20130227

The Aging “Crisis” in Physics

The silliness of relativity and the Big Bang Theory (BBT) has been plaguing thinkers for over a century. Some consider this a “crisis” in physics. If so, this crisis is certainly quite elderly. I imagine the flat-earth and the geocentric theories also overstayed their heyday as well. Once established, traditional mythology tends to stick around—with the various religions being among the better examples. In science, however, bad theories are supposed to get the boot even before they can be published. So we ask the question: How can regressive physics survive, producing much of the remarkable results of the 20th and 21st centuries without its flawed foundations being discarded as ineffective?

This is one of the tougher questions. A proper answer would involve a lot of detailed work that surely would be worth a Ph.D. or two. I guess the short answer would be the usual one: Any theory will do. As I explained in one of my most popular blogs, “Theory Formulation,” even a grossly incorrect theory can get us out of the office, interacting with the external world. Recent exponential growth in these interactions has led to corresponding growth in data accumulation. Most of our observations and experiments have nothing whatsoever to do with relativity or the BBT. The ones that do, invariably are interpreted from the indeterministic viewpoint. All the same, the ever-widening, progressive exploration of the universe nonetheless impinges upon both theories. The one characteristic of the theories—aether denial—is being inundated by rapidly accumulating data to the contrary. Regressive physicists not looking for aether have found it anyway. This cannot be openly admitted, of course, because use of the word is grounds for academic dismissal. Physicists necessarily working under the old paradigm have learned to handle these findings adroitly, as Kemp (2012) says so well:

“Various models of the aether are being published in current scientific journals under different names: Quintessence, Higgs Field, Vacuum Expectation Value Energy, Zero Point Energy, Weakly Interacting Massive Particles (WIMPs), and Ground State Energy. All are Aether Theories at their core, each with their own twist, but Aether theories never-the-less!”

All these are signs of the aging crisis in physics, which might have been averted altogether if Einstein’s (1920) public relations slip-up had not been swept under the rug: “There is a weighty reason in favour of ether. To deny ether is to ultimately assume that empty space has no physical qualities whatever." It is not quite that simple, of course. Einstein’s corpuscular theory of light actually requires the absence of aether. Once aether is reinstated as the medium for the wave motion of light, both relativity and the BBT will be but museum curiosities. In the meantime, physics will remain retarded, spending vast sums on all sorts of dead ends that nonetheless wrest huge amounts of data from the universe. The main difference between an incorrect theory and a correct one is the efficiency with which that is accomplished.

Indeterminists, of course, would not agree that there is a “crisis in physics.” It is what was desired all along. The foundational assumptions of regressive physics and of the greater society are similar. For instance, Big Bang theorists and most folks on the planet believe in creation, in opposition to the Fifth Assumption of Science, conservation (Matter and the motion of matter can be neither created nor destroyed). Many have tried to ameliorate this by proposing mathematical singularities, parallel universes, multiverses, or other embellishments. These only serve to highlight their desperation. As scientists, they know they should believe in conservation, but they just cannot. It is an assumption after all. There can be no proof that conservation holds at all times and in all places. Besides, they have been told to avoid assumptions. Better to stick with what you believe to be empiricism. At least you won’t get fired for sticking your nose into philosophy, which mostly is defunct anyway.  

Reference

Einstein, A., 1920, Sidelights on relativity: 1. Ether and relativity. 2. Geometry and experience: London, Methuen, 56 p.

Kemp, R.L., 2012: http://superprincipia.wordpress.com/about-the-author/, February 17,  2013.








11 comments:

Westmiller said...

Glenn writes:
"... Regressive physicists not looking for aether have found it anyway ..."

There are certainly physicists who insist that light has to be a wave - which requires some kind of Aetherial Medium - but every experiment attempting to find an aether has failed. Michelson, Morley, and Miller all admitted that they could not detect the motion of Earth through an aether, no matter how it was characterized. Aether is a mystical belief that happens to be convenient in explaining some characteristics of light.

