### Module I, *Microcosmos*, *the world’s only theoretical computational database for the properties of matter*, completed!

### Module II, *Macrocosmos*, work-in-progress!

*This is the Official Home for Reciprocal System Research on the Web!*

*This is the Official Home for Reciprocal System Research on the Web!*

* *Do you have serious doubts about “modern physics”?

*Do you have serious doubts about “modern physics”?*

**Do you question the Big Bang, black holes, worm holes, the nuclear theory of the atom, Quantum Mechanics, neutron stars, quarks, degenerate matter, dark matter, dark energy, strings, curved space, the hydrogen-to-helium conversion process in stars?**

**Do you question QED, virtual particles, and the “Standard Model” of particle physics? And do you doubt the existence of the “Higgs Boson” and gravitational waves and gravitons?**

**You’ve come to the right place! The Reciprocal System replaces all of the above with**

** ***a completely unified, rational, general theory of the universe*!

*a completely unified, rational, general theory of the universe*!

## Yes, the Reciprocal System is a “Theory of Everything!”

## It is a *fully integrated axiomatic system *and* is fully quantitative and mathematical*: the Postulates are *inductively* derived from observation and experiment; the theorems are *deductively* derived from the Postulates.

## Therefore, the Reciprocal System supersedes *all* other theories–

*All* physical quantities in the Reciprocal System are expressed solely in *Space-Time* terms! See for yourself!

*All*physical quantities in the Reciprocal System are expressed solely in

*Space-Time*terms! See for yourself!

# The Reciprocal System is *verified* *scientific* *knowledge*; for the proof, see the Database!

# Scientific “Establishment”: You may keep trying to ignore the Reciprocal System, but the truth will eventually out….

Dr. Ronald W. Satz

**Policy Statement:** You could read 100 books on Quantum Mechanics and still not be able to calculate the interatomic distance, specific heat, enthalpy, entropy, thermal expansion, compressibility, and numerous other properties of elements, compounds, and mixtures. But you could with the Reciprocal System of physical theory created by scientist-engineer Dewey B. Larson and presented in his numerous books, including *The* *Structure of the Physical Universe*, *The Case Against the Nuclear Atom*,* Beyond Newton*,* New Light on Space and Time*, *Quasars and Pulsars*,* Nothing But Motion*, *The Neglected Facts of Science*, *The Universe of Motion*, *Basic Properties of Matter, *and *Beyond Space and Time.*

The Founder and Chair of the International Society of Unified Science (founded in 1971 and still going strong), Dr. Ronald W. Satz, is currently working to computerize all Reciprocal System calculations into one easy-to-use database package. Module I, Microcosmos, is now complete and ready for download; see below. Work on Module II, Macrocosmos, has begun. Dr. Satz is the author of *The Unmysterious Universe–*a primer on the Reciprocal System–and 68 papers on the theory (listed here). The book is available from Amazon.com here.

Other purported Reciprocal System Web sites allow amateurs (i.e., non-scientists, non-engineers) to post. Unfortunately these individuals lack the requisite understanding of conventional physics and the Reciprocal System to comment intelligently and thus sow confusion in the minds of many who might be interested in a new, unified, general, and valid theory of the universe. In contrast, this blog is for serious, degreed scientists and engineers *only*. Comments may be sent to Dr. Satz at transpower@aol.com. If they are of general interest, they may be included in the archived posts.

**See Dr. Satz’s Critique of Stephen Hawking’s A Brief History of Time here. **

**See Dr. Satz’s Critique of Jay Pasachoff and Alex Fillipenko’s The Cosmos: Astronomy in the New Millenium, 4th ed. here. **

**See Dr. Satz’s Critique of Nova’s Quantum Leap episode of The Fabric of the Cosmos here. **

**See Dr. Satz’s Critique of David Johnson’s The Big Questions of Philosophy here.**

**Reciprocal System Database Screen Shots
**

**Module I, Microcosmos [complete as of as of January 28, 2014 (please left click on each to zoom in)]
**

Reciprocal System Database Microcosmos Graphs listed here

**Module II, Macrocosmos [in progress, as of 05/19/2016]**

*News Flash* (05/23/2017): The paper “Theory of Stellar Structure and Evolution” is now available! This is the first *computational* treatment on this subject for the Reciprocal System! It supersedes all conventional theories.

