This is a Wikipedia
user page. This is not an encyclopedia article or the talk page for an encyclopedia article. If you find this page on any site other than Wikipedia, you are viewing a mirror site. Be aware that the page may be outdated and that the user whom this page is about may have no personal affiliation with any site other than Wikipedia. The original page is located at https://en.wikipedia.org/wiki/User:Thermochap. |
I'm relatively new here, and not yet quite sure what to do with a user page. For the most part so far I've found the mechanics of interaction fairly self-explanatory, and the community by and large welcoming. I am particularly excited about the educational potential of Wikipedia. Thermochap ( talk) 14:44, 21 January 2008 (UTC)
Perhaps I should note here that author contributions to Wikipedia are, by default, protected by the GNU Free Documentation License discussed in more detail here.
an you imagine living with a ton of air sitting on you, |
...to which I've contributed might include some of the entries in this table...
...and what else? Thermochap ( talk) 10:36, 25 October 2013 (UTC)
My academic home is in physics & astronomy, although I'm an applied mathematician at heart. The label thermochap is a contraction of "thermo chapters", which in modern introductory-physics books (except e.g. for Tom Moore's text [1]) still introduce entropy (and hence the pivotal role of accesible-state uncertainty) last even though the "entropy-first" approach took over senior undergrad thermal-physics texts nearly 50 years ago and (by virtue of its connection to information theory and Bayesian inference) makes the strengths and limits of relationships like the ideal gas law, equipartition and mass-action clear from the start.
With help from regional employers & facilities for nanocharacterization I've thankfully encountered chances to explore nature on varied scales of space and time. Applications include mathematical nano-microscopy tool development, laboratory study of circumstellar dust, high temperature materials for electronic or aerospace applications, and Bayesian informatic studies of data analysis, complex systems, & algorithmic simplicity.
Key developments include:
Topic | Web Sites | Tools For Interaction | Papers |
---|---|---|---|
Labs at Home | Matt's Physics@Home |
Don't Just Look: Measure! Picture The Sound! NanoExploration w/Electrons |
A Fast Track Simulation Openworld Experiment Draft |
Model Selection & Net Surprisal |
Bayesian Model Selection | Phil Gregory's book voicethread |
Metric/Entropy-1st Surprises Avogadro\Boltzmann Constants |
Metric-First motion | Traveler Point Site |
Introducing Newton voicethread Metric relativity voicethread |
One Map Two Clocks One Class Period Draft |
Evolving Complexity | Correlation-1st Informatics |
Quantifying Risk Sampler Fraction Infectious voicethread |
Heat Capacity in Bits Units for Coldness Thermal Roots |
Task-layer Multiplicity |
Old Google Site Ellie's Video Contest Page New Google Site |
Attention-Slice Sampler Augmented Like Button |
1989 MSL-8857 Simplex Model Community Health |
A few of our "small project" (and possible talk) topics highlighting "one-new-fact" might include traveler point dynamics, task layer multiplicity, moon baseball, single-slice electron optics, dimensionless units in cycles/radians & mole/molecule, coldness in GB/nJ, concept-selection, organism-centricity, correlation-based complexity, carbon rain & Milky Way nannites, total-sound videography, and what else? Thermochap ( talk) 20:51, 24 December 2021 (UTC)
For instance, the "new fact" for:
and what else? pFraundorf ( talk) 12:48, 20 December 2021 (UTC)
Specialized areas of interest impacted in our carbon-rain project, on the other hand, are broader and include:
See more on this project below.
A key to dialog is to begin from where your target audience is at. This is important with editors, with specialist peers, and also with the general public. Observations and/or simple true assertions, on the contrary, won't work by themselves particularly if they are unexpected. The reaction in that case tends instead to be "likely story" and then move on.
Messages to try introducing in this context might include e.g.:
and what else?
we like to tell stories of how humans invented our world, let's momentarily imagine that human community is a natural phenomenon that (like microbial and multi-celled life in general) has self-assembled on earth's surface. Like all forms of layered complexity, it is: (a) constructed from a hierarchy of broken symmetries with respect to gradients, boundaries, or pool edges, and (b) expanded/maintained by flows of thermodynamic availability (e.g. available work and/or correlation information) e.g. from processes running lower in the hierarchy. The substrate for human community of course includes our galaxy arm, our star, our planet's surface, living cells and cell communities on the wide range of size scales that serve up the environment in which our ancestors (and ourselves) have emerged.
Within human communities (and metazoan ecosystems in general) we also find a layered hierachy that involves subsystem correlations which look inward and outward from the metazoan skin, given that then inward and outward from family e.g. the edges of our gene and amino acid (molecular) code pools, and further given that then inward and outward from the boundary of culture e.g. the edges of our language and idea pools. We might therefore, at its simplest, model any single-species metazoan community in terms of the fraction of its attention directed toward maintaining these six layers of organizational structure, i.e. in buffering subsystem-correlations that look inward and outward from the boundaries of skin, family, and culture. There is nothing fundamental about this, except that it for simplicity puts these disparate layers of organization on an equal footing.
Modern astronomy as well as paleontology now show us that, just as these amazing things can emerge on the surface of a planet, so the conditions that allow them to remain or even thrive are fragile, and likely to eventually end either gradually or abruptly. Therefore models of the decline as well as the bloom of complexity in metazoan communities are probably worth exploring.
There is a great deal of literature about individual and even "public" health in communities. However the focus tends to be on the individual perspective, e.g. on mental and physical health of the individuals within the community. To address well-being at the community level, it might be interesting to use the simple community-level model of task layer multiplicity (TLM) above to examine the fraction of effort in any given community directed toward those six layers: self-health, pair interactions, family, community, culture, and extra-cultural knowledge [7] [9]. Perhaps we will thereby gain some insight into guiding social policy as weil as our own behavior as we attempt to make the most of our blessings. Along the way, we may encounter some surprises that our focus on individual perspectives has helped us to miss!
