# The Periodic Table of the Elements

The familiar periodic table of the elements may be overwhelming in its usual initial presentation. You may not have noticed that there are four blocks of elements in the table, and they even have names! All good atomists need to become facile with the chemical elements though, because they are indeed the building blocks of the universe!

The table is usually presented as a partial grid, consisting of 7 rows and 18 (or 32) columns, although there are alternate representations. But columns (C) are called groups (G) and rows (R) are called periods (P)!

Within the grid, elements are arranged in four blocks, with the following properties:

• s-block: 2C x 7R = 14 (G1-2,18, P1-7) “sharp”
• p-block: 6C x 6R = 36 (G13-18, P2-7) “principal”
• d-block: 10C x 4R = 40 (G3-12, P4-7) “diffuse”
• f-block: 14C x 2R = 28 (between G2 and G3, P6-7) “fundamental”

Note how columns (groups) increase (by four!) as rows (periods) decrease! Blocks are named after electron orbitals which are also named s, p, d, and f.

Thus there are currently 118 elements having a unique “atomic number” in the usual periodic table, with the rows or periods having the following number of elements:

• P1: 2 (2s)
• P2: 8 (2s, 6p)
• P3: 8 (2s, 6p)
• P4: 18 (2s, 6p, 10d)
• P5: 18 (2s, 6p, 10d)
• P6: 32 (2s, 6p, 10d, 14f)
• P7: 32 (2s, 6p, 10d, 14f)

Note the number of groups increases as the period does. This is due to the properties of electrons and their shells. Familiar elements are scattered throughout the table, although they occur less and less as the atomic number increases. Elements can also occur as different isotopes due to having a differing number of electrons than usual, and so may have a positive or negative charge.

As an homage to the classical four elements, I’ve arranged the blocks as follows: the s-block has the reactive alkali and alkaline metals (fire), the p-block includes the noble gases (plus C, N, and O needed for life as we know it) (air), the d-block has the precious metals like gold, silver, and platinum (plus liquid at room temp mercury but not bromine) (water), and the f-block with the heaviest and often radioactive elements like uranium and plutonium (earth).

https://en.wikipedia.org/wiki/Periodic_table

https://en.wikipedia.org/wiki/Block_(periodic_table)#s-block

https://en.wikipedia.org/wiki/Block_(periodic_table)#p-block

https://en.wikipedia.org/wiki/Block_(periodic_table)#d-block

https://en.wikipedia.org/wiki/Block_(periodic_table)#f-block

https://en.wikipedia.org/wiki/Periodic_table_(electron_configurations)

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# Maxwell Relations

Maxwell Relations are commonly known as a set of four partial differential equations between four thermodynamic quantities or potentials: pressure (P), volume (V), temperature (T), and entropy (S). So for example the expression (∂T/∂V) |S  means the partial derivative of T with respect to V while keeping S constant.

• (∂T/∂V) |S = -(∂P/∂S) |V
• (∂P/∂T) |V = (∂S/∂V) |T
• -(∂S/∂P) |T = (∂V/∂T) |P
• (∂V/∂S) |P = (∂T/∂P) |S

In my diagram above, the expressions that are equal are on either side of the common leg of adjacent isosceles right triangles.

https://en.wikipedia.org/wiki/Maxwell_relations

https://johncarlosbaez.wordpress.com/2021/09/17/maxwells-relations-part-1/

https://johncarlosbaez.wordpress.com/2021/09/18/maxwells-relations-part-two/

https://johncarlosbaez.wordpress.com/2021/09/22/maxwells-relations-part-3/

https://en.wikipedia.org/wiki/Thermodynamic_potential

Thermodynamics and the Four Thermodynamic Potentials

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# On the Death of a Giant

Renowned physicist Steven Weinberg passed away recently. He was a giant in the world of physics and winner of the Nobel prize, advancing knowledge about the Standard Model and the unification of physical forces. He was also, famously, a materialist and atheist.

In his book “The Sophist”, Plato wrote (metaphorically?) about the battle of the gods and the giants. He related how the gods were friends of Platonic forms (perhaps being close to forms themselves) whereas the giants were materialists. Plato, being partial to forms, painted the giants as militant and unreasonable materialists, and the gods as a friendly and peaceful sort.

