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.