Kemp says: "Various models of the aether are being published in current scientific journals under different names: Quintessence, Higgs Field, Vacuum Expectation Value Energy, Zero Point Energy ... are Aether Theories ..."

Do you believe any of those theories are true? For example, do you believe that the Higgs Field "gives mass" to all material things, which would otherwise be massless, immaterial objects? Sounds self-contradictory to me.

"... Einstein’s (1920) one public relations slip-up ..."

There are a dozen other Einstein citations in which he says aether exists. The only reason why he created Special Relativity was to explain why aether effects could never be detected: the length of measuring sticks change in direct relation to their speed through the aether. This isn't even a good excuse for the experimental failures, since the length change can never be detected either.

However, the citation you offer from Einstein is hardly an endorsement of materialism, since it asserts that nothing must have qualities: "To deny ether is to ultimately assume that empty space has no physical qualities whatever." His General Relativity Theory is an extension of SR, asserting that space itself is "curved" by mass. I don't think you want to embrace that proposition.

"... Einstein’s corpuscular theory of light actually requires the absence of aether."

Einstein never embraced Newton's or Rutherford's corpuscular theory: he always believed light was a kinetic wave. He just had to make the wave media impossible to detect, through the mathematical gimmicks of Special Relativity.

Otherwise, I agree that the Big Bang Theory, singularities, parallel universes, multiverses, or other embellishments are logically incoherent.

Glenn Borchardt said...

Bill:

Thanks for the comment.

My response is in brackets:

“every experiment attempting to find an aether has failed. Michelson, Morley, and Miller all admitted that they could not detect the motion of Earth through an aether, no matter how it was characterized.”

[Definitely not true. MM87 tested for a fixed aether through which they wished to measure Earth’s 30 km/s motion about the Sun. That would be like trying to measure the velocity of the jet stream in your basement. Aether, like the nitrogen and oxygen of the atmosphere, is entrained. Miller33 measured up to 10 km/s on Mt. Wilson.]

“Aether is a mystical belief”

[Definitely not! Aether denial is mystical, being founded on the indeterministic assumptions of immaterialism, finity, disconnection, etc.]

“Kemp says: "Various models of the aether are being published in current scientific journals under different names: Quintessence, Higgs Field, Vacuum Expectation Value Energy, Zero Point Energy ... are Aether Theories ..."

Do you believe any of those theories are true? For example, do you believe that the Higgs Field "gives mass" to all material things, which would otherwise be massless, immaterial objects? Sounds self-contradictory to me.”

[Of course, I don’t believe any of those theories, just like I don’t believe in parallel universes. I agree that the whole Higgs thing is bogus, as I have pointed in the blog elsewhere.]

“There are a dozen other Einstein citations in which he says aether exists.”

[I could only find one. I would love to have the others. Could you please send them to me?]

“However, the citation you offer from Einstein is hardly an endorsement of materialism, since it asserts that nothing must have qualities: "To deny ether is to ultimately assume that empty space has no physical qualities whatever."”

[With this statement, he was showing his philosophical ignorance. He knows that, to be a scientist, he should be a materialist, but like many other wannabes he was really an immaterialist (e.g., immaterial “fields,” etc.). So he invented perfectly empty space that “had physical qualities,” but nevertheless contained no matter (e.g., particles) whatsoever.]

“"... Einstein’s corpuscular theory of light actually requires the absence of aether."

Einstein never embraced Newton's or Rutherford's corpuscular theory: he always believed light was a kinetic wave.”

[Einstein thought light was a photon, not a wave, and thus could travel through perfectly empty space. See my blog on wave-particle duality.]

“Otherwise, I agree that the Big Bang Theory, singularities, parallel universes, multiverses, or other embellishments are logically incoherent.”

[Agree, and they exist only because of aether denial.]

Westmiller said...

Glenn writes:
"... MM87 tested for a fixed aether ..."

Correct. From the 1887 paper: "... the displacement to be expected was 0.4 fringe. The actual displacement was certainly less than the twentieth par of this, and probably less than the fortieth part."

