Riddle Me This 5: All Of The Lights, All Of The Lights

These are the hardest set of flipping riddles I know, but when you get them, you'll light up for the rest of the day! Answers (along with a hint for the hardest one) can be found below each question, but feel free to ask for hints or let me know if you have the solution! :D

Easier:
I have 1000 numbered lights turned off, all in a row, each with associated light switches. I first flip all the lights (turning them all on). I then flip just the even numbered lights (2, 4, etc). I then flip just every 3rd light (3, 6, etc). I continue this through 1000 iterations (for the last one, I just flip the 1000th light). At the end, how many lights are on?

The first light will be flipped just once, on the first run. How many times will the 12th light be flipped? On the runs 1, 2, 3, 4, 6, and 12. Notice that these are the factors of 12, or all the positive integers that divide 12 evenly. The fun thing about factors is that they come in pairs! (1 * 12 = 2 * 6 = 3 * 4 = 12). So it would seem that every number besides 1 is going to be flipped an even number of times, and therefore end up off. But wait! What if a factor is paired with itself? For example, 4's factors are 1, 2, and 4 (2 is paired with 2!). That means that 4 will be flipped 3 times and end up on. If a number has a factor that is paired with itself, that means the number is a square. How many squares are there between 1 and 1000? It turns out that 32², or 2¹⁰ as many will know it, is 1024, which is just over 1000. So since there are 31 perfect squares under 1000, there will be 31 lights on at the end!

 

Harder:
There are 111 numbered lights turned off. You and I play a game where we take turns flipping lights. At least 1 and at most 10 flips must be made each turn. More lights must be flipped on than flipped off in any turn. The loser is the first one whose turn ends with all lights on. I let you choose who goes first. What should you choose, and what is your winning strategy? 

If the loser is the one who turns the last light on, you can force me to lose if you leave me with just 1 light off. You can make sure that happens if there are anywhere between 2 and 11 lights left off on your turn. How can you make sure that there are that many lights? By making sure that I have 12 lights left off on my turn! As you can see, the number of lights you want off on my turn is going to start at 1 and go up by increments of 11, or any number (11n + 1). 111 = 11(10) + 1, so you want to give the first turn to me!

 

Hardest (first found on Dr. Miller's riddle page here): 
A warden tells 50 numbered prisoners that he is giving them a chance to be released, or executed--a fun game (by his twisted definition of fun)! They will not be able to communicate with each other after one 3-hour-long planning session before they are taken to their rooms and the game begins.
There is a special room containing two light switches numbered 1 and 2, which can each be either up or down (on or off). They cannot be left in between, they are not linked in any way. Their initial positions are unknown to the prisoners. One at a time, a prisoner will be brought into the room. The prisoner must flip one and only one switch. The prisoner is then returned to his cell.
There is no fixed pattern to the order or frequency with which prisoners visit the room, but at any given time, every prisoner is guaranteed to visit again eventually. At any time, any prisoner may declare that all 50 of them have been in room 0. If right, the prisoners all go free. If wrong, they are all executed.
If you were Person 1, what plan would you give your cohorts during the meeting? 

Think about simpler versions of the riddle. Two switches where you are forced to flip at least one is similar to just one switch that you can choose not to flip. What would you do if there were just 2 people, and you knew the switch's starting position? Then see if you can remove assumptions to return to the original question.

 

You claim authority and says to the others, "Ok, listen up everyone! Here are the rules. The first two times you see Switch 1 down, flip it up. If Switch 1 is already up, or if you've already flipped it up twice, don't touch it and just flip Switch 2. If I ever see Switch 1 up, I'll flip it down. I'll flip Switch 2 otherwise. Once I see Switch 1 up 49 * 2 = 98 times, I'll know that each of you has flipped it at least once, though most if not all of you will have flipped it twice. Then I'll call the warden and we can get out of here."

 

Riddle Me This 5: All That Glitters Is Gold (Coins)

These are less straightforward than the card-flipping riddles, but it all comes down to flipping in the end! Answers (along with a hint for the harder one) can be found below each question, but feel free to ask for hints or let me know if you have the solution! :D

Easier:
You are blindfolded with 72 coins on a table in front of you. Exactly 1/4 of them are heads up, though you don't know which they are. Separate the 72 coins into 2 piles, each containing the same number of heads up. You can flip as many coins as you like, though you won't be able to tell if they are heads or tails up.

This is a fun math trick that always blows my mind. There are 18 heads up. Say we take 18 coins from the 72 coin pile, and there are x heads up in the remaining 54. Then there are 18-x heads up in the 18-coin pile, and x tails. But then if we flip all of those 18 coins, there will be x heads up in that pile too, leaving x heads in each pile. :D

 

Harder (first read on the riddle page of Dr. Miller here):
You sit blindfolded in front of a square with a coin in each corner. You want to get all coins heads up or all tails up. You have no idea what the starting formation is, of course; they could even be all heads up to begin with. You may flip however many you want, then ask if you are done (this constitutes a turn). If you are not done, the square is then spun an undisclosed amount clockwise or counterclockwise. You then get another turn and so the game continues. Is there a strategy that is guaranteed to work in a finite number of moves, and if so, what is that smallest number of moves you need?

Think about what possible states the four coins could be in. For example, there could be 1 head and 3 tails up. What other states could they be in? Do any of these states have a "guaranteed win" move?

