But no one has ever been able to prove that for certain. So you're moving into your new apartment, and you're trying to bring your sofa. The problem is, the hallway turns and you have to fit your sofa around a corner. If it's a small sofa, that might not be a problem, but a really big sofa is sure to get stuck. It doesn't have to be a rectangular sofa either, it can be any shape.
This is the essence of the moving sofa problem. Here are the specifics: the whole problem is in two dimensions, the corner is a degree angle, and the width of the corridor is 1. What is the largest two-dimensional area that can fit around the corner? The largest area that can fit around a corner is called—I kid you not—the sofa constant.
Nobody knows for sure how big it is, but we have some pretty big sofas that do work, so we know it has to be at least as big as them.
We also have some sofas that don't work, so it has to be smaller than those. All together, we know the sofa constant has to be between 2. The three letters correspond to the three sides of a right triangle. In a Pythagorean triangle, and all three sides are whole numbers. Let's extend this idea to three dimensions.
The 20 big questions in science | Science | The Guardian
In three dimensions, there are four numbers. In the image above, they are A, B, C, and G. The first three are the dimensions of a box, and G is the diagonal running from one of the top corners to the opposite bottom corner. Just as there are some triangles where all three sides are whole numbers, there are also some boxes where the three sides and the spatial diagonal A, B, C, and G are whole numbers. But there are also three more diagonals on the three surfaces D, E, and F and that raises an interesting question: can there be a box where all seven of these lengths are integers?
This is called a perfect cuboid. Mathematicians have tried many different possibilities and have yet to find a single one that works. But they also haven't been able to prove that such a box doesn't exist, so the hunt is on for a perfect cuboid. I find the greatest problem I face is scale. We are continuously investigating thinner and thinner reservoirs with subtle characteristics.
We're not in the Gulf of Mexico anymore. Reservoir Engineers are the first to point out the lack of vertical resolution in seismic data.
That said, there [have] been great strides in recording technologies, processing algorithms, and statistical methods that [are] narrowing the gap. The second problem I see is similar to scale, but not in the vertical sense. When you mention geomechanics to an engineer, they think of borehole stability.
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Understanding lateral and horizontal stresses and their relation or expression in the near-field i. Not only for exploiting unconventional reservoirs, but in multi-million-dollar international wells drilling down the flank of a fault. The third problem I see is more philosophical. When I went to school, much of what I learned could be explained in a pool hall.
The 20 big questions in science
Angles of incidence, reflections, velocities, all happened in front of your eyes. It was easy to grasp and explain to your manager. We are becoming very specialized and understanding, let alone explaining, the concepts of geophysics is becoming more and more difficult. We are in danger of isolating ourselves further from the asset team, which deems everything we do a 'science project'. Education and understanding has always been a problem in geophysics, and solving it doesn't seem to be getting any easier.
Interview with Kris. A very important seismic exploration and monitoring problem is the full integration of rock physics and seismic inversion. Another good one is the missing wavelengths in inversion. These are not easy questions. Interview with Mirko. Interview with Dimitri.
I remember watching a Star Trek movie once, and as they neared a new planet, the captain called a geophysicist up to the bridge. All the guy had to do was press a button on the com, and a full 3-D image of the planet emerged on the screen. But seriously, there could be a lot more automation in our processing and imaging, and we could harness modern technology more effectively for better interactive interpretation in terms of both data access and processing while interpreting. Interview with Amy. SC: Considering the challenges we are facing in characterizing the unconventional reservoirs, what kind of change do you think we need to bring into our approach or our workflows?
I think the biggest change that needs to happen is getting out of the mindset that we can accurately model the subsurface cheaply and easily. True integration of disciplines is also needed. We talk a lot about integration in our industry, but I rarely see it actually happen. We still work in silos. So in that respect I think organizational culture needs an overhaul. Interview with Eric. SC: As you have championed the benefits of integrated shale resource characterization, I would like to ask you about how much value do you think multicomponent seismic data can bring to such an exercise?
Some unsolved problems of geophysics
Most modern physicists who work with quantum field theory no longer consider these questions of interpretation to be relevant. The principle of decoherence is, to many, the explanation -- interaction with the environment causes the quantum collapse. Even more significantly, physicists are able to solve the equations, perform experiments, and practice physics without resolving the questions of what exactly is happening at a fundamental level, and so most physicists don't want to get near these bizarre questions with a foot pole.
There are four fundamental forces of physics , and the standard model of particle physics includes only three of them electromagnetism, strong nuclear force, and weak nuclear force. Gravity is left out of the standard model.
Trying to create one theory which unifies these four forces into a unified field theory is a major goal of theoretical physics. Since the standard model of particle physics is a quantum field theory, then any unification will have to include gravity as a quantum field theory, which means that solving problem 3 is connected with the solving of problem 1.
Many physicists believe that a fundamental theory of nature should have some method of unifying these particles, so they are described in more fundamental terms. For example, string theory , the most well-defined of these approaches, predicts that all particles are different vibrational modes of fundamental filaments of energy, or strings.
A theoretical physics model is a mathematical framework that, in order to make predictions, requires that certain parameters are set. In the standard model of particle physics, the parameters are represented by the 18 particles predicted by the theory, meaning that the parameters are measured by observation.
Some physicists, however, believe that fundamental physical principles of the theory should determine these parameters, independent of measurement.