Ninjinuity

Quaternions

2012-02-12T20:47:00.000-08:00

What are quaternions? Let's start with what quaternions once were: an attempt to extend Complex numbers to three dimensions.

Back when the geometric interpretation of complex numbers as a plane was reasonably fresh, Sir William Hamilton became interested in finding a system of algebra that would allow him to express three dimensional space in the same way. To do this, Hamilton needed a way to add and multiply points in 3 dimensional space together.

Addition came easy. Picking some arbitrary origin and axes 1, i, and j to work with, Hamilton just defined (a + bi +cj) + (d + ei +fj ) = ( a + d ) + ( b + e )i + ( c + f )j.

Multiplication, though, was a problem. Assuming that these new quantities were distributive, Hamilton needed to define ij in such a way that various other properties still held. Despite his best efforts, he couldn't do it.

Still, Hamilton found a way forward. By adding a fourth axis, k, Hamilton could define that i^2 = j^2 = k^2 = ijk = -1 and everything worked nicely. In Hamilton's view, he'd found the best way to represent 3D space. He called the new construct a quaternion and spent the rest of his life promoting their use in physics and chemistry.

Eventually, though, quaternions dropped out of style. They were elegant in some situations, but unintuitive and clumsy in others, and the vector math we have today often suited physicists better. For the better part of a century, quaternions went unused outside of some mathematics.

Clearly, though, quaternions are useful for something, or I wouldn't be writing about them. To understand why they're so neat, though, we need to change tack and talk about something else: gimbals.

Spinning Gimbals, courtesy of Wikipedia

A gimbals are a set of rings attached by pivots. Usually, as in the image above, there are three rings: an outer gimbal, which can rotate freely around, for instance, vertical with respect to the enviroment, and two inner gimbals, each is mounted at right angles with respect to the axis of the last gimbal.

The purpose of all this is generally to allow some sort of equipment (often a flywheel, whose inertia will keep it level) to rotate freely. If we want to think about the state of the gimbal mathematically, we can assign one angle to each set of joints, for a total of three numbers. This makes sense, of course, because we're trying to capture a three dimensional space (the surface of a sphere accounts for two dimensions, plus we need to be able to rotate around each point we choose).

Mathematically, we also might like to be able to think of rotations as something you can combine, one after another. In order to do this, we have so called Euler Angles: 3x3 matrices which we can combine through matrix multiplication. We also can apply this matrix to a three dimensional vector.
As you'll see later in this article

In most situations, this whole setup works nicely, and we're done. There is one time when it fails, however. Going back to the gimbals, it's possible for two of the axes to line up, constraining the rotation! In other words, while the gimbal usually provides three degrees of freedom, at two specific points, it only provides two. Euler Angles have the same problem.

This is a big enough problem that there is a mechanical solution for actual gimbals: add a fourth constrained ring. As long as you always have at least three non-parallel axes, you can rotate. As long as the fourth gimbal is always in position to take over if two other rings line up, the local space of movements will be three dimensional.

Now if we wanted to represent the gimbals mathematically, we'd have four numbers to worry about, but there would be a constraint on at least one of them. We might like to imagine that there is some constraint will be sufficiently strong to mean that given three of these numbers, we could find the fourth uniquely. In fact there is.

Let's back up for a second. If we're willing to accept that our experiments with gimbals will roughly hold, we've found that in order to properly express rotations, we're going to need more than three just some subset of normal three dimensional space. Specifically, we'll need some kind of three dimensional surface in four dimensional space to properly express rotations in all cases.

Now, where have we seen a four dimensional space before? That's right: quaternions are exactly what we're looking for. Specifically, the unit quaternions, the set of quaternions a + bi + cj + dk which satisfy a^2 + b^2 + c^2 + d^2 = 1, are useful.

Imagine we want to rotate 3-D space about an unit axis v = bi + cj + dk ( b^2 + c^2 + d^2 = 1 ) by an angle θ. Let q = cos( θ / 2 ) + sin( θ / 2 )v, and let q^-1 = cos( θ / 2 ) - sin( θ / 2 )v. Then, if we have an arbitrary vector u, the rotation applied to u will give us the vector quq^-1! That's it! The great thing about this method is that everything is uniform. There are no singular points, no weird exceptions, and combining the rotation q followed by the rotation p into a single rotation is as simple as finding pq. Nice, huh?

If you want to understand exactly why that works, you should look here. I'm not going to go into detail because I intend this just to be a functional primer.

Also, once I get it working, I may post some C++ code with python bindings( I'm in the process of porting various things ).

SPLASH!

2011-11-19T10:04:00.001-08:00

These are all the materials I used/planned to use in class. I'll also put some links below for topics/sites I find interesting. Hope it helps! If you leave comments, I can try to get back to you and direct you to resources.
Happy Coding!
~Will

Where to go in order to...

Install Python
Install Notepad++ (A good text editor for working with python on windows. On Linux/Mac, you should be able to use whatever you have on hand.)
Learn Python
Do fun problems!

Stuff I wrote for the class (I'm planning on teaching this class again next year, so I may write more worksheets...):

Neat Topics

Imaging Exoplanets: Out of this world pictures

2011-10-14T14:35:00.000-07:00

Back in 2008, the image at left was plastered across the front page of many science related publications. For the first time, scientists had directly imaged an exoplanet (a planet which orbits another star) with visible light.
Exoplanets themselves were nothing new. In late 2008, 333 exoplanet canidates were known, and 8 of those had been detected using direct imaging. In fact, Fomalhaut b itself, the planet pictured, was actually not truly a new discovery. Since 2004 scientists had been reasonably confident it existed because of the sharp inner edge of the band of dust around the star Formalhaut. The thought was that a large planet (namely Fomalhaut b) was sweeping the material from the inside of the band into itself.

Formalhaut b was an excellent choice for direct imaging precisely because it was large and it was clear roughly where it was. When the 2008 analysis of data from the Hubble space telescope was published by Paul Kalas, it was greeted with plenty of excitement, but not much surprise.
Since 2008, scientific consensus on Fomalhaut b has slowly disintegrated. The "planet" is much brighter than expected, which, according to models of planet formation, should mean it is very hot (and should radiate infrared light). Despite this, Fomalhaut b doesn't seem to show up in the infrared spectrum at all.
As of last month, there's another puzzling data point. A third image taken recently shows that Formalhaut b's orbit isn't as textbook-perfect it seemed back in 2008. If the new data is correct, the exo-planet would need to veer into the dust once every orbit. This means that it would be actively reshaping the cloud, which is entirely inconsistent with previous results. This is leading some scientists to doubt that Fomalhaut b is a planet at all, though it isn't clear what real alternatives exist.

Does all this mean we've never imaged an exoplanet before? To the contrary, we've imaged 24 other planets directly. Notable among these is HR 8788. Why is this particular system notable? There are two reasons. Also imaged in 2008 ( in infrared, rather than visible light), HR 8788 is to date the only star where we have imaged an entire planetary system.
In addition, in 1998, before any exoplanets had been detected, HR 8788 was imaged by Hubble in an attempt to find exoplanets. At the time, the study found nothing, but only because researchers didn't have the correct techniques to pick the exoplanets out of the data!
Recently, in a superb demonstration of how much astronomy had advanced over the last decade, astronomers went back to that 1998 data and used modern techniques to analyse the images. Lo and behold, out come the same three exoplanets (see below).

One can only imagine the data magic we'll be able to pull off in another 13 years of exoplanetary research.

Of mice, men, and microRNAs.

2011-09-25T18:58:00.000-07:00

Although RNA is most famous for acting as an intermediate between DNA and Protein, we've come to understand that RNA's role in the cell goes far further in recent years. Some kinds of RNA, like miRNAs, actually change the balances of proteins made, leading to a wide variety of effects.
What exactly is a miRNA? miRNAs or microRNAs are tiny segments of RNA. Where most RNA segments are about 1,400 nucleotides long, miRNAs are typically only about 22 nucleotides long. While miRNAs are sometimes written out by themselves on DNA (as in the video above), it's more common to see miRNAs created as a byproduct of the creation of other kinds of RNA. Unlike many other types of RNA, miRNAs don't encode for proteins or assist in their transcription of RNAs to protein. Instead, miRNAs prevent proteins from being made from mRNAs by latching onto them before they can be transcribed. In the past few years, miRNAs have been implicated in certain types of cancer, and been used as biomarkers to help detect and diagnose diseases.
All of this is very exciting on its own, but more exciting still is a paper recently published in Nature Cell Research which suggests that miRNAs can actually travel from material in the digestive system of an organisms you eat into its bloodstream. Scientists at Nanjing University, China found a certain miRNA from rice, called MIR168a, in the bloodstreams of both humans and mice. By varying the diets of lab mice, they were subsequently able to show that the miRNAs found in mouse blood were being ingested.
This alone is an important discovery, but the researchers further "hypothesized that [plant miRNAs] may play a role in regulating the functions of mammalian cells and organs". Looking through the known sequences of mouse and human mRNAs, they identified about 50 proteins which MIR168a was likely to interfere with, including LDLRAP1, a gene that codes for a liver protein in both humans and mice. By exposing a certain type of liver cell (HepG2) to increased miRNAs, they determined that "Plant MIR168a...significantly decreased the LDLRAP1 protein level in the recipient HepG2 cells" while LDLRAP1 mRNA levels remained unaffected. In other words, the miRNA was preventing the transcription of the LDLRAP1 mRNA, as expected.
Why care about this result? It further clouds the waters regarding the role environment plays gene expression, an area of much of interest in biology right now. In addition, if miRNA uptake turns out to be common (or at least easy to induce) in humans then it could lead to whole new classes of oral drugs that target the expression of specific proteins.

