I thought Paw Patrol had already covered this:
"‘Paw Patrol’ Writers Defend Episode Where German Shepherd Cop Shoots Unarmed Black Lab 17 Times In Back"[1]
[1]: https://entertainment.theonion.com/paw-patrol-writers-defend...
3,074 karma · joined August 31, 2013
rocksandwater.net
"‘Paw Patrol’ Writers Defend Episode Where German Shepherd Cop Shoots Unarmed Black Lab 17 Times In Back"[1]
[1]: https://entertainment.theonion.com/paw-patrol-writers-defend...
It is not surprising at all that almost all blind mathematicians are geometers. The spatial intuition that sighted people have is based on the image of the world that is projected on their retinas; thus it is a two (and not three) dimensional image that is analysed in the brain of a sighted person. A blind person’s spatial intuition on the other hand, is primarily the result of tile and operational experience. It is also deeper – in the literal as well as the metaphorical sense. […]
recent biomathematical studies have shown that the deepest mathematical structures, such as topological structures, are innate, whereas finer structures, such as linear structures are acquired. Thus, at first, the blind person who regains his sight does not distinguish a square from a circle: He only sees their topological equivalence. In contrast, he immediately sees that a torus is not a sphere […]
This is a quote from a book by Alexei Sossinsky, quoted here: https://onionesquereality.wordpress.com/2011/07/31/blind-geo...
Both of these papers discuss making 3D models of topography on the scale of a house and yard. You can also probably get colors mapped onto the surfaces.
(Note that I believe both use AgiSoft structure from motion software, which is probably expensive. I have no idea what the FOSS options are.)
[1]: https://pubs.geoscienceworld.org/gsa/geosphere/article/10/5/...
[2]: https://www.researchgate.net/profile/Steven_Micklethwaite/pu...
I've seen footage of hard mountain bike trails and class V kayak runs that I have done, and also seen non-first-person footage of the same drops, and it's pretty impressive how much the GoPro footage makes a 25 foot waterfall seem inconsequential relative to a 3rd person perspective (i.e. someone on the bank).
I wonder if having a stereoscopic camera could improve this situation. I pay no attention to VR or whatever so I don't know if this is the venue in which stereoscopic/3D movies would be viewed but it could be cool. Harder to share I suppose, and if your goal is to impress others on social media then it probably wouldn't work unless people start bringing those helmets to look at their phones while they poop.
The surface of the Earth is tesselated into irregular tectonic plates that (mostly) move rigidly, with little internal deformation. Plate boundaries are geological faults (dislocations where the crust on one side of the fault slides past the other side), but there are also faults within the plate interiors, especially near the boundaries, that accommodate strain within the tectonic plates in 'deforming zones'. The rigid interiors of plates generally have strain rates at the nanostrain/year level, i.e. a few parts per billion or less per year. This means that the relative deformation (not plate motion) between say Florida and Denver is on the order of 1 mm/yr.
Plate motions are pretty constant through time, such that the velocities measured over 10 year scales with GPS and other geodetic techniques are quite comparable to velocities estimated over the past ~5 million years by looking at longer-term proxies such as the bar-code-like pattern of magnetic anomalies on the seafloor produced at divergent plate boundaries[1]. Within about 20 km of an active fault, or 200 km from a subduction zone, the instantaneous velocities have a lot of variation related to earthquakes, though.
The horizontal velocity of any point on the Earth's surface can be described as a rotation around another point on the Earth's surface, with some angular velocity; this is sort of a corollary or application of Euler's fixed point / rotation theorem[2]: the point is where the rotation axis intersects the Earth's surface (so there are two antipodal points, actually).
Because tectonic plates are mostly pretty rigid, the motion of plates on the Earth's surface can be modeled as a rotation around a single point, even when the plate is huge like the Pacific plate, i.e. almost a hemisphere. However as stated in the OP, there is no 'true' reference frame, so plate velocities are usually described relative to another plate as a reference frame, or just considering a pair of plates. We'd say that relative to the Pacific, the North American plate rotates around a point near Hudson's Bay, or equivalently, that the Pacific-North America rotation pole is near Hudson's Bay. To go from N. Am. relative to Pacific, to Pacific relative to N. Am, flip the sign on the angular velocity.
