. Thus, The volume is 2L * 2L * 1/4L^2 = 1. It is just as hoped.

Next we must find some way to link this new distribution with the condition created earlier from the definition of the mean. The best way to do that conceptually, I think, is with a picture. Here is a picture showing two axis labeled x0 and x1 with two lines derived from the condition that x1 and x0 must be less than the absolute value of the mean, as described by the condition

The box is drawn for plus/minus L on both axis, and the grey region is where the the mean of x0 and x1 is less than the absolute value of ε.

But, I’m tired now. So, I’ll have to finish this next time. What I intend to do is to calculate the volume above the grey region using the condition and the probability distribution put together in this post.

Until next time batman!

The first case

2010-11-18T21:54:00.001-08:00

The problem:

What is the probability that the mean of n points picked randomly according to a distribution σ(x) will be within |ε| of the mean of σ(x)?

A solution:

We have three unknowns: σ, ε, and n. To figure out how to even approach this question lets pick a specific function for σ(x) and a particular value for n.

Let n = 1

Let σ(x) = 1/2L, -L <= x <= L

In the future I plan to try to figure this out for bigger n and a regular old bell curve, but this seems like a good easy place to start. It’s clear that the mean of one point is the value of itself. Also, the probability of a point being picked anywhere between –L and L in the distribution I chose is constant. Here is a graph of σ(x):

The terminology I will be using is to call σ(x) a curve (even though it isn’t curvy in this case). I will also speak about “the area underneath the curve”. Observe that we have a rectangle pictured here with an area of 1 (one side is 2L long and other side is 1/2L, multiply the sides to get the area). That is equivalent to saying that the area underneath the curve between –L and L is 1.

We are interested in the area underneath the curve between two points because it represents the probability of picking x between those two points.

Lets get back to the problem at hand. It had ε, so lets put that into the graph:

Since we are trying to find the probability of picking one point between –ε and ε, the equivalent question we are trying to answer is: what is the area underneath the curve σ(x) between –ε and ε?

We can answer that with our good knowledge of rectangles. The width is 2ε and the height is 2L. The area is 2ε/2L = ε/L.

Since that area is the probability of picking a point within |ε| of the mean of σ(x), which mean is zero, we can say that the probability P is ε/L.

Thus, we have an answer for the most easy case I can conjure, but this wasn’t without a purpose. This solution is helpful in pointing a way for more challenging cases.

In fact, the next case I want to try is the same distribution but with n=2.

The follow up post

2010-11-14T14:59:00.000-08:00

Okay, I'm going to move on from the last post because, well, lets face it, statistics isn't everyones favorite subject.

However, I wrote that little article as prep for this one, and so there is more fun ahead. What I brought up in the last post is that I think there is a problem with they way people are trying to tell that two sets of data are different. I think that people are trying to pawn off the responsibility of making decisions to the math. Since that doesn't work so well, my thought was that a better approach would be to develop mathematical tools that would help people make better decisions.

So, I formulated a little math problem that has been getting more difficult the more I try to figure it out. This won't solve the worlds problems, but it is related somewhat to what I was discussing previously. Here it is:

Given a probability distribution, what is the probability of picking n random points (where the randomness follows the distribution) where the mean of the picked points is within a specified distance from the distribution's mean?

While thinking about this problem for a few days, it has been flowering into a hardy exercise.

The problem with statistics, as I see it

2010-11-13T08:24:00.001-08:00

AAmong all of the subjects that leave students with a bad taste in their mouth and a burning desire to never broach the subject again, statistics seems to stand out. I have spoken with several people who particularly dislike statistics and some who didn't wan't to talk about it at all. Also, I have been left with a nasty taste in my mouth from my statistics experience.

I imagine that most people are well content to leave statistics behind and to never think about it again. However, I doggedly try to be genuinely interested in every course I study regardless of how painful it is or what grade I get, and I am interested in statistics. So, I have an inner conflict that has been stewing in me for quite some time, and I've been rolling the ideas around to see I can understand what the source of that conflict is.

Fortunately, I think I've figured it out what is bugging me (although I can't speak for the millions of others who suffer, I can venture a guess). It is all to do with significance tests.

For those not familiar, significance testing is a formalized method to decide if two sets of data are the same or different, and this method is used all the time. In fact, I can't eat my breakfast cereal without thinking about it because printed on the milk carton is:

According to the FDA, no significant difference has been shown between milk derived from rBST treated and non-rBST treated cows.

That smacks of a significance test! In fact, pretty much any scientific study that deals with statistical data will involve a significance test. They are everywhere.

And so here is my problem, from my reckoning, significance testing is bunk! And I think most students, including myself, when learning about significance testing have vague and uneasy notions that there is something fundamentally wrong with the material being presented. However, there is also general confusion about the topic because of a lack of intellectual maturity and a strong lathering of self doubt so that students will either throw up their hands in disinterest or silently suffocate any thoughts which don't fit the program.