The Greek gods were friendly and peaceful? Perhaps the giants of the legend were the easy-going and reasonable sort, since the gods of the Greeks seemed the opposite. They say that history is rewritten by the victors.

https://en.wikipedia.org/wiki/Steven_Weinberg

With Steven Weinberg’s death, physics loses a titan

https://www.scientificamerican.com/article/learning-to-live-in-steven-weinbergs-pointless-universe/

https://www.washingtonpost.com/local/obituaries/steven-weinberg-nobel-winning-physicist-who-united-principal-forces-of-nature-dies-at-88/2021/07/26/75d8d24a-ee31-11eb-bf80-e3877d9c5f06_story.html

A very nice article:

Steven Weinberg (1933-2021): a personal view

http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0172%3Atext%3DSoph.%3Apage%3D246

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# The Wolfram Physics Project

When I first started looking at Stephen Wolfram’s latest proposal to solve physics, I was somewhat disappointed. I was rather fond of his previous “New Kind of Science” based on the structural rigidity of cellular automata. However, I am now intrigued by his latest ideas, based on the looser but more flexible basis of networks.

And once you have pithy statements with space, time, energy, and matter (as momenta), you catch my attention:

• Energy is flux of causal edges
• through Spacelike hypersurfaces
• Momentum is flux of causal edges
• through Timelike hypersurfaces

I confess I haven’t read much about the project yet, but it seems to be using rewriting rules, perhaps similar to the notion of rewriting in Wolfram’s previous framework, cellular automata. Of course, cellular automata and also rewriting rule systems can be computationally universal or Turing complete.

Another idea might be to try some sort of computational metaphysics between nodes like the pi-calculus (or some other process calculus). After all, you have to support quantum entanglement! However if you can encode everything with simpler structures then do it!

https://www.wolframphysics.org/

https://www.wired.com/story/stephen-wolfram-invites-you-to-solve-physics/

https://writings.stephenwolfram.com/2020/04/how-we-got-here-the-backstory-of-the-wolfram-physics-project/

https://en.wikipedia.org/wiki/Digital_physics

https://www.scientificamerican.com/article/physicists-criticize-stephen-wolframs-theory-of-everything/

https://turingchurch.net/computational-irreducibility-in-wolframs-digital-physics-and-free-will-e413e496eb0a

View at Medium.com

Cellular automata:

https://en.wikipedia.org/wiki/Cellular_automaton

Note this quote for future reference:

The primary classifications of cellular automata, as outlined by Wolfram, are numbered one to four. They are, in order, automata in which patterns generally stabilize into homogeneity, automata in which patterns evolve into mostly stable or oscillating structures, automata in which patterns evolve in a seemingly chaotic fashion, and automata in which patterns become extremely complex and may last for a long time, with stable local structures. This last class are thought to be computationally universal, or capable of simulating a Turing machine.

Rewriting:

https://en.wikipedia.org/wiki/Rewriting

https://en.wikipedia.org/wiki/Semi-Thue_system

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“The new experiment shows that, in a quantum world, two people can end up disagreeing about a seemingly irrefutable result, such as the outcome of a coin toss, suggesting something is amiss with the assumptions we make about quantum reality.”

— From the Quanta article by Anil Ananthaswamy

As above, so below.

As we face the deadly onslaught of electron-microscopy-sized agents, remember to wash your hands for twenty seconds, follow physical distancing rules of six feet or more, and please be safe.

https://algassert.com/post/1904

https://arxiv.org/abs/2002.01456

https://www.scientificamerican.com/article/reimagining-of-schroedingers-cat-breaks-quantum-mechanics-mdash-and-stumps-physicists1/

https://en.wikipedia.org/wiki/Wigner%27s_friend

https://equivalentexchange.blog/2013/01/11/schrodingers-cat/

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# What is Turbulence?

In his science-fictional “Foundation Trilogy”, Isaac Asimov famously hypothesized a future science called “psychohistory”, a mathematically grounded theory of generalized and predictive human action, based on an amalgamation of psychology, history, and sociology. The future galactic empire was managed by this theory and practice (look out – almost seventy year old spoilers!) except for an exceptional character that was not anticipated and essentially unpredicable.