*News Flash* (11/27/2016): The paper “Theory of Microeconomics and Macroeconomics: Larsonian Econophysics” is now available! This economics theory supersedes all others. The Federal Reserve is totally incompetent; the cumulative inflation from 1913 to 2017 is 2360%; thus the theories and methods they use must be replaced!

*News Flash* (05/19/2016): Screen shots of all layouts (except the graphics) of the Reciprocal System Database Module II, Macrocosmos, are uploaded–see above! All of Halton Arp’s associations of peculiar galaxies and quasars are now in the Database. Extensive quotations from Dewey B. Larson’s *The Universe of Motion* are included in the relevant records. Also, to date, the Database contains records of 1 universe, 94 galaxy clusters/groups, 584 galaxies, 182 star clusters, 1444 stars, 131 planets, 64 moons, 88 minor bodies (asteroids, comets, dwarf planets), 168 nebulae, 23 voids, and over 3000 links to pictures and videos from NASA.

*News Flash* (05/21/2014): Reciprocal System Database Module I, Microcosmos, is now available! Free 30 day trial; a one-time charge of $295 for 5 simultaneous users after that; free updates for life of product. To obtain the *free download link *please email transpower@aol.com; the Dropbox link changes periodically. The product is also available from Amazon.com here.

*News Flash*(05/21/2014): Reciprocal System Database Module I, Microcosmos, is now available! Free 30 day trial; a one-time charge of $295 for 5 simultaneous users after that; free updates for life of product. To obtain the*free download link*please email transpower@aol.com; the Dropbox link changes periodically. The product is also available from Amazon.com here.**Free mini-course on the Reciprocal System–this is the alternative physics you’ve been hoping for. After you’ve carefully studied these papers, you will be in a good position to purchase and utilize the Reciprocal System Database. Download these free papers now:**

**Critique of Conventional Theories**

**Space-Time**

**Microcosmos**

Proposal for a Modified Rutherford Experiment–Includes Seven Papers (and numerous references)!

Reciprocal System Periodic Table of the Elements

**Macrocosmos**

The Grand Cycle of the Universe, According to the Reciprocal System

Table I: Mass Fraction of Elements in Sun’s Photosphere

Table II: Stellar Element Energy Generation Properties

**Metaphysics**

Existents and Interactions: The New Universal Axiomatic System–An Outline

**Microeconomics and Macroeconomics: Econophysics
**

The Continuous Flow Process of the Modern Fourth-Stage Economy

**Miscellaneous**

Test Your Knowledge of the Reciprocal System!

** Seminars / Lectures / Colloquia: **For a negotiated fee with Transpower Corporation, Dr. Satz is available to give seminars or lectures, in person, or via Skype, on the Reciprocal System of theory at your university or company. You can see the quality of the work in the above free papers. A seminar or lecture will give you a great opportunity to ask all the questions you ever wanted to ask on theoretical physics! And, if you’re a college or university professor, Dr. Satz can help you design a course on the Reciprocal System! transpower@aol.com

**Revision History / Notes**:

03/07/2017: uploaded color-magnitude diagram showing the stellar evolutionary paths for stars in the Reciprocal System

01/09/2017: changed theoretical fissioning element of Sun from Th to Lu in “Theory of Unit Space-Time and Displacements from Unit Space-Time: Material and Cosmic Photons, Subatoms, and Atoms”; the Sun is approx. 46% up the Main Sequence, so by proportionality, the fissioning element would be Lu, rather than Th

2017

11/27/2016: Uploaded “Theory of Microeconomics and Macroeconomics: Larsonian Econophysics”–a complete rewrite of “Outline of Larsonian Economics”; also uploaded two economics spreadsheets

09/03/2016: Added worked real world example calculations to the “Outline of Larsonian Economics”; also added 19 references

07/31/2016: Uploaded expanded version of the “Outline of Larsonian Economics”; you could read 200 books on macroeconomics, but you will not find the true equations in those books

06/16/2016: The alleged “gravitational waves” which have been “detected” from the merging of two “black holes” are actually fluxes of massless, chargeless electrons and positrons from the merging of two white dwarf cores.

06/05/2016: Uploaded new paper “Habitable Planets and Alien Civilizations in the Reciprocal System”

05/07/2016: Dr. Rainer Huck, host for the August 2016 ISUS Convention, has decided to temporarily postpone the convention, due to personal business; come back to this spot periodically to see what the new date will be.