Do we next need to discuss the importance of the 6 different "broken-symmetry" layers of organization in multi-celled lifeform communities, namely layers that look in (←|) and out (|→) from the boundaries of metazoan-skin (←1|2→), gene-pool (←3|4→) and idea-pool (←5|6→)?
Another sobering aspect of this story that might grab some attention is precisely how one might expect complexity's decline to unfold, namely in loss of the distinction between these 6 layers. For instance, the higher numbered (and later developed) ones may (at least in the long run) lose steam first.
If you are serious about any particular problem, ranging from how to fix a dripping faucet or a broken electrical circuit to making gerrymanders constructive, minimizing abortions, or reducing gun deaths, consider adopting a scout (versus soldier) mindset and embark on the cycle: Observe → selectModel → predictOptions → Implement → Observe....
This "V↔S" cycle (vary then select then vary etc.) is not only how (for example) science works (although it often also gets bogged down in doctrine), but also how life on earth has always worked. In other words it's part of perhaps our oldest constitution, namely that on the basis of which life itself continues to adapt and survive.
was long thought that diamond could only be produced under conditions of high pressure and temperature. We now know that metastable diamond can be grown at low pressure and temperature by chemical vapor deposition, perhaps because diamond is the stable phase for nanoscale carbon at low temperature and pressure.
In the same way, liquid carbon is thought to only exist at high temperature and high pressure, although low-pressure stability below the sublimation temperature on the nanoscale has also been predicted [18]. We report now observations in both nature, and in the laboratory, which suggest that metastable liquid condenses at low pressure from carbon vapor perhaps because nanoscale liquid is stable at low pressure, and hence able to grow metastably from the vapor in containerless settings to temperatures well below the melting point as do metallic liquids in general [19].
Moreover, when this low-pressure liquid is cooled slowly it appears to result in an unlayered graphene composite that may have diffusion barrier properties otherwise unrivaled in nature. Synthesizing practical quantities of this material, however, may involve finding a way to "slow cool" (e.g. << 105[K/sec]) condensed carbon vapor from temperatures in the 3000K range without triggering premature solidification.
To be more specific, on-going work addresses these topics:
units are seldom expressed in terms of natural or fundamental quantities (i.e. historical units named after people are normally used) because temperature was discovered to be a useful concept long before folks understood that temperature's reciprocal takes on negative values for inverted population state systems, and is most generally a measure of energy's uncertainty slope 1/T = δS/δE (AKA coldness) e.g. in nats of correlation information lost per joule of thermal energy added to any internally equilibrated system [34].
Hence Boltzmann's constant is the number of joules of heat energy for each nat of correlation information lost per Kelvin of temperature available in the ambient heat reservoir, and J/K is therefore simply a measure of correlation information in units like bits, bytes, or nats. In the new-SI, the number of bits of correlation-information in one J/K i.e. exactly 1029/(1,380,649ln[2]) is also the number of bits of correlation information potentially gained per joule of thermal energy lost for each reciprocal Kelvin of coldness in the world around.
Here positive absolute zero represents infinite coldness, which of course can never be reached for a finite system. The reciprocal of this 1,380,649ln[2]/1029 ≈ 9.5699296×10-24 is the number of joules per bit of state uncertainty increase associated with each Kelvin of temperature as well as Boltzmann's constant in J/(K bit) rather than the more familiar 1,380,649/1029 J/(K nat). The available work associated with correlation-information about the state of a system plays a particularly important role in forms of reversible (including quantum) computing [35] as well as in the study of correlation-based complexity [36].
an excellent 1968 article, Robert W. Brehme discussed the advantage of teaching relativity with four-vectors. This is not done for intro-physics courses. One reason may be that spacetime’s 4-vector symmetry is broken locally into (3+1)D, so that e.g. engineers working in curved spacetimes (including that here on earth) will naturally want to describe time-intervals in seconds and space-intervals e.g. in meters. In this note [4], we therefore explore in depth an idea about use of minimally frame-variant scalars and 3-vectors, perhaps first hinted at in Percy W. Bridgman’s 1928 ruminations about the wisdom of defining 3-vector velocity using an ”extended” time system rather than defining 3-vector velocity using traveler proper time instead.
The problem with the latter, of course, is that minimally frame-variant quantities like proper time, 3-vector proper velocity, and 3-vector proper acceleration are inherently local to one traveler’s perspective, hence we refer to them as ”traveler-point” quantities. The advantage is that they are either frame-invariant (in the case of proper time and the magnitude of proper-acceleration) or synchrony-free (i.e. do not require an extended network of synchronized clocks which of course is not always available in curved space time and accelerated frames).
In a larger context, general-relativity revealed a century ago why we can get by with using Newton’s laws in spacetime so curvy that it’s tough to jump higher than a meter. It’s because those laws work locally in all frames of reference, provided we recognize that motion is generally affected by both proper and “geometric” (i.e. accelerometer-invisible connection-coefficient) forces.
In that context, it’s probably time to give introductory students the good news. Here we discuss a way to do this without telling them to measure time and distance in e.g. kilograms, and without asking them to juggle more than one concurrent defintion of simultaneity.
The metric equation of course avoids these things (cf. Fig. 1) by specifying locally-defined frame invariants like proper-time, and contenting itself with a single definition of simultaneity i.e. that associated with the set of book-keeper (or map) coordinates that one chooses to describe the spacetime metric. Hence the focus here is on a metric-first, as distinct from transform-first, strategy for describing motion in accelerated frames, in curved spacetime, as well as at high speeds [2] [3] [4] [5] [6].