Therefore there is a bit of shared heritage between some aspects of graphics programming and tectonic geodesy, with respect to the mathematics of rotations, etc. However in practice the math is probably different (I'm not sure because I don't do graphics or game programming). For a good intro to the math used in this aspect of plate tectonics, see here[3].
In terms of the rates of the velocities, relative plate motion rates between adjacent plates are typically 1-10s of cm/yr. The fastest on earth is near Tonga and Vanuatu in the southwestern Pacific (north of NZ), at about 25 cm/yr.
[1]: https://divediscover.whoi.edu/mid-ocean-ridges/magnetics-pol...
[2]: https://en.wikipedia.org/wiki/Euler%27s_rotation_theorem
[3]: https://websites.pmc.ucsc.edu/~thorne/EART118/Lecture_PDF/le...
If it's easy to see that a piece of output (a paper, code library, machine learning model, whatever) or a job candidate is great, then the credentials behind it don't matter much. However if it's challenging to evaluate quality, then people will shift to looking at secondary signals such as credentials, price, etc.
As to why a lot of economists go with the signaling model of education, well, it might just say something about their field and how much they got out of their own educations.
Based on the data I can gather from a brief search, it looks like in 2017, 58% of Americans live in the state of their birth [1]. Because many people move states and then move back (for college or a temporary job or something) then it's reasonable to think that perhaps 50% of Americans move states at least once in their lives.
In 2016, 93% of EU residents were living in the nation if their birth; 4% were from outside the EU and 3% from another EU member nation [2]. (In the US, 14.4% of the population are immigrants, and this is ~20% of the total global immigrant population [3].)
Furthermore (and in the absence of any supporting data), I think that the assimilation process is for the most part easier for Americans moving between states, especially those who are at least second generation American. While there are definitely strong cultural differences between US regions, we generally all regard each other as American (although this is surely different for those from American territories such as Puerto Rico, Guam or American Samoa). Relocation may also be quite challenging for minorities, especially those moving to whiter states. But for the typical white American moving states, it is probably easier to relocate than for an Italian moving from Calabria or Napoli to Lombardia.
I've lived in 8 states and I think that some half-hearted jokes about dating cousins or eating possum are about the most trouble I've gotten by hailing from the Ozarks. In my experience there are also larger biases against neighboring states (sports rivals) than far-away states. Freud's narcissism of small difference and all that.
That being said, since at least the Reconstruction era following the Civil War, there has been some local to regional resistance to internal migration. Interestingly, today much of the resistance is put forth by residents of less economically developed regions against those from more well-off places moving in, pricing the locals out, and changing the culture. These changes are a sort of Californication, the gentrification of mountain towns by richer and more liberal whites, rather than poorer immigrants bringing down property values or taking manual labor jobs. While there is little by way of legislation against this, there is talk of some [3].
[1]: https://www.citylab.com/life/2019/03/mobile-stuck-us-geograp...
[2]: https://ec.europa.eu/eurostat/statistics-explained/index.php...
[3]: https://en.wikipedia.org/wiki/Immigration_to_the_United_Stat...
[4]: https://www.latimes.com/california/story/2019-11-10/go-back-...
"The Metrics of Backpacks" by Victoria Gannon
https://www.artpractical.com/column/the-metrics-of-backpacks...
Robert H. Miller, Kayaking the Inside Passage.
[1]: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2017...
edit: Whether this NN approximations will enable us going well beyond what PDE solvers can do is a tough question, especially because PDE solvers are generally needed to build the training sets as far as I understand (i.e. they are trained on synthetic, not observational, data). It's possible that one could strategically and judiciously train smaller components of a NN system and then assemble the system to do things that the PDE solvers couldn't do, perhaps, in the way that one can often write unit tests for scientific software but not really test the final results directly (because there is nothing to test against). However I think that in general the lack of training data for the more complex system will always be a major obstacle, whereas it's not really for PDEs.
