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I have some questions here, which I’m hoping someone might be able to help with. I’ve spent the last few years focussing on other things in my life, so I’m afraid I’ve lost touch with the some of the basics - I’ve recently attempted to once again put pen to paper and actually work out some GR tensor calculus practice problems from scratch by hand, and…let’s just say it didn’t go so well 😕 1. Notational question - assume we are working in the context of GR, ie we are on a semi-Riemannian manifold endowed with the Levi-Civita connection and a metric. What is the actual significance of the vertical alignment (or lack thereof) of indices on tensors and spinors? In other words, what is the actual difference between the following three notations (let B be a rank-2 tensor), if any at all? \[B_{\nu }^{\mu } \ vs\ B{_{\nu }}^{\mu } \ vs\ B{^{\mu}}_{\nu}\] 2. I need to really revise and - above all - practice my tensor calculus index gymnastics, but I’m having trouble finding a suitable text that actually focuses on the mechanics of index manipulation, rather than abstract definitions and proofs (which is what you most often get in GR texts). Does anyone here have recommendations? What I am specifically after is something not too high-level that goes through the various concepts in tensor index manipulation, provides worked examples, and then gives exercises to work through. The relevant chapters of MTW actually are good in that regard (they’re on a level I can follow easily enough), but I think the material is presented too concisely and quickly - I’m looking for something that introduces it more slowly and in more detail, including worked examples, and gives many more exercises of varying levels of difficulty to do. I understand the concepts involved reasonably well if I see them written down in an equation, I just need much more practice in actually using them in a pen-on-paper kind of way - which is an entirely different skill set. So I’m after something that really drills home the mechanics of index manipulation through worked examples and exercises. Any suggestions, anyone? TIA.

Making drugs legal doesn't automatically mean they're cheap, nor does it mean they're necessarily easier for kids to get, unless your conservative local government is either trying to make money or hire more police. Your stance assumes we're waving a wand and making the laws disappear, which isn't at all how these things work. Look to Portugal, where they took the money they used to use for drug prisons and drug police (which deals with "addicts" without helping them) and spent it on rehab, counseling, and job placement (which helped real people overcome addiction). Cheap housing should be paid for by citizens and businesses who're interested in helping real people overcome problems so they can better participate in their own economy, rather than being the double burden an addict is now (at least in the US). And this garbage about everybody slacking off all day if given the choice is just conservative bullshit. It doesn't happen to the degree you try to scare everyone with. It's always been hard for me to stomach this fearful approach to societal processes, where we pay TWICE for security AND prisons instead of simply supporting our fellow humans the right way ONCE. You folks whose countries invest in universal healthcare have no idea what it's like for your country to charge you taxes without representing your continued existence. The US taxpayers spend more on the average prisoner than the average US taxpayer earns, and the total cost of incarceration to society (lost earnings, health problems, breaking up families) is up to three times the direct costs. All because conservative thinkers don't think we're ALL worth it, because some of us are addicts or poor or foreign or melanated or not Christian.

Chicken and the egg. People did drugs before drug use was outlawed.

It's a lot more expensive to criminalize people than to help them. https://www.prisonpolicy.org/research/economics_of_incarceration/

It rains here today. Our aquarium water gets partially changed: (the surface as seen from below)

Simple - no, but not an approximation either. It is an exact matrix multiplication. Frame dragging comes with gravity, not with coordinate transformation.

Okay, that's great. Except Genady suggested the exact opposite of that: Get it? He sees a problem with a geologist believing that Earth is 5 thousand years old. That means he agrees with you: scientifically, it's not rational for a geologist to believe the earth that old.

As to index gymnastics, I'm very fond of Anomalies in Quantum Field Theory, by Reinhold A. Bertlmann --the famous mathematician of John Bell's article. The first third of the book has a lot of it, because he deals with gravitation a lot. Not in detail, but you can check the calculations page by page as a good gymnastics.

This is all WAY over my head, but have you ever tried using geometric algebra? It's supposed to be simpler and more versatile. Geometric Algebra Techniques for General Relativity GRAVITY, GAUGE THEORIES AND GEOMETRIC ALGEBRA Geometric Calculus in Gravity Theory Geometric Algebra, Spacetime Physics and Gravitation

City of Toronto has the largest homeless population in Canada. As a result, their shelter situation is at near or full capacity according to the following data Daily Shelter & Overnight Service Usage – City of Toronto Other cities, having less homeless, have lower occupancy rates. You don't have a funny bone, do you ? I don't care; the weather has got to be better than here.

Thx Genady, this dynamic change has convinced me to continue my education.

Which ones? I know, I know, they've made bad choices....

