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Saturday, March 14, 2015
Every day is Pi Day
Today is known as Pi Day in America, because the date (3/14/15) matches the first five digits of pi (3.1415...). Some people have even gone so far as to say that 9:26:53 AM/PM is even more worthy of celebration because that contains the first 10 digits of pi. A mathematician might say that there was a moment in time in which the time was pi itself (that is, sometime between 9:26 and 9:27 AM/PM, there was a time which was pi AM/PM).
I want to propose a couple things:
(1) That the idea of pi day is terribly American-centric. Many countries write the date not as MM/DD/YY (03/14/15) but as DD/MM/YY (14/03/15) -- so the idea that the date matches the first 5 digits of pi is a bit wonky.
(2) In effect, every day is pi day because every date and time because every date and time conceivable will appear in the digits of pi. Given that pi is an irrational number, pi is both never-ending and never-repeating. Thus, every combination of numbers you want (let's say, for example, March 15 at 11:05 AM -- or, in the non-American method of writing, 15/03/15 11:05 = 153151105) will appear at least once in pi ("The string 153141105 occurs at position 151419383. This string occurs 1 times in the first 200M digits of Pi" --according to http://www.angio.net/pi/). We can try to find the same string of numbers in other irrational numbers (say, the square root of 2, for example). Yes, the string might not start at the beginning, but any string of numbers is contained within pi.
Just a couple more pointers:
(3) There is a point in pi where the number 9 appears six times in a row (at position 762: ...11349999998372...). This is called the Feynman point. Just a fun little pattern.
(4) I have heard it argued that the existence of irrational numbers, such as pi, is evidence for the fact that we do not live in a computer-simulated world (we don't live in a Matrix). To contain an infinite number of digits (as we have not yet found the end of pi) means that a computer would require an infinite amount of memory/data processing to store the number pi in its hardware, which, as far as we can tell, is not possible.
Excuse the long delay in between posts -- I've been quite busy.
Cheerio.
I want to propose a couple things:
(1) That the idea of pi day is terribly American-centric. Many countries write the date not as MM/DD/YY (03/14/15) but as DD/MM/YY (14/03/15) -- so the idea that the date matches the first 5 digits of pi is a bit wonky.
(2) In effect, every day is pi day because every date and time because every date and time conceivable will appear in the digits of pi. Given that pi is an irrational number, pi is both never-ending and never-repeating. Thus, every combination of numbers you want (let's say, for example, March 15 at 11:05 AM -- or, in the non-American method of writing, 15/03/15 11:05 = 153151105) will appear at least once in pi ("The string 153141105 occurs at position 151419383. This string occurs 1 times in the first 200M digits of Pi" --according to http://www.angio.net/pi/). We can try to find the same string of numbers in other irrational numbers (say, the square root of 2, for example). Yes, the string might not start at the beginning, but any string of numbers is contained within pi.
Just a couple more pointers:
(3) There is a point in pi where the number 9 appears six times in a row (at position 762: ...11349999998372...). This is called the Feynman point. Just a fun little pattern.
(4) I have heard it argued that the existence of irrational numbers, such as pi, is evidence for the fact that we do not live in a computer-simulated world (we don't live in a Matrix). To contain an infinite number of digits (as we have not yet found the end of pi) means that a computer would require an infinite amount of memory/data processing to store the number pi in its hardware, which, as far as we can tell, is not possible.
Excuse the long delay in between posts -- I've been quite busy.
Cheerio.
Saturday, July 26, 2014
Decaffeinated Black Tea
I have 140k views on my Google+ profile. I didn't know I had a Google+ profile.
I am beginning to realize that I am far more blessed than I will ever know.
My finances, while not ideal, are OK for the time being; my family, while I have only seen them very briefly this year, is relatively healthy; my friends, though I miss them dearly, I got to talk to via webcam the other Thursday (did you know my computer comes with a webcam? I didn't) or through Facebook or text messaging; and my work -- well, at least I got a paycheck last week.
I finished reading Moby Dick somewhere near the end of June. It's not quite what I expected -- the plot is somewhat disappointing, but the characters are intriguing. I've also been learning how to play the guitar. I don't have a guitar so I try to borrow someone else's when I can, but, as you can imagine, not having a guitar makes it difficult to build up finger strength and callouses. I'm also learning Spanish (El pinguino es un pajaro blanco y negro). Progress is slow, but it's fun. I'm learning.
