Now, I must unfortunately begin this post by commenting that I think "the grass is always greener on the other side" is a silly phrase. That is to say, the state of greenness of a certain patch of grass does not change. It is in fact a scientific measurement of the wavelength of light that is reflected from the surface. Therefore, if it the grass is not seems, but is greener on the other side, then you should go over there and be done with it. The grass will not change on the spot, and the other side will no longer be more green. Now, I will move on from this technicality and get more to the point.
For all that the literal meaning of the saying is worthless (in my opinion), the figurative meaning behind it is remarkably accurate and applicable to nearly everything. In the last few weeks I've begun to do a fair amount of reflection. I've titled this process a game, that I call "Where I was a Year Ago Today". I don't think it will be as much fun next year because I will have been, well, here. Conversely, last year, I was...everywhere (see other blog for details). But, my reflection has pertained to more than just my trip. The months preceding the trip I was living in Illinois with one of my best friends. It was a LOT of fun. I golfed, played magic, played frisbee, cooked good food, saw friends. It was a lot of fun. But I didn't do anything.
A desire for free time is I think a craving many, if not most, people experience. However, there are few things worse than having free time, when it isn't by choice. It was a long process to find a job, and the time in between, while it may have started out pleasurable, soon became quite a drag. So, when day after day I found myself wishing for a job, I thought, "the grass is so much greener over there". However, I have since been fortunate enough to become employed, and I enjoy my job quite a lot. However, there come the days and the times when I feel like I have been working non-stop, day after day after day. It would be a lie to say I never thought, "the grass was so much greener back then..."
The truth of the matter is, I don't wish to be back in the shoes I was in before. Sure, free time to do whatever is nice, but it isn't what I wanted with my life. So, this is all I intended for the meaningful aspects of this line of thinking. As for some more random thoughts, since that's why we're here isn't it?
Has anyone tried to play a sport on a hot summer day, and felt like dying? Gone back inside and thought "I wish it were winter! The chill, the snow, etc..." Ah, yes... that's another case of the grass being greener! Well... sort of. With all that cold and snow, it's likely that the grass would die and become brown... which leads to our feelings in winter. When you become tired of the short days, long nights, frigid air and no snow as the freezing rain washes it all away. Then, there are few thoughts to keep other than "the grass is brown here and now! Of course its greener on the other side!"
I sometimes wonder if this saying is why I'm so bad at being decisive. I can always think of something to do, but fear committing to it. Why? Because the grass might be greener if I don't... I'm not saying this is a good philosophy... in fact, I'm more inclined to think its a poor one. But, I'll make do with what I have. After all, where I am, the grass is greenest! :)
Wednesday, January 18, 2012
Monday, November 21, 2011
A Bitter Taste
This is one of those times that I recall that silly joke "When is a car, not a car?" If you've never heard it before the answer may not be so obvious, but I find that once the answer is known, the saying comes as naturally as anything. "A car is not a car when it turns into a driveway." So, I think that now that we've gotten through the answer we can agree that is 1) funny... in that stupidly obvious joke sort of way and 2) a pretty intuitive thing to say afterwords. This raises my question though. "When is a pie not a pie?"
Now, to first clarify a potential point of confusion (while intentionally avoiding formal definitions). When I say "pie", I am specifically referring to that (usually) round, edible, dessert/breakfast/snack food dish.I am not being tricky and referencing a letter in the Greek alphabet, nor am I thinking about the irrational number between 3 and 4... That would obviously be irrational to assume. So, we're now on the same page as to what "pie" I am thinking of, and we can now address when said pie is in fact... potentially... not a pie.
This question first came to me when I sat down at a friends house for some dessert. For said dessert, we were presented a beautiful Tart. That's right... you all thought I was going to say PIE!!! But no, twas not a pie, but a tart. Now, I have no doubt that you can all envision a tart without too much trouble. So, just as you might picture, we had that light brown, gram-cracker-like crust, with a custard filling topped with an assortment of colorful fruits. Now, before I begin to delve into my dilemma a bit more, I want to mention that the Tart was delicious.
So, moving on... we see a tart now, before us. We're eating and enjoying it. And then the question arises... "What is the difference between a Pie and a Tart?" Has anyone wondered this before? I'm sure you have! You may not know you wondered it... but the wonder was there. Well, I decided to pose a theory to debate as we ate (rhymed...). I raised the question, and proposed (foolishly) that a Tart was clearly made with fruit as a focus. This was quickly countered with examples of apple, peach, blueberry, etc... pies. So I retracted my theory and wondered a bit.