E≈Mc^2?

2011-09-24T18:31:00.000-07:00

   If there's one result worth posting about from this week, it is the now famous (and in some circles infamous) exchange of neutrinos between CERN and OPERA, two European physics laboratories. Neutrinos are pretty cool as is, but what's really of interest here is what the neutrinos (muon-neutrinos, to be exact) appear to be doing on their trip from their creation at CERN to their detection at OPERA. They're arriving ever so slightly early: 60 nanoseconds early to be precise. For reference, quick calculation shows that light only travels 24 meters (just under 80 feet) in that time.
   How fast light travels is actually exactly what's at issue here; the neutrinos seem to be arriving at OPERA before light traveling along the same path would. If it is true this is the most significant find in physics for a century at least. For all practical purposes though, getting a result like this is a really good reason to check your equipment for obvious problems.
Having a particle like a neutrino (which has a rest mass) not just match, but actually exceed the speed of light is a discovery rather akin to the earth actually being hollow. It goes against so much previous evidence that it's probably wrong.
Pure incredulity isn't the only reason to be reserved. We know muon-neutrinos don't normally travel faster than light; If they did, we'd have seen a bunch of them arrive well before the light from the recent Supernova in M101. Instead, everything hit us at roughly the same time. In addition, two experiments very similar to the one at OPERA (but admittedly at lower energies) didn't observe muon-neutrinos breaking the cosmic speed limit by and statistically significant amount.
To their credit, the OPERA researchers seem to have taken every possible precaution to ensure that this result is real. They first observed this discrepancy almost six months ago, and since then, they've spent time making absolutely sure that they had the distance between the two labs almost exactly on (according to their paper, down to 20cm!), and making sure their timing systems were correctly synced up. They've repeated the experiment about 15,000 times with the same result, and they've take care to make sure there's no human bias sneaking in by blinding everything. Their arXiv paper is mostly a meticulous write up of their methodology and specific objections still haven't shown up.
What's next? Verification. If other sites observe muon-neutrinos moving faster than light, than we have the biggest experimental physics discovery of the past century.  If they don't, the OPERA scientists missed something, and those 60 nanoseconds have been conjured out of the math. It'll be a some time before we know for sure.

What is about to happen.

2011-09-21T10:21:00.000-07:00

Starting next week (and possibly this week for practice) you can expect to see two new articles per week (posted on Saturdays?)on current events in science along with some reasons you should care.
As part of my first semester at MIT, I'm taking a Science Journalism class. Part of this class is the creation (and weekly updating) of a blog on science, medicine, technology, and related topics.
Ninjinuity wasn't meant to be this sort of blog when I created it. It obviously isn't exactly this sort of blog right now. Going forward, however, I can only imagine that I will continue to spend time on STEM topics, and I can only imagine that I'll need to be in the practice of expressing myself cogently on them.
This is the reason I enrolled in Science Journalism. Even without the course, weekly blogging on what interests me in current science seems like an excellent idea.
There probably isn't going to be much else posted for a while. If I get the time to clean and post some sketches, great. If I get the chance to work on the 3D scanner code or some other project, that'll show up here too.
The honest fact is that time at MIT is valuble. The coursework is quite doable, but even once your work is done there's no end to the cool stuff to do in your free time here. Blogging for fun comes in low on the list.
That's all. If you'll excuse me, I'm going to tool out this 18.03 Pset, then head to career fair.
~Will

Living in Simmons

2011-09-06T19:16:00.000-07:00

My sketching is still awful, but at least I'm getting the hang of cleaning it up in gimp... More after the jump.

The Hough Transform: New and Improved!

2011-09-06T08:55:00.000-07:00

Ok, well it's still not better than a kerneled transform, but I am getting pretty pictures without the use of any trig! To sum up what I'm doing, I'm trying to use python's lambda expressions to generate a function in Cartesian space from the given points. Then I want to run BFGS over that function to find local maxima. By multiplying r = x_0 cos( theta ) + y_0 sin( theta ) through by r and rewriting as x^2 + y^2 = x_0 x + y_0 y , it's easy enough to see that the hough transform of a given point is actually a circle with one point at the origin and centered at \left( \frac{x_0}{2},\frac{y_0}{2}\right).
This has the nice property that it's easy to calculate the distance between a given line ( point in hough space ) and the nearest point on the circle as a single square root.

On the down side, because the hough transform usually takes advantage of the distortion of euclidean distance for small \theta , the end result has an absolute maxima at ( 0, 0 ). This maxima is very predictable, so I'm going to try just dividing by a function which is an idealized model near the origin, but quickly approaches 1 instead of 0 in every direction.
Still, without further ado, some pictures:

This image shows a single line: x + y = 10. In hough space this corresponds to the maxima at (5, 5). notice the nasty spurious point (0, 0).

x + y = 10, x + y = -10, and x + y = 20.

Just x + y = 10 and x + y = 20

x + y = 10, y - x = 10 and y = -7. This is a fairly unfavorable set of points. I think the top left maxima would be rather hard for a computer to locate.

The same three lines as above, but this time I picked sample points in the triangle. Much easier to locate all three maxima.

Update: Quotienting out the central maxima works! This is the same triangle data set as above.

An awful haiku.

2011-09-04T12:22:00.000-07:00

Deathcube, what great mass!
Rubber over the solid heart
of a neutron star.

A quick sketch from last night's "Welcome to Simmons" talk

2011-09-02T09:08:00.000-07:00

Done in the corner of some scrap paper. I've played around with some post editing in Gimp. Best part was the "Fire Alarm Prevention/ Popcorn Cooking 101" bit. Wish I could have sketched that instead, but I was out of paper space.

A Native Google Talk Client for Linux(Sort of)

2011-09-01T17:59:00.000-07:00

I've been using Google Talk more frequently as of late, but upon investigation, I was disappointed to learn that Google hasn't released a Linux client for Google Talk. I did, however, notice a reference to a "native" (whatever that's supposed to mean) ChromeOS client. Since I knew that ChromeOS is running Linux under the hood, I decided to check it out. Amazingly, despite wads of yellow tape warning me that it would wreak havoc on my computer and slay my firstborn, it seems to work seamlessly as a Linux client for Talk in Ubuntu 11.04! Video chatting between two semi-native clients doesn't always work, and using both the client and, say, gmail chat at the same time has it's rough edges, but it's fine.

Thoughts on Child Protection Legislation in Ireland

2011-08-30T18:16:00.000-07:00

[BBC] via [Boing Boing]
I'm not going to summarize the article above. That's been done enough. Just read it, poke around the issue for a while, then come back and read what I have to say.

This is a story where I'd usually feel justified shaking my head, having a cynical little laugh for myself and quietly walking away without further thought. This is (as the Primate says) an issue about the role of religion in a free society, and more importantly, when religion gets to exempt itself where a secular organization cannot.
I'll be upfront: I think that, in general, religious organizations should get no better treatment than a comparable secular non-profit, and often times they should be treated much like for-profit corporations, especially when it comes to potentially illegal activity they may engage in.
I think that the ONLY situation in which it would be OK to exempt confessions (or any other similar religious ritual with as potentially severe secular repercussions) from the scrutiny of normal secular law (specifically laws concerned with issues like violent crime or child abuse) is if they are shown by a properly conducted, double blind trial to reduce repeat offenses when compared to secular methods and punishments.
Given that this study would be difficult (if not just outright impossible) to conduct correctly, and the Church is about as likely to agree to engage in it as it is to reverse its stance on condoms, I think we ought to legislate on the null hypothesis until the Church sees fit to disprove it and the obvious null hypothesis is that confession is no more effective than taking to a secular counselor.
In short, I think the C. Church is in the wrong here. I don't care that this comes in the wake of a child abuse scandal in Ireland, and I hope I would say the same things if the C. Church had as impeccable a record in the child abuse department as it does in other areas.
Religious exemption IS an very important part of a free society. The Primate is dead on there. Unfortunately protecting citizens from child abuse is more important role of government in my mind.
On a related issue, I'm proud to say that my home state, Oregon, recently passed a bill explicitly removing exemption in cases where simple medical treatment could save children. I wish that parents letting their children die of treatable problems like Diabetes and Appendicitis for religious reasons was a non-issue. I wish I could write this both the Oregon bill and Ireland's policy off as political jousting directed at restricting religious freedom. I can't, because children die of religious ignorance all the time[whatstheharm.net - Very incomplete list, some entries are not due to medical ignorance.]. I can't dismiss the importance of this policy in Ireland because the Church's inaction in these cases has the potential to cause enormous harm to children (Again, I would be more than happy to revise my opinion here, of course, if the Church can show that Confession does a better job than Secular methods in a controlled trial.). That is a crime in the most basic sense of the word.
With all that in mind, there are some amazing things happening here at MIT. Instead of ranting in my dorm room, I'm going to go out and get involved in some of them. Later.
~Ninjinuity

Off to MIT

2011-08-20T05:42:00.000-07:00

I thought for a long time about what I was going to say here to show that I wasn't scared. In the end, that would be a lie. I am scared, scared out of my mind.
At least I'm excited.

On Regression to the Mean.

