User talk:Double sharp/Archive 22

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Archive 22

Invitation to join the Fifteen Year Society

Dear Double sharp/Archive 22,

I'd like to extend a cordial invitation to you to join the Fifteen Year Society, an informal group for editors who've been participating in the Wikipedia project for fifteen years or more. ​

Best regards, The Herald (Benison) (talk) 02:48, 7 August 2024 (UTC)

— The Herald (Benison) (talk) 02:48, 7 August 2024 (UTC)

@The Herald: Thank you! :D Double sharp (talk) 03:20, 7 August 2024 (UTC)

Nomination of Crossed square cupola for deletion

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Production of transuranium nuclides

I was wondering that, which of ²⁵⁰Cm, ²⁵⁴Cf, ^252-255Es can be produced in quantity at least of micrograms? I think ^253,254,255Es are available because they can be formed when ²⁵²Cf absorbs neutron; for the others, I don't think so. 14.52.231.91 (talk) 01:01, 16 August 2024 (UTC)

Seems to be just Es-253 and Es-254. Es-255 is shorter-lived...but I'm not sure it has ever been done even for Es-253 and Es-254. Double sharp (talk) 04:38, 16 August 2024 (UTC)

Thanks! At least we can have confidence with ²⁵³Es, as Wikipedia states explicitly that "Einsteinium is the element with the highest atomic number which has been observed in macroscopic quantities in its pure form as einsteinium-253". 14.52.231.91 (talk) 00:46, 19 August 2024 (UTC)

I think ²⁵⁴Es is also OK because it has been used in the nucleosynthesis of ununennium. As for ²⁵⁵Es, it has even longer half-life than ²⁵³Es... 14.52.231.91 (talk) 00:55, 19 August 2024 (UTC)

Back in that 1985 attempt, less than a microgram of ²⁵⁴Es was actually used – which was probably one of the reasons nobody saw anything. (Another is also probably that back then, the cross-section limit wasn't enough to see anything from ²⁴⁸Cm+⁴⁸Ca either.)

I actually have a significant worry that 119 will take a while to come after 120 (which has taken a long time already). That's because with the cross-sections likely to be the way they are, a ²⁴⁹Bk target might very well have significantly decayed by the time the first successful fusion occurs. And using ²⁴⁸Cm+⁵¹V gets the penalty of having the odd proton in the projectile instead of the target, while ²⁴³Am+⁵⁴Cr will likely have a smaller cross-section than ²⁴⁹Bk+⁵⁰Ti and leads to a more neutron-poor ER. But oh well, we've all waited fourteen years and counting for 120 in the first place. :) Double sharp (talk) 04:49, 19 August 2024 (UTC)

Either 119 or 120 coming first would be OK to me - we would be closer to finally finishing the periodic table up to n + l = 8 :) 14.52.231.91 (talk) 02:27, 20 August 2024 (UTC)

Haha, yes. The Janet table is great! But what I really want is to see the g-block. Hopefully, after that people will finally universally get group 3 correct (after Y comes Lu and Lr, certainly not asterisks or La-Ac). :) Double sharp (talk) 02:55, 20 August 2024 (UTC)

G-block would be a lot harder, and it's even worse that the first element with a 5g electron comes much later... 14.52.231.91 (talk) 07:00, 20 August 2024 (UTC)

Yeah, probably each change of projectile will mean things get one or two orders of magnitude worse. :( Probably already E121 has 5g low enough to participate in chemistry at least. But doing actual chemistry with the expected half-lives and low rate of production seems very far off. Still nobody has done Mt. (Okay, to some extent it's partly that Mt chemistry will probably be like Ir, making it hard to get into solution and also hard to find volatile compounds without using F₂.) Double sharp (talk) 10:00, 20 August 2024 (UTC)

What I also find curious is that only the lightest isotopes of Mt and Rg have been directly synthesized and no new hot fusion reactions have been attempted for those elements. ^Complex/_Rational 13:55, 20 August 2024 (UTC)

@ComplexRational: Considering the cross-section trend, wouldn't it be easier to fill them in from Mc, just like it's easier to produce Cn as an overshoot product from Fl? Though I have been hungering for ²³¹Pa+⁴⁸Ca for a while, especially now that ²³²Th+⁴⁸Ca has been successful. (And can someone please do ²⁴¹Am+⁴⁸Ca already? :D) Double sharp (talk) 14:57, 20 August 2024 (UTC)

