428:
recognised earlier: then Nd (maximum +4) vs U (maximum +6) somewhat brings to mind Fe (maximum +6 in bulk) vs Ru (maximum +8), and Cm–No will make a more extreme partner to Gd–Yb. The big drop in oxidation states near the end of the 5f series makes one think of the 4d series; I've thought for a while that if we had long-lived quasi-stable elements to the 6d series, then we wouldn't be having the La vs Lu argument, as it would be obvious that Lr is much more like a transition metal than Ac is. (Lu is also more like a transition metal than La, but not quite as obviously.) Ah well, I can dream about the chemical consequences while you dream of the nuclear-physics ones. ;)
53:
749:
my intuitions about sets. So when I say "I'm a fan of CH", I suppose what I really mean is that my fuzzy ideas about how sets should behave are more consistent with the consequences of CH than with those of ¬CH. If we speak this way, about properly axiomatising intuitions, I think it makes sense to say that "CH is true of my sets" and simultaneously "¬CH is true of somebody else's".
240:(see the article): we're about an order of magnitude away. I won't be surprised if it really gets confirmed as primordial at some point (though maybe we need to wait another decade or two). Of course Sm and Pu will still not be useful primordials, but it'd be fun to have them back (for a while we had Pu as primordial based on the 1971 result, that in retrospect cannot be right). :)
32:
384:
turning out to be a full-fledged metal at STP, not just a semiconductor. But who really knows?) It would also be nice to know more about radon chemistry: the absence of chlorides is still a mystery, but the ionic-looking difluoride is really cool. And it would be nice to know if the destabilisation of 6p
583:
Hi! I have just noticed the mass excess of Rn given in NUBASE is 16372.0 ± 1.9 keV, while the mass excess of Fr is 16378 ± 7 keV, corresponding to an atomic mass of 222.0175825(75) for Fr. While the data are not decisive, Rn has lower energy if we ignore the error margin. So what do you think of the
383:
If nothing else, such a universe would probably not make the mistake of predicting astatine to be a black solid. That always got on my nerves from the time I realised what was wrong with it. Groups 13 to 16 eventually turn metallic, so why shouldn't groups 17 and 18!? (I'm still betting on oganesson
748:
My personal take is basically: both consequences of CH and ¬CH are indeed equally valid. But the same holds for consequences of AC and ¬AC, despite the fact that mathematicians seem a lot happier to assume AC than otherwise. To that extent, I think it makes sense to ask which one conforms more with
449:
I'm not sure do Pa, Np, Pu comes together with U or have its own ore. Md and No have stable +2 cations, not sure will this let them become closer to Ba than rare-earth elements. I don't know do Po behaves more similar to Bi or Te. Both At and At are stable, I'm not sure which one will dominate the
752:
With that said, Hamkins' presentation strongly persuades me that CH (actually, GCH) should be true of more people's sets. This is because I think hyperreals are in some sense the "natural" way to do analysis, and that epsilon-delta formulations are to some extent dancing around the intuition. It
1003:
I think "don't overuse the power of " is sound advice. On the other hand, sometimes the proof that uses more firepower is the more intuitive one. So, maybe I'd say: do all the crazy stuff you want if it helps you get to the correct result. Then, after admiring your fireworks, step back and ask
999:
My philosophy is basically that the infinite should be like the finite when it comes to counting, on the grounds that ordinals seem to be the most obvious way to introduce "infinity" to children. So I have no issue with transfinite sequences indeed. If some funny things happen to measures, too
858:, and it is written in the Knowledge (XXG) page "It is possible to generalize the axiom to produce transfinite sequences. If these are allowed to be arbitrarily long, then it becomes equivalent to the full axiom of choice", so I have no doubt on AC. That said, my attitude is that whenever ZF/AC
766:. BTW, Nik Weaver's answer on that page gets at something interesting: it seems quite plausible that we are in the current situation because non-set-theorists would have quite different intuitions about sets from set-theorists. The former would likely be a lot happier with V=L than the latter.
427:
Come to think of it, a world where Rn is stable immediately suggests an earlier discovery of noble gas chemistry. That would be fun. I wonder what the last natural element would be in this case. If the actinoid series can be completed (or nearly so), then perhaps a separate f-series could be
753:
makes me think of, say, Cardano having to solve many types of cubics because he didn't like negatives. As such I think there's a strong argument that GCH "should" have the status AC currently enjoys among non-set-theorists (well, actually ZF+GCH implies AC, but you know what I mean).
482:
I kind of suspect that in this world Be is like Al: useless to biology because it's insoluble at physiological pH, but tolerated because it's so common. Copernicium would be weird indeed. Still, I think it'd be quite rare like krypton and xenon already are in the real world. :)
756:
Non-measurability was indeed a bit of a mind-blowing fact when I first encountered it in mathematical popularisations at about eight. :) I would find it intuitive now, but perhaps it has to do with von
Neumann's dictum about getting used to things in mathematics. But I think
445:
Tc probably lives together with Re, so do Rn with noble gases, Fr with Rb/Cs, Ra with Sr/Ba, and Pm, Ac, Am–Fm, Lr with rare-earth elements. Rf–Rg might be similar to their lighter congeners Hf–Au if the relativistic effects aren't too
497:
Before discussing implications for biology, we also have to consider how hypothetical beryllium burning would affect stellar evolution. A while back I had read a few interesting papers on the subject and written a bit about it
391:
That's true, but the shell closure strongly hinders SF, and is the only reason they're protected enough to be seen in the first place. When that protection gets lost, there's nothing holding back the terrible onslaught of
453:
Cn probably have some noble gas character, and its predicted melting point and boiling point might cause a rain of Cn happen in that world. I don't want to live in a world with copernicium rain, it is just too dangerous.
