Metas

Diana was telling me about a meeting given by the GM of her hotel to her and the rest of the employees. At the end of the meeting he asked who among them keeps a list of goals and objectives. Diana was the only one to raise her hand. When asked, she said that at the beginning of the year she writes down her goals for the year to come on the first page of her agenda. As the year progresses, she occasionally checks her list and, come mid-year, she does a complete evaluation of the list, making changes in her schedule and her life so that she can achieve what remains incomplete.

This really impressed me. Before, I would have thought it was good for her, but not really for me. In the last year or two, however, I have learned more about myself and what I am driven by, and I want to pursue what drives me. What's more, I want to pursue and succeed at what have become my passions.

But that is not all. She told me she does the same thing with her personal goals, but that she keeps those in a separate place. When she came back from her room, she layed her notebook open in front of me and started paging through the last two years that we have been together. She read aloud, "Be with Matt", "Send more messages to Matt", and several other goals related to how she could change herself to make me happy and to make our relationship stronger. I was more than impressed. I was affected.

It was one of those moments that changes a person. Here she is, one of the best, nicest, most caring people I have ever met in my life, selflessly changing the way she is to make the relationship that we have better. Not only that, but as I listened, I noticed a check in her voice. As my eyes followed her words along the page, I realized that she had successfully done everything that she could think of to make my (our) life happy.

At that moment, I felt more than just love. I felt a desire to make her feel the same way. Affected. Loved. Astonished. New. I wanted to change myself to make her happy and I wanted to be with her to support her and help her fulfill the rest of her goals.

So, I planned on making my own list of goals the next day after I finished teaching. The whole day I thought about my dreams and aspirations, excited about the permanent reminder I would have to provide me with ambition and motivation to do great things -- about having a simbol of the greatness and love that was shared with me the day before -- about carrying around in my pocket the power, strength, will, and vision that had given dominance to my stride and fire to my soul.

But classes went long and I grew tired and distracted. I went to bed without picking up a pad and pencil. Soon, my list became another goal to be accomplished some other day. Another thought to be pushed aside or forgotten -- a memory to smile at in a moment of reflection or a window to a time of what could be if I had the time to make it.

That is the danger that we all face, isn't it? It is the reason for the list. The list serves as a token against complacency and procrastination. It is a focal point to keep our attention on what is important, to remind us of the things that are bigger than our daily lives. It keeps us honest and gives us a reference to not only where, but to who we want to be.

And having a list of positive things to constantly be reminded of only leads to more positivity. Sure, I feel great pursuing my list, but I feel even greater helping some one else fulfill theirs. It is one thing to be great and a-whole-nother thing to share it and make great the world around you.

So, in the name of greatness, here are some of my goals for the rest of this year, in no particular order. I hope I have inspired you to write your own.

• Create my "Potentials and Fields" class and make an effort to put it on YouTube
• Contribute at least twice a month to Casual Science
• Gather parts for the Watch-a-Doodle (a.k.a. Wetch-a-Sketch)
• Do not let work keep me too busy nor play keep me too idle.

And lastly (for this blog, anyway), but certainly not leastly,

• Help Diana fulfill the rest of her goals.

Khan Academy

Through my frequent readings of Saturday Morning Breakast Cereal, I came across a link to the Khan Academy and watched their featured video. It is of Salman Khan, the founder and sole teacher of the Khan Academy, speaking about his youtube school at a TED convention.

Khan was a hedge fund analyst at a brokerage firm when he started making youtube videos to help tutor his little cousins. After receiving numerous positive emails and comments from his family, friends, strangers, and teachers, he quit his job and decided to found the Khan Academy.

There are over 2,100 educational videos on the site (mostly pre-/highschool level), all made by Khan. Each video is 10-15 minutes long and consists of Kahn's voice explaining a topic while the video shows Khan's notes appearing on a computer-based blackboard (via SmoothDraw).

Additionally, there is a fantastic organization and homework scheme created by the software crew. All of the videos are thrown into an intricate flowchart that creates a smooth learning path through and across subjects. You can start at the beginning and be guided through harder and harder topics. Each topic requires 10 consecutive correct answers before permitting you to move on.