I thought about what my previous impressions of tarts had been, and there I thought I had it. In my mind when I envision a tart it is a small, single serving dish. I figured a tart was perhaps a small pie! But no, the tart we were in the midst of consuming was the same size as a typical pie, so that thought went out the window. My friend proposed then that a tart did not have a crust covering it. Nodding, it seemed to make sense. I can think of no tart I've ever had that was covered. But then... there were the thoughts of pumpkin pie. I do love pumpkin pie with whipped cream, but that's not the point. Were pumpkin the only exception we might have still gone with it, but there are other pies, like chocolate, that had to sway us to deny this theory.
With all current theories denied, we thought about the name, "tart". Was this a description of the dish? No! What we were eating was sweet, not tart. And if a pie isn't fully ripe, it can be tart, while still being a pie! Perhaps it was a flaky crust versus a gram cracker crust? Again, counters were provided. Frustrated, and out of ideas, I was defeated, gave up, and resided myself to another slice of tart...
With a bitter (not tart) taste in my mouth from losing an argument to my food, I sought the answers at home. I looked up the definitions, and discovered no clear distinction between the two. I even found the claim that the two categories frequently overlap. Still not satisfied, the question stuck with me. This last August I was at a 1 week seminar and dessert one night was... that's right... a tart! I got a chance to speak with the chef afterwords and inquired to the difference. Not knowing, she sought her resources to return with the answer. Upon her return, she went through the definition and claimed that she too saw no true distinction. With that I was willing to let the topic drop, as I figured if she did not know, nobody would.
I thanked her for checking, and she said it was an intriguing question. She asked about the history of this puzzlement to me, and I explained. Then, as she got up to leave, she mentioned... "What about a cheesecake?" AND I WAS DOOMED! Cheesecake falls into none of these categories and I cannot define it. I have not sought the definition. I've decided I will not lose another fight to this realm of dessert, and will instead continue to eat it and enjoy!
Now, to first clarify a potential point of confusion (while intentionally avoiding formal definitions). When I say "pie", I am specifically referring to that (usually) round, edible, dessert/breakfast/snack food dish.I am not being tricky and referencing a letter in the Greek alphabet, nor am I thinking about the irrational number between 3 and 4... That would obviously be irrational to assume. So, we're now on the same page as to what "pie" I am thinking of, and we can now address when said pie is in fact... potentially... not a pie.
This question first came to me when I sat down at a friends house for some dessert. For said dessert, we were presented a beautiful Tart. That's right... you all thought I was going to say PIE!!! But no, twas not a pie, but a tart. Now, I have no doubt that you can all envision a tart without too much trouble. So, just as you might picture, we had that light brown, gram-cracker-like crust, with a custard filling topped with an assortment of colorful fruits. Now, before I begin to delve into my dilemma a bit more, I want to mention that the Tart was delicious.
So, moving on... we see a tart now, before us. We're eating and enjoying it. And then the question arises... "What is the difference between a Pie and a Tart?" Has anyone wondered this before? I'm sure you have! You may not know you wondered it... but the wonder was there. Well, I decided to pose a theory to debate as we ate (rhymed...). I raised the question, and proposed (foolishly) that a Tart was clearly made with fruit as a focus. This was quickly countered with examples of apple, peach, blueberry, etc... pies. So I retracted my theory and wondered a bit.
I thought about what my previous impressions of tarts had been, and there I thought I had it. In my mind when I envision a tart it is a small, single serving dish. I figured a tart was perhaps a small pie! But no, the tart we were in the midst of consuming was the same size as a typical pie, so that thought went out the window. My friend proposed then that a tart did not have a crust covering it. Nodding, it seemed to make sense. I can think of no tart I've ever had that was covered. But then... there were the thoughts of pumpkin pie. I do love pumpkin pie with whipped cream, but that's not the point. Were pumpkin the only exception we might have still gone with it, but there are other pies, like chocolate, that had to sway us to deny this theory.
