Numerology

A few years ago I came across another teacher at the college I teach at who claimed to know something about numerology. He was in his mid eighties and had been studying it for 30 or 40 years. I have always had a broad interest in all things natural and supernatural, and I knew that numerology (whatever it was) fit into one category or the other. So, instead of just explaining it to me, he just gave me a reading. I don't remember all of the information he gathered from me, but my birth date was one item on the list. (I still have the paper he wrote for me somewhere.) It did not take him long and I was caught off guard by how much he knew about me as a result of the reading (I suppose). Right away he told me that I love to learn, that I'm a lifelong student, that I'm not happy unless I'm learning, and that this is a burden on me. This is all true, and he seemed to know about my personal struggle of always needing to learn, and constantly seeking (but rarely finding) fulfillment through learning. In my experience, this is not a common struggle. Even among my colleagues (at a college), there are none I know of who seem to have broad academic interests. Even if I am typical, and he made a good guess, it was even more surprising that he knew that it was a source of psychological pain for me.

In any case, he knew me as well as I knew myself, and seemed to be able to do it with numerology alone. But he made one more prediction: he said that in my late thirties (roughly, I can't remember) that the burden and psychological pain that my desire to learn causes me will abate. Time will tell.

Tennis Elbow

I guess it was about 3 years ago that my tennis elbow became too painful and uncomfortable to ignore. Many years before that, I had just begun to irritate the tendon by fidgeting while reading, thinking and studying. Then it was the enormously strenuous and time consuming task of pruning our Lady Banks roses that took me to the stage of the injury that warranted a trip to the doctor. The original prescription of rest and ice made it moderately better, but did not cure it. Furthermore, re-injury was very easy. About one year after the first appointment with the doctor, I started physical therapy. The short story on that is the pain is gone, and my comfort level is quite good. The problem is that re-injury seems to still be too likely, since 4 months after finishing physical therapy the pain and discomfort is back, for no good reason. Once again, I am very certain it was thinking, reading, and fidgeting that did it. Originally, when the pain was back, I tried to do the same physical therapy exercises that helped me last summer. But it seemed that they only made it worse. Should I have gone trough a period of rest first? I remember that while attending the therapy sessions last summer, I was advised would work through some of the mild pain. I guess I done know at what point to start the exercises. In any case, I have done mostly rest for a week or so. And today I decided to try some of the exercises. Before I started, there was some pain, but it was mostly discomfort, "tightness" and weakness in the tendon. As I did the exercises, I had the idea that they have to be done "just right." For example, jerky movements are no good. When I was doing eccentric loading with the dumbbell, I would use two hands, and very gradually release the weight with my right hand as I made the eccentric motion very slowly with the weight in my left hand. The bottom line is that it felt very good, and had continued to feel good for the rest of the day. I guess it's only beneficial to definitely use the tendon, but without causing any pain or discomfort; there's a balance between the two to work for. I'm excited about this since, as far as I understand, tendons do not tend to heel properly once injured. They are slow to heal, and heal with some sort of weaker tissue that is vulnerable to re-injury. Apparently, eccentric loading does cause a more proper and resilient healing of the tendon. So, this time around I will practice my physical therapy, but keep doing so well past the point of relief in hoping to restore the tendon as much as possible.

Arboricola

This is the newest addition to our collection of houseplants. I've come to have increasing confidence recently about my skill at keeping houseplants alive and healthy. Plus, it was on sale for only $2.44. Originally, before I had a yard of my own, my interest in and attraction to plants was solely directed at houseplants. It's not the way I wanted it to work out, but I killed so many plants during that period. A big turning point for me was that I read Howard Garrett's Organic Manual at about the same time I got a yard of my own. Those events together activated my instincts about what plants need in a way that neither could have done on their own, and I started to have success with outdoor plants. In any case, I found later that the same skill I developed worked with houseplants too, although I still see them as a greater challenge.

Devil's Ivy

Here is a picture of two of three Devil's Ivy plants that I have. The foliage on one appears to very thin when compared to the other. I think that, all other things being equal, the difference between the two is that the one with denser foliage spent about a month in late summer in a shady spot in the yard (where it is much brighter than inside). The one with thinner foliage has spent all of it's time inside. Otherwise, they get the same treatment: each gets a continuous supply of compost from kitchen waste, and you can often find some pillbugs and earthworms living in the soild. The soil is alive, not sterile. They are a type of plant that is suited live inside, but maybe they should all have a turn to spend some time outside. Why not all of them spend all of their time outside? That's fine in the spring, summer and fall, but they will not survive the winter that way. Plus, I like to have a few plants inside.

Binary arithmetic, logic gates and electronics.

A few years ago, I had a question occur to me: Computers are composed of many tiny wires, each of which can be considered either on (state 1) or off (state 0). Part of the network of all of these wires are various logic gates. So, if computers are logic gates and wires, how can computers add, subtract, multiply or divide? In other words, how can arithmetic be reduced to logic?

In any case, this question really stuck with me, and eventually I started reading about it. It turns out that it is somewhat easy to understand how adding can be done with logic gates, as long as the numbers are expressed in binary. Tonight I created my first simulator in Excel that will add two four-bit binary numbers by only using logic gates. Maybe I can build the actual machine someday? In any case, this simulator seems to work perfectly. Plus one can tell that it should based on an understanding of binary arithmetic and logic. I hope I build this device someday. I considered a string a dip switches for the input number, and either LED's or a binary display (if I can find one) for the output. Transistor logic gates themselves are easy to find. For the logic gate schematic, you will find something similar on page 75 of "How Computers Do Math."

All work and no play...

I have made this claim before, but this semester really has been the busiest yet. I have way too many students, and have too many of my office hours occupied. It's Saturday morning at 2:25 AM right now. I finally fell asleep at 3:30 or 4 AM on Friday morning, but then I woke up at 9 AM. Watched Neil and Olivia by myself all day, and then at about 10 PM on Friday (about 4 hours ago) started grading papers. I kept track with a timer, and I graded for 2.75 hours. Every paper I graded was over a week old. In any case, I graded 24 papers total, and don't want to do anymore grading for a long, long time.

Bruschetta

The tomato garden was a success this summer, and so I have been eating a lot of bruschetta. Even now, in early August, my tomato garden is history, but I've still eaten bruschetta made from commercial tomatoes. There's a little more to it than just tomatoes, so it's still worked out fine.