If you don't find research compelling, then don't go for a PhD. It's not worth it on any front--you'll be broke, stressed and miserable for years and then quite possibly quit with little to show for it.
I think the concerns about a typical software engineering job not being interesting or allowing for intellectual growth or exploration are also overblown. Programming is pretty special in that there are a lot of different ways to do things, and the barrier to entry is incredibly low. If you're bored you can spend what work time you can get away with, and what personal time you have, and explore side channels or new approaches to optimizing parts of what you're already working on.
Interactive theorem proving is indeed cool, but it's not the only thing out there, and if working on it comes with a certain lifestyle that you find untenable, then don't feel bad about passing on it. There are lots of cool things to do, and plenty of other trains to be one of the first aboard--just keep a look out while you're doing whatever you end up doing.
Furthermore you can always go back and get a PhD unless other circumstances (i.e. kids and the need for a higher income) get in the way.
That being said, I got a PhD and it definitely made my life more interesting, but I'm a committed research scientist and would rather do nothing else, so there weren't a lot of other options for me.
Some of the more academically-focused (private) schools don't have much of an MSc program but they're atypical, and they don't dominate research like they do in other fields.
A ruthless man named Edgar Watson, who had purportedly killed several people in Oklahoma and Florida, settled in the coastal Everglades of Florida (Chokoloksee area) around the turn of the last century and started a sugar cane plantation. He was known for the 'Watson payday' where, at the end of the harvest season, he would gather all of the drifters and ne'er-do-wells he had hired as fieldhands and gun them down. Additional bad behavior toward his neighbors lead to all of the town's men standing in line and gunning him down as he landed his boat on Chokoloskee Island one day.
Then, once you've gotten the problem and solution framed the way you like, you start implementing the numerical solution of your problem.
There are a few exceptions, particularly when things do get hairy. For example one of my colleagues has created a radial basis function finite difference solver[1]. In some of the modules, it manipulates the RBFs using SymPy and then compiles that to C which is then executed by Cython as part of the solution process.
Earth's magnetic field isn't stable with time and has (geologically) frequent pole reversals. We don't have a great idea of how long this process takes, whether it is near-instantaneous or takes hundreds of years (or perhaps longer?). The poles are currently 'wandering' relatively fast and some geophysicists think this may be a sign of a pole reversal to come.
I wonder about how the Van Allen belts fair during a pole reversal, and if for some time interval the amount of incoming radiation on the Earth's surface is much greater, perhaps at dangerous levels.
Earth also has a much stronger geomagnetic field than other rocky planets because it has a solid iron-nickel inner core that rotates inside of a liquid iron-nickel outer core, inducing the magnetic field (the so-called 'geodynamo'. If the resulting Van Allen belt is indeed a safeguard to the development of life on Earth, it may be part of the reason that Earth is unique in life development versus its neighbors.
I'm not sure that there is one. Researchers in every subdiscipline have their own, and plate tectonics has tied everything together enough that there aren't as many huge overarching questions that everyone is waiting for an answer to.
Some big ones:
How and why does magma travel through the crust and how does it accumulate in enormous bodies? Does it do so in small batches, displacing the rocks outside? Does it do so in huge batches, melting and incorporating the rock that it takes the place of? Why does (more dense) basalt magma rise through (less dense) continental crust?
Are tectonic plate velocities constant over 10 to 100,000 year timescales? Do the faults that are the boundaries between these moving blocks of crust slip at a constant rate (i.e. do the rocks on either side of a fault move at a constant relative velocity)? This relative movement produces earthquakes, so we also want to know if the rate of earthquake production is constant, and if big earthquakes are quasi-periodic (happening regularly spaced in time, with a similar magnitude) or if they are random (happening randomly but with a constant mean rate, like a Poisson process). Observational evidence suggests that big earthquakes on nearby faults are clustered in time, but we don't have good statistics for it because the data are sparse and a lot of data get erased by geologic processes, and we don't have good mechanical models for why this would happen in the first place.