This "expanded" table is meant to move from more familiar relations, to relations that are useful not just at high speeds but (with help from the "geometric force" approximation) also in curved spacetimes and accelerated frames. Here green backgrounds involve purely kinematic integrals of constant proper acceleration, blue backgrounds involve dynamical quantities connected to motion's causes, and red backgrounds flag more technical relationships that may come in handy for doing calculations.
relation | w<<c | (1+1)D | (3+1)D |
---|---|---|---|
map time t | t ≈ τ | t = c/α sinh[ατ/c] | t = ½(wo/c)2/(γo+1) τ + (ατo/c)2τo sinh[τ/τo] |
map position r | r ≈ vot + ½at2 | x = (c2/α)(cosh[ατ/c]-1) | r = ½(τ+τosinh[τ/τo]) wo + τo2(cosh[τ/τo]-1) α |
aging factor γ ≡ δt/δτ | γ ≈ 1 + ½(v/c)2 | γ = cosh[ατ/c] | γ = ½(wo/c)2/(γo+1) + (ατo/c)2cosh[τ/τo] |
proper velocity w ≡ δr/δτ | w ≈ v ≈ vo + at | w = c sinh[ατ/c] | w = ½(1+cosh[τ/τo]) wo + τosinh[τ/τo] α |
relative velocity wAC | vAC ≈ vAB + vBC | wAC = γABγBC(vAB+vBC) | wAC = wAB∗ + wB∗C where wB∗C ≡ γABwBC and wAB∗ ≡ wAB⊥wBC+γBCwAB||wBC |
momentum p | p ≈ mv | p = mw = mγv | p = mw = mγv |
energy E | E ≈ mc2+½mv2 | E = γmc2 | E = γmc2 |
felt (ξ) ↔ map-based (f) force conversions |
f ≈ ξ | f = ξ | ξ = f||w + γf⊥w f = ξ||w + ξ⊥w/γ |
work-energy | δE ≈ Σf•δr | δE = (Σf)•δx | δE = Σξ•δr |
action-reaction | fAB = -fBA | fAB = -fBA | fAB = -fBA |
map-based force (f)-momentum (p) felt force (ξ)-acceleration (α) |
Σf = δp/δt ≈ ma | Σf = δp/δt = mα | Σf = δp/δt Σξ = mα |
"purely felt" static/kinetic breakdown f = fE + fB |
fE ≈ ξ ≈ ma fB ≈ 0 |
fE = ξ = γ3ma fB = 0 |
fE = ξ||w + γξ⊥w = γ3ma fB = (1/γ-γ)ξ⊥w = -γ(v/c)2ξ⊥w |
electromagnetic static/kinetic field breakdown f = fE + fB |
fE = qE fB = qv×B |
fE = qE = qE' fB = 0 |
fE = qE = q(E'||w+γE'⊥w)-qw×B' fB = qv×B = q(1/γ-γ)E'⊥w+qw×B' |
The foregoing velocity parameters, especially Lorentz-factor γ ≡ dt/dτ and proper-velocity w ≡ dx/dτ, also connect up simply to dynamically-conserved quantities like the relativistic total energy E, and the relativistic momentum p, via:
where m is rest mass, c is lightspeed, w is proper-velocity dx/dτ, v is coordinate velocity dx/dt, K is kinetic energy, and the Lorentz-factor γ may be written:
These equations may also work locally in any spacetime, provided that we approximate connection-coefficient effects with "geometric forces" (like gravity and inertial) which are undetectable by on-board accelerometers, act on every ounce of an object's being, and can be made to disappear from the vantage point of a free float frame.
Symmetry-breaking is an integrative-theme [37] which cuts across disciplines [38]. On the molecular level [39], for instance, the relatively-featureless isotropic-symmetry of liquid water [40] may first be broken by local translational pair-correlations (resulting in spherical reciprocal-lattice shells) as the liquid turns to polycrystal ice, and eventually by global translational and rotational ordering (resulting in reciprocal-lattice spots) as the ice becomes a single crystal.
Partly along the way to single-crystal form a quasicrystal phase might have rotational without translational ordering, while a random-layer lattice might have rotational and translational ordering in one "layering" direction only. Thus even within a single layer of organization, broken symmetries play a role in the (at least temporary) development of order.
Hierarchical ordering in the layer just above a pair-correlated level (e.g. interacting organisms) may generally require a higher-level symmetry-break (e.g. recognition of differing organism groups), which in turn gives rise to processes that select for inward-looking (e.g. from the group boundary) post-pair correlations as well as outward-looking pair-correlations on the next level up (e.g. between groups).
Thus shared-electrons break the symmetry between in-molecule and extra-molecule interactions, bi-layer membranes allow symmetry between in-cell and out-cell chemistry to be broken, shared resources (like steady-state flows) may break the symmetry between in-tissue and external processes, metazoan skins allow symmetry between in-organism and out-organism processes to be broken, bias toward family breaks the symmetry between in-family and extra-family processes, membership-rules break the symmetry between in-culture and multi-cultural processes, etc.
Although modern physics courses often concentrate on history, the very name of the course suggests that we should also be on the lookout for unfolding-themes. For instance:
The temporal vs. spatial frequency theme includes stuff like the relationship ν = c/λ between broadcast-frequency & wavelength/antenna-size, resonant oscillations, waves, kinetic-energy vs. momentum plots since E = hν and p = h/λ, metric-1st relativity with proper-velocity w ≡ dx/dτ = p/m and proper/geometric accelerations, radar-time simultaneity, x-cτ & x-ct plots, reciprocal-lattices in diffraction & scattering theory, dispersion-relations e.g. of ω vs. k, band-structure, pair & pair-pair correlations, least action, and what else?
The number of choices = 2#bits = eS/k theme instead leads us through stuff like Bayesian data analysis including parameter-estimation (e.g. least-squares fits) & model-selection (e.g. AIC), surprisal-based risk-estimation, entropy-1st and correlation-1st studies [3] of analog & digital order-disorder transitions, Boltzmann & quantum occupancy-factors, natural units for temperature, heat-capacities as multiplicity-exponents, phase-changes, symmetry-breaks, information-engines including organisms & quantum computers, data compression, clade analysis, (d)evolving complexity in context of both cosmic and biological evolution, task layer-multiplicity, and what else?