I am getting older. Perhaps it is starting to show.
-----
My finances, while not ideal, are OK for the time being; my family, while I have only seen them very briefly this year, is relatively healthy; my friends, though I miss them dearly, I got to talk to via webcam the other Thursday (did you know my computer comes with a webcam? I didn't) or through Facebook or text messaging; and my work -- well, at least I got a paycheck last week.
I finished reading Moby Dick somewhere near the end of June. It's not quite what I expected -- the plot is somewhat disappointing, but the characters are intriguing. I've also been learning how to play the guitar. I don't have a guitar so I try to borrow someone else's when I can, but, as you can imagine, not having a guitar makes it difficult to build up finger strength and callouses. I'm also learning Spanish (El pinguino es un pajaro blanco y negro). Progress is slow, but it's fun. I'm learning.
There's a funny thing I have slowly begun to realize, and it is this: though I am not as successful as I would hope, though I don't get as much work done as I (or my boss) would like, though I don't have as much money as I want -- I have enough. And, as I am still learning, I have more than enough. I am very blessed to have all the materials and people in my life, and very blessed to get to invest my time in these (self-actualizing, some might say) activities like reading and learning a new language and playing the guitar. And besides these more overt blessings, there are the "little things" -- living in a safe area, warm clothing, a radio that plays music, a paying job, a phone that can beat you at chess, being a citizen of a country with political stability -- there are these little things that you never quite appreciate until you realize that other people don't have them.
It's quite sad to think that the friends I make now I may not see again, for each of us shall diverge along our separate ways. The remaining time I have with them left is short (though it may not seem like it), and I am sad to see them go. For while I have met many people throughout my schooling and my work, there are only a small handful whom I have really connected with, and they are the kindest, funniest, most understanding people I have known. It is exciting to see what is in store for them in the future and saddening to know that I will never have the opportunity to express my gratitude or make it up to them.
I bought a box of decaf black tea at the store a couple weeks ago. I can't drink caffeine (a cup of green tea at 3PM means I will be awake until at least 4AM), so to have found tea that I can drink -- no matter how poor the quality -- is wonderful. Great taste. Perhaps they sell it at other stores. Maybe I'll buy another box of 100 bags before I go, just to be safe.
So many blessings, and I am only beginning to understand the magnitude of them. Family, safety, books, friends, tea -- I think I'm beginning to know what the psalmist meant when he wrote "My cup runneth over."
It's quite sad to think that the friends I make now I may not see again, for each of us shall diverge along our separate ways. The remaining time I have with them left is short (though it may not seem like it), and I am sad to see them go. For while I have met many people throughout my schooling and my work, there are only a small handful whom I have really connected with, and they are the kindest, funniest, most understanding people I have known. It is exciting to see what is in store for them in the future and saddening to know that I will never have the opportunity to express my gratitude or make it up to them.
I bought a box of decaf black tea at the store a couple weeks ago. I can't drink caffeine (a cup of green tea at 3PM means I will be awake until at least 4AM), so to have found tea that I can drink -- no matter how poor the quality -- is wonderful. Great taste. Perhaps they sell it at other stores. Maybe I'll buy another box of 100 bags before I go, just to be safe.
-----
I started writing this blog post on July 3 (and, of course, I thought about it for quite a while before actually beginning to write it). What day is it now, the 26th? It is taking longer and longer for me to articulate my thoughts.
I am getting older. Perhaps it is starting to show.
Sunday, July 6, 2014
My Dream, 07/06/14
I had a dream last night where my left hand was cut off with a knife, so when I woke up this morning and saw my left hand was perfectly fine, I was quite pleased.
Sunday, March 30, 2014
John Cage's 4'33"
The postmodern composer John Cage put out an interesting composition in 1952: 4'33" (four minutes, thirty-three seconds, or just four thirty-three) is four minutes and thirty-three seconds of silence; you can go on YouTube and watch a man sit at a piano for the entire length of the composition. The idea was that we don't listen enough to the sounds of the places where we are, that there is music wherever we are and that we just have to listen to it.
