Category Archives: Science

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.

Further Reading:

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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Linear Process Algebra

One of computer scientist and Professor Emeritus Vaughan Pratt’s most recent conference papers is on “linear process algebra,” which relates several of his previous interests on linear logic, Chu spaces, concurrent processes, events and states, etc.

The paper opens with a nice overview of computer science research primarily concerned with concurrent processes. Computation itself divides into the aspects of logical and algorithmic, formal methods into the logical and algebraic, concurrent computation into operational and denotational, and then the author gives a brief list of models of processes by a variety of mathematical structures until he comes to his theme of using Chu spaces.

As an example, he presents processes as Chu spaces over the set K, where K = { 0, T, 1, X}, with names and meanings :

  • 0: Ready
  • T: Transition
  • 1: Done
  • X: Cancelled

and then details four binary operations as working in Chu spaces over K:

  • P ; Q: Sequence
  • P + Q: Choice
  • P || Q: Concurrence
  • P ⊗ Q: Orthocurrence

Further Reading:

Vaughan Pratt / Linear Process Algebra

Click to access bhub.pdf

Click to access lpa.pdf

Click to access bud.pdf

https://www.researchgate.net/publication/2663060_Chu_Spaces_A_Model_Of_Concurrency

https://www.researchgate.net/publication/222310260_Types_as_Processes_via_Chu_spaces

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

https://dblp.org/pid/p/VRPratt.html

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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.

Further Reading:

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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Our Demarcation Problem

I have a foreboding of an America in my children’s or grandchildren’s time — when the United States is a service and information economy; when nearly all the manufacturing industries have slipped away to other countries; when awesome technological powers are in the hands of a very few, and no one representing the public interest can even grasp the issues; when the people have lost the ability to set their own agendas or knowledgeably question those in authority; when, clutching our crystals and nervously consulting our horoscopes, our critical faculties in decline, unable to distinguish between what feels good and what’s true, we slide, almost without noticing, back into superstition and darkness.

— Carl Sagan from The Demon-haunted World

As science is confused with pseudo-science, as real news is conflated with fake, we need much better ways to judge the truth of the information we require to be good citizens. Unfortunately, in this age of nontraditional television networks, kitchen-sink cable, and internet news sources, our information sources can be subverted by entities that wish to bend our mindset to their agenda, rather than giving us measured and reasonable knowledge. When these entities wish to fracture and divide our polity, our social fabric strains and unravels.

Here are four (or five minus one) distinctions for information or knowledge claims, based upon their type of warrant, or context of truthfulness. Three of them are modalities from Kant’s doctrine of judgments, and I suggest that Dialectic could reasonably be added to them, but I do not know if they form a complete set or not. I would suppose they can be ordered by their level of assurance, from low to high. Another more scientific option might be Probablistic instead of Dialectic, based upon measurements or even theoretical arguments. Certainly there must be something between a bald assertion or the questionable and the certain.

  • Assertoric: assert to be true or false without (inherent) proof
  • Problematic: assert as possibly true (or false)
  • Dialectic: philosophically reasoned as true or false (qualified?)
  • Probabilistic: quantified or theoretically argued as mostly true or false
  • Apodictic: clearly provable as true (or false) or logically certain

From Wikipedia:

Apodictic propositions contrast with assertoric propositions, which merely assert that something is (or is not) true, and with problematic propositions, which assert only the possibility of something being true. Apodictic judgments are clearly provable or logically certain. For instance, “Two plus two equals four” is apodictic. “Chicago is larger than Omaha” is assertoric. “A corporation could be wealthier than a country” is problematic. In Aristotelian logic, “apodictic” is opposed to “dialectic,” as scientific proof is opposed to philosophical reasoning.

For example, the president’s language (“many say”, “everyone knows”, “we’ll see”) is full of assertoric and problematic claims (to be extremely generous), and perhaps that’s the limit of his ability. I don’t think he could manage part of a measured dialectical argument if pressed, and if he manages an apodictic statement it would be like a clock that tells the time correctly twice a day. To have the head of the executive branch of our government to be so untrustworthy in providing information and knowledge hurts us all, and misleads those that takes his words at face value.

And then there are the news sources that cater to the president and his followers. Perhaps they present some warranted information, but mix plenty of misleading punditry in to tickle the fancy of unquestioning minds. As a result we have citizens who only digest information from sources that appeal to their sensibilities. Some of these news sources disseminate their fabrications via a flood in social media and the internet, because our ability to stifle them is almost nonexistent. And when these news sources originate from foreign countries wanting to influence us for their own purposes, how is it that they are allowed to continue?