Sadly it seems like no one cares about ²³¹Pa + ⁴⁸Ca, even the most recent reference about it was from 1981. :(

On the other hand, ²⁴¹Am + ⁴⁸Ca got a recent reference. In there, reactions involving ²⁴¹Am was even considered to create elements 119~122. :) Nucleus hydro elemon (talk) 16:01, 20 August 2024 (UTC)

@Nucleus hydro elemon: T_T Thanks for the papers! (Though I'd want to stick to ²⁴³Am for going beyond 118, at least at first. I wonder how close we are to the proton drip line in this region...) Double sharp (talk) 16:11, 20 August 2024 (UTC)

For cross sections, targeting Mc and observing its decay chains would certainly be more feasible based on experimental data. However, indirect synthesis is said not to be optimal for investigation of chemical properties.

And re below, the KTUY chart that I uploaded some time ago suggests that we are already very near the drip line for odd-Z superheavy elements, but the partial half-lives for alpha/SF are expected to be longer than those for proton emission, so I'm not sure if we'd even know. ^Complex/_Rational 18:50, 20 August 2024 (UTC)

@ComplexRational: Sure, though Cn and Nh were both investigated through indirect synthesis. So at least it's a possible option when the cross-section is likely to be worse for the lighter elements. :) Thanks for the answer on the drip line! Double sharp (talk) 02:55, 21 August 2024 (UTC)

@ComplexRational: Double sharp (talk) 10:09, 18 August 2024 (UTC)

References

Leep year setting for octal and nonary civilizations

I've come up with the calendar for civilizations living on Earth that use octal or nonary. I suppose that a week is still 7 days, because the number seems to be base-independent. I will use our seconds for comparison, even though a non-decimal civilization would have defined a second to be something else than 1/86400 of a day.

For people using nonary: Set a leap year in every 4₉ years, then eliminate one every 130₉ years, and add one back every 800₉ years.

This will make 184₉ leap years out of every 800₉ years, so a year would be 31638.3₉ seconds longer than a multiple of a day. The tropical year is 31631₉ seconds longer than that, so the difference is 7.3₉ seconds. A period of 800₉ years contains exactly 51337₉ weeks.

For people using octal, there are two choices. The more natural one would be to set a leap year in every 4₈ years, then eliminate one every 200₈ years. But we have to wait for 1600₈ years until the weekdays repeat themselves. Another choice with a period of 1600₈ years is to set a leap year in every 4₈ years, eliminate one every 160₈ years, then add one back every 1600₈ years.

In either case there will be 331₈ leap years out of every 1600₈ years, so a year would be 50675₈ seconds longer than a multiple of a day, which is only one second short compared to the tropical year!

In conclusion, the octal calendar wins by accuracy but the nonary one wins by a shorter period of weekdays (for comparison, our decimal calendar has yet lower accuracy but an even shorter weekday period). Still, it's amazing that the orbital period of the Earth can give a calendar in periods of a multiple of centuries which is accurate enough, for people using either decimal, octal or nonary :) 14.52.231.91 (talk) 06:51, 22 August 2024 (UTC)

By the way, my edit triggered filter 1321 when I tried to post all the paragraphs as a whole. But when I performed the edits in posting just some paragraphs at a time, the edits were OK. 14.52.231.91 (talk) 06:55, 22 August 2024 (UTC)

It seems that the edits were limited to 1280 characters. (Of course, since I did not mean to do any vandalism, my test stops here.) 14.52.231.91 (talk) 07:03, 22 August 2024 (UTC)

Very cool! The edit filter may not have appreciated these calendars, but I do! :) Double sharp (talk) 07:56, 22 August 2024 (UTC)

Thanks! :) 14.52.231.91 (talk) 00:49, 23 August 2024 (UTC)

Picture of astatine?

Astatine or something else?