2011-08-09T18:51:00.000-07:00

   It's been almost a full year and a half since I wrote On Grades. On that time, I've come a lot further than I imagined possible then. I managed to patch up my mediocre grades and scored 5s on all 6 APs I took that march. I won the State Siemens Award for Oregon (Dad - if you ever read this, thank you for believing in me when I didn't believe in myself). Somehow, my sub-par GPA didn't keep me out of MIT, a school which I'd already given up all hope of attending (I still catch myself once or twice a week wondering if there's been some mistake, or I applied to the wrong MIT somehow, or if I'm just downright bonkers. It's been more than a half year since I was accepted.).
   There are some bit of the On Grades pessimism that still apply. I am still living in a very small pond, and I am about to be thrown into an ocean. I am certain that at MIT I will not be in the to 10% as I am here. I probably won't even measure up to the average student. I still lack diligence. I lack experience, and I'm too used to running into tests and quizzes unprepared, counting on my logic and intuition to get me good scores. That will not, cannot, work here.
   Most of all, I'm afraid of how I might react when I'm faced with a challenge that will take more intelligence than I possess to overcome, while surrounded by people who may very well see obvious solutions. I'm afraid of being thrown into an environment where so much of my self identity will be so common place, because to at least some degree, I rely on that to drive me.
   I have hope. I was easily out gunned by some people at SUMaC last year, and it just made me work harder. What I have considered my identity has changed in the past, and as it does I generally become more comfortable. Perhaps being in an environment where I'm no longer near the top of the pack will give me an opportunity to find an identity that's more healthily linked to my academics. Despite my fears, I really can only look forward to being surrounded by people who share the same sorts of enthusiasms as myself.
I have one more week left here, and then it is time to fly away from this little valley behind for the time being. Despite my constant complaining, I'm going to miss everything about it.
~Ninjinuity

An open letter to Google.

2011-07-25T14:29:00.000-07:00

Here we are, only a little more than a week after I've deleted my facebook, and I can't help but feel the temptation to go back and stop the process. Only my lingering anger, and the time I invested in getting my data out are keeping me from doing it.
At the heart of why I'm writing this (still pointless) apostrophe to you. At stake here is your cleanup of Google+ accounts with false names. I wish there was some sort of official statement I could link to instead of that article, but I can't find one. Basically, those users who either have used pseudonyms on Google+, or have multiple Google accounts, seem to be at risk of being locked out of (in some cases at least, though accounts vary) the rest of their Google account. I admit, this is especially disturbing to me because I technically fall into both categories (if you're from Google, please read on as I explain why I believe this is a technicality.).

Like countless other middle schoolers, I came up with [what seemed at the time to be] an awesome screen name. I made a Google account under that name, and used it for several years. As I got older, the novelty obviously wore off, and I've moved to a Google account registered under my actual name (with the exceptions I'm going to note below). I really tried to keep a single account. Who wants to deal with POP forwarding due to a changed email address, not to mention the other data migration that has to happen? Not me. Still, the long and short of what I found was that I could keep my screen name, or move to an account with my actual name on it. I chose the latter.
I'm gonna come straight out and say that my name is Will. That's the name I've used in real life for as long as I can remember, and that's the name I've used in my digital interactions for most of high school. If I called myself anything else online or in real life, people would have trouble finding me. Isn't that what's in a name?
If my account was suspended could I stand up to your alleged litmus test? According to Kirrily “Skud” Robert, who had her account suspended, said she was asked to "give them [Google] a scan of my photo ID (obscuring “personal information”, whatever that means), or links to places on the web that demonstrate that this is my name." in order to restore her account.
I could link to a few locations on the web that would say my name was Will. There's an odd photo from a seminar I did, there are a few newspaper articles, etc. I might be able to pull that off.
If I couldn't? I'd have to send in my ID, where it would quickly be discovered that my legal name is, in fact, William.
This would probably (and hopefully) be no big deal. But still, there's a lesson here: names are kind of nebulous. Pseudonyms are common, and they aren't always attempts to obscure things. There are times when they're the sincere representations of a person and the legal name isn't.
Google, I totally get where you're coming from here. You don't want Google+ turning into Myspace or Twitter. You want a mirror of the real world, and you want to capture the way people interact offline and bring it into their online lives. I think that's admirable, and I see where fake names (especially total pseudonyms) get in the way of that. Can't you see where pseudonyms fit in? One of the core premises of the Google+ project is that people interact with different groups of people differently. People will adopt separate public personas on Google+. You should want them too, because some of those public personas have a lot more influence than their real ones.
I guess I'm just disappointed. It's reasonable for you to strictly police a limited field trial of your big push into social networks. Though I think your reasoning is pretty naive in some cases, I see why you're doing it. Locking people out of the rest of their accounts? That's different.
I came to Google+ because of data liberation concerns. I hope I don't have to leave it because of concerns that entrusting you with my social data will mean you prevent me from accessing other pieces of data. As of now, I've taken the following steps, which, as a company, I hope you find disturbing:

I've exported all my Google Docs, and begun to delete all but my shared documents. I intend to avoid using Google Docs at all until my concerns on this issue have been laid to rest.
I've ensured that I have backups of all my pictures from Picasa, and I no longer intend to use Picasa to share images.
I've exported this blog with the intent to look into hosting it elsewhere.
I've exported all data associated with Google+ and Gmail. I will continue to use these services for the time being (albeit with frequent backups).

Wherever I run into a Google service I rely on for anything of substance, I intend to export my data and look fully for an alternative that I can manage myself. In fact, this whole incident turns makes me distrust cloud computing even more than I initially did. Beyond privacy and bandwidth hogging, why should I trust you ( or anyone else ) with my data if you can just lock me out of it? I'm making myself my own NAS, and I'll be posting a tutorial at some point in the near future.
It saddens me to see one of the few companies I trust act in this manner. I'd appreciate at least a formal statement on the matter.
~Ninjinuity

3D Scanning, the Bowyer-Watson Algorithm, and Real Time (maybe) Delaunay triangulation.

2011-07-19T00:37:00.000-07:00

Wasn't that a mouthful! I'm taking another look at my 3D scanner. I really haven't talked about this scanner very much on this blog, so I've posted a video of it I made earlier this fall as part of my MIT application above. I'll move a good deal of the content from that portion of my application onto this blog over time, so long as it doesn't become too obsolete.

There's still certainly room for improvement in the scanner itself. Much to it's detriment, it's still mostly manual and requires far too much tweaking on the software side to be actually useful. The hardware itself is also really flimsy. The Knex gearbox you can see in the video above keeps snapping apart if it's brushed wrong. In addition, it's final output is a point cloud, not an actual model. Yea. It's that bad. I have no idea how I got into MIT showing this kind of work off...
I've been inspired by this - a much more sophisticated way to 3D scan - to improve my own methods. I've already emailed ProFORMA's creator, (Dr.?) Qi Pan, asking if he has recommendations, or if he ever released the promised demo of ProFORMA, but I've decided to work on the assumption that I'm on my own in this for the time being.
This post will attempt to work on the implementation of basic methods adapted from ProFORMA to turn the point clouds into something coherent. I'm still in the process of porting my existing code to python (and making much needed simplifications to several parts of it.), so I'm going to assume I have a working way to obtain point clouds. In fact, I'm going to be extremely optimistic and assume that at some point I'll have a way to get bits of this point cloud in real time (FYI, I'm thinking of real-time in a 2-10 Hz sense, not a 30Hz sense).
All this relies heavily on producing the Delaney Triangulation of the pointcloud. If you don't understand the Wikipedia article (or don't want to read it), a Delaney Triangulation is a way obtain a reasonably sparse (and somewhat physically sensible) mesh from a pointcloud. The Bowyer-Watson algorithm is a way to build a Delaney Triangulation by adding a single point at a time to an existing Delaney Triangulation of part of the final pointcloud.
I've got my own (to my knowledge) way to improve the algorithm a little bit: I'm going to represent the resulting triangulation with a graph. Simplexes will be nodes, and their shared surfaces (in the 3D case, faces) are edges. While researching the Bowyer-Watson algorithm, I saw a couple different data structures used to represent the Triangulation. All of them improved performance, but none of them worked as naturally as I think a Graph does. The Graph is most obviously advantageous this has comes when identifying the cavity created by the addition of each new point. Since this cavity has to be simply connected, finding it becomes as simple as finding the first invalid simplex and performing a fill algorithm. The cavity itself (and the exterior space) can even be represented as a dummy node (since it's not necessarily a simplex itself), making it easy to identify the interior surfaces.

Anyways, it's late, and I'm going to catch some sleep. I'll finish this post up (and slap up some code to go with it) in the near future.

Why I'm leaving: An open letter to facebook

2011-07-15T17:22:00.000-07:00

Dear facebook,
A few years ago, in a fit of rebellious teenage rage, I joined facebook. I knew my parents didn't want me to have an account. I knew "all" my friends already did. I wanted to fit in.
Since then the idea of social networking has grown on me; I've come to know and love my facebook profile and it's not an easy decision to leave. What's triggered my decision to jump ship is simple: you won't give me my contact data back. I wanted some numbers to put on my phone and some gmail addresses. Your APIs wouldn't give them to me.