So, why do I think significance tests are bunk? As I said, the goal of a significance test is to tell if two sets of data are different. This is done by first, making a few reasonable assumptions about the distribution of the data, and second, by observing how far apart the averages of the data is. That observation is done via formulas which depend on how big your sample sizes are, what the distribution is, what the means are, and a magic number which tells to what degree of certainty you are happy with to tell if the data sets are different.

So, what is the problem? The dependence on the sample size coupled with dependence on the magic number is the problem. That problem renders this problem as accurate as a crap shoot. You see, as the sample size increases, the test becomes more sensitive because there is more confidence with more data. This means that you must use the magic number to tune the significance test to the right sensitivity. But, it is impossible to know what the "right" value for that number is. So, to do a significance test "right" you are supposed to set the number before looking at the data, and everyone almost always chooses 5% because there isn't really a good way to set the number anyway.

So, what does this mean? I draw two conclusions from it. First, it is silly to even think that the formula can magically tell if data are different without the human error. Second, people really like significance tests because it removes the responsibly they have to decide if they think the data is different or not. That is why they are so attractive. It is because you don't have to think to use a significance test, it thinks for you.

So, what is to be done? I don't know, but I have the intention to stab at this again in another blog.

The missing spaghetti flavor

2010-05-29T17:44:00.000-07:00

Ciow,

In our cooking adventures we have been making spaghetti from scratch. And, by the phrase "from scratch" I mean that we have been growing out our fingernails and scratching wood shavings from wooden table tops and counters for the special added "woodland" flavor.

In addition, we have been using canned tomatoes with Italian flavoring in our sauce to give it that delicious fundamental spaghetti taste flavor essence. We were using other seasonings as well to give the sauce a flavor boost. Those are Italian seasoning, onion powder, and garlic powder.

Unfortunately, we have been having difficulty finding those same canned tomatoes in the grocery store lately, and our table is getting ruined from all the scratching that we've been doing. So, we've had to experiment with our spaghetti sauce to find the right flavor combination from our spices.

The initial assumption was that we just needed to add more spices to compensate for the ones lost in the special tomatoes. However, we've been finding that our sauce was only almost like spaghetti no matter how much Italian seasoning, onion powder, garlic powder, oregano, or parsley flakes we've put in.

However, as of today we've discovered the missing flavor!!!!! It was basil. I looked on the back of a spaghetti flavor pack at the grocery store to see what the ingredients were. Indeed, it was the missing flavor, and now our spaghetti is like spaghetti.

This is blog worthy

2010-05-06T19:54:00.000-07:00

I am proud of a little perl script that I wrote to replace scientific prefixes with scientific notation in text files.

Now okay, why would I want to do this. Well, at work I work with a program that produces numerical output like 100n or 50M. Well, when I try to look at the output in other programs like excel, it blows up. So, I wanted a script that would neatly replace the n or M with e-9 or e6 so that excel (or anything other program) will be happy.

As an added bonus, it will also chop off any trailing units on numbers.

So, here it is in all its perly glory.

#!usr/bin/perl
my ( $fileName ) = @_;
open(FILE, "< $ARGV[0]") or die "Can't open $ARGV[0] : $!";
my @lines = ;
close(FILE);

foreach $line (@lines)
{
$line =~ s/([0-9][0-9]*)T[A-Z,a-z]/$1e12/g;
$line =~ s/([0-9][0-9]*)G[A-Z,a-z]/$1e9/g;
$line =~ s/([0-9][0-9]*)M[A-Z,a-z]/$1e6/g;
$line =~ s/([0-9][0-9]*)k[A-Z,a-z]/$1e3/g;
$line =~ s/([0-9][0-9]*)c[A-Z,a-z]/$1e-2/g;
$line =~ s/([0-9][0-9]*)m[A-Z,a-z]/$1e-3/g;
$line =~ s/([0-9][0-9]*)u[A-Z,a-z]/$1e-6/g;
$line =~ s/([0-9][0-9]*)n[A-Z,a-z]/$1e-9/g;
$line =~ s/([0-9][0-9]*)p[A-Z,a-z]/$1e-12/g;
$line =~ s/([0-9][0-9]*)f[A-Z,a-z]/$1e-15/g;

$line =~ s/([0-9][0-9]*)T/$1e12/g;
$line =~ s/([0-9][0-9]*)G/$1e9/g;
$line =~ s/([0-9][0-9]*)M/$1e6/g;
$line =~ s/([0-9][0-9]*)k/$1e3/g;
$line =~ s/([0-9][0-9]*)c/$1e-2/g;
$line =~ s/([0-9][0-9]*)m/$1e-3/g;
$line =~ s/([0-9][0-9]*)u/$1e-6/g;
$line =~ s/([0-9][0-9]*)n/$1e-9/g;
$line =~ s/([0-9][0-9]*)p/$1e-12/g;
$line =~ s/([0-9][0-9]*)f/$1e-15/g;

$line =~ s/([0-9][0-9]*)[A-Z,a-d,f-z][A-Z,a-z]*/$1/g; #chops off the trailing unit

print($line);
}

Thinking about Units

2010-03-19T10:04:00.001-07:00

While in the shower this morning I had the opportunity to think about what units are. When I say "units" I mean things like inches, feet, meters, and seconds. I don't mean refrigerators or oven units. My thoughts were quick and jumpy, but I think they were interesting. So, I'll try to be clear.

