The Logical Leap: Induction in Physics

[Brant Gaede]

You confuse me by saying something confused and then dismissing it as nonsense. Maybe you mean that you admit that you cannot speak clearly, and dismiss others who cannot do so? If I have it wrong you can explain.

I didn't really dismiss it as nonsense and I dismiss nobody any more than I dismiss myself. The basic fact is that nobody has ever gotten his brain around existence in its totality except that it is the totality.

--Brant

thought I was going to get a brain medal

[Brant Gaede]

Just as if you walk straight in any direction on earth you will come back where you started after 24,000 miles,

This is twice a false statement. Please recast it into a correct one. You cannot walk straight anywhere on earth and you are assuming you start on the equator if you could or that your path will cross it.

--Brant

Edited July 21, 2010 by Brant Gaede

[kiaer.ts]

My speculations are well defined and testable. You can tell that the surface of the earth is curved by starting at a point on the equator and traveling to the north pole. When there, make a right turn, and travel back to the equator. You will now be at a point on the equator one quarter of the way around the erath. Make a right turn and return to your starting point. You will have traced out a great triangle. But at each of the three corners you will have made a 90° turn. This provides a triangle with 270 internal degrees, rather than the 180° of a flat triangle. Do the same with the universe. Travel a great distance to make a triangle and measure the angles at every turn. If the degrees add up to more than 180, then the space you have flown through is curved. Do that in multiple planes and you can directly measure the higher dimentional curvature of spacetime. The more accurately you can measue the angles, the less distance you have to travel to do the test.

We have direct visual confirmation that all distant galaxies are receding from us, and the further away the faster. We have direct visual confirmation that the furthest galaxies are more primitive in their development, as if they were from a younger universe. We can model a closed higher dimensional spacetime. Our math and our direct observation imply that the universe has been expanding from a earlier condensed state, and this explains also the uniform microwave background radiation and the observed H/He ratio. The theory predicts that spacetime is curved, and that curvature could be measured given the ability to travel far enough and measure angles accurately enough - both of which are eminantly doable if not currently practicable.

The statement that "existence has always existed" is equivocal. Always means as old as the universe, and it is hardly helpful in this debate to insist that the universe is as old as the universe. The relevant question is, is that existence finite or infinite? Since Objectivists hold that to be is to be something definite and that there are no actual infinities, the assumption of a universe infinite in time is a contradiction. There is no contradiction in the finite yet unbounded universe model, only some simple trigonometry measurements yet to be made assuming we do not permanently abandon space travel.

[Brant Gaede]

Yes, Ted, you know a lot. In fact I believe you know more than Peikoff. However you share his knowledge arrogance. You are bringing scarely more than his ignorance to the table against what Newton called the vast unknown that lay all about him on the beach filled with sand where here and there he found an interesting object to contemplate. And as you stated previously you cannot test your idea about travelling around the universe to verify your supposition.

--Brant

I do believe in the finite and unbounded universe model and so far as I know that old Big Bang!

Edited July 21, 2010 by Brant Gaede

[Ellen Stuttle]

The discussion I've seen thus far both here and on Amazon sounds as if the book is going to be disastrous for the reputation of Objectivism in whatever is left of the scientific community.

I can't see how it could help, in the natural-science community.

But how much respect did "closed-system," Peikovian Objectivism previously enjoy among genuine natural scientists (a category in which I would not include the likes of Michael Mann and Phil Jones)?

I expect the book will just be ignored by working physicists, chemists, and the like.

The "closed-system" notion, of course, wouldn't be respected by genuine scientists. But scientists, like others, have political and ethical views. The overwhelming majority of physicists I know or know of are liberal in political persuasion, and resistant to any idea of getting government funding out of science. Rand has gotten so much press attention over the last year as to arose curiosity, even amongst physicists (who often have no interest in reading philosophy). I fear that if they get a whiff of a book like Harriman's, they'll conclude that tales they've heard (e.g., from Schermer's book Why People Believe Weird Things) of Objectivism's being a pseudo-religion are true and they'll lose any nascent interest they might have had in checking further.

PS. I put "closed-system" in scare-quotes because Harriman draws heavily on post-1982 Peikovian ideas, such as Peikovian proof and the "gen" theory.

You inquired in a later post about the term "gen." As Shayne Wissler explained on Amazon, the term is just an abbreviation for "generalization." Peikoff used "gen" in his course "Induction in Physics and Philosophy" so as not to keep repeating the multi-syllabic "generalization."