In my view, our relationship works like this: You give me a service, I give you screen time. In respect for this agreement, I spend the time to look over your advertisements. I click on ones that interest me. I've upheld my part of the bargain, and you've gotten paid for it. I would hope you're providing a service to me in exchange for this time: distributing the information on your servers so that other people I trust can find it and use it to contact me. I expect people to use this information to contact me outside of facebook as well as within it. It has come to my understanding that you feel differently about my user data. That's a big part of why I'm leaving.
I'm in the process of agglomerating all my data together, and I'd love to include all the info I've put into facebook, as well as what others have. This includes, for instance, most of the phone numbers of my close friends, which they've kept current. It includes birthday information, shared interests, and emails, much of which I can't get elsewhere. It's a treasure trove of data each and every piece of which ought to belong to the people who uploaded it. If you have reason to believe that it will be misused if downloaded by the people who can see it, you need to work on your privacy system.
I trust Google, and I don't trust you. Google's products work smoothly, and bugs tend to be quickly fixed. Your phonebook thinks there are 100 numbers between 1 and 99. Your chat continues to have graphical glitches on a semi-regular basis. I still don't know how the heck to retroactively manipulate lists after hours of clicking blue buttons. You've tweaked around with my privacy settings regularly, and, while Google has their screwup with Buzz, they seem a heck of a lot more sincere when they explain that they value user privacy.
Most of all, Google largely knows their place. They understand that, if I want to, I should be able to grab my stuff and leave. In contrast, you mess with your APIs to ensure I have to be tied to you. Google offers an austere "delete account" page. You jerk me around without restraint. You've lost my trust simply because you consistently send the message that you couldn't care less about your users, so long as they give you screen time.
This is my response: For the time being, I'm taking my ad revenue elsewhere.
~Ninjinuity
P.S.: If anyone wants an invite to G+, leave a comment with an email address. Comments are moderated, and I'll stop emails from showing up publicly. I'll send you an invite as soon as I can. Right now, you can only sign up if [google thinks ;)] you're 18 or older. Google has stated that this will not be the case once G+ becomes fully public, which is close enough now that I'm willing to jump ship.

Fear my pixelated magic!

2011-07-08T13:29:00.000-07:00

I got bored with my header, and decided to make a new one. Made with GIMP (From scratch!), uploaded to Dropbox, done. I wish I'd been able to give my ninja alter ego a slightly better left foot, but overall I'm happy with how it turned out.
I've also changed titles and dates over to a visually-consistent font with the font-family command. At the moment, this won't show up on firefox because my font files are hosted on dropbox and firefox won't show externally loaded fonts. I'll be tinkering around with this a little more.

Up, Up and Away

2011-07-08T12:02:00.000-07:00

It's over. The last launch has happened roughly on schedule (somewhat surprisingly, given the weather), and Atlantis is in orbit. The shuttle is something I grew up with. I had shuttle shaped toys throughout childhood. A picture of an old discovery launch taken by my mom hung on my wall until very recently. The shuttle is a symbol of what humanity can do when we work together towards a higher goal in the same way the ISS is. I can only hope the event we've seen is, ultimately, a step forward, not a step back. I'm all for commercialization of space flight, but I hope that we're not sacrificing our capability to put humans into space for nothing. Here's to a safe final flight for Atlantis.

Ordinals...

2011-07-06T19:02:00.000-07:00

Said Conrad Cornelius O'Donald O'Dell,

My very young friend who is learning to spell,

"The A is for Ape. And the B is for Bear.

The C is for Camel. The H is for Hare.

The M is for Mouse. And the R is for Rat.

I know all the twenty-six letters like that...

... through to Z is for Zebra. I know them all well.

So now I know everything anyone knows

From beginning to end. From the start to the close.

Because Z is as far as the alphabet goes."

Then he almost fell flat on his face on the floor

When I picked up the chalk and drew one letter more!

A letter he never had dreamed of before!

And I said, "You can stop, if you want, with the Z

Because most people stop with the Z

But not me!

In the places I go there are things that I see

That I never could spell if I stopped with the Z.

I'm telling you this 'cause you're one of my friends.

My alphabet starts where your alphabet ends!"

~Doctor Seuss

How to liberate your phone book from facebook

2011-07-06T18:37:00.000-07:00

This is a quickly written, hacky script for personal use. For the time being, this script will only work on 99 friends at a time (Amusingly, facebook thinks there are 100 on the first page, but you're welcome to count. There are 99. Buggy programming FTW!). I'm playing with a workaround, but don't hold your breath. In the meantime, you can do the following to take your friend's phone numbers back into your own care:

Login to facebook.
Go to http://www.facebook.com/friends/edit/?sk=phonebook&offset=0 (or, if you're looking to get contacts 100-199, etc, change the "offset=" term).
Press ctrl+a, ctrl+c to grab your info.
Open up your favorite text editor and paste (ctrl+v) into a blank file. Save this file as "raw_phones.txt".
Download "fb_phone_to_csv.py"[Dropbox]. Save it into the same directory as "raw_phones.txt". Run it (you'll need python.).
You ought to see a new file in the directory, "phone_numbers.csv". This contains your phone's information, formatted in a Google CSV.

This CSV can be directly uploaded to Gmail, and merged into any existing data you might have, as is described below.

Login to Gmail.
On the left, click Contacts.
Click "More Actions">"Import"
Select "phone_numbers.csv" (created above) and hit import!
Once this is done, click "More Actions">"Find & merge duplicates". Check the duplicates it finds and accept what you want to.
Done! Your facebook phone numbers are all integrated. You can go to "More Actions">"Export" to move your Gmail contacts elsewhere if you want to.

It's a shame facebook doesn't hold itself to the same kind of integrity and responsibility when it comes to user data that Google does. If they did, this tutorial would be a hell of a lot shorter.

Boring legal stuff, etc:
I'm releasing the .py file above under an MIT Software Licence. You are free to make derivative works, ports, or apps (and even sell them). I do appreciate credit though, and I ask that you seriously consider releasing any derivatives for free.
If you have improvements you'd like me to incorporate, feel free to comment with a Dropbox link (or similar). I'll patch it if your code looks useful and give you credit.
~Ninjinuity

Coding music...

2011-06-25T12:28:00.000-07:00

When I'm planning, I play Mozart or similar. When I'm coding, it's Techno and Electronica all the way (The Frozen Synapse soundtrack is good too, by the way...), for debugging, Amiina. Some days, I have a feeling I'd put my keyboard through a window any other way...

Cellular Turing Machines(Physics Simulation)

2011-01-12T16:40:00.000-08:00

If everything works as planned, we've go our creature all the way manufactured, popped out, everything. It's sitting in the environment, ready to rock and roll. Now what?

Ultimately, I want these creatures to do everything you might expect of a normal creature. They should move around, mate, sense their environment, etc., all in a continuous simulation. I don't want to be that complicated off the bat. The first version will only have the one creature at a time, but I do need to consider how these sorts of things might be implemented later when I'm designing the physics now.
Here's what we have to work with: we have our creatures, and every tick of the game, every node in their body engages in a cyclic cellular automata, the end result being a new state. Each node has a list of other node's its linked to. It has a number associated with it, which for the purposes of the physics simulation I am going to take to be amath 1, 2, 3, 4, ..., n endmath.
I'm not planning to emulate real world physics. There will be similarities (I'm going to introduce a gravity force (and perhaps a sort of friction force if necessary), for instance) but there will also be differences (I won't implement velocities into the nodes. Forces applied to the nodes will just directly move them, and every step those forces are recalculated.). I'm looking to create an interesting and complex environment, but also one that is quick and simple to implement and simulate.
The physics simulation is going to treat each link a a weird sort of spring whose equilibrium length can change. If we are considering the link between nodes amath A endmath with value amath a endmath, and amath B endmath with amath b endmath, then the equilibrium length will be amath e = ab % n +1 endmath. The force exerted by a spring that is stretched to length amath l endmath will be amath F(l)=e^2-l^2 endmath, the force on node A being exerted in the same direction as the vector from B to A.
Gravity will simply be a constant downward force. The ground will exert a normal force exactly sufficient to keep every node no lower than the level of the ground. If friction is implemented, it will be a force that simply opposes horizontal movement of nodes that are on the ground.
Every step, all the forces acting on a node will be summed up, and the node will move, its new position being the sum of its old position and the net force. Then I'll pass the creature back to the Cyclic Automata to update the node values, and do it all again.

I only wish you could dream.

2011-01-06T17:50:00.000-08:00

May God us keep From Single vision & Newtons sleep.
—William Blake

   Science is amazing. Think about it, take a look around, and hopefully you'll see what I mean. Heck, don't take a look around. Stare straight at these words on this screen, and realize how incredible it is that we can control electrons to such a degree we can make them take these words from my screen onto yours. It's something almost laughably absurd, it's absolutely ludicrous, but it's reality, the reality we live in because of the generations of scientists who first messed around with amber and cat fur. We owe our modern standard of life to the generations that sought not just to live in, but also to understand the universe and to the people who wrenched every drop out of our collective knowledge and back into the bucket of tools we have to confront and observe the natural world.