Into

What are units? Doing a little internet search revealed that "uni" is a Latin word for the number 1. So the word unit means one. I think the idea of a unit being 1 goes back to the geometry days when geometers would think of numbers as lines and of lines as numbers. These days we tend think of numbers as quantities of objects, like the number of apples in a bag, but times change.

However, in the olden days people went at it from a different direction, and their first thought was about ratios. In fact, the most important and foundational idea to the old geometers was the idea of ratios. A line by itself was just a line, but they understood the concept of numbers by comparing the lengths of lines. So, if they had two lines, one twice as long as the other, then they would say the ratio of the lines was 2. Now, that isn't a number quite yet the way they thought about it back then. It was a ratio.

To get their concept of numbers they added an additional concept. They would label the shorter line as the "unit line", meaning the line had a length of 1 by definition. Then, it follows that the longer line would have had a length of 2 because it was twice as long as the first. And, this is the kicker, because lines were numbers in their thinking, a line of length 2 was the number 2.

So, they had the idea of ratios, from ratios they got numbers, and then some jerk came and proved that you can't get every number from a ratio, and Pythagoras had him rubbed out. The rest is history (what I've said really isn't history, it's a gross caricature).

Historical blemishes aside, we have the smaller line acting as the unit line, and it became the reference from which all of the other lines were measured. Really, we haven't gotten away from those old geometry days. If we want to measure a distance, we go to the store and buy a stick with unit markings on it that are supposed to be close to an inch in length.

Musings in the Shower

Now I didn't make this stuff up, and those ideas are rather common. However, my thoughts in the shower took a different track. Instead of thinking of units as defining a distance, I thought of units as a proportionality constant.

A common way to show proportionality is with the algebraic expression , where m is often thought of as a slope or a proportionality. If we were to visualize the proportionality graphically then we would have the following.

Of course, the graph shows the linear relationship between x and y. If the slope is more steep, then y grows faster than x, if it is more shallow, then y grows more slowly with x.

This all may seem to be a bit old hat, but be patient. Let's substitute new ideas in for y and m to make this applicable to our discussion of length and units, so that we get

How is that the same equation? Well, y became length and m became inches, and I switched it around because we typically write inches after everything. But, really the equation is

It is written this way to emphasize the fact that the length is proportional to x according to the proportionality constant, inches. If we had a bigger unit, like feet, then the slope would be more shallow. That means that as x grows, that length will increase more slowly than in inches.

I can here you saying, yea great, everybody knows this. This is easy. Why are you wasting my time with this grade school stuff. Okay. Okay. I'll just ask a simple question. What is x again? Think about it, what is x!?

There are two ways to look at the equation .

The first interpretation:

x is a unit-less number telling us how many inches we have
length is a distance
in is the unit

The second interpretation:

x is a quantity of space, a distance
length is a measure of distance
inches is a proportionality constant

What do I mean by the second interpretation? Here I am splitting hairs, but I mean that there are no units like we think of them. Length is a real number, inches is a real number, and x is a real number.

Now, that is a different beast! Later, I'll write about what I think this may mean.

Not Wasting Any More

2010-02-20T19:31:00.001-08:00

I'm excited because I rather recently got boinc on my computer. Boinc is a software program that allows me to donate my computing power to some worthwhile causes. It downloads jobs to do, and then while I'm not using the computer it works away at them. It sends the results back when it is done.

I'm happy for this because it seems that my computer is quite underutalized. Now the CPU is happily slammed at 100%.

Eigen Kazoo Progress

2010-02-17T21:42:00.000-08:00

I have been working on the keyboard design. However, it is getting a bit complicated, and I think it would be worthwhile to put off the whole idea until I've actually got the microprocessor making sounds. Then I'll know what works, I'll have a few more tools, and I'll be less worried about how to make the microprocessor work.

Here is the idea so far.

The cloud on the left represents 32 buttons. Each line coming out of the cloud (except for power and ground which I included to make this diagram more busy) represents four data lines from the keyboard. Those are going into the multiplexers which can select which signals to forward, like a train switching station. The multiplexers switch based on the values of S0, S1, S2, and S3, which are outputs from the counter (which counts from 0 to 15 in binary). At the end, the microprocessor will be able scan though and check each button, two at a time.