However, MM made a simple error: they took half of their measurements at 6pm, when the device was perpendicular to the orbital motion of Earth and could not possibly have detected any aether "friction". Those results were nearly identical to their noon measurements, when the device was parallel to orbit. Therefore, the sum results have to be regarded as null: no aether detection.

"Aether, like the nitrogen and oxygen of the atmosphere, is entrained."

Entrainment requires friction. If the Earth was "pushing away" the aether media for 4 billion years, it would now be in the same orbit as Venus: a dead planet.
"Miller33 measured up to 10 km/s on Mt. Wilson."

That's not what Miller said: "if there is any effect of the nature expected, it is not more than the hundredth part of the computed value," which would be 0.079 km/s. So, even at a much higher altitude, the effect claimed was less than MM87. Modern reviews of his data shows that this measurement was less than a tenth of the sensitivity of his equipment: less than null.

I'm a determinist and a materialist, but facts are facts.

"I could only find one [Einstein quote endorsing aether]."

A good starting point is Wikipedia's citations, with references.

Einstein thought light was a photon, not a wave ...

He described the photon as a "packet of quanta energy" with zero mass. The only way anything can have energy without inherent mass is as a kinetic wave (which requires an aether). Only later did scientists meeting in Copenhagen settle on "wave-particle duality" as a useful (rational??) compromise.

Glenn Borchardt said...

Thanks Bill. My comments are in brackets.

Glenn writes:

"... MM87 tested for a fixed aether ..."

Correct. From the 1887 paper: "... the displacement to be expected was 0.4 fringe. The actual displacement was certainly less than the twentieth par of this, and probably less than the fortieth part."

However, MM made a simple error: they took half of their measurements at 6pm, when the device was perpendicular to the orbital motion of Earth and could not possibly have detected any aether "friction". Those results were nearly identical to their noon measurements, when the device was parallel to orbit. Therefore, the sum results have to be regarded as null: no aether detection.

[Bill, thanks for pointing this out. Bryant (2008) claims that they calculated the data wrong by mistreating Wavelength as if it were Length. Otherwise, they would have gotten the expected 30 km/s. What is your opinion of this?]

"Aether, like the nitrogen and oxygen of the atmosphere, is entrained."

Entrainment requires friction. If the Earth was "pushing away" the aether media for 4 billion years, it would now be in the same orbit as Venus: a dead planet.

[No. Entrainment means just the opposite. For instance, at ground level, our atmosphere produces little friction between air and soil. Even at high elevations involving the jet stream, there has not been enough friction to slow the planet significantly. That is because the atmosphere is held gravitationally as part of Earth. In "Universal Cycle Theory: Neomechanics of the Hierarchically Infinite Universe" (Puetz and Borchardt, 2011) we propose the same for aether. Every rotating body is part of a vortex containing ever-more dense matter proximally and ever-less dense matter distally. This means, of course, that the “less dense matter” we call aether must rotate with Earth as well. Only the fixed aether of the 19th century could produce friction (relative motion) between Earth and aether. Earth cannot “push away” aether in the same way that Earth cannot “push away” the atmosphere. We envision this aether vortex as being responsible for any data that might provide a “proof” for the “curved empty space” of GRT (such as Gravity Probe B???). Uncle Al lucks out again for the wrong reason.]


"Miller33 measured up to 10 km/s on Mt. Wilson."

That's not what Miller said: "if there is any effect of the nature expected, it is not more than the hundredth part of the computed value," which would be 0.079 km/s. So, even at a much higher altitude, the effect claimed was less than MM87. Modern reviews of his data shows that this measurement was less than a tenth of the sensitivity of his equipment: less than null.

