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It has nothing to do with 'spinning' the death toll, JC. His policies, such as pressuring State Governors to re-open, and lack of policies, such as not making medical supplies available to certain States, have led to the situation in the US. Canadians and Americans are generally very similar, and our own response has been far from perfect. Yet Canada, with 1/10 of the American population, has 42x less infections. And 23x less deaths

Would it be helpful to say "the spacetime coordinate system" instead of just "spacetime"? Would people be less tempted to interpret it physically ?

Generally to create a paradox you would have two inertial frames in relative motion, each capable of instantaneous information transfer within themselves. Example: You are in a spacecraft which passes Earth at 0.8c as both your and the Earth clock reads the same. Trailing 1 ly behind you ( as measured by you) is another spacecraft. 1.25 yrs later, by your clock, you are 1 ly from Earth and the trailing craft is next to Earth. The time on earth is just 0.75 years later than when you passed it. (An Earth observer would also agree that the trailing craft passed the Earth 0.75 years after you passed. At that moment, you transmit an instantaneous message to the trailing craft, and that craft hands it off to the Earth as it passes. The Earth, in turn, send this message to a buoy floating in space which is 0.6 ly away and long your path. Because, in 0.75 yrs at 0.8 c, that is how far you have traveled from the Earth. So you will be right next to that buoy. Your clock will read 0.45 yrs past what it read when you passed Earth. You will also agree that you passed the buoy when you clock reads 0.45 yrs, As the 0.6 ly distance ( as measured by the Earth) is 0.36 ly as measured by you, and it take 0.45 yrs to travel that distance at 0.8 c. The buoy hands the message off to you as you pass it. Thus a message you sent 1.25 yrs after leaving Earth is received by you 0.8 yrs before you sent it!

It may seem linear, but when you think you're drawing from relevant sources you've been accumulating since birth. You choose the knowledge you need to apply to a situation from a large range of information you've previously put together from selected data. It's like your box of tools to deal with a particular problem. If you need to fix yourself something to eat, you're going to think of just those things you need to make it happen, and select the ones that will successfully turn your thoughts into action. As you gain more experience, your knowledge is broader and deeper, so the information you're able to draw from is richer as well. It's pretty amazing, really. The moment you feel hungry, your mind starts grabbing all the knowledge available to you, including your current preferences and available resources. You fill your tool box with what you need (no money but stuff in the fridge to make an omelet, grab a pan and a bowl and a spoon, turn on the stove, get the bacon, etc), and don't bother with anything else (you didn't grab the cat brush, or start your car, or check to see if you have any blue paint). Change the parameters of the situation, and your thinking is going to change as well (hungry roommates need food too, or the eggs went bad, or you find a bunch of money). It's a lot more than going from a to b to c to d.

If you are asking whether your body is using the zinc, yes it does. In fact it is an essential micronutrient. In case there is a bigger misunderstanding, there is no way to create elements biologically. You can only synthesize more complex biomolecules using simple components. Things like Mg, Ca, Zn and so on are all taken up from the environment.

I find this very relatable, though being inseparable from two young kids for 10 long months and having a preexisting condition of my own adds additional layers to the experience. Focus that worry into finally quitting. When you want a smoke, do 10-20 push-ups instead. Sip a tall glass of water very very slooowwww-ly. Eat some carrots. Just distract yourself for about 10 minutes until the craving naturally passes. Then when the next craving comes, do some more pushups and be proactive... have a plan to do something else for those times like at bars or after lunch at work where you always had a cigarette out of habit... next time go for a walk or wash your hands or something... anything... else.

Is this a matter of being concerned that someone will steal your idea? If you post your actual problem perhaps someone can offer some help. For what it's worth, here's what I did with inclusion/exclusion. Suppose we want to know how many numbers from 1 through 30 are not divisible by any of 2, 3, or 5. We calculate how many ARE divisible by at least one of them as follows; 1/2 x 30 = 15 1/3 x 30 = 10 1/5 x 30 = 6 That adds up to 31. Now for the double counts, which must be subtracted: 1/6 x 30 = 5 1/10 x 30 = 3 1/15 x 30 = 2 That adds up to 10, to be subtracted. Now we must ADD back the triple counts: namely, 1/30 x 30 = 1. So we have 31 - 10 + 1 = 22. Therefore there are 30 - 22 = 8 numbers NOT divisible by any of 2, 3, or 5. Indeed we can count them by hand: 1, 7, 11, 13, 17, 19, 23, and 29. Eight as calculated. Now the problem is that we have not accounted for the pairs 29/31, or 23/37, etc., because the larger numbers of the pair are out of our range. So if you figure out how to account for the "sum to 60" aspect of the problem, you'll be able to work this out. Do feel free to give more information about your actual problem, or not, as you see fit. Then again when Hilbert offered to help Einstein with general relativity, Einstein at first welcomed his offer; but then realized that Hilbert was trying to solve the problem first and take credit. So maybe you're right not to give too much away! LOL. ps -- Wait DUH! We forgot 11/49. I don't know why we both got confused about this. I solved the problem. The trick is that if n is divisible by one of 2, 3, or 5, so is 60 - n. So the pairs (n, 60-n) where both elements are relatively prime to 2, 3, and 5 are exactly the same as the numbers n with the same property. So the solution is to do inclusion/exclusion on 30 to determine how many numbers are not divisible by 2, 3, or 5; and that's the number of pairs. In the case of 60 there are exactly 8 pairs: 1/59, 7/53, 11/49, 13/47, 17/43, 19/41, 23/37, and 29/31. That's eight. You can now write a program to do inclusion/exclusion on your original number N, or half of 2N if you think of it that way (that is, 2x3x5 = 30, multiply by 2 to get 60, then do inclusion/exclusion on 30). The "sum to 60" is a red herring, an aspect of the problem that adds confusion but doesn't change the problem. I believe that's it, but if I messed up I hope someone will jump in.