With all current theories denied, we thought about the name, "tart". Was this a description of the dish? No! What we were eating was sweet, not tart. And if a pie isn't fully ripe, it can be tart, while still being a pie! Perhaps it was a flaky crust versus a gram cracker crust? Again, counters were provided. Frustrated, and out of ideas, I was defeated, gave up, and resided myself to another slice of tart...
With a bitter (not tart) taste in my mouth from losing an argument to my food, I sought the answers at home. I looked up the definitions, and discovered no clear distinction between the two. I even found the claim that the two categories frequently overlap. Still not satisfied, the question stuck with me. This last August I was at a 1 week seminar and dessert one night was... that's right... a tart! I got a chance to speak with the chef afterwords and inquired to the difference. Not knowing, she sought her resources to return with the answer. Upon her return, she went through the definition and claimed that she too saw no true distinction. With that I was willing to let the topic drop, as I figured if she did not know, nobody would.
I thanked her for checking, and she said it was an intriguing question. She asked about the history of this puzzlement to me, and I explained. Then, as she got up to leave, she mentioned... "What about a cheesecake?" AND I WAS DOOMED! Cheesecake falls into none of these categories and I cannot define it. I have not sought the definition. I've decided I will not lose another fight to this realm of dessert, and will instead continue to eat it and enjoy!
Tuesday, September 6, 2011
Cutting Corners
There are times in life when we all like to take the easy road, short-cuts, cut corners. Many times in life this is acceptable. Sometimes in life it's not, but works out anyway. Some do like to say, "its better to be lucky than good". That said, cutting corners usually entails doing something more risky, or skipping steps, and has a much high risk potential.
I would say that this is most frequently experienced when people are on long road trips to places they are ... sort-of ... familiar with. Not familiar enough to actually have a local map committed to memory, but comfortable enough to think one does. So, as one approaches there location, they decide that rather than take an hour to go the safe route, they're save 10 minutes by taking a short cut. How does this result? Frequently in getting lost and having a short-cut turn into a 30-60 minute detour, just to return to one's original location prior to this foolish decision.
So, in the world of carpentry there is a saying "measure twice, cut once." The idea being, follow a procedure, double check your work, take your time. An object can always be cut shorter, but not longer. So, this whole system is designed to be a check, to prevent stupid and irreversible mistakes. I have adopted many of these exact sayings into my life, and find myself using them as rules to govern many of my choices.
I bring this up now to make a special aside to some of these rules, and point out a crucial flaw. Years ago I was helping my father build our new garage. The foundation was all set and ready to go. We were moving onto our favorite step... Framing. Few tasks in carpentry are as satisfying. You get massive amounts of visual improvement for the amount of time spent, as well as it being the most fun aspect. So, we were each assembling a wall after making the first one together as a template. By assembling a wall I am referring to attaching the studs to headers and footers, basically making the walls' skeleton. Once assembled we could just stand them up in place and fasten them in.
So, with the first wall done together we each set out to make the remaining two. Following proper carpentry procedure, I measured every stud twice before cutting them. Then, I checked to make sure all the studs were of equal length before fastening them into the headers and footers. All in all, there was much double checking. So, with the frame finished we stood up each section, and upon completion of erecting the walls we immediately noticed that my wall... was 4 inches shorter than the other two...
Huh... Well, turns out, the rule of "Measure twice, cut once" is only helpful when you know the correct size you wish to be measuring. Otherwise, you can be very confidant that your project is consistently incorrect. So, while I still firmly support that double checking is valuable, and that one should take the time to do so, one should make sure that they know what is correct, before confirming that they are consistent.
I would say that this is most frequently experienced when people are on long road trips to places they are ... sort-of ... familiar with. Not familiar enough to actually have a local map committed to memory, but comfortable enough to think one does. So, as one approaches there location, they decide that rather than take an hour to go the safe route, they're save 10 minutes by taking a short cut. How does this result? Frequently in getting lost and having a short-cut turn into a 30-60 minute detour, just to return to one's original location prior to this foolish decision.
So, in the world of carpentry there is a saying "measure twice, cut once." The idea being, follow a procedure, double check your work, take your time. An object can always be cut shorter, but not longer. So, this whole system is designed to be a check, to prevent stupid and irreversible mistakes. I have adopted many of these exact sayings into my life, and find myself using them as rules to govern many of my choices.