The program allows teachers to get a microscopic view of what their students are spending their time on and having troubles with. A teacher can see where, when, and how long/often students pause or replay a video, which types of problems they get stuck on, how long the spend on each question, and where holes in their knowledge base are. With all of this information being made available, teachers are able to assign lectures for homework and do homework during lecture, thereby increasing student-teacher and student-student interaction.

Furthermore, the student progress can be tracked through each class and grade, providing a great tool for evaluating of the quality of student being generated by the school system and of the school system and teaching staff itself.

The most amazing thing was seeing how the self-paced learning was going for each individual student and how, after progress flatlined for a period of time, their learning curve suddenly rose sharply upon the mastery of a difficult topic and continued to climb quickly and steadily.

Fin.

(To get a proper, resolving conclusion, you will have to check out the site and see it for yourself.)

Hard work pays off

Currently, I am teaching six physics labs of 15 students, each of whom write a weekly lab report that I have to grade. That makes 90 lab reports, or roughly 650 pages to read and make comments on. Often, the reports need alot of improvement and my comments are ample. Unfortunately, that takes time and the students probably do not make an effort to read them.

One thing that makes their lab reports bad is the lab manual itself. Before the procedure, there is an objectives and a theory section. Between the two, all of the concepts and ideas that the students are suppose to discover during the lab are given away. As a result, the students think that instead of analyzing their data, they can say that their data corroborates the theory and be done with it.

So, I end up writing "Discuss more than the theory, error, etc. Compare, analyze, and discuss the results", "Results --> Theory --> Error", and other such things about 70 times per week. In order to cut time, I made a document that lists all of the comments. I assigned numbers to general comments that can be applied to any lab and letters to comments that pertain to the results and objectives of the particular lab being graded. The result? My grading time got cut in half.

An added benefit is that now, after having made the comments list available to my students via a Google Docs shared document, I can now see when my students are looking at the list. As I am typing, Anonymous User 1337 is checking the comments I left on his or her lab report, and I am smiling knowing that my efforts are not entirely in vain.

Thank you, Anonymous User 1337.

Think again

In an effort to prove or disprove any of my recent hypotheses, I began to think up experiments that could be performed for such a purpose. In my last Mison Space entry, "Barriers, shmarriers", I argued that particles, instead of actually tunneling into and through classically forbidden regions, they enter into Mison Space and go around said region by releasing energy.

One misconception that I had, which S.R.D. Rosa cleared up in his paper, "Student Understanding of Tunneling in Quantum Mechanics", is that particles lose energy during the tunneling process. In tunneling problems, the classically forbidden region is usually represented by a barrier whose height represents is energy, leading to the misconception that the particle wave amplitude is a measurement of its energy. What the amplitude actually represents, however, is the probability that the particle will be found at that particular location.

So, contrary to my previous argument, particles do not release energy as a means of entering Mison Space. On the otherhand, within the classically forbidden region the amplitude of the particle's wave function decreases exponetially, which means that the probability of it being found diminishes exceedingly fast the farther in one looks for it. The rapidly decaying wave function could still be evidence for the particle's escapade around the barrier.

To prove this, one would simply need to put a detector within the forbidden region to see if the particle can be found there. I found an article entitled "Detection of particles under a potential barrier". It is a theoretical paper in which the authors propose a 1- and 3-D model detector for finding particles within potential barriers. The detector is able to locate a particle without significantly disturbing its wave function (to do so, the time of encounter is left unknown). By stringing several together in a simulation, they were able to encounter particles at various locations within the barrier and found that their trajectories are straight line paths.

That may debunk my side-stepping hypothesis, but then again, the simulation is based on the creator's pre-conceptions of how particles behave as they enter into the forbidden region. At any rate, in trying to reconcile this finding with previous hypotheses, I have begun to consider space in a different light, but that will have to wait for a future post.

References

1. Rosa, S.R.D. Student Understanding of Quantum Mechanics. Proceedings of the Technical Session, 22 (2006) 47-52. Institute of Physics, Sri Lanka
2. Vilenkin, A. and Winitzki, S. Detection of particles under a potential barrier. Phys. Rev. D. 30, 8 (1994)

Priorities

Last week, my best friend had a baby and has been understandably out of touch and (pre-)occupied. Thus, my random comments, odd stories, comic discussions, and good-for-nothing banter has been piling up waiting for his return. Mixed in with that is my excitement and concern for him and his family.