 

This one is really tricky. The key is to enumerate all the possible states and work through them to see which you can solve fastest. First, all the states:
All 4 of one kind (4:0)
3 of one, and 1 of the other (3:1)
2 each, with same-sided coins next to each other (2:2 adjacent)
2 each, with same-sided coins diagonally opposite each other (2:2 diagonal)
Next, let's define some flips:
No flip (N)
Just one coin (O)
2 adjacent coins (A)
2 diagonally opposite coins (D)
The first thing to notice is that if we do a diagonal flip (D) from the 2:2 diagonal state, we win! This is good news. Even better, this has no effect on the 3:1 state or the other 2:2 state!
Now, what happens if we try to solve the 2:2 adjacent state by using A? Either we win (yay!) or we get to the 2:2 diagonal state! Then we can do D again and win!
Fortunately, neither of these 2 coin flips affect the 3:1 state. If we try to solve this state by using O, either we win or we get to one of the 2:2 states. Then we can do the same sequence of D, A, D to be sure of success!
Since we also want to check the case where we're done to begin with, we'll check that first by flipping no coins. In sum, we have N, D, A, D, O, D, A, D. Just 8 flips and we're sure to win! :)

Riddle Me This 5: Luck And Intuition Play The Cards

This is the first of a series of 3 sets of flipping riddles, which will get progressively harder. Answers can be found below each question, but feel free to ask for hints or let me know if you have the solution! Enjoy! :D

Easier:
I have 5 cards on a table, showing L, 1, F, E, 8 face-up. How many cards do you need to flip to test the rule "If there is a consonant on one side of a card, there is an odd number on the other side"? Which ones?

You definitely need to check the consonant cards, L and F. If they don't have an odd number on the other side, the rule is definitely broken. Now, which do you need to flip, the 1 or the 8? Suppose the 1 was flipped, and there was an A on the other side. That wouldn't actually invalidate the rule! Instead, it is the 8 that should be flipped to make sure that there is a vowel on the other side. In total, then, you need to flip 3 cards--the L, F, and 8.

Harder:
There is a standard deck of 52 playing cards lying face-down on a table. How many do you have to flip to guarantee a straight somewhere (eg. 4, 5, 6, 7, 8)? How about a straight flush (same suit as well)?

Without 4 and 9 (or 5 and 10), no sequences of 5 cards from {1,2,3,4,5,6,7,8,9,10,11,12,13} can be made. That means that you could have picked 11 * 4 = 44 cards without having picked a 4 or a 9, and thus without having made a straight, or a straight flush.

I'm...back?

Kinda, anyway. A lot of things happened in the past month or so (it seems so much longer). The last few weeks of my hectic internship, the first few weeks of school, and a week or so of suffering a nasty viral or something. Mostly fun, but no time for this, amazingly enough.

The strange thing is that it's not as though I don't have stuff to write about. If anything, I have more than before. Unfortunately there are just so many things that take priority over this that it just falls off the bottom of any list I make. :( And I still have hundreds of pages of reading to do.

Even as I write these lines, I'm still trying to decide whether or not to continue with this. I have a journal to eat up my thoughts now, so does this blog still have a purpose in life (specifically, my life)? At the risk of having to change my mind again within a month, I'm going to say yes. Actual posts soon to come, then... :)

Resolutions

Resolved: To not be insecure about anything, and yet maintain humility.
Resolved: To learn Hindi and become ambidextrous.
Resolved: To speak clearly, in terms of both enunciation and thought.
Resolved: To think more and yet less before I talk.
Resolved: To be curious and ask questions.
Resolved: To not speak of myself for more than 5 sentences in a row.
Resolved: To find passion.
Resolved: To make art--literary, musical, and visual.
Resolved: To not make people cry.
Resolved: To make a bubble as big as a watermelon as big as my head.

On the Purpose of Religion: Causality

By causality I mean explanations for the apparently unexplainable, e.g. the creation of the universe or complex natural phenomena. This is most obvious in ancient religions like those of Mesopotamia, Greece, and Rome, but they continue today. Indeed, this facet of religion causes the most controversy when science and doctrine conflict.

While the ancient Greeks were a quickly developing civilization, they were mystified by innumerable natural phenomena like earthquakes, waves, lightning, and seasons. The human need for explanation was met by creation of gods and myths. Earthquakes were a result of the gods' anger. Large waves were created by Poseidon, while lightning bolts were thrown by Zeus from the clouds. The changing seasons were a result of Demeter's grief over the loss of her daughter to Hades.

One of the most universal features of religious explanation is creation. How was the Earth created? How was life created? How were we created? These are the deep questions that religion attempts to answer. While other religious explanations have been rejected as we have learned the physical mechanisms of natural phenomena, creation myths have an abnormal sticking capacity, perhaps because they are more personal or fundamental.

For example, while the idea of the Earth moving around the sun was heretical in Galileo's era, it has now been accepted as fact. Yet many people believe that the Earth is some thousands rather than billions of years old, when the evidence is equally clear. Likewise, the "war" between creationism and evolution has been raging for centuries, while evidence for natural selection is piling at an ever-increasing rate with advances in genetics, molecular biology, and organic chemistry, among other fields.

I began this list with comfort, which I said was the trait I admire most about religion. I end it here with this abnormal (and annoying) attachment to belief that is characteristic of not just religion but belief itself. Religious phenomena like terrorism, crusades, and outright rejection of evidence are a result of belief's irrefutable nature. There is simply no answer to "because I believe it."

On the Purpose of Religion: Order

As far as I can tell, order includes unity and structure. (I used to have power as a fifth purpose, but these two seem to cover that fairly well.)  The first is self-evident, as religions without unity die out, while successful religions are often examples of the strongest communities around. 

Structure is automatically generated then, because groups must have leaders (with a few exceptions). The larger a religious community grows, the more levels of authority are needed to control it, rendering a sort of government invested with divine authority and with the charge of enforcing the religion's laws and/or customs. 

