Meadow Garden Update

I don't know what these are, but here are some better photos of the wildflowers in the meadow garden.

Meadow Garden

For several years now, I have wanted to let wildflowers grow in the spring in a certain reserved part of the yard. This goes along with several other moods of thought that have welled up in adulthood, such as looking forward to, and enjoying, mowing the yard, and keeping tabs on the rainfall amounts. In any case, I did get some wildflower seeds as a gift last year, and last fall I planted them after scalping the grass with the mower. There wasn't much to do after that, except resist all temptation to mow over there once the mowing season began. We have been lucky to have gotten plenty of rain already this year (enough to have flooded the septic tank, something that only happened for the first time in our third year in this house). There are some wildflowers, but not as many as I hoped for (of course), and no Bluebonnets (even though some were supposedly in the mix). But, I'm happy with it.

New Hatsan Gun

I got a Hatsan gun for Christmas, but have only put less than 30 rounds through it since then. I've just been too busy. Luckily I've grown up enough to be patient about things like this, and today I spent some quality time with the gun. Photographed is the gun and a group I shot at 60 feet (20 yards). I used the bipod for this group. I found as I was warming up that my groups were not nearly as good shooting with the artillery hold (without the bipod, of course). The gun is a 0.25 caliber and has a gas-spring power plant. How powerful is it? I could have logged more detailed information on it's power, but I did notice that it will shoot cleanly through a stack of about 40-50 sheets of tightly packed copier paper at 30 feet.

The garden now.

A day at the Fort Worth Nature Center

We spent much of today at the Fort Worth Nature Center. In fact, we have gone there about this time every year for several years now, and it's because of the Dallas-Fort Worth Herpetological Society having their annual "Snakes of Tarrant County" exhibit. The exhibit is a rare opportunity for me, since I like to learn about and observe snakes, but only in the presence of experts. (I'm not an amateur snake-handler.) The kids loved it, and the society has done a good job at making it kid friendly, as you might expect. I guess there is a single primary family that is responsible for the exhibit, and their older children are there to help. They were friendly to our kids, and seemed to understand small children, even when Neil was being difficult. In any case, we visited the snake exhibit first, and I realized then that I wanted to go hiking just as much, maybe because of the overcast and warm weather. There are extensive hiking trails there, of great variety. Some are rocky and hilly. Some are flat and smooth. There is a variety of scenery, from dense woods, to plains with bison and prairie dogs in view. What do I know? I've only hiked on two of the trails, actually. But after today, I want more. Hiking is one of my favorite pastimes. Actually, I like taking walks, so as I see it, I like hiking a fortiori. Hiking with small children can be a bad idea, so I thought we'd get our feet wet with what I thought was a small and easy trail adjacent to the visitor's center. I didn't have a map, and we got off course of that easy trail and onto a rocky and hilly trail, in dense woods. Neil liked it. He curiously wonders if snakes are in the tall grass, as we warned him there were a few weeks ago at Fort Griffin. He notices the rocks (and boulders), and the fire ant "mountains," and the various bugs. Olivia, on the other hand, thought the trail was "dangerous." She refused to enjoy anything she normally would, such as seeing a butterfly. As if her mood wasn't plain enough, I asked her, "Is hiking awesome?" She replied, "No, hiking is not awesome." I don't know if she just didn't want to be hiking, or if she was actually nervous about the difficulty of the trail, the dense woods (which can make a person feel lost and disoriented), the tall grass, etc. We eventually came to one of the park's roads and just decided to try to find our way back to the visitor's center to get a map of the trails, rather than continue hiking further away from it. Once back there, I noticed a trail that we had seen a little of last year, with the kids (and they enjoyed it). I remembered this trail, that it has wide, flat and soft dirt paths, bison and prairie dogs are in view, has an open view of the land, and it is a popular trial. I thought if we had a chance to enjoy hiking, this would be the trail. So we drove to it, and parked. The kids did like it (even Olivia), and we went much further down the trail than last year. Maybe a little too far, since we each had to carry one of the kids for part of the way back. Sometimes, we all enjoy the same things about hiking (or going to the zoo, or botanic gardens), such as seeing a bison, or flower, or bug. Sometimes we don't see it the same way that the kids do. For the first ten minutes on the trail, all the kids wanted to do was play in the dirt and pretend their toy snakes were eating the dirt. At that time,they were enjoying the trail as much as we, just for different reasons. Eventually, I had enough, and thought I wasn't going to stand around while they played in the dirt. I had to think of a diversion. I said, "Why don't we go find some berries for the snakes to eat?" (Just one day earlier, we had found some wild berries growing at the botanic gardens, which they were intrigued about.) It worked they were ready to explore the trail and find berries. We never found them, but we were just there for the pursuit, anyway.

