tikej

I think a relatively simple explanation is that on one hand mercury is liquid due to its closed-shell (a bit "noble-gas-like") electron configuration: [Xe] 4f14 5d10 6s2 and that it since its electrons are paired it makes it less energetically favorable to create strong bonds. So consequently Hg does not form conventional, strong covalent bonds (although it probably does form some weak van der Waals complex) like, for example, gold (with the unpaired electron on 6s orbital so [Xe] 4f14 5d10 6s1 configuration) and other "horizontally neighboring" elements which consequently create stronger bonds. However, this alone is not enough and would not explain why Cd isn't liquid.

And here come the relativistic effects, which essentially scale with nuclear charge of the nucleus come to play and they are significantly stronger for Hg than Cd. If I remember correctly (although I read about it a long time ago so I may be a bit rusty) these strong relativistic effects cause something called "relativistic contraction of the 6s orbital" which results in the electrons on this orbital being more strongly bound than they would be, if there would be no relativistic effects (which can be theoretically compared by setting c -> infinity in the equations used to solve electronic structure theory). AFAIR Copernicium should also be liquid in room temperature for similar reasons, but since it is not very long lived and it is difficult to produce testing this will likely be very hard if not impossible to check (though if I remember correctly there was something called "relativistic maximum" which happens in the 6th and not 7th row of periodic table for some reason, so it should be higher than for mercury; though I can't remember the details why this is so).

Of course this is a bit simplified picture and there are surely more details regarding how exactly relativistic effects influence the energies and consequently how this influences the melting temperature of mercury (I suppose they are in the Calvo, Pahl, Wormit and Schwerdtfeger paper linked earlier in this thread), but I think the combination of the electron configuration and strong relativistic effects explain why other neighbors are not liquid.

What kind of emacs distribution is on the screenshot?

The 128 bit arithmetic part is really interesting. I wonder whether they used libquadmath and whether they needed to implement any extra funcitons beyond what’s available there.

In the process of “shut up and calculate” (SUAC) you often come upon much deeper insights about the involved processes and quantities than you ever could with wordy and “understandable” explanations. Of course simple, explainable models are great, but they have limited ability to describe the world, which is much more complicated. I don’t see how successfully handling this complexity (and getting the successful predictions) could take away from understanding.

It’s not like those SUAC disciplines don’t have simple explainable models. In my opinion It’s just that in order to describe phenomena really accurately or if the described phenomena are complicated enough the only way to get reliable and improvable predictions is via complicated SUAC-type calculations.

I don’t have full explanation of the connection that would be satisfying. However, I think it mainly comes down to symmetry group of the spinors and their 720 degrees symmetry. It is called plate trick for a reason after all: https://en.m.wikipedia.org/wiki/Plate_trick

I find Julia’s Pluto to be reasonably close alternative.

Of course it lacks many features, but plugins systems and overall architecture gives hope for possible extension to include many of the desired features.

This is of course very true but doesn’t take into account invention of computer that is relatively recent.

Since it in principle never makes mistakes (in practice there are of course bugs, but they are usually different in nature than human errors) it changes what is possible and most convenient. You no longer have to optimise for simplicity as heavily for example. On the other hand computers basically can’t deal with ambiguity, so the rules and statements have to be stated very simply and clearly.

I believe computers can change the landscape of what’s best notation. This is an interesting, interdisciplinary topic to explore.

Chess programming is fascinating but it seems for me that it has somewhat stalled in creativity in terms of classical (non DNN) engines. They all seem to use improved versions of min-max/alpha-beta. Which results in computer players that are extremely powerful but also quite dull. This is because they assume that the opponent will play perfect game and will do it at the full strength of the engine.

Basically there is no point playing against the engines at full strength as a human, since it will beat almost any human beyond grandmaster level. And that’s for weaker engines – the medium tier ones will regularly beat grandmasters and the top ones around the stockfish tier will probably not loose 1 game in 100 plays.

That considered I’ve wondered what’s possible dropping the assumptions about perfect play of the opponent. Some probabilistic models of opponent or different way of rating whole tree of moves in the context, instead of position only. For example considering the alternative moves and how difficult it would be to play perfect game for the opponent, it might be better to play combination with a lot of traps with possibility of loosing some position if the opponent plays perfectly. Current engines wouldn’t play such kind of move because they’d assume (via min-max/alpha-beta) that opponent will have perfect answer. Of course, if the opponent is an engine it will, but against humans it would make things much more interesting.

Wow, thanks! I had no idea it existed. I’ve searched for something like it not that long ago.

Mathpix is a great product that perfectly fills its niche and I’m very happy it exists.

I wish some open source alternative existed. Even much less accurate would be quite useful. I know latexify but it does only single symbols.

Maybe it will be implemented as an extra language in tesseract someday.

Yes! Those are exactly some of the alternative frameworks I had in mind. Also things like using differential algebra instead of classical epsilon-delta analysis and using Liouville's theorem to calculate integrals gives similar vibes.

Large parts of constructive mathematics seem to also be aligned well with physics and engineering (using only things that can be explicitly constructed) and hopefully could lead to interesting mathematical physics results. Same with, for example, quaternion analysis, which is very rarely used (contrarily to complex analysis), due to difficulties in operating quaternion valued functions, or computable analysis with its surprising result about differentiation of real an complex functions. I get similar feelings about non-classical logics. Somewhat more fringe examples that come to my mind, but are also interesting are for example non-Diophantine arithmetics or Holors theory (tensor generalisations).