I hope to come up with a simpler way to do this all. One reason that it is so convoluted now is because I haven't really looked around the market for options with counters and multiplexers yet. I just found some that seemed to work and figured out how to do the design with those.

But, before I go shopping for those things, I've got to get the microprocessor development environment.

Statistical Calculator Fun

2010-02-17T05:55:00.000-08:00

Since I got Windows 7 from school I've enjoyed many of the new features it sports. In fact, I enjoy using Windows 7. It flows surprisingly well.

However, that isn't the purpose of this post. I was playing with the new windows calculator, which has a statistics mode. The statistics calculator lets you have a dataset of numbers from which it will calculate the mean, standard deviation, and a couple of other statistical things.

I created a data set by "randomly" entering numbers from 1 to 9. During this process I figured that the mean should be somewhere around five because five is in the middle of 1 and 9. When I started to get board from typing numbers I hit the mean button to see how close it would be to five.

Guess what. The mean was exactly five. I thought that was pretty cool.

Here are the numbers I just so happened to type in.

I doubt these numbers are very random at all, but they were as mixed up as I could make them.

A New Plan for a New Project

2010-02-09T16:30:00.000-08:00

A while ago my brother Matt showed me a cool thing called the Eigenharp from http://www.eigenlabs.com/. Because the Eigenharp is so cool I'm going to try to put together the next best thing.

I'm going to build the EigenKazoo!!!

The EigenKazoo will look like this

First there are the buttons. I have no idea how I'm going to do these, but these will be used to play notes.

Second, there is going to be the ATTiny microprocessor from Atmel. The chip itself is going to be about $2. However, the development setup is going to be about $70, but I'm happy about that because I would be able to use this same development platform for many of Atmel's microprocessors, some of them being way more powerful than the ATTiny (the ATTiny is pretty tiny, ya know).

At any rate, I'm going to need to save a little bit of money before I can bring myself to make such a big purchase for something so non-essential.

Third, there is the PWM output. This is going to be used as the audio signal. A PWM (pulse width modulation) signal is basically a high frequency square wave with an adjustable duty cycle, and the duty cycle is the ratio of how long the pulse is "up" to how long it is "down". These are the poor-man's way to get an analog signal from a digital signal. (Actually, this is THE way to do it in many applications.)

Fourth, the low pass filter. This will be used to smooth out the PWM to make it into a more natural sound. The filter cutoff will be able to be adjusted so that the tenor of the sound can be played with (by controlling the amount of higher frequency harmonics in the sound). I was thinking of doing this with an opamp.

Fifth, the amplifier. I've been studying hard to try to understand amplifiers, and this is my opportunity to apply my studies.

Sixth, the speaker. This is going to be a junko cheap speaker.

Fun with the translator

2010-01-11T19:17:00.000-08:00

I suppose I'm pretty board, because I started feeding sentences through bing's translator to see how they would become scrambled.

Input: I am a sentence which did not survive the translation.
Output: Surviving the translation, but experts

Input: I shot the elephant, and he died a quick death.
Output: The death of elephants.

Pretty dumb hu? Well, it took a few iterations to lose the information out of the sentence, but it didn't seem to come up with any wacky interpretations. Darn.

I don't believe

2009-11-09T12:04:00.000-08:00

I think this blog is pretty silly. The only problem is I think it is serious.

The site is apparently about finding a group of people called the "Illuminati" by use of numerological methods. Of course, numerology is pure bunk, but by the authors infallible logic, he has linked the Illuminati to the Mormons! Gasp.

Illuminati Under the Microscope

School is Amazing

2009-10-18T07:27:00.000-07:00

When I say amazing, I mean amazingly crazy. Actually, I'm working harder this semester than I've ever worked before. I wonder if it will pay off to the point where I will be able to get the grades that I want and need. However, perhaps this has just been a special week because moving into a new apartment has augmented the stress. I've been trying to deal with the stress by doing little exercises and also by trying to not amplify the stress in any way. In other words, I've been trying to not worry about it.

First lisp function

2009-09-26T11:49:00.001-07:00

I'm pretty excited because I wrote my first real lisp function. It's not anything special, but it represents all of the effort to get the development system going and all of my (super novice) bugs worked out.

Unfortunately, blogspot isn't going to let me indent the code. So, it will be harder to read than normal.

Here it is

(defun GCD (a b)
(if (= b 0)
(eval a)
(myGCD b
(mod a b))))

It calculates the greatest common denominator of two numbers. So, when someone calls:

(GCD 100 10)

The answer will pop out"
10

On that note, I've also written my second lisp function which incorporates a loop. It was tricky to do because lisp is so different. But, here it is

(defun newton (seed icount)
(loop for i from 0 to icount do
(setq seed
(+ (* .5 seed) (/ 2 seed)) ))
(eval seed))

This uses newtons method to solve y=x^2 - 4. That is not too hard (the answers are x=-2 and x=2), but it works.