Unfortunately, religion can also validate structures such as the caste system with divine justification, separating humanity on an arbitrary and often detrimental basis. Of course, over the course of history, people have come up with plenty of ways to justify harmful social structures such as slavery without the help of religion, so the fault lies less on religion and more on humanity itself. :P

On the Purpose of Religion: Morality

Morality is typically provided via a combination of great incentives and equally severe punishments. These are often some of the core tenets of the religion and dictate people's actions every day.

Karma is the supernaturally enforced version of "what goes around comes around." As an extension, some Eastern religions' versions of reincarnation include a sort of judgment. Do good, and be reborn as a human; do evil, and be reborn as a slug. At the end of the scale is the divine judgment of the afterlife found in religions such as Christianity, where the stark contrast between heaven and hell is all the motivation required to be a moral citizen. 

I would think that people can be moral without such positive/negative reinforcement, and I gain hope from the fact that atheists are not simply evil. Mechanisms like the philosophy of ethics and psychology of social norms indicate that there are other avenues to give a society morality.

On the Purpose of Religion: Comfort

There is nothing quite like the comfort that religion gives to people. The troubles of the past, present, and future are taken away by the magical hope of the afterlife or reincarnation. The terrifying unknowns of darkness, death, and the currently unexplainable are answered. The loneliness and sorrows of life are ameliorated by the unconditional(?) love of a powerful supernatural being and the tremendous support of a unified religious community. I don't know of any other mechanism to provide such comprehensive and deep hope and comfort, and it is perhaps the trait I admire most.

On the Purpose of Religion: Introduction

First, to preface: I have not yet taken a course or even read a full book on religion, though I ought to have by now. I have not yet traveled the world on my own to truly learn about its myriad cultures, though again I ought to do so.

These thoughts, then, come from a mind that is functionally illiterate in religion but nevertheless takes the liberty of having thoughts about it. Therefore, any corrections, additions, or (dare I hope) agreement would be very, very much appreciated. I know I know nothing, but I would like to.

Although the purposes of religion are perhaps uncountable, I believe the original functions of many are to give some combination of comfort and morality, order and causality. These are obviously interdependent and likely incomplete, but they will do as a starting point for now.

Social Media: What Am I Doing Here Anyway?

Pinterest. Facebook. Blogger. Picasa. Tumblr. Twitter. Deviantart. Google+. Instagram. LinkedIn. Flickr. Foursquare. Myspace. StumbleUpon. If I could come up with 14 sites on my own within a minute, then there must be over 100 well known social networking sites out there. What are they all for? What is their purpose in life? What is the point?

Well, I've been on only half of the above list, but it still took quite a bit of thinking to understand my presence in that limited fraction. Indeed, I go through that kind of reflection every few months and often find some redundancy in the sites I do use. We use social media to share our stories, but I'd like to share the story of my social media.

In the beginning, I used Blogger for everything: thoughts, stories, and pictures. Then Facebook came along, and all of a sudden the thoughts and pictures were shifted there, and the stories just vanished. I don't know where they went, because presumably I should still have them, but I've never been able to return to that carefree storytelling.

Anyway, my extended family began using Picasa for sharing pictures with each other, and still do, but ultimately I stayed with Facebook for sharing pictures with people I knew and actually cared about. Similarly, Google+ threatened to take the thoughts away from Facebook, but it never caught on as much as expected.

On the other hand, I suddenly became interested in sharing my pictures with people I didn't know or care about; this phase is a little hard for me to rationalize, even now. I went through Picasa, Blogger, and Deviantart before turning (as I am currently) to Tumblr.

So here is the status quo, then: my short thoughts go to Facebook, which is also used for contact and sharing pictures with friends and family. Tumblr is used to share pictures with people I don't know and will probably never meet. Finally, this blog is for my long thoughts, my ramblings, my musings, my poems, and basically anything else. And of course, most of all, my excitement and joy at random and sometimes trivial things, which I'm learning to cultivate even though it's my most immature and childish feature. :)

Variations: Blue Flame

A wavy flower, with a pink-purple-blue shading

When I'm playing around with GIMP, I often find a particular piece, a monomer if you will, that somehow has a lot of potential uses. I can warp it, rotate it, flip it, and more to make "polymers" of greater complexity by using tricks of symmetry and space.

A crab or spider with peacock tails or wings

These four pictures are all variations on a single blue flame, shaped in different ways to create quite distinct results. (In fact, I made around ten, but these are the best and most distinct of them all.)

An icy blue fern-like frond

The flower was made by simple rotation about the center of the picture. The crab-spider required three different kinds of warping for the tails, legs, and center flames. The frond just contains repeatedly scaled down versions of the very same tail. Finally, the butterfly was made with a single different warp, followed by rotations and fun color trickery. :D

A pair of glassy blue butterfly wings

Independent Indicators: Trial by Jury

This week, one of my friends in a probability class showed me a problem about jurors and Bayes' rule. The jurors voted a guilty person innocent or voted an innocent person guilty some not-so-small fractions of the time, and a person was convicted if at least 9 jurors voted guilty. They were asked to find the probability of an correct jury decision given that some percentage of people tried were actually guilty.

This problem can be solved well with some indicator random variables (1 if a juror votes guilty, 0 otherwise), and the assumption is that they make their votes independently. In reality, however, this is generally not the case. In most (if not all) jury-based judicial systems, the jury meets and discusses the trial, making their decisions very much interdependent. So here is my question: is this desirable?

On one hand, some jurors lacking in critical thought or engagement in the trial might benefit from the knowledge and thoughts of those who are thinking about the case. On the other hand, a few "loud" jurors might heavily bias the decision merely by virtue of their persuasive abilities, regardless of the facts presented in court.