For bruschetta, all you need are tomatoes, olive oil, salt, garlic, and French bread. French bread is made with no added fat, and so I think that makes it crispy when toasted. I think that's important when making bruschetta. Actually, I don't have any clue what makes some breads crispy when toasted. Staleness? Lack of preservatives? Who cares? The point is that crispy is good, and crispy is what you want. It's worth getting good tomatoes if you can, but if your only choice are those pretend tomatoes from the grocer, then you can still get by. Good garlic seems easy to find. Most olive oil comes in a fancy package, but they're not all the same. I suppose you get what you pay for there. That's it for ingredients, but we've also added mozzarella, balsamic vinegar, and I've heard prosciutto is good too.

One thing worth saying more about is the garlic. There are reasons why I like to eat a lot of fresh garlic, but it is very hard for me to do. It's easier for me to drink straight whiskey than to eat raw garlic. But bruschetta is made delicious by abundant and raw garlic. If the bread is sufficiently crispy, the first step would typically be to cut a clove of garlic in half, and then scrape half of it evenly on the bread. Then follow with olive oil and other ingredients. This is how I learned to make it in Italy. Eventually, I found this to not be the best way to add garlic to bread. Now, I make use of a garlic press, where I press the garlic and spread it across the bread. This way I can easily consume 2 to 4 cloves of fresh garlic in one meal of bruschetta. It would be objectionable for me to eat that much fresh garlic by itself, in a brief period of time. But, it is what makes bruschetta delicious.

Food

I watched a few movies over the past few days, which were Food, Inc., and Ingredients. I'm certain that I didn't get the whole message from them, but they each have renewed my interest in growing my own vegetables. I used to spend a lot of time in the garden, but not so much anymore. This summer, I have grown and harvested more tomatoes than I can eat. They've been delicious and abundant. I always say that you can't buy tomatoes this good; you have to grow them yourself. Despite that, I don't tend to the garden much anymore. It's looking unkempt right now. I rarely go out there, and now I've come to feel it's a shame. Maybe it's the heat. Or, maybe it's that I'm expecting to move.

Back to the movies. What struck me was the footage of small-scale commercial gardens, and the interviews with the caretakers. Seeing the open space, the variety of crops, the neatness and order of it, was wonderful for me. Growing food can be messy and hard work, but one may not get that impression from these films. I temporarily forgot about the labor of growing food, and lost myself in the beauty of it. But it wasn't only the large-scale order of the farm, or the vast greenness of the valley that got me. The plants themselves are to attractive. I saw dinosaur kale, kohlrabi, broccoli raab, lettuce, various salad green tomatoes, okra and more. And when I saw the food grown in such abundance, and then distributed locally, it makes me feel generous. With some of the gardens, strangers cooperate on the work of growing the food, and then share the harvest. It'd be nice if things really were like that. Maybe they are. Maybe they can be.

But back to the beauty of the gardens. I can see why an animal would be drawn to take a bite of these plants. And then there's the soil! This would be surprising to non-gardeners, but the most lovely part of gardening may be the experience of the soil. Good soil is as attractive as any other plant, animal, or insect out there. It's soft, uniform, crumbly, not wet or dry. You'll find worms and other creatures. To smell of good soil is a unique experience. To me there is something that just seems right about good soil. It's almost moral, as if it is in obedience to the way things ought to be. But the point is this all reminded me that I have grown good food myself in the past, and I suppose I could do it again.

Now, I can't live off the land by my gardening ability. But I'm certain I can provide an inexpensive, perennial, and nutritious supplement to my diet. For the most part, the food right out of my garden cannot be matched in flavor, price (and probably nutrition) by food from the supermarket. I grow and eat what is in season and grows well in my garden. I don't undertake extreme measures to force what doesn't grow well for me.

So, as part of my renewed interest I thought I make a quick list of some plants that are a good bet for me.

(1) Lettuce. I've had excellent success with Black Seeded Simpson and Romain varieties. Sow Black Seeded Simpson directly in early/mid September, and harvest until the first hard freeze. Romain works well when planted very early in the spring, perhaps around valentines day.

(2) Mustard greens. I'll probably never grow anything besides Florida Broad Leaf. Seed directly in early/mid September, and harvest well into winter. I'm still eating mustard greens in December and even January. I haven't made a spring planting yet. Easy to grow, and provides an abundant harvest. Some aphids will appear, but won't significantly degrade the crop. These took some experimenting to learn to cook, but the best method turned out to be really easy. Chop finely and simmer them for about 10 minutes, and then drain very well (I toss them is a stainer to drain). This is the key: they are best served somewhat dry, in my opinion. Some seasoning with salt is in order. Sometimes I like pepper sauce too. I only cook them because they are too coarse to eat raw.

(3) Collards/Kale. Cultivation and cooking is similar to mustard greens, but they are more cold hardy and require a little longer cooking.

(4) Broccoli. I originally had great success with the Packman variety. They way a knife cuts through broccoli that's fresh from the garden must be experienced. Supermarket varieties are tougher and less tasty, of course. The bad news is i have not had much success with broccoli in recent years. The heads form, but then quickly bolt to seed. The problem is relying on transplants. I think the nurseries sell the transplants not when they need to be sold, but when people are in the seasonal mood to buy them. I had the best luck with broccoli when planted in early Febrary.

(5) Tomatoes. There are many good varieties. The problem is that the seasons where I live are not a good fit for tomatoes, but it can be done. The summer gets too hot to plant in summer, so they must be planted in early spring. How early? As early as possible. But as you gamble on earlier plantings you will encounter cold temperatures and wind. But early to mid March will work.

(6) Okra. Emerald is good. So is Clemson Spineless. I have usually grown my own transplants, even though that is discouraged by the experts. The advantage of okra compared to other garden vegetables is that it stands up to the heat of summer. In fact, okra can be harvested into the early fall. Okra is one plant that makes the garden perennial, since it can be harvested all summer.

Why can't all functions be linear?

Today I thought I'd write about a few of the types of functions that you would learn about in an algebra class. Now, let's put the insanity of this undertaking aside. I want to do this in a way that sounds nothing like how it would be in an actual math class. The objective is that I'd like to talk about the functions, but I want to do so in a way that involves no algebra, and only a little bit of arithmetic. You will not see a single equation or formula!

In math there is not just one kind of function, or formula, but many. There are different functions for different situations. But let's start with the notion of a function. A function does something like this: if I'm at the gas station to buy gas, then two numbers become relevant, and they are (a) the number of gallons of gas that get put into my car and (b) the dollar amount that I have to pay. Now, you can get many different amounts of gas, and pay many different prices. But, there is a definite order and predictability to the whole situation, and a mathematical function does the job of telling us how.