   There is a tendency (which has existed, to some extent, since science first truly came to bat) to see this world, the world that Science has shaped for us, as a place that undervalues humanity, a place where we must either reject and decry Science (but not, of course, our televisions, computers, or modern medications) as "soulless", suffering from Blake's "Single vision", or one where we must sit passively by and wait for mad Science to kill us all.
   I think it's in this kind of pessimistic spirit that people will casually banter about how, for instance, "[In eastern Europe,] if you're smart, they don't teach you how to think, they teach you how to do Physics and Math.", as if the two were unrelated, or even antithetical. It's this mindset that leads individuals to ask, without a trace of irony, "Have we become robotic? ... Is {name of my highschool} just one more place that teaches you to be robotic?". There's this weirdly prevalent idea in the public that Science is an uncreative process, some sort of unskilled labor where you just pick the laws of the universe off some cosmic manufacturing line and package them up for publication in textbooks.
    Part of the problem is outreach. Scientists occasionally have this unspoken assumption that the public will automatically appreciate that their work has practical applications and aesthetic beauty, which (unfortunately) doesn't seem to be true. We need more people like Sagan who are willing to dedicate time to helping the public understand how their field appreciates the world. We need them from more fields than just Astronomy. Where are the biochemists who are capturing the popular imagination? Where are the Mathematicians? Mathematicians, who get an especially short stick in the public eye, need all the public excitement they can get. Science can't treat PR as given, and it's to blame for this part of the discrepancy.
   Nonetheless, there are also cultural problems for science that really aren't its responsibility. Americans can have a hard time accepting the mix of certainty and uncertainty science thrives on. Its not part of our philosophical heritage. To some people, I think, the process of systematically shooting down your own ideas whenever you cannot find reason not to seems like a practice in closed thinking, a way to destroy any source of human wonder at the world. To the layperson, math often seems like what it was for them in school-a blind trudge through dark woods on the way to a robotic hell, glowered over by their own faculty of beasts. In their view, who could stand to devote their life to such a pursuit? How boring and masochistic mathematicians must be!
   If you're one of these people, I'm sincerely asking you to reconsider. Please, don't take my word for it. Read some of the many books written by scientists and mathematicians about their field and it's wonders. I'd suggest Ian Stewart's Letters to a Young Mathematician.

Holophonic Sound (Head Design)

2010-12-26T21:30:00.000-08:00

After some Searching in the SketchUp Warehouse, I found this model of a shaved head. It's exactly what I was looking for: accurate, but very low poly and not overdone. I decided to take a lateral slice every inch, and disaster struck.

The slicer plugin I use has some problems, especially when it's working with complex or imported models (I think this was originally put together in Collada), it tends to "miss" slices. It's free, and it usually works like a charm, so I can't really complain, but it still hung me up for a while.

In the end, I found a workaround. First, I sliced caudally with amath 1/4 endmath " slices(It still missed slices, but not near as many.), then sliced laterally with my originally planned 1 inch slices (I also paired slices that were similar to each other). I then used the Arc/Beizer curve tools to make smooth approximations.
Done! I have my file ready to print out and cut, I just need to make a hot wire and get some foam (I'm thinking polystyrene from HomeDepot). I think I'll make the modifications to make it a bust once I've printed it. It's difficult to make the bust sheets of foam in SketchUp.

Holophonic Sound (Overview)

2010-12-26T20:12:00.000-08:00

Given that I'm about done with my 3D scanner (I promise I'll put an overview up soon), I've been looking around for a new project. I recently happened across this mp3 (Headphones are needed for the full effect)

It's not the first time I've heard it, but it's still impressive. On a whim, I decided I'd try my hand at my own holophonic recording setup (might make long distance Skype calls more pleasant if the audio is good enough), and I started to do some research. Cetera doesn't seem to have commercialized their technique, and I couldn't find much in the way of software to simulate the effect, so it comes down to the physical setup (which also doesn't seem to be commercialized), and homebrew code tinkering.

To get the best effects, it seems you need not just to position two microphones in the correct places, but also to put a physical "head" between them. This seems like the hardest part to me, so it's where I'll focus my efforts, at least until I get things working.

What still isn't clear to me is exactly how much detail the head needs. Other homemade setups I looked at had a nose on the head, and depressions for eyes, but my guess is that these don't add much in the end (I'll probably do them anyways though, for aesthetic reason if no others. A head without a face might be too creepy for me.). I'd imagine that good models of the ears are important (they're certainly hard enough to find), and of course that the microphones need to be high enough quality to pick up on the detail necessary for the sound.

At this point in time, my plans are as follows (I'll probably do a blog post on each part):

Find good model ears (or figure out how to make good resin casts of my own. Seems unpleasant, but it might be the cheapest way.) and reasonably priced small microphones(?).
Get a good model of the human head online, and slice it up in SketchUp to get rough cross sections, say, every inch and a half. I'm thinking something like a bust so it can stand itself up.
Build a hotwire (something that's been on my list for a while) and make cross sections out of inch and a half thick insulation foam to assemble. Make it look pretty (or at least OK. I know how these things go.), and cut out internal spaces so all the electronics fit, etc.

Equations Work!

2010-12-20T17:43:00.000-08:00

With some help from this post, my blog now supports awesome looking equations (no more blurry bitmaps!). As such, I no longer hesitate to note that E=m c^2 , e^{\pi i}+1=0, and of course that amath \frac{d}{dx}\int_C^x f(t) dt = f(x) .
Cheers!
Ninjinuity

Note: Equations seem to look best in Firefox. They don't work at all in IE (no surprises there), and they don't quite work in Chrome. I'll keep looking into this. The script also seems to be picking up weird elements of the page and replacing them. I need to stop that.

Edit: The old equations code was inconsistent and had a habit of changing stuff not inside it's tags. With this new back end, they should work everywhere.

Math Puzzler #3

2010-12-20T17:27:00.000-08:00

There are six Dudeney numbers, positive integers whose decimal digit sum cubed is equal to the original number. they are
amath 1=1^3=(1)^3 endmath,
amath 512=8^3=(5+1+2)^3 endmath,
amath 4913=17^3=(4+9+1+3)^3 endmath,
amath 5832=18^3=(5+8+3+2)^3 endmath,
amath 17576=26^3=(1+7+5+7+6)^3 endmath,
and amath 19683=27^3=(1+9+6+8+3)^3 amath.

Prove there are no larger Dudeney numbers.
Find all numbers where the fourth power of the digit sum is equal to the number itself.

Hint: A computer may be useful to check cases, but it is possible to do this problem by hand, albeit with a bit of paper.
Solution 1 after the jump, Solution 2 next week.

I've done this all by hand, and I'll write it out here(save a bunch of space consuming checks at the end) then post python code I used to check the solutions more efficiently.
First, let's show that sufficiently large numbers cannot be Dudeney (Thanks to Hostile Fork for the idea). Note that
amath DigitSum ( n ) <= 9 * DigitCount ( n ) endmath and amath DigitCount ( n ) < log_10 ( n ) + 1 endmath so amath DigitSum ( n ) < 9*log_10 ( n ) + 9 endmath. amath n^3 endmath is a Dudeney number if and only if amath n = DigitSum ( n^3 ) endmath. This means amath n < 27*log_10 ( n ) + 9 endmath. By hand, it's clear that amath 10^2=100 endmath is an upper bound for amath n endmath. Solving the inequity above with a computer shows that amath n < 57 endmath. Either way,now we can check each possible n to see if it is a Dudeney number. 19683 is indeed the largest Dudeney number. Here's my code.
If you looked at my code above, the solution here should be obvious. We know we want amath n = DigitSum ( n^4 ) endmath, so amath n < 36*log_10 ( n ) + 9 endmath.This gives us amath n<77 endmath. Testing cases gives us that 1, 2401, 234256, 390625, 614656, and 1679616 are the fourth powers which satisfy our condition. My code.

Still pinching myself.

2010-12-17T19:06:00.000-08:00

I waited for a day to make this post, to make sure there was no mistake.

I got in to MIT. I suppose its hard to communicate how excited I am about this. It's been a major goal since middle school, but always kind of the ideal that I shot for, never expecting to really make it. Now I'm in. Surreal feeling, let me tell you.

I plan to apply a few other places, and I'll give them fair hearing in the spring if I get in, but there's a major part of me that just wants to tell MIT yes and be done. I mean, it's MIT. Come on.

I was really touched today by the sheer number of people who contacted me to see whether I got in, did a little jig when I said yes, or told me today they'd had little panic attacks on my behalf (though that's kinda perverse sounding when I think about it). I didn't know so many people cared. Thanks guys (not exactly like anyone reads this though. ).

I admit, I've let this blog lie fallow. In the interest of not becoming this guy, I'm going to leave that statement there, and move on. I've certainly got some exciting things (I think) to talk about: I've built a 3D scanner in the past year, I've collected gaboodles of interesting math problems (harder than the ones I've posted so far), and I'm looking around for a new project. I may even post some more sketches soon. In any case, I think I'll post more often unless circumstances change.

Best,
~Ninjinuity

Yet another sketch...

2010-03-07T10:43:00.000-08:00

This time from my sophmore biology lab book. This is a sketch of a bullfrog hand from when we were doing dissections. I've got quite a few sketches from my lab book, so I'll post them periodically.

Math Puzzler #2

2010-03-05T22:50:00.000-08:00

Take a power of two. Rearrange the digits. Can you ever have a second power of two? For simple problem, neglect leading zeros. For a harder one (which I haven't yet solved), don't.

Solutions after the jump.

The solution for the simple problem...

For proof by contradiction, assume there are two such powers:

`n=2^l`
`m=2^k`

Further assume amath n>m endmath.

Like the difference of any two rearrangements of the same digits, `n-m` must be a multiple of nine (A future puzzler will make clear why this must be so).

However, amath n-m=2^l-2^k endmath can be factored into a Mersenne number and a power of two ( amath 2^k(2^(l-k)-1) endmath ). If `n` and `m` are the same length, `l-k` must be less than `4` (`2^4>10`), so the Mersenne number can only be `1`, `3`, or `7`, none of which are multiples of nine.

Therefore such `n` and `m` cannot exist.

Another sketch...

