The Sackur-Tetrode Equation

May 18, 2015 Martin K. Jones Leave a comment

The Sackur-Tetrode Equation expresses the entropy of a monatomic classical ideal gas. Including quantum aspects of the system gives this formula a more detailed description than it would have otherwise. Above I’ve tried to represent the four uncertainties that constitute the equation in its information theoretic version: positional, momenta, quantum, and identity.

From Wikipedia:

In addition to using the thermodynamic perspective of entropy the tools of information theory can be used to provide an information perspective of entropy. The physical chemist Arieh Ben-Naim rederived the Sackur–Tetrode equation for entropy in terms of information theory, and in doing so he tied in well known concepts from modern physics. He showed the equation to consist of the sum of four entropies (missing information) due to positional uncertainty, momenta uncertainty, the quantum mechanical uncertainty principle and the indistinguishability of the particles.

http://en.wikipedia.org/wiki/Sackur%E2%80%93Tetrode_equation

http://en.wikipedia.org/wiki/Entropy_%28information_theory%29

[*9.4]

fourfolds, Philosophy

Four Philosophies

May 14, 2015 Martin K. Jones 3 Comments

If one could divide all philosophies into four groups, what would those groups be? There doesn’t seem to be a strong consensus on how to do this although several have tried.

My first inclination is to start with the Archic Philosophers, discussed by Robert McKeon and his students Walter Watson and David Dilworth. These would be the Sophists, Plato, Democritus, and Aristotle. Philosophies aren’t usally divided in this way, but pros of doing this is that all four groups emerge from classical Greek thought. One of the main cons is that many would not agree that all philosophies are decendents of these four philosophers, or even combinations of aspects from each.

Another student of McKeon, Robert S. Brumbaugh, thought the process philosophies starting from those of Heraclitus and Anaxagoras (both pre-Socratic) and ranging through Whitehead should be represented instead of the Sophists. Otherwise he choose the same three as McKeon, giving Anaxagorean, Platonic, Democritean, and Aristotelian philosophies. By doing this he can form the double dual of Materialist-Formalist (direction) and Holoscopic-Meroscopic (method).

Anaxagoras: Materialist, Holoscopic
Platonic: Formalist, Holoscopic
Democritean: Materialist, Meroscopic
Aristotelian: Formalist, Meroscopic

Two works older than Brumbaugh’s that divide philosophy into the same four groups are those of Ralph Barton Perry and James Donald Butler. Their division is Naturalism, Idealism, Pragmatism, and Realism. I believe that the Realism in these books means Platonic Realism, instead of the more recent Scientific Realism thought of today. Of course Realism has many shadings as seen below.

It might be advantageous to consider Naturalism as a group instead of Realism, since the very concept of the real has so much disagreement. Naturalism does too, but not the extent that Realism does.

Several web sites divide four philosophies of eduction into Idealism, Realism, Pragmatism, and Existentialism. To me, Existentialism is similar to the Relativism of the Sophists. But what about Phenomenalism? Is that more like Relativism or Idealism?

There is also the monumental work “The Sociology of Philosophies” by Randall Collins but I haven’t examined it yet. I suspect they are not condensed or simplified into four groups.

So for now I’ve settled on Relativism, Idealism, Pragmatism, and Naturalism.

http://en.wikipedia.org/wiki/List_of_philosophies

Walter Watson / The Architectonics of Meaning: Foundations of the New Pluralism

David Dilworth / Philosophy in World Perspective: A Comparative Hermeneutic of the Major Theories

Robert S. Brumbaugh / Western Philosophic Systems and Their Cyclic Transformations

Ralph Barton Perry /Present Philosophical Tendencies: a critical survey of naturalism, idealism, pragmatism, and realism together with a synopsis of the philosophy of William James

James Donald Butler /Four Philosophies and Their Practice in Education and Religion

Randall Collins / The Sociology of Philosophies: a global theory of intellectual change

[*8.138, *8.151, *8.152]

alchemy, fourfolds

The Fourfold Democritus

May 4, 2015 Martin K. Jones Leave a comment

Old Democritus under a tree,
Sittes on a stone with booke on knee;
About him hang there many features,
Of Cattes Dogges, and such-like creatures,
Of which he makes Anatomy,
The seat of black choler to see.
Over his head appears the skye,
And Saturne Lord of Melancholy.

— From Robert Burton’s Anatomy of Melancholy

Truth lies at the bottom of a well.

— Democritus

References:

Christoph Luthy / The Fourfold Democritus on the Stage of Early Modern Science
Isis, Vol. 91, No. 3 (Sep., 2000), pp. 443-479
The University of Chicago Press on behalf of The History of Science Society
http://www.jstor.org/stable/237904

http://www.gutenberg.org/files/10800/10800-h/10800-h.htm