How and why do huge plateaus such as Tibet and the Altiplano form? Do they pop up in a broad swath, or do they form like a narrow mountain range and then grow outward? What controls this?
How does the development of topography affect weather and climate, and how do weather and climate affect topography? For example at a local scale, concentrated erosion due to landsliding from topography-induced precipitation can impact where and how fast faulting and earthquakes occur by altering the force balance in the upper crust. On a more broad scale, the development of mountain ranges increases the rate of weathering and erosion of minerals which alters the CO2 budget of the atmosphere and sea, which changes climate.
How do geological events affect the ecology of an area and the world, and how do changes in ecology affect geology? Grasslands erode very differently than forests. The development of land bridges between continents causes exchanges in flora and fauna that can radically alter ecosystems.
So many of these questions aren't like we think of physics in the 20th century, where a singe discovery alters the field and everyone wants to do that thing. It's more like complex systems science where affects everything else and we want to see how.
I did some energy consulting, tried to be an independent research scientist but got pushed around too much by NSF, and now work as a seismic hazard modeler for a nonprofit[1]. Seismic hazard and the related science has always been closer to my interests than longer-term plate tectonic stuff, but we couldn't get access to our intended field area in Tibet so I sort of pulled that project out of my... hat based on some other research we were doing on a neighboring mountain range during that expedition.
I never liked school (although parts of grad school were great and my postdoc was fabulous); I like doing science but don't want to be an academic. Most people with my background go into energy or stay in academics.
The seismic hazard work is great. It's programming and stats-heavy but there is still a lot of room for looking at the Earth (topography data in GIS, earthquake data, etc.) as well as travel and working with people from all over the world. There is also still a huge amount of room for improvement at all levels, from the science to the modeling techniques and tools, UIs and workflows.
I keep thinking of starting a little research institute (nonprofit) so that I could more easily get grants, etc. but I'm busy enough with work and unfunded but fun side projects that I never getting around to tackling all of the legal and paperwork. One day...
The 660 km boundary (aka the 660 km discontinuity) is primarily* a mineralogical phase transition in the mid-Mantle. What that means is that the bulk geochemistry above and below this boundary are the same, but the crystalline structures are different (different mineral assemblages are stable at different temperatures and pressures given the same bulk rock chemistry, and the transitions are sharp-ish rather than gradual). The rock below the 660 boundary is maybe 10% more dense than the rock above. Because rock in the mantle is viscous (say, 10^20 Pa s) in the absence of persistent stress or pressure gradients, any topography on this boundary should eventually level out. So seeing kilometers of topography on the boundary means that there are some sort of persistent differences in force in the mantle of magnitude 10-100 MPa that can sustain the gravitational potential energy gradients produced by irregular topography and therefore irregular density distributions. Over broad scales (hundreds to thousands of km laterally) this could be from the big mantle convection cells that drive tectonic plate motion on the Earth's surface. At smaller scales I have no idea what could be driving it.
Another interesting thing about the 660 km (and 410 km and shallower) phase transitions is that I think that the density and viscosity contrasts due to the phase transitions causes a lot of the deep earthquakes such as the Bolivian earthquake from the paper. These earthquakes are in a subducted (sinking, falling if you will) old slab of oceanic crust. As these sink due to density contrasts (they are cold from being at the Earth's surface), they will slow down when they pass through the 410, 660, etc. phase transitions and should deform, kind of like a big icicle that falls of a cliff into water fracturing when it hits the water's surface (except it may continue to sink).
* Some say it's a chemical boundary as well, i.e. that the material above and below doesn't mix. I think most high-resolution seismic imaging of the mantle shows that many convective features such as mantle plumes and subducting oceanic plates penetrate the 660 discontinuity so I don't know if I believe this but it's hard to say and this isn't my area of expertise. It could be either or both although we have solid experimental and theoretical thermodynamic evidence for saying that these are phase transitions.
