We should note this new work, Others in Mind  by Philippe Rochat, extending the following topics in Objectivity:

Self-Consciousness V1N2 48, 57, 59–60, V1N4 50–52, V1N5 30–35, 47–48, 83, V2N1 116–18, V2N2 48, 51, V2N6 101–2

Self-Mirror V1N2 67–75, 80, V1N3 96–97

Social Cognition V1N2 81–83, V1N5 48–49, V1N6 21–33

Child-Learning of Mind V1N6 2–11, 21–33

Personal Mind V1N2 35, 48, 51, 57, 59–63, 72, 87–88, V1N3 27, 64–65, 94, 97–99, V1N4 24, 91, V1N5 20–22, 30–34, 41, 47–49, 52, 60, V1N6 153, V2N1 116–19, 135, V2N2 35–46, V2N3 8–9, 12–13, 93, V2N4 6, 50, 214, 218, 222, 224, V2N5 107–13, 135, V2N6 12, 37–38, 101

Science, Mathematics in V1N1 5, 15, 27–28, V1N2 1, 30, V1N3 14, 39–40, 48–49, 104–5, 107–8, V1N5 13–17, V2N1 32–44, V2N2 27–28, 116–19, V2N3 52–54, V2N4 96, 105, 109, 123–27, 146, 149–57, 168, V2N5 9–10, 18–19, V2N6 131–86.

V1N1 p.28  “Capturing Concepts”

“Solids are distinguished from fluids in virtue of the fact that they have moduli of rigidity that are not (too close to) zero; any solid is capable of withstanding shearing forces up to some particular measure. The particular modulus of rigidity of a particular solid object is part of what constitutes its individual identity, and the fact that its particular modulus is not zero is what qualifies it for the class solid.”

V2N2 pp.27–28  “Space, Rotation, Relativity”

“It was Huygens who named the tendency of a body in circular motion to recede from the center the centrifugal (“flees from center”) tendency. He succeeded in quantifying the strength of this tendency; he gave us the formula of what we, after Newton, take to be centrifugal force. Imagine sitting on the edge of a merry-go-round holding a plumb bob. The bob hangs vertically initially while the merry is still, but moves outward from the hand as the speed of the merry increases. Let the speed of the merry be made constant. Huygens computed from pure kinematics that were the bob released, rather than held by a wire, it would travel outward a distance proportional to the rotation speed squared divided by the merry’s diameter and directly proportional to the time interval since release squared. This is so provided that time interval is small, and small is all we require for a formula of the instantaneous parameters of circular motion.

“Huygens knew that distance in one of Galileo’s expressions for free fall is also proportional to the square of the time interval. Huygens still thought of the tendency of bodies to fall and their centrifugal tendencies as an inherent force, or power, they exhibit in those situations. He did not yet have clearly our Newtonian concept of force as external cause acting on the body. A whirling body has a centrifugal tendency, and like the falling tendency of bodies, it yields not a uniform motion but one proportional to the duration squared, at least for short durations. So for Huygens, as for everyone after him, a body rotating at uniform speed is [classified as] undergoing an acceleration. Huygens initiated what we should now call the dynamics of circular motion, as he quantified the centrifugal tendency, by determining what rotational speed the merry would need to for the bob to have a centrifugal tendency equal to its gravity.”

V2N3 pp.53  “Space, Rotation, Relativity”

“Newton imagined a square inside of which is circumscribed a circle. Let the sides of the square be banks of a square billiards table (without pockets). Launch a ball so as to strike and rebound at a point, on each of the four banks in consecution, midway between corners; the very point at which the imaginary circle touches the square. The angles of incidence and reflection will be 45°. In making one complete circuit, Newton figured, the force that the ball exerts on the banks in reflections is to the force of the ball’s linear motion (the ball’s linear momentum) as the path length of the ball’s circuit is to the length of the circle’s radius. Newton then showed that whatever regular polygon is fitted about the circle (replacing the square about the circle), the ratio of the ball’s reflecting forces exerted in a complete circuit to the force of the ball’s linear motion is always as the circuit’s length to the circle’s radius. Then if we allow the sides of the polygon to become infinitely short and numerous, the polygon becomes the circle, and we have that the ball’s force exerted on its circular container in one revolution about that circle is 2πr/v, where r is the circle’s radius. Then the instantaneous force the ball exerts outward when in circular motion, the endeavor of the ball to flee the center, is m(v·v)/r, as Huygens had earlier found, unbeknownst to Newton at the time of his own discovery.” [Newton on planetary orbits: this.]

