A possible talk on this cycle for physics teachers (e.g. at the 2016 ISAAPT Fall meeting in Peoria IL) might have an outline of the form:

- [observation] with our real-time sheet-music app,
- [model-selection] with a discussion of "surprisal power",
- [prediction-strategy] with a discussion of "traveler-point dynamics", and
- [experiment setup] with a discussion of electron-optics on-line.

Note that this cyclic view of the scientific method (figure at right) avoids the true/false-hypothesis component of scientific method characterizations: It asks "Which concept set is most effective in a given situation?" rather than the binary-logic question "Is that assertion a perfect match to the world around?".

This approach also makes explicit the gestalt pattern-recognition problem, i.e. the fact that evolving concept-sets (and shifting paradigms) are key to guiding which aspects of future observations will make it at all into the record for downstream analysis. Finally, of course, one might see the cycle portrayed in the figure as a key element for models of scientific method as a continuously evolving physical process, as distinct from an activity with a beginning and an end.

Although physics courses have historically focused on "prediction strategy" rather than
on other elements in the cycle, we begin here with observations, because in the "chicken
or egg" problem it makes sense that the cycle began with input from our senses about
goings-on in the world around. In what follows, we then proceed around the cycle, in the
process introducing quite **disparate elements of intro-physics content-modernization**
that are relevant to the changing world in which our students find themselves.

This usually involves taking some sort of data. Although it would be nice to imagine that we were recording the truth, the whole truth, and nothing but the truth, in fact the sensory-instruments and asked-questions that are used to take the data inevitably color the kinds of concepts that might serve to model what you find, as well as the data you have to work with.

Theory and practice here includes:

- applied pattern recognition
- data acquisition, storage, transmission strategies

and what else?

To illustrate this we describe
a Firefox app,
inspired by our electron
scattering studies of crystal lattice defect structure, designed to
make sounds accessible (including Fourier phases not generally audible) in
real time to **YOUR** neural-network for visual pattern recognition [1].

The key to phase-visualization over a wide dynamic range of intensities is to use pixel-brightness/saturation to represent the log-amplitude of a complex number, and pixel-hue to represent the Fourier phase. This method of using color images to display 2D arrays of complex numbers of course has many other uses in physics education, one of which is illustrated in the (lower left) digital darkfield panel of the electron optics simulator discussed below.

As shown in the figure at right, following musicians we lean toward "*log-frequency*
vs. time spectrogram" formats, since they make frequency-ratios (like octaves) much
easier to recognize. In this context, look for *visual field guides* to all kinds
of sounds in the days ahead, as well as (hopefully) an improved path for folks with
hearing impairments to enhance their expertise in both sound recognition and generation.

Given data, "What set of concepts is most helpful for putting it to use?" is perhaps the most difficult question of all to answer. One reason is that the choice of concepts to use in modeling processes is an open-ended question. Another reason is that models useful for predicting often are not easy to operate in reverse, i.e. the "inverse problem" is not easily or unambiguously solved.

Theory and practice here includes:

- studies of model selection, and paradigm evolution, in the field at hand,
- inverse problem-solving (e.g. inferring an object-model from diffraction data),

and what else?

To introduce the quantitative science of model-selection (which may be less familiar than parameter-estimation to academic physicists), we begin with something that is familiar: the now half-century old switch to the statistical approach (cf. Reif, Kittel and Kroemer, Stowe, Garrod, Schroeder, etc.) for teaching thermal physics in senior undergraduate (and later) courses. Although one might think of this as "entropy-first", it is unavoidable that in the years ahead we'll be seeing this (cf. [2]) as a "correlation-first" approach instead.

In that context we may want to carefully point out, even to conceptual-physics students
via the expression #choices = 2^{#bits},
the robust connection between **surprisals** (e.g. s≡ln_{2}[1/p] in bits)
and wide-ranging __cross-disciplinary__ uses for "the second law" in statistical
terms i.e. that correlations between *isolated* subsystems generally do not
increase as time passes.

