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timo last won the day on January 9

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About timo

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    Math, Renewable Energies, Complex Systems
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    Data Analysis
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    school, civil service, university, public service, university, university, research institute (and sometimes "university", as of lately)
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    Ensuring a steady flow of taxpayer money to burn

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  1. The explanation of the photoelectric effect and the theory of relativity would match that criterion. I kind of thought that Isaac Newton had a job as master of coin or something like that, but I could not verify that. I am not aware of any more recent examples - not even the proverbial exceptions that prove the rule. That makes me wonder to what extent "only scientists make contributions to science" is a tautology (i.e.: science is defined as "what professional scientists do"). For example, you could argue that Mark Zuckerberg has started the largest sociological experiment in the history of mankind. But the people credited for scientific contributions are the hitchhiking university scientists that write papers about it.
  2. Not sure I understand what you are asking for - I certainly don't know what you mean by empirical cycle or retrospective study. But to me, the general approach seems to be: 1) Define one or more quantitative measures for the sale of phishing tools, e.g. number of sales, volume of sales, number of different products offered, number of different products sold. 2) Find data source from which you can determine these measures. Note: The actual progress may be doing this step first and then defining measures that you have data for - it was just easier for me to describe the steps in this order. 3) Plot the measures over time in a suitable time binning (bonus points: with statistical error bars). 4) Define the time that you count as "Corona pandemic" and see if there are any visible trends in your graph. 4a) Alternatively, just try a few assumptions. E.g., for a suitable binning, fit two different constants to the data for the non-Corona and the Corona time intervals and check if these constants look significantly different (bonus points: calculate a statistical measure how different they are). I imagine step 2 to be the hardest by far. Despite often planning to do so I have never tried to navigate around in the dark web. But the term already indicates that it will not be easy to get reliable overview data from it - especially since you are trying to monitor activities that are at least borderline illegal.
  3. I don't think I understand anything you just wrote. But I'll give it a try: - "Does -f"(x) imply -1 ?": -f''(x) means -1*f''(x), if that was your question. It does not mean that f(x) = -1 or f''(x)=-1, if that was the question. - "Does linear differential reffer to a "radius"?": Differential equations are a special type of equations that relate functions and their derivatives. They one of the most important mathematical concepts in physics. 'Linear" is just a mathematical property of this equation. - "When you say normalization is ignored, is that for ""All QM waves?"" ": Usually, wave functions must meet a requirement that they are "normalized". In my example, I ignored this requirement because it is irrelevant for the point I wanted to highlight. - "After all the electron isn't that easy to figure out, plus the nature of its movement is not yet confirmed... ": I kind of disagree with this statement. Moreover, I think it has really little to do with the question why the constant Pi shows up in the context of QM. I think my first attempt to answer your question did not go very well. So let me try an alternative story: In many important cases, wave functions can be expressed as sine and cosine functions. The Pi comes from the 2*Pi periodicity of these functions (if you'd express the arguments in terms of degrees you'd get 360s popping up in the equations, I guess). For example, if a wave function looks like f(x) = sin(x), it has the wave length (the distance after which it repeats itself) of 2*Pi. If the function should have the wave length 1, the function would look like f(x) = sin(2*Pi*x).
  4. Wave functions are solutions of linear differential equations. Mathematically, solutions to linear differential equations contain sine and cosine (or, equivalently, exponential functions with imaginary exponents). The Pi comes in from them. Example: Imagine the Schroedinger equation for a free particle would be f(x) = -f''(x), where f''(x) is the 2nd derivative of f(x) with respect to x. A possible solution for this is f(x) = sin(x) (normalization ignored for this example). The wavelength of this wave is 2*Pi.