Asimov had in mind well validated continuous and statistical theories of physics, for example for idealized gases and their laws. I was stuck by an image for an explanation of turbulence that highlighted key elements of velocity, density, pressure, and viscosity, and how it was (in my mind) analogical to antagonistic individuals, dominating leaders, submissive society, and affiliated coteries. Of course, an article below states that turbulence is still too complicated to provably model correctly at this point in time.

I had no idea that psychohistory was claimed to be an actual field of study these days, albeit being somewhat controversial in its authenticity. And it doesn’t seem to have any mathematical basis yet, as far as I know. Mathematician Dan Crisan gave an inaugural talk a few years ago that was hypothesizing using heat equations instead of fluid dynamics as a basis. Even so, we can’t seem to properly model any sort of social action so how could psychohistory be within our grasp?

In these turbulent times perhaps we should make an effort to understand ourselves a bit better, as we hope to navigate between the Charybdisian whirlpool of civil discord and environmental collapse and the Scyllaian rocks of fascism, authoritarianism, and / or totalitarianism. But hey, isn’t Apple doing an Apple TV+ series based on Asimov’s books? Let’s all tune in!

https://en.wikipedia.org/wiki/Psychohistory_(fictional)

https://en.wikipedia.org/wiki/Psychohistory

https://en.wikipedia.org/wiki/Foundation_(TV_series)

https://www.quantamagazine.org/why-turbulence-is-a-hard-physics-problem-20190128/

https://www.quantamagazine.org/videos/what-is-turbulence/

https://en.wikipedia.org/wiki/Navier–Stokes_equations

Philip Ball / Critical Mass : How One Thing Leads to Another (2004)

Concerning Professor Dan Crisan:

Click to access talkinaugural230113.pdf

And also this quite long but interesting essay:

Prolegomena to Any Dark-Age Psychohistory

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# The Free Will Theorem

The Free Will Theorem of Conway and Kochen is an interesting argument that tries to suggest free will goes “all the way down”. If experimenters can make their choices freely on how to measure certain experiments then the elementary particles being measured can make “free choices” as well. But the contrapositive of this result seems more interesting to me: if some elementary particles are not free, then the experimenters aren’t either!

I’ve cheated some here because it is really based on three axioms or assumptions, and not four. All for the sake of science (and philosophy)!

• Fin : Information transmission has a maximal (finite) speed, and obtains from causality
• Twin : For two elementary particles, it is possible to quantum “entangle” them, separate them significantly, and measure the square of their spin in parallel directions (but “full entanglement” is not required)
• Spin : For certain elementary particles of spin one (the vector or gauge bosons: gluons, photons, Z and W), the squared spin component (taken in three orthogonal directions) will be a permutation of (1,1,0)
• Min : Instead of Fin, the weaker assumption Min states that the spin measurers need only be “space-like” separated and make choices independently of each other
• Lin : Instead of Fin or Min, Lin is an even weaker assumption that rests on experimentally testable “Lorentz Covariance”

If nothing else, trying to understand this theorem teaches you a bit about elementary particles and quantum physics!

https://en.wikipedia.org/wiki/Free_will_theorem

https://plus.maths.org/content/john-conway-discovering-free-will-part-i

https://arxiv.org/abs/quant-ph/0604079

Click to access rtx090200226p.pdf

https://www.informationphilosopher.com/freedom/free_will_theorem.html

https://en.wikipedia.org/wiki/Gauge_boson

https://en.wikipedia.org/wiki/Lorentz_covariance

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# Combogenesis: a constructive, emergent cosmos

I just finished reading Tyler Volk’s “Quarks to Culture: how we came to be”. In this book Volk outlines an interesting model for what he calls combo-genesis, a “great chain of being” leading from basic physical law up through the highest organizational structures that we know of, human societies. He traces a path through human knowledge: physics, chemistry, biology, zoology, sociology, etc., and I am reminded of E. O. Wilson’s “Consilience: the unity of knowledge” that argued for some of the same things.

But Volk’s work has some good new ideas. He details twelve hierarchical levels, where each level is constructed on a “lower” previous level, and the new “higher” level has new things and different abilities than its predecessor. These levels range from the level of fundamental quanta (the quarks of the title), to geo-political states (the culture of the title).