Now, about this function. For the situation at the gas pump, the simplest (in my opinion) type of function does the job. It's called a linear function. Before I get into that, let me state that I realize most people understand how to buy gas and most people probably don't know what a linear function is. And so that may seem to make a discussion of the function unnecessary? All I can ask is to hear me out. Right now gas is about $3 per gallon. As I said, people know what this means: 1 gallon costs you $3, 2 gallons costs $6. We could really get complicated and say that 2.5 gallons will cost $7.50. But to just list numbers like that, although it is correct, does not reach for the whole truth of the situation. What I'd like to do is describe what happens to my bill as I put more gas in the tank. The more gas I buy, the more I pay, and the general truth is that for each additional gallon of gas I buy, I will pay an extra $3. The truth I want to capture here is that no matter how much gas is already in the tank, the next gallon I put in will cost an extra $3. This being the case is what makes the function that determines my bill for buying gas a linear function.

Now, I'd put money on it that most people would accuse me at this point of providing unnecessary details for something already sufficiently understood. But that may be because they think the mathematics of all situations are like the aforementioned one about buying gas. True, many common ones are (for the most part), such as getting paid by commission, or getting paid by the hour, or paying taxes. The explanations for these examples would be of the same nature as that of buying gas. If you get paid $10 per hour, then every extra hour you work gets you $10 more dollars, regardless of how many hours you have worked already (barring complications, such as overtime). This is the essence of a linear function: two quantities (i.e., gas and money, time and money, etc.) are linearly related if there is a specific change in the one that always produces the same change in the other. But now I offer you to consider that not all situations call for linear functions.

To begin to get a grasp of how a situation could be unsuitable for a linear function, consider the population of a city at any given time. Here, various moments in time will correspond to various levels of population in the city, so one may think there is a function that explains how. First, we can probably all agree that as time goes on, the population gets bigger. But is it linear? For it to be linear, something like this would have to be true: for every 20 years that goes by, the population will increase by 750 people. Now, let me see if I can convince you that population growth in general will probably not be linear. Consider for the sake of argument that the original population was 500, and then 20 years later it was 1250 (or it grew by 750). Just like in the gasoline example, we have to start by agreeing on our the mechanics of example. So, let's assume something like this happened: all couples will have 3 children and they all live a very, very long time. Of the 500 original people, there were 250 couples who each has 3 children, which is 750 children total, and a new population of 1250. But what will happen over the next 20 years? Will the population increase again by the same amount, 750 people? No, if the 750 new children, form 375 couples and each has 3 children over the next 20 year period, then there will be an additional 1125 new people and the new population will be 2375. In other words, the population grows by 1125 people during the 2nd 20 year period.

The point here is that the way the population grows cannot be linear: with my assumptions, it cannot grow by the same amount every 20 years. The general reason for this is that there is a repeating cycle that each reproductive group creates a new generation larger than itself. Now, you can argue with my assumptions that nobody died, or that there were no singles, or that all couples had children, or that all couples had 3 children. I concede that my assumptions are easily see to not true. But, it turns out that once all those complicating factors are considered, and we look at the raw numbers, populations usually grow in a way that is as if all new children form couples and then have a certain number of new children, and so on. This is commonly what happens, and population growth is commonly not linear. The type of function that describes populations such as this one is called an exponential function.

Before I go to the next type of function, I want to emphasize that in each situation I have been describing the effects of change: what happens as you put more gas in the tank, or what happens as time goes on. I'll start this last example the same way. Consider the perfectly reasonable situation that I am having new floors installed in my house. Suppose that each man that works on the floors can install 50 square feet per hour, and I have 2000 square feet for the new floor to go. Doing a little dividing will yield that one man can finish the job in 40 hours. It would be reasonable to think then that 2 men can finish the job in 20 hours, since two men would seemingly accomplish 100 feet in one hour. What happens if we push this further? Can 10 men finish in only 4 hours? Maybe. If we follow the math to its logical conclusions then 100 men can finish the job in only 24 minutes!

This is where I stray a little from my earlier examples. The math on its own is correct is saying that 100 men can finish the job in only 24 minutes, but practical considerations will prevent this. 2 men may not work individually at the same rate as one man will. And so on with 100 men. The reason involves things such as that there are limitations on tools available and space. Will 100 men on the floor, the crowded conditions alone will prevent them from individually working at the same rate of any one man working alone. We might then grant some reality to this assumption: as more men work on installing the floors, then the effect will they will individually work more slowly. To give some numbers, it may work something like this: one man working alone can work at 50 square feet per hour, but for each additional man they will each work at 10 square feet per hour slower. Now, if we are concerned with how the number of workers affects the time it takes to finish the project, then what kind of function will we get? It turns out that the decreased productivity caused by additional workers here leads to a function that's not linear or exponential. Doing some math will give these results: 1 man finishes in 40 hours, 2 men will finish is 25 hours, and 3 men will finish in 22.2 hours. So it seems that more men means less time to finish, despite decreasing individual productivity. But as we keep going, we find that 4 men will take 25 hours, and 5 men will take 4 hours. So, as we add more men to the job, the time to finish decreases to a minimum and then increases thereafter. That's what's unique to this function, and it's called a quadratic function.

relaxation

Today I have felt a little restless. I didn't really feel like doing anything, so I didn't, but then I wasn't entirely happy to be so lazy. As is typical for me, I almost never enjoy doing nothing due to feeling the drive of chores or ambition. Certain prescription drugs will allow me to enjoy doing nothing, but that's about it.

I guess that's what I really wanted today: to be a little bit high, to be lazy AND enjoy it. I tried to do a little meditation instead. I don't really have any interesting beliefs about meditation, but I do believe it helps some people relax. More and more, I believe that it will not work for me, maybe because I don't practice enough or give up too easy. But it may not be working because I want it to work.

Let me explain. You might conclude that wanting it to work would be a good thing because it would entail having some motivation. But I'm considering that being motivated is what impedes the process. You see, if I take a pill, I can relax. And if I'm motivated, then I can walk 5 miles to take get that pill. But how do you "just relax?" Being motivated or ambitious is in opposition to the state of mind that I'm talking about. The more motivated or desiring I am of it, the further I get from my goal. But those are the only tools in my toolkit, so it seems there is really no way for me to do it.