Cage has a wonderful quote attributed to him: "I have nothing to say and I'm saying it." It is remarkable how he has such a unique (postmodern?) view about things. The traditional (conservative?) view holds that that which is not worthy of being said should not.
Unfortunately I find my blog at a difficult crossroads of sorts...I am running out of time to post and when I do, I don't have anything to post about. Fortunately, this is not a blog about sports or games or art -- it's a blog about me. It is strange to see the ways in which I have changed (and not changed) over the years (you could call this a poorly-kept diary; you would not be wrong). Five years...
It seems that I have reached the end of my (creative?) limits, however. It is now almost April, and I have not posted since February; I have not posted anything of substance since...August of 2013? That long ago? That's half a year. I have nothing to say, and I know not whether I should continue to "say it" or whether I should cease and be quiet.
I suppose that is a simplification; I have plenty of things to say, just not necessarily things I wish to post online or make public.
The human psyche is a wonderful and vast space, wonderful to describe and easy to get lost in.
...I suppose that is not entirely true. Over the last five years, I have transitioned from being loud to being quiet. There's not true change here, I suppose. I have always been introverted, but I have gone from wanting attention to avoiding it (I shudder to recall all the posts that I deleted during the Great Purge of ATWC...why I put them up in the first place I don't know).
I suppose there is one change. I have become increasingly bitter as I have aged -- ah, no, bitter is not the right word. Mature, perhaps. I have become increasingly aware of the reality around us, and I know not whether to be heartened or discouraged by it.
It is saddening(?) to look back at some of the older posts and read over what I thought then. Truly, a different person was sitting at the computer back in 2008 or 2009 than the person sitting here now in 2014. Oh, how the times have changed!
What a fascinating line [from Shakespeare's A Midsummer Night's Dream, Act II Scene I]. Oberon reminisces about something in the past, and Puck has this beautiful response: I remember. There is such weight in it -- what a lovely response. An element of age, wisdom, and beauty, but more than that. There is a heavy, dark side to it -- yes, I was there, but no, that which once was cannot be any more. I remember.
Looking back over this blog (and I haven't forgotten it -- almost every day I remember this blog, wondering if I have the time or the content to post -- I don't, a painful reminder) has made me remember. It has made me realize that I had nothing to say when I posted back then -- I certainly thought I did!-- but I said it anyway. Now that I realize I have nothing to say, I don't know whether to continue or to cease.
I am confident that I am either far too old to be a post-modernist or far too young.
What existential bravery!
And how time conquers us all.
Musa, mihi causas memora...
Cage has a wonderful quote attributed to him: "I have nothing to say and I'm saying it." It is remarkable how he has such a unique (postmodern?) view about things. The traditional (conservative?) view holds that that which is not worthy of being said should not.
Unfortunately I find my blog at a difficult crossroads of sorts...I am running out of time to post and when I do, I don't have anything to post about. Fortunately, this is not a blog about sports or games or art -- it's a blog about me. It is strange to see the ways in which I have changed (and not changed) over the years (you could call this a poorly-kept diary; you would not be wrong). Five years...
It seems that I have reached the end of my (creative?) limits, however. It is now almost April, and I have not posted since February; I have not posted anything of substance since...August of 2013? That long ago? That's half a year. I have nothing to say, and I know not whether I should continue to "say it" or whether I should cease and be quiet.
Musa, mihi causas memora...
I suppose that is a simplification; I have plenty of things to say, just not necessarily things I wish to post online or make public.
The human psyche is a wonderful and vast space, wonderful to describe and easy to get lost in.
I have nothing to say...
...I suppose that is not entirely true. Over the last five years, I have transitioned from being loud to being quiet. There's not true change here, I suppose. I have always been introverted, but I have gone from wanting attention to avoiding it (I shudder to recall all the posts that I deleted during the Great Purge of ATWC...why I put them up in the first place I don't know).
I suppose there is one change. I have become increasingly bitter as I have aged -- ah, no, bitter is not the right word. Mature, perhaps. I have become increasingly aware of the reality around us, and I know not whether to be heartened or discouraged by it.