Calling it with a starting value of .5 and to do 10 iterations looks like this:
(newton .5 10)

The result:
2.0

These things I want

2009-09-17T09:43:00.000-07:00

In my religion class the other day my professor spoke about how in the beginning we were with God, saw His immensely awesome Lifestyle and bonafide mastery of everything, and we deeply wanted it. Thus we were very happy and excited for the plan of salvation to enable us to obtain it, God's way.

That day the concept struck me, and I have been reshaping my understanding to fit with that idea.

Much like that feeling we must have had before God, I am feeling that deep urge to have greater mastery. Right now, I am feeling this desire to obtain two categories of knowledge which seem to posses something greater.

What are they?

Lisp and Tensors.

Yet, what would I have to do to obtain these? What is the cost? Is it too great? I don't know the answer to those questions.

I have wanted to know more about lisp for a long time now. The language promised an amazing elegance and power, but I've always worried that there is something wrong with lisp because it's not heavily in use. Yet, it still intrigued me. I recently read an article speaking about it which has dispelled that concern.

My desire to know tensor analysis goes back to high school learning about matrices (tensors, I'm told, generalize matrices). I felt that there was something deep and powerful about them, but I wasn't in any position to understand it then. But, here and there I've seen vectors, matrices, hints of tensors, and even was flatly confused by them in General Relativity. Eventually, I identified them as something I didn't understand, and have tried to understand them. But, I'm still in the dark.

Tensors, like lisp, promise great elegance and power in mathematics and physics. I desire to have that power.

So, now I have crystallized my desires.

The Everything Function

2009-09-16T19:55:00.000-07:00

A time ago I devised a mathematical function to solve all of my problems. So far, it has.

It is simply defined as a function f which takes any problem as an input and as an output produces a solution. For example,

f( "What is x^2 + y^2 = 0" ) = "This is a circle."

The everything function has infinite utility. It can do more than naively answer questions, but it can anticipate what the answer based on the intent and purpose of the user. I suppose this is a foray into a whole new branch of mathematics. What should it be called? Let's see:

f( "What should this new mathematics be called?" ) = "C-rank Dynamics."

An undeniable answer!

We were all wrong

2009-08-27T17:11:00.000-07:00

Sometimes at work we get bored and to keep the time we ask questions to each other. One question I asked was what is the maximum amount of spheres that could be touching another sphere, assuming that they are all the same size.

I have thought about this much after I asked the question and I convinced myself that the number was 14. Somebody at work was vacillating between 14 and 18, and another worker thought about it for five seconds and decided that the number is 14.

I recently looked up the answer on the internet. Apparently this is called the kissing number problem (I didn't dream up the concept, and I remember hearing something about it before). Anyway, the correct number is 12.

We were all wrong.

Badgering Myself

2009-08-23T11:45:00.000-07:00

Several days ago I found myself in an argument with my wife. I wasn't intending to be disagreeable, but apparently I was anyway because she was convinced that I started the argument.

After puzzling over the roots of the discussion I concluded that I was simply in an argumentative mood. To get over it I got a piece of paper and started writing down a debate with myself. The material is likely not any good, but it was fun to write. Unfortunately, I didn't finish it and there is no clear winner.

So here it is.

Custom justifies nothing.

Yet, you write that in custom, the custom of the English language. Nothing in the language has meaning except by custom.

Truly said, but so, I could have said it in any other language. Yet more, any language is not justified by custom. Languages are always in flux, denying custom. There is always a better way to speak. Languages may be learned by habits and observations of behavior, but when bound by custom they stagnate!

Perhaps so. But, just because something is changing doesn't mean that it is not custom. We have just assumed that custom is constant.

I am willing to assume custom in not constant if a satisfactory definition is provided. I think custom is simply a group's consensus about what something is or ought to be.

There is more to custom than that. It is time honored tradition. It is the refinement of trial and error. Honor is the quality your definition and attitude lack.

What of honor do I need?

Honor is respect that is due for a society. It is an attitude of solemn sacredness towards custom. It allows society to fully adhere to a custom so that random deviations from it do not wreck havoc.

Is there more to honor than this?

Yes. Honor is born in love and gratitude. Love and gratitude are always justified. Those feelings create honor toward custom, and such are reflected by respectful actions, feelings, and words towards custom. All of which your definition lack. I suggest that custom are those parts of society which people think or do that define or characterize that society.

And you naturally assume that all a society does is not necessarily good?

Yes.

So, if a society has some evil actions, the evil actions are not justified, and custom characterizes that action, then that custom is not justified.

