My review of The Logical Leap.

Mike,

In "Chapter 4: Newton's Integration" under the subhead "The Development of Dynamics" on page 123 (ppb), discussing Torricelli, Harriman ignored Empedocles of Akragas whose experiments with the "klepshydra" (water thief), a kitchen utensil of antiquity, demonstrated that air is a substance with weight, in support of the atomic theory of matter.

I'll have to read more on Empedocles but my guess is that he was left out because of being so much more mystical than scientific. For instance, he believed that Love is what brings (all) things together.

Even beyond that (and that's already bad enough), he believed that earth, air, and water were all just one thing (and fire was another thing) -- so that his conceptual intent cannot be differentiated when he uses the words:

1) earth
2) air
3) water

... because, for him, they are all essentially the same thing.

At that same place, Harriman likens a water pump to a lever: "... the weight of the air will lift that same weight of water per unit surface area)." But that is not how a lever works at all.

That bugged me, too. If you press down on one kind of a lever, something goes up (whatever the lever is attached to). If you pull up on another kind of a lever, something goes up. An example of the first kind of lever is your tricep muscle, which pulls up on your elbow to lower your forearm. An example of the second kind of lever is your bicep muscle, which pulls up on your forearm to raise your forearm.

In either case, the force required to move the forearm is not equal -- but much greater than the weight of your forearm -- because levers change the proportionate force required to move the same object. I don't yet know why Harriman likened a water pump to a lever.

Ed

Post 21

Friday, November 19, 2010 - 6:24pm

Mechanical advantage.

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

"
A fundamental feature of hydraulic systems is the ability to apply force or torque multiplication in an easy way, independent of the distance between the input and output, without the need for mechanical gears or levers, either by altering the effective areas in two connected cylinders or the effective displacement (cc/rev) between a pump and motor. In normal cases, hydraulic ratios are combined with a mechanical force or torque ratio for optimum machine designs such as boom movements and trackdrives for an excavator.
"

Post 22

Saturday, November 20, 2010 - 7:10am

Harriman's analogy with a lever is not very good. You could say that the weight of the atmosphere pushes down on the water and the water transmits that force (through pressure) to the water in the tube. If the top of the tube is closed, then the weight of the atmosphere can't push down on the top of the column of water, so there is a net upward force that equals the weight of the column of water. (See a picture of a barometer here and replace the mercury with water.)

So, the water can be said to transmit the force from the surface of the water to the column of water. But there's no mechanical advantage as you would have with a lever; it's just the weight of a column of air, going all the way up to the "top" of the atmosphere, holding up a column of water 34 ft high with the same weight.

Thanks,
Glenn

(Edited by Glenn Fletcher on 11/20, 7:12am)

Post 23

Saturday, November 20, 2010 - 8:21am

Ed: The story of Empedocles and the klepshydra is debatable, I admit. My objection stands: Harriman relies on an unnamed collective called "the Greeks" to ignore evidence that contradicts his claims. As for the mystical beliefs of the time, it is (first) important not to project ourselves on the past and (second) to recognize that Sir Isaac Newton's religious writings vastly eclipsed his scientific publications.  Newton was an Arian and devoted hard thought and scholarship to arguing against Trinitarianism -- and he commited perjury about his beliefs in order gain his professorship. Imagine if Immanuel Kant or Rene Descartes were guilty of either of those.

Mike: Thanks for the reply. Yes, all machines work on an exchange of actions in different dimensions. Conservation of energy must be held, but energy is the ability to do work; work is force through a distance; work over time is called power. The wheel, pulley, wedge, inclined plane, lever, and pool all allow those exchanges. In a sense, you drive a thumb tack by the same laws that apply to hydraulics: a force over a large area is transfered to a small area: 2 pounds over 1/100 of a square inch is 200 lbs per sq, in. but you lose the distance traveled.  Nowhere is Harriman so conceptually clear about the physical principles involved.

Glenn: Thanks. Yes, I did not see any mechanical advantage in the weight of the air pushing down on the liquid to move the same weight upward. As Mike pointed out, there is a wider viewpoint there that Harriman did not make explicit.

I think that the root of the problem is that his audience is not well defined.  Who is Harriman's audience? Physicists? Philosophers? Objectivists? The average educated reader? Harriman uses the analogy of the hydraulic pump to the lever with no essential standard for that choice. Ed didn't get it. I assumed conservation of energy would show the link, but it was not explicit in my mind, either. In this example, as in others I will write about later, Harriman fails to make his case, or fails to make it well.

I do want to go on record that I found the book valuable because it was stimulating. Most of what Harriman suggests seemed right enough that I followed his arguments and benefited thereby.

(Edited by Michael E. Marotta on 11/20, 8:26am)

Post 24

Tuesday, November 23, 2010 - 1:28pm

I don't know why this reminded me of this, but it did.

Things we know should not work, that in fact don't work, but at first glance almost seem like they might work, but at second glance...

1] Build a tower 1000 feet deep and 10 feet wide out of steel plate.