The core of the "theory" is this, which I believe is a direct quote. I listened to the segment of the tape a couple times trying to get the exact wording. (I don't have the course; I heard a couple of the lectures courtesy a friend.)

A gen is no more than the perception of cause and effect conceptualized. [....] Induction is measurement omission applied to causal connection.

Ellen

[kiaer.ts]

Not at all. I am certainly certain of the positive truth of what I say. But that's not arrogance, its simple certainty. Peikoff claims only the negative knowledge that he knows that the big bang conflicts with his preconceptions. I am not interested in being accepted on authority. You can confirm what I have said above and understand it yourself with Hawking's Universe in a Nutshell and the excellent Dover text I referenced. I will answer any questions you may have. And I don't care if you believe me or not, I simply offer the explanation of what I understand. There are also matters I do not claim to understand, such as why there should be three evident macro space dimensions, and whether the number of dimensions is finite or infinite, or if the question is even well formed What I am saying is mainstream, so it really doesn't even have to be fought for - any astrophysicist worth his PhD can explain it. (Since its math, I wonder if Robert can - I expect so.) As Hitchens says, "A case has not been refuted until it has been stated at its strongest." The issue that is relevant here is that if Peikoff and Harriman want to argue against the theory I have outlined they should be able to present it clearly. As I have said, I know Peikoff can't. With Harriman I wonder.

One confusion I think I see is the notion that new space is created as the galaxies move apart. This again sounds like the absolute space model, where the universe is a puff of gas expanding to fill an empty room, converting its empty space into real space. This implied that there is some front of expanding space moving into formerly empty space. There is no such front. The expansion of the universe is more like the expansion of the surface of a balloon which stretches as you blow it up. Paint some dots evenly spread out on the balloon. As it blows up the plastic stretches, and the dots become further and further apart. The surface, space, simply "stretches." Just as the dots on the balloon do not move into a formerly unoccupied area of the balloon, the galaxies of the universe are not moving into previously unoccupied space. Rather, space is stretching equally in every direction.

[James Heaps-Nelson]

My speculations are well defined and testable. You can tell that the surface of the earth is curved by starting at a point on the equator and traveling to the north pole. When there, make a right turn, and travel back to the equator. You will now be at a point on the equator one quarter of the way around the erath. Make a right turn and return to your starting point. You will have traced out a great triangle. But at each of the three corners you will have made a 90° turn. This provides a triangle with 270 internal degrees, rather than the 180° of a flat triangle. Do the same with the universe. Travel a great distance to make a triangle and measure the angles at every turn. If the degrees add up to more than 180, then the space you have flown through is curved. Do that in multiple planes and you can directly measure the higher dimentional curvature of spacetime. The more accurately you can measue the angles, the less distance you have to travel to do the test.

We have direct visual confirmation that all distant galaxies are receding from us, and the further away the faster. We have direct visual confirmation that the furthest galaxies are more primitive in their development, as if they were from a younger universe. We can model a closed higher dimensional spacetime. Our math and our direct observation imply that the universe has been expanding from a earlier condensed state, and this explains also the uniform microwave background radiation and the observed H/He ratio. The theory predicts that spacetime is curved, and that curvature could be measured given the ability to travel far enough and measure angles accurately enough - both of which are eminantly doable if not currently practicable.

The statement that "existence has always existed" is equivocal. Always means as old as the universe, and it is hardly helpful in this debate to insist that the universe is as old as the universe. The relevant question is, is that existence finite or infinite? Since Objectivists hold that to be is to be something definite and that there are no actual infinities, the assumption of a universe infinite in time is a contradiction. There is no contradiction in the finite yet unbounded universe model, only some simple trigonometry measurements yet to be made assuming we do not permanently abandon space travel.

Ted,

The General Theory of Relativity gives the basis for curved spacetime in a generalized energy-momentum tensor. So you would have to know something about the distribution of mass and energy in the universe to know the character of the curvature of spacetime. In fact, one of the results of General Relativity is that the deflection angle of light around a massive object in space due to gravity is twice what you would expect from gravitationally bending photons with a given energy in the absence of the curvature of spacetime.