  5. I find it really hard to get a coherent picture of the opening post. I see three different aspects that trigger different tones of response, some of which are pretty redundant with the replies given already. So maybe I'll just briefly touch all three aspects to show why at least I have problems with getting a clear picture of this thread. First, there is the relatively long explanation about sums or averages not giving the full information about the individual components that contribute to them. That is correct, mathematically trivial and well known to everyone working in any field of complex systems. It is also pretty banal, and applies to pretty much every science or society related number you ever hear in the TV news: the gross-domestic product, the number of Covid-19 infections, salaries in the IT sector, the time that kids spend on social media, ... . Now, admittedly, there are a lot of people who, for different reasons, appear to limit the discussion of a topic essentially to these numbers. So for this aspect of the opening post I am torn between a sarcastic "great work, Sherlock" and an honest "it is great that you are aware that this one number is not the full picture". I think the relative volume of the sub-optimal example pushed a few people towards the former reaction. Second, there is the aspect of the specific role of an average temperature in climate science, or more specifically its role in the climate change debate. For me, this would be a great topic of debate and learning. I worked as a scientist in a somewhat related field for several years, and still my understanding of it is very basic and with a lot of "that's how I imagine it is". I'll not formulate a coherent story for this post, but just throw in a few imho relevant pieces: In the context of the greenhouse gas effect the average temperature is a very sensible, experimentally-measurable observable with some weaknesses (energy stored in the oceans). Climate scientists don't model average temperatures but create sets of future scenarios for the evolution of complex systems. The evaluation of these scenarios cannot be reduced to a single number that tells you how good or bad the scenario is. What you can do is group your scenarios according to some meaningful parameter, see what typical scenario effects are for that parameter, and then have some delegates barter about how bad you want it. Remember: The problem with climate change is not the increase in the mean temperature, but increase in extreme weather conditions, change in habitability on the planet, the self-enforcing mechanism (loss of reflective ice, melting of permafrost, methane emissions from the oceans), and possibly a bit of land loss from rising sea waters. And finally, there is the third aspect of the opening post which really turns me off: The first half of the first sentence and the last sentence. Thanks to them, the post with potential for an interesting discussion comes in a wrapping that says "troll, ignorant or political agenda inside" to anyone with a bit of experience in social media. So despite giving the OP a huge benefit of doubt with the time I put into this post I don't want to leave them without comment: 1) "Climate scientists are concerned with deviations in the average global temperature": No, they are mostly not. Type "climate science" into Google and check out what they do. 2) "Has there been any research in this area [of what is really going on]?": Yes. There is a complete scientific discipline called Climate Science that is concerned with these questions.
  6. C++ supports state-of-the-art random number generation. So it would be easiest to use a c++ compiler for the code (I expect that it should compile the C parts just fine) and pick an rng that is provided by the language standard library. So: Pick up to one: http://www.cplusplus.com/reference/random/ . I do not expect that the choice of the rng matters for this case. But it is a good habit to never run a Monte-Carlo simulation without a good rng, and including one is really easy in most programming languages.
  7. Do I understand it correctly that the issue you see is the following: One unit in x-direction is a different amount of pixels (or cm on paper, if you'd print it out) than one unit in y-direction. Is that what you mean? That is indeed the case. I have never considered a problem. In my experience, this is the default behavior of most plotting engines. It is normal that in addition to looking at the shape of curves you also have to look at the numbers on the axes (small effects can often look large if you just zoom-in into the graph). And I do think there are more use-cases for having different spacings in x- and y-direction than for having the same spacing. In fact, it is very common that x- and y-values are not even comparable (e.g. one can be a time and one can be a number of people). If you really want to have identical spacings, I think you can at least approximate that by setting the ranges by hand and forcing the aspect ratio or the size of the picture to fit to the ranges (same height and width of the x- and y-ranges are the same, double width if the x-range is double the y-range, etc). To set the range by hand, you can use curve(x^3, -3, 3, ylim=c(-3,3)); grid() Not sure how to set the window size by commands, but it should be possible. For an approximate solution, if you use R-Studio (which I really like for working with R) you can just resize the plot window to have the aspect ration you want and then export the image.
  8. I kind of did what in hindsight I feel should have been provided by you in your starting post: Created the plots you spoke about and posted them here. The code is f = function(x) x*x*x d3 = seq(-3, 3, 0.1) d5 = seq(-5, 5, 0.1) dx = seq(-3, 5, 0.1) plot(d3, f(d3)) grid() plot(d5, f(d5)) grid() plot(dx, f(dx)) grid() The created plots are attached. I see no problem with them. I am not aware of any technical problems that R has. While not the question: I do not recommend to get used to R just because it has the reputation of being the most common software used in statistical data analysis. The statement may actually be true. And R is not bad, either. But I feel that Python can already compete with R in terms of (advanced) functionality, and will be the future. And for just plotting functions, there should be much easier solutions / more comfortable solutions (I had used gnuplot with lots of success for a long time).
  9. That news came as such a shock to me that I dropped my coffee cup. Okay, seriously: You probably heard that in some context of "... is in reality just curvature of a four-dimensional space-time" (or even more weird context - my example quote at least makes sense on the mathematical level). A guy named Albert Einstein revolutionized our understanding of gravity some 100 years ago - from an understanding that can be taught to every school kid to an understanding that is taught as an elective specialization course for university students of physics. I imagine there are a lot of ways to make strange-sounding claims coming from that. But I think it is safe to say that it can be demonstrated that gravity exists. Edit: too late and even with the same joke ... 🙄
  10. Quarantine recommendations are 14 days. And I think this is exactly for this reason: The general time-scale that an infected person is infectious is 14 days (not taking into account re-infections which are still an open question). At the beginning of the Corona situation I did some simple simulations for the development. Apparently, I used 12 days back then, but I do not recall where I got the number from.