This is a big ordeal for me. The setting can be perfect for relaxation, but it makes no difference for me. I can be outside witnessing wonderful scenery, with nothing pressing to do. Here's what I do INSTEAD of relax: I will doubt that I am fully appreciating the scenery; I will wonder about how some artist perceives it and start feeling deficient about it; I will start thinking about how my accomplishments are so thin, and I question that I should be spending time doing nothing anyway. Now, this wouldn't seem remarkable at all, but the right pill has showed me that there is another very different way to be. With the right pill, I have seen that there is perfection in doing nothing. There is something very different that's left behind when all ambition, doubt, craving, etc., is taken awayBut I'm afraid that the pill is the only way for me to experience it.

kWh

Well, it's been an exciting evening. I decided to do some math about our electricity use here at the house. At 9:20 PM the electricity meter read 25711 kWh (which is suppose is a cumulative number). Later, at 10:42 PM it read 25720 kWh. So, we used 9 kWhs of electricity in 82 minutes. This is equivalent to 6.59 kWh of energy used per hour.

Now, here's how money enters the picture. We pay about $0.15 per kWh. So, that's about $0.99 of energy used per hour, or about $670 per month. If that sounds high, it's because it is. I'm expecting to pay less than half of that this month. So, why is it so high? Consider what was going on tonight during the time I measured energy use: the thermostat was only at 78, but both the washer and dryer were running the entire time. Must have been that, but I'm planning to check the meter tomorrow morning to calculate the average rate of energy use overnight, for comparison.

Unusual DIY Project.

Here is an unusual DIY project: the self haircut. Two days ago, out of nowhere, I became convinced I could give myself a good haircut. I'm not surprised that my mind wandered into this: going to get a haircut has always been a nuisance for me (there's the scheduling, the time, the money, etc.). Anyway, after some time spent thinking about it, the whole process made sense and seemed so easy. I already own scissors, electric clippers, and an assortment of guards, like what a barber would use. So, I found a few videos on the internet and did some reading. That same night, I gave myself a haircut, with some help from Darcy. It's as good as any haircut I've ever paid for. As long as I don't wait to long between cuts, it will be easy to do again. And that's one thing I like about it: I used to get haircuts every 6 weeks or so, but I always thought that I needed some touch up after 2 or 3 weeks. Now, it's all easy and convenient to do.

Inversely Proportional

I am embarrassed to admit that at about the time I learned to drive I reasoned as follows: in order to get better gas mileage, the car should be driven faster. This wasn't thought through very well, and it was just instinct. But there was a reason buried in my mind, and it was that at higher speeds we can cover more distance per unit of time, by definition. And so, as we cover greater and greater distances for the same unit of time, we will get more miles to the gallon. Now, that is not true, but here is what does make it true: if the car always used fuel at the same rate (in volume of fuel per unit of time) then, yes, greater speed would always lead to greater gas mileage. If the car always uses fuel at 2 gallons per hour, no matter what the speed is, then the more miles you can cram into that hour, then the greater the miles per gallon will be. But the car's fuel use does diminish with increasing speed. Anyone who has ever run or ridden a bike can be persuaded of this: For how long can you run at your top speed? For how long can you walk. Now I don't know the details on how the human body works, and I'm sure it's more complicated than I know, but I take it to support maintaining higher speeds of travel take more energy.

So let's take that a step further: Suppose that the car will use fuel at a greater rate as the speed increases. Perhaps that as the car idles, it uses fuel at 1 hour per gallon, but at 60 miles per hour, it uses fuel at 0.6 hours per gallon (taking only 36 minutes to use the same volume of fuel). This would mean that the fuel use depends on the speed, and that the two quantities are inversely proportional: as one quantity goes up, the other goes down. Now if we further assume that the two values are also linearly related, then we can get an equation that gives the fuel use (y) in terms of the speed (x): y = (-1/150)x + 1. This equation has two implications of note: the car takes one hour to burn a gallon of fuel at idle, and for each increase in speed of 15 miles per hour thereafter the car will 0.1 fewer hours to burn a gallon of fuel.

There is another issue of note here. I started this post with the erroneous assumption that the car always used fuel at the same rate, and the implication was that the gas mileage would be limited by the speed of the car (or the best gas mileage is obtained by traveling at the top speed). Another, every crazier scenario would be that the car used less fuel with increasing speed. But neither of those scenarios is realistic: Life seems to always involve trade-offs, and the more we have of one thing usually entails the less we have of another. Thus, in our real world example, as we increase speed we sacrifice fuel use, and so neither too slow or too fast will yield the optimum gas mileage. At some middle speed there is the best compromise between speed and fuel use. Note that gas mileage (z) is x times y , or z = x((-1/150)x + 1). With methods of algebra or calculus we can find that the maximum value z takes is 37.5 miles per gallon at 75 miles per hour.

Although it's probably intuitive to believe that there is some moderate speed that will give optimum gas mileage in our situation, let me now consider a more meaningful and mathematical reason why that is. This reason has to do with the way the fuel use increases with increasing speed. We agreed that as the speed increases, it will take less time to use the same volume of fuel, and that for each increase in speed of 15 miles per hour thereafter the car will 0.1 fewer hours to burn a gallon of fuel. But it's not the absolute changes that matter here: Take for example that we start by considering that the car takes an hour to burn one gallon of fuel when idling. If the car is later traveling at 15 miles per hour, it will then take only 0.9 hours to burn a gallon of fuel. But in terms of a percentage, the fuel use only decreased by 10%. But as the car speeds up, the fuel use keeps decreasing by a greater and greater percentage of itself.

It's the percentages that are the key here, not the absolute change. Although the fuel use increases with increasing speed, you will find that initially the fuel use is changing by a much smaller percentage than the speed, then they change by equal percentages, and then the fuel use changes by a greater percentage than the speed. It turns out that the optimum speed is the speed at which the fuel use and speed are changing by the same percentages.

One final word: there are some things about this that are no doubt untrue, and this entire blog post may be pointless. Are the fuel use and speed linearly related? Probably not, but I wouldn't be surprised that they are under portions of the graph excluding the extremely fast or slow speeds. Another thing is to consider the price of item and the quantity that can be sold at that price, and the resulting revenue: it's the same problem with the variables relabeled.

Selling a house

Today we are as close as we have ever come to selling our house and buying a new one. I've done a lot of math regarding this, and today I'll write about one aspect. We are asking $180,000 for our house, and we owe $155,000. If there were no commissions, fees or other costs to selling a house then we could keep $180,000 - $155,000 = $25,000. But the truth is that there are such things. It's complicated to explain all the costs of selling a house. Some are calculated as percentages of the sell price, others are flat fees. But it is probably a safe assumption to say that the cost of selling the house will be 10% of the price at which it is sold. Now, I can from this number calculate our profit from selling the house at various prices, but it would have more explanatory power to have a single equation whose features explain the general relationship between the sell price and our profit.