In the world of binary logic, surprisal gives practical meaning to the phrase "bits of evidence", while in the world of probabilities (0≤p≤1) it shows how to relate coin-tosses to decisions e.g. about games of chance and medical choices for a visceral feeling of what very small and very large odds mean. More importantly, it serves up a more general way to quantify available work (i.e. ordered energy from things like renewable and non-renewable sources), not to mention a way to understand the "kids on a playground" force behind heat flow (including systems with inverted population states).

For our purposes here, surprisal independently lies at the heart of parallel themes
in the physical [3] and behavioral [4] sciences for choosing which models work best. The
elegant Bayesian solution in *both* cases (albeit not always easy to quantify in practice)
is simply to choose the model which is "least surprised" by incoming data. The shared
basis for both approaches automatically addresses the more familiar reward for "goodness
of fit", along with an Occam-factor penalty for model complexity e.g. through the number
of free parameters involved. When there is no time for the formal mathematics, students
might instead be encouraged to discuss which historical ideas
in wide-ranging areas
were surprised by new data, and what happened as a result.

I should also mention that, thanks to connections made by Claude Shannon and Ed Jaynes, surprisal as a correlation-measure fits nicely into the information age of both regular and quantum computers [5]. It further shows promise for helping us develop cross-disciplinary measures of community health [6], which focus on correlations that look in/out from skin, family and culture.

Obtaining predictions from one's collection of models is an evolving challenge in most fields. This is certainly true with most quantitative models, because the tools for obtaining and vetting predictions from a model (especially the former) are changing rapidly as the digital logic tools available to support those processes continue to change.

Theory and practice here includes:

- choosing parameters for best fitting what's known into the chosen model,
- inferring model answers to the question(s) at hand, with and withou help from computers,
- inferring the consequence of uncertainties, in both the data and the models,
- clear communication where possible by letting the data speak for itself,

and what else?

The metric-equation's *synchrony-free*
"traveler-point parameters",
namely proper-time τ, proper-velocity **w** ≡ d**x**/dτ, &
proper-acceleration **α**, are useful in
curved spacetime
because extended arrays of synchronized clocks (e.g. for local measurement of
the map-time t increment in Δx/Δt) may be hard to find. These same parameters
can better prepare intro-physics students for their everyday world, as well as for the
technological world e.g. of GPS systems where differential aging must be considered
explicitly. However, some old ways of teaching may need minor tweaks.

For instance, high-school students in AP Physics are sometimes taught that centrifugal force is fake, even though:

- (i) movies like ''The Martian'' and ''Interstellar'' show it to be a practical way to create artificial gravity, and
- (ii) our cell-phone accelerometers show gravity (as well as those fake inertial forces) to be "undetectable".

In fact Einstein's general relativity revealed that Newton's laws work locally in *all*
frames (including accelerated-frames in curved-spacetime), provided that we __recognize__
geometric forces like gravity and inertial forces [7], which often link to
differential aging (γ≡dt/dτ) with "well-depths" (e.g. in rotating habitats,
accelerating spaceships, and gravity on earth) directly connected to
(γ-1)mc^{2}. Moreover, the net proper-forces [8] that our cell-phones measure
(which are generally __not__ rates of
momentum change) are "frame-invariant" much as is proper-time, making
curved spacetime (like that we experience on earth's
surface) a bit simpler to understand than we might have imagined from a "transform-first"
course in special relativity.

Since this insight came into focus a century ago, perhaps it is appropriate (as is already
happening with the increasing textbook use of proper-time) to tell physics
students in general, and not just folks who've become grad-students with a theoretical bent,
that traveler-point parameters (as complement to familiar variables like coordinate-velocity)
can help us both understand and predict. At the very least perhaps it's a good excuse to say
that time elapses differently on all clocks, according to both position and rate of
travel, but that we appoximate by saying that t
represents time-elapsed on *synchronized* clocks connected to the yardsticks which
define our frame of reference.