V1N3 p.14  “Induction on Identity”

“Inference to the existence of atoms is a case of induction in the genre of what William Whewell (1794–1866) termed the consilience-induction. By 1900 atoms and molecules were evidenced by Dalton’s law of multiple proportions, Gay-Lussac’s law pertaining to the volume of gases, Avogadro’s law (which made possible the determination of molecular weights), and the kinetic theory of gases (which could approximately predict molar heat capacities). After 1908, when Jean Baptiste Perrin published his results on the sedimentation distribution of (visible) particles suspended in a still liquid and his measurement of Avogadro’s constant, the existence of atoms could not be reasonably doubted.” [Note also.]

V2N2 pp.116–19  “Three Chances”

V2N1 pp. 32–44  “Chaos”

V2N6 131–86  “Invariance, Electrodynamics, and the Special Theory” (Available also here.)

V1N3 107–8  “The Complexion of Number” —David Ross

“Every analytic function is a solution of Laplace's differential equation, the most important equation in mathematical physics. The class of analytic functions provides an abundance of solutions to problems in steady state fluid dynamics, electromagnetic theory, elasticity, and minimal surface theory. In fluid dynamics, free boundary problems (problems in which no wall contains the fluid) and airfoil problems can be treated particularly effectively and elegantly. In all these cases, the highly structured nature of analytic functions allows us to infer a lot of qualitative and quantitative information about the behavior of these solutions. Analytic functions can also be regarded as mappings of the complex plane into itself. They are referred to as conformal mappings in this context. This geometrical interpretation aids in the construction of solutions of Laplace’s equation in geometrically complicated regions, e.g. regions with corners or holes.

“The Laplace-equation / conformal mapping techniques constitute the most striking and direct contribution of analytic function theory to mathematical physics. However, this theory has probably contributed much more in another way. Often, a problem involving functions of a real variable can be viewed as a special case of a more general problem involving complex analytic functions. This permits us to bring all that is known about the qualitative structure of analytic functions to bear on the problem. Virtually every branch of mathematical physics has benefitted from this technique.

“An example of this is the technique developed in the 1970s by Garabedian and co-workers at NYU for designing shockless transonic airfoils. When an airplane moves at a high subsonic speed (as many commercial planes do), the air accelerates past the sound speed as it crosses the wing. It is then decelerated and compressed suddenly by a standing shock wave as it leaves the wing. This deceleration causes considerable drag, which could be eliminated if the air could be decelerated smoothly. Until the early ’70s, no airfoil shapes that would decelerate air smoothly at transonic speeds were known. By extending the equation of momentum conservation to complex values and applying complex variable techniques to solve the extended equation, the NYU group was able to generate the first shockless airfoils.”

V1N2 p.30  “Philosophy of Mathematics” —Merlin Jetton

“There have been parts of mathematics developed with no knowledge of the relevance to the real world . . . . An example is Riemann's geometry. But it turned out to be essential for Einstein's geometrical theory of gravity. Another example is group theory (a kind of hyperabstract algebra). It turned out to be very useful in quantum mechanics about a hundred years later. Without group theory, the unification of the electromagnetic force and the weak nuclear force would not have been achieved.”

V1N3 pp.39–40  “Induction on Identity”

“Under the supposition that time is homogeneous, we can derive from Hamilton's principle . . . conservation of energy. The conservation of mass-energy is a very robust principle, experimentally and theoretically. . . . The conservation of mass-energy can be derived also as a consequence of Einstein's field equation and one of the geometrical identities known as Bianchi identities. . . . On the left of [Einstein’s field equation], we have geometric structure of spacetime; on the right, we have matter (stress-energy tensor), the source of the geometric structure. Bianchi identities on the left correspond to conservation of mass-energy on the right.”

V1N5 pp.13–17  “Can Art Exist without Death?” —Kathleen Touchstone (Available also here.)

