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A nearly invisible dwarf galaxy is challenging the model of dark matter. An international team of astronomers, led by the Instituto de Astrofísica de Canarias (IAC) in collaboration with the University of La Laguna (ULL) and other institutions, discovered this fascinating galaxy dubbed "Nube."
Nube, which means "Cloud" in Spanish, was named by the 5-year-old daughter of one of the researchers, aptly reflecting the galaxy's ghostly and diffuse appearance. Its discovery is significant because its faint surface brightness allowed it to remain undetected in previous sky surveys, despite its considerable size.
"With our present knowledge we do not understand how a galaxy with such extreme characteristics can exist," says study first author Mireia Montes, researcher at the IAC and the ULL, in a media release.
Nube is unique in its properties, being ten times fainter yet ten times more extended than other dwarf galaxies with a similar number of stars. Its discovery is akin to finding a hidden treasure in a well-explored attic. Nube is large and yet faint, a ghostly apparition in the universe. To put it into perspective, it's about one-third the size of the Milky Way but has a mass comparable to the Small Magellanic Cloud.
What sets it apart is its significant amount of dark matter, an invisible substance that does not emit, absorb, or reflect light, making it undetectable by traditional telescopes.
Related: Bizarre Galaxy Discovered With Seemingly No Stars Whatsoever
(Score: 1) by khallow on Thursday February 01 2024, @10:00PM (5 children)
The logical system has to be sufficiently complex. For example, in the empty logical system there's nothing to prove and hence, validity is trivial. In a simple system of axioms without implication, you have a similar situation - such as "A is true." The only logical statements in the system are Boolean expressions of the finite axioms. And thus, the system is provably valid.
Once your system is complex enough to include a representation of the natural numbers, then you can't prove the system of logic is valid. This is a sufficient not necessary condition.
(Score: 2) by Immerman on Friday February 02 2024, @03:13PM (4 children)
You might have an argument in the degenerate case -but even if your only axiom is "A is true", it's impossible to *prove* that A is true within that framework. Your axioms are *always* unprovable within the framework they create.
You can absolutely prove that everything else you've created within that framework is true if your axioms are true - but the axioms themselves can only ever be assumptions.
(Score: 1) by khallow on Friday February 02 2024, @04:10PM (3 children)
That's a different business. Within the framework, axioms are always true and hence, A is true would be trivially true. My point is that the system of logic is sufficiently limited that you can't construct statements that are unprovable within this framework.
(Score: 2) by Immerman on Friday February 02 2024, @05:14PM (2 children)
No, that's exactly what I'm talking about.
Not sure what you're trying to say, but virtually all statements possible within any given logical framework are unprovable - including the small subset that can be disproven.
Example:
If all crows are pink, then elephants are watermelons
is a perfectly valid logical statement that's completely unprovable. Almost all possible statements within any logical framework are similarly nonsensical, and thus unprovable.
(Score: 2) by Immerman on Friday February 02 2024, @05:27PM (1 child)
Wait, no, my bad - that's absolutely a provably true statement. All statements of the form
If [false] then ...
are true, since the "then" portion will never be invoked, so to prove it you only need to establish that a single non-pink crow exists.
But my point stands - the vast majority of possible statments within most logical systems will be nonsensical, and thus improvable.
The problem is that, while you can absolutely prove:
IF the axioms on which arithmetic is based are true, THEN 3+5 = 8.
You CANNOT prove
3+5=8
because the axioms on which the statement is based cannot themselves be proven.
(Score: 1) by khallow on Saturday February 03 2024, @06:38AM
And as I noted, you have a special class of unprovable statements which aren't unprovable because of nonsensicality.
Axioms are always true in the logical system by definition. When operating in a system of logic, they are their own proof.
Again, this is a different issue. In any system containing natural number axioms, one can come up with unprovable statements which do not conflict with the axioms of the system or are nonsensical. It's a deeper reason.