Jim

Edited July 21, 2010 by James Heaps-Nelson

[kiaer.ts]

My speculations are well defined and testable. You can tell that the surface of the earth is curved by starting at a point on the equator and traveling to the north pole. When there, make a right turn, and travel back to the equator. You will now be at a point on the equator one quarter of the way around the erath. Make a right turn and return to your starting point. You will have traced out a great triangle. But at each of the three corners you will have made a 90° turn. This provides a triangle with 270 internal degrees, rather than the 180° of a flat triangle. Do the same with the universe. Travel a great distance to make a triangle and measure the angles at every turn. If the degrees add up to more than 180, then the space you have flown through is curved. Do that in multiple planes and you can directly measure the higher dimentional curvature of spacetime. The more accurately you can measue the angles, the less distance you have to travel to do the test.

We have direct visual confirmation that all distant galaxies are receding from us, and the further away the faster. We have direct visual confirmation that the furthest galaxies are more primitive in their development, as if they were from a younger universe. We can model a closed higher dimensional spacetime. Our math and our direct observation imply that the universe has been expanding from a earlier condensed state, and this explains also the uniform microwave background radiation and the observed H/He ratio. The theory predicts that spacetime is curved, and that curvature could be measured given the ability to travel far enough and measure angles accurately enough - both of which are eminantly doable if not currently practicable.

The statement that "existence has always existed" is equivocal. Always means as old as the universe, and it is hardly helpful in this debate to insist that the universe is as old as the universe. The relevant question is, is that existence finite or infinite? Since Objectivists hold that to be is to be something definite and that there are no actual infinities, the assumption of a universe infinite in time is a contradiction. There is no contradiction in the finite yet unbounded universe model, only some simple trigonometry measurements yet to be made assuming we do not permanently abandon space travel.

Ted,

The General Theory of Relativity gives the basis for curved spacetime in a generalized energy-momentum tensor. So you would have to know something about the distribution of mass and energy in the universe to know the character of the curvature of spacetime. In fact, one of the results of General Relativity is that the deflection angle of light around a massive object in space due to gravity is twice what you would expect from gravitationally bending photons with a given energy in the absence of the curvature of spacetime.

Jim

Yes. This amounts to agreement that spacetime curvature can be measured by travelling long distances and measuring the internal angles of the triangles created.

[Brant Gaede]

The statement that "existence has always existed" is equivocal. Always means as old as the universe, and it is hardly helpful in this debate to insist that the universe is as old as the universe. The relevant question is, is that existence finite or infinite? Since Objectivists hold that to be is to be something definite and that there are no actual infinities, the assumption of a universe infinite in time is a contradiction. There is no contradiction in the finite yet unbounded universe model, only some simple trigonometry measurements yet to be made assuming we do not permanently abandon space travel.

No. Always means always. This universe doesn't mean there was no previous one. The Big Bang presuposes an infinity of previous universes and an infinity of universes to follow. I mean, how can we imagine only one--the one we're in, and not imagine infinity? Why are we so special? Infinity is the basic nature of existence, plus those sub-atomic particles, simply because there is no such thing as non-existence save for consciousness blanking out come death or whiskey. As I've said, God is existence! Existence is God!

--Brant

live on, live on!

[Brant Gaede]

One confusion I think I see is the notion that new space is created as the galaxies move apart.

I think not of new space being created but space being stretched, space being distance and/or density of things in space. This is different than the "space" the universe is expanding into. The universe is expanding into nothing. It is merely expanding. It is complete unto itself in time.

--Brant

[BaalChatzaf]

^^^

The metric tensor of the spacetime manifold is changing over time. Spacetime is not expanding into anything.

See http://en.wikipedia.org/wiki/Metric_tensor_%28general_relativity%29

Why does that bother anyone one?

Ba'al Chatzaf

Edited July 21, 2010 by BaalChatzaf

[James Heaps-Nelson]

One confusion I think I see is the notion that new space is created as the galaxies move apart.

I think not of new space being created but space being stretched, space being distance and/or density of things in space. This is different than the "space" the universe is expanding into. The universe is expanding into nothing. It is merely expanding. It is complete unto itself in time.