So, here goes. Let x be the sell price and y be the profit. The equation would be y = x - 155,000 - 0.1x, which would simplify to y = 0.9x - 155,000. This equation says a number of things about how the sell price determines our profit.

(1) The sell price and profit are linearly related. One thing this means is that the graph is a line. Now, it is a fact that the graph is a line, but it does not enlighten the situation at all. Something better is this: being linearly related means that if the sell price increases by a certain amount, the increase in profit will be some constant multiple of that amount. Mathematician or not, everyone would believe that if the sell price were to increase, then so would the profit, but for a linear equation the point is that it doesn't matter what the sell price increases from. An increase in the sell price from $1 to $2 has exactly the same effect as an increase from $100 to $101. The key to understanding precisely what this means is by examining the slope of the line.

(2) The slope of the line is 0.9/1, and here's what that means: if the sell price increases by $1, then the profit will increase by $0.9. But any other proportion is also true, so if the sell price changes by $1,000, then the profit changes by $900. So, a $1,000 increase in the selling price will mean an additional $900 in profit.

(3) The x-intercept of the line represents the sell price at which the profit is zero. For our equation y = 0.9x - 155,000, the x-intercept is 155,000/0.9 = 172,223. So, for every $1,000 that we sell above that, we profit $900. But if we sell any less than $172,000, we would have to pay to sell the house.

Inflation

Today I was reading a book by Murray Rothbard, and I hope I learned something about inflation and the business cycle. First, let me get clear about definitions. I read in my economics textbook that inflation is a general rise in prices. To me, this says that there is no good definition of inflation. I suppose that during any given time period, some prices will have gone up and others down, but what proportion of prices have to go up for the rise in prices to be "general"? Obviously, this definition is as good as it can be, and there would be no benefit to making it more precise. Perhaps if I consume only one item, wheat, then inflation to me would mean that the price of wheat is rising. But any one consumer will consume a great number of items, and not all consumers consume the same set of items. So inflation must need to be measured by some kind of average, squishy number.

Next, what can I say about the cause of inflation? Let's suppose for now that the money supply is fixed in an imaginary economy. It's reasonable to also suppose that not all of the money supply is circulating. Any given person in this economy will probably consume a certain amount and save a certain amount, with those being the only two options. But what would happen if consumption started to increase while the number of goods in the economy stayed the same? This extra desire for consumption relative to the same number of goods would drive their prices up. I think this is called demand-pull inflation.

Let me now take this a little further and more general. It seems that any time the amount of money being offered for goods rises with the amount of goods staying the same (or decreasing) then prices will go up. I believe this is just what the law of demand claims. And so the inflation I just described seems like nothing but a corollary of the law of demand. Now I wonder how else this rise in circulating money relative to goods can happen. From reading Rothbard's book it seems this can also happen as a result of government creating new money, which he reasonably claims they would do as an easier alternative to taxation. If new money is created by government, then it seems there would have to be some inflation. But the inflation would be uneven. The initial recipients of the new money would be able to spend it at un-inflated prices. Eventually, later recipients would have to suffer the inflated prices, as would those who were saving money which turned out to be spent at inflated prices. Maybe there is some good to money creation by government, but it does not seem to do any good for those who see their monetary units decline in real value as a result.

Rothbard also explains that inflation is also a cause of the business cycle, which is a cycle of high and then low employment and real GDP. Here's how money creation by government seems to cause this cycle. Suppose that the newly created money is loaned to businesses, who intend to use this money to invest in future growth. What I mean by that is that this money business put to use does not increase their output in the present, but will do so at some time in the future. The problem with that is that these counterfeit loans to business do not reflect savings on the part of consumers. If they did, then it would be some indication of consumers deferring consumption for the future. But the loans are not of the result of savings and consumer willingness to defer consumption. So, what we have is business planning for greater future output, rather than present output, and consumers wanting greater present output. Because of this mismatch, the businesses will then find it best to liquidate the original investments, and I suppose the misdirected energy and resources which results in the down side of the business cycle.

Now, I'm sure that I've gotten a lot wrong about this. But like most arguments I read concerning economics, it seems that if the premises are true, then the conclusion does logically follow. I guess the controversy lies in whether the premises are really true. With this explanation of the business cycle, I'll take the premise that the counterfeit loans cause businesses to devout resources to future output. If that doesn't turn out to be what consumers want, then why don't businesses just re-employ those resources to the present? It seems that part of being successful in business would be to adjust to consumer demands.

Caffeine

I know that the posts on this blog are almost always extremely boring. Normally, I don't have any good excuse for writing such boring material, but tonight I do. Once again, I'm having trouble falling asleep, so maybe some boredom is in order.

So, here's what I'm thinking about tonight. I know that tea has caffeine in it, but I find myself thinking about what caffeine is. Now, the truth is that I have no idea what caffeine is. Does that sound like an absurd statement? Let me clarify: I know how people use the word "caffeine," and I know that "caffeine" appears on the label of migraine medicine, and I know what foods and drinks are said to contain caffeine. I also know that caffeine is said to cause insomnia in some people, and is reputed to lead to increased mathematical abilities (all other things being equal). But my point is that I don't know what caffeine is in a scientific way.

So let me start my scientific pondering in this way: I have read that an 8 ounce cup of green tea has about 30 mg (milligrams) of caffeine in it. Now, that is a claim about the weight (or mass) of this substance in a cup of tea. But how much caffeine is that? If the cup of tea evaporated and left the caffeine behind, would their be a visible residue? (I don't know if that's even possible.)

Let's get an idea of how much 30 mg weighs. It turns out that 30 mg is 0.03 grams. One teaspoon of volume of water weighs almost 5 grams. That means that the water used in making one cup of green tea is about 165 times as heavy as the caffeine in the tea. Equivalently, if you remove the caffeine from 165 cups of green tea, that amount of caffeine would weigh the same as one cup (8 ounces) of water.

What about the volume of the caffeine in one cup of green tea? The infallible internet has provided me with the proposition that 1 cubic centimeter of volume of caffeine weighs about 1.23 grams. Since one cup of green tea has 30 mg of caffeine, the volume of caffeine in one cup of green tea is 24.4 cubic millimeters. So, imagine a cube that is 24.4 millimeters on each edge, and that would be the volume of caffeine in one cup of green tea. This would be equivalent to 0.005 teaspoons, or one part out of 200 of a teaspoon.

