That Brainteaser from A Beautiful Mind

Two bicyclists start twenty miles apart and head toward each other, each going at a steady rate of 10 m.p.h. At the same time, a fly that travels at a steady 15 m.p.h. starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner till he is crushed between the two front wheels.

Question: what total distance did the fly cover? (Highlight below for answer)

If you are trying to solve this using calculus or differential equations, you are wasting time. The two bicycles start 20 miles apart, each going the same speed, so each bicycle must travel 10 miles before meeting the other bicycle. Since they are each traveling at a rate of 10 m.p.h., this will take 1 hr. In the meantime, the fly will zoom back and forth at 15 m.p.h., for one hour. So, he will cover a total distance of 15 miles.

World Labyrinth Day

So, lately I have become interested in Labyrinths.I suppose, to the extent that I ever knew anything about them (not much), I always thought that they were interesting. When I was a kid, I LOVED maze books. I even made some of my own on paper, just simple mazes to draw a line through. At one point, in high school, just before I started considering architecture as a possible major, I liked to sketch and draft various things. I sketched out a possible LaserTag maze once. Also, once when I was about 10 I saw the movie Labyrinth (David Bowie, Jennifer Connelly and Jim Henson), and loved it - especially the Escher castle, but also the whole labyrinth itself.

I now have a relatively large, and empty, yard that I am trying to figure out what to do with. I keep getting gardening books from the library, hoping for inspiration. Right now I'm in the middle of a book on Labyrinths. First of all, it's interesting that labyrinths and mazes are actually different: labyrinths consist of a single path, and mazes have choices. So, I think I actually like mazes better (and the "labyrinth" in Labyrinth was actually a maze). Still, the book is more about labyrinths, and it is interesting to know the history. The first historical reference to a labyrinth seems to be with King Minos of Crete, who supposedly had a Labyrinth with a Minotaur at the center (the story reminds me of Hunger Games). Later, the the labyrinth was adopted by many medieval Christians, who took it as symbol of one's spiritual walk: you many not know where you are right now, but your path invariably leads to the center (these early labyrinths were usually made with the paths forming a cross in the center). Supposedly, walking one of several official labyrinths setup in churches throughout Europe could substitute for making a required pilgrimage to Jerusalem. In the 1600s-1800s, the labyrinth somehow morphed into hedge mazes, which were popular in public spaces and on wealthy estates. Recently, there seems to be a renewed interest in Labyrinths, both by Christians of more traditional denominations, as well as people seeking general spiritual and meditative experiences. There also seems to be more interest in mazes, as a form of novelty and entertainment - but I haven't gotten around to any books on mazes yet (still need to finish the one I have on labyrinths).

The is now a World-Wide Labyrinth Locator, and a World Labyrinth Day (today!). So, I found some labyrinths in our state and Adrian and I went to check them out. There wasn't really much variation in the design, but it was interesting to see some actual labyrinths. The denominations most likely to have labyrinths seem to be: United Methodist, United Church of Christ, Episcopal, Presbyterian, Lutheran, and a few non-denominational sounding churches, often with "Unity" in their names. Also, several hospitals and health centers seem to have labyrinths. Which makes sense, both walking and mediation have known health benefits.

So here are the some labyrinths I walked, and I decided to put them together in a post today:

'Manifesting' DNA Testing

Adrian and I watched a documentary Human Family Tree which is about the National Geographic Genographic Project. I was fascinated, and found myself vaguely wishing to participate. I started following a certain reviewer on Goodreads, and when I saw that he had read (and reviewed) a related book: DNA USA, I decided to pursue these fascinating ideas by getting the book from the library and reading it. The documentary was more of a macro-view of human history, and although the book discusses this, the book was more about personal genealogies. Now I really wanted to participate. I saw that I could probably participate in the geographic project for a minimum of $200. However, if I wanted to do the full battery of tests, the cost would probably start getting closer to $1000. Then I started looking at some of the sources mentioned in the book, and saw that there were even more tests. Now, if I really wanted to, I could certainly spend $1000 on DNA testing. However, to spend that much on something as abstract as DNA testing certainly feels like a splurge. Besides, how to choose which test(s) to start with? Also, for some of the tests, I would need to recruit the cooperation of a male relative, since I don't posses a Y chromosome. Also, probably in the future they will develop cheaper, more comprehensive tests, and then I will feel like I wasted money and time if I buy tests now. Nevertheless, I wanted to participate. Hmmmm... What to do, what to do? I remembered reading a blog post by Steve Pavlina about manifesting coins, a game he played with his daughter based on the Law of Attraction. Law of Attractioners often focus on how to attract wealth into their lives - there's nothing wrong with that, but there are reports of people often circumventing the money step and directly manifesting what the money would have bought. That always sounded like a more efficient, time-saving strategy to me. The idea is to keep your main goal in mind, and not get to attached to any one way of getting there. Also, be open odd detours and taking a baby-step now, even if you don't think it makes much difference to your end goal, small actions can snowball in unforeseen ways.