--Brant

Brant,

Bob K is right in post 61, you have to start thinking about things in terms of interrelated variables in tensor form rather than spatial expansion. I found a good layman's version with everything explained at a Caltech website:

http://www.black-holes.org/numrel1.html

Jim

[Brant Gaede]

Thx, Jim. I just (re)learnt the P. Theorem. Next will be how to solve without a right angle. For some reason this seems easier than when I was in high school. I know you, Ted and Bob are a lot smarter than I about these things. While I have no good reason to teach myself math at my age, I am intrigued by the thought of whether I could if I wanted to. Petr Beckmann told me that algebra was "easy," for instance. I asked him to reconsider his statement and he said that, well, there were some special forms of algebra that were difficult. I'm completely out of the league he could play in.

--Brant

onward to Einstein's equations!

more edit: I never said that space-time was expanding into anything, only that it was expanding.

Edited July 21, 2010 by Brant Gaede

[kiaer.ts]

The universe is unbounded because space is unbounded, space being nothing there is nothing to bound the universe. What we know as outer space is not the space I'm talking about; that space has things in it, radiation at least. The space I'm talking about is beyond the universe, assuming there is a beyond the universe. The 15 billion year-old light that is now reaching us also went out in the opposite direction. If 15 billion years have passed since the light started its journey that in itself is a 30 billion year light spread before you can even logically think about where empty space or non-existence begins. All this is expanding, too boot. Where is the source of that old light now?

--Brant

this ain't physics, just ignorant-intelligent blather--seriously

It was I who implied that Brant might be talking about real space expanding into empty space because of the above statement.

[Ellen Stuttle]

I received a copy of the book and, too curious to wait, started reading the first chapter ("The Foundation"). I don't rule out that Harriman might offer some insights I'll find useful. However, he's already gone off the rails questing for the unobtainable -- and furthermore declaring that the unobtainable is obtainable -- in his opening remarks.

The Logical Leap: Induction in Physics

David Harriman

With an Introduction by

Leonard Peikoff

New American Library, 20010

pp. 6-8

The central issue here is the failure of philosophers to offer a solution to what has been called "the problem of induction." Induction is the process of inferring generalizations from particular instances. The complementary process of applying generalizations to new instances is deduction. The theory of deductive reasoning was developed by Aristotle more than two millennia ago. This crucial achievement was a start toward understanding and validating knowledge, but it was only a start. Deduction presupposes induction; one cannot apply what one does not know or cannot conceive. The primary process of gaining knowledge that goes beyond perceptual data is induction. Generalization--the inference from some members of a class to all--is the essence of human cognition.

When we reason from "Men in my experience are mortal" to "All men are mortal"; or from "These fires burn me when touched" to "Fire by its nature burns"; or from "This apple and the moon obey the law of gravity" to "Every physical object in the universe obeys the law," in all such cases we are passing from one realm to another: from the observed to the unobserved; from the past behavior of nature to its future behavior; from what we discover in a narrow corner of a vast cosmos to what is true everywhere in that cosmos. This passage is the epistemological dividing line between man and animals.

Animals are perceptual-level organisms. They learn from experience, but only by highly delimited perceptual association. They cannot imagine the unobserved, the future, or the world beyond such associations. They know, deal with, and react to concretes, and only concretes. But this is not a level on which man can live and prosper. To act successfully in the present, a human being must set long-range goals and a long-range course of action; to do so, he must know the future--perhaps months ahead, often years, sometimes decades.

A generalization is a proposition that ascribes a characteristic to every member of an unlimited class, however it is positioned in space or time. In formal terms, it states: All S is P. This kind of claim, on any subject, goes beyond all possible observation.

But man is neither omniscient nor infallible. His generalizations, therefore, are not automatically correct. Thus the questions: How can man know, across the whole scale of space and time, facts that he does not and can never perceive? When and why is the inference from "some" to "all" legitimate? What is the method of valid induction that can prove the generalization to which it leads? In short, how can man determine which generalizations are true (correspond to reality), and which ones are false (contradict reality)?

The answer is crucial. If a man accepts a true generalization, his mental contents (to that extent) are consistent with one another, and his action, other things being equal, will succeed. But if a man accepts a false generalization, it introduces in his mind a contradiction with his authentic knowledge and a clash with reality, leading unavoidably to frustration and failure in his actions. Therefore the "problem of induction" is not merely a puzzle for academics--it is the problem of human survival.

The problem is to identify the method of induction, not to seek its "justification." One cannot ask for a justification of induction, any more than for a justification of deduction. Inducing and deducing are man's means of justifying anything. Their validity as cognitive processes, therefore, is an unchallengeable given. Aristotle did not ask: Is deduction legitimate? but rather: How should it be performed so as to reach valid conclusions? Similarly, our question regarding induction is not: Is it legitimate? but rather: Given the validity of induction, how should one perform it so as to reach a knowledge of facts?

