Imaginary numbers are ordered (sort of I guess, they're just real multiples of i, so you can sort by the real), complex numbers aren't. /nitpick

I recall being taught about the number line and putting things on it - whole numbers, fractions etc Couldn't swear to it but I don't think it was ever called the 'real number line'. It would have raised the obvious questions about what the real and unreal numbers were and I don't think that ever happened.

We did have vulgar factions.

x^2>0 in an ordered field so you already run into problem with purely imaginary numbers by the standard definition of order. Of course the method you say would be the obvious way to do it if you had to (choosing i>0) , but since it doesn't let you order complex numbers and there is never really a natural reason one would like to order purely imaginary numbers to begin with it's basically useless.

Fair point. I mean, purely imaginary numbers is a pretty useless classification anyway, it's just a+bi in the special case where a=0.

Sure. But real numbers are just the special case when b=0 and they are a useful classification. It's sort of nontrivial fact that purely imaginary numbers aren't that useful. At least I can't convince myself that that should have been obvious the first time somebody defined i for me.

Hmm. Truth be told, I never really looked at it like that!

Some materials on climate change, motivated by a conversation in another thread.

Climate change forecasts. Soure - Nature; Cliffs - Depends on what we do right now.

https://www.nature.com/articles/d41586-020-01125-x

Climate change effects. Source - Wiki; Cliffs - Many: most bad, some irreversible.

https://en.wikipedia.org/wiki/Effects_of_global_warming

Climate change causes. Source - NASA; Cliffs - Humans.

https://climate.nasa.gov/causes/

How accurate are the models? Source - NASA; Cliffs - Accurate.

https://climate.nasa.gov/news/2943/s...ections-right/

2010-2019 was the hottest decade on record. 2020 has decent chance of being the hottest year on record.

So the Nobel prize committee in physics kind of went crazy, giving 1/2 of the prize to Roger Penrose. Not that Penrose doesn't deserve every award there is, but usually the Nobel prize was reserved for results that were clearly verified experimentally and Penrose's results are mathematical rather than predictive.

It's also sort of bittersweet in that Hawking almost certainly would have been honored as well had he still been with us. So it's weird that after 30 plus years of specifically not awarding this type of work, they wait until the most famous person in the field dies to do it. It also brings up the question of whether people like Witten or Maldacena, who's work maybe doesn't tell us directly about the universe but tells us about the limits of the theories we use to describe the universe might be similarly honored in the future.

Interesting. I did hear that the Nobles are not awarded posthumously, but I didn't know the other criteria. What are the full (stated) criteria?

I'm not aware of any strictly stated criteria. The main prestige of the physics award is it's history and as precedent, they normally don't award work like Penrose's. Even in Einstein's citation, they mention his work on the photoelectric effect but leave out any specific mentions of relativity because the experimental confirmation wasn't that obvious at the time of his award.

As more of a math guy, I'm all for changing the criteria a bit if it means people like Witten and Maldacena get recognized. Of course Maldacena has 2 hurdles to overcome; his work isn't experimentally testable and also can't be proven to a mathematicians level of rigor. Of course physicists have no doubts about it.

Given how we have seen in the last century that these theoretical frameworks have been the driving force also for experimental breakthroughs, it is perhaps prudent that prizes also change with the times.

I mean, something like the standard model, which we kind of take for granted in physics these days, has been a history of slowly moving towards stronger and stronger experimental verification and less assumptions.

Witten did get the Field's medal, which is even better. But his work on String/M theory is not yet worthy of a Nobel Prize, imo, as the field is not unified in its thinking yet. By contrast, there were no competing versions of Relativity in Einstein's time.

On a tangent, my bias is that Physics has a similar issue that Econometrics has had. In Econometrics the problem has been that they have misapplied complex mathematics due to faulty starting assumptions. In Physics, in my opinion, they are equally blinded, particularly with respect to their belief that the concept of mathematical dimensions and physical dimensions are synonymous.

I am assuming you're referring to Edward Witten? (I have not read through this thread). String theory is definitely still highly debated within the Physics community, and I would agree with this comment. Anyone that says otherwise is probably not that educated of the field. It does not necessarily mean string theory will not potentially be proven to be accurate in the future, but at the current moment it hasn't.

I personally don't debate religious people generally speaking, but the disconnect between science and religious people has always interested me. I am not trying to come off as condescending, but a decent % of the arguments religious people make comes from a state of ignorance. "How could there not be a god when the earth happens to exist within the Goldilocks zone?" (very low probability of occurring for a planet) Religious people don't usually frame this question in the manner in which I did, but you guys get the point. The obvious answer to this question is simply probability. Considering the size of the universe, it's not unreasonable to assume that of all planets that exist within this universe, a certain % or X amount of those planets will inherently exist/"fall" within the Goldilocks zone. In analogical terms you can think of it like playing the lottery. Obviously the probability of buying a ticket and winning the lottery is extremely low (just in the same way that a planet falling into the Goldilocks zone is also extremely low) but guess what? Humans do in fact win the lottery, just in the same way that certain % of planets fall into the Goldilocks zone. This is just one example of religious people not understanding certain concepts, but unfortunately it happens to be very common regardless of the claim they are making. It really does just come down to poor logic.

How comes puddles of water are such a perfect fit for the hole?

And if the earth is really round, how come all the water doesn't just flow down to the south pole and drip off the end? I just tried it with a LOLglobe in my kitchen and that's exactly how it works. #Science #Evidence #RealTRUTH #OpenYourEyes

Me: How come I feel a but not v?
Mach: goddidit.

Confucius says, “Don’t complain about the snow on your neighbor’s roof when your own doorstep is unclean.”

I know we are just joking and that's all good, but as someone that has lived/grown up my entire life in the American south, it's very frustrating to say the least. And yes, most of these conspiracies come from the Republican/Christian types (You didn't make this claim, but I did). It does not matter if it's chemtrails, flat earth, Bill Gates microchip, they ALL come from these people. What's so terrifying is how common these conspiracy theories are down here, it's just ****ing sad!

If you read this thread you will see that I have in fact made this claim and many others like it. I'm the OP (sort of - it was spun off from a different thread).

The faith blinds the « purest » soul !

Funny cos I heard something about the sun and built a smaller version in my kitchen. The ****er exploded #lolscience #thataintevidence #bollocks #runawayfast

Speaking of which:

https://futurism.com/mit-researchers...ry-likely-work

This bit

made me laugh.

I get that they are on a design stage and that things are different, but given the history of fusion reactor development it was perhaps a poor choice of words.

I wasn't really thinking of Witten's work on String/M theory for the Nobel. But stuff like conformal field theory which has greatly improved our understanding of quantum field theory itself in the most general sense in which it is understood.

this is basically what i mean..

if you think you are put here to/and are "exercising god's will in government" that should absolutely be disqualifying. that's a mental disorder

if you just attribute your morality to your specific space man, that's whatever. as long as you dont think your morality is better than someone else's because of that space man.