I think Markus explained very well why the proposal just would not solve the issue and others have chimed in on the legal ramifications. Now if we want to move into the realm of realistic solutions, there are studies on it that we can turn to, rather than trying tried and failed brute force methods. One of the key elements that Markus described is instilling motivation for change. We do know that force does not work. In fact, it may be very well what created a situation that benefits addiction in the first place. In Europe and Canada, there have been "housing first" initiatives, which aims to provide housing, not shelters and use that as a leverage to address e.g. substance abuse or mental illness. It is likely not a perfect solution, but it was found to be at least competitive in cost compared to other initiatives (especially when medical costs are considered) and compared to other measures shows at least trends in the right direction in terms of most indices (i.e. homelessness, health outcomes etc.). It does not work equally well for everyone, but it does move the needle in the right direction. On the other hand, even using historic knowledge using force on people for their own good on that scale and without individual consultations and deliberations has mostly resulted in trauma and even atrocities. I also note that OP has not shown any evidence how that has helped in the past, while others have mentioned negative outcomes. And this is fundamentally an issue if we deal with vulnerable or powerless populations using very simplified reasoning. This line of thought does not really take their perspective and trajectory into account, but it is strictly top-down level of thinking. If we remove them and do something magically it will all better, though what really changes is that one does not need to deal with them anymore. This magical thinking is of course only harmful to the people affected which unfortunately makes it very popular. We see similar reasoning for dealing with asylum seekers, folks tried to "help" folks by kidnapping kids into residential schools and/or forced adoptions, folks still try to coerce folks into unneeded medical procedures. The issue is that even if intentions were good (which at times is clearly disputable), it uses a very limited perspective of us vs them, assuming that our perspective and experience is the norm and if we forced everyone into that line, they would improve. Clearly this is not the case and betrays as rather limited perspective on the complexity of the matter.

Speaking of the devil... Here is a fresh photograph of our own walking fish, frogfish. Not very rare but often gets unnoticed because of the wonderful camouflage. Taken by a friend of mine, much better uw photographer than me.

I'm not convinced of your idea either, but I'm open to discussing it. And this is a discussion forum, and as such, it is intended for discussing ideas, without fear of being called names, or labelled. This is done with reasoned, valid arguments, not insults and down-votes.

What you suggest seems like an obvious solution, but unfortunately it does not and cannot work. Addiction is much more complex than just being a physical dependency on something. Yes, you could (ethical concerns aside for now) round them all up, put them in a camp, and forcibly put them through physical detox - the trouble with this is that it doesn’t actually address the underlying issue at all, because the dependency is in large part of a psychological, social and systemic nature. No one wakes up one morning and decides “I’m going to become a homeless addict…seems like a cool career choice!”. That’s not how it works. Most long-term addicts are in this situation because of multiple factors connected to their social environment, upbringing, past trauma, etc etc, many of which they have little or no control over. These are all complex issues that are not easily nor quickly fixed. It’s a common mistake to think that people remain addicts purely because of their physical dependency, and if we kick the physical dependency they cease to be addicts - that’s quite simply not true at all. So as for your proposal - you take them to your camp, forcibly put them through detox, and at some point will have to let them out again to re-join their families and social environments. What do you think happens then? I can pretty much guarantee you that within days or weeks almost all of them will be right back on their drug of choice, with perhaps the odd exception. Why? Because the underlying reasons for why they have begun to use substances in the first place have not been addressed. Addiction is a symptom of an underlying disease, not really the cause itself - just putting people through detox is like giving painkillers to a cancer patient; it alleviates the symptoms for a little while, but it doesn’t cure the disease. People don’t start off using because they are physically dependent, but for other reasons. It’s those initial reasons that need to be addressed. You cannot help an addict who doesn’t want to be helped - the impulse must always come from him/herself. People have to be ready to change, before therapy has any chance of success, and even then the relapse rates are still high. Forcing people into a treatment they are not ready for does not work. I don’t know if there are actual studies to show this (there probably are), but everyone who has ever actually worked with addicts knows that this is a basic fact. BTW, rounding up addicts and forcing them into rehab camps is what the Taliban in Afghanistan tried to do. Needless to say, it didn’t work. But it makes for an interesting case study if you want to research into it. So as for your proposal - it certainly has political appeal to those who don’t know much about drug addiction, but ultimately it does not and cannot work. It would just create a revolving-door kind of situation with people going in and out of camps, and the ones who ultimately profit will be the dealers and cartels, as always. Until we begin to treat homelessness and addiction as the social and health issue which it is, and stop criminalising something that the victims have little or no control over, no progress can be made on this problem. Criminalising the addicts and waging a “war on drugs” has never once worked, does not work now, and never will work. A complete re-think is needed.

You’re mixing up reference frames

They are trying to not be boring but they made them self look stupid.

In space, no one can hear you talk ballocks.