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I have to say that I am not a great fan of (formal) 'Logic'. I find it too narrow a concept. I much prefer the phrase, "rational deduction" which has a much wider scope. We had a thread a while back (not mine) debating whether 'Logic' is a subset of maths or Maths is a subset of 'Logic'. Of course, they have much in common but there are differences. A more interesting comparison, in my view, is between Maths and English and Rational Deduction.

You can action this all you want when you start your own forum. For now, you're doing more harm than good by continuing to comment as you are. Logic dictates that you shouldn't act abrasively toward those from whom you need help to get what you want.

I am not sure they are the worst (though in some ways they may be), but growing up in an area where you have underfunded schools and little career encouragement has been shown to be a big hindrance. Especially in working class areas there is often the base assumption that the kids will not go on to higher education. Even if there is interest, the quality of the high school has been shown to be a determining factor in entering higher education. Often, students in poorer school areas are underprepared, may never of hardly had any access to computers or the internet etc. Even overcoming these issues there is of course the cost of higher education in many systems (such as UK or NA) is prohibitive for many (which feeds back into the thought process for lower-income folks who just do not expect to be able to afford it to begin with). Even after getting university there are additional hardship for low-income folks which especially now has become quite apparent. Some cannot afford a laptop or stable internet, for example. I think that if especially affluent folks which all the benefits fail, it is more likely on them. However, for the others, there are clearly barriers that they need to overcome and they are not always well prepared for it. That all being said, an inquisitive mind with willingness to learn is clearly an important element. At the same time, I do understand that this in itself is a luxury that not everyone can afford.

Why is it always barriers imposed by, or the fault of society, when someone fails ? What part does personal responsibility play in this ? Markus Hanke taught himself GR ( and many other aspects of Physical Science ). It was not provided for him, but he wanted it and he got it. Barriers did not hinder him. You, yourself, have displayed a questioning attitude. One of the best ways to learn about things you know little about. Yet others come here with the attitude that what little knowledge they have , is all there is. They ask no questions, but make conjectures and proclaim results which more learned members quickly dismiss. And yet their attitude, not barriers, allows them to double down and insist they are right ( until they are banned ). A good attitude, and a willingness to learn, go a long way in these days of internet access and on-line courses.

The outcome is the same. The statistical distribution of many individual hits on the detector. The which-path information does not need to be physically observed, it only needs to be accessible in principle, for there not to be an interference pattern.

"Could we be wrong about everything?" Not any more. Not since you, or someone, asked that question. Imagine that we were wrong about everything. If that was the case then one thing we would need to be wrong about was our belief that we were right about things In that case, saying "I am not sure about knowing everything" would be right. In order to ask the question in the thread title, you need to realise that there's doubt and, in that case, having doubt would be the right thing to do.

The earth is orbiting the sun, the solar system is orbiting the milky way, the milky way is moving towards the andromeda galaxy, those galaxies are moving towards the great attractor, this super clusters is moving with the Hubble flow, etc, etc, etc...

There are two long range forces, gravitational and electromagnetic, and two very short range forces, color and weak ( flavor ). As far as we know, Dark Matter interacts with all other matter, including itself, gravitationally, but does not interact via the Electromagnetic force at all ( or only extremely weakly ). That means we cannot detect it by electromagnetic means ( no visible, radio, infrared, uv, x-ray or even gamma emissions ), but its gravitational interactions with matter and itself, will produce 'falls' or orbits around its center of gravity. It could also be captured by BH event horizons when it intercepts them. Dark Matter particles may get very close to each other, or even collide, but, since they don't interact via the color force, they will not clump together like quarks in nucleons, or protons and neutrons n the nucleus due to residual. And since they don't interact electromagnetically, they won't clump like electrons and protons in atoms. So I see very little chance of being able to localize a large enough mass of Dark Matter that it would be able to collapse to a BH. One type of neutrino is being investigated as a candidate for Dark Matter, so there is the possibility that it also interacts via the weak ( flavor ) interaction, but again, this interaction does not produce bound states.

I don't understand what you mean. Can you rephrase? On a humorous note, the point of calculus is x.

