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## Popular Content

Showing content with the highest reputation on 09/22/21 in all areas

1. ## Sign rule for multiplication

It's good that you asked in Linear Algebra And Group Theory, because we're going to need some algebra you likely have never seen (unless you went to college) to answer it. Multiplication isn't one thing. What multiplication is depends on what you're multiplying. Algebra is how we define this. In Algebra, there are a handful of different kinds of structures. Here, we're interested in Groups, Rings, and Fields. Rings and Fields are kind of made of Groups, so we'll start there. Say we have a set (the lay concept of set will work fine for our purposes), and we'll call it S. On this set, we need to define a rule called a "binary relation" that takes any two things in the set and gives some output. We want this set to be closed under this relation, so the relation can only give us things that are already in the set. For this combination of set and relation (for now, we'll use ? to denote the relation) to be a Group, they need to have the following properties: 1) Associativity: for any three things a, b, and c in the set, the relation doesn't care about where the parentheses go. a?(b?c)=(a?b)?c 2) Identity: there is a special thing in the set (traditionally denoted by e when talking abstractly) where, for any other thing a in the set, a?e=e?a=a 3) Invertability: for any thing a in the set, there is another thing in the set a* where a?a*=e=a* That's enough to be a Group. But we want a special kind of Group, called an Abelian Group. That's just a regular Group that has an extra property: 4) Commutativity: for any two things a and b in the set, a?b=b?a Tradition dictates that for Abelian Groups, + is used in place of ? and 0 is used in place of e and -a in place of a*. If a Group is not Abelian, we often use × (or nothing at all) in place of ? and 1 in place of e and 1/a in place of a*. If S is the set, we write (S, +) or (S, ×) for the group, but we often just write S if it is clear from the context that we're talking about a group. This is enough to let us build a Ring. With Rings, we still have a set S, but we have two relations. (S, +) is an Abelian Group, but × is a bit more lax. × only has to satisfy two properties: 1) Identity, and 2) Distributivity: for any three things a, b, and c in S, a×(b+c)=(a×b)+(a×c) Like how (S, ?) is a Group, (S, +, ×) is a Ring. If a Ring is commutative and has inverses for each relation, then the Ring is called a Field. There are four particularly important facts mentioned above that are important to why a negative times a negative is a positive: 1) a+(-a)=0, 2) a+0=a, 3) a×0=0 (not mentioned above, but still important), and 4) a×(b+c)=(a×b)+(a×c) Proof -a×-b = a×b: Let a and b be positive numbers in our field (S, +, ×). 0=b+(-b)=a(b+(-b)) -a×-b = (-a×-b) + a(b+(-b)) = -a×-b + a×b + a×-b = -a×-b + a×-b + a×b = -b×a + -b×-a +a×b = -b(a+(-a)) + a×b = a×b TL;DR: It's because Fields are commutative, have identities, and are distributive
2 points
2. ## Strange rocky material fell from the sky with odd surface features and microbiology inside it

I don't think this object can have fallen from space. The chem analysis shows an amazing % carbon so it did not travel very fast through the atmousphere or it would have burned up. Sorry about the ? mark, I chose a sigma from the character set but it seems to have come out as ? mark. The other interesting thing about this analysis is the absence of hydrogen. However at 45% carbon I would guess some industrial chimney (there are plenty of these around Birmingham) or other was being cleaned out that night. If you have seen industrial chimneys at night you can often see the sparks and or material be ejected.
2 points
3. ## Strange rocky material fell from the sky with odd surface features and microbiology inside it

Sadly the Natural History Museam (London) were not able to further this investigation, so it has stalled and I think it's as far as I can take it. I'd like to preface my reasoning for pursuing it even this far, with a series of logical statements: - did the material fall from the sky = YES - is it unusual and have strange surface features = YES - did it fall at the start the Perseids shower (caused by the debris field of comet Swift-Tuttle) = YES - are there any confirmed cometary meteorites in the collections = NO - does the material contain microbiology = YES apparently undamaged diatoms and other structures are embedded deep inside the fragments and within the material matrix - has this happened before = YES, reference Polonnaruwa stones 2012 (though these findings are not universally accepted) The investigations to date (SEM, EDX, EDX & XRPD, EDX & petrographic) were not able identify characteristics akin to existing meteorites, nor any of the expected characteristics of meteoritic materials, but it still remains unidentified. I have not been able to confirm the age or origin of the material by analysis such as Triple Oxygen Isotope, Cosmic Ray Exposure (as these are highly specialized), or even if it has a 'terrestrial' age by carbon dating. The prevailing theme is that that the material is anthropogenic, and possibly the remnents of an artificial satellite that have fallen back to earth. That might explain the: - observable differences between adjoining fragments (perhaps different components?) - some of the odd biological looking structures found on the outside (perhaps something collected from the atmosphere?) However that does not answer anything relating to the intact biologicial structures found inside the material. The anonymized petrographic report is uploaded in post #16 here: Treasurenet Forum Post, because there is no capacity to add more files to this post. To be clear, I'm not claiming that this material is one thing or another, instead putting it, and what I have found, out there for posterity and open discussion.
2 points
4. ## Sign rule for multiplication

Well thank you. It took some doing to fix my bbtex mistakes on the phone with autorendering
1 point
5. ## Making jelly (that's jello in USA I believe)

Are there any aspics of this topic we haven't covered? More depth can be found in collagen universities, perhaps.
1 point
6. ## Making jelly (that's jello in USA I believe)