2] Sink it in the Gulf of Mexico, in 990 feet of water.

3] Seal the bottom, pump it out.

4] At the bottom, there is a 12" diameter precision machined pipe, an opening, lined with a precision Teflon seal.

5] It is 'plugged' with a 12" diameter plastic ball, a float.

6] The float is one of 2000 such floats on a continuous chain. It is flexible, like those bathtub plug chains.

7] The chain is on a pulley wheels/guides that carries the chain over the top of the tower, and at the bottom, guides the chain through the machined Teflon seal/opening. Depending on the lower seal design, maybe there are 3 or 4 or even more floats in the seal at any one time. But the net pressure breakdown is effectively across a single float with full pressure on one side and near atmospheric on the other.

8] On the water side of the chain, a bouyant force of nearly 1000 floats is pulling up on the single float that is sealing the pipe at the bottom.

9] On the inside/airside, a 1000 floats are hanging from the upper pulley with negligible bouyancy, but whos weight balances the weight of the bouys on the water side. The net motive difference is the difference in bouyancy of 1000 floats, minus the hydrostatic force acting on the single float in the seal..

10] There is a hydrostatic force on the single float being pulled out of the 12" seal by the chain of 12 inch floats, equal to the pressure at depth times the area of that one ball. On one side is near atmospheric. The water pressure pushes the seal float in, but the 1000 floats outside pull the seal flout out. Which will 'win,' if any?

Is the bouyant force of the thousand floats pulling up enough to pop the single float out of the seal, assuming minimal friction in the seal?

If not, would building a 2000 ft deep tower, and doubling the amount of floats pulling upward and outward against just that single float, help any? 4000 ft?

Then, would building an underwater system of pulleys, so that the floats could serpentine(ie, several angled courses of floats, not just one vertical tower of floats, help?

Suppose the 2000 foot long chain of floats actually does net rotate, but not in the direction we'd like (out). Can we still generate net power from the moving chain?

Maybe....if we could figure out how to pass the float from outside to inside without admitting any water that we would need to keep pumping out of the tower...we'll work on that one.

Now, if we painted the tower 'green', and went to Congress, could we talk them into funding this anyway?

We could give it the old college try...using OPM, anyway.

(Edited by Fred Bartlett on 11/23, 1:35pm)

Post 25

Wednesday, November 24, 2010 - 8:20am

Fred,

If you replace the discrete balls by a continuous, flexible solid tube, then it's easy to show that there is no net motion of the tube for any values of the depth, area of tube, or density of the tube material. The pressure at the bottom of the tank pushing the tube up into the tank just cancels out the buoyant force on the tube outside the tank, in the water. You wouldn't get much water leaking into the tank, but you also wouldn't get any motion of the tube. :)

I haven't thought about the discrete case, but I have a feeling that it would be a perpetual motion machine, which won't work.
Thanks,
Glenn

Post 26

Friday, November 26, 2010 - 4:23am

I am not clear on what David Harriman means by an elastic collision on page 166 (ppb) "Chapter 5 The Atomic Theory"; subhead "The Kinetic Theory of Gases." Would that not be an inelastic collision?

Elastic collisions have considerable (ponderable; measurable; consequential) deformation of the bodies. It is the difference between a tennis ball and a billiard ball. There is always elastic deformation -- we have high speed photographs of golf balls and baseballs at the instant of impact -- but like relativity on the baseball diamond, elastic deformation it is not consequential on the billiard table. So, does elasticity apply to this example?

(BTW, yes, it is a standard homework problem from conceptual physics where given Planck's equation, you calculate the wavelength of that 100 mph high heat from the pitcher's mound.)

Post 27

Friday, November 26, 2010 - 5:43am

Regarding elastic and inelastic collisions:
http://en.wikipedia.org/wiki/Elastic_collision

Post 28

Friday, November 26, 2010 - 4:14pm

Got it, Merlin! Thanks!

Post 29

Tuesday, November 30, 2010 - 6:32am

I finished the first read and I am halfway through the second, working against my notes. Thanks, again, Merlin for pointing me to the Wikipedia article on elastic collisions. Clearly, I did not understand the meaning, confusing "elastic" with "deforming." However, if I had known, I would have marked an earlier passage on page 127 ppb where Harriman discusses Newton's methods for determining conservation of momentum. Harriman says that Newton tried all kinds of balls, metal, cork, even tightly wound wool and found that his theory applied to both elastic and inelastic collisions. As I now understand it, those inelastic collisions would not have been explorated via the swinging pendula, unless (perhaps) Harriman also intended "elastic" to mean "deforming" as with the woolen balls.