When dimensionless units take on multiple forms, it is often helpful to be explicit about which of those forms are being used in any given situation. Some examples of these are shown in the table below, using the most recent "new-SI" definitions to make two of them rational as well as exact:
larger unit | × conversion factor | = smaller unit |
---|---|---|
mole | AvogadroConstant 6.02214076×1023 |
molecule |
cycle | 2π 6.2831853071... |
radian |
nat | 1/ln2 1.4426950408... |
bit |
nat | 1/BoltzmannConstant 1023/1.380649 |
J/K |
In this note we address applications involving angle units and information units where the dimensionless units are not always explicit. Although this is often not a problem within the jargon of a given field, being explicit about one's choice should help in communication between disciplines. In some areas, it may also provide insight into physical connections which might otherwise be missed. Thermochap ( talk) 11:08, 28 September 2021 (UTC)
Here's a reference table of "sometimes hidden" dimensionless units that may be worth making explicit. Can you think of any others that we might mention?
Quantity | Version w/unit hidden | Version w/unit exposed |
---|---|---|
temporal frequency f or ν angular frequency ω |
reciprocal seconds reciprcoal seconds |
cycles per second or Hertz radians per second |
period τ | seconds | seconds per cycle |
spatial frequency or g-vector wave vector or k |
reciprocal meters reciprocal meters |
cycles per meter radians per meter |
wavelength λ | meters | meters per cycle |
angular momentum L | kilogram meter2/second | kg m2/s per radian |
PlanckConstant h "h-bar" or ħ ≡ h/(2π) |
Joule seconds = kg m2/s Joule seconds = kg m2/s |
Js per cycle = J/Hz Js/rad = kg m2/s per radian |
BoltzmannConstant kB | joules per kelvin | J/K per nat |
AvogadroConstant NA | molecules | molecules per mole ≠ but ≈ Daltons/gram |
Note that per cycle units are more general than per radian (which may however simplify some expressions), since not all application of these above quantities involves a physicsl angle. Note also that wavelength, angular momentum, and the Boltzmann constant are generally fixed in the dimensionless unit that they assume, even though other choices are available.
One may think of the familiar uncertainty-relation in QM as a statement about subsystem-correlations between features of an object (like position or momentum) and an external knower. In the same way that shortening the duration of a musical note expands the range of frequencies that you hear (i.e. Δtime⇓ means Δfreq⇑) regardless of how well the musical instrument is tuned, measurement in general correlates one parameter's value with the knower's state of mind while unavoidably de-correlating that parameter's Fourier transform e.g. its frequency-space footprint.
A special case of this arises in the study of small systems because of energy/momentum's proportionality to temporal/spatial-frequency through Planck's constant i.e. since h = E/ν = p/g = 2πL. In fact some groups assert that all of quantum theory (not to mention other sciences) can be reduced not to studies about the state of stand-alone systems but to studies of our relationship as knower to structures in the world around.
Is this related to recent interest in thermodynamic explanation of e.g. spring & gravity forces in terms of information gradients on holographic surfaces, or to this 2013 note on time flow from sub-system correlations which, at least at first glance, follows a similar pattern?
It's probably worth putting together an overview on use of log-probability measures to provide quantitative insight into:
Aside: One advantage of this integrative notation is that we deal exclusively in positive quantities, except of course when we are calculating differences between them.
We'll gradually flesh in details on this topic, which are presently available only on limited-access mediawiki sites. If you are interested in more on any particular item in the list above, leave a note for me on my talk page here: Thermochap ( talk) 14:28, 13 November 2011 (UTC)
item ⇒ | ⇐ value | item ⇒ | ⇐ value |
---|---|---|---|
Elementary charge -qe | ≈ 1.6×10-19 Coulomb or J/eV | Electron mass me ≈ mp/1836 | ≈ 9.1×10-31 kg ≈ 1/1823 u ≈ 511 keV/c2 |
Selected isotopes AZXN | 4018Ar22, 19779Au118, 23892U146 | Unified mass unit u or dalton Da | ≈ 1.66×10-27 kg ≈ 1/(6×1023) gram |
Lightspeed constant c | = 1 ly/y ≈ 3×108 m/s ≈ 0.98 ft/ns | Atom radii are near 1 Ångstrom | ≡ 10-10 meter = 105 femtometer |
Boltzmann constant kB | ≈ 1.38×10-23 J/K ≈ 8.6×10-5 eV/K | Room temperature 20oC = 68oF | ≈ 293 K ≈ 4×10-21 J/nat ≈ 1/40 eV/nat |
Planck constant h ≡ 2πħ | ≈ 6.626×10-34 Js ≈ 4.14×10-15 eVs | Coulomb constant ke ≡ 1/(4πεo) | = c2μo/(4π) = αħc/qe2 ≈ 9×109 Nm2/C2 |
A curious resonance involving the re-framing of variables shows up in each of the 4 parts of today's modern physics course. Lastly (in part 4) decay-constant λ ≡ ln[2]/τ½ e.g. in [e-folds/second] is the dog that wags half-life's tail e.g. in [seconds/2-fold], much as (in part 2) vector spatial-frequency g ≡ k/(2π) = p/h e.g. in [cycles/Ångstrom] is the dog that wags wavelength and d-spacing's tail e.g. in [Ångstroms/cycle].