Yes. Evil actions, and the customs that produce them, are never justified, but that was not your argument. Rather you were arguing that customs justify nothing at all, and this is only a case where customs don't justify an action. Do you wish to amend your position?

Not yet. I've just won a case! I have shown that when a custom produces an unfavorable outcome that it is not justified. Now all I must do is show that even when customs have favorable results they are still not justified.

Good luck.

I do not think it will be difficult, and I suspect you will soon be asking me if you may restate your argument. Consider that even though a custom may not produce a strictly evil outcome that the outcome could be better. If the goal of society is to improve, then it should be willing to put down and rethink customs in every circumstance so that it may obtain endless improvements. Thus to rest on a custom, letting it justify itself for it's own sake, is foolishness. So, no custom justifies itself.

Do not move so fast, my head is spinning with your rhetoric. You are telling me that the road to improvement is by abandoning customs. Yet, customs run deep into people's hearts and minds. Customs form a web of dependency and fulfill subtle functions in society that both the most sensitive and most cynical people may overlook. Consider wedding dresses and their function in society. What do you think of them?

I think they are perfunctory, expensive, and detract from the enjoyment of weddings because of the fuss and hassle they induce, but more they subtract from the sacred meaning of weddings.

Indeed, that is what you think. But, I've spoken to one man who said that the wedding dress is for the mother-in-law because they are really the ones who set the standards for what the wedding is to be. However, I've spoken to a woman who said that the wedding dress is for the man so they can appreciate the beauty of the bride. My own opinion is that they are for the woman, so they can feel beautiful. What effect would it have if it were removed? Many angry mothers, many hurt brides, and many grooms who would be annoyed at all the painful fuss (regardless of their liking to the dress).

I can see your obvious conclusion that removing the custom would be worse than keeping it, but what about the custom itself? Doesn't this example show even more how unjustified the custom is?

First Forseen Problem

2009-06-19T17:16:00.000-07:00

The first problem that I can foresee since starting research to design and build my own VGA output is how to handle the video memory. The video memory will need to hold all of the picture data which will be read out very quickly to a digital-to-analog converter (DAC). That memory will need to be both read and written very often. Two new valuable websites I've found are www.tinyvga.com which is about another homegrown VGA project and a class website about implementing VGA on an FPGA (all the abbriviations in this world!). I'm excited because of all the information will be useful.
I do not yet know the best method to use for handling the memory. I have two ideas so far. The first is to have a single data bus and address bus which the processor, ram, and DAC all share. The processor will then coordinate when which device will drive the bus. This method assumes that I have a specialized DAC which will drive the bus like www.tinyvga.com did.
The other method I'm considering is to have a microprocessor which has it's own ram, and to transfer the data to the DAC by using DMA. I believe that I would prefer this way because it seems less hacky than the first. My only concern about that DMA method is timing because I need to feed the DAC at very regular intervals to keep VGA happy. I'm not knowledgeable enough about DMA to know if I can get it to behave like I need.
To accomplish this I need to look deeper into what DMA can do, and I need to get spicific about what microprocessor and DAC I'll be using.

Here are some video DAC data sheets I've found for reference.
TI Video DAC
Analog Devices Video DAC

What to do?

2009-06-17T19:55:00.000-07:00

Since my last post I've been rethinking my game plan. If I want to do this project then I might as well make it good. The aspect to improve to make the project better is how things are displayed. The initial idea was to use an LCD panel with all the circuitry figured out. However, the new plan is to construct a VGA output. I can tell already that doing that is possible, but the trick is that I want the display to look good.
Unfortunately, that challenge calls for a new batch of thinking. There are not many resources on the web for doing this, but the few there are have been helpful in helping me understand the VGA protocol better and what a system will need to be effective.
The main difficulty (as I understand it now) is how to set up the memory so that I can write and read from it at the rate demanded, about 25MHz.
I did find a product which can do this for me, but that would not demonstrate any skill on my part.

The best source of information I've seen is this simple VGA/Video adapter a fellow built.

I don't have a fully baked plan yet, but let's see what will happen next.

The 8-bit Computer: Yet Another Project

2009-06-11T10:04:00.000-07:00

It seems about every three weeks I want to undertake another new project. However, each of those projects seems to demand about 10 years of time. In response to this I try to think of more projects which are less demanding but that will still somehow retain value. As a consequence, about every three weeks I want to try something new.

I believe (hope) that sometime, as I make progress and develop a career, all the projects I wish to undertake will all blend together into one great project and my efforts and time will be unified.

In the meantime... Here I'm going to share my thoughts for a little 8-bit pic microprocessor based computer. So far, the steps seems relativity easy and this will be a good starting point for other projects. In the future I may just share more details.

