Most groundbreaking proofs these days aren’t just cross-discipline but usually involve one or several totally novel techniques.
All that to say: I think you’re dramatically underestimating the difficulty involved in this, EVEN if the author(s) were a(n) expert(s) in machine readable mathematics, which is highly UNlikely given that they are necessarily (a) deep expert(s) in at LEAST one other field.
people on hn love making these kinds of declarative statements (the one you responded to, not yours itself) - "for X just do Y" as a kind of dunk on the implied author they're responding to (as if anyone asked them to begin with). they absolutely always grossly exaggerate/underestimate/misrepresent the relevance/value/efficacy of Y for X. usually these declarative statements briskly follow some other post on the frontpage. i work on GPU/AI/compilers and the number of times i'm compelled to say to people on here "do you have any idea how painful/pointless/unnecessary it is to use Y for X?" is embarrassing (for hn).
i really don't get even get it - no one can see your number of "likes". twitter i get - fb i get - etc but what are even the incentives for making shit up on here.
I wish we were a bit more self-critical about this, but it's a tough problem when what brings the community together in the first place is a sense of superiority: prestigious schools, high salaries, impressive employers, supposedly refined tastes. We're at the top of the world, right?
I know HN can be volatile sometimes, but I sincerely want to hear more about these parts of math that are not pure deductive reasoning.
Do you just mean that we must assume something to get the ball rolling, or what?
Stuff that we can deduce in math with common sense, geometric intuition, etc. can be incredibly difficult to formalize so that a machine can do it.
I think the subject at question here is mathematical truth, not "mathematics" whatever that means.
The article clearly states that there are multiple reading groups across the world attempting to get to grips with each small aspect of the ideas involved. That they even attempt this implies to me that the ideas are considered worth studying by some serious players in the field: the group (its way more than just one Fields toting bloke) have enough credibility for that.
We might get lucky that some ToE would generate low-energy predictions different from GR and QFT, but there's no reason to think that it must.
It's not like there's some great low-energy predictions that we're just ignoring. The difficulty of a beyond-Standard-Model theory is inherent to the domain of the question, and that's going to plague any alternative to String Theory just as much.
1. interactions at the event horizon of a black hole -- could the theory describe Hawking radiation?
2. large elements -- these are where special relativity influences the electrons [1]
It's also possible (and worth checking) that a unified theory would provide explanations for phenomena and observed data we are ascribing to Dark Matter and Dark Energy.
I wonder if there are other phenomena such as effects on electronics (i.e. QM electrons) in GR environments (such as geostationary satellites). Or possibly things like testing the double slit experiment in those conditions.
[1] https://physics.stackexchange.com/questions/646114/why-do-re...
re: "GR environments (such as geostationary satellites)" - a geostationary orbit (or any orbit) is not an environment to test the interaction of GR and QM - it is a place to test GR on its own, as geostationary satellites have done. In order to test a theory of everything, the gravity needs to be strong enough to not be negligible in comparison to quantum effects, i.e. black holes, neutron stars etc. your example (1) is therefore a much better answer than (2)
For geostationary orbits I was thinking of things like how you need to use both special and general relativity for GPS when accounting for the time dilation between the satellite and the Earth (ground). I was wondering if similar things would apply at a quantum level for something QM related so that you would have both QM and GR at play.
So it may be better to have e.g. entangled particles with them placed/interacting in a way that GR effects come into play and measuring that effect.
But yes, devising tests for this would be hard. However, Einstein thought that we wouldn't be able to detect gravitational waves, so who knows what would be possible.
AFAIK an EoT is not required to design experiments to determine if it's a real physical phenomenon vs. a mathematical trick; people are trying to think up those experiments now (at least for hidden variable models of QM).
About tests of quantum gravity, there have been proposals for feasible tests using gravitationally-induced entanglement protocols:
(I more or less do have the background to read these things, but it's super off-putting to start the article about a crazy new proof from a Fields medallist with an introduction to manifolds.)
I think it's nice someone wrote about this, even if it's super technical and I cannot understand it completely.
I got it for free!
I think Steve Jobs very much enjoyed life, and you know what kind of an attitude he had about things.
We're all wired up differently.
"You want many folds!" We gottem!
I think half a billion isn't that expensive for a program that searches for a potential "theory of everything" that can profoundly change our understanding of the universe (even if it brings no results!)
Right?
aside from that, this number is meaningless without context: how much do other fields of research get?
We won’t build a city on the Moon, nor Mars, nor any of Jupiter’s moons, nor anywhere outside of Earth, and we won‘t do this even if engineeringly possible, for the exact same reason we won’t build a bubble city inside the Mariana Trench.
The Moon is interesting because it's there, it's fairly close, it's a test bed for off-world construction, manufacturing, and life support, and there are experiments you can do on the dark side that aren't possible elsewhere.
Especially big telescopes.
It has many of the same life support issues as Mars, and any Moon solutions are likely to work on Mars and the asteroids, more quickly and successfully than trying to do the same R&D far, far away.
Will it pay for itself? Not for a long, long time. But frontier projects rarely do.
The benefit comes from the investment, the R&D, the new science and engineering, and the jobs created.
It's also handy if you need a remote off-site backup.
With current tech, it's practical enough to extract rocks from a rock. We've already done this on a comet, which I think is much harder to do. With current economics, not practical to fund such an endeavor, even if it was to haul back an asteroid made of solid gold. Regardless, we're discussing the far future, rather than current state.
If raw materials (again, an unknown) continue to become more scarce, it's hard to say what economics might support extra-planetary resource collection. What's for sure, is mining Mars will be harder than mining asteroids for water or metals, et al.
However, it is much easier to see us send robots to mine these asteroids, or send robots to the moon to build a giant telescope on the dark side (if that makes sense), then it is to see us build cities on the moon to build said telescope, and to mine those asteroids.
You see the difference here is that the end goal of mining asteroids are resources being sent to earth and exploited, while the goal of space settlements are the settlements them selves, that is some hypothetical space expansion is the goal, and that makes no sense, nobodies lives will improve from space expansion (except for the grifters’ during the grift).
You can start with a single Moon base but generally it isn't worth the mission control investment once you start to build out Mars.
Not like Mars is an amazing trip either, but the Moon is simply unsafe long term.
The prospect of a Mars colony would be that except a million times worse. Humanity will never migrate to Mars, we will never live on Mars, we have nothing to gain by living there, and it may even be impossible for us to live a normal human life over there (e.g. we don‘t know if we can even give birth over there). The only thing it will give us are bragging rights to the powerful individuals which achives it first, who will likely use that as political capital to enact horrible policies on Earth, for their own personal benefits, at the cost of everybody else.