I feel that if you're going to be idealistic and follow the first train of reasoning, why would you not be equally optimistic that there simply won't be such poor jurors at all? If we are going to be realistic enough to admit that there will be jurors who neglect to use their own critical abilities, we should admit that it is more likely that a persuasive individual will influence them to follow rather than to think for themselves--in which case, their presence is not only useless but also detrimental to a fair decision.

A Spring Morning

 

My coffee spiked with cinnamon and chocolate,

I pass by smiles and yawns and squinted eyes.

Robins with hearts of fire play hide-and-seek

With squirrels in bushes and blossoming trees.

Through layers of translucent verdant leaves,

Drops of sunshine filter and fall on my head.

The childish breeze plays with a tuft of hair

And tickles my face with its misty fingers.

A panda trundles through my messy room,

Nomming on bamboo shoots of graphite

Grown with care on crinkled notebook pages

 By the light of the flames burning there.

Riddle Me This 4: Picky People

What does each person like?

1) Alice likes avocado but not squash, okra but not zucchini, eggplant but not bell pepper.

2) Bobby likes cookies but not cupcakes, apples but not bananas, blackberries but not grapes.

3) Drew likes cheese but not crackers, trout but not salmon, brie but not gouda.

4) Huck likes blues but not reds, straws but not sticks, elders but not youngsters.

5) Irene likes arugula but not sage, oregano but not tarragon, basil but not coriander.

6) Katy likes coffee but not mocha, milk but not cream, tall but not grande.

7) May likes suns but not skies, corn but not cabbage, and passion but not power.

Hint: They are all happy with themselves.

Riddle Me This 3: Between The Lines

FIREVESAL | _ _ _ _ _ _ _ _ | DAMMN        

 EINTRANCE | _ _ _ _ _ _ | PALPENIPE
    CRONDOC | _ _ _ _ _ _ | SEDIMONSE
FORDFRYING | _ _ _ _ _ _ _ _ _ _ | WRANCALVE         

REMURCY | _ _ _ _ _ _ _ | NATURS   

DRELVANE | _ _ _ _ _ | YILL      

     MOGOL | _ _ _ _ _ _ | ENLODGE

Hint: Candy Fruit Capital House God Flower Poke

Sunshine

This blog is about the things I find cool, the things that make me happy, the things that make me smile. The fact that there are so many is one of the reasons I have this blog in the first place, but if I were to try to write them all down, sunshine would be at the top of the list.

This is a time when sunshine makes the world a brighter place. The sun's radiance supports practically all life in some way. It's crazy awesome, and without it, this wonderful world would be a much more depressing place.

Sunshine makes trees grow and plants blossom! It spreads energy and warmth everywhere. It's like smiling, only more so; sunshine makes people happy, and compared to all the limited resources in the world, it touches everyone. 

The moments when the sun rises to the day and sets to sleep are some of the most beautiful. It paints the surface of the Earth with colors, rendering verdant trees, vibrant flowers, vivid seas and skies. It's so amazing that it's hard to imagine life without it! :D

Spring: The Most Wonderful Time Of The Year

SPRING IS GREEN!!!

NEW PLANTZ!!!

I don't care what the carols say about mistletoe-ing and hearts-a-glowing. Spring is the real hap-happiest season of all. I've already talked about why, based on purely numerical and grouping reasons, spring ought to come at the beginning of the year. But one of the most important reasons that Spring should come first is that it's simply the best.

EFFLORESCENCE!!!

1. Spring is full of sunshine.
2. Spring is optimally temperate weather, in contrast to summer hot and winter cold.
3. Spring contains the birthdays of all the coolest people.
4. Spring is a time of sex, birth, and growth of flora and fauna.
5. Spring is a beautiful contrast to lugubrious winter.
6. Spring is an exciting prelude to summer break.
7. Spring is the biggest time to sow seeds for gardeners.
8. Spring's beginning is marked by Holi, a festival of colors.
9. Spring contains Spring Weekend.
10. Spring provides life (especially plants) a vital combo of light, rain, and warmth.
11. Spring also means a source or supply, especially of water.
12. Spring also means to dart, fly, or bounce, or to be quick, resilient, or elastic.
13. Spring is prime, like the number of reasons in this list.
14. Spring is youth in a year-life metaphor.
    
15. Spring is also often metaphorical rebirth after fall's decay and winter's death.
16. Spring is green, and green is the best color.
17. Spring is a time when trees are filled with leaves, flowers, and birds.

Flame Bookmark

But don't set your book on fire.

Observations On Five Games Of Mafia

1) Observation, knowledge, and communication are all vital for success.
2) A pin in a pile of nails is hard to find.
3) Do not accuse people if you are not prepared to be accused.
4) People's educated guesses can be worse than random choices.
5) Most people are not skilled at lying.
6) People act differently in different circumstances.
7) Sound and sight are equally valuable.
8) One good public action can save one's reputation for life.
9) One suspicious public action can ruin it.
10) God can get things wrong.

A Is For Apple

What to start with? An apple, of course. Regardless of the fact that Eve's apple-eating threw mankind into sin and Eris' golden apple started a major war, apples are well-liked by most of the world. Babies eat applesauce, and apples are common and delicious (haha), so it's reasonable to start their English vocabulary with "A is for Apple." And that's besides the fact that, well, A is the first letter of the alphabet. Similarly, the apple is one of the first things novice artists typically learn to draw (or so has been my experience). So here is mine! :D

In case it isn't clear, I did not actually draw these very lines for the apple (for one, it's left and right half are perfectly symmetric, and I've never been that good at drawing). :P Instead, I drew a flame and warped it into a crescent. For the leaves, I actually drew a straight bay-like leaf and then warped it into the curves you can see above. I do feel like I'm cheating by drawing in this way, but hopefully I'll someday be able to draw something like this directly. :)

Tablet Pen or Wooden Pencil?

