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actually I have exactly 15 questions. I've done 10 of them, but I couldn't understand them and that's why I found this place. Maybe I expected the people here to understand them and show me a solution. You may have scolded or humiliated in your own way, but there was no need to humiliate that much because I uploaded it with an incomplete explanation. I'm sure more well-intentioned people will come across. have a nice day. actually I have exactly 15 questions. I've done 10 of them, but I couldn't understand them and that's why I found this place. Maybe I expected the people here to understand them and show me a solution. You may have scolded or humiliated in your own way, but there was no need to humiliate that much because I uploaded it with an incomplete explanation. I'm sure more well-intentioned people will come across. have a nice day.

Hello Col and welcome. +1 for a good start, I look forward to further worthwhile contributions. I've been a member since 2012 and in that time I have seen many threads started discussing the question, "What is space ?" So it is indeed apressing question. So pressing that in fact we now need to separate what is meant by a physical space and what is meant by a mathematical space. Defining a mathematical space is easy. You need a set containing at least three (perhaps four) sets of objects. 1) A set of mathematical objects you wish to work with. 2) A set of coefficients you wish to apply 3) A set of axiomatic relations between these objects 4) Perhaps if you want to be complete then a set of results (theorems lemmas etc) you can deduce from these. Hi Markus, I think you have this the wrong way round. Mathenmatical structures are models of physical reality, rather than physical reality being a model of mathematics.

I'm no expert either, so be my guest. And of course it would be nice that some of the local experts can give us a hand. Yes, DNA does get old. That's at the basis of cellular aging, and thereby the organism's aging itself, AFAIK. The replication mechanism is some kind of bi-directional zip assembly, so it's always imprecise at the ends. In one direction the replication process is very smooth, because the initial fragment (RNA primer) and the DNA polymerase work in the 5' to 3' direction, but in the opposite strand, primer and polymerase are forced to work against the uncoiling of the double strand, so it must interrupt and restart the copying work over and over again --the so-called Okazaki fragments. That's why there's always a mismatch at the end. Eukaryotes use a meaningless[?] chunk of DNA at the end --telomere-- which is partially replenished with every replication process, to kind of delay this ongoing degrading of the information. Also, as you point out, different cells down the line of cellular development, have different adjustments to their particular function. Red blood cells being the perfect examples of cells that will never go back to be able to produce anything in the way of stem-cells or higher-potent cells, because they've completely lost their DNA. Other extremes are neurons and cells from the digestive lining. The average life of the latter is, if I remember correctly, 48 to 72 hours. And neurons, because they never get replenished by sister cells mitotically splitting. Although new neurons do appear directly from stem cells, especially in the hippocampus*. Also, they retain some ability to reconnect, or change connections. That's about the summary of what I know. * Google search: "newborn neurons in hippocampus and olfactory bulb"

1. A topological manifold 2. The Levi-Civita connection 3. A metric with the correct signature 4. A local constraint on the metric which guarantees the automatic conservation of the Einstein tensor (=the Einstein field equations) This is pretty much the minimum structure required to get GR, as opposed to other models of gravity.

Cyanoacrylate adhesive ( superglue ) is often used to 'seal' open wounds, where stitches might be too obtrusive. Doctors don't seem to be worried about absorption and toxicity. And superglue might keep your hairpiece on for months at a time. Better yet, shave your head and grow a beard.

But the sister cells are just as old. Excepting cells that are manufactured (*), all bad (damaged, stressed) cells are replaced by mitosis of the remaining ones, all of which are essentially as old as you are. Maybe I'm wrong about that. Hardly an expert here. The DNA is also replicated this way, not manufactured from scratch, so all the DNA is effectively as old as you are,. Neurons can't just split since their connections cannot be reproduced, so they're intended to exist without replacement after their initial allotment is complete some months after birth. * Blood is a nice example of manufactured cells. Red blood contains no DNA and cannot reproduce by mitosis. They're short lived (1/3 year?) and manufactured continuously by non-blood cells.

That goes for neurons. But I meant it --more in general-- in the sense that the cell --every cell, including neurons-- is the basic unit that carries out a particular function within the organism. In order to do that, they specialize down the line of cellular development. Cells have a finite life though, so when they no longer work, they are replaced by releasing stress signals that activate their destruction and further mitosis in other sister cells. As long as the cell is performing its function, it's important that it does it well --cancer being an example of how bad it is that a cell stops working properly. Cancer cells get stuck in continual mitosis and just can't stop. It's their function that's essential. Gametes, on the contrary, are some kind of "inter-phase" between one organism and the next generation. They carry random arrangements of half the genetic material --haploid cells-- of the parent organism; and they're fundamentally like a throwing of the dice. Not a functional cell really. Not yet. So chromosomes are expendable. On the contrary, the organism cannot afford to have malfunctioning DNA in the nucleus of working cells. That's why eukaryotes have mechanisms to destroy tissue cells that are not working properly. It doesn't play around trying to fix it --replace it. During replication cells do have an impressive proofreading mechanism, very precise --transcription and translation don't have to be that accurate--. But when DNA that's being read for transcription is just too messed up, the cell must be destroyed. When the cell malfunctions, the DNA is replaced... by replacing the whole cell. Not taking any chances. But a gamete turns bad? No problem for this organism. That's more or less what I meant.

