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Objectivism And The Principia

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In the past I have studied indepth the Philosophiae Naturalis Principia Mathemitica, (Sir Isaac Newton's Mathematical Principles of Natural Philosophy). His mathematical notation was quite bulky compared to the modern notation but it was very interesting converting it to the modern. Lately I have been studying the philosophy of Objectivism and was taken back by how well the two meshed. Following Newton's Axions (Laws of Motion) to their logical ends seem to have helped me much later with the foundation of Objectivism.

Anyone else see the similarity?

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In the past I have studied indepth the Philosophiae Naturalis Principia Mathemitica, (Sir Isaac Newton's Mathematical Principles of Natural Philosophy).  His mathematical notation was quite bulky compared to the modern notation but it  was very interesting converting it to the modern.  Lately I have been studying the philosophy of Objectivism and was taken back by how well the two meshed.  Following Newton's Axions (Laws of Motion) to their logical ends seem to have helped me much later with the foundation of Objectivism.

Anyone else see the similarity?

I too have studied the Principia in depth, and I fail to see the connection of Newton's mathematical presentation to the foundations of Objectivism. Perhaps you could be more explicit and identify clearly one or two of these connections you have made.

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i'm double majoring in math and economics. while i have not read The Principia by Newton...i understand where you are coming from. since i began studying objectivism and logic ...doing calculus proofs is a WHOLE lot easier. its nice to understand the concept behind the mechanical...

and not have a blank stare on my face like half the class.

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i'm double majoring in math and economics. while i have not read The Principia by Newton...i understand where you are coming from. since i began studying objectivism and logic ...doing calculus proofs is a WHOLE lot easier. its nice to understand the concept behind the mechanical...

and not have a blank stare on my face like half the class.

Well, yes, having a proper philosophy and using proper logic tends to make everything more understandable. :P

But OldGrayBob said that following Newton's laws of motion to their logical ends helped him with the foundation of Objectivism. I would still like to understand the sense in which that is meant, especially with an example or two.

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The best example I can think of is Newtons (Second?) Law: every action has an equal and opposite reaction.

Isn't this the law of causality stated in other words?

In fact I have this pet theory that all sciences can be translated into one another via math or philosophy. And I have often seen the logic of Ayn Rand's philosophy translated into other sciences. Some quick examples:

A is A is equivalent to A = A is equivalent to 1=1 which also helps me to understand that mass is energy via e=mc^2

In economics; aren't the laws of supply and demand equivalent to the law of causality?

Can't the laws of evolution be explained using a driving force from vibrations (engineering) and the laws of probability?

As I learned from engineering: all energetic systems can be translated into one another and in fact share the same formulas. Whether mass-velocity, voltage-current, pressure-flow ... they are all equivalent.

And I don't think these equivalencies are only intradisciplinary, I theorize that these relationships are interdisciplinary and can unite all the sciences.

Only a hypothesis at this point so hammer softly.

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The best example I can think of is Newtons (Second?) Law: every action has an equal and opposite reaction.

Isn't this the law of causality stated in other words?

I was after some direct connection with a bit more substance, something more profoundly connected to what was claimed, namely the "foundation of Objectivism." Of course the laws of physics, or, for that matter, all of reality, is bound by the law of causality. Watching a cat batting around a ball of yarn is also a demonstration of the law of causality. The issue was, specifically, how following Newton's laws of motion to their logical ends helped OldGrayBob with the foundation of Objectivism, as he claimed. Hopefully OldGrayBob will tell us, before we all become gray. :P

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In fact I have this pet theory that all sciences can be translated into one another via math or philosophy. And I have often seen the logic of Ayn Rand's philosophy translated into other sciences. Some quick examples:

A is A is equivalent to A = A ...

No. A = A is not the equivalent of the law of identity. Identity is not equality.

... is equivalent to 1=1 which also helps me to understand that mass is energy via e=mc^2
But mass is not energy; it is mass, and energy is energy. The law of identity is not the same as putting things on different sides of a formulaic equal sign.

In economics; aren't the laws of supply and demand equivalent to the law of causality?

All action is governed by the law of causality. Is everything then equivalent to everything else?

Can't the laws of evolution be explained using a driving force from vibrations (engineering) and the laws of probability?

As I learned from engineering: all energetic systems can be translated into one another and in fact share the same formulas. Whether mass-velocity, voltage-current, pressure-flow ... they are all equivalent.

That different physical dynamic processes can be described (to some degree) by certain forms of differential equations does not make the physical processes equivalent.

And I don't think these equivalencies are only intradisciplinary, I theorize that these relationships are interdisciplinary and can unite all the sciences.

There are unifying principles that cut across many scientific disciplines, but these are primarily abstract mathematical principles, such as symmetries. Noether's theorem, for instance, is how we get conserved quantities from symmetries of physical laws. [Noether's theorem, by the way, is due to a woman who was an heroic figure in mathematics and physics, at a time (early 1900s) when women were not exactly welcomed in those fields. Emmy Noether made some absolutely brilliant insights.]

Only a hypothesis at this point so hammer softly.

I really like the way you said this. I tried to use a rubber mallet rather than a steel hammer. :P

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Thank you for your reply Stephen. I have taken note of your soft touch in other posts and I respect your style.

I agree with you and will defer to you on most things scientific (though I do have a specific question which I will pose at the end of this post) and for this reason I am having a difficult time formulating a response. I think our differences may only be a matter of perspective.

To me the “foundations of Objectivism” are: reality, reason, and axiomatic truths. These things are so fundamental that they are manifest, as you indicate, in all science and reality itself and we can see them in action even when a cat bats around a ball of yarn. But that these simple truths can be observed (and even understood to some degree) by any 7 year old seems very profound to me indeed. That these truths are denied by a large proportion of adults too seems significant.