I love arts and crafts--drawing, coloring, painting, sculpting, the list goes on. Unfortunately, my skills at all of them haven't really grown since I was in 4th grade or so (and I'm sure I could find plenty of 4th graders far better than me).

But I still love it, even if I'm no good. As I've mentioned before, GIMP has allowed me to bypass many of the fundamentals to arrive at passably pretty abstract art ("nice" is the most appropriate adjective), mostly using tricks like gradient rendering, rotation, and symmetry. :)

Recently though, I've started to wonder whether going on this way is really acceptable to me. Making perfectly symmetric glowing flowers and vibrant colors is all well and good, but art should really be something more, some expression of an idea or memory or emotion or story. I can't do that with the skills I have now.

So it was with great pleasure that I opened a postage box on my birthday a few weeks ago and found a drawing tablet to use with my computer! It will take me a while to learn to use it well, but it's encouraging that I can already draw something I never could on my computer: the flames above, which are practically omnipresent on my class notes. And of course, now I can add in my pretty colors. :D

I don't know which comes first--learning how to draw with a tablet, or just learning to draw at all. Regardless, exciting times await!

On Uniqueness

Uniqueness is a big deal. Mathematicians are ecstatic to find that there exists a unique solution to a problem, biologists love to try finding unique pathways to various diseases, and product managers work to make their brand as unique as possible. "Of which there is only one; one and no other" is the OED's first definition, encompassing the existence and the solitary nature.

Counselors often say "everyone is unique" as though it ought to make someone feel better about themselves; interestingly, it usually does. Somehow, the very thought of being different is highly gratifying to the self-esteem, in spite of all the effort we put in to be just like everyone else.

It's certainly true, of course, that no two people are exactly the same, but why is this inherently a good thing? I believe it stems from people substituting another definition of unique: irreplaceable. That is, "everyone is unique" translates to "every person has special talents or qualities unlike any other."

The subtle problem is that those qualities may or may not be positive. Taking the edge case, if a person A is absolutely talentless at any and every non-basic activity, the fact that A is unique is not any reasonable cause for comfort.

However, such an edge case is non-existent, and given the vast number of possible talents and the combinatorially explosive number of sets of talents, it is pretty rare to for some person A to encounter a person B whose positive talents are a superset of A's. But in such an instance, should A feel any rational solace in the fact that he is unique, but in a strictly inferior way? Should B feel pride in achieving all that A has, and more? What is each of them justified in thinking?

Birthday a la Duck and Bunny

Scones! With jam and theoretical Devonshire cream!

For once, we celebrated my friend's birthday this year at the Duck and Bunny rather than the Cheesecake Factory. I'd never been, but it definitely earns its self-title of "snuggery." A cozy place with warm and bright decor, it seems like a bunny's version of the Cheesecake Factory, specializing in crepes rather than cheesecakes. :)

A crepe masquerading as a burrito! o_O

I only had the bean dip and the Creperrito, but I would heartily recommend both. The former blew all of our minds with its surprising depth of flavor, and the latter had all the right touches for a satisfying meal--lightly dressed greens, rich crepe and beans, and touches of guacamole, tomato, and sour cream. NOM!

Newton on Graduation

As I was strolling through the CIT today, these three pieces of paper on a professor's door caught my eye.
Thirty seconds later, I was laughing out loud, and I hope that you are too. =D Enjoy!

Apparently, credit should be given to the PHD program at Stanford University. Yay Stanford!

And So I Declared.

Last week, I formally submitted my declaration for computational biology. I've been flip-flopping since the start of freshman year, and I'm still not convinced that I've made the right choice, but I have made one, for whatever it is worth.

Applying to and arriving at Brown, I was confident that I would leave with a degree in neuroscience. The brain was the most fascinating object I had ever considered; as V.S. Ramachandran once said, “It can contemplate the meaning of infinity, and it can contemplate itself contemplating on the meaning of infinity.” It truly is a remarkably plastic, self-regulating, parallel-processing biological computational machine, and I wanted to find out how it works. I still do, of course, but I have since gained a profound appreciation for computation itself, as well as the systems and algorithms humanity has developed to assist in solving more and more complex problems.

Yet I am, now and forever, a biologist at heart, and the problems I am most excited about solving are biological ones. How are gene expression and translation regulated? Why do proteins fold the way they do? What are the protein networks and pathways in any given cell? How do they interact to perform a distinct function (or malfunction, say cancer, when an error is introduced)? Returning to neuroscience, how does the complex circuitry of the brain generate its fantastic abilities? The answers to these questions lie in the realm of computational biology.

Food, Glorious Food

Sometimes, the Ratty has really, really awesome food. Those days are happy days.

I'm talking about crusty, chewy sourdough and a variety of crackers
topped with bright brie and gouda with a side of succulent strawberries. NOM!

Bio-Hardware: Patterns

Fractals are generated by repeating a pattern--over and over and over and...

From the smallest toddler to the oldest senior, we all love patterns. Even if you think you don't like patterns, your brain does. Patterns are not just the spice but the life itself. Associations, fractals, habits, cycles, noun-verb syntax, symmetry--they are all just examples of patterns: things that repeat in a predictable manner.

One of my flower fountains: symmetry in action!

We are evolutionarily hardwired to find patterns. If you eat a certain berry and get sick, you had better learn to associate that berry with sickness. If you walk into a cave and it turned out to be a snake retirement home, you had better not walk back in there again. 

"A for apple"?