This reference showed their bismuth target that contains ²¹¹At after irradiation (Fig. 1). Even better, the license is CC BY 4.0 and thus the picture can be used in Wikipedia. The problem is I'm not sure is the black stuff in that picture is real, visible ²¹¹At in nanogram quantities, or is it just burnt bismuth or anything else? If it is indeed real ²¹¹At then we might be able to use it in the infobox. :) --Nucleus hydro elemon (talk) 13:49, 24 August 2024 (UTC)

References

@Nucleus hydro elemon: I hate to give this answer, but it's just physically implausible that you're seeing At in any visible quantity. Still, it could be a good picture to illustrate astatine production, just not in the infobox. :) Double sharp (talk) 14:17, 24 August 2024 (UTC)

Polyhedra nets

Hello Double Sharp! On the Wikipedia Page "Rectified truncated icosahedron" there are listed several related polyhedra, including their nets. Somehow two nets are missing, namely for the btI and mtI (in Conway notation). Is there any possibility for you to upload the last missing nets? This would be great. Kind regards, Sakura787 (talk) 16:06, 7 September 2024 (UTC)

@Sakura787: I'm terribly sorry, but my copy of the Stella software died with my previous computer. Since I no longer have the serial number, I'm no longer in a position to make such diagrams. :( Double sharp (talk) 16:47, 7 September 2024 (UTC)

The page "List of nuclides"

I see you changing the split point 5 × 10⁸ years to 10⁸ years. But now, "Primordial radioactive nuclides (half-life > 10⁸ years)" looks inconsistent: A radionuclide having suffered 9 half-lives would be primordial, but certainly not one that has suffered 45... 103.166.228.86 (talk) 18:40, 15 September 2024 (UTC)

Well, current sensitivity is actually not that far off finding ²⁴⁴Pu (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 ¹⁴⁶Sm and ²⁴⁴Pu will still not be useful primordials, but it'd be fun to have them back (for a while we had ²⁴⁴Pu as primordial based on the 1971 result, that in retrospect cannot be right). :) Double sharp (talk) 04:29, 16 September 2024 (UTC)

I would indeed be happy to see ¹⁴⁶Sm be confirmed as primordial, for the sake of completeness - the hole of even-even nuclides between ¹⁴⁴Sm and ¹⁴⁸Sm is just unbearable... 129.104.241.231 (talk) 00:02, 18 September 2024 (UTC)

The N = 82 shell closure is a harsh mistress. :( Double sharp (talk) 06:01, 18 September 2024 (UTC)

The magic numbers only care about their own comfort and don't care about the lives of others :( 129.104.241.231 (talk) 11:20, 19 September 2024 (UTC)

The combo of Z = 82 and N = 126 is also harsh, killing Po~Ac with no mercy... :( Nucleus hydro elemon (talk) 15:12, 19 September 2024 (UTC)

But at least Ra gets enough beta-stable isotopes that it gets out of the killing zone of N = 126, with ²²⁶Ra (Z = 88, N = 138) able to have a respectable 1600-year half-life. :)

Unfortunately, as if making new superheavies wasn't hard enough already, the 5g row will probably head straight into the firing squad of N = 184 when it comes to doing Cf+Ni for 126. :( Double sharp (talk) 15:17, 19 September 2024 (UTC)

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 :( 129.104.241.231 (talk) 15:29, 19 September 2024 (UTC)

Yeah but the cruelest enemy of superheavy elements is SF, not alpha decay... 129.104.241.231 (talk) 15:32, 19 September 2024 (UTC)

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 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_3/2 is enough to make francium have oxidation states above +1. Ah well. Such forbidden mysteries. :(

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 fission. :(

P.S. the superheavy I would most like to see "stabilised" is copernicium. :D Double sharp (talk) 15:50, 19 September 2024 (UTC)

Gd would have 9 naturally occuring isotopes, At would behave like Ta to occur mainly as ²¹⁵At and a small portion of ^214mAt, and there will perhaps be no more beta-decay mystery for ²²²Rn and ²⁴⁷Cm. What a fantastic world... 129.104.241.231 (talk) 18:19, 19 September 2024 (UTC)

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 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. ;) Double sharp (talk) 10:38, 20 September 2024 (UTC)

I dream about their geochemical properties then. :) I only guess up to Rg because Cn will be too weird, see below.

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 crazy.

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 geochemistry of At.