So, I guess as far as weight and volume are concerned, a cup of green tea has very little caffeine. It has surprised me then that one can easily buy pure caffeine. It seems that any tangible quantity of pure caffeine would be enormous compared to the amount in common beverages. I found that people have died from taking as little as four grams of caffeine, and that you can buy 100 grams of pure caffeine on Amazon. The label of the product I found on amazon says that 2 grams will send you to the ER. It's crazy to think there is even demand for such a product. Caffeine is common enough, and 100 grams of such a potent and seemingly benign substance seems like an insane amount to want to possess.

These past few weeks have been very exciting. On second thought, I think I should limit that statement: anyone else would probably opine my outer and inner life to be either ordinary or boring. What I think has happened is that the same old life has started to seem so much more interesting. In fact, all of the perceived excitement has been keeping me awake at night, and during the day too. Money is much less of a prolem, mainly because I stck to a budget. Part of the enjoyment in that is having to be creative at times to make the sum of all our expenses be within budget. Most people would find this obligation to be a real annoyance. Why do I like it? We also avoid eating out as much as possible. But doing so has caused the chore of cooking to become somewhat of a craft or hobby for me. I have somewhat expensive taste in food, but I'm too lazy to make recipies out of cookbooks, and also too frugal to eat out. But I've learned to cook simple recpies to my taste.

Also, a newfound fascination about electronics overcame me during the drive home one day in February. (I still remember the occasion very well.) Part of this fascination is just as a hobby, but I have also become optomistic (for no reason I can think of) that it will advance my career. Part of it might be this: I feel like I could study electronics non-stop. It seems this new fascination is more than it seems. I feel all powerful, like I can do anything. Maybe that's a delusion, but it feels real, as all delusions do.

Another thing that I feel like I've become more efficient in all aspects of everyday life. I used to think that it all had to get done at once, but now that drive doesn't nag me too much (as if work and leisure always had to be kept seperate). Now I just do what I can when I can, as if easy and frequent transitions between work and leisure are easy to make. The bottom line is that more gets done with what seems like less investment.

The real meaure of my new attitude is how much I am looking forward to the summer, which is more than ever. I have no anxiety about not working or about all the free time there will be.

Email

At this time, I am a full-time math instructor at the Northwest Campus, where I teach the full gamut of math courses, and I am formerly a full-time South Campus math instructor. For various reasons, I want to diversify my profession, and I am looking to learn if it would be practical for me to teach electronics or engineering related courses at TCC. I think it would be a worthy ambition to teach full-time in that capacity, but I am at this time considering that it may only be possible for me to teach some combination of mathematics and electronics related courses.

Of course, I am open to the possibility that this may be an impractical move for me, but let me try and make my case as follows. I have bachelor's and master's degrees in math, but I also have recent electrical engineering coursework with no degree earned. I have taken 2 sophomore-level classes in circuit analysis, 1 course in electronics, and 1 junior-level course in electromagnetism, all at UTA. I realize that this coursework alone is not enough to qualify me to teach in your department, but I am ambitious and I would pursue additional coursework at TCC if needed.

So, my bottom line here is to seek answers to a few questions in order to see if this is a practical ambition for me.

(1) Would it qualify me to teach at TCC in the "electronics" field if I completed such classes at TCC? I don't see myself finishing the EE degree I started at UTA, due to the expense of doing so. But I would be willing to complete the entire range of coursework at TCC if it meant that I could diversify what I could teach.
(2) How much professional experience in the field (or outside of the classroom) would I have to have to be qualified to teach? In the math department, we do hire teachers with no related industrial experience, but I expect that's not the case for every department.
(3) Are there any reasons why this is not a practical goal for me of which it does not appear I am aware?

Thanks for taking the time to read this message. As for why I sent this message to you, I remember when I was at South Campus listening to you speak on a few occasions, and as a result I am inclined to think that you might be able to answer some of my questions. Please excuse me if that is not the case.

Spanish Rice

Here's how to make Spanish rice. I created this recipe with little hope that it would be good. But I got lucky and it is very good.

about 1 cup white rice (rinsed)
about 1 cup water
about 1/2 cup tomato sauce
about 1/4 cup canned green chilies
some parsley
about 1/2 teaspoon garlic salt

Combine all ingredients, apply medium heat, and stir together as the mixture heats to boiling. Once boiling, reduce heat and cover for about 20 minutes. Once cooked, transfer the rice to a serving dish. Slice and distribute about 1/4 cup butter over the top layer of the rice, and cover to let melt. Then stir the rice and re-cover and serve.

Insomnia

Insomnia has been frequent this semester. For example, last night I fell asleep at 4 am and then woke up at 8:30. I didn't rest during the day and it's now midnight and I'm still awake. It hasn't even been that noticeable to me that I've only had four hours of sleep. So, maybe it's not insomnia. Truth is I usually find myself lying awake excited about hobby interests and time off this summer.

knife sharpening

Why have I become curious about knives and knife sharpening recently? Well, knives are practical, and so is knife sharpening. And knife sharpening seems to require experience, knowledge and skills of observation. Anyway, here's what I've learned about it after a morning reading about it.

First, there are tools: a sharpening stone and lubricant. Most stones come with two sides: a rough grit and a fine grit. The finer the grit, the finer or sharper you can get your blade. You usually start off sharpening on the rough grit and then finish sharpening it on the finer grit. Additionally, you would have to observe the grind of the blade. My kitchen knives and my pocket knife are of the sabre grind. Then there is the angle. No matter the grind, it seems that a knife's edge is nothing more than two planes that intersect along a line with a constant angle of intersection. As far as I can tell, this angle is between 10 and 20 degrees, but I'm not sure how you tell what it is for a particular blade.

Now for a brief description of the sharpening process. There are many methods, but the method/process of sharpening matters way less than the end result. A "dull" blade has some degree of ’rounded edge.’ A sharp edge is nothing more than two planes intersecting at a point. When sharpening all you are doing is removing metal until the bevels on both sides of the blade meet at a point. This can take six strokes or six hundred depending on the blade's current condition and the type and grit of stone you are using.

So, how can you tell if a good edge has been created? Look directly at the edge with a light behind you, and you'll notice that rounded areas will reflect light. Keep sharpening until no light gets reflected. The sense of touch can also be of use. Carefully feel the edge with a finger. Don't underestimate what you can learn this way. Does the edge feel rounded? Is there a burr? Are the bevels even on both sides of the blade? Finally, what's a good test of a well sharpened blade? Apparently, a blade can be sharpened so that it can sever a hair with almost no pressure applied.

