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timo last won the day on May 31

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583 Glorious Leader

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. Joigus already mentioned is implicitly, but I think it's worth pointing it out explicitly: When it comes to the exact integral, the different methods with equal-width rectangles that approach dx->0 do approach the same limit (with some exceptions that are not relevant here). And this common limit is called "the integral". For many important functions, e.g. polynomials, we know how to compute the limit exactly. And we don't even care about the rectangle construction in these cases, and just jump to the known solution - which does not depend on the exact rectangle-method that has been us
  2. Try to formulate your collection of mathematical symbols in English and then try to understand what it says. Then, adapt it according to the other situation. Translate back into mathematical symbols after that.
  3. Yes, both methods approach the same limit. In this case, you can explicitly write that down: Assume you integrate from 0 to 1, and you split the range into N intervals of equal length. In the first case, your integral approximates as [math]I_{1, N} = \frac 1N \sum_{i=0}^{N-1} f(i/N) = \frac 1N \left( f(0) + f(1/N) + f(2/N) + \dots + f((N-1)/N) \right)[/math]. In the second case, your integral approximates as [math]I_{2, N} = \frac 1N \sum_{i=0}^{N-1} \frac 12 \left( f(i/N) + f((i+1)/N) \right) = \frac 1N \left( \frac 12 f(0) + f(1/N) + f(2/N) + \dots + f((N-1)/N) + \frac 12 f(1) \right)
  4. I was already chuckling when you posted this, and the thread seems to prove this part of your prediction wrong. In my experience, it is the non-scientific content that get the most attention on sfn. Probably because it is easier to respond to. I certainly put less effort into this post than into science-related posts. Possibly even less than into my one-liner that is the first reply in this thread when I thought this was a genuine question.
  5. I helped my colleagues to move a Volkswagen E-Up for ~50 km between two cities about eight years ago - highway in one direction, smaller roads in the other. The car was used in a field test in the city I lived in, so it made sense for me to just go from/to work by car instead of by train. I drove on a cold but typical German winter day. Turning on the heating approximately halved the remaining range, and I ended up turning heating on and off periodically during the trip. I found that experience quite impressive back then, because I was not aware of such basic issues as heating before. I imagin
  6. I agree that a lot of information is readily available. In fact, I propose that young, critical and open-minded scientists should use these information to answer the questions they might have.
  7. Perhaps reading up on Climate Change would answer some of these questions to the young, critical and open-minded scientist.
  8. In most cases, two days to reply to an email is not considered much (and neither would a week).
  9. I felt the urge to quote this. Fun fact: A Greek influencer named Archimedes became famous for his obsession for lifting heavy objects with little force by using a lever.
  10. I also think the bandwidth to transfer the satellite images that show the whole earth being flooded was very limited back then 📧. On topic, in case it wasn't clear by now: Since all the water for flooding already is on earth, and already pushes as weight on the ground (including the ice), you should expect no significant effect on the stability of the ground when it rains. Also, as studiot said, if all ice melted, the water would not cover all of the land. Here's the first Google hit I found regarding this: https://www.nationalgeographic.com/magazine/article/rising-seas-ice-melt-ne
  11. Where would the water for the rain come from?
  12. What you talk about seems more like a method for calculation to me than an actual measurement. You can indeed calculate the volume of a body by taking a surrounding volume and then subtracting the parts of the surrounding volume that does not belong to the body (in your language: the volume filled with gap values). This may in some cases be an efficient method, e.g. for a block of stone with a cylindrical hole. In the general case, if you have a generic way to calculate the amount of gaps then you could probably use that method to calculate the volume of the body in the first place. This, as y
  13. I never heard that mentioned as an issue for actual projects. But yes, maybe. How, specifically, do you think that lack of water is a problem for solar power projects?
  14. Or you take the engineering approach and just read-off provided numbers: https://globalsolaratlas.info/map. If I remember correctly, the tool even has a "mark an area and integrate" functionality. I'd like to say something constructive here. But I find it hard to make out what this thread is about, or to add anything meaningful on this very vague level. I mean: Yes, solar panels generate electricity. Yes, you can put them on rooftops. And yes, there is lots of sun in the equatorial regions. And to Swansont's post: Yes, there are problems in detail. Transport and storage are somewha
  15. When it comes to experiments on black holes, it gets a bit tricky. You cannot produce them in the lab, and none of these things exists naturally on earth. In fact, we had put lots of efforts into even detecting anything in the universe that we concluded/agreed must be a black hole. While double-checking if even that has happened, yet, I ran into an article claiming that 2019 was the first time you could get an image of a black hole (https://www.sciencemag.org/news/2019/04/black-hole). Don't pin me on the accuracy of that statement, but my point is: It is already pretty challenging to detect bl
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