In essence, learning itself is biochemical pattern-finding. A parent shows a baby girl a picture of an apple 10 times and says the word "apple," and she learns to associate the two. "Clearly," her brain thinks, "there's a pattern there." A rat presses a lever and receives a tasty morsel. "Aha! Lever --> NOM!" 

"Neurons that fire together, wire together."

On a molecular scale, synapses between neurons that fire together are strengthened by NMDA receptors, which are aptly called "coincidence detectors." Not a "lucky coincidence" kind of coincidence, but a "two-things-happened-together" kind. Co...incidence.

Hint: What do preschoolers learn about?

Personally, I really really really love patterns. They are everywhere, they are mentally and even almost emotionally satisfying, and the act of finding a pattern is often inherent in all kinds of puzzles and problems that I enjoy. Besides which, I like learning, and learning is patterns, after all. :D

Nuclear Catastrophe: When Life Goes Wrong

Nothing in life is perfect. Nothing in biology is either. As DNA replicates inside the nucleus, errors happen--a deletion, an insertion, a duplication, maybe an inversion of a couple bases. DNA polymerase, which copies out a new strand, is pretty good- only one in 10⁷ bases are wrong, and with the built-in proof-reader in the very same protein, that goes down to one in 10⁹. Not bad, not bad at all! On top of this, there are even more DNA repair proteins that routinely scan for bumps or nicks to make sure that everything is as it should be.

Some examples of DNA mutation

But sometimes, much bigger changes can happen. Deletions of entire genes, inversions of regions on the scale of kilobases (kb), translocations that cause one chromosome to attach to another! These larger structural errors are called, unsurprisingly, structural variants. As you might imagine, these are somewhat more likely to be serious enough to impair cell function, though several point mutations can be deadly as well.

But wait! Sometimes, something even worse happens: a really catastrophic nuclear event. These are called complex events (and at the far end, chromothripsis). Just look at these graphs! Each of the outer colored segments is a chromosome. One of the curves inside connects two breakpoints, where the chromosome broke and then reconnected to a different spot. In these cases, you can even see many with multiple breakpoints at multiple chromosomes!

We used to just say, "Oh, these are just one mutation happening after another, collectively creating this scrambling." But with this new data and visualization, it's clear that the breakpoints are often clustered around particular areas, which suggests a shattering of the chromosome around that point and then scrambled rearrangement. We're still not sure how this happens though.

In particular, such a catastrophic event should definitely just kill the cell, right? So why do we ever see these? The answer is that we usually don't. These are from three cancerous tumors, and tumors are where we are increasingly finding these complex variants. Do these crazy rearrangements cause cancer? Or do some cancer pathways enable the dramatic events to occur? These are the kinds of questions that some computational biologists are working to answer. 

Hot Tails

No, really. Hot tails. In 2007, researchers discovered that when ground squirrels and rattlesnakes face off, the squirrels heat up their tails. We already knew that rattlesnakes have infrared(IR) sensors (heat vision), and we knew that squirrels wave their tails at snakes, but this was the first time scientists had detected such a vivid heat-mediated signalling mechanism. Scientists built a robo-squirrel to confirm the deterring effect of the heat shift, but for some reason news sources are getting excited about it all over again lately. Robo-animal fan clubs, I assume.

Presumably, heating up their big, bushy tails either serves to make the squirrel look bigger and more intimidating, or just to make its warning more noticeable. ("Warning?" you ask? Adults are largely immune to the venom, and can therefore harass and fight the snake fairly well. Mostly rattlers favor surprise attacks, and the tail-waving warns it that it's been seen.) As far as I know, we're still not sure which. Either way, it's pretty cool, especially considering that squirrels themselves can't see IR. o_O

This reminds us of some important lessons. To well-analyze a particular species, we have to think about the other organisms it interacts with in addition to the species itself. Squirrels can't see IR, so if we hadn't been focusing on the snake-squirrel interaction, we never would have found this cool example of evolution. Moreover, another reason this took us so long to find out is that we can't see IR either. It's important to break out of our human-centered box, because the world is full of things we can't see, hear, smell, or detect, and we'll never know about them if we don't think to look.

Hi Qu

A feathery fire

Struggles to stay dry and fly

In shimmering sheets

In times of trouble,

Strengthen or weaken your limbs:

Fight or drop away.

Where dragons burrow,

Worms will always find their place,

Like bees in a hive.

Fortune will find you,

A strange truth will confuse you,

A lie will blind you. 

Lugubrious shell,

Once occupied, now empty,

Awkward no longer.

The Twelvefold Way

1...2...3.

The triple gems (Ratnatraya) in Jainism are Right Vision, Right Knowledge, Right Conduct. The first involves belief and conviction, the second clarity and reality, and the third action and application. This is similar to the eightfold path of Buddhism, which can be broken down into Wisdom (right view and intention), Conduct (right speech, action, and livelihood), and Concentration (right effort, mindfulness, and concentration).

As you might expect, the twelvefold way is also a paradigm with great power and application. However, it has absolutely nothing to do with ethics, and instead is used to count! I know what you're thinking: "Look, I know how to count. Why on Earth would you need a twelvefold way to do something as simple as counting?" The short answer is that life is full of things that are too complicated or too large to enumerate easily, and so we need combinatorics, the art of counting. Plus, if you can count something in general, you don't have to count it again. :)

So what is the twelvefold way? It is a classification of 12 commonly occurring counting problems, based on functions from a set to another set. This creates a useful simplification of larger or more abstract problems, making them easier to count. For example, how many ways are there to distribute 6 distinct candies to 3 kids? This is the same as:

• The number of ways to put 6 items into 3 boxes, which is the same as 
• The number of ways to line up 6 dots and 2 bars, which is the same as 
• The number of ways to get 2 heads on 8 coin flips, which is the same as
• The number of bit strings of size 8 with exactly 2 ones, which is the same as 
• The number of ways to choose 2 things from 8 things.