Later (in part 3) coldness or energy's uncertainty-slope i.e. reciprocal-temperature 1/kT ≡ d(S/k)/dE e.g. in [nats/eV] turns out to be the dog that wags temperature's tail e.g. in [Kelvin] or [eV/nat]. One may also point out (in part 1) that proper-velocity w ≡ dx/dτ = p/m = γv e.g. in [lightyears/traveler-year] is the dog that wag's coordinate-velocity's tail e.g. in [lightyears/map-year], but that relationship is not similarly reciprocal.
|
This is a Wikipedia
user page. This is not an encyclopedia article or the talk page for an encyclopedia article. If you find this page on any site other than Wikipedia, you are viewing a mirror site. Be aware that the page may be outdated and that the user whom this page is about may have no personal affiliation with any site other than Wikipedia. The original page is located at https://en.wikipedia.org/wiki/User:Thermochap. |
I'm relatively new here, and not yet quite sure what to do with a user page. For the most part so far I've found the mechanics of interaction fairly self-explanatory, and the community by and large welcoming. I am particularly excited about the educational potential of Wikipedia. Thermochap ( talk) 14:44, 21 January 2008 (UTC)
Perhaps I should note here that author contributions to Wikipedia are, by default, protected by the GNU Free Documentation License discussed in more detail here.
an you imagine living with a ton of air sitting on you, |
...to which I've contributed might include some of the entries in this table...
...and what else? Thermochap ( talk) 10:36, 25 October 2013 (UTC)
My academic home is in physics & astronomy, although I'm an applied mathematician at heart. The label thermochap is a contraction of "thermo chapters", which in modern introductory-physics books (except e.g. for Tom Moore's text [1]) still introduce entropy (and hence the pivotal role of accesible-state uncertainty) last even though the "entropy-first" approach took over senior undergrad thermal-physics texts nearly 50 years ago and (by virtue of its connection to information theory and Bayesian inference) makes the strengths and limits of relationships like the ideal gas law, equipartition and mass-action clear from the start.
With help from regional employers & facilities for nanocharacterization I've thankfully encountered chances to explore nature on varied scales of space and time. Applications include mathematical nano-microscopy tool development, laboratory study of circumstellar dust, high temperature materials for electronic or aerospace applications, and Bayesian informatic studies of data analysis, complex systems, & algorithmic simplicity.
Key developments include:
Topic | Web Sites | Tools For Interaction | Papers |
---|---|---|---|
Labs at Home | Matt's Physics@Home |
Don't Just Look: Measure! Picture The Sound! NanoExploration w/Electrons |
A Fast Track Simulation Openworld Experiment Draft |
Model Selection & Net Surprisal |
Bayesian Model Selection | Phil Gregory's book voicethread |
Metric/Entropy-1st Surprises Avogadro\Boltzmann Constants |
Metric-First motion | Traveler Point Site |
Introducing Newton voicethread Metric relativity voicethread |
One Map Two Clocks One Class Period Draft |
Evolving Complexity | Correlation-1st Informatics |
Quantifying Risk Sampler Fraction Infectious voicethread |
Heat Capacity in Bits Units for Coldness Thermal Roots |
Task-layer Multiplicity |
Old Google Site Ellie's Video Contest Page New Google Site |
Attention-Slice Sampler Augmented Like Button |
1989 MSL-8857 Simplex Model Community Health |
A few of our "small project" (and possible talk) topics highlighting "one-new-fact" might include traveler point dynamics, task layer multiplicity, moon baseball, single-slice electron optics, dimensionless units in cycles/radians & mole/molecule, coldness in GB/nJ, concept-selection, organism-centricity, correlation-based complexity, carbon rain & Milky Way nannites, total-sound videography, and what else? Thermochap ( talk) 20:51, 24 December 2021 (UTC)
For instance, the "new fact" for:
and what else? pFraundorf ( talk) 12:48, 20 December 2021 (UTC)
Specialized areas of interest impacted in our carbon-rain project, on the other hand, are broader and include:
See more on this project below.
A key to dialog is to begin from where your target audience is at. This is important with editors, with specialist peers, and also with the general public. Observations and/or simple true assertions, on the contrary, won't work by themselves particularly if they are unexpected. The reaction in that case tends instead to be "likely story" and then move on.
Messages to try introducing in this context might include e.g.:
and what else?
we like to tell stories of how humans invented our world, let's momentarily imagine that human community is a natural phenomenon that (like microbial and multi-celled life in general) has self-assembled on earth's surface. Like all forms of layered complexity, it is: (a) constructed from a hierarchy of broken symmetries with respect to gradients, boundaries, or pool edges, and (b) expanded/maintained by flows of thermodynamic availability (e.g. available work and/or correlation information) e.g. from processes running lower in the hierarchy. The substrate for human community of course includes our galaxy arm, our star, our planet's surface, living cells and cell communities on the wide range of size scales that serve up the environment in which our ancestors (and ourselves) have emerged.
Within human communities (and metazoan ecosystems in general) we also find a layered hierachy that involves subsystem correlations which look inward and outward from the metazoan skin, given that then inward and outward from family e.g. the edges of our gene and amino acid (molecular) code pools, and further given that then inward and outward from the boundary of culture e.g. the edges of our language and idea pools. We might therefore, at its simplest, model any single-species metazoan community in terms of the fraction of its attention directed toward maintaining these six layers of organizational structure, i.e. in buffering subsystem-correlations that look inward and outward from the boundaries of skin, family, and culture. There is nothing fundamental about this, except that it for simplicity puts these disparate layers of organization on an equal footing.
Modern astronomy as well as paleontology now show us that, just as these amazing things can emerge on the surface of a planet, so the conditions that allow them to remain or even thrive are fragile, and likely to eventually end either gradually or abruptly. Therefore models of the decline as well as the bloom of complexity in metazoan communities are probably worth exploring.
There is a great deal of literature about individual and even "public" health in communities. However the focus tends to be on the individual perspective, e.g. on mental and physical health of the individuals within the community. To address well-being at the community level, it might be interesting to use the simple community-level model of task layer multiplicity (TLM) above to examine the fraction of effort in any given community directed toward those six layers: self-health, pair interactions, family, community, culture, and extra-cultural knowledge [7] [9]. Perhaps we will thereby gain some insight into guiding social policy as weil as our own behavior as we attempt to make the most of our blessings. Along the way, we may encounter some surprises that our focus on individual perspectives has helped us to miss!