In truth, people can be misled on scientific topics like the coronavirus and COVID-19, vaccinations, face masks, climate change or global warming, environmentalism and pollution, pseudoscience, and political topics like mail-in voting, Russian meddling with the 2016 and 2020 elections, conspiracy theories such as QAnon, etc. The lists seem almost endless.

Further Reading:

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

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

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

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

https://plato.stanford.edu/entries/aristotle-logic/

https://plato.stanford.edu/entries/kant-judgment/

Immanuel Kant: Logic

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

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

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

https://en.wikipedia.org/wiki/Russian_interference_in_the_2016_United_States_elections

https://en.wikipedia.org/wiki/Russian_interference_in_the_2020_United_States_elections

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

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The Logic of Universalization Guides Moral Judgment

From the abstract:

To explain why an action is wrong, we sometimes say, “What if everybody did that?” In other words, even if a single person’s behavior is harmless, that behavior may be wrong if it would be harmful once universalized. We formalize the process of universalization in a computational model, test its quantitative predictions in studies of human moral judgment, and distinguish it from alternative models. We show that adults spontaneously make moral judgments consistent with the logic of universalization, and report comparable patterns of judgment in children. We conclude that, alongside other well-characterized mechanisms of moral judgment, such as outcome-based and rule-based thinking, the logic of universalizing holds an important place in our moral minds.

  • Universalization: What if everyone did this?
  • Rule-based: An implicit or explicit rule says I may not do this.
  • Norm-based: I shouldn’t do this because many say not to.
  • Outcome-based: How would it be bad if I did this?

Further Reading:

Sydney Levine, Max Kleiman-Weiner, Laura Schulz, Joshua Tenenbaum, and Fiery Cushman / The logic of universalization guides moral judgment

PNAS first published October 2, 2020; https://doi.org/10.1073/pnas.2014505117

https://www.pnas.org/content/early/2020/10/01/2014505117

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Charles Fourier and the Theory of Four Movements

Nothing is too wonderful to be true if it be consistent with the laws of nature.

— Michael Faraday in his Laboratory Notebook

There are many things to scratch one’s head about in Charles Fourier’s “Theory of the Four Movements,” first published anonymously in 1808. However, his progressive political thought influenced many in France and in the United States. Fourier was a utopian and a socialist, and thought social cooperation and unity were the only ways to overcome the discord and strife he observed in his times. His theory is based on a hierarchy of “movements” within four realms, from low to high: the Material, the Organic, the Animal, and the Social.

As he elaborated on these movements, Fourier claimed that social history went through four main periods of unhappiness and happiness, ascending from a chaotic period, through two harmonious periods which were each seven times longer, before descending into another chaotic period of length equal to the first. In order to achieve this happiness, he thought that we must envision and engineer a new social order to achieve a common purpose. Nowadays, of course, socialism has a noxious connotation to those of the right-leaning and hyper-capitalist persuasion.

  • Ascending Chaos
  • Ascending Harmony
  • Descending Harmony
  • Descending Chaos

And now, the United States teeters on the brink of choosing four more years of terrible leadership, all to maintain the status-quo of funneling more money into the pockets of the wealthy and more power into the hands of the already dominant.

Further Reading:

Charles Fourier / The Theory of Four Movements

https://libcom.org/library/charles-fourier-theory-four-movements

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

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

https://publicdomainreview.org/essay/get-thee-to-a-phalanstery-or-how-fourier-can-still-teach-us-to-make-lemonade/

https://quadriformisratio.wordpress.com/2013/07/01/886/

https://quadralectics.wordpress.com/4-representation/4-1-form/4-1-4-cities-in-the-mind/4-1-4-2-the-future-city/

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Humankind, Unbound

Many books detail how we are our own worst enemy, how we are too smart for our own good, or not smart enough in the right way. This one traces the origin and evolution of eight technologies that make us who we are today, for better or worse.

  • Fire
  • Tools (incl. Digging tools, Weapons)
  • Language (incl. Writing, Music, Art, Symbolic Communication, Ethnicity, Culture)
  • Clothing
  • Shelter
  • Farming (Agriculture, Husbandry)
  • Machines (incl. Ships, the Wheel, and on to Precision Machinery)
  • Computers

Instead of having two technologies, “Clothing” and “Shelter,” Currier combines them, and lists “technologies of interaction” which includes writing, water-craft, the wheel, etc.

Can we overcome the myriad conflicts that threaten our survival? Please check back in a hundred years to see how we’re doing! It’s not very long, compared to how far we’ve come.

Further Reading:

Richard L. Currier / Unbound: how eight technologies made us human, transformed society, and brought the world to the brink

Some reviews:

https://www.tandfonline.com/doi/full/10.1080/25729861.2019.1596211

Book Summary: “Unbound: How Eight Technologies Made Us Human” by Richard L. Currier

Click to access Volume8-Number1-Article7.pdf

Also:

https://equivalentexchange.blog/2016/12/05/the-anatomy-of-technology/

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Classes of Automata

Here is one way to carve up abstract (mathematical) automata into different classes of complexity (from low to high).