• QUA: fundamental quanta
• PRO: nucleons, which are protons and neutrons
• NCL: atomic nuclei
• ATM: atoms
• MOL: molecules
• PCL: prokaryotic cells
• ECL: eukaryotic cells
• ANI: multicellular organisms, including animals
• ASG: animal social groups
• HUM: human tribal meta-groups
• AGR: agro-villages
• STA: geo-political states

These levels are within three dynamical realms, the first realm being of physical laws and then those realms of biological and cultural evolution. Each of these realms has a base level that has a capability for great constructive and emergent potential via an “Alpha-kit”. An alpha-kit has two facets, an element set and a cornucopia set, that operate like an alphabet and the myriad combinations that that alphabet can produce.

Dynamical realms:

• Realm of physical laws: QUA -> MOL
• Realm of biological evolution PCL -> ASG
• Realm of cultural evolution HUM -> STA

Base levels and their Alpha-kits:

• QUA, means for chemistry and molecules (atomic)
• PCL, mechanisms for biology and its evolution (genetic)
• HUM, faculty for culture and its evolution (linguistic)

As Volk’s model has each higher level based on or constructed from the previous lower one, I make the following suggestion utilizing my four-fold Structure-Function. The structures of each lower level serve as the parts of the next higher level, and the functions of each lower level serve as the actions of the next higher level. In this way a chain of actions and parts, structures and functions are built giving different entities and capabilities to different operational domains.

In the diagram shown, the sets of structures (S) and functions (F) of level i are used for the sets of parts (P) and actions (A) of level i+1, so S(i)=>P(i+1) and F(i)=>A(i+1). Not all structural information or functional abilities are necessarily accessible in the higher level of parts and actions, similar to the information and method hiding in object-oriented programming, and so reducing overall complexity. And as I have argued before, parts are combined to create the structures and actions are combined to create the functions of each level, so P(i+1)=>S(i+1) and A(i+1)=>F(i+1). In this way we have a bottom-up combo-genesis leading from quarks to culture.

Are we now entering another dynamical realm, perhaps based on some technological or computational alpha-kit? But, unfortunately we have to ask, will it take us forwards or backwards?

Tyler Volk / Quarks to Culture: how we came to be

https://en.wikipedia.org/wiki/Tyler_Volk

https://blogs.scientificamerican.com/cross-check/how-quarks-turned-into-cultures/

http://www.integralworld.net/smith56.html

http://www.integralworld.net/visser114.html

https://inquisitivebiologist.wordpress.com/2019/03/06/book-review-quarks-to-culture-how-we-came-to-be/

Tyler Volk and Robert Wright discuss:

mol-2017-09-28-wright-volk

Edward O. Wilson / Consilience: the unity of knowledge

https://en.wikipedia.org/wiki/Consilience_(book)

https://en.wikipedia.org/wiki/Consilience

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# Noether-Pauli-Jung, V2

What happens when the fourfold of Noether’s Theorem is spliced together with the fourfold of Pauli-Jung? Both have Space-Time and Matter-Energy. The former has Conservation and Symmetry, and the latter has Causality and Synchronicity. And if Space-Time and Matter-Energy are both divided into Space and Time and Matter and Energy, one obtains this eight-fold.

Causality means that some action or cause in time (say a process) of things in space can have an effect (another process, say) on different things in space, and Synchronicity means that different events (say processes) separated in space can have non-causal relationships between them.  Conservation means the consistency of a quantity of matter or energy or matter-energy through time, and Symmetry means the consistency of a measure of a structure or form through space.

I am reminded of my fourfold Four Bindings, consisting of Chains, Grids, Blocks, and Cycles. Causality and Synchronicity are Chains (or non-chains for the latter) Space and Time are Grids (or flexible meshes), Matter and Energy are Blocks (or chunks of stuff), and Symmetry or Conservation are Cycles (of the group-theoretic kind or the equivalence class kind or just loops).

https://en.wikipedia.org/wiki/Causality

https://en.wikipedia.org/wiki/Synchronicity

https://en.wikipedia.org/wiki/Symmetry

https://equivalentexchange.wordpress.com/2012/05/04/noethers-theorem/

https://equivalentexchange.wordpress.com/2018/01/23/atom-and-archetype/

https://equivalentexchange.blog/2016/04/06/four-bindings/

This is a reworking of a previous six-fold diagram that I believe is served better as an eight-fold.

https://equivalentexchange.blog/2018/03/29/noether-pauli-jung/

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