04/04/2016: Uploaded first nine layouts for *The Reciprocal System: Macrocosmos Database*; data for the universe as a whole, and that for individual galaxy clusters, galaxies, star clusters, stars, planets, and moons have all been entered, as well as some Reciprocal System astrophysical calculations have all been entered; the user can “drill down” and “drill up” through all the celestial bodies

2016

12/29/2015: Revised calculation of second gravitational limit in “Calculation of the Gravitational Limits and Hubble Constant for the Local Group”

12/15/2015: Dr. Satz’s paper “The Case Against Modern Physics” is published in the Nov./Dec. 2015 issue of *Integra*, the journal of Intertel, the top 1% society.

08/05/2015: Added Appendix C to “Calculation of the Gravitational Limits and Hubble Constant for the Local Group” to calculate the time span spent by the Local Group between the two gravitational limits; this appendix also discusses the space and time limits to matter in our sector of the universe

07/22/2015: Added Appendix B to “Calculation of the Gravitational Limits and Hubble Constant for the Local Group” to calculate the jerk of the “universe”

06/14/2015: Uploaded list of *The Reciprocal System: Macrocosmos* References

01/24/2015: Announcement–Dr. Rainer Huck and Dr. Ronald W. Satz are planning an ISUS Conference for August 19, 20, 21 2016 in Salt Lake City. (Yes, *2016*, not 2015). Huck will be celebrating his 70th birthday, and Satz will be celebrating his 65th! Satz will come in a week earlier to provide free training and coaching for anyone who has purchased *The Reciprocal System: Microcosmos Database,* and will assist Rainer in his experimental work. Satz will also provide a work-in-progress report on the *Macrocosmos Database*. Huck will report on his experimental work in the Reciprocal System. Other attendees may give papers, as well, but it would be appreciated if they follow the same format as that used in Satz’s papers. Conference details will be forthcoming later.

**2015**

05/21/2014: Module I, Microcosmos, is now available!!!

01/28/2014: completed fields, layouts, and overall design of the Reciprocal System Database, Module I, Microcosmos, and began beta testing!

**2014**

11/16/2013: uploaded first draft of “Theory of Unit Space-Time and Displacements from Unit Space-Time: Material and Cosmic Photons, Subatoms, and Atoms”; this completes Dr. Satz’s papers on the microcosmos (for the time being)–now all of this material must be put into the Microcosmos Database

10/10/2013: uploaded first draft of “Motion of the Sun in the Milky Way Galaxy”

10/05/2013: added appendix to the Hubble calculation paper giving the acceleration of “the universe”

08/11/2013: uploaded final two fluid properties layouts; will now work on developing all of the graphs

07/27/2013: uploaded revised Reciprocal System Database layouts, including the first three fluid properties layouts

04/04/2013: update of 07/04/2012–rather than just one, two “Higgs bosons” have been discovered, with masses given as 123.5 GeV = 132.583 u and 126.6 GeV = 135.911 u. These particles are therefore most likely Cs- 133 and Cs-136. Cs-133 is stable in our environment, Cs-136 is not. In Reciprocal System terminology, Cs-133 has 23 isotopic charges and Cs-136 has 26 isotopic charges. Prediction: because there are many isotopes of Cs, there could be many more supposed “Higgs bosons” to be “found.”

03/14/2013: completed and uploaded first draft of “The Case Against Modern Physics”

01/17/2013: completed and uploaded first draft of “Space-Time Dimensions and Natural Unit Values of Physical Quantities”

**2013**

11/18/2012: completed and uploaded first draft of “Theory of Liquids, Vapors, and Gases”

08/22/2012: took a break from physics and compiled/annotated/uploaded an outline of Larson’s economic work

07/23/2012: completed over 100 runs of the two capacitor experiment, with the Rigol 1102E oscilloscope on the second capacitor and the Fluke 289 digital multimeter on the first capacitor, and also vice versa, and also using capacitors of different capacitances and with capacitor two having lower capacitance than the first, and vice versa; in *all* cases, the conventional theory value for the voltage of capacitor two is considerably *too low*, whereas the Reciprocal System value is considerably *nearer* the measured value. Note: it’s necessary to measure the* maximum voltage* and set the Rigol for *peak detection*, particulary for the case where capacitor two has higher capacitance than capacitor one. This experiment proves energy conservation (as would be expected!) and disproves the conventional theory that “charge conservation” is applicable here.