So then I just started thinking about what it was I really wanted to get out of all of this? Did I want to know my genealogy? Sure, that would be cool, but I could wait on that too. Probably genealogy DNA databases weren't quite complete yet either. Also, do I really want to have my DNA stored in a database that is not under my control? In the day and age of Monsanto patenting seeds, that is a scary thought. However, what will be will be, do I want to live a life of fear or do I want to LIVE with all of the risks that entails?

"Life is either a daring adventure or nothing" - Helen Keller

I guess I'll take my chances with life. Still, what do I want out of this? I don't know exactly, but for starters it would be cool to get my own DNA sequenced, even if I don't know what to do with it yet, just for the experience. So, then I started thinking about all the different situations that might leads to someone getting their DNA sequenced. Obviously, there has to be alot of this going on in the name of academic research, and medicine. I had always thought it might be cool to participate in studies (medical or psychological) as a subject, so even if I found something to participate in that was unrelated to DNA, that might be cool. I found a database of open medical studies, and started poking around for information on things relevant to me. I have "missing knuckles" on some fingers of both hands. A bit of prior speculative internet research has led me to believe this is due to Brachydactyly Type E. As it turns out, there was a DNA study going on for a number of deformities, including brachydactyly. Bingo!When life gives you lemons.... make lemonade :) As it turns out, I was eligible to participate. They were also interested in studying the DNA of any of my blood relatives. I got my sister to participate, and also my younger brother (cooperation of a male relative - check!). So, this probably won't lead to me getting my DNA fully sequenced, or my even getting any report on the results. But, it's just so interesting what a little action can lead to...

What is the Purpose of Life?

Fundamentalist Christians (ie, the set of people that I grew up amongst, and obtained most of my formative information from) will mostly say that the purpose of life is to do God's will. The problem with this answer is that it is so vague. It qualifies as a "correct answer" according to Christian dogma, but it is not practically useful. Furthermore, there is a deeper sense of the question that Christianity still does not answer at all. I discovered this through the following conundrum: Christians generally assume that A) Abortion is wrong, and B) Aborted babies go to heaven. Non-aborted babies who live a normal life have several decades to exercise free-will, and may do so in such a way that they end up going to hell. Ergo, the aborted babies who never really lived are better off eternally and spiritually (...ecumenically? grammatically?) than the babies who were not aborted. So, what is the purpose of life (and why isn't abortion actually a good thing)? Even King Solomon said it is better to have never been born (Ecclesiastes 4:3). Even if you take a Calvinist tack, and don't assume that all aborted babies go to heaven (because God is omniscient, and knows what those babies would have done had they lived, and so the ones that were predestined for hell will still go there.), it still does not explain the purpose of life. If God knows where we are all going to end up anyway, then why doesn't he just put us there to start with? Why even go through the motions of life? What is the point?

There was a time in my life when I was very depressed and thought about suicide alot. I would not go so far as to say that I was actually suicidal, because I didn't have the guts to actually do anything. But I thought about death alot, and often wished for it. I could not make up my mind if suicide was a sin or not. The God of the New Testament seems to be fairly forgiving, so even if suicide is a sin, perhaps he would forgive it. Then again... on the off-chance that it is a sin, and will not be forgiven - the whole point of suicide is as an escape, and committing suicide only to then be sent straight to hell was not really the escape route that I had in mind :-/ . Anyway, I got through that rough patch of my life and started thinking about suicide less often. Later, I saw the film What Dreams May Come with Robin Williams, and also read the book The Great Divorce by CS Lewis. Bot of these got me to thinking of one's destination in the afterlife as more a function of one's mindset during life, than as a decision that God makes about you. So, if you commit suicide, you may go to hell, and whether or not God forgives you may not have anything to do with it. So, perhaps the purpose of life has something to do with working on your mindset so that you can create a "heavenly mindset" and actually make it to heaven. There may actually be a path to heaven (ie, The Eightfold Path?), and suicide as a (Cartesian?) point simply does not lie on that path.

So then I started thinking of the purpose of life as practice for a higher level. Part of that practice probably even involved trying to figure out what the purpose of life is! Or maybe more the idea that the more you could improve your mindset, the more of a "head start" you would have once you got to the afterlife. Several Steve Pavlina blogs seemed to go along with this idea of "levels" and the afterlife ("Life - The Ultimate Game," "Levels of Consciousness," and "Life After Death,"). Also, somewhat before I began reading Pavlina, I read The Divine Conspiracy by Dallas Williard (and wrote a review). I suddenly got the idea from Williard that the next level could start NOW. Why wait for the afterlife? Then when I read Pavlina, I started to think that there may actually be practical things that one can do to advance in "levels." So then maybe the purpose of life is not to "practice" for a higher level, but to actually start climbing the ladder. For REAL!

As I think about that, and try to figure out what kind of a ladder life is, where is is going, what are the rungs, and where am I on it, I began to come up with another hypothesis as to the purpose of life. I have been getting exposed to the idea of The Law of Attraction from many different sources: Steve Pavlina, Napolean Hill (who may have more responsibility for popularizing this concept than anyone - I had his book recommended to me while attending real-estate investment meetings with my Dad), Tony Robbins, and a movie called The Secret (recently recommended to me by someone at work). Now I am thinking that the purpose of life is just this, to get you to answer one very crucial question: "What do you want???". I also thougt of something that may be a big HINT: In any conversation with life, actions speak much louder than words. Interestingly enough, this actually brings me back to a very short humour piece I read as a teenager The Cookie Principle.

