Senate What are the greatest mysteries in science?

Epic's right on this. At least somewhat. Some of the constants of the universe, if they were not well balanced, wouldn't allow for things like the existence of atoms or fusion or the like. So that is sort of a key thing. That said, I am not sold on how anything of significance should be tied to that, just due to a lack of method to get a statistical handle on that.

 

Alright, as promised, I'm going to attempt - and most likely fail miserably, since they're sufficiently out there I only understand cursory information - to explain the three things I mentioned. Who will care? No one.

Preface - I picked these not because I think they're the broadest or most universal great mysteries, but for personal preferences. I like these mysteries the most. If you asked another mathematician, you'd get different picks. Ask someone in another field, you'll get a completely different list. We're all sort of concerned with our own pocket universe, and I think that's what's so fun about it.

Ah, but first:

Well, you know, some men ask why, great men ask Y Not?

This is arguably the most straightforward of them and thus I'll handle it first. The Clay prize for this bad boy reads:

where 45,35 is another paper. Shock of shocks, the goal here is to show that a quantum Yang-Mills theory holds. What this would mean, without going into the terrifying details of a quantum Yang-Mills theory, is that four dimensional quantum field theory would have a mathematical model we understand really well and expect it to have. You get Yang Mills, you get the Standard Model for free, and we should be able to get the Standard Model because of that Higgs thing you might've heard about.

Thing is, Yang-Mills groups are the ugliest goddamn things you will ever look at in your entire life. They're what are known as non-abelian, and to get a grasp of what that means, think of a mathematical operation between two numbers, a and b.

Got one?

Okay, you know how if you switched a and b in your operation, it probably still worked (Unless you divided them, in which case 1/b -> b and repeat, I'm trying to motivate something here, you jerk)? Math dorks call that an abelian operation.

Needless to say, non-abelian groups suck. But it's good news for mathematical physicists since it's very much anyone's race to get to the end of this one.

Remember when I said not every mathematician would agree with my list? It's because of this. Most mathematicians really like choice. It lets them do everything they want to be able to do, and since they're often implicitly concerned with maximality/minimality conditions (More on that in a bit), they don't even have to second guess it.

Okay, got that? Because now I get to say I'm unfond of this exceedingly popular bit of mathematical "truth."

Among its many equivalent statements, one finds the "easy" statement to think about:

The problem is not immediately apparent, but this is basically the mathematical equivalent of Bat Anti-Paradox Spray. It prevents an infinite set from becoming bigger than itself - it is, to me, by no means instinctive, because of how weird infinities actually are, but we throw it in to make things pretty. The issue I have is that this is really the only axiom of the common set theory system where we do that - the others are all mathematically intuitive. Choice is, in other words, a "But thou must" definition which exists because things ought to behave one way, so we force them to.

I've got strong philosophical (Hoo boy, there's a word) objections to that, but I also recognize that there actually are things that should happen and even have a "naturalistic" basis for happening that Choice provides. It's a sticky wicket.

Because of that, I'm fond of the school of thought which attempts to verify as much as possible without invoking Choice. I also like playing with new axiomatic systems. Will this change over time? Maybe, I dunno; some day I'll sit down and have a really good chat with my advisor about the damn thing and we'll sort it all out. Perhaps I'll even check this thread that day and have a good laugh at myself over this. For now, it makes me blanch.

Mother.

Rarely do I shirk away from trying to explain math but here's exactly where I want to. The statement of the singular cardinals hypothesis is:

where κ+ is the "successor cardinal" of κ.

I don't... quite know where to begin on this one. Cardinal numbers are numbers we use to talk about how "big" a set is, limit cardinals are better, strong limit cardinals better still. Everyone's favorite cardinal, aleph-naught (The size of the set of every natural number, also the integers, also the rationals, also those by themselves, infinities!) is a strong limit cardinal.

The continuum hypothesis, which is ZFC (Standard set theory, ZF are two names, the C stands for Choice) independent - the deader than dead of the mathematical world, meaning even if it's true it can only be proved outside of our usual axioms, "good luck" - says that 2^(aleph-naught) (The size of the "every number ever" set we call the reals, also the complex numbers, also both of them at once, infinities!) is the next strong limit cardinal after aleph-naught. SCH extends this because, to quote Mitchell: "**** you." (Not an actual quote). It's also independent but because it's been generalized you can work on it more. Thus we're busy bounding it. Infamously, Saharah Shelah conjectured

which, if true, would mean that SCH breaks down when you start talking about the alephs of successor cardinals of cardinals that were already larger than any natural number to begin with.

Needless to say, this is everything that is beautiful and cool about set theory and I don't have enough machinery under my belt to do it justice. I've probably stated something incorrectly. But I'd like to work on this someday.

... For money, hopefully.

 

Keep in mind this is a Senate thread. Also, that meme doesn't work that way. - Lowbacca_1977

 

Lord Vivec, does this mean what the article says it means? About the Higgs boson, and something about the end of the universe

http://news.yahoo.com/confirmed-newfound-particle-higgs-130317830.html

 

WHO SUMMONS ME?