Their lawyers claimed they're referring to "the cherries" they use in the "combination of five fruits". The amount of cherries you get is half of one. It's like Flip Wilson's All-You-Can-Drink-For-A-Dime Lemonade Stand. You already had a cup? Well, that's all you can drink for a dime! How corny! I'm sure there's a peas full resolution for those that carrot all. Lettuce stand together in hominy!
1 point
7. ## Making jelly (that's jello in USA I believe)

You cannot fight the Man from Del Monte
1 point
8. ## Strange rocky material fell from the sky with odd surface features and microbiology inside it

Before the petrographic analysis I approached an author of a paper on volcanic bombs and they confirmed 2 things at least: The material is compositionally different to volcanic material and certainly different to anything from Iceland. A piece weighing several 100 grams wouldn't travel that far. I also approached many academics from various fields, with little interest, most either didn't reply, or pointed me to the NHM London, who appear to be a sort of 'gatekeeper'. I suspect with the petrographic report, the response would be even more tepid, and that's why I asked them for the prefacing email, imaged in the linked post. No worries, I'm happy to share it all and answer any questions. Yes for sure I know it did - the answer is probably best served by looking at some reports I've put together over the last year or so (linked on dropbox, you might need to copy and paste them into the address bar it did not work in preview mode for some reason): Fragment #1: https://www.dropbox.com/s/sgdo7j02n4gonqw/Birmingham Fireball and Assumed Meteorite Fragments - Phase 1.pdf?dl=0 Other Fragments: https://www.dropbox.com/s/070n54kopcg0beg/Birmingham%20Fireball%20and%20Assumed%20Meteorite%20Fragments%20-%20Phase%202.pdf?dl=0 Density and relative magnetic attraction study: https://www.dropbox.com/s/gvt1jdvg0207bdi/Birmingham Fireball and Assumed Meteorite Fragments - Density and relative magnetic attraction study.pdf?dl=04 Bulk composition: https://www.dropbox.com/s/45uoj0zvify7nwu/Birmingham Fireball and Assume Meteorite - Bulk Compositional Analysis.pdf?dl=0
1 point
9. ## Political Humor

Meanwhile, in the USA
1 point
10. ## Making jelly (that's jello in USA I believe)

https://www.mvfarmmarket.com/blogs/news/16861488-whats-the-difference-between-jams-jellies-preserves-spreads-and-butters We've been making jelly, jam and butter since as long as I can remember. Varies by year but this year alone we've made both apple and peach butter, wild grape jelly, and jams from strawberries, blackberries, raspberries, plums, and probably some I cannot remember. The ONLY ingredients that ever go into jellies and jams when we make them is fruit, sugar, lemon juice and dairy butter. A batch will typically be 1 c. smashed fruit or juice, 1 c. sugar, 1 tbsp lemon juice, and 1 pat of butter. Boil until it is the right consistency (about 6-7 minutes but varies based on water content of fruit). That's it. Getting the right consistency is a matter of experience and a little bit of luck. If when cooled it turns out too thick we just add a little bit of apple juice, and if it is too thin we just boil again for a short while.
1 point
11. ## Why is there a growing movement to deny reality in America?

I think that is a big part of it. Fundamentally, we are utterly unprepared in dealing with social media. Or rather, our psychology is not well suited to deal with it. Fundamentally the issue at hand is one of trust. Few folks have the expertise and time to evaluate each claim they encounter and there is at best a superficial, intuitive evaluation of the facts. Moreover, we are prone to trust folks that we know or feel that we know more. In societies without with no mass media that makes a lot of sense. However, eventually mass media created celebrities. By seeing folks on a regular basis, even if one a screen, it creates the illusion of familiarity and this is why celebrities have a disproportionate influence on public opinion (see their role in promoting anti vaccination sentiments over the last decades). Now with social media, that effect further extends to random folks, youtubers and so on. Those folks are more trusted than individuals with actual expertise, in part because the latter are busy working in their field of expertise than using psychological tricks to make folks like (and subscribe) them. You can see that effect in classes now. College students increasingly cite random youtubers as sources of information, which I find rather worrying (and I used to be worried about wikipedia in the past). So the combination of a big network of trust without expertise and mistrust of gatekeepers seems to create a system where outrageous misinformation can speed happily along, leaving fact checking and similar slow measures in the dust. And I will also say that this is not an US-specific problem.
1 point
12. ## What taxes a billionaire?

Wooosh! At first that literaly went over my head! 😁
1 point
13. ## What taxes a billionaire?

The blatant obfuscation and ambiguity in your posts points the troll detector in your direction. Those who wish to imply ethical failings in others have an obligation to be specifc and not adopt the pseudo-angst of an offended teen.
1 point
14. ## If I could create a human being

If I had the chance and technology to create a human being. -Athletic, fast metabolism, Won't get fat after High School and College -cheerleading since she was 8 -Member of both High School and competitive cheer squads -Became a cheerleader for fun not popularity -Plays other sports like Volleyball and Soccer -Determined -Nice -Social butterfly -Genetically programmed to be happy, Would not be jealous of other people's wealth or intelligence -Loves Bring It On and Disney movies -Funny -Fun to be around -Selfless -Mentally stable -Psychologically perfect/health, No greedy sociopathic psychiatrist would dare medicate her -Average intelligence, High IQ people suffer a high rate of mental illness
-1 points
15. ## What is normal?

What do you think is a normal human? You psychiatrists and big pharma seemed to want half the U.S. population doped up. Also some of these meds cause weight gain. I would prefer to see less overweight females. I prefer cheerleaders not fat feminists!
-1 points

I like the idea of a smart girl becoming a cheerleader. Break stereotypes! Do you think the cheerleaders force the one in the glasses to do their homework for them?
-1 points
17. ## Is psychiatry to blame for obesity?

Some of these meds cause weight gain. Should the DSM be fixed?
-1 points
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