07/14/2012: uploaded jpg of the database screen for spectra and ionization energies calculations; the calculation of the possible set of time region spectral quantum numbers (n1 and n2) and time-space region spectral quantum numbers (m1 and m2) works very well!

07/04/2012: 125 GeV = 124.25 amu, and so all that CERN did is obtain the energy *equivalent* of Cs (with 25 isotopic charges); they didn’t discover some new “boson”; and please keep in mind: matter can be *changed* to energy and energy can be* changed* to matter, but matter does not *contain* the conversion energy as such, nor does energy *contain* the conversion mass as such

06/19/2012: finished experiments with capacitors and concluded that the capacitance is s^{3}/t for all types; therefore revised the circuit section in “Theory of Dielectrics, Diamagnets, Paramagnets, and Ferromagnets”

06/10/2012: uploaded third revision of “Theory of the Capacitor”–this implements the note on 06/09/2012; before updating the “Theory of Dielectrics, Diamagnets, Paramagnets, and Ferromagets” we will wait for experimental work with vacuum capacitors

06/09/2012: uploaded “Capacitor Theory Update”–it now seems evident that capacitance actually has the dimensions s^{3}/t, not simply s; the dimensions of permittivity, s^{2}/t, must be included!

05/16/2012: The equations in “Theory of the Capacitor” apply to *ordinary* capacitors, not to *electrolytic* capacitors. These latter have conductive electrolytes (ions); the Reciprocal System equations for this type of capacitor are in “Electrolytic Capacitor Equations”–in the Free Papers to Download section above. Update: this has been superceded by the notes on 06/09/2012-06/10/2012

05/06/2012: completed first draft of “Theory of Atomic Spectra and Ionization Energies”

04/28/2012: Xi_b, a newly discovered particle, can be quite clearly identified as c-H^{2} with four material isotopic charges. Its mass is m = 1862.95/1 + 4 x 931.478 = 5588.862 MeV/c^{2}. It then naturally decays to c-H^{2} with two material isotopic charges. In the Reciprocal System, each subatom (whether material or cosmic) is a rotating photon; each atom (whether material or cosmic) is a combination of two rotating photons. It is this rotation (when sufficient) which causes gravitation. There are no quarks and no Higgs boson.

02/22/2012: finished data base work on isotopes and uploaded the current data base layouts; will now begin work on the spectra calculations!

02/01/2012: completed first draft of “Theory of Subatomic and Atomic Masses and Half-Lives”

**2012**

12/11/2011: uploaded section 1 of “Theory of Subatomic and Atomic Masses and Half-Lives”

11/12/2011: uploaded jpg of the database screen for electric and magnetic calculations; all equations and data from the *Mathcad/Excel* work have been successfully transferred to the Reciprocal System Database (written in *Filemaker Developer*); this completes the work on the electric and magnetic properties of matter (at least for the time being)

10/31/2011: uploaded second draft of “Theory of Dielectrics, Diamagnets, Paramagnets, and Ferromagnets, including Calculation of Electric and Magnetic Susceptibilities”; corrected various typos.

10/01/2011: uploaded first draft of “Theory of Fast Neutrinos”–this provides the theoretical explanation of faster than light neutrinos observed in the recently-reported CERN experiment

09/22/2011: Members of ISUS are often asked how Einstein’s theories relate to the Reciprocal System. Answer: the Reciprocal System is in agreement with *some* of Einstein’s concepts and rejects others. Specifically, the Reciprocal System accepts Einstein’s criticism of the “ether”, his criticism of Quantum Mechanics, his famous equation E=mc^{2}, his work on Brownian motion and the photoelectric effect, his Principle of Equivalence between inertial and gravitational mass, and the Lorentz equations (although we place all the variation on time, not both space and time). However, the Reciprocal System rejects the notions that all motion is *purely* relative, that mass increases with velocity, and that space is curved. This latter concept is as faulty as would be the idea of curved time. The deflection of a photon near a massive body, like the sun, is often used as support for curved space, but Larson has a much better explanation (*The Neglected Facts of Science*, p. 36):

“The photon has no mass, and therefore no gravitational motion toward a massive aggregate, a star, for instance. But the gravitational motion of the star is distributed scalar motion, and this scalar motion of the star toward the photon (AB) is inherently nothing more than a decrease in the distance between the objects. It can equally well appear in the reference system as a motion of the photon toward the star (BA). On the basis of probability, the total motion is divided between the two alternatives. The total motion of the star toward the photon is distributed among so many mass units that the motion of each is unobservable, but the photon is a single unit, and it is deflected a small, but measurable, amount toward the star.”