Do we next need to discuss the importance of the 6 different "broken-symmetry" layers of organization in multi-celled lifeform communities, namely layers that look in (←|) and out (|→) from the boundaries of metazoan-skin (←1|2→), gene-pool (←3|4→) and idea-pool (←5|6→)?
Another sobering aspect of this story that might grab some attention is precisely how one might expect complexity's decline to unfold, namely in loss of the distinction between these 6 layers. For instance, the higher numbered (and later developed) ones may (at least in the long run) lose steam first.
If you are serious about any particular problem, ranging from how to fix a dripping faucet or a broken electrical circuit to making gerrymanders constructive, minimizing abortions, or reducing gun deaths, consider adopting a scout (versus soldier) mindset and embark on the cycle: Observe → selectModel → predictOptions → Implement → Observe....
This "V↔S" cycle (vary then select then vary etc.) is not only how (for example) science works (although it often also gets bogged down in doctrine), but also how life on earth has always worked. In other words it's part of perhaps our oldest constitution, namely that on the basis of which life itself continues to adapt and survive.
was long thought that diamond could only be produced under conditions of high pressure and temperature. We now know that metastable diamond can be grown at low pressure and temperature by chemical vapor deposition, perhaps because diamond is the stable phase for nanoscale carbon at low temperature and pressure.
In the same way, liquid carbon is thought to only exist at high temperature and high pressure, although low-pressure stability below the sublimation temperature on the nanoscale has also been predicted [18]. We report now observations in both nature, and in the laboratory, which suggest that metastable liquid condenses at low pressure from carbon vapor perhaps because nanoscale liquid is stable at low pressure, and hence able to grow metastably from the vapor in containerless settings to temperatures well below the melting point as do metallic liquids in general [19].
Moreover, when this low-pressure liquid is cooled slowly it appears to result in an unlayered graphene composite that may have diffusion barrier properties otherwise unrivaled in nature. Synthesizing practical quantities of this material, however, may involve finding a way to "slow cool" (e.g. << 105[K/sec]) condensed carbon vapor from temperatures in the 3000K range without triggering premature solidification.
To be more specific, on-going work addresses these topics:
units are seldom expressed in terms of natural or fundamental quantities (i.e. historical units named after people are normally used) because temperature was discovered to be a useful concept long before folks understood that temperature's reciprocal takes on negative values for inverted population state systems, and is most generally a measure of energy's uncertainty slope 1/T = δS/δE (AKA coldness) e.g. in nats of correlation information lost per joule of thermal energy added to any internally equilibrated system [34].
Hence Boltzmann's constant is the number of joules of heat energy for each nat of correlation information lost per Kelvin of temperature available in the ambient heat reservoir, and J/K is therefore simply a measure of correlation information in units like bits, bytes, or nats. In the new-SI, the number of bits of correlation-information in one J/K i.e. exactly 1029/(1,380,649ln[2]) is also the number of bits of correlation information potentially gained per joule of thermal energy lost for each reciprocal Kelvin of coldness in the world around.
Here positive absolute zero represents infinite coldness, which of course can never be reached for a finite system. The reciprocal of this 1,380,649ln[2]/1029 ≈ 9.5699296×10-24 is the number of joules per bit of state uncertainty increase associated with each Kelvin of temperature as well as Boltzmann's constant in J/(K bit) rather than the more familiar 1,380,649/1029 J/(K nat). The available work associated with correlation-information about the state of a system plays a particularly important role in forms of reversible (including quantum) computing [35] as well as in the study of correlation-based complexity [36].
an excellent 1968 article, Robert W. Brehme discussed the advantage of teaching relativity with four-vectors. This is not done for intro-physics courses. One reason may be that spacetime’s 4-vector symmetry is broken locally into (3+1)D, so that e.g. engineers working in curved spacetimes (including that here on earth) will naturally want to describe time-intervals in seconds and space-intervals e.g. in meters. In this note [4], we therefore explore in depth an idea about use of minimally frame-variant scalars and 3-vectors, perhaps first hinted at in Percy W. Bridgman’s 1928 ruminations about the wisdom of defining 3-vector velocity using an ”extended” time system rather than defining 3-vector velocity using traveler proper time instead.
The problem with the latter, of course, is that minimally frame-variant quantities like proper time, 3-vector proper velocity, and 3-vector proper acceleration are inherently local to one traveler’s perspective, hence we refer to them as ”traveler-point” quantities. The advantage is that they are either frame-invariant (in the case of proper time and the magnitude of proper-acceleration) or synchrony-free (i.e. do not require an extended network of synchronized clocks which of course is not always available in curved space time and accelerated frames).
In a larger context, general-relativity revealed a century ago why we can get by with using Newton’s laws in spacetime so curvy that it’s tough to jump higher than a meter. It’s because those laws work locally in all frames of reference, provided we recognize that motion is generally affected by both proper and “geometric” (i.e. accelerometer-invisible connection-coefficient) forces.
In that context, it’s probably time to give introductory students the good news. Here we discuss a way to do this without telling them to measure time and distance in e.g. kilograms, and without asking them to juggle more than one concurrent defintion of simultaneity.
The metric equation of course avoids these things (cf. Fig. 1) by specifying locally-defined frame invariants like proper-time, and contenting itself with a single definition of simultaneity i.e. that associated with the set of book-keeper (or map) coordinates that one chooses to describe the spacetime metric. Hence the focus here is on a metric-first, as distinct from transform-first, strategy for describing motion in accelerated frames, in curved spacetime, as well as at high speeds [2] [3] [4] [5] [6].