As for Empedocles, Harriman cannot be expected to cite every wisp of ancient wisdom. However, he does deal with "the Greeks" broadly as an unnamed collective. I found that uninsightful. Except for minor gems such as the poems of Archilocus; or Aristotle's "Athenian Constitution" -- both alluded to, but lost; and then recently discovered -- everything we have from the Pre-Socratics comes from one compendium assembled by Hermann Diels and Walther Kranz, published in 1903. Die Fragmente der Vorsokratiker. The work is so authoritative, that modern writers still refer to these fragments by their DK Number. (The book was translated into English, and then with ancilla by hellenist Kathleen Freeman. You can find these as Pre-Socratic Philosophers and Ancilla to the pre-Socratic philosophers: a complete translation of the fragment in Diels, Fragmente der Vorsokratiker both by Kathleen Freeman.)

Here is what we have on Empedocles.

Introduction-this is the way all things breathe in and out.
'In all [animals] there are tubes of flesh, empty of blood, stretched all over the
surface of the body, and over their openings the outermost surface of the skin
is pierced through with close-packed holes, so that the blood is hidden but a
free passage is cut through for the air by these holes.'
When the blood rushes
away
from them, the air rushes in
with a mad gush. .
and when the blood runs back the air breathes out.
It is like what happens when a girl plays with a clepsydra.
When she closes the vent at the top and dips the clepsydra into the water, no
water enters; it is prevented by 'the weight of air falling on the many holes'
of the strainer at the bottom..
until she unblocks the compressed [air-]stream; then, as the air leaves,
the due quantity of water enters.
In the same way, when there is water in the clepsydra and the vent at the top
is closed by the hand, air pressure from the outside,
exerted upwards on the strainer at the bottom, holds in the water ...
until she lets go with her hand; then in turn, the opposite happens-as air
enters [through the vent at the top] the due amount of water flows out.
In the same way, when the blood in the body 'rushes back again to the inmost
part' a stream of air enters .
and when it runs back again an equal stream [of air] breathes
out again.

Post 30

Thursday, December 2, 2010 - 7:57am

Hi, Mike.
In all of the cases of different materials colliding, Newton found that momentum was conserved, which confirmed his theory that the colliding objects exerted equal and opposite forces on each other (his 3rd law). And, in all cases the objects colliding were deformed in the collision. However, in the elastic collisions, most of the energy lost in the deformation of the objects was recovered because of the elastic properties of the objects. Metal is very elastic, while cork and wool are not. So, the metal objects underwent elastic collisions, in which most of the energy was recovered and reconverted into kinetic energy (like the energy stored in a spring), while the others didn't (some kinetic energy was lost).
Thanks,
Glenn

Post 31

Thursday, December 2, 2010 - 2:45pm

Glenn, funny you should mention it. I completed my second read of the book against my original notes. When I came to this, again, I went to my standard reference, University Physics by Sears and Zemansky, 2nd ed., 1955.

Harriman Page 126. �[Newton] deduced from F = ma that the inertial mass of a pendulum bob is proportional to its weight multiplied by the period squared (assuming the length of the pendulum is held constant.)�

I = (T²mgl)/4(pi)² (Sears & Zemanski, 2^nd ed .) page 204 Equation 11-14)

Actually, then, the length can change because l is a variable and the constant of proportionality is
only 4(pi)².

Harriman page 127 �elastic versus inelastic.� Paragraph 4: �� he deliberately varied the mass of the bobs and thereby proved that his law applied to both elastic and inelastic collisions.�

Sears and Zemansky sec 8-3 (pp 148-151). In a perfectly inelastic collision the two bodies stick together, their kinetic energies before and after are not conserved, (though momentum is conserved) and the difference lost is converted to heat. I beleive that Newton measured nothing of this with his pendulums, but I have some books here, including a couple of Principias and the Westfal biography, so let me check.

(Edited by Michael E. Marotta on 12/02, 2:50pm)

Post 32

Friday, December 3, 2010 - 5:43am

Michael,
Harriman didn't say on page 127: "he deliberately varied the mass of the bobs and thereby proved that his law applied to both elastic and inelastic collisions". He said: "he deliberately varied the hardness of the bobs and thereby proved that his law applied to both elastic and inelastic collisions". Hardness is related to the elastic properties of a material. That's why he was investigating both elastic and inelastic collisions.
Thanks,
Glenn

Post 33

Friday, December 3, 2010 - 6:54am

Michael,
In the equation you wrote in post #31, "I" is the moment of inertia which, for a mass on the end of a string (a simple pendulum), is I = m l² . So, if we solve for the mass, m, we get:

m = wT²/ (4 pi²l), which says that the mass is proportional to the product of the weight times the square of the period if the length l is held constant. This is what Harriman used and I think it's correct.

I've been through Harriman's book a couple of times and, even though I haven't checked everything carefully, I didn't find any problems with the physics that he explains. There may be questions about the historical accuracy of some of the things he claims, as McCaskey has argued, but I think the physics is correct.

Thanks,

Glenn

Post 34

Friday, December 3, 2010 - 8:17am

I believe Isaac Newton's experimenting would have been more fun if he had varied the hardness of the boobs. :-)
(Edited by Merlin Jetton on 12/03, 8:18am)

Post 35

Saturday, December 4, 2010 - 8:21am

Or their mass ...

Saturday, December 4, 2010 - 6:20pm