Thanks for the "receding shoulders climbing problem" it’s a very nice way to frame the problem. I agree that there is a lot to be done to make shoulder-climbing process faster, easier and more widely available. It should also be possible, to make it more easy by for example storing not only results, but also derivations of many mathematical relations and computations. E.g. nowadays, there is no reason to put only results of integration in the integration tables, but whole derivations should be available as supplementary materials (preferably even in some form of symbolic computing code; this is somewhat realised with RUBI – rule based integration package). Size of the paper book is no longer the problem, so such “interactive derivations catalogues” should be extended to as many possible branches of mathematics, physics and engineering as possible.

I absoultely admire creativity and skills it takes to pursue developement of novel branch/framework of mathematics like this Super Calculus. I think that such original thinking at the fundamentals of mathematical formulations that underlying physical theories is required to overcome at least some difficulties modern physics struggles with. The problem is that it's nearly impossible to tell which one (even combination) is the right one.

The process to create one is so long and difficult, that there often isnt enough time to pursuit and find applications in which these novel mathematics coud prove to be superior over the existing ones. It creates a chicken and egg problem, where there are no arguments strong enough for the physics practicioners to switch these new formulations (as it takes a lot of practice and time with no guarantee of being any better than classical mathematics) and, on the other hand, the creators of these theories dont have enough time/audience/manpower/practice in practical calculations to go as far as where the problems of modern physics lie.

I've been thinking about this problem for some time and I think the right kind of design of the symbolic manipulation and calculation software could be of great help. The design of such software is certainly not an easy task, but hopefully somewhere along the road I, and hopefully others, will find some time and creativity to get started with it.

In Europe this is required in European grants, but also in many country specific funding agencies as well.

In 2018, 11 European research-funding organizations formed what is known as cOAlition S with the primary objective to ensure full, immediate, open access to all publications containing research data obtained in projects funded by its member agencies. The chief premises of cOAlition S were laid down in Plan S, which is scheduled for implementation in June 2020. So nowadays when someone wins grants from these agencies he’s required to publish his results in open access.

It’s not ideal, because many people reserve grant money for open access fees but AFAIK the policy also allows to publish behind paywall as long as you provide publicly available copy in repository (institutional or public like arxiv etc). In my opinion the second option is much better (as it saves money), but not all journals allow to put copy of the article in public repos (sometimes they require that the public version is either before editor’s revisions or puts some time embargo, like a year or 6 months, for publishing final version of the article).

How I wish papers in science and engineering were written in such format (or were created with org-mode source files with code which one could download and play with), where we could preview steps of derivations in some symbolic manipulation program, instead of "after simple transformation we get..."

Have you checked beorgapp?

I find that it supports surprisingly large parts of org mode.

I’m in similar situation. Didn’t upgrade from Mojave and like my system so far but wondering where to go from here. What competition would you recommend in terms of hardware+system?

The difference is, that there's very advanced mathematics behind string theory and at leas that part can be checked/verified by independent researchers.

But aren’t the shorts for like 140% of the GME stock? That means if everyone holds with prices, sooner or later the shorters will have to buy ALL that stock anyway at nearly any price to cover for the losses and give back shorted stock.

I also like pipe syntax and I've found there is nice support for it in Julia. There are some nice packages to improve it over base [1].

Have you checked queryverse [2]?

[1] https://github.com/jkrumbiegel/Chain.jl [2] https://www.queryverse.org

What kind of alternative to maths and models, that has predictive (preferably in quantitative way) power, would you propose?

Why wouldn’t it be pursued? Is string theory not pursued by “mainstream science” because (at least for now) it has less predictive power than standard model?

Sure it is valid, but in reality most scientists don’t religiously stick to Ockham’s razor and oppose alternative theories that give correct predictions.

If hard sticking to Ockham’s razor was true, Quantum loop Gravity, String Theory and many other theories wouldn’t be intensively studied for past 50 years. Or development and studying interpretations of quantum mechanics (which btw yielded results in Quantum Information Theory).

It’s just that constructing something correct and new IS really hard.

This text mainly shows that author either misunderstands chess, probability and science, likely at the same time, or just wants to critique for critique’s sake.

Of course while it’s good to search for alternative models/theories/explanations, unless you can provide something with better with more predictive power than the existing/widely accepted ones, it’s a good idea to hold the critique.

EDIT: To clarify: by less predictive power I mean that it neither explains new effects or predicts new unknown ones, nor explains known phenomena or generates existing theories as special examples. I didn’t mean theories such as for example string theory, that has little predictive power at the moment, but has current theories as special cases and holds the promise of explaining things that current theories cannot. /EDIT

Physicists are “stuck” with existing theories not because they like them, but because they work so well it’s hard to invent something that even works equally well (not to mention something that works better). There a lot of smart that are brave in thinking and propose wild explanations. Yet, in most cases they don’t stand up the test of time.

Einstein couldn’t deal with randomness of Quantum Mechanics, put forward a hidden variable theory and it was (and still is) seriously considered, but he (and many others) weren’t able to put forward better-working theory. We stick to QM despite its weirdness/randomness because it works extremely well, not because we like it or think things must be this way and require no further study/“it is the most efficient and parsimonious possible model“.

But on the other hand, if you knew you have a year to live would you save for retirement? Life is always a balance between now and the future

It is always a pleasure to watch/read about something that works very well it it’s domain. Nice that they put so much heart in optimising the rendering process.

If getting as many as possible and as big as possible grants is incentivised, that isn’t a surprise.

More permanent positions, longer funding (like for 10 years), funding good people, letting them do risky projects without penalising them for failures, and relying less on underpaid PhD students and postdocs would probably lead to more explorations. Nowadays , funding incentives are placed in such way, that incremental discoveries of known/expected things for largest possible amount of money are expected and praised.

Julia is kind of nice example of what’s possible with dynamic language and static types.