I bring this up now to make a special aside to some of these rules, and point out a crucial flaw. Years ago I was helping my father build our new garage. The foundation was all set and ready to go. We were moving onto our favorite step... Framing. Few tasks in carpentry are as satisfying. You get massive amounts of visual improvement for the amount of time spent, as well as it being the most fun aspect. So, we were each assembling a wall after making the first one together as a template. By assembling a wall I am referring to attaching the studs to headers and footers, basically making the walls' skeleton. Once assembled we could just stand them up in place and fasten them in.
So, with the first wall done together we each set out to make the remaining two. Following proper carpentry procedure, I measured every stud twice before cutting them. Then, I checked to make sure all the studs were of equal length before fastening them into the headers and footers. All in all, there was much double checking. So, with the frame finished we stood up each section, and upon completion of erecting the walls we immediately noticed that my wall... was 4 inches shorter than the other two...
Huh... Well, turns out, the rule of "Measure twice, cut once" is only helpful when you know the correct size you wish to be measuring. Otherwise, you can be very confidant that your project is consistently incorrect. So, while I still firmly support that double checking is valuable, and that one should take the time to do so, one should make sure that they know what is correct, before confirming that they are consistent.
Wednesday, August 24, 2011
Skeletons in the Closet
To anyone who may not know, I have spent much of the last month moving into my new apartment at the Millbrook School. That said, it is not the most up-to-snuff place in terms of finishing work. So, being that there are few things I love more than carpentry and the associated tinkering, I have been spending much of my time redoing moldings, pulling excess nails and screws, etc, etc.
That being as it is, I have done lots of projects in the past, be them professional, or just helping my family in the house. But, every now and then something really cool is found during a project. The first example of this was when we moved into our house on Sunnyside. The basement had a dividing wall, and due to some... structural irregularities... the floor above was sort of sagging, and thus the dividing wall was creating a ridge in the upper floor. So, long story short, we added some supports and rigidity, so that we could remove the troublesome wall. n the process of removing said wall, we found within it an old bayonet. It is now hanging on the workshop pegboard.
Last summer we began to demolish/rebuild our back porch. One of the first steps was removing the roof, so that we could remove the support beams without dropping what they supported onto our head. That would have been unfortunate... to say the least. So, when I cut through the roof and pulled off the plywood, I found an ancient slide-square with a build in miniature level. This is one of the tools that I find very useful in many construction projects. I in fact already owned and used one of my own. With a bit of work, we rubbed it down, cleaned it off, and it still works, is square, and completely legible.
So, from these two examples I think its clear that skeletons, or memories from the past in a sense, are often found when one digs deep enough in "closets". But, that brings me back to my current project. In my apartment there are 3 sets of drawers built into the walls. Unfortunately, they all bothered me. When pushed in, some where twisted and not straight, some sagged, some could be pushed in 2-3 inches too far and some stuck out an inch or two. So, I set about reworking the frames and adding spacers so that all the drawers were straight, even and functional. Now, the first step to this project is pulling the drawers out of the wall, which is quite easy. It was on my third and final set of shelves that I pulled out and in the bottom, I found myself a LOT of sawdust, a hanger, an instant coffee packet wrapper, and a full and intact skeleton of a bat.
I mean really... How often do you see a full and complete skeleton of a bat?!? It's awesome! A little bit gross and/or disconcerting... but awesome! So, always check your closets... you'll never know what you'll find. :)
That being as it is, I have done lots of projects in the past, be them professional, or just helping my family in the house. But, every now and then something really cool is found during a project. The first example of this was when we moved into our house on Sunnyside. The basement had a dividing wall, and due to some... structural irregularities... the floor above was sort of sagging, and thus the dividing wall was creating a ridge in the upper floor. So, long story short, we added some supports and rigidity, so that we could remove the troublesome wall. n the process of removing said wall, we found within it an old bayonet. It is now hanging on the workshop pegboard.
Last summer we began to demolish/rebuild our back porch. One of the first steps was removing the roof, so that we could remove the support beams without dropping what they supported onto our head. That would have been unfortunate... to say the least. So, when I cut through the roof and pulled off the plywood, I found an ancient slide-square with a build in miniature level. This is one of the tools that I find very useful in many construction projects. I in fact already owned and used one of my own. With a bit of work, we rubbed it down, cleaned it off, and it still works, is square, and completely legible.