09/11/2011: completed first draft of “Theory of Dielectrics, Diamagnets, Paramagnets, and Ferromagnets, including Calculation of Electric and Magnetic Susceptibilities”–this paper is a 303 page *Mathcad* document (saved as a PDF), with 150 equations, 42 figures, and 8 tables; Quantum Mechanics is now dead. (Oh, and if you’re wondering how the Reciprocal System explains the famous “two-slit experiment,” here’s how: each photon (a linear vibration) goes through *one* and *only one* slit. Each slit perturbs each photon passing through so that the photon moves *from* its original progressing space unit *to* *another* progressing space unit–and these are *distributed* over all vectorial directions. This then causes, of course, the interference of the photons coming from the two slits which is seen on the target screen.)

08/11/2011: uploaded first *six* sections of “Theory of Dielectrics, Diamagnets, Paramagnets, and Ferromagnets, including Calculation of Electric and Magnetic Susceptibilities”–see above

07/12/2011: uploaded first *five* sections of “Theory of Dielectrics, Diamagnets, Paramagnets, and Ferromagnets, including Calculation of Electric and Magnetic Susceptibilities”–see above

05/25/2011: Dr. Rainer Huck (Salt Lake City, UT) has agreed, in a telephone conversation with Dr. Satz, to conduct the capacitor experiments as proposed by Dr. Satz. The Reciprocal System says that the energy stored in an ordinary capacitor is directly proportional to the voltage (1/2 x C x V x conv_const), whereas conventional theory says the energy stored is proportional to the square of the voltage (1/2 x C x V^2). Dr. Huck says, “But please be patient–this will take some time….” The conv_const = 4.9412 if C is in farads, V is in volts, and E is in joules.

05/15/2011: uploaded first *four* sections of “Theory of Dielectrics, Diamagnets, Paramagnets, and Ferromagnets, including Calculation of Electric and Magnetic Susceptibilities”–see above

03/23/2011: uploaded first *three* sections of “Theory of Dielectrics, Diamagnets, Paramagnets, and Ferromagnets, including Calculation of Electric and Magnetic Susceptibilities”–see above

01/18/2011: uploaded PDF of Figure 17 of *The Unmysterious Universe*–the Grand Cycle of the Universe; still working on the calculation of electric and magnetic susceptibilities and studying the atomic and molecular beam experiments; note: conventional physics says that these experiments reveal underlying atomic or molecular electric and magnetic moments, whereas the Reciprocal System says that the fields *induce* electric and magnetic charges in the atoms or molecules!

01/04/2011: uploaded PDF of seven papers describing the proposal for a crucial experiment

**2011**

11/13/2010: uploaded metaphysics paper; still studying Von Hippel’s works

08/17/2010: still working on the paper listed below; the works of Van Vleck, Von Hippel, Bhatnagar, Stoner, and Selwood have been very helpful in understanding conventional theory, as well as the experimental data–these authors, from the 1930’s, 1940’s, and 1950’s, are much less dogmatic than more contemporary authors and actually express doubt about the validity of various aspects of Quantum Mechanics!

04/08/2010: start of work on first draft of “Theory of Dielectrics, Diamagnets, Paramagnets, and Ferromagnets, including Calculation of Electric and Magnetic Susceptibilities”–this will take many months to complete; in the meantime, ponder this: the conventional time constants for electric circuits include RC and sqr(LC), where R = resistance, C = capacitance, L = inductance–but in the Reciprocal System the correct time constants are RC/V and sqr(LC/V), where V = the appropriate voltage; hence we now have another crucial test! Of course, L/R is OK…

02/21/2010: completion of first draft of “Theory of Thermoelectricity, Thermomagnetism, and Thermal Resistivity”

01/10/2010: completion of third draft of “Theory of Electrical Resistivity”; start of first draft of “Theory of Thermoelectricity, Thermomagnetism, and Thermal Resistivity”