***********
Parts:
PIC10F200 $12 for 25 => http://www.microchip.com/wwwproducts/Devices.aspx?dDocName=en019863#2

Developer Kit $37 => http://www.microchip.com/stellent/idcplg?IdcService=SS_GET_PAGE&nodeId=1406&dDocName=en010053

Newhaven Serial Display $20 => http://www.newhavendisplay.com/specs/NHD-0216K3Z-FL-GBW.pdf

Protoboard, solder, wires, power supply, buttons, etc. $20
***********

Since each of those money values are very rounded this project would cost about $100 in parts, and some more in time. However, the developer kit, the serial display, and the odds and ends and one-time-only costs. So the next project would cost significantly less money.

The PIC10F200 is one of the lowest grade microprocessors available. There are lesser, but this is the least that the Microchip company sells. The advantage of low power is the corresponding low complexity. For future projects, I will likely get more powerful microprocessors, but the hope is that with the development platform built and experience with all of the unforeseeable difficulties of the lower complexity situation then the new level of complexity won't make the project impossible without full time effort.

What will this be when I'm done? With my best Paint artwork, it should look something like this.

In this picture there are three boxes. One of them represents the circuit board with the 6 pinned pic microprocessor and all of the places around the board that wires will plug into. The part that has text displayed is the Newhaven LCD display. The other box with two black squares are buttons. I believe there is enough I/O left on the microprocessor for one more button, and if I get real clever I think I could have eight buttons total (3 wires = 3 bits = 8 different values).

At this point I won't bother with details, but programming it will be the most fun. The pic microprocessor can hold exactly 256 instructions in it's program. For it's memory, it has 16 bytes. With only sixteen bytes I can keep track of everything with my fingers and toes, with four to spare!
I suppose it will be some time before this is realized because I don't have loads of free time and energy, but with planning, the time will come.

An Almost Original Idea

2009-06-07T17:09:00.000-07:00

Ever since my uncle has procured an electron microscope I've been trying to think of what could be done with it. Last night I came up with an idea. Imagine being able to not just look at an amazingly detailed image of a fly head as created by an electron microscope, but being able to view the fly head in 3D.

The idea is to take multiple images of the same object from different point of views, and to let a computer figure out the 3D details from the picture information. Thinking about that kept me up for awhile because it is such a neat idea, and I was creating a plan how I would be able to do it.

I thought of it first, right? Well, today looking on the internet I've found that there are people who do that already. How sad!

However, I'll keep looking at the idea because this is a whole new thing which I've never heard of before.

Get a Band Name

2009-05-24T19:25:00.000-07:00

So, you need a band name. You've come to the right place.

However, if any of these resemble any already existent band names then let me know so I can remove or modify them.

There will be more to come.

Green Spleen
Blasted Varmints
Chinese Remainders
Radical Racists
Doberman
Placid Platters
The Final Ten Billion
Camera Phone Brothers
Thick Boned

Toenail Paint
Apricot Sundae Smoothies
Copious Fugitive
Cat's Cradle Super Strings
Leap Year Frogs

Lamentation Station
Audio Sounds
Good Music People
The Observables
Bit Stream
Scantily Band
Submarine Woofer
Automata
Emphatic Lymphatic
Fiber Bundles
Exultant Space
Eating Daffodils
Americanizing American Americans
In the Order Strange
Intense Elegance
The Squeaky Cheese Boys
More Carmichael
Nondisclosure Disaster
5D Personalities

Don't Read This Alliteracy

2009-05-24T17:03:00.000-07:00

Once upon a time in public school I had an English class. Now, I had a bad attitude, and I resented every English class I've ever attended before I graduated High School. I can't define the reason exactly, but it was a conglomeration of reasons, one being the fact that I read slowly. (However, I can compensate now by being able to use the word conglomeration in a sentence and spell it without annoying red lines underneath.)

Anyhow, we had an assignment where we had to write a poem with each word starting with the same letter. I chose the letter 'S' and I couldn't do it. I looked at my neighbor's paper and saw that she did better than I did, but she cheated by using connective words like "the" that weren't consistent with the rule.

So, the other day I wrote a poem with all the letters starting with the same letter. I had practice with this sort of activity since then because of my developed love for alliteration.

Tea Time Toddy

Tea Time Toddy ticked though timeless thought.
Though, today terrible tidings thrashed Toddy throughout.
Tragic things. Totally terrible.

The thoughts turned turquoise and they thistled.
Tis, Tis, Tea Time Toddy.
Tragedy Triumphed Toddy's thought.

Person A writes blog B

2009-05-24T16:43:00.000-07:00

Since I am confident that nobody reads this I suppose that I am free to post just about anything and that I can feel pretty good about it. However, I suppose that I should be somewhat careful. As we learn from x-files, "someone is always watching."

So, I thought I would relax somewhat and just gab. I suppose that is what blogging is for. Person A writes on blog B while hoping that person C will read it. However, person C doesn't, but A can feel better about C not reading B because person D will read B. Yet, the hope is that person D is not an employer from company X and that B will not offend D so that A can work for X.