It is saddening(?) to look back at some of the older posts and read over what I thought then. Truly, a different person was sitting at the computer back in 2008 or 2009 than the person sitting here now in 2014. Oh, how the times have changed!
I remember.
What a fascinating line [from Shakespeare's A Midsummer Night's Dream, Act II Scene I]. Oberon reminisces about something in the past, and Puck has this beautiful response: I remember. There is such weight in it -- what a lovely response. An element of age, wisdom, and beauty, but more than that. There is a heavy, dark side to it -- yes, I was there, but no, that which once was cannot be any more. I remember.
Looking back over this blog (and I haven't forgotten it -- almost every day I remember this blog, wondering if I have the time or the content to post -- I don't, a painful reminder) has made me remember. It has made me realize that I had nothing to say when I posted back then -- I certainly thought I did!-- but I said it anyway. Now that I realize I have nothing to say, I don't know whether to continue or to cease.
I am confident that I am either far too old to be a post-modernist or far too young.
I have nothing to say and I'm saying it.
What existential bravery!
I remember.
And how time conquers us all.
Musa, mihi causas memora...
Sunday, February 2, 2014
When I was little...
When I was little, I thought "pass out" and "pass away" meant the same thing, so was rather confused when I read in a book or heard on the news that someone "passed out" but was walking an hour later or was expected to make a full recovery.
Tuesday, December 24, 2013
It's December
It's December now and I haven't posted in ages.
I think I'm working too hard.
As we approach this holiday season, please be sure to take some time to celebrate your friends and your family. It's a lesson I wish I had taken to heart a while ago.
Take the time to do something you enjoy.
Merry Christmas!
I think I'm working too hard.
As we approach this holiday season, please be sure to take some time to celebrate your friends and your family. It's a lesson I wish I had taken to heart a while ago.
Take the time to do something you enjoy.
Merry Christmas!
Tuesday, October 22, 2013
September...I mean October
It's October.
Strange, isn't it? Time passes by so quickly. I knew I hadn't put a post up in September, but I didn't have anything to say, so I didn't. (A valuable lesson, that is...)
It's gotten colder. I think it's going to start snowing soon...I'm on a trip in Canada right now. It's a mild trip (just hanging out in Toronto tonight and tomorrow) but it should be fun. I'll post pictures of whatever excursions I'm on at some point, I think. One of my friends is in Rome and he is putting up pictures of the art of Catholic Rome. It makes me somewhat excited and jealous because being able to go to Rome would be such an amazing experience.
The contrast is rather striking (Canada is no Rome, that's for certain) [but one of the things I've been trying to do is to be thankful for what I do have...it really is a blessing to be able to be out here on a business trip, even if it's not exactly what I had in mind]. Unfortunately, I am stuck on a bus for a good part of this week, a factor that makes it extremely difficult to get work done -- normally not too big a deal, but there are a number of applications and a variety of paperwork I should have completed by the end of this week and unfortunately it doesn't look like I will be able to get that done without staying up late.
I wish I had something interesting or remarkable to say, but then I realize that this blog was made when I was a wee ambitious young'un so I've never had anything interesting or remarkable to say.
Pray for us!
Strange, isn't it? Time passes by so quickly. I knew I hadn't put a post up in September, but I didn't have anything to say, so I didn't. (A valuable lesson, that is...)
It's gotten colder. I think it's going to start snowing soon...I'm on a trip in Canada right now. It's a mild trip (just hanging out in Toronto tonight and tomorrow) but it should be fun. I'll post pictures of whatever excursions I'm on at some point, I think. One of my friends is in Rome and he is putting up pictures of the art of Catholic Rome. It makes me somewhat excited and jealous because being able to go to Rome would be such an amazing experience.
The contrast is rather striking (Canada is no Rome, that's for certain) [but one of the things I've been trying to do is to be thankful for what I do have...it really is a blessing to be able to be out here on a business trip, even if it's not exactly what I had in mind]. Unfortunately, I am stuck on a bus for a good part of this week, a factor that makes it extremely difficult to get work done -- normally not too big a deal, but there are a number of applications and a variety of paperwork I should have completed by the end of this week and unfortunately it doesn't look like I will be able to get that done without staying up late.