[Brant Gaede]

Induction. Deduction. Whatever floats your boat. What did Maxwell use?

--Brant

[Brant Gaede]

Given "the validity of inducton" how to use it? Is THAT his book? Using induction I concluded at the age of 14 most kids my age were stupid, unthinking fools. Today they vote. Applying induction again I concluded because of them the world is always going to hell one way or another but not generally: progress has an inertia that can only be retarded, not stopped. Unfortunately, life is too short to smooth out all the bumps and necessarily enjoy a benevolent future. I'm going to spend the rest of my life watching a world-wide great depression and its aftermath. If I'm lucky some goon cops won't be breaking down my door and I won't die in stir, just in the bigger jail of my country--my country which is starting to treat its rich citizens like 1930s' German Jews respecting their property and everybody like cattle.

Even at $10.88 I think I'll skip this.

--Brant

moo! moo!

go to war; die for shit

[Ellen Stuttle]

Induction. Deduction. Whatever floats your boat. What did Maxwell use?

Genius.

Ellen

[BaalChatzaf]

Induction. Deduction. Whatever floats your boat. What did Maxwell use?

--Brant

Abduction, Induction, Deduction. Plus a mathematical grasp of Faraday's idea of the electromagnetic field. Faraday's idea of the field was pure artistic genius. By the way, Faraday did not posses a dozen lines of mathematics. His thinking was purely pictorial, but Maxwell showed that his visualizations were a new kind of mathematics, or proto-mathematics waiting to be developed fully.

Ba'al Chatzaf

[Philip Coates]

> I just (re)learnt the P. Theorem.

Brant, isn't that the one about the distance in inches of the furthest extent of the stream from your body being proportional to the product of how much you had to drink and how long ago it was?

Edited July 22, 2010 by Philip Coates

[merjet]

> I just (re)learnt the P. Theorem.

Brant, isn't that the one about the distance in inches of the furthest extent of the stream from your body being proportional to the product of how much you had to drink and how long ago it was?

It's also depends on the peer's age.

[James Heaps-Nelson]

Thx, Jim. I just (re)learnt the P. Theorem. Next will be how to solve without a right angle. For some reason this seems easier than when I was in high school. I know you, Ted and Bob are a lot smarter than I about these things. While I have no good reason to teach myself math at my age, I am intrigued by the thought of whether I could if I wanted to. Petr Beckmann told me that algebra was "easy," for instance. I asked him to reconsider his statement and he said that, well, there were some special forms of algebra that were difficult. I'm completely out of the league he could play in.

--Brant

onward to Einstein's equations!

more edit: I never said that space-time was expanding into anything, only that it was expanding.

Brant,

It's terrific when people take strides in understanding whenever they do it and at whatever level is appropriate to them. I like Csikszentmihalyi's exhortation to embrace being an amateur in certain areas. What's important is that we give our best shot to the things that interest us and be true to ourselves in selecting those interests.

Jim

[Michael Stuart Kelly]

I like Csikszentmihalyi's exhortation to embrace being an amateur in certain areas...

Jim,

As an aside, he is referenced all over the Internet marketing literature (and nobody can pronounce his name ). Getting into the flow is almost a catch-phrase in shooting for excellence and improving your performance. I looked on Wikipedia just now to jog my memory on the names of his works: Mihaly Csikszentmihalyi.

I saw a graphic on mental states in that article I thought was cool, so I decided to copy it and print it out. But when I clicked on the graphic, it took me to another Wikipedia article, which had the same graphic. I clicked on that one and was taken to another article. Then I realized, they mapped the graphic and hyperlinked the different parts so you will go to the different articles based on where you click on it. I have never seen that on Wikipedia before. That's actually kind of cool.

Here's a screenshot of the graphic I was talking about (without the hyperlinks).

Anyway, back to the discussion.

Michael

[kiaer.ts]

Mihalyi Csikszentmihalyi? Easy!

Me holly Chick sent me holly with the accent on the capitalized syllables.

[James Heaps-Nelson]

Mihalyi Csikszentmihalyi? Easy!

Me holly Chick sent me holly with the accent on the capitalized syllables.

Cool!