All of these can be simplified into the same category in the twelvefold way, so once we've found the answer to that, we know the answer for all of them! Which is 28, by the way. 2 and 8, see? :D

Why The Year Is Messed Up

January, February, March, April, May, June, July, August, September, October, November, December.

Notice: September, October, November, December. 7,8,9,10.
So why are they the 9th, 10th, 11th, and 12th months respectively!?

Apparently, there used to be only 10 months, back in the Romans' time. There were also 60 or so days of winter that just weren't part of a month. When they decided to do so, January and February came into being, giving us the full 12 that we see now.

But that still doesn't explain something. Why aren't January and February at the end of the year instead of the beginning!?

1. It would mean that the "numbered" months would retain their proper numerical positions.
2. It would mean that the 4 seasons would actually be grouped together, instead of being silly and splitting winter. Spring-Summer-Autumn-Winter. So clean, so ordered, so much better.
3. It would actually make sense that February is a weird month, because it comes at the end of the year.

So I hereby humbly suggest to the powers that be in full knowledge that such a suggestion shall never be taken that we should move January and February to the end of the year where they belong.

Dream of Death

Diving into torrid sands, riding over ancient lands,

Drizzling on wrinkled hands remembrances from oceans green,

Envying the waters that they've never seen and never will.

Devil voices in their heads, rousing them from cozy beds,

Ever pressing on the threads and links that span their tortured brains,

Make them take a walk into the pouring rains that pierce and chill.

Apples drop upon their skulls, messy reason quickly dulls,

Ending in a song that lulls a soul into a siren's sleep,

Masking flashes pouring out away into a chasm deep.

Nudibranchs: Beauty of the Sea

Hypselodoris edenticulata: Florida Regal Sea Goddess

Okay, normally I would put these links and outside references at the end of the post, but there are so many beautiful pictures that you should REALLY look at that I am putting them right here for your convenience, so that no one is scared away by the long post itself.

More Pictures And Awesomeness!!
The Sea Slug Forum 
NudiPixel
National Geographic Nudibranch Gallery (David Doubilet)
Blue Dragon Pictures (Flickr--paulhypnos)
Nudibranch Gallery (Sergey Parinov)
The Right Blue


Now, on to the post! Pretty Sea Slugs!!
 Nudibranchs are shell-less mollusks upon which nature has decided to paint in pretty much every color imaginable. But these jelly-like sea slugs aren't just beautiful; with a spectrum of hues and adaptations, nudibranchs are masters of incorporating what they eat into their own bodies.

Halgerda terramtuentis: Gold lace nudibranch

If you're a nudibranch, you really are what you eat. They are carnivores that graze on everything from algae, sponges, and corals to anemones, barnacles, hydroids, and even other nudibranchs. Their color and their very survival is often derived from what they eat.

Many incorporate pigments from the coral they eat into their bodies, resulting in effective camouflage. Some can even store chloroplast in their outer membranes and let these chemical factories make sugar for them. Others instead incorporate the nematocysts (stinging cells) of jellyfish, hydroids, anemones, and other nudibranchs into the cerata (dorsal body wall) and use brighter colors to warn predators of their toxicity.

Glaucus atlanticus: Kinda looks like a Pokemon

Glaucus atlanticus (sea swallow), feeds on siphonophores like the deadly Portuguese Man o' War, collecting the stinging nematocysts in their feathery cerata. In fact, their sting is even worse than the original, because they appear to store the worst ones in high concentration. Beautiful but scary. o_O

Hexabranchus sanguineus: I whip my dress back and forth

Hexabranchus sanguineus is called the Spanish dancer for its beautiful red and white body and the fluttering dance-like swimming it exhibits, looking for all the world like a flamenco dancer's dress. Most nudibranchs chill out at the bottom of the sea, but the Spanish dancer swims freely. :)

Pteraeolidia ianthina: Great Blue Sun Dragon!!!

Pteraeolidia ianthina, otherwise known as the blue dragon, is solar powered! Yes, it's an animal, not a plant. Yes, it's blue. But just under that beautiful blue are green-brown zooxanthellae (microscopic plants), which it acquires as a juvenile form by nomming on hydroids. After it's developed enough, it can go quite a while without feeding, just subsisting on the sugars that the zooxanthellae provide in exchange for a sweet place to live.

Images:
Scuba Diving Magazine: Regal Goddess (Douglas Kahle)
The Right Blue: Gold Lace
Fuck Yeah Biology: The Blue Sea Slug
The Sea Slug Forum: Blue Dragon (Sukhdev Singh)

Technical Difficulties

"Vishesh! The computer is too far away!"

The Best Color

Happy Saint Patrick's Day! Yes, the best color is indeed green. It is the color of this text, it is the color of this blog, it is the color in the middle of the visible spectrum, it is the color of plants, it is the color of spring (which is of course the best season), it is the color of nature, it is the color of life! 

The etymology of green involves the proto-indoeuropean root "ghre-" for "to grow", and the OED notes that "the associations with verdure, freshness, newness, health, and vitality are widespread among the Germanic languages." GREEN IS THE BEST!

But really, why are plants green anyway? Because plants use chlorophyll for photosynthesis, and chlorophyll absorbs and uses red and purple but reflects green. (Incidentally, if it weren't for chlorophyll and photosynthesis, there wouldn't be so much oxygen around, and we wouldn't be around, so green really is the color of life!)