2010-03-04T21:30:00.000-08:00

Normally, I can't draw anything. I really can't. No perspective, and my scaling is horrible. Once in a while though, something just comes out. This picture came out yesterday. It's not great, but hey, it's better than most of my scribbles! I was thinking about fruit flies and dinosaurs, and I drew this in the midst of my randomness. So here it is. Enjoy!

Math Puzzler #1

2010-02-25T19:48:00.000-08:00

I'm going to post math problems, both those I write, and those I find interesting. So for the first math problem!
Question:

Two quadratics both pass through opposite corners of a rectangle whose sides are parallel to the xy-Cartesian axes. One quadratic has it's vertex on the lower left corner, but also passes through the upper right corner, and the second has it's vertex on the upper right, but also passes through the lower left. These two quadratics form a region within the rectangle. What fraction of the area of the rectangle is the area of this region?

Answer:Relocate the coordinate axes so that the origin lies on the lower left hand corner. The upper right hand corner is at a point `(m,n)`. The equation of one polynomial is `(n/m^2)x^2`, the equation of the other is `(n/m^2)(2mx-x^2)`. This results in the following integral: `int_0^m (n/m^2)(2mx-2x^2) dx = (2n/m^2)int_0^m mx - x^2 dx` evaluating gives `(2n/m^2)(m^3/2 - m^3/3)=1/3 mn ` ,so the total fraction of the area is `1/3`.

On grades

2010-02-23T20:52:00.000-08:00

This week has not been my best. The long and short of it is that my academics is in, if not dire, at least mediocre straits, and I have no one to blame but myself, as usual. The damage I've done is not horrible, and with hard work over the next few weeks, I can mostly erase it, but it falls inconveniently across a progress report, so I will likely catch some flack from my parents. More than that though, I've realized that I've been, up to now, motivated out of fear of my parents.

My academic goals are not really my own, and that needs to change. It isn't the first time I've realized this, but nevertheless, I truly want to change this. A first step, I figure, is putting my thoughts into words on a page, so I can comeback and revisit my conviction when I feel unmotivated in the future.

Right now, I'm a small fish in a small pond. Sure, I can do some math, run a few miles, or program when I want to, but ultimately, all this adds up to very little. Right now, I'm a kid sitting around in a backwater of I-5, playing with my calculator and doing little else. I want to change that. I can assure you that this is my own conviction, and one I hold very deeply. I want to be someone, and do something meaningful, even if I am never recognized for it, because I truly believe that the hard work of an individual can make a positive difference on the world, large as it is, and a significant one at that. Since I was in middle school, it's always been very clear to me that I can make the best use of my talents in math and science.

I am no longer as naive as I once was, however, and I cannot pretend that latent talent and potential will ensure a good future. More than that, I understand that all the talent in the world is useless without proper perspective and diligence. In these two areas, I find myself badly lacking. Perhaps through deep thought, I can come to have better perspective, but diligence is more of a conundrum for me.

So right now, I'll state my goals, in the hopes that I can keep them in view when the rat race gets boring. I want to go to MIT, find a subject that I love, and devote the rest of my life to prying out it's secrets and examine it's crannies. I want to push some field forward, find applications to save and improve lives, however distant a possibility that might seem in the process. If I can, I'd like to live a life so that neither joy nor regret are felt when I am extinguished. I feel strongly about all of this.

My GPA as it stands may ruin my chances at MIT. I can no longer naively expect to demonstrate to them that they should take me by merit of high test scores alone. MIT doesn't want students who can't stay focused when they are not interested in a subject. Without diligence, I cannot expect to have a shot at acceptance there. It is only my arrogant nature that perceives classes as below me, not any fact. If I cannot excel in subjects I find uninteresting, I will never succeed at my admittedly lofty goals. So yes, I do want to do well in all my academics. For myself, not for others. I want to achieve something, something I think is truly important, and to do that I need to stop motivating myself with fear, with whims and fancies. I need to gain focus, and diligence. I need to find organization, and order. Talent is far less than half the battle, an as I've learned this week, it's a battle I'm slowly but surely losing, just as the fighting within me has begun.

Life...

2009-12-17T19:26:00.000-08:00

...Isn't at it's best right now. I've come down with a nasty crud, and I have a ton of homework to try to get my GPA to a 4.0 before the semester finishes. Luckily I have a break after tomorrow. I'm just gonna ramble for a while, and see if it makes me feel better. Feel free to skip this one.

In other news, I've developed one of my peripheral interests, Computational Neuroscience. Ive come up with a method to quantify which cells in a given neural network are providing or interpreting "information"(not in the technical sense of the word, but I don't know a better term). By my reckoning, it's either probably really interesting, or it's something done decades ago that I just rediscovered. Either way, I find it interesting, so perhaps I'll do a post on it in the near future. The reason for all this interest is a summer program, RSI.

If you don't know, RSI is an amazing program at MIT. Basically you spend the summer writing a paper, and at the end of the program, you publish. You have a mentor (usually a professor at MIT), and some field in which to do research. If you get in, it's also an indicator that you're top stuff: overwhelmingly, attendees are accepted at MIT, etc. In short, this is an amazing program I really want to attend. The catch? There are only 80 spots. 30 are given to international students, the remaining 50 go to US students by region. That works out well for me (an Oregonian), but I'm still not absolutely sure I have the stuff to make it. I have my fingers crossed, and my application is in the mail.

In any case, one of the essay question asked me to list two fields->sub-fields interests I'd like to study and interesting questionions in those sub-fields. Given a recent fascination with neural networks (which is kind of a strange result of studying physiology along with data mining and AI at Stanford this summer), my first (and in my opinion better) choice was computational neuroscience. I wrote about the potential for new computer algorithms to attempt to duplicate the remarkable success of the brain when it comes to image recognition, and the potential for existing data mining techniques to uncover broad patterns of neuron behavior, and assist in statistical analysis of networks.

My second essay, was on material science, and specifically the nondestructive evaluation of structural ceramics. This is a practical interest of mine: it would be wonderful to be able to detect strains on materials in use, especially if such a technique could be make cheaply. In this manner, one could automatically detect structural defects in, for example, bridges or other common structures. This would lead to an effective early warning system for such structures.

We shall see. I'm pretty proud of my essays, my PSATs (CR:77, M:79, Wr:80, NMSF with any luck!), etc. I just hope that a)My non 4.0 GPA doesn't kill it, and b) I'm not putting myself into a pond I'm vastly unprepared for.

TI83+ Programming....

2009-11-16T19:26:00.001-08:00

After today's WSJ article about the TI83+'s codes, I have a renewed interest in programming. I'd love to make my own Mathematics and/or Chemistry OS.... I'll keep you posted.

And I made pong on my calculator! Quite neat. Runs better on a TI84 than my TI83+, but still, the code's pretty short, and I'm happy with how it turned out. Perhaps I'll do a separate post with some screenshots. Gonna try PacMan next.

Drosophila Suzukii

2009-11-11T17:15:00.000-08:00

Edit: This is in need of a rewrite and an update. It's on my list.
So I've kept kinda quiet about this up to now(at least on this blog if nowhere else), but I figure I might as well recount what's happened in the week or so leading up to this post. It's a long and convoluted story, so you might want to get comfortable.
This all starts with a rather simple lab in Sophomore year biology: paper cutouts of different colors were thrown on different patterned/colored backgrounds, the students had about half a minute to grab cutouts, then the cutouts were tallied, and replaced with more cutouts of equally proportioned colors, and the cycle was repeated. Pretty standard demonstration just to show how unconscious (and hence somewhat natural) selection can have huge effects on allele frequency. Simple enough. However, after reading Richard Dawkin's book, The Greatest Show On Earth, and learning Dr. Lenski's brilliant E. coli experiment (as wells as several others mentioned in the book), I wanted to try to take this a step further.
My initial idea was to attempt this with rotifers and vary the salinity of their solution, but several problems with this quickly showed up. I wasn't sure where to find a food (algae presumably) that could endure both salt and fresh water, and didn't want to have to worry about varying algae populations. I wasn't certain how to quantify changes that could occur in the rotifers, and I wasn't sure how I was going to get a culture of water with only rotifers in it, to minimize predation. None of these things are unresolvable, but it was certainly enough for me to start shopping around for other options.
At this point (Early October), I began to correspond with my AP Bio teacher. He suggested using fruit flies(D. melanogaster) as the species of interest, given their short generation time, and the large number of mutations that have been breed out over time (not to mention the fact that AP Bio already has a fly lab, and thus I would have samples to work with). I agreed. I was, however, slightly worried that all the domestication would lead to a lack of variation: that all the flies (with the exception of the afore mentioned mutations) would effectively be genetically identical. I proposed catching wild flies, and then breeding them with the mutated flies to get a nice mix of both extreme mutation, and more subtle variation. So far so good.
Noticing a lot of fruit flies around our compost bin, I set out to capture some. My initial attempts at suctioning capture devices were no good. I inhaled three flies by accident, before realizing that even those flies I didn't ingest were dying of shock. I finally developed a more successful method, namely trapping the fruit flies under a test tube, then knocking it against a funnel until the flies fell into a larger jar. This worked pretty well, and over the course of a weekend, I had four colonies set up. This whole time, I wasn't paying a whole lot of attention to what I was catching (I actually later found a single mosquito in one of the colonies. Presumably I mistook it for a fly at the time). In any case, I didn't notice anything strange until the following Wednesday, when I first saw my flies next to the D. melanogaster from the lab. The first thing that stood out was the size. The wild flies (henceforth just my flies) were a lot bigger than the domesticated ones, as much as twice the size. There was also a significant variation in size among my flies, and several other strange features: the wings were a lot longer in proportion to the body, and some of the flies had spots on their wings. I admit, my first though was "That's just the local subspecies. It's good the flies are this strange, it'll help to introduce a lot of variation". In retrospect, this was exactly the wrong thing to think. My AP Bio teacher, however was spot on, suggesting that I might even have several Drosophila species in my cultures.
We went back and forth in email for a while, me (wrongly) arguing that there was only one species, my teacher arguing for multiple species. I'm pretty stubborn, and despite the fact that he had some extremely compelling arguments for why the flies couldn't be D. melanogaster, and why further more, they couldn't be the same species, I continued to assert that they were. If I learn anything from this experience, I hope it's that I should have given in as soon as he presented his evidence. It probably would have saved my some time.
In any case, I began (semi-secretly) searching for other species of Drosophila that I might have captured. I found one. Remember those wing spots? On an impulse,I googled "Wing Spot Fruit Fly". The fifth result? "Potential Fruit Fly Invasion Serious Threat For Oregon". I clicked it. The more I read, the more matched up. My flies were Spotted Wing Drosophila(Drosophila Suzukii), an invasive fly. I emailed my biology teacher, and after some deliberation, he agreed with me. We sent a sample home with a classmate of mine whose father works at the local extension agency. I also sent a sample up to the Department of Agriculture in Salem. And guess what? Apparently, not only was I right, but my flies are the first to be confirmed in my county! I got on the front page of the Locals section in two papers! Cool!
So what next? Well, I plan to do my selection lab with either them or the D. immigrans flies I caught at the same time, and I'll now be studying SWD overwintering patterns in the wild. I also MAY have discovered something quite neat, and also quite important, about SWD breeding in the lab, but I'll have to confirm it with experimentation before I post it here and make myself look like a fool.
Till Next Time,
Will