See this link:

http://artofmanliness.com/2009/03/05/how-to-sharpen-a-pocket-knife/

Thoughts about commodity money.

Here is an argument against the goodness of a commodity money: that it will lead to deflation, which is a fall in consumer prices. The basic premise of this argument is that the supply of the commodity money will be outpaced by the supply of all other goods in the economy. So, there will be relatively less "money" being exchanged for a greater quantity of goods, and so prices of goods will generally fall.

Now, this argument against the goodness of a commodity money is not due to its causing price deflation. Rather, the argument is that price deflation will discourage borrowing in terms of the commodity money. Here's how: suppose that one day A lends B 5 pounds of gold (which at the time would by 5 widgets). Later on, when the loan is to be repaid, the principal amount of 5 pounds would have more buying power, let's say 10 widgets. That must be paid with interest. Thus price deflation means that the borrower is actually paying the loan back more dearly than if prices were inflating. If prices were inflating, then the borrower would be paying back a principle amount that actually has less buying power than when it was borrowed, and so it seems the borrower is paying back the loan less dearly.

Now, why is that bad? The argument goes that no one would want to borrow in terms of the commodity money, and so commodity money is bad. I suppose then that the desire is to have a make-believe money, one whose amount can be adjusted at will. I believe this is one of the aims of the federal reserve bank: to increase the money supply to outpace the overall supply of goods in the economy. This would cause some degree of price inflation rather than deflation, and would be impossible to accomplish with a commodity money.

The truth is that I don't understand why this argument is conclusive with respect to borrowing ceasing in terms of commodity money. It seems to me that if borrowing is desired, then a commodity money would not prevent an agreement being reached between the borrower and lender. It seems that some agreement could be reached so that the lender and borrower each benefited. Since prices are deflating, it may be that each party could still benefit if the loan were paid back without interest, or paid back at slightly less than principal.

In any case, I guess the real question is whether people are generally wealthier in an economy based on a money supply that is outpaced by the supply of other goods. This is an economy with price deflation. Now, this question is not going to be answered on a blog post by someone who has no education in economics, and the question may not even be properly stated in the first place.

In any case, this post of mine was all caused by a (one star) review on Amazon.com of Ron Paul's book End the Fed. I copy the review here and add some of my own remarks.

"But, for an easy to understand response on why Paul's tract is a load of baloney, here's a good way to think about it: gold is, in itself, a commodity. That means it's worth as much as laws of supply and demand say it's worth. It's subject to bubbles (some would say we're in one now, though I haven't spent enough time analyzing the gold market to have an opinion one way or the other) driven by what people are willing to pay for it. But it's a HORRIBLE currency because, simply, it's completely detached from output. Here's a simple model for understanding why. Imagine a closed economy with 100 people and a fixed supply of gold. Say output over 25 years doubles (a perfectly reasonable assumption if that economy grows 3% annually), but the supply of gold stays fixed. Now you've got twice as much output chasing the same amount of gold, so prices deflate (by half). Wages do the same thing. Now imagine for a second that you took out a loan in year 1 for 5 pounds of gold. Now, in year 25, the nominal value of your principal is the same, but the real value of the loan is double, PLUS interest. Given that kind of deflation, no one's going to be too willing to borrow in gold. Instead, they'll spend as little of their gold as possible and sit on it, waiting for it to appreciate. [Okay, one sentence ago, it seemed the claim was no one will want to borrow in gold, due to price deflation. Then, the next sentence seems to claim that no one will want to lend in gold, which doesn't seem to follow from price deflation.] But if everyone's doing that, then where does the demand for goods and services come from? The simple answer is: from nowhere. [Okay, so people would hang on to their appreciating gold, even if it means forgoing food, shelter, etc.?] Instead the gold standard discourages credit, depresses demand, and makes the money supply contingent on something as random and unpredictable as the amount of gold that is mined in a given year."

Money

A penny saved is a penny earned, and I find it easy to save money. At the same time I feel that money is worthless; money can't be consumed. The value of money is as money. I save money because I feel that there isn't very much to spend money on. I live in an age where labor is more valuable than ever before, and it is relatively easy to meet basic needs. But saving money is the responsible thing to do, so I do it.

In any case, it occurred to me that it is also a risky thing to do. This is obvious to many people, I'm sure. But it is an historical fact that the buying power of the dollar has steadily diminished over time. So, it seems risky to store so much wealth for the future in the form of saved money. But now I am starting to wonder whether or not saving money is risky depends on what "money" is. The dollar has certainly depreciated. I understand that this is uncontested, although I haven't done my own empirical research on it. I do understand the argument, however. The argument goes that the dollar is not "backed" by anything and its value depends on its management. Now, this would be true of anything used as money. I believe one necessary characteristic of money is that it must be somewhat scarce. Gold is in fact somewhat scarce. Gold cannot be produced from nothing. That is not true of the dollar, and the claim goes that the quantities of dollars has not been properly controlled by its creators. A progressively greater number of dollars chase the same or fewer goods and the result is less buying power for the dollars. This is easy to understand.

But I'm sure it's only one side of the story. Perhaps the dollar isn't a perfect money, but it may be the best available. There are other advancements of science that for all of there value still are not perfect. Because the dollar is an artificial money, it can be perfectly controlled. In fact, I wonder if physical dollars will cease to be circulated in the near future. If some commodity or physical object were used as money on the other hand, then there can be no central control; what is scarce today might not be scarce tomorrow.

Now I can see what many of the critics of the fed and fiat money are libertarians. Giving the government the peculiar power to manage the money supply has allowed (and will allow) them the ability to bypass the approval of the people for their policies. Governments have no resources of their own, so it if needs money for war it must ask the people for it directly for money or create the money out of nothing. That sounds like a criminal act, but I guess that's the privileged that the creator of money is entitled to.

What's the truth? I don't know. In fact, I don't have a lot of confidence that what I have written above is the truth. I'm just trying to repeat a story I've heard about money in general on the dollar in particular. I would just like to discover some way to store wealth without having to keep up with inflation by making investments that I don't understand.

Projects

Here I will compile a list of projects that I'd like to finish someday. Today I'll write a few things down that have been on my mind recently, lest I will forget them. Projects occur to me all of the time, and, as silly as some of these I can't describe how excited I get about them. I'll come back and add to this list in the future, but the common link between all of the projects is that they are all due to some math or science that I want to either learn more about or put to the test.