Can you show your work in detail? I still don't understand the basic question. 2*3*5 = 30. Multiply that by 2 and you get 60. Please explain the rest because I totally do not understand what we are doing here. Where did the -2's come from, that hasn't been part of your exposition. ps -- Ok I totally don't get this. Pairs that sum to 60 and have no divisors among 2,, 3, 5: I get 1,59 11,49 13,47 17, 43 That's already four, eight if you distinguish order, and there are plenty more. So please explain clearly what you are doing. Others are 19, 41 23, 37 29, 31 That's a total of 7, times 2 to account for order as you said earlier, so there are 14 pairs that satisfy your requirement, not 3. Where do these -2's come from? In one example earlier you had 17-2 as a factor but that's not prime. Maybe it's just me but I do not understand what is being calculated. Can you work out a complete example, a simple one? Apologies if I'm being dense and this is obvious to everyone but me. Those of you who wrote programs to solves this problem, what problem are you solving? Am I just missing something that's obvious to everyone else?

The University of Edinburgh does online postgraduate courses in Physics. I have just recommended some of their lectures in Mathematical Physics in another thread here. https://www.ed.ac.uk/studying/postgraduate/degrees/index.php?r=site/bysubject&sid=4 A couple of years ago we had a doctor staying with us who did an online MSC in Pharmacology with them. The course was totally online, including the award ceremony. (With some universities you have to attend that for the final award) Some of the students on that course never actually visited this country! These courses are pretty intensive though so be warned.

When you arrive at point C, you will see the same light coming from both stars as someone who never moved from point C; Light that left both stars 5 yrs ago. You see both stars as they were 5 yrs ago.

I did look at this one, but I am sorry to say that all of us have parts of our subject we like more than other parts. And amongst my personally least liked parts are combinatoric and number theory. There seem to be several problems of this type going around at the moment. On another (maths) forum they have been debating this simpler one for a couple of weeks now. and this is only a four digit number. The one here is a nine digit number so I would expect candidate numbers for addition to be of the form xxxxxxxxx + yyyyyyyyy Which has a lot more combinations. This really is problem that lends itself to a computer solution so I am suprised at Sensei's response, which is incorrect. since the last digit is a zero, there must be a carry so possible choices for pairs in the last positions are [0,0}, {9,1} , {8,2}. {7,3), {6,4} and {5,5} So {x,y} can be selected in 6 different ways. But any number ending in a 5 is divisible by five so the last one can be discounted. Further reduction can be had by noting that any pair containing an even number can be discounted as divisible by 2, another orignal factor. You can work through the digit pairs to find out how many possibilities there are for each other pair. Then multiply these together an see the final result, using the laws of combinatorics. Tina please note this first result and compare with your answer. I don't think there are any two irrational numbers that can be added together to make a rational one. In any case none of these are irrational.

The OP may mean vitamin D which increases the absorption of certain minerals in the human body.

A very interesting development, but it raised a question in my mind. As you all know, superconductivity was originally achieved by cooling to a very low temperature. Now it has been achieved by applying a very, very high pressure. It occurs to me that these two approaches have a common element-- they both involve moving the atoms closer together than they normally would be at room temperature and one atmosphere pressure. I have no knowledge as to whether distance between atoms is a factor in producing superconductivity-- but I wonder about it. If atomic distances are a factor, this achievement may not bring us closer to practical room-temperature conductivity.

@koti BTW, I have advice for you Koti, and for other members for the future.. When you're quoting something found on the Internet, don't thoughtlessly copy'n'paste it, but remove any tracking code which allows uniquely identify who you are.. e.g. strip URL to the absolute minimum e.g. without query string and fragment string. Sometimes tracking code is inside of path (and translated by rewrite_engine, but it is minority, at the moment). I can tell when somebody read my e-mails sent to customers with precision to second, and how many times they opened e-mail prior replying with the all details what they used to read it etc etc.. Link https://www.sciencenews.org/article/physics-first-room-temperature-superconductor-discovery Works as good as yours...

Oh, I thought this thread was literally about 'playing with yourself' ...

Depending on the type of seaweed of course. You pick the seaweed from the beach, bring it home put it in a big colander and rinse it with cold water to remove any sand, salt etc. Then when the seaweed is very clean you can liquidize it(or not). You transfer this to a pot of water and bring to the boil. After it has reached a boil you reduce it down to a simmer for about 30 minutes. Then you pour the result through a sieve into a second pot. Leave to reduce depending on how much water you had at the start this can vary. Here the water turns lightly orange. Then I like to sieve the result through a fine sieve into a bowl I leave overnight in the freezer. In the morning the liquid will have formed a gel.