So, from these two examples I think its clear that skeletons, or memories from the past in a sense, are often found when one digs deep enough in "closets". But, that brings me back to my current project. In my apartment there are 3 sets of drawers built into the walls. Unfortunately, they all bothered me. When pushed in, some where twisted and not straight, some sagged, some could be pushed in 2-3 inches too far and some stuck out an inch or two. So, I set about reworking the frames and adding spacers so that all the drawers were straight, even and functional. Now, the first step to this project is pulling the drawers out of the wall, which is quite easy. It was on my third and final set of shelves that I pulled out and in the bottom, I found myself a LOT of sawdust, a hanger, an instant coffee packet wrapper, and a full and intact skeleton of a bat.
I mean really... How often do you see a full and complete skeleton of a bat?!? It's awesome! A little bit gross and/or disconcerting... but awesome! So, always check your closets... you'll never know what you'll find. :)
Friday, July 15, 2011
The Second Cliche
Has anyone ever watched a movie where the hero disarms a bomb with 1 second left? How about in Armageddon when the asteroid is detonated literally at the "do-or-die" moment. Then of coarse there's Independence Day when the alien ship is blown up as the weapon is about to fire on the last civilization on Earth. Now, I'm open to hear more and potentially even better examples, but those are the two that for some reason come to mind first.
So... doesn't anybody think this is a bit silly? Why can the hero never save the day with like, 8 seconds to spare? I'm not saying it would be "better", just different. Because honestly, we all know that our hero is not gonna go boom. So, why do I write about this now? What brought this assault on common movie, story telling methods to the forefront of my mind? That would be the semi-final game of the Women's World Cup this year between the USA and Brazil. (Note: if you have not seen it, don't want to know the result, or any combination of those or other reasons that lead to a spoiler being undesirable... don't read on) (Note on the note: If you did not see it... and don't know what happened... and don't care then you and I are going to have to exchange... words.... cause it was amazing)
http://www.sportsonenetwork.com/videos/18265/usa%27s-megan-rapinoe-to-abby-wambach-goal-usa-vs.-brazil-2011-wo
(it is possible that this link will not work ... cause sometimes there are copyright claims made by FIFA that cause them to be taken down)
Anyway, I will not recite the entirety of the game. But rather, I wish us all to recall the game tying goal that occurred in the stoppage time of the second overtime. Now, when I watched the game, and when I look back at the event, (call me bias) but Team USA was my protagonist/hero. I watched the game start to finish, and all the heart-wrenching calls and plays in between that made me swear endlessly at the poor television. From the opening seconds, when the US took a one goal lead, to the questionable red card at minute 66. Watching Hope Solo deny Marta her penalty shot, only to have it called back due to another questionable call. Then, Team USA holds the score, carrying the game to overtime against the Brazilians, despite being down a player. Then, only a few minutes into the first of 2 overtimes periods, I watched as Marta gave the Brazilians the lead. Then, despite all odds, I watched as Team USA attacked again and again to score the equalizer. There was endless waiting as Brazilians fell to "injuries" right and left, burning out the remainder of the clock. As stoppage time in the final period of overtime seemed to draw to a close, team USA mounts yet another drive, and puts away a goal to tie the game!
From here there were at most 90 seconds left in the game, which was taken to penalty kicks where Team USA won. Having watched this game, and possibly the most intense and satisfying game of any sport I have ever watched, I had to notice that my protagonist pushed until the last second and pulled through in what seemed to be, the very last second. I have to admit, for all that is seems a bit cliche that heroes always pull through with a countdown stopping at 1 second, had Team USA scored the equalizing goal with 15 minutes left, it would have been great; fantastic even, but it would never then have been among the top most dramatic moments in sports... ever!
So, with all that said, I will now always second-guess myself when I think a last second "save-the-day" is cliche (...rhymed...). This Sunday I will be watching USA take on Japan in the World Cup finals. You all should be too!