Oh.

Well let's start with the "it being confirmed to be the higgs" thing. Yes, there's been more analysis, and we've seen the decay into the W bosons, which is what we want to see. However, CERN has yet to confirm the spin 0. After all, theory says the Higgs is a scalar field, not a vector field. Here's the actual announcement.

Now to the quack part. So, here's a discussion of the calculations.

I'm not a mathematical physicist (meaning for this second part Ramza will be more helpful on this than myself, but the essential premise involves the universe being on semi stable false vacuum and would eventually quantum tunnel into a true vacuum. This would only happen IF our universe were really at a false vacuum. As you'll see, the paper refuses to make a declaration either way thanks to uncertainties in top quark and higgs masses.

But that doesn't stop all the laymen news from going "HIGGS PREDICTS UNIVERSE'S DESTRUCTION."

 

OH LAWDY.

Vivec's got the right of it, the paper even acknowledges that we don't have the technology to determine if the electroweak force behaves the way it has to behave for the "All is lost in billions of years" scenario. They also admit it seems very likely that we're not in that case to begin with, but again, we're nowhere near the tech necessary to see whether or not that pans out.

Essentially, you're looking at a very elaborate, mathematically sound version of this:



with the word "protons" replaced with "electrons and positrons". This is actually really common in theoretical physics since most "immediate" implications are figured out in semi-lockstep with the experimental results, often resulting in two possible scenarios. Theoretical physicists will then pick their favorite take the side of the physical reality they view as more likely, and extrapolate from that scenario. This is actually kind of cool in that it's only about three degrees removed from current work.

And as always, the tl;dr here is that when a physicist says "if," that's a colossal sized IF probably based on a couple more IFs of which maybe one is "only" a basic supposition.

 

Where do people go to for science news? Besides general news sites, I've only gone to LiveScience, but there better ones out there (that don't require a paid subscription)?

 

Physorg, Science Daily Magazine, Space.com, KerzweilAI, Centauri Dreams--and on this site there is a large list of links I sometimes marathon through though many of them are not updated often. Biosingularity, Sentient Developments, Space Daily, and every so often I go HERE as I sometimes forget about some site that I don't regularyl visit and just scroll through and clickity click.

 

Unfortunately I don't think I have any non-paid site recommendations, I primarily keep abreast of submitted mathematics papers via the American Mathematical Society's various submitted lists (Although those papers, if you dig around, are usually available as PDFs on faculty webpages), and sometimes I see what the various physics journals are up to for nostalgia's sake. But I otherwise don't bother with science news unless there's a thread or a discussion that grabs my interest - it tends to be... I dunno, sexy without being fun? It looks nice, sounds nice, I get why people like it; I personally prefer the fun stuff.

 

I visit science blogs a lot...to name a few:

anthropology.net
Astronomy Blog
Bad Astronomy
NASA Space News
Scientific American

 

This is more than a little scary... a machine has been created that allows one human to involuntarily move the hand of another human through only a mental command:
http://blogs.discovermagazine.com/crux/2013/10/25/mind-meld-future-of-brain-to-brain-communication/

Any thoughts on this new development? To me, it seems uncomfortably close to potentially becoming the beginning stages of mind control.





Also, DNA evidence suggests the "Yeti" might actually be a Himalayan version of the Polar Bear, that's a little more bipedal than other bears:
http://gma.yahoo.com/blogs/abc-blog...-yetis-dna-171145440--abc-news-tech.html?vp=1

 

How do you think we're planning to regulate the boards in the future?

I can actually see it being incredibly useful for a brain surgeon, just for example-you could literally "plug in" to a patient's nervous system and probably be able to determine (with further development) what exactly is screwed up.

 

We do have a type of bacteria called archea bacteria on Earth. It is found in places where there is very little oxygen (in fact, high concentrations of oxygen are poisonous to it) and are able to live in extreme environments where normal bacteria and eukaryotic life (cells with organelles such as nuclei) would not be able to survive. It is likely, that if we did find life elsewhere that it could be life like that, but it would still be carbon based. One question I would like to answer is if in other environments have organisms like these which have evolved beyond being prokaryotic and into a form of eukaryotic and multicellular life? If it has, do any of these possess sentience?

I thought about this a while back about could life exist using different chemical compositions. It is possible that life on other planets could have different nucleic structures to what is found on Earth. I found out that there are more than just the nucleotides found on Earth exist. What you've got to consider though is how the molecular structure of nucleotides and amino acids will interact with each other. It may well be that they can only do so in a certain way and if that is so, then the building blocks of like will be the same has it is on Earth. For this reason, we probably won't get non-carbon based life forms. If it is the same though and we get enough knowledge of it to be studied in any detail, I think it would make the tree of life look interesting because you could have organisms which aren't genetically related to each other but appear that they are because the DNA is very similar! (It wouldn't make Evolution an invalid theory, but it would raise questions for life that is considered less primitive because it may well be that life evolved more than once among bacteria).