New User here. Hi everyone. Please advise me where to go and what is appropriate, my apologies in advance for getting it wrong so far. 1. Thanks for pinning this post to the top of the board, it seems like a good one for newbies to start with. 2. It would help if the original creator(s) posted an update, so that we could see what the article looks like after 4 years of comments and editing. I've only had a scan through all the comments and that took a whole day. 3. Are you sure people often ask "What is space made of"? Have you got any surveys or other evidence for that? In my limited experience, most are happy to assume it's an empty vaccum. However, I do agree that people are quicky and frequently mis-lead into thinking that space is a stretchy fabric. I also agree with many of the later comments about quantum foam and vaccum energy that you could try to incorporate into your definition of space. If you are determined to incorporate QFT then I suppose spacetime does have to have fields in it. The problem is being certain that you have covered everything in your attempt to say what space is made of or even what mathematical objects must be supported and exist in space. There is almost no way of future-proofing the idea. Early General Relativity only really considered simple particle theories. It's unlikely anyone knew that anything like QFT, dark energy or vaccum energy could be added later. It's amazing that GR still seems to hold so well given that we have incorporated so much more into it than it was originally designed to model and we would be extremely optimistic to assume that nothing more will ever be added. As a consequence, I suspect the original creator would be better off not trying to tell people what space is actually made of - but instead focuses on what is the least amount of structure required for GR. Therefore, his/her definitions of spacetime as a (pseudo) metric space seem the better way to go. It is an ambitious target to try and describe all the (intangible) objects, like fields, that may be inferred or required to exist in space.

@MigL Hope you don't mind, but I'm gonna take our PM exchange into the thread here (keeping your point unquoted, will share my reply here instead). We're still talking passed each other. While I said I can understand the underlying motivations, I have NOT made excuses for violence perpetrated in the name of BLM. There is violence happening as part of the movement. I don't agree with it. I'm not making excuses for it. I'm not pretending it doesn't exist. My primary point has been that the violence is the extreme outlier in BLM. It's marginal. It's super rare. It's uncommon. It's been inflated as a rightwing talking point. There has been violence. Some of it came from BLM protestors unprovoked. Some was provoked by police being too heavy handed and hitting peaceful protestors with clubs and firing tear gas into the faces of unarmed grandmothers. Some of it was rightwing extremists engaged in false flag operations. My primary point has been that it's a mistake to focus so much energy there... another example of of our white privilege. In these threads, people keep saying "it's horrible that another innocent black man was killed by another cop in another city, but destroying property has to stop." Yeah, okay... but try saying instead, "It's horrible that property is being destroyed, but these continued killings of innocent black men by police has to stop." See the difference? The pushback is saying you're prioritizing the wrong part... not that the violence is acceptable because it was done by "my team." Focusing so much on the tiny amounts of violence happening at the extreme margins of the movement distracts us from dealing with the issues motivating the movement itself. I'm not making excuses for the violence. I'm saying it's so rare that bringing up so often suggests an agenda, whether you're conscious of it or not. Please stop saying I support the violence. Please stop suggesting I'm making excuses for it. I'm simply not.

An alternative proof from direct Taylor expansion in the metric coefficients and counting how many parameters are left that I cannot set to zero by changing the coordinate system: https://www.youtube.com/watch?v=gf-G4QiAHLY&list=PLaNkJORnlhZnwjIXnOHrX50FEyoyiTh4o&index=5 Those must coincide with the number of independent components of the Riemann. \( \frac{1}{12}n^2\left(n^2-1\right) \) Uses Young tableaux, which allows you to count free parameters very easily.

Neither, the police are quite adept at inspiring violence at an otherwise peaceful protest. Like I said, the difference is the intent on the part of the protester's and I think there's little doubt the Trump army intended violence, when they descended on the capital, because they didn't get their way in the polls; so no, the two aren't equivalent. You can't/shouldn't just dismiss a legitimate protest because some of them defended themselves when attacked. Violence is never Ok, is more of an excuse to deny legitimacy in this context; I have every sympathy with pacifism as an ideal, but then I've never been attacked for waving a banner. The difference is, they used that motivation as an excuse to be violent, rather than a reason to protest.

Umm, windows are one thing, Zap. Would you feel better if you were one of the 5 killed at the Capital, or on of the 18 killed during the BLM protests? And lets not confuse the issue with self defense; we are discussing perpetrating violence, up to and including the death of innocent bystanders. At both protests people were there by choice, and some ( not all ) willfully harmed ( and killed ) innocents. In my opinion, violence is violence, no qualifiers. I recognize that others may have a different opinion, as you've stated ( personally, I would have used hate crimes as an example ) But it's like pulling teeth trying to get others ( hi, INow ) to admit they qualify their violence. Ahh, but here's the rub, those 'rapscallions' ( interesting choice of word ) firmly believe they were saving the country from an insurrection mounted by the Democrats, to steal an election which D Trump actually won. In their minds, they were modern day G Washingtons, rebelling against an attempt to install an illegitimate Government. They were told so by their/your President !

Homework Help is where members guide other members towards deriving answers to their homework. It is not where members provide full answers to members too lazy or indifferent to at least make some effort to answer those questions. Perhaps, if you make an effort now to describe what work you have done to attempt an answer and what uncertainties you have, then some members may be willing to offer you help. That's "help", not "complete answers".