So... doesn't anybody think this is a bit silly? Why can the hero never save the day with like, 8 seconds to spare? I'm not saying it would be "better", just different. Because honestly, we all know that our hero is not gonna go boom. So, why do I write about this now? What brought this assault on common movie, story telling methods to the forefront of my mind? That would be the semi-final game of the Women's World Cup this year between the USA and Brazil. (Note: if you have not seen it, don't want to know the result, or any combination of those or other reasons that lead to a spoiler being undesirable... don't read on) (Note on the note: If you did not see it... and don't know what happened... and don't care then you and I are going to have to exchange... words.... cause it was amazing)
http://www.sportsonenetwork.com/videos/18265/usa%27s-megan-rapinoe-to-abby-wambach-goal-usa-vs.-brazil-2011-wo
(it is possible that this link will not work ... cause sometimes there are copyright claims made by FIFA that cause them to be taken down)
Anyway, I will not recite the entirety of the game. But rather, I wish us all to recall the game tying goal that occurred in the stoppage time of the second overtime. Now, when I watched the game, and when I look back at the event, (call me bias) but Team USA was my protagonist/hero. I watched the game start to finish, and all the heart-wrenching calls and plays in between that made me swear endlessly at the poor television. From the opening seconds, when the US took a one goal lead, to the questionable red card at minute 66. Watching Hope Solo deny Marta her penalty shot, only to have it called back due to another questionable call. Then, Team USA holds the score, carrying the game to overtime against the Brazilians, despite being down a player. Then, only a few minutes into the first of 2 overtimes periods, I watched as Marta gave the Brazilians the lead. Then, despite all odds, I watched as Team USA attacked again and again to score the equalizer. There was endless waiting as Brazilians fell to "injuries" right and left, burning out the remainder of the clock. As stoppage time in the final period of overtime seemed to draw to a close, team USA mounts yet another drive, and puts away a goal to tie the game!
From here there were at most 90 seconds left in the game, which was taken to penalty kicks where Team USA won. Having watched this game, and possibly the most intense and satisfying game of any sport I have ever watched, I had to notice that my protagonist pushed until the last second and pulled through in what seemed to be, the very last second. I have to admit, for all that is seems a bit cliche that heroes always pull through with a countdown stopping at 1 second, had Team USA scored the equalizing goal with 15 minutes left, it would have been great; fantastic even, but it would never then have been among the top most dramatic moments in sports... ever!
So, with all that said, I will now always second-guess myself when I think a last second "save-the-day" is cliche (...rhymed...). This Sunday I will be watching USA take on Japan in the World Cup finals. You all should be too!
Sunday, July 3, 2011
A Simplified Solution
Continuing my attempt to catch up on blogs I've meant to write in the past, I've one that led to quite a family discussion between myself and my parents a few weeks back. The topic was raised of students having difficulties learning mathematics, because the subject matter terrified the teachers. Apparently early math concepts frighten many math teachers just as much as they do students. Lets look, for example, at a word problem where the objective is to calculate the area of a pizza.
First lets break this down to see its steps, and figure out why this is frightening. First, we assume the pizza is a circle. Then, we must know, or look up that the area of a circle is described as A = πr^2. (Unfortunately, I can not type superscripts here, or don't know how, so we will have to tolerate the "^" notation.) From there, one must know that π is no more than a constant number and they must calculate the radius of the circle. Then, plug and chug. However, that is the simple point of view. We can also look at the equation as such:
Obviously, A is the area, our goal, what we are trying to identify. But as for π? Pi is a symbol. It is not recognizable as a number or a letter. In fact, we are now introducing an entire new lever of language skills required to complete this problem. And lets be honest... Greek is not the most heavily taught language in schools. Then we must deal with r. When was the last time anyone has ever ordered a 6 inch radius pizza? (The answer is likely frequently... just in different words). But NO! Everyone orders 12 inch diameter pizzas (assuming you want that size). So what's with this r nonsense, when it is clear that radius is not a commonly used measurement to describe a pizza. Lastly, we started this all out by knowing that our pizza, like most pizzas, are rounds... like... a circle. And yet, now we have to square the radius? What does that even mean. How do you square a circle? And how did a square come into the picture at all?!?!
At this point in our discussion (we had not talked about all this in so much detail... but we'll go with it), I claimed that those who feared solving for the area of a circle had no perspective. I will now take some time to "edit" and "simplify" the area of the circle. Then, perhaps those who fear this clear formula will have a bit more perspective.
Let us begin by dealing with the objective: area. Area of what? The sheer vagueness of the letter A could lead many people astray. It could be our pizza, thought what if our pizza is square? Then we're clueless. So, we will clarify by introducing a subscript that labels the area. (Unfortunately, like superscripts I don't know how to do subscripts here so we will use underscores (_).) Now, we will be working towards solving for A_c. Much better!
