Interesting Things

I’m currently reading “The Holographic Universe” by Michael Talbot. I expected quite a bit more science than is actually present in the book,  but it’s an interesting read nonetheless. (Though the book definitely explains science through a super new-age lens.) Only a quarter of the way through so far, but chapter three bought something up that blew my mind.

First, holograms 101:

The reason we can see stuff is because light bounces off of everything. Traditional images taken by cameras record incident light intensities as the photons hit the elements in a CCD or whatever sensor the camera is using. A hologram also records the phase of this light as well, meaning that playback of the recorded image retains all of the information during the recording phase.

To record an image, a coherent light beam (aka laser) is sent through a beam splitter so we have two identical beams of light. One beam is reflected off the object to be recorded while the other beam serves as the reference of the recording laser. The two beams (object & laser) form interference patterns when they intersect, and this is recorded on the photographic plate.

When the image is to be read/reconstructed, the original recording beam (or laser of same wavelength) is shone through the plate. Interference allows the original beam to be recovered, restoring the recording of the object to the identical state it was in when the image was recorded. Because we literally recorded the light bouncing off the image, the holographic result is actually identical.

In this way, a mirror recorded as a hologram will also reflect light. And a holographic recording of a magnifying glass will actually magnify objects behind it. The recording plate can also be cut into as many pieces as desired, while the full original image can still be restored albeit being a little more blurry because of the cutting. SO COOL. TOO COOL.

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*Edit 10/21/16: Fixed broken link to pdf, sorry. :C

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tl;dr contents:

• Material Properties of Bone
  • Classifying bone trauma by time of occurrence
• Types of bone trauma
  • Ballistic
  • Blunt force
  • Sharp force
  • Thermal

I’m not gonna include a lot of pictures because this is a topic that not everyone will want to see images of. You can google stuff if you want to see examples, or read my final paper where everything is cited.

Material Properties of Bone

Bone is divided into two kinds of osseous material. Cortical bone is about 80% of the mass of the exoskeleton, and forms a hollow cylinder in which the cancellous bone resides. The main purpose of cortical is for structure, while cancellous bone is spongy interior that is responsible for nutrient storage and transport. 

Injuries to bone are classified based on when the injury occurs.

Ante-mortem trauma: Refers to trauma on the skeleton that occurs prior to the death of the individual. In-vivo bone exhibits healing, and edges of a fracture will be fairly smooth. As healing rates differ depending on the characteristics of the individual, the same injury may look different from case to case.

Peri-mortem trauma: Refers to trauma occurring around death. Fracture patterns observed in peri-mortem trauma can be similar to those seen in ante-mortem trauma, but have sharper edges since no healing will have occurred (in most cases). Patterns will show evidence of some terminal event, i.e fast collision with an object, but fracture edges will show characteristics of plastic deformation as the external fibers of the bone tissue begin to show micro-tears.

Post-mortem damage: Refers to damage occurring after death. Bone becomes brittle once it has dried out, and exhibits ceramic-like material properties. Fractures will be jagged and exhibit no healing, and may also be irregular. I.E: Fractures lack a common correlation to an event that caused the damage, such as those resulting from post-mortem bone shrinkage.

Types of Bone Trauma

Ballistic
Ballistic trauma on bone is usually the result of a bullet or an explosive, though this categorization may be applied to any fast traveling object that has collided with bone. Features that indicate possible ballistic trauma include the presence of a projectile that can be associated with bone, fracture patterns corresponding to a high velocity impact, or fragmentary foreign material found within the bone or the environment.

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Infinity is a well explored concept across many disciplines. As of yet, I’ve managed to only interact with infinity behind the safety net of definite integrals and unbounded limits. So I thought I’d take a deeper look at infinity though the lens of Zeno’s paradoxes. But first, a short discussion about English.

When I was 6, “red” was the color of my favorite rain jacket. That was it.

When I was 14, “red” was no longer simply a color, it was an emotion, an object, a physical force. I could smell the redness of a cherry orchard and hear the redness of a laugh.

In fact, if I were imaginative enough, I could make the word “red” mean anything I wanted. “You are a poet!” my teacher cried, “Bend your words, twist them, pepper them with your thoughts; present to the world a feast of poetry.” English was quite a willing and malleable medium, which was great, but this foray into non-literal completely defeated the sure-ness of words that I had believed in as a kid. With poetry, even the most innocuous sentence like “today was sunny” could have ten different meanings.

Now, I’ve held on to the belief in the certainty of mathematics since my days of Algebra I. Unlike poetry, the result of a definite integral doesn’t change with the whims of the one grading the problem. Math was unmoved by emotion, and (to borrow the words of Bertrand Russell) I felt that it was the turtle that could hold all other turtles.

However, take a hard look at this concept called “infinity”. Infinity is to mathematics what poetry is to English—it takes the previously solid math of algebra into the fuzziness of philosophy. Though I knew nothing of its intricacies, I often invoked the threat of infinity upon my childhood friends when I “triple times infinity dared” them to do something dumb. Infinity was a big deal, since we didn’t know anything of what it was other than the fact that it was really, really big. But what is the actual value of infinity? How can a mere concept of “really, really, big” become something we can realistically use?

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To provide some background information for my N-link pendulum project, I’ve broken the methodology for solving the equations of motion (EOM) for a simple double pendulum into a separate post. I’ll explain to the best of my abilities!

The pendulum that we are solving for is composed of two masses, m1 and m2, suspended from each other by strings of length l1 and l2. Their positions relative to 0 is represented by theta1 and theta2. The entire pendulum is supported by point 0, which is a frictionless, massless point. The whole thing is a pain to create digitally, so I drew the setup below:

This will be a pretty long post, so scroll to the bottom for the cool graphs!

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