Here is the list:

(1) make a sundial: timekeeping and astronomy are both interesting subjects to me, and here is one project that concerns both of them.
(2) make a simple calculator: I don't know how far out of my reach this one is, but I
I'd be happy no matter how simple it was. Perhaps with a microprocessor and devices for input and output I could at least add in binary. I have at this point at least learned how binary arithmetic can be reduced to logic circuits; it's knowledge of electronics that I am lacking.

2012 Tomatoes

I planted my tomatoes today. I bought 7 total transplants today, and this season I will be planting more tomatoes that ever. The varieties are Arkansas Traveler, Celebrity, Jet Star and Big Boy.

Actually, only 4 or the 7 transplants were planted directly into the garden. This is because I'm conducting an experiment this season, but I want to say a few preliminary remarks before I describe the experiment. I planted today, of course, but I think the truth is that the crop would have been unsuccessful if I had waited until mid to late April to plant them. The reason: tomatoes will not set fruit during very hot weather. On the other hand, the tomatoes will become mature and set fruit in suitably warm (but not too hot) weather by planting them in early spring. But planting them in early spring leads to other problems: occasional frosts and high winds. In any case, 4 tomatoes went directly into the garden, and the other 3 were planted into bigger pots with additional potting soil and alfalfa meal (fertilizer) added. These plants will keep growing as long as bigger pots are provided when needed, but they are portable enough to be hardened off gradually. They can easily avoid the cold and wind and they will be planted into the garden when conditions are right.

Update 3/24/2012: So far, anyone would agree that the tomatoes in pots "look better" than ones in the garden, although the ones in the garden look normal for their time of planting. All plants were fertilized with an even mix of bone and blood meal, then watered with a molasses solution.

What's new.

The past few weeks have been unusual for me, at least as far as the quality of my experience goes. I have felt remarkably un-competitive. Not non-competitive, since that is the opposite of being competitive, which doesn't seem like the right description. "Indifferent" may be the best word. If someone insults me, I don't get obsessed with revenge, or feel indignant. Rather, I think, "Well, sometimes I'm a loser. Sometimes I'm foolish and unintelligent," etc. All without anger and with acceptance. But when someone praises me I think that sometimes I do get it right. I look people in the eye, but calmly, indifferently. I don't mind when the weekend is over, and I don't get anxious about the week. I'm not ashamed to say I don't know the answer, but i'm not proud of it either (as if to be proud of my honesty). The onset was sudden, as if a day came and shackles were removed. But it's not black-and-white either. I can imagine it being cultivated to become more intense. That's what it's like.

My main point, however, is how certainly different the quality of my experience has been. I used to believe, "You are who you are." The best you can do is learn to cope. That doesn't seem true anymore. I don't think I've been fooled here, or persueded by wishful thinking; what I've described is genuine. My description of it may be totally wrong, but I am certain my experience is changed. The experience seems unlimitedly powerful, even though it hasn't been there continuously. I have had definite moments of relapse throughout all of this. I felt ambivalent about writing this record of it, and I think I've said enough.

Fasting

So far today I've eaten a handful of berries and one-third of a banana, but I've had plenty to drink. Other than that, I've been conserving energy by staying in bed, and I'm having a wonderful time indifferently listening to music, thinking and daydreaming. The short story is that I am physically comfortable and am otherwise pleased, content, nostalgic, grateful, lucid and serene. (Well...Compared to what's normal for me, anyway.) It's no surprise then that I think it's good to spend a day like this periodically.

There's more to the story. A few years ago, I spent a day like this hoping to hasten my recovery from the flu, and it did seem to work. Moreover, once recovered, there was a period during which I felt more energetic and healthy than before the illness.

Progressive Muscle Relaxation

I have created a version of progressive muscle relaxation that works for me. But, first, some background. Over the past year or so muscle tension in my face, jaw and neck has become worse. The muscle tension is uncomfortable on its own. But there's more. Here are some other symptoms that seem to be caused by muscle tension: low quality sleep, dull migraine-like headaches that are continuous for days, feeling like I just got off a roller coaster, neck pain, feeling unfocused and detached from my environment, dizziness and unsteadiness. Right or wrong, I believe that all or most of this is due to almost constant muscle tension. There has been scientific observation that progressive muscle relaxation and breathing exercises are good treatment for muscle tension, anxiety (and its symptoms?), headaches and neck pain, fatigue, and some other conditions. I have learned and tried the method of progressive muscle relaxation and breathing exercises, but neither have ever worked for me. In fact, breathing exercises make it worse: each inhalation is almost always directly tied to a further painful constriction of the already present muscle tension in my head and face. It just makes it worse. Progressive muscle relaxation doesn't make things better or worse. Until now.

The traditional method of progressive muscle relaxation is to first consider a particular muscle or muscle group, such as the forehead, eye lids,lips, jaw, etc. You would then tense the muscle very tightly, hold the tension for 5 seconds or so, and then abruptly release and relax it. After release, really appreciate the difference in the experience between tension and relaxation. Those are the common instructions, now I'll speculate a little. I suppose the reason for the procedure is to teach yourself to notice overlooked muscle tension. You can't relax muscles that you don't know are tense; but you can relax a muscle that has been intentionally tensed. And if the release is abrupt, the difference between tension and relaxation can be more easily noticed.

As I mentioned, this method has never solved any of my problems. But I have stumbled upon a modification of it that does work very well. For me the key is to tense the muscle just to the point of being noticeably tensed. This is much different than tensing very tightly. As far as muscles in the head and face are concerned, this allows me to easily focus on just one muscle group at a time. Furthermore, this barely noticeable tensing followed by abrupt relaxation allows me to sequentially relax the muscle group further and further to the feeling of complete comfort (or lack of tension). I may spend 5 minutes or so gradually "stepping down" the tension on just one group. I'll usually follow that with some time just observing the relaxed state. This seems to work very well: I was able to achieve relief and comfort after the first session, and I woke up the next day feeling remarkable different and better than recent mornings. My explanation is that over-tension the muscle make it much harder to perceive and relax the muscle tension that was already present. Tensing just barley enough to exceed the muscle tension that was already present gives me a much better perception.

This may be one of the most boring blog posts ever. But the discovery is worth it to me since it seems to have caused the first non-pharmaceutical relief in my muscle tension and associated problems ever: No headache, neck pain, detachment from reality, unsteadiness, and I've had better sleep. These symptoms have been so pervasive and unpleasant, especially over the past few months. It's a big discovery if progressive muscle relaxation continues to work.