Time, Part IV: Free Will as Time Travel in a Many Worlds Universe?

I think that time is still a very poorly understood concept. That is because we are beings trapped in time. We can try to imagine what it might be like to be a being outside of or above time, but so far I think that has never been more than conjecture since nobody really has any experience being anything other than a being trapped in time.

Why is it that in the other three dimensions, we can move around more-or-less at will, but in time we seem to be stuck going forward at a generally constant rate? If we were to travel at extreme velocities (close to the speed of light), relativity says we could travel forward in time a bit slower. However, most of us will never have that opportunity. Earth-bound people have aged less than a second compared to astronauts using this method. But who wants to get older? We're all doing that anyway! Traveling backwards in time would be a much greater trick (physicists don't even know if we can do it), and nobody seems to know how to stop themselves in time either.

There are similarities, I think, with gravity. We feel as though we have control of our movements in the standard 3 dimensions, but in fact gravity does limit our up-down movement, also thanks to gravity we are stuck to the Earth, constantly rotating at the same velocities, both about the Earth's axis and about the sun. We don't even feel this movement, but we are actually stuck moving in the current 3 dimensions, as well as time. If you could take a spaceship out of orbit of anything, and just float around in a space suit, then perhaps you could actually be at rest relative to all the reference points I can imagine. However, most of us will never have the opportunity to do that - even astronauts stay in orbit in their missions (so far as I'm aware).

Kurt Gödel provided certain solutions to Einstein's relativity equations that describe a universe where the geometry of time is a circle, meaning that it is possible to travel all the way around the circle, and revisit the same point again. The relativity equations have been amazingly accurate at predicting various phenomena, so most physicists are hesitant to question those equations. Also, Gödel (a friend of Einstein's) was a notoriously thorough person, and no problems have been found with his solutions. These premises imply that time travel must be possible. We are quite certain that our universe does not have time running in a circle, however from the point of view of modal logic (Gödel was a logician), that does not matter. Because, if the equations can allow a universe to exist with such a geometry, then time travel cannot be logically forbidden in any universe resulting from the equations (including our universe). So, thanks to Gödel, time travel cannot be expunged from the realm of possibility.

So now there are many speculations about how one could travel back in time. Electrons and other sub-atomic particles may actually be doing it all the time! Positrons seem to be nothing more than electrons traveling backwards in time. In fact, electrons are all indistinguishable from one another, causing some to posit that the entire universe may in fact be nothing more than a single electron zig-zagging back and forth through time interacting with itself! However, just because an electron can do this does not mean that a human body could. If we think of space-time as a fabric, then it is theoretically possible to twist and tear this fabric into a geometry that folds back and touches itself at certain points, thereby allowing time travel. It would probably take a large amount of gravity and/or energy to warp space-time in this way, thus creating a time portal. We do not currently know how to create this much energy or gravity, though perhaps some black-holes may already be doing this. Could a human survive passage through a black hole? In most cases no, but there might be certain sub-classes of black holes that we could travel through and survive. Maybe.

But then, supposing we could go back in time: Perhaps you've heard of the Grandfather Paradox? This can take different forms, for instance if you go back in time and kill your grandfather, then you should never be born, which means you could never go back in time to kill your own grandfather. Or, suppose you go back in time and marry your grandmother (assuming you are a man), and thus become your own grandfather? How could such things be logically possible? Many physicists insist that they cannot be possible, and that is a large part of why time travel is not usually held in high esteem by physicists. Also, if time travel is ever going to be invented, why don't time travelers ever come here? Stephen Hawking has proposed the idea of a "Chronology Protection Agency," so that even if time travel is allowed, paradoxes cannot be created. Or, what if free-will is truly an illusion and everything is in fact deterministic? That would mean that even if you could go back in time, you would not be able to change a thing. Anyone able to travel back in time would simply experience Nietzsche's Eternal Recurrence.

However, all of this is still looking at time as something linear, something to be traversed either forwards or backwards. But what if their are multiple time dimensions? What if each possible series of events is a timeline, and we simply live in one of these? What of lateral time-travel, or timeline jumping? What if you traveled diagonally in time, that is to the past of a timeline that has an identical past with your current timeline, but a different future? Within that timeline, everything would still be deterministic, but determined to a different end (or at least a different end for your lifetime) than the timeline you had just left. The "many worlds" interpretation of quantum physics might allow just such scenarios. Perhaps each quantum observation is a moment of choice, an inter-dimensional-handshake between the deterministic endpoints of first and final causes, and each individual free will is in fact a lateral time journey, where we are free to move to any adjacent timeline at any present moment, even though they all originate and terminate in singularities? In that case, free will cannot change the ultimate fate of the universe, and all past choices limit your present choices - but it is still totally up to you, of the options available to you in the present moment, whether you take a road less traveled (less probable) or more traveled (more probable).