Ok, but why is chlorophyll green? Why doesn't it use the entire visible spectrum instead of just the edges of it? Scientists don't know for sure, but there are three major hypotheses that seem the most reasonable (compared to others that just sound like excuses):

1. In the same way that we can't take in 100% of the oxygen in the air we breathe (it would be toxic) and don't release all the energy in glucose when we undergo cellular respiration (it would be explosive), using all the visible spectrum might involve dangerous energy levels that would damage cells.
2. Evolution is not engineering. Having evolved chlorophyll and photosynthesis (which, let's be honest, work pretty well as is), it might not be trivial to make the switch without passing through suboptimal levels. In general, this evolutionary constraint explains many differences between man-made and biological machines.
3. Certain archaea use retinal to utilize solar energy, and retinal does absorb the middle of the visible spectrum (these appear purple in color). If these evolved first in the ocean, the first cyanobacteria/algae might have lived under this purple film and thus been restricted to only using the tail ends of the visual spectrum, resulting in the chlorophyll we know today. 

Anyway, I wonder if it would make a difference to us--if plants were black or purple instead of green, would we love green as much as we do now? Would black and purple seem less dark? Or would we just like trees less? These answers lie in the realm of neuroscience and psychology (and perhaps philosophy), but until they're answered, I'll just say that I'm very glad our world is green. :D 

Biomemories: Golden Silk Orb-Weaver--A Natural Architect

Nephila clavipes

The genus Nephila are masters of architecture; derived from the Greek words nen(thread) and philos(love), their name epitomizes their spinning skills: they have the strongest silk in the world, are skilled builders, and can basically catch anything that can fly through a forest. From the equipment to the material to the design, they've got it all.

Nephila clavipes are part of the Arthropod subphylum Chelicerata, which includes scorpions, mites, and spiders. The male is a rather uninteresting brown and about 5 times smaller than the female, which has yellow and red stripes and spots and can grow up to 4 cm in length. It is the female who does all the extensive and elaborate web-building, while the males essentially just sit around about 5 cm above her, waiting for food and sex. She, on the other hand, stays quite busy building and repairing her web and wrapping and eating her food, using venom to paralyze it as she does so. Talk about gender inequality...

A weaver in her web

The Web:
Although she consumes part of her web at night for protein and rebuilds it every day, a Nephila can make webs that can last for 2 years, stretching to over a meter in diameter. In addition to the fine mesh orb seen above, she can construct barrier webs that protect the web from weather, birds, and other larger objects and also function as an alert to invaders and prey smashing against the web.

Furthermore, she may install zig-zag lines of structural silk to increase stability or open a hole to allow wind to blow through without destroying the entire web. Her silk's slightly yellow color has been shown to act both as an enticement for flower-seekers like bees and as camouflauge in shady areas with mottled sunlight. 
 She may incorporate more or less yellow pigment in her silk depending on light conditions in the area, revealing rather a complex mind behind that pretty body. Dr. Catherine Craig, an expert in the dynamic and active nature of spider webs, has explained that "Yellow is a very generalized visual signal that both herbivorous and pollinating insects associate with flowers and new leaf material...the insects may have a much harder time evolving a mechanism to avoid it."

Spider silk spigots

The Silk:
First of all, all silk is not made equal. Both the ingredients and the process differ from species to species, and Nephila clavipes, among others, can spin up to seven different kinds of silk, each with unique properties and purposes in its web.

With a tensile strength of 4×10⁹ N/m, their dragline silk is six times stronger than steel and 10 times more effective than Kevlar at dissipating energy, it has a plethora of potential uses, from parachutes, bullet-proof vests, and ropes to sutures, tendons, and ligaments.

One excellent example is the use of Nephila clavipes dragline silk in nerve guidance. Besides being incredibly strong, it is not only nonimmunogenic but also has antibacterial and antifungal properties. Furthermore, its structure promotes cell migration and adhesion and can even obtain its own myelin sheath in the presence of human Schwann cells. You'd think it was meant to be.

Just keep spinning, spinning, spinning...

So how on earth do they do it? Think of silk making in terms of steel manufacture: in order to make it, you need not only the iron but also the Bessemer process to transform that iron into beautiful, powerful steel. Silk works in much the same way. Spiders have both the proteins to make it and the tools to transform them into long, strong silk. Using alternating parallel molecules and random-ordered regions, spider silk is able to contract or expand according to pressure, thus enabling both flexibility and strength.

Biomimic Garry Hamilton elaborates, "A single spider-silk thread can be as small as one micron (i.e., one-thousandth of a millimetre) in diameter. The protein chains that form the threads are roughly another 1,500 times smaller still. What scientists suspect is that during spinning, the spider exerts a force that causes microscopic fistfuls of these protein chains to bend back on themselves and align with one another to form tiny crystals. These crystal chiplets, containing thousands of neatly arranged amino acids, apparently prevent microscopic cracks and hold the silk together....there's not an overabundance of crystal, thereby limiting the silk's density and maximizing elasticity."

This allows Nephila dragline silk to combine incredible tensile strength with elasticity up to 40% of its original length. In contrast, capture silk trades rigidity for serious flexibility by implementing spiral structures that allow for 300% extension to snag insects flying at high speeds without breaking.

Nature's architects are the best of the best from hundreds of millions of years of development, and we have a lot to learn, if we're willing to listen.


Image Sources and Cool Links:

Images:
Keith Ramos - Golden Silk Orb-Weaver
Wikipedia Commons - Nephila Clavipes - Merritt Island
Arachnology - Spider Silk (Dennis Kunkel)
Protein Spotlight - Nephila Clavipes (Frank Starmer)

General:
Animal Diversity - Nephila Clavipes
New York Times - Crafty Signs Spun in Web Say to Prey, 'Open Sky'

Web and Silk:
YouTube - Nephila Weaving Circumferential and Radial Fibers
Protein Spotlight - The Tiptoe of an Airbus