Next, let us deal with the radius, r. Since we've reviewed that r is not the best unit to describe a circle, we will look at d the diameter. So, in place of r we will use (d/2). Therefore, when the diameter is known, the formula becomes plug and chug once more, with no thinking involved. This is a wonderful improvement to r where we had to do division simply to come up with the number required by the formula.
Now to simplify the confusion of shapes. We don't like dealing with squares when we're talking about circles, because lets face it.... that's just confusing. So, we know that to "square a number" means to multiply it my itself. So, rather than squaring r, or as we have now simplified it, (d/2), we will rewrite r^2, as (d/2)^2, which we can further simplify to: (d/2)(d/2). Then, to make it a single fraction so there is less to look at, yet avoiding any "squared" notation, we henceforth be using (d*d)/4 (note the * represents multiplication, for lack of a more clear symbol).
Lastly, we must remove π from the equation. Euler, one of the greatest mathematicians of all time, came up with an identity, which to this day, I do not fully understand. But, I do know what it is. Euler's Identity is e^(iπ) = -1. So, if we are to proceed with our equation to a point of having no Greek letters in it, we can write an equivalent statement in terms of π. Then we find that, π = ln(-1)/i. Now, when we substitute this into our area of the circle, we have gotten rid of all characters belonging to foreign languages and don't have to deal directly with any irrational numbers.
So, at long last we have a new and "simplified" area of a circle:
A_c = (ln(-1)*d*d)/(4i)
So, to anyone who previously thought the area of a circle was terrifying, I have done my best to simplify it, and remove from the equation the elements that I thought would be the basis for confusion. I hope this helps and that you look forward to determining the area of the next pizza you buy!
First lets break this down to see its steps, and figure out why this is frightening. First, we assume the pizza is a circle. Then, we must know, or look up that the area of a circle is described as A = πr^2. (Unfortunately, I can not type superscripts here, or don't know how, so we will have to tolerate the "^" notation.) From there, one must know that π is no more than a constant number and they must calculate the radius of the circle. Then, plug and chug. However, that is the simple point of view. We can also look at the equation as such:
Obviously, A is the area, our goal, what we are trying to identify. But as for π? Pi is a symbol. It is not recognizable as a number or a letter. In fact, we are now introducing an entire new lever of language skills required to complete this problem. And lets be honest... Greek is not the most heavily taught language in schools. Then we must deal with r. When was the last time anyone has ever ordered a 6 inch radius pizza? (The answer is likely frequently... just in different words). But NO! Everyone orders 12 inch diameter pizzas (assuming you want that size). So what's with this r nonsense, when it is clear that radius is not a commonly used measurement to describe a pizza. Lastly, we started this all out by knowing that our pizza, like most pizzas, are rounds... like... a circle. And yet, now we have to square the radius? What does that even mean. How do you square a circle? And how did a square come into the picture at all?!?!
At this point in our discussion (we had not talked about all this in so much detail... but we'll go with it), I claimed that those who feared solving for the area of a circle had no perspective. I will now take some time to "edit" and "simplify" the area of the circle. Then, perhaps those who fear this clear formula will have a bit more perspective.
Let us begin by dealing with the objective: area. Area of what? The sheer vagueness of the letter A could lead many people astray. It could be our pizza, thought what if our pizza is square? Then we're clueless. So, we will clarify by introducing a subscript that labels the area. (Unfortunately, like superscripts I don't know how to do subscripts here so we will use underscores (_).) Now, we will be working towards solving for A_c. Much better!
Next, let us deal with the radius, r. Since we've reviewed that r is not the best unit to describe a circle, we will look at d the diameter. So, in place of r we will use (d/2). Therefore, when the diameter is known, the formula becomes plug and chug once more, with no thinking involved. This is a wonderful improvement to r where we had to do division simply to come up with the number required by the formula.
Now to simplify the confusion of shapes. We don't like dealing with squares when we're talking about circles, because lets face it.... that's just confusing. So, we know that to "square a number" means to multiply it my itself. So, rather than squaring r, or as we have now simplified it, (d/2), we will rewrite r^2, as (d/2)^2, which we can further simplify to: (d/2)(d/2). Then, to make it a single fraction so there is less to look at, yet avoiding any "squared" notation, we henceforth be using (d*d)/4 (note the * represents multiplication, for lack of a more clear symbol).