  11. I am aware that this is not the point of the thread, so sorry for nitpicking on this. But since CharonY's point B) was my initial reaction when I saw this thread, I'd like comment on this: Saying that "Corona virus disease first emerged in Hubei province China in Dec 2019" is much less specific than the "current global pandemic caused by Sars-cov-2 got it's start about the middle of last November when patient zero contracted an infection from a wet market in Wuhan province when he purchased a pangolin from a wet market which he had for dinner". Specifically, "first emerged" can be read as "was first discovered", which is actually very different from "was first transmitted to a human" (i.e. patient zero). That sounds like it could be correct to me. Your story sounds like an American president could have made it up while straying away from an unrelated question asked by a reporter. I cared much for the origins of Covid-19, so I am not even an interested layman on that topic. But the very first Google hit I get on "origin of Covid-19" is a relatively recent report about a WHO spokesperson saying that Wuhan may not even be the location of patient zero (let alone a pangolin sold at a seafood market): https://www.foreigner.fi/articulo/coronavirus/who-admits-wuhan-may-not-be-the-origin-of-covid-19/20200803155142007196.html @Buckeye.: I am aware this post may appear a bit rude. That is not my intention, and no offense intended! I just feel you should question if what you think you know is really correct, and I don't know enough about the topic myself to do that in a more constructive way.
  12. It isn't. Car traffic makes up ~10% of the world's energy-related emissions (https://www.fia.com/sites/default/files/global_reduction_in_co2_emissions_from_cars-_a_consumers_perspective_0.pdf [*]), and that's not even considering construction, agriculture, forest fires, melting of permafrost ground, methane-release from the sea, etc. Assuming the thread is not about how realistic the consumption values are: I did not follow the link, but there are two (related) ways to solve such questions: 1) First try to find out how much the consumption would be per single km. Then, from that number find out the consumption per 100 km (hint: it's 100 times the number before). 2) If you know how to solve equations, solve "88 l / 100100100 km = x / 100 km" for x. I strongly advise to try solving it in the form I wrote down, i.e. including the units, not as "88/100100100 = x/100". Especially since the thread title is "Dimensional Analysis". [*]: I am totally aware that this is a car lobby publication and that their choice of world-wide values has probably been to downplay the share in the major car markets. But I have no reason to doubt the approximate value.
  13. Not sure what the focus of this thread is (and the two replies so far certainly don't help me to identify a focus). So I'll just throw in a few random comments: - You do explicitly mention "hiring recently-unemployed people". I am not sure how different that is to "hiring people" to you. For hiring people to do X, there are the obvious questions who hires/pays and often also how X competes to other things that could be done with the (monetary) resources. I think there is no shortage of good ideas that someone could do if they were just given the resources. Restricting your hiring to recently-unemployed people would be considered inefficient from a free-market perspective (note: I explicitly do not mean that the free market perspective is the one you need to take - but it is a major voice in economic decisions in most countries). Maybe it is more efficient to re-assign a trained lumberjack and have the unemployed history teacher help in a children daycare, for example. - If you do not re-grow the trees, burning wood is not much different from burning fossils fuels with respect to the climate impact. It is the re-growing that makes wood count as a renewable energy source. (Of course, burning the wood to replace some fossils is better than just burning the wood in forest fires - greetings to Brazil ...). - To burn wood instead of fossil fuels you have to change the energy-generating technology, for example replace oil burners with wood burners for heating houses. This is not a problem in principle. But you need to make sure in practice that this pays off. I would actually not be too surprised if the current wood market in the US could simply absorb some extra wood you cut, and that you would not need to "make room" in the fossil energy sector. - For educational purposes, I strongly suggest you try to do some estimate calculations about how much fossil fuel usage you could reduce by having extra wood. In my experience, most people do not understand how extreme a replacement of fossil fuels is in terms of scale / the numbers. The US national oil consumption should be easy to find, a kg of wood has roughly the same energy content as a kg of oil => just have a look at how much of an impact that replacement would have. Spoiler: I am not aware of any future energy scenario that assumes that we can simply replace fossils with wood and forget about all these annoying issues with solar and wind.
  14. I meant the function in the sense of a mathematical function in this case. The point is just to highlight that you have five different functions. The code of the functions would be: def fun1(e): return e+0 , def fun1(e): return e+1 , etc. Except that the functions are not named fun1
  15. You are not invoking the function fun1(e) and storing the results in the list. You are storing five different functions fun1(e) in a list and never invoke them. Namely, the functions you store are fun1(e)=e+0, fun1(e)=e+1, fun1(e)=e+2, fun1(e)=e+3 and fun1(e)=e+4. What the print tells you is exactly this: Your list contains five functions named fun1 at the memory locations 0x7f6d8a364e18, 0x7f6d8a28a158 etc. If you wanted to invoke the function and store its values you'd need to invoke the function and type something like fun_list1.append(fun1(42)) (in this case you invoke it with the parameter 42 - every other number would work, too). And of course writing fun_list1.append(42 + j) would be the cleaner code to do the same without the unnecessary function. There are legitimate reasons why sometimes you want to store an actual function instead of the function result (you don't know the argument at the moment, you want to execute it multiple times, ....). You can call the stored function fun1(e) just like any other function. If you want to see evaluated results, change your print statement to print(x(42)) and your output should become 42, 43, 44, 45, 46 (again, the argument 42 is just a random number, and any other number should work).
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