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Given names, family names... since when ?
It is. You could in principle trace your family tree back to the Middle Ages in Spain. In actuality, of course, very few people --if any-- can do that. Trusting that your great-great-great grandparents and beyond had everything under control when it came to procreating is another matter. 😅 Some Basque family names, like Urrutikoetxea ("house from afar") or Etxebarria "new house" are a bit more dicey as to their origins being based on a gild, or a piece of land.
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≤ can mean- till it or till it OR infinity ?
@HbWhi5F , could you rephrase the question, please? Obviously, said function cannot be bigger than its value at x=1. It cannot be less than zero either, so there you go.
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What the mathematician saw while scuba diving
Why doesn't the spoiler work? It's the plural of @Genady 's visual answer.
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Why did motivated reasoning evolve in humans?
I think we tend to overestimate the immediate evolutionary value of high-level reasoning and data gathering that we see today in sophisticated science, at least for the individual and the close kin. I doubt individuals or clans tens, hundreds or even millions of years ago did anything much in the way of, eg, considering counter-arguments to a given argument. The most important thing was probably to act quickly in a way that's not obviously contrary to survival conditions, and has worked within reasonable limits. And now that I think of it, @exchemist has very much answered to this in a way I would subscribe to. So sorry I initially misunderstood the premises.
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Why did motivated reasoning evolve in humans?
I still would like to know whether @Otto Kretschmer means 'motivated reasoning' in a sense that specifically can be phrased as, As defined in https://www.sciencedirect.com/topics/psychology/motivated-reasoning
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Why did motivated reasoning evolve in humans?
Thank you. I hope people who know more about this than you or me can illuminate the nuances. I must say I tend to see much that's going on among humans (in evolutionary terms) as a product of the needs of small clans having to struggle for survival 50'000 years from now until the present. Agreed. Cephalopods and corvids come to mind too for relatively complex congnitive features. Sea mammals and great apes immediately spring to mind, of course. I also find difficult to believe that dinausaurs didn't develop fairly complex cognitive abilites, given that they we here for more than 200 million years.
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Why did motivated reasoning evolve in humans?
Where do you place the starting gun, then? I'm thinking now that I may have misunderstood what the words 'motivated reasoning' mean in psychology. If I understand correctly, it's about emotional bias. From https://www.sciencedirect.com/topics/psychology/motivated-reasoning:
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Why did motivated reasoning evolve in humans?
My take: For tens of thousands of years humans must have done well enough with mostly inductive thinking: It's always worked, let's keep doing it --in its crudest form. In order to do better than 'well enough', the most powerful driving force behind why people would have been led to motivated reasoning --that I can think of-- is: This time it didn't work. Why? Something like "we've lost two members of our clan, even though we did exactly the same. What could have failed this time?"
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Some basic assumptions of human body and celestial nine planets
Most people, Oceanians, pharmacists and books would find this kind of listings categorically incorrect.
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Scientists discover liquids can fracture like solids under extreme stress
Unfortunately, no. I didn't say it was necessary though. It could be sufficient. It could be neither: only highly correlative statistically. But any illuminating comments on your part are very welcome.
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Scientists discover liquids can fracture like solids under extreme stress
Gravity plays a big part though, somehow analogous to the high stress that the authors of the paper mentioned for the case of fluids.
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Today I Learned in Mathematics
Brilliant. I didn't know the joke.
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Scientists discover liquids can fracture like solids under extreme stress
This is very interesting. Granules in any conglomerate are several orders of magnitude bigger than molecules, so this suggests that the surrounding processes, playing the role of a re-scaled 'solvent' perhaps? replicate what molecules would do in a fluid, only re-scaled. Does that imply something like landslides being pictured as some kind of re-scaled phase change similar to what the original post by @paulsutton seemed to imply? When I say 'solvant' I include air, water, the vacuum... The vacuum is a solvant, as far as any of us should be concerned.
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Scientists discover liquids can fracture like solids under extreme stress
I don't know, as the abstract doesn't mention what this phase change consists in. I would be surprised that it didn't somehow involve a discontinutity in the velocity field. Eg: They don't mention domain walls either, but I'm sure they are involved as well. Upon further reading, you may be right that it's more about density than velocity. As to the materials, it is my understanding that the fluids they use are mostly polymers, while they also claim the phenomenon is quite universal. I don't see where metals are involved, but again, I could be wrong, of course.
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Scientists discover liquids can fracture like solids under extreme stress
In fact the authors describe a sonic effect too, reminiscent of what happens in the case you mention. I agree on TOEs and quantum hallucinations, etc. This is much more interesting. x-posted with @studiot