I remember our Primary School teacher telling us that we needed basic English and Maths so that we could get jobs in factories. My response was to do anything to prove her wrong. Most of my colleagues accepted her view without comment. I feel terrible when teachers say this stuff to people. As a teacher (now out of retirement) in my whole teaching career of 22 years, I have never told a child they could not do something. I have always stressed that they could do anything that they set their mind towards. I apologise on behalf of teachers. Sorry about your friend's son, that appears to be a mindset. However, a person has only failed when they admit it to themselves, in my opinion. I have taught in an area which can be described as an equivalent of the projects, and the mindset of a significant minority of students was exactly the same as the one that I viewed as a child. I take your point about generalisations and I did mention that doctors and other professionals came out of the same tough environments. It would appear that the successful minority of people have a different mindset and that mindset is maintained despite external circumstances. So, in my opinion, the rest of the people who are stuck in the ghetto have a mentality that is a story that they relate to themselves to keep them stuck in their circumstances. I have read your reply and the link. I take the point, underfunding and racism do contribute to negative attitudes. I also take the point that ghettoes exist in geographical location from deliberate Governmental legislation and decades of maladministration, and that other people have a mentality of what is expected from ghettoes. Despite those points, I can state that I am working with a teacher who was educated at primary level under a tree. Under a bloody tree! Yet she showed an aspirational mindset and is now the best Science teacher in my school, by some margin. The keyword in my opinion is aspiration. It was aspiration that took me out of Glasgow, took you out of Edinburgh and took that teacher out of a small village in Pakistan. Aspirational mindset disregards environment, in my opinion, regardless of what racists and class supremacists do in any part of the world. A person fails and stays in a stagnant situation when they relate the story of their failure to themselves. It normally starts when they blame others for all their problems...

Just elaborating on what @mathematic and @swansont have said... It wouldn't even make much sense geometrically. An angle is naturally (more simply) expressed as a ratio of lengths (arc/radius). The sine itself is a ratio of lengths too. If you define x in cm it's as much as saying that there's one circle which is the mother of all circles. The 1-cm radius circle!! A 1-cm-radius circle is a French thing. Why should a circle be French? (There is a 1-m bar in Paris keeping this standard of length.)

! Moderator Note We need some physics in discussions about physics.

Palpable entitlement and privilege. You also use "logically" impossible/possible incorrectly. Which is ironic considering the mention of Math. Seriously moderators can we have a logic section already so people can stop misusing the tool of logic like this? I can't even engage with this seriously due to this complete misunderstanding of what logic is. Basic logic skills are in serious need of overhaul in this post.

Yeah, my behaviour is clearly the problem. Only asking for my field to not be denigrated and insulted. Clearly I'm bang out of order. Projections are a pound a piece here it seems. It's not like I'm not also stressed.

Hume would disagree but then whether or not something is "abrasive" is subjective. Some undergrads find compatabilism "Abrasive" to their beliefs in free will. No but it is a requirement to do science well. God forbid any premise to any scientific argument is missing or wrong. Not a strawman. Learn some manners and respect when people go out of their way to do the same for you. You're easily the most "Abrasive" moderator here. No one is going to convince me that I'm in the wrong here without first learning how to speak respectfully to others. Your comments to me yesterday were uncalled for and they were off-topic to the discussion and you put words in my mouth. Philosophy birthed your entire field as it is today. Show it some respect. If you'd climb down off your pedestal and apologise, like I did yesterday for upsetting you, just for stating some facts about science and philosophy, then maybe we can have an adult conversation instead of a pissing contest. Next time you want to talk about fallacies in logic, like strawmen. Do so in the appropriate logic forum.. Oh, wait

Everyone should read this book. Until you've read it, don't talk about logic. You don't know what you're talking about.

I would but there is no section for it all to be found. Why should I have to promote logic at all? It's a field of study you can take a class in at most University's and you can get degrees in it. It's important. It's not my job to explain the reality of that to others who allegedly went to university. Just so you're all aware, I could have 1000 downvotes and still not give a shit. They aren't real communication and half the reason they are programmed into anywhere is to make the screen more addictive. "Oh yay I got an upvote, free dopamine!" "Oh no I got a downvote from a stranger, I must have been bad boohoo." So yeah, downvote away. I couldn't give less of a shit. It's the go to response for people who have no good response.