838:
761:
gets philosophically at the issue here. Though actually his argument persuades me towards V=L, because I would indeed take AC's attitude towards measurability as a "precedent" of sorts, which is why I reject
974:
732:
734:
because 85 is my favorite neutron number, but I really do have no opinion: both consequences of CH and of ¬CH are equally valid for me, and it is worthy to state them both. :)
667:
994:
925:
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I would indeed be happy to see Sm be confirmed as primordial, for the sake of completeness - the hole of even-even nuclides between Sm and Sm is just unbearable...
355:
You guess what? My biggest wish is to live in my next life in a universe where the energy of the alpha nuclide is at least 5 MeV higher than in our universe :(
517:
If Be is stable because He is destabilized, then He and Li might be bound too. This will drastically change the Big Bang nucleosynthesis at that universe.
884:
669:
be so great that every subset is measurable? The existence of non-measurable sets rather than the non-existence is what looks more natural for me.
647:
Reply to "Doesn't the existence of Vitali sets (a result of AC) already challenge intuition?": No, not at all in my opinion :) Anyway, why should
221:
10 years)" looks inconsistent: A radionuclide having suffered 9 half-lives would be primordial, but certainly not one that has suffered 45...
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Unfortunately, as if making new superheavies wasn't hard enough already, the 5g row will probably head straight into the firing squad of
469:
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transcendental. (The Euler zeta product naturally makes it clear that the infinitude of the primes is related to the irrationality of
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I see you changing the split point 5 × 10 years to 10 years. But now, "Primordial radioactive nuclides (half-life : -->
930:
442:
I dream about their geochemical properties then. :) I only guess up to Rg because Cn will be too weird, see below.
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Gd would have 9 naturally occuring isotopes, At would behave like Ta to occur mainly as At and a small portion of
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P.S. Regarding another case of set-theorists and non-set-theorists having quite different intuitions, see
840:) that seems extremely natural to non-set-theorists and yet is generally rejected by set theorists.
468:
There would be no need to worry about copernicium rain - remind that this is a world full of Be :)
883:
Well, if you like interesting remarks on what's actually necessary to prove what, you might enjoy
650:
206:
413:, and there will perhaps be no more beta-decay mystery for Rn and Cm. What a fantastic world...
388:
is enough to make francium have oxidation states above +1. Ah well. Such forbidden mysteries. :(
286:
The magic numbers only care about their own comfort and don't care about the lives of others :(
976:. But this is about transcendence. Though there are some issues on whether you can even define
611:
of this isotope and tried to find it. I'm naturally quite curious which way round it'll go. :)
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Well, in that case all the elements might've been made in that universe's Big Bang, just as
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But at least Ra gets enough beta-stable isotopes that it gets out of the killing zone of
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properly in a setting where you cannot show that there are infinitely many primes...) :)
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237:
887:, regarding whether or not the infinitude of prime numbers is necessary to prove
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P.S. the superheavy I would most like to see "stabilised" is copernicium. :D
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Yeah but the cruelest enemy of superheavy elements is SF, not alpha decay...
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833:{\displaystyle \kappa <\lambda \implies 2^{\kappa }<2^{\lambda }}
862:/DC is enough to prove a proposition, don't overuse the power of AC :)
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I am neither a fan of CH nor a fan of ¬CH. I could have insisted that
758:
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865:
Thanks for the link provided, and by the way, I just remembered
236:
Well, current sensitivity is actually not that far off finding
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26:
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Rodrigo Freire's answer to a MathOverflow question about V=L
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672:
By the way, I love the reference you gave, thanks a lot :)
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I think we should leave it open still, since Belli et al.
334:= 138) able to have a respectable 1600-year half-life. :)
784:(2012), where he gives a specific example of an axiom (
308:= 126 is also harsh, killing Po~Ac with no mercy... :(
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Thanks! I added the source to both page I mentioned.
584:status of Rn? This will affect how we formulate in
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500:Beryllium-8#Hypothetical universes with stable 8Be
969:{\displaystyle \zeta (2)={\frac {\pi ^{2}}{6}}}
341:= 184 when it comes to doing Cf+Ni for 126. :(
8:
727:{\displaystyle 2^{\aleph _{0}}=\aleph _{85}}
1004:yourself how much of it was really needed.
272:= 82 shell closure is a harsh mistress. :(
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1:
867:this interesting implication
662:{\displaystyle \mathbb {R} }
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18:User talk:Professor Fiendish
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579:About Rn/Fr
392:fission. :(
927:, because
189:Archive 22
182:Archive 21
177:Archive 20
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165:Archive 18
160:Archive 17
155:Archive 16
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304:= 82 and
114:Archive 9
109:Archive 8
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97:Archive 6
92:Archive 5
87:Archive 4
80:Archive 3
75:Archive 2
70:Archive 1
39:real life
507:Rational
58:Archives
1000:bad. :)
869:of CH.
446:crazy.
330:= 88,
1010:talk
875:talk
846:talk
818:<
795:<
772:talk
740:talk
678:talk
631:talk
617:talk
598:talk
588:and
541:talk
523:talk
502:). /
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474:talk
460:talk
434:talk
419:talk
401:talk
375:talk
361:talk
347:talk
314:talk
292:talk
278:talk
268:The
260:talk
246:talk
227:talk
533:αβγ
386:3/2
1012:)
984:π
953:π
935:ζ
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20:)
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