Yup, it's the classic A-offends-D-not-C-with-B-and-looses-job-X scenario. It's a terrible shame.

Subjunctive Precipitate

2009-03-11T15:09:00.001-07:00

This phrase is so descriptive that I'm tempted to change the name of my blog to it. Just consider it's meaning.

Subjunctive: represents an act or state; used to express a wish or a possibility; a verb form indicating an existence as doubtful or dependent

Precipitate: Bring about abruptly; fall from clouds; rain, snow and sleet; the formation of a solid in a solution during a chemical reaction; dissolving in reverse

Since this phrase is used nowhere I've seen (except once in really old psychology babble) I am convinced that there is no meaningful interpretation of it.

If anyone can give a good explanation or proffer an example then I will award that person 10 coolnesses.

Oh, Can Such a Thing Be?

2009-02-16T14:53:00.000-08:00

As a child growing up I was often swayed by the popular disdain of Microsoft Windows. I've spent much time carefully listening to evangelistic Apple and Linux supporters who have often taken time out of their busy lives to point out that Apple computers, or the Linux operating system, are superior to 3rd party mix-and-match computers and the completely ill-conceived, dysfunctional Windows operating system.

In spirit, I have often joined in with the Microsoft bash, and have wanted to veer away from the popular Windows crowd. However, more recently, feelings have germinated in my soul, and I feel a deep urge to have a different variety of computer that can not be bought from anywhere that I've seen.

I want a computer which is in the true homebrew spirit. I want a computer which I could build and program myself. I wish to have a computer which is accessible to my understanding, but which does not loose computing power from its simplicity, a system which can be used to solve mathematical problems, a system which has only a few layers of abstraction, and a system which has a simple uniform syntax. I want a computer with power comparable to modern machines, but with simplicity in hardware and software.

Will such a computer ever be? I'm sure people would want it, but is there any in this world who will make it?

Slipping to Another Dimension

2008-11-25T13:05:00.000-08:00

As is well known, there are people who occupy more than three spacial dimensions at any given time.

These individuals often simply don't talk about their "other Ds" because the topic opens up a deep store of awkward social situations and endless questioning. Besides having to answer technical questions which most people, even multidimensional people, don't know the answer of(such as about gravity in multiple dimensions, string theory, and crazy geometry problems), they are quite often pressed to describe what it is like to live beyond three-space, what "multiple dimensions" actually means, whether they must have 4-dimensional beds to sleep comfortably at night, where people might buy those beds, and if they can travel through time, which they can't.

Often these people with the gift of extra-dimensionality are asked to prove that they really are multi-dimensional. Being watched moving between dimensions is a rather personal and revealing trick, and it would as improprietous to ask someone to do this as it would be to ask someone to change their clothes in public.

My wife Katherine just happens to be 5-dimensional. Not only does she extend into a fourth spacial dimension, but also into a fifth. This is rare indeed, but not impossible. I happen to have a picture of her slipping out of our dimension. It was an accident while taking the picture, and I'll include it for the interested public. Note that the revealing portion of her is facing away from the camera. I would never show a picture of the other side to the public.

If you are ever so interested about this more, I believe there are pictures of dimensional slippage available in medical journals.

A Simple Discussion of Angles

2008-11-24T21:12:00.000-08:00

Triangles are composed of three line segments which join at three points. At these joining points the lines fan out in different directions. When we look close at where the lines join, we see the lines are close together, but as we look farther away from the joining points, the distance between the lines increase.

The amount which the lines diverge as we look further away from the joining point is not always the same. Sometimes the lines diverge much, sometimes not so much. This divergence between the line segments is a measurable thing, and is called an angle.

To measure angles it is necessary to look at a circle around the joint where the lines come together. Small angles include small segments of the circle between the lines. Larger angles include larger portions of the circle. The angle can increase until the lines rotate all the way around the whole circle, at which point the angle is defined to be 360 degrees.

Another way to measure angles is with the radian. Radians are defined such that the angle which separates the lines in a complete circle is 2π radians.

However, the other day I came across an idea new to me called solid angles. They are like angles for three dimensions. I don't know much about them. I'm looking into it.

My Way in The Universe

2008-10-31T14:46:00.000-07:00

If I had my way in the universe, I would have abolished all of the complexity, confusion, ugliness, and hassle involved with solving problems. Every idea, principle, or thing would be deducible from a small set of simple, intuitive ideas.

It is very apparent, however, that I do not have my way in this universe.

I am speaking about the principle of abstraction. I call it a principle because it is used everywhere in the world. Abstraction makes life more easy. It removes complexity by hiding it away into small boxes.

I often wish I could peer into every box, and very often attempt to do so. However, every time I do I am reminded how ugly, complex, and hard to understand this universe is.