This "expanded" table is meant to move from more familiar relations, to relations that are useful not just at high speeds but (with help from the "geometric force" approximation) also in curved spacetimes and accelerated frames. Here green backgrounds involve purely kinematic integrals of constant proper acceleration, blue backgrounds involve dynamical quantities connected to motion's causes, and red backgrounds flag more technical relationships that may come in handy for doing calculations.
relation | w<<c | (1+1)D | (3+1)D |
---|---|---|---|
map time t | t ≈ τ | t = c/α sinh[ατ/c] | t = ½(wo/c)2/(γo+1) τ + (ατo/c)2τo sinh[τ/τo] |
map position r | r ≈ vot + ½at2 | x = (c2/α)(cosh[ατ/c]-1) | r = ½(τ+τosinh[τ/τo]) wo + τo2(cosh[τ/τo]-1) α |
aging factor γ ≡ δt/δτ | γ ≈ 1 + ½(v/c)2 | γ = cosh[ατ/c] | γ = ½(wo/c)2/(γo+1) + (ατo/c)2cosh[τ/τo] |
proper velocity w ≡ δr/δτ | w ≈ v ≈ vo + at | w = c sinh[ατ/c] | w = ½(1+cosh[τ/τo]) wo + τosinh[τ/τo] α |
relative velocity wAC | vAC ≈ vAB + vBC | wAC = γABγBC(vAB+vBC) | wAC = wAB∗ + wB∗C where wB∗C ≡ γABwBC and wAB∗ ≡ wAB⊥wBC+γBCwAB||wBC |
momentum p | p ≈ mv | p = mw = mγv | p = mw = mγv |
energy E | E ≈ mc2+½mv2 | E = γmc2 | E = γmc2 |
felt (ξ) ↔ map-based (f) force conversions |
f ≈ ξ | f = ξ | ξ = f||w + γf⊥w f = ξ||w + ξ⊥w/γ |
work-energy | δE ≈ Σf•δr | δE = (Σf)•δx | δE = Σξ•δr |
action-reaction | fAB = -fBA | fAB = -fBA | fAB = -fBA |
map-based force (f)-momentum (p) felt force (ξ)-acceleration (α) |
Σf = δp/δt ≈ ma | Σf = δp/δt = mα | Σf = δp/δt Σξ = mα |
"purely felt" static/kinetic breakdown f = fE + fB |
fE ≈ ξ ≈ ma fB ≈ 0 |
fE = ξ = γ3ma fB = 0 |
fE = ξ||w + γξ⊥w = γ3ma fB = (1/γ-γ)ξ⊥w = -γ(v/c)2ξ⊥w |
electromagnetic static/kinetic field breakdown f = fE + fB |
fE = qE fB = qv×B |
fE = qE = qE' fB = 0 |
fE = qE = q(E'||w+γE'⊥w)-qw×B' fB = qv×B = q(1/γ-γ)E'⊥w+qw×B' |
The foregoing velocity parameters, especially Lorentz-factor γ ≡ dt/dτ and proper-velocity w ≡ dx/dτ, also connect up simply to dynamically-conserved quantities like the relativistic total energy E, and the relativistic momentum p, via:
where m is rest mass, c is lightspeed, w is proper-velocity dx/dτ, v is coordinate velocity dx/dt, K is kinetic energy, and the Lorentz-factor γ may be written:
These equations may also work locally in any spacetime, provided that we approximate connection-coefficient effects with "geometric forces" (like gravity and inertial) which are undetectable by on-board accelerometers, act on every ounce of an object's being, and can be made to disappear from the vantage point of a free float frame.
Symmetry-breaking is an integrative-theme [37] which cuts across disciplines [38]. On the molecular level [39], for instance, the relatively-featureless isotropic-symmetry of liquid water [40] may first be broken by local translational pair-correlations (resulting in spherical reciprocal-lattice shells) as the liquid turns to polycrystal ice, and eventually by global translational and rotational ordering (resulting in reciprocal-lattice spots) as the ice becomes a single crystal.
Partly along the way to single-crystal form a quasicrystal phase might have rotational without translational ordering, while a random-layer lattice might have rotational and translational ordering in one "layering" direction only. Thus even within a single layer of organization, broken symmetries play a role in the (at least temporary) development of order.
Hierarchical ordering in the layer just above a pair-correlated level (e.g. interacting organisms) may generally require a higher-level symmetry-break (e.g. recognition of differing organism groups), which in turn gives rise to processes that select for inward-looking (e.g. from the group boundary) post-pair correlations as well as outward-looking pair-correlations on the next level up (e.g. between groups).
Thus shared-electrons break the symmetry between in-molecule and extra-molecule interactions, bi-layer membranes allow symmetry between in-cell and out-cell chemistry to be broken, shared resources (like steady-state flows) may break the symmetry between in-tissue and external processes, metazoan skins allow symmetry between in-organism and out-organism processes to be broken, bias toward family breaks the symmetry between in-family and extra-family processes, membership-rules break the symmetry between in-culture and multi-cultural processes, etc.
Although modern physics courses often concentrate on history, the very name of the course suggests that we should also be on the lookout for unfolding-themes. For instance:
The temporal vs. spatial frequency theme includes stuff like the relationship ν = c/λ between broadcast-frequency & wavelength/antenna-size, resonant oscillations, waves, kinetic-energy vs. momentum plots since E = hν and p = h/λ, metric-1st relativity with proper-velocity w ≡ dx/dτ = p/m and proper/geometric accelerations, radar-time simultaneity, x-cτ & x-ct plots, reciprocal-lattices in diffraction & scattering theory, dispersion-relations e.g. of ω vs. k, band-structure, pair & pair-pair correlations, least action, and what else?
The number of choices = 2#bits = eS/k theme instead leads us through stuff like Bayesian data analysis including parameter-estimation (e.g. least-squares fits) & model-selection (e.g. AIC), surprisal-based risk-estimation, entropy-1st and correlation-1st studies [3] of analog & digital order-disorder transitions, Boltzmann & quantum occupancy-factors, natural units for temperature, heat-capacities as multiplicity-exponents, phase-changes, symmetry-breaks, information-engines including organisms & quantum computers, data compression, clade analysis, (d)evolving complexity in context of both cosmic and biological evolution, task layer-multiplicity, and what else?