There is a somewhat different and older one that is based on the Chomsky Hierarchy (where ND stands for non-deterministic), and the associated language or grammar that they recognize:

Further Reading:

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

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

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Flowing and Falling

Some philosophers say everything is process. From the cosmic scale of the universe to the submicroscopic scale of atoms, physical forces marshal matters and energies to and fro. In between these at the human scale, biology is ruled by flows of energy from the sun and nutrients from the environment as well as from other living beings. Dynamical forces such as temperature, weather and tides also affect biology and even the cultural processes of higher lifeforms.

At the scale of the solar system, gravity collects gases to ignite stars and form planets. Once stars reach their limits to burn, gravity can collapse them to dense cinders and black holes or even to rebound and spread their atomic matters in novas and supernovas. Even light spread by the stars can be gathered together into gravity wells such as black holes. Stars in turn are gathered into galaxies by the gravity of black holes and even unknown dark matters.

At the scale of atoms and molecules, temperature differentials and water can partition certain types of elementary constituents to form membranes and segregate insides from outsides. If an inside is protected sufficiently, then there is time and the conditions to harbor and perpetuate the delicate structures and processes that form cells. Cells can even gather together and continue as multicellular communities, or only temporarily to fruit and disperse again as simple creatures known as slime molds.

At the individual human or societal scale, there are flows for nutrients and excreta, materials for habitation and the manufacture of tools, distributed energies such as electricity, fossil fuels, and information for learning, work, and civic participation. Even speech and writing can be thought as flows of information. But just as flows of nutrients and materials and energies can prove toxic to biological health or ecologies, so can information.

For two-dimensional dynamical systems, certain common elements can be mapped out: sources and sinks, saddles and centers. Sources have flows out from a point or region, and sinks have flows in. Saddles have a roughly stationary center, due to balanced flows in and out at (not necessarily) right angles. Centers are circular vortexes about a stationary point or region. Sources and sinks can spiral, saddles can twist, centers can become eccentric or elliptical.

For example, think about everyday weather forecasts. The atmosphere is relatively thin compared to the earth and so the flows of air can be considered two-dimensional, at least at the ordinary strata of human habitation. There are air pressure highs and lows (sources and sinks), and air temperature cold and warm fronts (usually not saddles though), stationary fronts (centers?), and even circulations (hurricanes are spiraling sinks I guess).

Ordinary, human-sized change has conditioned many of our intuitions and insights about the way the universe works. Heraclitus famously said that all was change, and so he thought fire was the primal element. His predecessor Thales thought that water was instead the basic element, and it is pretty mutable also. Lucretius, inspired by Empedocles, thought none of the four classical elements were foundational, but all were composed of tiny bits that fell and bounced against each other through an endless void.

As earth is in opposition to air, and fire to water, the seasonal changes of temperature and moisture were considered by Hippocrates. Heat gains dominion over cold in Spring and Summer, but cold replaces it in Fall and Winter. Similarly wet and dry quarters cycle through the seasons. These oppositions gave rise to the theory of the four temperaments or humourism. Even to this day these considerations have inspired various theories of personality, like the Myers-Briggs Assessment.

Is everything a struggle of opposites? Empedocles, already mentioned, thought love and strife were the relations that respectively attracted and repelled all matter in their dance and change. Now we know that things fall towards the earth, not for the love of it, but because of the shape of space that the earth’s mass makes. Heat flows into the cold because both even up. Order dissolves into chaos since the latter is more likely, unless fed by other sources of order turning to disorder.

Is everything a flow between opposites? Light spreads out and diminishes into darkness, but gravity gathers matter together. Enough gravity can even gather light and bind it into the darkness of a black hole. A drop of ink spreads out in a glass of water, never to return to that inky state, unless the glass sits and the water evaporates until only a drop remains. Even epidemics and pandemics can be thought to be flows of transmission and contagion. Here, the small becomes the large, and the few the many.

Further Reading:

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

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

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

Also note that these four classifications are somewhat analogous to four valued logic: True is Source, False is Sink, None is Center, Both is Saddle.

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Conditional Branching is Not Necessary

Four simple instructions are sufficient to evaluate any Turing computable function using self-modifying programs: LOAD, STORE, GOTO, INCREment.

Further Reading:

Raul Rojas / Conditional Branching is Not Necessary for Universal Computation in von Neuman Computers, Journal of Universal Computer Science 2,11 (1996) 756-768

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.101.757&rep=rep1&type=pdf

William F. Gilreath, Phillip A. Laplante / Computer Architecture: A Minimalist Perspective

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