**2010**

12/20/2009: addition of figure captions and section numbers, correction of resistivity calculation for boron, and elimination of typos in “Theory of Electrical Resistivity”

11/24/2009: publication here of the first comprehensive Reciprocal System treatment of electrical resistivity for metallic and semiconductor elements and compounds and alloys

08/26/2009: derivation of first, accurate, complete equation for electrical resistivity of the 73 known elemental conductors; proceeding to work on insulators and semiconductors; will not add display until all electrical and thermoelectric properties are calculated for elements and compounds and alloys

04/21/2009: addition of mean forces on unit cell faces to compressibility display

02/07/2009: completion of valence calculations of the elements and over 1000 inorganic and organic compounds!

**2009 **

07/28/2008: launch of data base, with displays and calculations for interatomic distance calculation, specific heat, energy/entropy, thermal expansion, and compressibility!

** Other Work: **Dr. Satz is the author of numerous commercial software packages for scientists, engineers, and managers; visit www.transpowercorp.com for the details. He is also the author of one other book,

*Theory and Design of the New Rational Combustion Engine*, his doctoral dissertation. This work is 459 pages long and has 800 equations, 30 tables, 17 figures, and 28 engineering drawings. It is available from Amazon.com here. Satz’s paper summarizing this book is “The Solution to the Gas Turbine Temperature Problem,” published in Vol. 20, pp. 49-63 of the

*International Journal of Energy Conversion and Management*. You may purchase this paper from Elsevier here. Dr. Satz is also a Professional Registered Parliamentarian.

**Membership in ISUS, Inc.: ** Membership is open to all scientists and engineers and others who agree to the Bylaws (which can be found online) and who do* not* work on competing theoretical paradigms. To join, please send a declaration of agreement to our Bylaws and your email address to transpower@aol.com. There are currently no dues.

**Acknowledgements:** This research is funded by Transpower Corporation, a commercial and custom software manufacturing and certified systems engineering company. Please visit www.transpowercorp.com to see all of Transpower Corporation’s products. Unlike our competitors in conventional theoretical physics, we do *not* run to the government for handouts. The free papers available here may be reprinted elsewhere *provided that nothing is changed and full attribution is made*. These papers are peer-reviewed, voluntarily, by the world-wide Reciprocal System community; any error found in the logical and mathematical derivations from the Postulates of the Reciprocal System will be corrected as soon as feasible. Dr. Satz is listed in *American Men and Women of Science, Marquis Who’s Who in Engineering and Science, Marquis Who’s Who in Finance and Industry, Marquis Who’s Who in America, and Marquis Who’s Who in the World*. He is available for consultation in science and engineering at Transpower Corporation’s regular rates. Donations may be made through www.paypal.com to transpower@aol.com; the contributions will go to Transpower Corporation’s overhead expense, not to salaries.

**A Tribute to Dewey B. Larson: **Great thanks, of course, go to Dewey B. Larson (1898-1990), the originator of the Reciprocal System. Dr. Satz was extremely fortunate to have him as his theoretical physics mentor from 1965 to 1990; to Satz, he was, by far, the most intelligent and most logical of any individual he (Satz) has ever known. Other testimonials here.

**Online Version of Dewey B. Larson’s Books–in Scribd Format:**

*The Case Against the Nuclear Atom* here

*Beyond Newton* here

*New Light on Space and Time* here

*Quasars and Pulsars *here

*Nothing But Motion* here

*The Neglected Facts of Science *here

*The Universe of Motion* here

*Basic Properties of Matter* here

________________________________________________________________________________________

**YouTube Videos:**

*From Dewey B. Larson:*

On the Development of the Reciprocal System here

*From Ronald W. Satz:*

The Case Against Modern Physics, *Part I* here *and Part II* here

The Space-Time Dimensions and Natural Unit Values of Physical Quantities, *Part I here *and *Part II* here

The Theory of Unit Space-Time and Displacements from Unit Space-Time: Material and Cosmic Photons, Subatoms, and Atoms, *Part I* here * Part II* here * Part III* here * Part IV* here * Part V* here * and Part VI* here

________________________________________________________________________________________

**All Rights Reserved**.

* Ringleaders for the Reciprocal System, from left to right: Robin Sims, Ronald W. Satz, Dewey B. Larson, Rainer F. Huck *