When I sit down and look for him on chat, I think about him, his baby, and his wife and wonder how they are doing and how they are coping with such a giant, fantastic change. At the same time, the typical idiocies that we pass back and forth come to mind and I am sort of hit with a weight of realization. Here I am, working, goofing off, reading comics, teaching, grading, and generally just sort of living non-chalantly, and there he is with a baby. A human baby. A defenseless, dependent, pure, innocent human baby that will need nurturing, attention, education, morals, and an unfathomable amount of love.

I realized that, compared to having a baby, everything I do must be pretty insignificant... and with that realization came a double dose of hope. Firstly, and rather selfishly, is that having a baby does not change everything everything; and secondly, that I will one day be able to experience such a change.

Barriers, shmarriers

Continuing the development of my light-as-a-fourth-dimension hypothesis, I know embark upon potential barriers and tunnelling.

For this, matter needs to be thought of as a potential wall more or less proportional to its viscocity. We can run through air like a hot knife through butter because air just moves out of the way. Our mass, viscocity, potential barrier, or whatever you want to call it, is much greater than that of air, so we move through it easily.

But now think about running through water. Or worse yet, honey or molasses. Much more difficult. They are more dense and have a higher viscosity (a greater potential).

Finally, try running into a brick wall or a barn door. Actually, don't. It hurts. Think of them as huge potential spikes. The cumulative energy of your body is not sufficienty high enough to pass over the potential spike, so you bounce off of it and are turned away.

Small, energetic particles, the subjects of quantum mechanics, are known to tunnel through matter. Classically, their energy is lower than the potential barrier and should be turned away. Quantumly*, however, on occasion, they pass through the barrier and wind up on the other side.

My claim is the following: Each object is seen as a potential barrier with a certain height and thickness. On either side of the barrier, the potential feel drops steeply to that of "empty" space. Depending on the size and thickness of the barrier, these small particles can sense the lower potential on the other side of the barrier. Its energy field feels out the a way around the barrier through the 4th dimension that light travels through. In effect, the particle is able spend its energy to create a small wormhole-like link to equipotential field on the other side of the barrier, then passes through it.

I support this claim by first re-iterating my previous claim (see 4D Glasses) that electrons orbit atoms on equipotential field lines of this 4th dimension (which will here-to-forth be called Mison Space), then by noting that a change between electron orbits results in the emission or absorption of a photon (which, as I argued earlier, lives in Mison Space).

The loss of energy that occurs when a paticles tunnels through a potential barrier, I argue, is not simply expended in the particle's efforts to penetrate the barrier. Rather, the energy is released and travels through Mison Space, creating a portal for the particle to travel through. The portal exists on short temporal and spacial scales and is a link that traverses a space perpendicular to the 3D space that we live in. Essentially, the particle goes around the barrier, which is a perfectly reasonable thing for it to do.

Future Mison Space topics to be oublished:

• Why are electron orbits so crazy and how can they go through the nucleus iteslf (partially answered previously)?
• EM waves, as the name implies, are made up of both electric and magnetic fields, which travel perpendicular to one another, so how can Mison Space be just one extra dimension?

Lab Reports

I am currently general physics laboratories in Spanish at the University of Costa Rica. Teaching phsyics at the university level is a career goal of mine, and though I am not teaching theory classes quite yet, I am developing some of my own material.

Thus far, I have written a document explaining what a lab report consists of and how to write a good one, a sample lab report, as well as a rubric and a grading scale for each section of the lab reports. As I read and comment on my students' lab reports, I take notes, refine, and update my description of what a good lab report is.

I uploaded all of my teaching resourses to a Google Docs folder and shared it with the world, so you can find them here. So far, they are only in Spanish, but eventually they will be in English, and I will keep uploading and oublishing about everything that I make.