Lastly, we must remove π from the equation. Euler, one of the greatest mathematicians of all time, came up with an identity, which to this day, I do not fully understand. But, I do know what it is. Euler's Identity is e^(iπ) = -1. So, if we are to proceed with our equation to a point of having no Greek letters in it, we can write an equivalent statement in terms of π. Then we find that, π = ln(-1)/i. Now, when we substitute this into our area of the circle, we have gotten rid of all characters belonging to foreign languages and don't have to deal directly with any irrational numbers.
So, at long last we have a new and "simplified" area of a circle:
A_c = (ln(-1)*d*d)/(4i)
So, to anyone who previously thought the area of a circle was terrifying, I have done my best to simplify it, and remove from the equation the elements that I thought would be the basis for confusion. I hope this helps and that you look forward to determining the area of the next pizza you buy!
Tuesday, June 21, 2011
Not All Houses Were Created Equal
I discovered that my last post on this thread was over a month ago. I have been bored far more than once in the time frame... and by my description that means I should have written more. But, before I start... know that my song of the day is "Anna Sun" by Walk the Moon.
Anyway, I've been working construction on my house here in pville for the past two months or so. I have done a LOT of carpentry projects through my life, and in general, I enjoy building/renovating houses. Through the years I have learned my much about what is the norm, and regulations as well as some aspects of code. Knowing all of these facts is truly wonderful when you are working on a house. But, when you are working on an old house... all of these rules by which you structure your projects fall apart.
My first project, which took me through May, was removing and then replacing the plaster ceiling and walls in my parent's bedroom. (it was far past time... the plaster did not need much... encouraging... to let go of the lathe) Anyway, I tore down all the plaster, which was messy, and by no means fun, but it was fine. I was then prepping to install new sheetrock on the surfaces. Normally this means the following steps:
1) clean off the remaining surfaces of lathe so the sheetrock can lay flush
2) mark the rafter locations
3) cut sheetrock to size
4) hold and screw it
Now, all of these go fine (or so one hopes) regardless of the age of the house. Step 2 however... is not so simple. In a modern house, there will be a rafter directly over one of the side walls. Then, there will be a rafter, on center, every 16 inches. Thus, it is very easy to both measure and mark the rafters. This is not however the case in old houses. Not only are the rafters non-equadistantly spaced, but they are not all continuous. I found multiple cases of rafters where 2 2x4's were spliced together to span the distance. Therefore, the distance between any given 2 rafters is not even constant. It's so frustrating!
Long story short... new houses may not have the history of some old houses... but they follow certain rules... and some of those rules are nice if you're a do-it-yourself-renovator. I recommend keeping this in mind before you start your next project.
Anyway, I've been working construction on my house here in pville for the past two months or so. I have done a LOT of carpentry projects through my life, and in general, I enjoy building/renovating houses. Through the years I have learned my much about what is the norm, and regulations as well as some aspects of code. Knowing all of these facts is truly wonderful when you are working on a house. But, when you are working on an old house... all of these rules by which you structure your projects fall apart.
My first project, which took me through May, was removing and then replacing the plaster ceiling and walls in my parent's bedroom. (it was far past time... the plaster did not need much... encouraging... to let go of the lathe) Anyway, I tore down all the plaster, which was messy, and by no means fun, but it was fine. I was then prepping to install new sheetrock on the surfaces. Normally this means the following steps:
1) clean off the remaining surfaces of lathe so the sheetrock can lay flush
2) mark the rafter locations
3) cut sheetrock to size
4) hold and screw it
Now, all of these go fine (or so one hopes) regardless of the age of the house. Step 2 however... is not so simple. In a modern house, there will be a rafter directly over one of the side walls. Then, there will be a rafter, on center, every 16 inches. Thus, it is very easy to both measure and mark the rafters. This is not however the case in old houses. Not only are the rafters non-equadistantly spaced, but they are not all continuous. I found multiple cases of rafters where 2 2x4's were spliced together to span the distance. Therefore, the distance between any given 2 rafters is not even constant. It's so frustrating!
Long story short... new houses may not have the history of some old houses... but they follow certain rules... and some of those rules are nice if you're a do-it-yourself-renovator. I recommend keeping this in mind before you start your next project.
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