V2N4 pp.123–27 and 149–57  “Mathematics and Intuition” —Kathleen Touchstone (§VII “Computational Synapses” and §XI “Neural Networks”)

~~~~~~~~~~~~~~~~~~~~~~ 

See also: “Functions of Mathematical Description in Astronomy and Optics, Illustrations from Antiquity”

I am pleased to announce the completion and installation of the comprehensive Subject Index for Objectivity.

Here is a stretch of the “L” section:

Life; of the Absolute V1N5 109; Cellular V1N5 39, V2N1 109, 111, V2N3 97, V2N4 192–93, V2N6 4–5; Colonies of V1N5 39; and Contingency V1N4 84–86, V1N5 4–7, 10–12, 36–42, 165, V2N3 7, 11, 17–18, V2N4 188–91, 194, 197–202, V2N5 162; Extension V1N5 1–3; and Growth V1N4 88–95, V1N5 6, V2N3 19, V2N4 188–89, V2N6 216; Making One’s V1N3 93–100, V2N1 112, 118–21; Meaning of V1N5 166; of Organisms V1N5 4–6, 36–39, 41, V1N6 148, V2N1 101–2, 109–10, V2N3 17–21, 97–98, V2N4 188–93, 217–19, V2N5 35, 79–80, 88–89, 100–101, 131, 138, V2N6 4–5, 20–25, 215–16, 225–26, 231; without Purpose V1N3 97–99, V1N4 82–83, 94–95, 154–55, V1N5 9, 162, V1N6 145–46, 152; Quality of V1N5 7, 26, V2N5 87, 132; and Thought V1N2 49, 63, 73, V1N3 67–68, 78, 84–86, 94–95, V1N4 16, 49, 56–57, V1N5 53–54, 101–2, 110, 162, V2N3 24–25, 102, V2N4 36, 193, 220, V2N5 35–36, 76; and Time V1N3 19, V1N5 25, V1N6 146–47; Unity in a V1N2 70–71, V1N3 98, V1N4 92–93, V1N6 138–40, 144–59, 165–70, V2N3 18–20, V2N4 216, V2N5 35 101–3, 110–11, 125–30; and Value V1N4 81–96, V1N5 4–12, 18–26, 41, V1N6 138–49, 176, V2N1 102, V2N2 87–89, V2N3 2, 4, 6–11, 17–25, 94, 100, V2N4 199–200, 208–9, 216–22, V2N5 67–91, 100–105, 110–11, 131–32, 133–35, V2N6 215–16, 229–30. See also Evolution; Reproduction.

Literature V1N2 67, 71–74, 88–90, V1N3 37, 93, 97–99, V1N4 37, 81, 83, 87–88, 94–96, V1N5 25, 95, 103, 154, V1N6 14, 153, 190, 192, 199, V2N1 72, V2N3 78, 131, V2N4 205–6, 232–33, V2N5 78, 86–87, V2N6 191–210, 213

Logic; as Art of Non-Contradictory Identification V1N2 33, V1N3 40–41; Certainty of V1N2 17, V1N3 5, 33, V1N4 26, 45–51; Formality of V1N2 21, 23–24, V1N3 4, V1N4 22–23, 33, 52–54, V2N4 227–28; and Habit V1N2 37–41, V1N3 21–32; as Ideal Reasoning V1N1 34, V1N3 34, V2N5 56, V2N6 96–98; and Intentional Objects V1N2 1–3, 10–11, 14, 21, 23–26, V1N3 49–51, V1N4 16–17, 28, V2N6 106; and Language V1N2 17, V1N3 33–34, 74–76, V1N4 8, 44–50, 56–58, V1N6 87–95, V2N4 113–16, V2N6 103–4; and Mathematics V1N2 2–6, 8–9, 15–17, 19–24, V1N3 46–47, 50, 76–77, V1N6 77, V2N4 106–8, 227; Neuronal Implementation of V1N3 34, 36; and Objectivity V1N2 33–35, V1N3 40–41, V1N4 8, 19–23, 26–28, 59, V1N5 89–91, V2N1 134; and Ontology V1N2 9, 33–35, V1N3 3–4, 12, 25–26, 30–32, 34, 44–45, V1N4 26, 33, 37, 44–45, 48–49, 51, 54–59, 63–64, 73, V1N5 109, 112–13, V2N2 67, V2N4 227–28; Origins of V1N1 24, 31–33, V1N3 20, 33–34, 95–96,  V1N4 50–52, V2N2 67–68, 80, V2N4 106, V2N6 104–10; and Probability V1N3 86–87, V1N4 26–27, V2N1 2–3, 15–17, 28; Refusal of V1N4 56–57; as Second-Intentional V1N2 21, V1N3 4, V1N4 50–52; v. Science V1N3 4, V1N4 33, 50–52, V2N4 227–28, V2N6 184–85. See also Deduction; Induction; Propositions; Contradiction; Relations, Logical; Predication; Identity; Truth, Logical; Necessity, Logical; Possibility, Logical; Value, Cognitive Truth; Knowledge.

Logical Atomism V2N4 227–33

Logical Positivism V1N5 127, 133–34, V1N6 60, 86, 92, V2N2 80, V2N4 2

Loneliness V1N2 83–84

Love V1N6 162, 169, V2N1 31, V2N4 224, V2N5 136; Romantic V1N2 68, 71–72, V2N3 29–30, V2N4 16, 208–9, V2N6 192, 194–97, 204. See also Friendship.

Click on my name right here in this thread, then select the Contact tab.

Leonid