I wish I had something interesting or remarkable to say, but then I realize that this blog was made when I was a wee ambitious young'un so I've never had anything interesting or remarkable to say.
Pray for us!
Tuesday, August 20, 2013
VBS 2013
Last week I had the opportunity to take a break from work and help out with my home church's Vacation Bible School, a week-long day camp for kids. I was in charge of a romping crew of 5 first-graders and my job was to make sure I didn't step on or lose any throughout the day (neither the VBS director nor the nervous parent of a shy child appreciated my comment, "I'm usually really good about keeping the kids very focused. Last year, I only lost three of them") and to help them pay attention to the different crafts and stories. It is a wonderful ministry and I have found that I learn as much from it as the kids do. Here is my reflection on this year's VBS.
The Mystery of Faith
Perhaps the greatest thing I have learned this week at VBS lies in a greater revelation of the integrity of the Christian gospel. The truths that were taught to me when I was growing up are the same as those I tried to teach to my kids, the only difference being that I used my personal experiences to frame my narratives.
There is no greater or more objective principle than this: God loves you and He sent his son Jesus to die on the cross for your sins, and Jesus came back to life so that He could reconnect you to God upon acceptance of His sacrifice. I cannot add or take away clarity or veracity to so simple and elegant a message. The mystery of faith lies in the duplicity of the complexity of this paradox: "Why" this happens is apparent to all of us (even my first graders know: "Because God loves us"), but "Why me" begets the question no theologian, philosopher, mathematician, economist, or mystic can answer: "How much?" At the core of the human element lies our innate imperfection and sinfulness, and a simple glimpse or mere exposure to this core evokes feelings of disgust, horror, and dread. It is not difficult to understand "why" God chose to redeem humanity -- for even we know that human love will cause others to do things which we might regard as sacrificial, strange, noble, or foolish -- but as we begin to understand the depths of our failures we must also begin to question the extent of the love that can redeem us.
I love reading a good book but I would not sacrifice my life, much less a toe on my left foot, for the chance to read a good book, much less for someone else to have the chance to read a good book. How much grater that a Father should send His Son to die in order to reconcile the sins of humanity! Why am I worth it? Why does God love me so much? How much love does God have for me and when does it run out? The pillars of this week's VBS, no matter how for cornily presented, tackle these questions and doubts head-on. How do I tell the children that God's love or prayer or the Bible helps us stand strong? Is it with a hand motion or a song? What keyword or mnemonic device do I use to help them understand the theology behind the Crucifixion? How can you get the kids to understand the absolute and objective truth behind the Christian Gospel when you can't get them to understand that they should not try to cut each others' hair during craft time?
There is no greater frustration than to know the Truth and be unable to communicate it because of language, cultural, age, or other barriers -- to have Reality itself presented in front of you but be unable to share it with others. How can I get these kids to understand the truth presented to them when they are still at an age where their first guess at my age is 46? [Note: I am not and (I hope, anyway) don't look 46, either.]
Herein we return to the mystery of the common Christian faith: The Gospel transcends these barriers of age because it is true. Regardless of my struggles or interpretation of the Gospel, it is this objective truth behind this core element of faith that my crew is able to understand the teachings presented to them each day; not because we did an excellent job being leaders, but because there is no other alternative, because there is no other objective principle, because there is no other truth than that revealed by Christ's Crucifixion and Resurrection. That the kids can understand the greatest truth they will ever know -- that Jesus came to for them so they can be reunited in holy union with God -- in spite of the flaws and distractions of me, the leaders, VBS, and the church -- that is the mystery of faith.
The Mystery of Faith
Perhaps the greatest thing I have learned this week at VBS lies in a greater revelation of the integrity of the Christian gospel. The truths that were taught to me when I was growing up are the same as those I tried to teach to my kids, the only difference being that I used my personal experiences to frame my narratives.