Casual Science

QuestionEverything and I have a little project in the works. A book club of sorts, only in this club, the books are articles published in scientific journals. My goal is to find an article in a field that is receiving a lot of attention, or just one that suits my fancy, read it, oublish a review, and pose some questions about it. Then, QuestionEverything will try and find an article to answer one or a few of those questions, write a review, and pose more questions. In the meantime, I read his review and answer a couple questions that he posed. This little back and forth repeats until all of the current knowledge in and about the universe has been amassed and assimilated, and until all of the possible questions have been answered. Whatever remains will be beyond the grasp of human knowledge and experience and thus is unimportant.

But, you might ask, what about the loose ends? The questions that are being asked right now but for which no answers yet exist....

Ahhhh! Now you see! That is the science for our brains.

4D Glasses

I have been contemplating the constancy of the speed of light and the relationship between electric and magnetic fields for a long time and think I may have stumbled onto an interesting hypothesis.

One of the axioms of general relativity is that the speed of light is constant in all inertial frames, even ones that are moving at nearly the speed of light. However, in the normal world, if you travel at the speed of something, that something appears to be moving with velocity zero from your perspective. How can it be, then, that light is different than everything else in the universe?

I will tell you how it can be: light travels orthogonal to space. Consider yourself to be holding a radar gun that police use to catch speeders and driving a car approaching a crossroad. Travelling towards you along that crossroad is a race car. You flash your lights, signalling a race, and begin to speed up. The race car, not knowing that he has been challenged, continues at a steady pace.

As you speed up, you expect the difference in speed between you and the racecar to diminish, but, dishearteningly, the race car continues to move in the positive direction, even as you surpass its meager pace.

If the racecar had been travelling in the same direction and along the same road as you, it would have appeared to stop, then travel backwards towards you as you reached its speed and surpassed it.

The difference? Orthogonality. Light always appears to be travelling at 3x10^8 m/s, no matter what, because it is moving perpendicular to three dimensional space.

But how to prove it... One way would be to spontaneously combust hot enough to turn all of your molecules into light and see what happens. Unfortunately, the reverse process is not very predictable, so gathering evidence and showing reproducability would be difficult. Another way is to consider things that behave sometimes like light and sometimes like particles: electrons in the double slit experiment.

Electrons have charge that produce an electromagnetic (EM) potiential and fields. There is an upper limit on their mass, but they could very well be massless. When there is a single slit present, electrons pile up behind the slit in a gaussian distribution, behaving like a particle. When there are two slits present, however, it is believed that they travel through both slits in a wave-like manner, causing an interference pattern behind the slit.

Now change your idea of what an electron is. Think of it as an EM particle living in the EM space that is perpendicular to our 3D space. We already know that EM waves can interact with things in our world. Afterall -- we can see. How they move, however, could very well be a mystery, if there is indeed a 4th dimension.

As an aside, imagine yourself at a campfire in late autumn. You forgot to bring a sweatshirt, so are sticking fairly close to the fire. There is a ring around the fire in which the temperature is comfortable and you feel like you can hang out for the rest of the night. Closer in you start sweating or start to feel burnt, whereas any farther out you get cold and start to shiver. This heat field is like a potential well. It attracts you to the ring around the fire at which you body heat lets you be in comfortably.

Now, consider 3D space to be the campfire and you to be the electron. The electron can be in any ring of 3D space that is an equipotential to its own potential field. It spreads out over that space in a way that is not alltogether clear, it being a 4th dimension and whatnot. The two slits comprise two equipotentials that the electron can pass through without problem. It follows the 3D potentials through the holes to the detector plates and causes an interference patter. Not, however, because it is a wave, but because it is travelling along the 3D equipotentials of space.

If one of the slits is closed, the potential of that particular path is increased by a whopping amount, and the electron can no longer pass through it. It must stick to the single, open slit, behind which the 3D space potential is that of a macroscopic particle.

If you believe me this far, you might be wondering how we can map this 4th dimension. Ponder for a moment, if you will, the orbits of electrons around an atom. They move along EM equipotentials at discrete energy levels. If the EM dimension is perpendicular to 3D space, then these equipotials have to be wrapped around the fabric of space itself. All we have to do is map the electron orbits to see how EM space fits in with our own.

And there you have it. The culmination of my thought experiment. Now to prove it...