I'm living outside of USA and cannot pay by check. Is it possible to pay by credit card? Can you supply contact numbers or e-mail address to arrange payment and mailing?

Leonid asked yesterday how one can obtain Objectivity in hardcopy. Visit this site: http://www.bomis.com/objectivity/. Click on Prices and follow the directions. Be sure to include your name and mailing address.

 All issues are still available in their original hardcopy.

Your site is excellent. I'm making my way through it bit by bit and am finding it a very helpful resource. Thankyou!

Kenny,

Thanks for adding your photo. Sorry to be so long in responding to your note. I was out of pocket a few days.

All of the articles in Objectivity are at a widely accessible level of philosophical discussion. They are as accessible as the philosophy writings of Ayn Rand. No special prior study of philosophy is required to absorb these essays and remarks.

I think the quickest way to decide what to check out in the journal is to scan down the CONTENTS sector, where subsection headings of the essays and titles of the remarks are listed. A fuller guide to what is covered in the essays is in the ABSTRACTS. When the SUBJECT INDEX is complete, you will have available a way of seeing all the topics treated in the journal and all the locations of a given topic accross the entire journal. This will be a very fine-grained conceptual index.

As you might expect, the philosophical views of the various writers on a given topic in Objectivity are different from one another. Let me tell you all a little more of the orientation of this journal.

When I created Objectivity, I had not intended to make an Objectivist journal. I had intended for it to be open to writers who wanted to discuss Rand's philosophical ideas, but the journal was open to contributions from anyone who prized rationality, objectivity, and modern science. As it worked out, a great many of the contributors were friendly to some of Rand's ideas, and they wanted to discuss them.

One thing the journal contains is science education. That is on purpose. Discussions in this journal move freely back and forth between science and philosophy. (I mean standard science, nothing kooky, nothing reactionary.) Integration between these disciplines permeates the journal.

Another educational feature of the journal is the history of philosophy. I think that is a great way to learn philosophy. Actually, I have found that the further reaches of science are also more accessible when learned in their historical development. There is some history of science in Objectivity.

I hope you will find the journal enjoyable and a resource of information and reasoning in the coming years. Keep reaching.

Oh, I almost forgot. You may have gotten the impression that there is no political philosophy in Objectivity. That is correct, and that was by design. My first degree (1971) was in physics, and I had minored in philosophy. I was a political activist for fifteen years after graduation, and I studied a great deal of social and political philosophy during those years and even up to launching this journal (1990). But I missed all the other areas of philosophy to which I had awakened back in undergraduate days. Outside academia there were plenty of magazines and journals devoted to politics, and those that started out with a more inclusive range of topics were soon overrun by the single topic of politics. So with Objectivity I created a haven, outside academia, for serious discussion of philosophy in areas not primarily social. It turned out that others had been longing for such a forum.

I will visit the site over Easter. However, I am not a philosopher and would be grateful for any additional information or guidance.