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. Nucleus hydro elemon (talk) 11:28, 20 September 2024 (UTC)

There would be no need to worry about copernicium rain - remind that this is a world full of ⁸Be :) 129.104.65.10 (talk) 12:07, 20 September 2024 (UTC)

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. :) Double sharp (talk) 14:46, 20 September 2024 (UTC)

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 (Beryllium-8#Hypothetical universes with stable 8Be). ^Complex/_Rational 16:18, 20 September 2024 (UTC)

If ⁸Be is stable because ⁴He is destabilized, then ⁵He and ⁵Li might be bound too. This will drastically change the Big Bang nucleosynthesis at that universe. Nucleus hydro elemon (talk) 04:36, 21 September 2024 (UTC)

Well, in that case all the elements might've been made in that universe's Big Bang, just as αβγ originally expected. :) Double sharp (talk) 04:40, 21 September 2024 (UTC)

(And considering a famous work by the γ in question, perhaps this discussion about living in universes with altered physical constants is apropos. ^_^) Double sharp (talk) 04:43, 23 September 2024 (UTC)

About ²²²Rn/²²²Fr

Hi! I have just noticed the mass excess of ²²²Rn given in NUBASE is 16372.0 ± 1.9 keV, while the mass excess of ²²²Fr is 16378 ± 7 keV, corresponding to an atomic mass of 222.0175825(75) for ²²²Fr. While the data are not decisive, ²²²Rn has lower energy if we ignore the error margin. So what do you think of the status of ²²²Rn? This will affect how we formulate in Isotopes of radon and Double beta decay. 129.104.241.231 (talk) 11:23, 19 September 2024 (UTC)

I think we should leave it open still, since Belli et al. explicitly predicted the single beta of this isotope and tried to find it. I'm naturally quite curious which way round it'll go. :) Double sharp (talk) 13:30, 19 September 2024 (UTC)

Thanks! I added the source to both page I mentioned. 129.104.241.231 (talk) 15:08, 19 September 2024 (UTC)

The existence of Vitali sets

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 $\mathbb {R}$ 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.

By the way, I love the reference you gave, thanks a lot :) 129.104.241.231 (talk) 21:33, 21 September 2024 (UTC)

I am neither a fan of CH nor a fan of ¬CH. I could have insisted that $2^{\aleph _{0}}=\aleph _{85}$ 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. :) 129.104.241.231 (talk) 21:39, 21 September 2024 (UTC)

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 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".

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 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).

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 Rodrigo Freire's answer to a MathOverflow question about V=L 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 Freiling's argument for ¬CH. 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. Double sharp (talk) 03:55, 22 September 2024 (UTC)

P.S. Regarding another case of set-theorists and non-set-theorists having quite different intuitions, see this other paper by Joel David Hamkins (2012), where he gives a specific example of an axiom ($\kappa <\lambda \implies 2^{\kappa }<2^{\lambda }$) that seems extremely natural to non-set-theorists and yet is generally rejected by set theorists. Double sharp (talk) 08:13, 22 September 2024 (UTC)

Most of the real analysis relies on DC, and it is written in the Wikipedia 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_ω/DC is enough to prove a proposition, don't overuse the power of AC :)

Thanks for the link provided, and by the way, I just remembered this interesting implication of CH. 129.104.241.231 (talk) 14:22, 22 September 2024 (UTC)

Well, if you like interesting remarks on what's actually necessary to prove what, you might enjoy this MathOverflow question, regarding whether or not the infinitude of prime numbers is necessary to prove $\pi$ transcendental. (The Euler zeta product naturally makes it clear that the infinitude of the primes is related to the irrationality of $\pi$, because $\zeta (2)={\frac {\pi ^{2}}{6}}$. But this is about transcendence. Though there are some issues on whether you can even define $\pi$ properly in a setting where you cannot show that there are infinitely many primes...) :)

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 bad. :)

I think "don't overuse the power of [just about anything really]" 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 yourself how much of it was really needed. Double sharp (talk) 16:06, 22 September 2024 (UTC)

P.S. and thanks for that CH implication. :) Double sharp (talk) 04:47, 23 September 2024 (UTC)

P.S. another way CH makes NSA so much nicer. :) Double sharp (talk) 07:31, 25 September 2024 (UTC)