When dimensionless units take on multiple forms, it is often helpful to be explicit about which of those forms are being used in any given situation. Some examples of these are shown in the table below, using the most recent "new-SI" definitions to make two of them rational as well as exact:
larger unit | × conversion factor | = smaller unit |
---|---|---|
mole | AvogadroConstant 6.02214076×1023 |
molecule |
cycle | 2π 6.2831853071... |
radian |
nat | 1/ln2 1.4426950408... |
bit |
nat | 1/BoltzmannConstant 1023/1.380649 |
J/K |
In this note we address applications involving angle units and information units where the dimensionless units are not always explicit. Although this is often not a problem within the jargon of a given field, being explicit about one's choice should help in communication between disciplines. In some areas, it may also provide insight into physical connections which might otherwise be missed. Thermochap ( talk) 11:08, 28 September 2021 (UTC)
Here's a reference table of "sometimes hidden" dimensionless units that may be worth making explicit. Can you think of any others that we might mention?
Quantity | Version w/unit hidden | Version w/unit exposed |
---|---|---|
temporal frequency f or ν angular frequency ω |
reciprocal seconds reciprcoal seconds |
cycles per second or Hertz radians per second |
period τ | seconds | seconds per cycle |
spatial frequency or g-vector wave vector or k |
reciprocal meters reciprocal meters |
cycles per meter radians per meter |
wavelength λ | meters | meters per cycle |
angular momentum L | kilogram meter2/second | kg m2/s per radian |
PlanckConstant h "h-bar" or ħ ≡ h/(2π) |
Joule seconds = kg m2/s Joule seconds = kg m2/s |
Js per cycle = J/Hz Js/rad = kg m2/s per radian |
BoltzmannConstant kB | joules per kelvin | J/K per nat |
AvogadroConstant NA | molecules | molecules per mole ≠ but ≈ Daltons/gram |
Note that per cycle units are more general than per radian (which may however simplify some expressions), since not all application of these above quantities involves a physicsl angle. Note also that wavelength, angular momentum, and the Boltzmann constant are generally fixed in the dimensionless unit that they assume, even though other choices are available.
One may think of the familiar uncertainty-relation in QM as a statement about subsystem-correlations between features of an object (like position or momentum) and an external knower. In the same way that shortening the duration of a musical note expands the range of frequencies that you hear (i.e. Δtime⇓ means Δfreq⇑) regardless of how well the musical instrument is tuned, measurement in general correlates one parameter's value with the knower's state of mind while unavoidably de-correlating that parameter's Fourier transform e.g. its frequency-space footprint.
A special case of this arises in the study of small systems because of energy/momentum's proportionality to temporal/spatial-frequency through Planck's constant i.e. since h = E/ν = p/g = 2πL. In fact some groups assert that all of quantum theory (not to mention other sciences) can be reduced not to studies about the state of stand-alone systems but to studies of our relationship as knower to structures in the world around.
Is this related to recent interest in thermodynamic explanation of e.g. spring & gravity forces in terms of information gradients on holographic surfaces, or to this 2013 note on time flow from sub-system correlations which, at least at first glance, follows a similar pattern?
It's probably worth putting together an overview on use of log-probability measures to provide quantitative insight into:
Aside: One advantage of this integrative notation is that we deal exclusively in positive quantities, except of course when we are calculating differences between them.
We'll gradually flesh in details on this topic, which are presently available only on limited-access mediawiki sites. If you are interested in more on any particular item in the list above, leave a note for me on my talk page here: Thermochap ( talk) 14:28, 13 November 2011 (UTC)
item ⇒ | ⇐ value | item ⇒ | ⇐ value |
---|---|---|---|
Elementary charge -qe | ≈ 1.6×10-19 Coulomb or J/eV | Electron mass me ≈ mp/1836 | ≈ 9.1×10-31 kg ≈ 1/1823 u ≈ 511 keV/c2 |
Selected isotopes AZXN | 4018Ar22, 19779Au118, 23892U146 | Unified mass unit u or dalton Da | ≈ 1.66×10-27 kg ≈ 1/(6×1023) gram |
Lightspeed constant c | = 1 ly/y ≈ 3×108 m/s ≈ 0.98 ft/ns | Atom radii are near 1 Ångstrom | ≡ 10-10 meter = 105 femtometer |
Boltzmann constant kB | ≈ 1.38×10-23 J/K ≈ 8.6×10-5 eV/K | Room temperature 20oC = 68oF | ≈ 293 K ≈ 4×10-21 J/nat ≈ 1/40 eV/nat |
Planck constant h ≡ 2πħ | ≈ 6.626×10-34 Js ≈ 4.14×10-15 eVs | Coulomb constant ke ≡ 1/(4πεo) | = c2μo/(4π) = αħc/qe2 ≈ 9×109 Nm2/C2 |
A curious resonance involving the re-framing of variables shows up in each of the 4 parts of today's modern physics course. Lastly (in part 4) decay-constant λ ≡ ln[2]/τ½ e.g. in [e-folds/second] is the dog that wags half-life's tail e.g. in [seconds/2-fold], much as (in part 2) vector spatial-frequency g ≡ k/(2π) = p/h e.g. in [cycles/Ångstrom] is the dog that wags wavelength and d-spacing's tail e.g. in [Ångstroms/cycle].
Later (in part 3) coldness or energy's uncertainty-slope i.e. reciprocal-temperature 1/kT ≡ d(S/k)/dE e.g. in [nats/eV] turns out to be the dog that wags temperature's tail e.g. in [Kelvin] or [eV/nat]. One may also point out (in part 1) that proper-velocity w ≡ dx/dτ = p/m = γv e.g. in [lightyears/traveler-year] is the dog that wag's coordinate-velocity's tail e.g. in [lightyears/map-year], but that relationship is not similarly reciprocal.
|