joigus

Science today is vast, but interesting epistemological problems arise in all fronts. Ethical too, taking @swansont's cue. Philosophers today, willing to say anything significant --that scientist will pay attention to--, must learn at the very least the conceptual framework of scientific theories, their degree of success, as well as the point at which they fail, falter, or simply shrug their shoulders. Their limits, in short, and a working knowledge of how these limits appear. It takes a very special kind of person, and it requires a considerable degree of specialization. There are people like this, and sometimes they do a thankless job.

I must confess I'm at a loss at defining what makes a good politician, in the sense that @MigL has used as a definition, which I think is quite appropriate for starters. But I suspect it's a lot more about wiles than it is about pure intelligence. I very seriously doubt that we will ever meet a successful politician that's a problem-solving whizz, or a paragon of creativity, or a master at engineering economic miracles. I also think there's an element of unpredictability. Enough people must like you --the hairdo, the way you speak or even smirk may play a part there--, and then you must manage to get some work done, so I suppose being able to spot the right people for the "real" job is a big part of it. I tend to see leading politicians as the final decision for the logo of your car make, TBH. Something like this, I suppose:

It depends on what you mean by "information", and on what you mean by "the system". For example: If you mean accessible (macroscopic) information, and the system is the whole universe, it's never true. If you mean all information (the negative of so-called fine-grained entropy), and the system is the whole universe; it's also never true (fine-grained entropy is always constant for the whole system+environment). ... Only very rarely it's true (example: living organisms). Living organisms can organize (the information stored in them grows) at the expense of "disorganizing" the environment. So you see, you must be a lot more careful when making sweeping statements like that. I also agree with what you've been told by other users on numbers and the infinite.

The Picts wouldn't wear it!

I couldn't agree more. I think the sooner we make this discussion less political and passionate, the better for the flow of ideas on a topic that interests us all. I don't want to commit an opinion yet. I want to consider more arguments. Very interesting topic BTW.

I think @Peterkin has a point and should be given a fair hearing before anybody gives them another flurry of neg-reps. I would like to hear more arguments. After all, I don't know of any waiting list of well-to-do people in line for handling the LHC accelerator to produce QCD jets --wo. the assistance of a professional physicist. What about well-to-do people waiting in line to extract ice cores in Antarctica? --wo. the assistance of a professional field geologist? Aeronautics has an undeniable element of thrills for the rich that we should discuss dispassionately. Having said that, I totally understand @iNow's point: That element plays too. Mind you, amateur astronauts can fall on our heads. Perhaps irrelevant?

You're welcome. I didn't know that form either. I did remember that the equation of an ellipse in polar coordinates is an ungodly mess if you try to express it in polar coordinates with the foci equidistant from the centre, but looks nice and simple with one focus sitting at the origin. I just assumed something similar happens for the catenary. The rest was a wikipedestrian approach.

https://en.wikipedia.org/wiki/Whewell_equation Homework. No linear algebra or group theory here.

I don't think MigL would have any problem with those. They're not of the insect variety.

Naked mole rats are not really rats, and they're not just any mammals: (Wikipedia) Sharks are also very resistant to tumours. I don't know what this has to do with beauty, but it does have a lot to do with the unexpected. Nature is truly amazing.

I hesitate to hesitate.

He's the only one who's objected to the beauty standards of this thread. But he didn't mention any wars...

As always, we should ask the beholder. https://en.wikipedia.org/wiki/Naked_mole-rat I think they are. But I'm no expert on beauty. Let's ask @MigL.

Are those naked mole-rats?

OK. I would like to make it up to you all for having posted that beautiful but non-legit picture. A real tepui (mount Roraima in Venezuela): https://en.wikipedia.org/wiki/Mount_Roraima The extraordinary plants of mount Roraima: https://www.bbc.co.uk/programmes/p00lx3pb Lack of nitrates in mount Roraima is due to heavy rain, that washes away all the nutrients. BTW, I strongly recommend BBC's The Private Life of Plants. Enjoy!

Well spotted, @Ghideon!! My bad. I didn't give it a second thought. You really have an inquisitive spirit. Keep it up, is all I can think of saying now. 😮

Oh boy, I didn't see those. You're right; they look human made...

Karsts are amazing. Experts will tell you more and better, but they basically consist of sedimentary rocks formed by many millions of years of deposition, made up of carbonate-rich substance from scheletons of marine animals; and later eroded by water. I suppose that those column-like features come from particular locations where the rock is less soluble in water for whatever reason. Differential erosion is the key. Very nice picture. You always post a picture you took yourself. That's even more valuable! Thanks. +1.

Roughly, @MigL's point was that every thought that you have is influenced by the history of how that thought was formed. Whether you like it or not, your thinking is influenced by the thinking of those that came before. Again roughly, @studiot's point was that even the most apparently obvious statements are presumably 'contaminated' by hidden assumptions. (I think) More arguments have cropped up, and I'm finding difficult to keep up with all of them, but what I can say for the time being is that I do not think the question of reality affects very much the activity of scientists. Perhaps it's just a matter of stance. Some scientists may believe that there is an ultimate reality to be discovered and described; others --most scientists today-- prefer to think that science is about elucidating in more and more detail how Nature works. Physical theories should be --and are-- the same and be used in the same way no matter what stance one adopts. Concepts like 'reality' are more of an --occasionally inspiring-- philosophical motif for some than the reflection of an actual professional commitment to a goal. And may I remind you 10 million light-years from any of them, both Frank Sinatra --the singer-- and a poached egg are the same: a pointlike particle of approximately the same mass.

Promised. But it'll take some time until I sort my ideas. The yolk was too tempting.

This morning I've had Kant for breakfast. It was noumenal! Brilliant.

Ignore my answer on thread "Four-vector" and follow this excellent tip by Markus. Studiot's recommendation looks fine. It's just that I'm not familiar with it. The simpler toys to play with are called "affine tensors". They do not depend on the point of space you're considering. Special Relativity is the place to start --> nothing depends on the location. Then make tensors depend on the point of space --> tensor analysis. You will become familiar with a monster called "the connection", and "the Riemann tensor" and everything else come from that "connection".

Tensor analysis. A very complete classic book of which affordable paperback editions exist: https://www.amazon.es/Tensors-Differential-Variational-Principles-Mathematics/dp/0486658406

(My emphasis) Interesting. But what are you going to do with all those diffeomorphisms? Differentiability is hard-wired into GR.

Sure, if you're interested. Let me PM you as soon as I have the time to write some words to explain what it's about. It would be quite off-topic and improper here.