People do seem to be interested in landscape development, minerals (pretty crystals are cooler than pieces of shale), earthquakes, etc. Paleontology is typically housed in geoscience departments too.
From a research perspective, geoscience is extremely fun. Even to those infatuated with the Earth such as myself, the individual topics of study can get a little dry. However, geologic problems can be approached from a wide variety of methods, and to solve those problems that are still standing, a research group will come at it from many angles. This includes, but is not limited to, physics-based computational modeling, hiking, isotope geochemistry, fossil collection, statistics, satellite imagery analysis, acoustic physics, technical drawing, computer simulation, spherical geometry, and smashing boulders with sledge hammers.
For example, one chapter[0] of my PhD thesis (studying the development of fault-bounded mountain ranges in Tibet) I spent several months camping in beautiful Tibetan mountains doing geologic mapping and sampling (which is hiking, making qualitative and quantitative field observations and measurements, as well as digging holes and picking up rocks), then I came home and did a lot of radioactive isotope geochemistry of the minerals apatite and zircon within the rock samples: These minerals contain uranium and thorium; as the U and Th decay, they produce 4He (an alpha particle). At high temperatures, those particles diffuse out of the apatite and zircon crystals, but at low temperatures the 4He is retained in the crystals. So you measure the ratio of 4He to U and Th, and get an idea of when the crystals cooled below the diffusion 'closure temperature' (which is dependent on cooling rate). By taking these measurements over almost a vertical kilometer along the mountain range, I could estimate how fast the mountain range was rising, because it cools as it rises out of the surrounding crust. But it's a bit complicated to do the calculations right because there are lots of small issues (how fast the rock in the mountain range cools is dependent on the ambient temperature of the crust, the thermal properties of the rock, how much radiogenic heat production there is from K, Th and U decay, the temperature of the surface of the earth, the irregularities of the topography, ...) so to do it right you have to make a finite element model of the crust and simulate the thermal evolution as the crust deforms due to faulting and mountain range development. This is only a forward model, so to figure out the whole history of deformation including faulting and mountain range uplift rates through time, and deal with uncertainty in the thermal parameters of the crust, I had to run thousands of forward models. Lacking a cluster, I had to teach myself Python and how to use AWS EC2 instances to do embarrassingly parallel finite element modeling (I used the PiCloud library which was incredible but died in an aquihire event).
[0]: http://onlinelibrary.wiley.com/doi/10.1002/tect.20053/abstra...
Today's earthquake was a strike-slip earthquake, where two parts of the crust slide laterally by each other on a fault plane inclined close to vertically in the crust. The fault is probably oriented NW-SE [1], parallel to the San Andreas fault, although from the pattern of energy release from the earthquake (known as the focal mechanism[2] or moment tensor[3]) it also could be on a NE-SW oriented fault, with the direction of shear being the opposite. Because this was a strike-slip earthquake on a vertically-inclined fault, there won't be more than a few cm of uplift or subsidence of any parts of the earth's surface.
The domino-style faulting that occurs in the Basin and Range of the US, basically from Owens Valley to Salt Lake City, is an expression of 'normal faulting' (rather than strike-slip faulting). Normal faults are inclined from the horizontal, and the block of crust above the fault slides down the fault, like down a ramp. After a lot earthquakes (hundreds to thousands of M6+ earthquakes) the blocks have rotated on a horizontal axis quite a bit, so that they are no longer upright [4]. Furthermore, and quite importantly, as a result of this faulting, the crust (or at least the upper crust where the faulting happened) is both thinner from top to bottom than it was previously, and wider than it was previously--we say that the crust got 'extended' because it is horizontally lengthened/widened. You are absolutely right that Death Valley is forming in this kind of environment.