To give you a taste of the traveler-point variable notation in classic terms, imagine
a traveler with book-keeper coordinates **x**[t] seen from the vantage point of a
"free-float" or inertial frame in flat spacetime
with no geometric forces, so that the equation of motion
DU^{λ}/dτ - Γ^{λ}_{μν}U^{μ}U^{ν}
= dU^{λ}/dτ in the form "proper + geometric = observed" predicts
that the net proper-force
Σ**F**_{o} alone will be 3-vector m**α** (e.g. to moving charge q a Lorentz force like
qF^{λ}_{β}U^{β} =
qγ{**E**•**v**/c, **E**+**v**×**B**} becomes spacelike yielding a 3-vector force
q**E**' = q(**E**_{||w}+γ**E**_{⊥w}+**w**×**B**) which
is purely electrostatic), where m is
frame-invariant rest-mass and **α** is "frame-invariant" proper-acceleration (with a
traveler-defined 3-vector direction).
Then differential-aging factor γ ≡ dt/dτ =
√1+(w/c)², proper-velocity **w**
≡ d**x**/dτ = γ**v** where
coordinate-velocity **v** ≡ d**x**/dt, momentum
**p** = m**w**, kinetic energy K = (γ-1)mc^{2},
rate of energy change dK/dτ = m**α**•**w**, and
the rate of momentum change is d**p**/dτ =
m**α**+(γ-1)m**α**_{||w}.
As Tony French suggested in his classic text, coordinate-acceleration
**a** ≡ d^{2}**x**/dt^{2} is *simply* related to neither of these
latter two dynamical quantities, and so mainly serves to approximate the
proper-acceleration **α** (as measured e.g. by your phone) at low speeds.

For example in nanoscience, this generally involves synthesis, preparation of specimens for analysis, as well as the design, operation, and funding of instrumentation for finding out what you either found, or created.

Theory and practice here includes:

- theory of experimental design,
- theory and practice of data-acquisition-tool design, operation, and funding,
- material preparation of the system to be studied for analysis,

and what else?

Although general multi-slice calculations remain too slow, web-browsers on many platforms now make possible real-time single-slice (strong phase/amplitude object) simulation, with live image, diffraction, image power-spectrum, and darkfield-image modes, including specimen rotation e.g. for atomic-resolution images with specimens having several tens of thousands of atoms [9]. Moreover, a wide range of qualitative phenomena emerge that include diffraction-contrast effects associated with thickness, orientation changes, and defect strain.

Hence students with no math background can get a visceral feel for the way 2-D lattice-projections, diffraction-patterns, image power-spectra, aperture size/position, and darkfield images relate to a specimen's structure & orientation, as well as microscope contrast-transfer, well before access to a real electron microscope is available. Our JS/HTML5 platform even shows promise for the construction of procedurally-generated (in effect, arbitrarily large) worlds from the atomic-scale up, to be explored on-line.

The caveat is that we are accessing the nanoworld using simulated electron optics, which
involves unfamiliar contrast-mechanisms perhaps accessible only with help from a "physics
filter".
As a result **developing a knack** for experimental setups, e.g. to focus and astigmate
the lenses, orient the object being examined, and decide what signals to record via the
position of apertures, creates a very robust physics-rich (and realistic) challenge
for prospective nanoexplorers.
As you might imagine, these skills may prove useful in a variety of job settings for
students downstream.

[1] Stephen Wedekind and P. Fraundorf (Sept 2016) "Log complex color for visual
pattern recognition of total sound" (patent pending) *Audio Engineering Society Convention*
**141**, paper 9647 AES library
mobile-ready link.

[2] James P. Sethna (2006) **Entropy, order parameters and complexity** (Oxford U. Press,
Oxford UK) (e-book pdf).

[3] Phil C. Gregory (2005) **Bayesian logical data analysis for the physical sciences**:
*A comparative approach with Mathematica support* (Cambridge U. Press, Cambridge UK).

[4] Burnham, K. P. and Anderson D. R. (2002) **Model selection and multimodel inference**:
*A practical information-theoretic approach*, Second Edition (Springer Science, New York).

[5] Seth Lloyd (1989) "Use of mutual information to decrease entropy: Implications for
the second law of thermodynamics", *Physical Review A* **39**, 5378-5386
(link).