There is no greater or more objective principle than this: God loves you and He sent his son Jesus to die on the cross for your sins, and Jesus came back to life so that He could reconnect you to God upon acceptance of His sacrifice. I cannot add or take away clarity or veracity to so simple and elegant a message. The mystery of faith lies in the duplicity of the complexity of this paradox: "Why" this happens is apparent to all of us (even my first graders know: "Because God loves us"), but "Why me" begets the question no theologian, philosopher, mathematician, economist, or mystic can answer: "How much?" At the core of the human element lies our innate imperfection and sinfulness, and a simple glimpse or mere exposure to this core evokes feelings of disgust, horror, and dread. It is not difficult to understand "why" God chose to redeem humanity -- for even we know that human love will cause others to do things which we might regard as sacrificial, strange, noble, or foolish -- but as we begin to understand the depths of our failures we must also begin to question the extent of the love that can redeem us.
I love reading a good book but I would not sacrifice my life, much less a toe on my left foot, for the chance to read a good book, much less for someone else to have the chance to read a good book. How much grater that a Father should send His Son to die in order to reconcile the sins of humanity! Why am I worth it? Why does God love me so much? How much love does God have for me and when does it run out? The pillars of this week's VBS, no matter how for cornily presented, tackle these questions and doubts head-on. How do I tell the children that God's love or prayer or the Bible helps us stand strong? Is it with a hand motion or a song? What keyword or mnemonic device do I use to help them understand the theology behind the Crucifixion? How can you get the kids to understand the absolute and objective truth behind the Christian Gospel when you can't get them to understand that they should not try to cut each others' hair during craft time?
There is no greater frustration than to know the Truth and be unable to communicate it because of language, cultural, age, or other barriers -- to have Reality itself presented in front of you but be unable to share it with others. How can I get these kids to understand the truth presented to them when they are still at an age where their first guess at my age is 46? [Note: I am not and (I hope, anyway) don't look 46, either.]
Herein we return to the mystery of the common Christian faith: The Gospel transcends these barriers of age because it is true. Regardless of my struggles or interpretation of the Gospel, it is this objective truth behind this core element of faith that my crew is able to understand the teachings presented to them each day; not because we did an excellent job being leaders, but because there is no other alternative, because there is no other objective principle, because there is no other truth than that revealed by Christ's Crucifixion and Resurrection. That the kids can understand the greatest truth they will ever know -- that Jesus came to for them so they can be reunited in holy union with God -- in spite of the flaws and distractions of me, the leaders, VBS, and the church -- that is the mystery of faith.
Saturday, August 3, 2013
Oh, Yeah, July...
It seems July has passed me by entirely without having a single post...
Whoops.
Here's how I spent the month of July:
1) Reading: I finished, at the end of July, Ayn Rand's magnum opus Atlas Shrugged. I'm not sure if I will post a review of it or about it. It's simply one of those works that
2) Shopping: I discovered two new websites, one called eBay and the other PayPal. They make purchasing things online very easy, but you probably knew that, because, as my friend related to me, they "are already 'a thing.'"
3) Working: I have been very busy this summer -- not bad, since I've been rather productive. But having to come in on weekends and staying late has been a bit inconvenient. I would estimate I have been at work 9 or 10 hours a weekday and about 9 hours on a weekend for the most of July.
4) Traveling: I had the opportunity to go home and see my family for a week in July. That was a lot of fun, since I haven't seen any of them since Christmas.
Anyway, that was my July. With a bit of luck, I'll have more opportunities to post in August.
Have a great day!
Whoops.
Here's how I spent the month of July:
1) Reading: I finished, at the end of July, Ayn Rand's magnum opus Atlas Shrugged. I'm not sure if I will post a review of it or about it. It's simply one of those works that
2) Shopping: I discovered two new websites, one called eBay and the other PayPal. They make purchasing things online very easy, but you probably knew that, because, as my friend related to me, they "are already 'a thing.'"
3) Working: I have been very busy this summer -- not bad, since I've been rather productive. But having to come in on weekends and staying late has been a bit inconvenient. I would estimate I have been at work 9 or 10 hours a weekday and about 9 hours on a weekend for the most of July.
4) Traveling: I had the opportunity to go home and see my family for a week in July. That was a lot of fun, since I haven't seen any of them since Christmas.
Anyway, that was my July. With a bit of luck, I'll have more opportunities to post in August.
Have a great day!