There are two main reasons for crustal thinning and extension. One reason is that the boundary of that part of the crust moved away, so the crust stretched or extended to fill the gap. The other is that the crust was too thick and high, so it spread out. The continents are kind of like rafts of granite floating on more dense, hot, ductile rock below (the mantle). The density contrast between the lighter crust and the mantle is sort of like icebergs floating in sea water, so most of the continents are below the surface of the ocean basins. When a big mountain range is built that gets high, it also has to have a thick root to support its surface elevation, like the undewater part of an iceberg. However, the crust isn't always strong enough to support a big mountain range for a long time, and so it will break apart under the force of gravity and spread out laterally, reducing the gravitational potential energy contrast between the (formerly) high mountains and the surrounding lower elevation crust.
It is thought that in the western US, both processes (the moving boundary condition, and the gravitational collapse and spreading of the crust) have been the cause of the crustal extension that produced the domino-style block faulting. The big collapse was probably during the Miocene, say about 15 million years ago, which produced a lot of the faults and smaller mountain ranges that we see today. Many geologists think that California was one or two hundred kilometers closer to Colorado, and the area that is now Nevada and western Utah was narrower and much higher--say a mean elevation of over 10,000 feet. This has been nicknamed the 'Nevadaplano' in reference to the Altiplano of Bolivia and Peru, which is an analogous geologic feature. I think that there is also a slight component of extension between the North American and Pacific plates at this latitude, i.e. the Pacific plate is mostly sliding by North America on the San Andreas and parallel faults, but it might also be moving away from North America (i.e. Kansas) at a few mm per year.
[1]: https://earthquake.usgs.gov/earthquakes/eventpage/ci38457511...
[2]: https://en.wikipedia.org/wiki/Focal_mechanism
[3]: http://seismo.berkeley.edu/~rallen/eps122/lectures/L12.pdf
The magnitude scale that is most used is an expression of the total energy release in the earthquake is called the 'moment magnitude' or 'work magnitude' because it's measured in those units (Newton meters or dyne-cm). It is calibrated to be similar to the original Richter scale, which was an empirical, I believe unitless, scale based directly on seismometer readings. If someone credible says that an earthquake is a 3 or a 7 or something, they are almost certainly referring to the moment magnitude. The 1989 Loma Prieta event was a M 6.9 event, Northridge was M 6.6 or 6.7.
There is another measure called the 'intensity' that you may be referring to with the 'apparent magnitude' reference. This is a non-quantitative, basically ranked categorical description of the amount of ground shaking and subsequent damage that occurred. The most common intensity scale is the Modified Mercalli intensity scale; it is usually (and correctly) denoted in Roman numerals. The Wikipedia page for the Mercalli scale [1] is good, however I prefer [2]. The intensity has a sort of tree-falling-in-the-woods element to it: the categories are based on how people and the built environment respond to the earthquake, so did earthquakes in the 4.6 billion years before humanity have intensities? They had magnitudes.
Quantitatively, ground shaking is measured as 'peak ground acceleration', a force, usually compared to gravity 'g' (i.e., 9.81 m/s^2), as 'peak ground velocity' which is a velocity (m/s), or as 'peak ground displacement' which is a distance.
The intensity of an earthquake will be related to the peak ground acceleration and velocity, as well as the duration of the shaking. These are functions of both the earthquake properties (magnitude, faulting style, depth) as well as the properties of the ground in the region of the earthquake, and the distance from the earthquake (as the amplitude of the waves decreases with distance). Solid rock does not shake nearly as much as loose or wet sediment, for example, and some geologic basins that are deep pockets of sediment surrounded by bedrock can amplify earthquake waves and make the shaking locally much worse than it was elsewhere, even closer to the earthquake. This was a big deal in Loma Prieta, for example--the damage in Oakland, built on water-saturated sediment, was worse than in some of San Jose, or in my (current) house in the Santa Cruz mountains just a few km away (I was safely dodging tornadoes in Tulsa at the time).
[1]: https://en.wikipedia.org/wiki/Modified_Mercalli_intensity_sc... [2]: https://www.mcsweeneys.net/articles/levels-of-the-mercalli-s...