What I was trying to convey in my last post, albeit sloppily and inexactly (I may need to withhold hypotheses until they are more fully formed), is not that everything is equivalent but rather that everything is interconnected and that underlying this interconnectedness are the laws that govern reality as expressed by axiomatic truths; discoverable and learned only by reason. Not that evolution is equivalent to vibrations, but that since everything is interconnected on a basic level, perhaps we can help explain how evolution could occur using the laws that govern vibrations and probability.

I’m not sure how most people come to recognize and accept axiomatic truths but for me it wasn’t by first studying philosophy. We all must accept them in order to live and learn as rational human beings but for many people this is blind acceptance. It is a much more profound breakthrough to recognize your usage of these truths and their application in nearly every field of endeavor. In my case the recognition of the axioms of reality was made much easier by my knowledge of Newton’s Laws. To me it was a beautifully elegant, rational revelation to see philosophy related to physics on such a fundamental level.

I try to be conscious of this when teaching algebra, because I remember some of those breakthrough moments coming in algebra class. Algebra, to me, is almost the first course in deductive logic. To say: if A=B and B=C, then A=C; is so rudimentary and common sensical that many laugh it off. But to apply this same logic in a math class to figure out what X is; and to see light bulbs of recognition appear over student’s heads, to me, is profound.

------------------------------

Now, Stephen, for my specific scientific question, the topic of which I have devoted much thought. I thought I had this question conquered until your last reply, now I’m in a quandary. I thought the basic building block of mass was energy, that all mass is condensed energy. That what occurs in thermonuclear reactions is the conversion of mass to energy according to e=mc^2. That if the Universe (or bubble) in which we exist started out as pure energy, then all the matter (mass) around us is some condensed form of that energy which cannot be created or destroyed. (Note: I recall that you have expressed some reservations about the “Big Bang” so perhaps this is where my faulty notion lies).

This question is basic to my understanding of the Universe so any light you could shed on it or any source you could refer me would be greatly appreciated.

Thanks,

Marc Kroeger

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Marc, I'm only going to comment on the scientific question you raised.

I thought the basic building block of mass was energy, that all mass is condensed energy. That what occurs in thermonuclear reactions is the conversion of mass to energy according to e=mc^2.

This is a very misunderstood subject, taught rather poorly in beginning physics courses and texts. In relativity the mass of a particle is an invariant quantity, an intrinsic property of the particle. Being an invariant means that it is not a frame-dependent quantity, i.e., it is measured to be the same in all inertial reference frames. By contrast, energy is a frame-dependent quantity, and its value varies depending on measurements made in differing frames that are in relative motion. Technically, mass is the norm of a particle's 4-momentum, and as such is an invariant.

Now, e=mc^2 is not the proper equation to use because it only applies when there is no momentum. The governing relativistic equation is E^2 = (mc^2)^2 + (pc)^2, which reduces to the simpler form when the momentum, p, is zero. In the thermonuclear reaction we are looking at an entire system, and it is the change in the binding energy that is converted into kinetic energy of any fragments. The total energy and momentum of the system has not changed, so neither has the mass in the relativistic formula I gave above.

It is true that any nucleus mass is now smaller in summing the mass of the fragments, but there was a change in mass because there was a release of energy; there was no "conversion of mass to energy according to e=mc^2." In other words, the system mass changed as a consequence of the energy release; the change in system mass did not cause the energy release.

That if the Universe (or bubble) in which we exist started out as pure energy, then all the matter (mass) around us is some condensed form of that energy which cannot be created or destroyed. (Note: I recall that you have expressed some reservations about the “Big Bang” so perhaps this is where my faulty notion lies).

It is true that I do not accept the Big Bang cosmology, but the problem here is even simpler: this business about the universe starting out as pure energy is just some arbitrary speculation that has little to no meaning.

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  • 2 weeks later...

Stephen,

I'm a little disappointed that you found nothing in the first part of my last reply on which to comment.

Do you agree or disagree? Am I on the right track? Did you consider everything I wrote to be completely outrageous or so rudamentarily self evident that it didn't require or warrant consideration?

I'm not trying to needle you, I'm sure you have better things to do. I'm just curious as to whether you consider my ideas baseless, self evident, simple or fallacious.

Also, I'm still confused on the energy/mass conversion:

If "the system mass changed as a consequence of the energy release", then doesn't that necessarily mean that some mass was changed to energy? I'm having trouble with the distinction.

If a system has a certain mass to start with and subsequently energy is either released or binding energy is increased and the resulting mass is less, then wasn't mass converted to energy? Where did that mass go?

I guess this also means my assertion that "mass is condensed energy" is completely off-the-wall?

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Stephen,

I'm a little disappointed that you found nothing in the first part of my last reply on which to comment.

I'm sorry, Marc, but nothing personal. I already commented in my earlier post and did not want to pursue it further.

Also, I'm still confused on the energy/mass conversion:

If "the system mass changed as a consequence of the energy release", then doesn't that necessarily mean that some mass was changed to energy? I'm having trouble with the distinction.

If a system has a certain mass to start with and subsequently energy is either released or binding energy is increased and the resulting mass is less, then wasn't mass converted to energy? Where did that mass go?

The mass of a system is not the sum of the masses of each of its components. In relativity, mass is not additive, just like angles are not additive, as in tan(x + y) is not equal to tan(x) + tan(y). It becomes a property of the system. The invariant mass of a particle makes a lot of sense in many contexts of physics, but so does the system property. So, change the system and you change the system mass. Asking where it went is a little like asking "Where did my lap go when I stood up."

You really have to study relativity to see how these notions are justified. The popularizations do not give it justice.

I guess this also means my assertion that "mass is condensed energy" is completely off-the-wall?

You will not get an argument about that from me. :lol:

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