Christmas shopping with Olivia

Today I took Olivia Christmas shopping, just the two of us. We did the same last year, and it occurred to me that it would be a good tradition. I asked her if she wanted to get Mrs. D. something for Christmas. She said yes. I asked her what she wanted to get. She said that she wanted to get a bracelet and a necklace. This was all I needed to hear, so we soon left to go shopping. Darcy also needed me out of the house for a few hours, since apparently she preparing something for me for Christmas that takes some time and assembly. So, Olivia and I left, and just like this occasion in the previous year Darcy tried to recreate the picture of Olivia and I standing by the blue car. It also came out at some point that she was in the mood for ice cream, so we made Brahms our first stop. It was definitely warm enough for eating ice cream today. Olivia knew she wanted strawberry ice cream, but I still had to hold her up in order to she what was behind the counter. We eventually make it to Chico's, which is a place that Darcy suggested Olivia would have good luck picking something out. On the way there Olivia found an etch-a-sketch and started focusing on that. What follows is a digression: Neil is two and three-fourths right now. He loves to learn about shapes. He loves to look at shapes. I like to draw two- and three-dimensional shapes for Neil. He loves demonstrate what he knows when I ask him, "Is there a triangle in the room?" "Is there a sphere in the room?" I just assumed that Olivia wasn't interested in this, so I didn't bother with it. I had no reason for that; I just had a stereotype. Olivia is artistic, creative and emotional, so I believed. But she has edged in on Neil's and my shape games, and has picked up on it as well as Neil has. Okay, digression over. While in the car, Olivia drew a cylinder on the etch-a-sketch, and I was very impressed with it. When we arrived at the University Mall, Olivia wouldn't leave the etch-a-sketch in the car. I thought this could be a problem, but what could I do? I was right. We got to Chico's and Olivia wasn't interested in picking something out for Darcy. Vanity and pride had struck me earlier. I thought about how good I would look to bystanders in the store: "What a great father and cute little girl picking something out for mom." Everyone else there would be doing run-of-the-mill Christmas shopping, and we were really going to standing out and lead people to give pause. But Olivia was not interested in playing along with that. I tried to force it, and took her over to a jewelry table. "Don't you want to pick out something for Mrs. D.?" She just grabbed the nearest object, the low hanging fruit. "Come on!" I thought to myself. So I took here to the next table to she if she would act any different. She looked away from the etch-a-sketch to do more of the same. So I picked something. We walked to the check-out. I thought she might want to hold what we picked out. We had earlier gone to QT for a drink for me and gummy bears for her. She was enthusiastic to hold the gummy bears and credit card then, but not anymore. Still though, while in like she was happy to tell the attendant how she was buying this for mommy, and that I was daddy, and I play monster and dinosaur, and about our dogs. Another lady behind us was charmed by her, but I think she may have regretted it. It was funny how much Olivia had to say to her, some of it quite random. We actually had been to University Mall the day before, as a family. For some of the time, I had to watch Neil and Olivia. It was I warm day, and we waited in the courtyard. Both of the were obsessed with all of the acorns. They wanted nothing else but to pick up acorns and put them in my pocket. My pockets were getting full and I realized this was not sustainable. So I would secretly toss some in the air, and I gave the suggestion that they fell from the trees. This way, my pockets did not fill up. Olivia and I continued this game when just two two of us came back. The whole day was a good experience, and I think I'll be nostalgic of it. Now, on to another topic. I am nostalgic of so much in the past. Not all of it good. Some of it very ordinary. Some of it very exciting. I like to revisit old places. I have wondered why I am so nostalgic, and why the recollection of an experience is vastly better than the original experience itself. I began to think that the experience of being nostalgic is like that of dreaming. Many of my dreams are very ordinary, but much more pleasant than the experience would be in waking life. I think the secret may be the great amount of tension I am perpetually feeling. Tension about the world, injustices everywhere, lousy people everywhere. Tension about not accomplishing enough, about learning enough, knowing enough, doing enough. Existential worries. It's constant. But it's absent in dreams. For some reason it's absent in nostalgic recollection. Maybe because recollection is not reality. In any case, it's then I get to experience something from the past without all the tension and worry, and it's much better than it was the first time around.