Wednesday, June 26, 2013
Spain, Summer 2013
In late May-early June, some friends and I visited Spain for 2.5 weeks. We first visited a number of cities and then walked the last bit of the Camino de Santiago, the Way of St. James. The pilgrimage has many routes to Santiago; we started at the end of the French Way, which starts in southern France, takes pilgrims through northern Spain, enters Galicia (northwest Spain), and ends at Santiago de Compastela, the burial place of the Apostle James (the Lesser), a total distance of about 770km. We walked the last 130 or so kilometers.
MADRID  |
| A woman re-creating an original painting at the Prado A guard scolded me for taking this picture. |
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| The football stadium |
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| Plaza Mayor |
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| Cathedral de la Almudena |
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| Palacio Real de Madrid |
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| The bear and strawberry tree are the symbol of Madrid. This symbol was on the sidewalk. |
TOLEDO
"And if you look to your left, you will see Toledo, built by the Ohians as a stronghold against Michigan..."
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| The view of the city from one of the upper floors of the building's library Toledo is the notable because it has a synagogue, mosque, and a cathedral. The sword-making industry is also quite popular. |
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| A fresco from the walls at the Cathedral of Toledo |
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| Dome from Cathedral of Toledo |
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| Doorway, organ, and image of Christopher at the Cathedral of Toledo |
BURGOS
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| The Cathedral of Burgos |
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| The Cathedral of Burgos |
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| The dome of the Cathedral of Burgos The way the dome let in light was truly amazing. |
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| Light from stained glass windows on the floor. |
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| The window that caused the light to hit the floor in the picture above. |
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| We were walking through the city at night and passed by the Cathedral. They had lights projecting patterns onto the Cathedral. The effect was quite interesting; the textures of the light on the Cathedral were very vivid. |
LEON
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| View from my hotel overlooking Plaza Mayor |
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| Plaza Mayor, Saturday night The noise was horribly loud. Even at 2am I found it incredibly difficult to sleep. The next day, Sunday, the plaza was deathly empty for most of the day, a stark contrast to the noise, lights, and fellowship of the day before. |
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| The Cathedral at Leon |
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| This is called a Doner Kabob and it was delicious. It cost 4.50 euros. |
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| The Cathedral of Leon |
LUGO
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| Lugo is surrounded by Roman walls. |
O CEBREIRO (START OF THE CAMINO DE SANTIAGO)
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| The church where we got out first sello, stamp on our passport. It was about 150 km from Santiago. |
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| The scallop shell is the symbol of St. James. Pilgrims (pereginos) wear the shells on their bags or persons to identify each other. This shell cost me 1.5 euros and is marked with the cross of St. James. |
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| All along the Camino are these yellow arrows to help you find where to go. They can be found on trees, rocks, road signs, on the ground, and even on buildings. |
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| These kilometer markers tell you how far you are from Santiago. |
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| A road marker Pilgrims carry rocks with them as a symbol of their sins along a stretch of the Camino and leave them on the kilometer markers or these road markers. |
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| Passsport with stamps The one in the upper left is from the monastery at Samos; the one from the upper right is from a hotel. Stamps can also be obtained also from churches, bars, cafes, and restaurants. |
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| A small community graveyard along the Camino. I noticed that the graves were all above ground and not in the ground. |
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| Along the Camino |
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| Along the Camino |
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| Along the Camino |
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| Along the Camino |
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| Along the Camino |
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| Along the Camino The Camino goes through many old towns. Most of these small towns are sparsely populated, with most of the buildings having fallen apart. Some of the buildings still operate as alburges, hostels for pilgrims, or as cafes for lunch. |
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| The interior of a monastery |
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| Along the Camino |
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| Along the Camino |
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| Along the Camino |
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| Along the Camino |
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| At one of the towns along the Camino, we stopped to eat octopus. It was rather oily and salty but very good. |
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| The Mount of Joy is the first place along the Camino where pilgrims can see the Cathedral de Santiago. This marker commemorates the time Pope John Paul II celebrated mass on the mountain. |
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| The Cathedral of Santiago de Compostela |
FINISTERRE
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| After reaching Santiago, pilgrims traditionally continued West until they reached Finisterre, what was believed to be the end of the world. This is the most Western point in Europe. |
SALAMANCA
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| The Cathedral at Salamanca |
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