P.S. anyone on the west coast interested in tracking SWD populations near them should go here, where Mark Bolda has an excellent set of posts describing how to make and bait traps for them.

For once, a productive debate on Facebook!

2009-11-08T18:09:00.000-08:00

I had quite an interesting debate last night, in Facebook of all places! It hasn't quite come to any sort of close yet, but I figured I would post it here anyway. It all started when I posted this XKCD cartoon on Facebook. A few minutes later Mike commented, saying that he disagreed with the premise of the cartoon. This led to the following impromptu debate.
NOTE: I preformed a spell check on the text, and made a few very minor changes (second->2nd for consistency, etc.) but it is otherwise unedited.

Mike- I don't agree. First, the "house" is still there, just broken apart. A box of Legos is anything that can be built with them. Secondly, Cryonics.

Me- Aren't the Legos therefore anything that could be built with them, even if they haven't been put into that configuration yet? What about other interchangeable parts, like atoms, or molecules? Does that mean that people who don't yet physically exist, or even never physically will exist, do? It's an awful slippery slope to equate potential with existence.
And second, from a practical stand point, don't you find it arrogant to value an undeveloped, and even questionably possible procedure to perhaps save your own life over a procedure we KNOW can save multiple others?

Mike- Yes. The amount and quantity of atoms to make a Will [my name] is Will, it just hasn't been assembled yet. A young me is me in the same way that an old me is me. And why is believing in that a slippery slope? Because it is unconventional or something?
Yes. Your body is yours, and you do not owe it to humanity when your are dead. By your logic, wouldn't it be arrogant to smoke, eat fast food, or do anything remotely bad to your health because your body could be used by others?

Me- I disagree. First off, it's that assembly we are talking about. not the potential for the assembly to exist, but the actual existence of that assembly, even withstanding it's physical existence.The configuration of atoms used to make a young you is completely different than that of you now. The configuration changed, and that old configuration no longer physically exists.
Where are these endless configuration stored? Do they take up space, or clutter the proverbial attic? If not, by what definition do you argue they exist? This is the slippery slope. How can you define existence to include these configuration but not include, say unicorns, at least to some extent physically possible. If your definition does allow unicorns to "exist" without evidence of their physical existence, hasn't your definition lost it's potency, even it's usefulness?
@2nd I think there is a balance to be struck between selflessness, and self-service. As a social animal, living in a society, there is a level of debt that I do owe to humanity, solely because I expect to partake in it's benefits. In addition to this, I actually can become a happier person (and who wouldn't want that?) by giving back more than my share. As a communal animal, I can expect only to receive that I'm willing to give. I don't see cryogenics as a truly viable option (much akin to a sort of scientific Pascal's Wager), and thus have no qualms with being an organ donor. If I needed an organ, I would certainly want others to be organ donors, and thus I see no reason not to be one myself. I'm certainly not going to be around to care.

Mike- Yes, I am made differently that I was when I was young. But, I am still me.

As unicorns must be made of atoms, atoms can be considered unicorn pieces. The assembled unicorn doesn't exist, but it's pieces do. They could have existed at some point in time. I fully support what you are saying, that parts by themselves do not constitute existence. What I disagree with is when the comic says the assembly is gone. It was never there in the first place; even the concept of an "assembled" object is subjective. People give meaning to the concept of house, logically, just because the parts exist is evidence of the whole existing.
@2nd: Debt is a non-natural concept. Happiness is made for yourself. I do not expect to receive something, but I do not reject it. Cryogenics is far from being analogous to Pascal's Wager; as the state of "life" is electric signals being transmitted to form a level of sentience (effectively a program), and as humanity is continually increasing technological boundaries, the ability to repair and control things at the atomic level is inevitable.

Me- @1st The assembly was never there in the first place? I would say it certainly was (unless you mean this in the trivial sense that it was never technically in the cartoon). Certainly the idea of what constitutes assembly is subjective, but it can be objectively defined to a point! Even withstanding this, I'm sure we could agree that some things are assembled. Both you and the Lego house have properties parts alone would not (even objective ones, I bet the house could keep some water in, something the blocks alone, or in some other configuration, couldn't), and that some of these are properties that other physical ordering wouldn't have produced. While there is a subjective element that clouds the discussion, I think it a step to far to declare the Lego house never existed.
@2nd As is society itself. And i might even disagree that you distinction is valid or sensical. Animals can show that they feel indebted to others, have senses of Justice and morality. Are these all "non-natural"? I would also point out your subtle use of naturalistic fallacy here. What is natural is not what is right, wrong, or really anything else. It's what is natural.
Happiness (like debt) is a useful tool developed in our evolution. It can be (and is) used to produce behaviors by incentive. As a social animal, some of the behaviors I receive joy from come out of helping others, and being helped by others. Happiness to a large degree does drive us to do communal things, because doing communal things is more beneficial to all of us than doing solitary things. Society itself stands as evidence. As for cryogenics,if we were to have that much atomic control, would it truly matter should you be missing your heart or liver? Why not give these things to people who need then NOW, rather than pretend that such advanced future technology would be unable to provide suitable replacements? The parallels with pascal's wager persist. Here's a quote with only a few words replaced.
"It makes more sense to be cryogenically preserved than not. If you are preserved, and the technology is developed, you will be revived, and live on in the future. If you do not preserve yourself, and the technology is developed, you will not be revived. If technology is never developed, you have lost nothing either way."-I had to change very few phrases at all, hmm?

Mike- @1st: Things may be assembled in the societal definition of the world, but a bunch of random atoms = a bunch of random atoms, and a human = a bunch of random atoms. Unless you somehow figure out how to fuse the most currently known elementary particle, really, nothing can be assembled. The house does not exist, it is a term we use to refer to a specific collection of atoms.
@2nd: Yes, all society is unnatural. I am using the concept of natural as that of what would be considered most efficient, not that of animals, and trees. Emotions, and culture trained responses, such as love, obligation, ect, have no value other then to produce pleasure which really is a self induced occurrence.
I am not assuming that it is likely said technology will exist. I am using scientific precedent, in the case of Moore's law, to reliably predict we will advance that far. Pascal's wager was pure conjecture, as it is impossible to know for sure of god, the very definition of which makes it impossible to know....

Me- @1st All definitions are societal. They are pragmatic, and they are to some degree necessary. As such, I think we can define something as assembled in the same way we might define a table or chair. I think we could, should you agree, define an assembled object as one that has properties beyond those of it's constituent parts alone. It's a poor definition, and one in need of refining, but it might work for this discussion. Every thing is "a bunch of random atoms". You, the computer, the world. It's simply not practical to think of things that way.
@2nd Strangely, I think we are on the same page as far as the debt thing (I still see hints of Naturalistic fallacy though). Yes, all this is self induced, but that's kinda the whole point. The desire to survive is self induced as well, isn't it?
@3rd I think the existence of future Cryogenic technology is a lot like the Existence of God, regardless of Moore's Law. To pull two of the afore mentioned objections...
How do you presume to know that current cryogenic technique will be compatible with future technologies? Certainly those used in the past have been deeply flawed, including suchblunders as freezing bodies without an antifreeze, puncturing cell membranes all around. Why do you thing freezing the whole body is the way to go anyways?
Will a future society want people who do stuff like freeze themselves, rather than be organ donors (since this is how the whole thing came up)? Why would they revive such people, even supposing they could?