I have a patch of weeds growing in my yard. Actually, there are weeds all over my yard, since I don't see a problem with them. They look fine when mowed, and the lawn is mostly made of a uniform looking grass anyway. My point is there is a section of the yard full of weeds that I haven't mowed in several months. The reason? Ladybugs love this particular weed that grows there. It's a spiny, sticky weed with aphids on it. Maybe the Ladybugs go where the aphids are? Anyway, Neil loves to look for Ladybugs, and we can always find them on the weeds in this un-mowed part of the yard. We have a good time looking for and catching Ladybugs. I have met people panic at the first sign of a weed, or take measures to keep weeds away. To me, that's silly.

New Garden

I'm glad to say that I have a garden. Now that's its built, I wouldn't change anything about its construction or location. It is a great undertaking of manual labor, money, time, and planning to do this, and so I am happy it got done so soon. (We have only lived here since July.) So far, I have 8 tomatoes, 1 eggplant, and a few summer squash seeds planted.

The mental work of decided how and where to build a garden from scratch is very difficult and stressful for me (And this is before the manual labor even begins.) Originally, I was going to have the vegetable garden in the flowerbed on the south side of the house. I made that decision from caving to laziness. The beds already there, even if it's not perfect. It'll work, I thought. But I decided against that once I found that the foundation had been treated for termites a few years ago. So, I decided to use the yard on the south side of the house. Raised beds seemed like the only way to go. The next issue was to decide on wood, masonry, or what else?

I decided to build a wood-frame raised bed, initially out of cedar. I even went to Home Depot expecting to buy cedar. The reason for the cedar was because I wanted to build a more sturdy version of one of the cheaper kits I saw online. (Cedar kits are ubiquitous in garden magazines and catalogs. I almost bought two cedar kits for $80 each for this project. That kit was the cheapest I could find, and I eventually decided it was too cheap and I lost confidence in it.) At Home Depot, an employee in the lumber department suggested that cedar isn't automatically a good wood for the project. The hardiness of the wood depends on from what part of the tree it is cut, and he had no idea about the cedar that happened to be in the store. It's no surprise that everything labeled "cedar" is not the same. The use of cedar for raised beds was a fad, he suggested. My father was there and he found this easy to agree with. Additionally, cedar lumber is very expensive, but untreated pine is not.

It worked out that I can build 4 feet by 8 feet (8 inch tall) bed from yellow pine boards that are nominally 2 inches thick for $25 - $30. From talking to employee at Home Depot, and from reading on the Internet, I expect to get 3 to 5 years out of such a bed. After all, the only function of the frame is to hold the soil in place. The wood will gradually rot and be incorporated into the soil. Then, I'll rebuild it again, perhaps the same way all over again. So I bought enough southern yellow pine for two 4 feet by 8 feet beds with a frame that is about 8 inches tall. The wood was untreated, just cut from the tree and dried. I bought untreated wood, even though the pressure treated wood is officially allowed for food gardens (many gardeners don't trust this, however). The older type of pressure treated wood contained arsenic, and was used for many years before being recently banned. I certainly don't know what's safe, so I err on the side of caution.

The assembly of the bed was simple, and it looks square, level and even. I was very careful measuring and cutting, and I took my time. I was worried it wouldn't look good in the yard, but it looks fine. The hard part was removing the Bermuda grass and weeds, which I did with a pickaxe. It was also very hard to haul the 21 cubic feet of compost and amendments to fill the bed. I bought about $90 of that sort of stuff from Archie's. I bought an assortment of cotton burr compost, cow manure compost, greensand and "landscaper mix" which I think I was misinformed about (it seems like a fancy mulch, not a soil amendment). I have never gone to these lengths before. I had another garden at our old house, but I filled it with homemade compost, most of which was not totally finished composting. The new bed is filled to the top. It was hard work. I plan to repeat this procedure in a week or so for the second bed.

Delusions of Grandeur

Tomorrow is the first day of a new semester. Earlier I was imagining myself conducting my class with dignity, significance, and respect, which is probably making it all out to be much more important than it is. This easily led me into a daydream of a man confined to a mental hospital having delusions that he is a king or a knight. The truth is, in some ways, I wouldn't mind being that man.

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.