[6] P. Fraundorf (2017) ''Task-layer multiplicity as a measure of community health'', hal-01503096 working draft on-line discussion.

[7] cf. Charles W. Misner, Kip S. Thorne and John Archibald Wheeler (1973)
**Gravitation** (W. H. Freeman, San Francisco CA).

[8] P. Fraundorf (2017) "Traveler-point dynamics", hal-01503971 working draft on-line discussion webpage.

[9] P. Fraundorf, Stephen Wedekind, Taylor Savage and David Osborn (2016)
"Single-Slice Nanoworlds Online", *Microscopy and Microanalysis* **22**:S3, 1442-1443
Cambridge
hal-01362470
pdf
mobile-ready link.

- Melanie Lipp, Taylor Savage, David Osborn and P. Fraundorf (2017) "Laboratory evidence of slow-cooling
for carbon droplets from red-giant atmospheres",
*Microscopy and Microanalysis***23**:S3 (in press) pdf discussion. - P. Fraundorf, Melanie Lipp and Taylor Savage (2016) "Analogs for Unlayered-Graphene
Droplet-Formation in Stellar Atmospheres",
*Microscopy and Microanalysis***22**:S3, 1816-1817 Cambridge hal-01356394 pdf webpage. - Jamie Roberts, David Osborn and P. Fraundorf (2017) "Finding unstrained 10-nm lattice defects
in Si given 10^11/cc",
*Microscopy and Microanalysis***23**:S3 (in press) pdf discussion. - P. Fraundorf, Jamie Roberts and David Osborn (2017) "Exploring sub-10[nm] oxygen clusters in
Czochralski silicon" (
**59**th*MRS Electronic Materials Conference*, U. Notre Dame, South Bend IN) pdf discussion. - Jamie Roberts, P. Fraundorf, Jai Kasthuri and David Osborn (2016) "Exploring
Boltzmann-Factor Distributions of Precipitation-Nuclei in the TEM",
*Microscopy and Microanalysis***22**:S3, 942-943 Cambridge hal-01367881 pdf webpage. - P. Fraundorf (2017) "Real-time digital-darkfield TEM determination of nanocrystal 3D-lattices",
*Microscopy and Microanalysis***23**:S3 (in press) pdf discussion. - P. Fraundorf, David Osborn and Melanie Lipp (2017) "Some novel uses for three-dimensional data
from SPM and stereo SEM",
*Microscopy and Microanalysis***23**:S3 (in press) pdf discussion. - P. Fraundorf (2016) "Piecewise-continuous nanoworlds online." hal-01364382 current pdf.
- P. Fraundorf and Melanie Lipp (2016) "Molar standards & information units in the `new-SI'" hal-01381003 current pdf.
- P. Fraundorf and Melanie Lipp (2015) "A graphite-prism defintion for Avogadro's integer" arXiv:1201.5537 [physics.gen-ph].
- David Osborn, Tianna McBroom, and P. Fraundorf (2017) "Sensitivity of TEM data on lightspeed to
camera-length's voltage variation",
*Microscopy and Microanalysis***23**:S3 (in press) pdf discussion. - Tavish L. E. Hill and P. Fraundorf (2015) "A Spacetime-Constant Experiment Using Electrons",
*American Association of Physics Teachers***2015**Summer Meeting Program Book, page 57 pdf. - P. Fraundorf (2016) "The proper-force 3-vector", hal-01344268 current pdf webpage.
- P. Fraundorf (2016) "Wall clocks on a shuttle to Vega" draft pdf.
- P. Fraundorf (2016) "Moon-baseball in bullet-time" draft pdf.

This page is http://www.umsl.edu/~fraundor/playwork/obsCycle.html. This page is hosted by the Department of Physics and Astronomy (and Center for Nanoscience, formerly Molecular Electronics) at UM-StL, although P. Fraundorf is responsible for errors. Whole-site page requests est. around 2000/day hence more than 500,000/year. Requests for a "stat-counter linked subset of pages" since 4/7/2005: .