Cellular Turing Machines(Creature Genetics and Development)

2009-08-08T19:01:00.000-07:00

Rewritten on 1/12/11
Genetic code for these creatures is going to be an 11 character language based off brainfuck. The commands for the creatures is as follows:

'<' and '>' increment/decrement the pointer to the primary node.
'v' and '^' increment/decrement the pointer to the secondary node.
'.' link the secondary node and the primary node. If the two already linked, do nothing.
',' unlink the primary and secondary nodes if they are linked, else do nothing.
'+' and '-' increment/decrement the value of the primary node (note that this value is cyclic!).
'[' and ']' will preform looping functions, as in brainfuck. The loop terminates when the value a the primary node is zero when a check is made.
'*' is a special character--it does nothing in the developmental code. Instead, it's used to mate creatures, maybe even to speciate them in a later version: '*'s are point of possible crossover. Actually, this command is where I can't wait to see what the program does. How will these characters, which have nothing directly to do with fitness, position themselves in the genome? Will it be random, haphazardly strewn around in the middle of loops and such? Could these start to partition off genes somehow, segments of the program which are independent from each other? I hope it's the latter. It would be really neat to see the evolution of alleles and such--some kind of more complex genetic code.

To ensure we aren't infinite looping, I'll probably limit the number of commands a creature can execute somehow--perhaps based on it's ancestral build times. Once a creature has been built from it's program, it needs to be cleaned up a little bit: we want to be sure that only one creature was built, and we don't want a bunch of unlinked nodes floating around. I'm going to take the build results and find the largest connected bunch of nodes--that'll be called the creature, and that'll be what is tested.

As for development, I see one important characteristic: I want determinism. There should be no chance that a single program creates radically different creatures every time it's run. If something works, I want to be able to go back and see exactly why. I fiddled around with the idea of some kind of pseudorandom placing of nodes before linking, but eventually rejected it on the grounds that I don't want some hidden pattern in the pseudorandom generator to influence evolution. I want all the patterns of evolution to be quite out in the open, and this includes developmental patterns.

I still have one qualm--I want chance to be part of the process. If I run this program twice, I expect slightly different results from the same starting conditions. I think, however, that I'll introduce this randomness into the environment, not into the development of the creatures themselves. Nodes will initially be laid out in a gigantic + sign, indexes spiraling clockwise from the crossing. Negative indexes will be converted to positive indexes in such a way that decreasing (i.e. increasing in magnitude) negative indexes will spiral counterclockwise. I'm going to make all the links, do the node culling process, then put the creature through a few rounds of the physics engine in zero gravity to pop it into an equilibrium shape, then a few more in gravity to get it ready to be simulated (we wouldn't want any gigantic one-shot springs winning the day, although I don't think my physics system will allow such creatures to exist anyways.).

This leaves four big (and not unrelated) problems to consider before I get down to the dirty part of coding:

The physics simulation (which I have a basic plan for already).
How fitness is determined (again, I have an idea).
How this fitness affects what the program does with the creature.
How mating of two creatures works.

Topic 1 will be the focus of the next post, 2, 3, and 4 the post after.

~Ninjinuity

Cellular Turing Machines(Overview)

2009-08-06T00:05:00.000-07:00

One of my other fascinations is evolutionary processes. In the past, I have written simple, computer programs in which short strings compete to become simple words, but I want to try something more complex. One of the big holdups? I've never developed a sufficiently complex and interesting way to representing these creatures before now.
One way I'd like to represent a creature would be as a complex set of nodes and links. Treating nodes as points, and links as springs or pistons between the nodes, creatures could be made to move. This is all really nice on paper, but I've always run into an implementation problem: How to give the creature a simple to implement but functionally meaningful way to manipulate its own movement.
This is where a cellular automata come in. These simple games can work as a method to control movement. If each node is given a state, and alters that state based on a simple set of rules, as in the game of life, the links can change their length based on the states of the nodes they are connected to. Of course, the game played on the creature needs some basic properties that some games just don't have. Conway's game of life assumes that each node has exactly four neighbors, while Langton's ant needs to have an order defined on the nodes. Any game that's to work needs to have coherent and interesting behavior regardless of the number of nodes, and it needs to have consistent behavior regardless of ordering. While not required, I'd love it if it were capable of sending signals down a single strand of nodes, and it'd be nice if it were possible to make some kind of resetting muscle.
I have at least one game that fits this bill: the Cyclic Cellular Automaton. This is what I hope to use in my program. Next post, I'll explain how I plan to build creatures from a linear genetic code.

Professor Stewart's Cabinet of Mathematical Curiosities

2009-08-04T20:25:00.000-07:00

This book, written by Professor Ian Stewart, is possibly one of the best books I have ever read. Despite this, it has a format quite unlike an ordinary book; it has no coherent theme, and is full of tricky, and sometimes unsolved, math problems. When I first picked it up, I read the first few problems, and was about to set it down when I decided to flip just a few more pages ahead, and fell upon an essay about Fermat's last theorem.

What had at first had seemed like a book full of trivially simple math and logic problems had another side. I bought the book, and I'm very glad I did. Stewart does an amazing job of mixing those first few trivial problems in with harder ones, and ones so hard that it makes your head hurt just thinking about it. Interspersed thought this are short essays about various unsolved (or previously unsolved) math problems, colorful biographies of Gauss and Euler, and simple but thought provoking explanations of topology or just mathematics in general. About halfway through the book, I realized how much I was learning: random math factoids, the importance of unspoken assumptions in proofs, the Poincare' conjecture: each new paragraph contained some new, fascinating jewel. Though all of this I could not help but be reminded of the closing paragraph of Innumeracy, by John Allen Paulos.

The discrepancies between our pretenses and reality are usually quite extensive, and since number and chance are among our ultimate reality principals, those who possess a keen grasp of these notions may...more easily become subject to feelings of absurdity. I think there's something of the divine in these feelings of our absurdity, and they should be cherished, not avoided

I think that this kind of book is exactly what Paulos had mind when he wrote of the widespread innumeracy in modern culture; Stewart's book is an ambassador of the “warmly rational” sense of wonder that can come from taking a closer look at even the most mundane and boring of situations.

Cellular Turing Machines(Introduction)

2009-08-03T21:56:00.000-07:00

EDIT: I'm going to come back to this project soon and really finish it up, because I think it's worth doing. All my posts are bloated and badly formatted, and I've read up on a lot of relevant material, so I'm going over these with a fine tooth comb and clean them up, post clean code. Basically, I'm going to bring this up to speed, and hopefully release a nice clean application with some features that I really have wanted to see in other programs.

I have known for some time about Conway's game of life, but today I learned two things that surprised me.The first (and less surprising of the two for me) is that the game of life is a Universal Turing machine. In more common terms, it can act as a computer. I guess this doesn't surprise me so much because, in seventh or eighth grade, I remember making something very much like an AND gate in the game of life: Single cell inputs, and a single indicator cell. My gate destroyed itself in computation, but I saw no reason why a stable one could not be constructed (at the time, I was trying to do something other than make a gate, I cannot recall what).

The second, and somehow more surprising discovery (for me at least) was that Conway’s game is not alone. While reading though the book Professor Stewart’s cabinet of mathematical curiosities, I came across a short essay on a mathematical “creature” known as Langton’s Ant. The rules for the ant are simple, arguably simpler than those for the game of life and there is another amazing feature of the ant. Given long enough, the ant always seems to build a “highway” (see the link if you are confused). No one has ever proved this to be true, but no finite configuration of tiles is known that performs otherwise.

Another thing that struck me about the ant: If one imagines the ant to be flipping tiles on a glass plane, then looking at the plane from underneath yield the exact inverse of the view from above. Black tiles are now white, white now black, but the ant obeys the same set of rules. On further investigation of both games, I discovered that even more games exist. Some of these others have similarly interesting properties, like Day & Night, where the inverse of a pattern behaves in exactly the same manner as the original. So anyway, while reading about these various games I had an interesting idea. All the games I have encountered so far are played on a simple grid. As I considered various ways to implement such a grid in a program, one that stood out was a linked data structure, where a node indicated each square, and links showed which squares were adjacent. A second or so later I realized I could construct "loops" from the connections in such a system, and therefore assess the topology to the shape, at least in theory.

For example, most of the games with Langton's ant that I found allowed the ant to roam across the screen, wrapping in both directions as it came to the edge.This describes the topology to a torus: some loops (sets of connections between squares) cannot be "deformed" to a point, in fact, all loops that pass over the edge of the screen cannot be deformed in this manner. If you are confused, try this image, which comes from this page (WARNING: a LOT of math I don't understand EDIT: Oh. Now I do!). The picture shows a grid, which is what is displayed on the screen, and the topological interpretation, a torus. Note that straight lines on the square are circular "loops" on the surface of the torus, and that these loops cannot be moved (imagine rubber bands around a doughnut) in such a way as to squeeze and stretch them down to a point while they remain on the surface.

In any case, I got to thinking about different shapes I could deform the network into, including sphere like shapes, mobius strips (EDIT: I now know I was really thinking of a projective plane here- A kind of double mobius strip that can't be neatly embedded in three space. It's neat. Check it out.), and twisted versions of these shapes (while topology may not care about twists and deformations, the Game of life certainly would), when I had an idea. It will take a while to explain, even on its own, so I will end this post here and pick up the rest later on in another post.Watch for part 2 soon!

A note on my editing policy...

2009-08-03T15:51:00.000-07:00

As this blog is a bit like a notebook for me, I will not hesitate to edit old posts, and may not leave evidence of my doing so. Most of these changes will be minor (i.e. adding tags, fixing grammer, etc.). However, should I change a post in some major way, I will try to write a note explaining why I did so. No promises though.

A sketch

2009-08-03T15:45:00.000-07:00

Just a quick image. This is something I sketched a while back. I am not completely certain what exactly it is supposed to be. Your call.