[From what I just wrote about the aether vortex, you can see that I would be inclined to agree with you and Roberts (2006). However, maximum aether measurements seem to be a square root function (r2=0.994) of elevation (TSW, p. 202) and here. I got the highest data point (6,000 ft) from Miller. These are Miller’s (1933) actual words, which he repeated in a nice summary written for the local newspaper (Miller, 1940):

"A relative motion of the earth and the ether should produce an effect which, as observed in the interferometer, would vary both in magnitude and direction as the earth rotates on its axis and as it revolves in its orbit; the effect further depends upon the latitude of the station of observation. The actual observations indicate an ether drift of ten kilometers per second which varies in a manner wholly consistent with the theoretical requirements; however, the observed velocity of the drift is smaller than had been expected, as though the ether through which the interferometer is being carried by the earth's motion was not absolutely at rest."

Thanks for the Roberts reference, though I am still puzzled by the high correlation I got for measurements at increasing elevations. If you or Roberts could explain that away, our vortex theory would be a lot happier.]

Continued ...

Glenn Borchardt said...

Continued ...

"I could only find one [Einstein quote endorsing aether]."

A good starting point is Wikipedia's citations, with references.

[Didn’t know that. Thanks for the tip.]

Einstein thought light was a photon, not a wave ...

He described the photon as a "packet of quanta energy" with zero mass. The only way anything can have energy without inherent mass is as a kinetic wave (which requires an aether). Only later did scientists meeting in Copenhagen settle on "wave-particle duality" as a useful (rational??) compromise.

[Remember that energy, much less a “packet of quanta energy,” cannot exist. It is neither matter nor motion, but a calculation describing both. I explain that in my E=mc2 paper. The term “kinetic wave” is redundant, as the word “kinetic” means motion, and all waves are the result of motion in a medium. Sorry, but the folks at Copenhagen were really not acting as “scientists,” but as politicians. The program involved keeping the gang moving on the path toward immaterialism. As I explained here, wave-particle dualism was only needed if you didn’t have an aether. Note that Freeman and Couder remain aether deniers, even though the analogy to aether is right in front of them. Freeman ends up concluding: “they are particles and waves.”]

References

Bryant, S., 2008, Revisiting the Michelson and Morley experiment to reveal an Earth orbital velocity of 30 kilometers per second ( http://www.relativitychallenge.com/papers/Bryant.CICS.MMX.Analysis.06302006.pdf ): Galilean Electrodynamics, v. 19, no. 3, p. 51-56.

Miller, D.C., 1940, The Ether-Drift Experiment (http://freespace.virgin.net/ch.thompson1/Papers/Miller40.htm), Cleveland Plain Dealer: Cleveland, OH, p. 1 & 6.


Puetz, S.J., and Borchardt, G., 2011, Universal cycle theory: Neomechanics of the hierarchically infinite universe: Denver, Outskirts Press (www.universalcycletheory.com), 626 p.

Roberts, T.J., 2006, An Explanation of Dayton Miller’s Anomalous “Ether Drift” Result (http://arxiv.org/ftp/physics/papers/0608/0608238.pdf): arXiv, p. 23.

Glenn Borchardt said...

Here is the stuff from Wikipedia on 20130301:

Einstein's views on the aether

In 1916, after Einstein completed his foundational work on general relativity, Lorentz wrote a letter to him in which he speculated that within general relativity the aether was re-introduced. In his response Einstein wrote that one can actually speak about a "new aether", but one may not speak of motion in relation to that aether. This was further elaborated by Einstein in some semi-popular articles (1918, 1920, 1924, 1930).[A 18][A 19][A 20][A 21][B 11][B 12][B 13]
In 1918 Einstein publicly alluded to that new definition for the first time.[A 18] Then, in the early 1920s, in a lecture which he was invited to give at Lorentz's university in Leiden, Einstein sought to reconcile the theory of relativity with his mentor's cherished concept of the aether. In this lecture Einstein stressed that special relativity took away the last mechanical property of Lorentz's aether: immobility. However, he continued that special relativity does not necessarily rule out the aether, because the latter can be used to give physical reality to acceleration and rotation. This concept was fully elaborated within general relativity, in which physical properties (which are partially determined by matter) are attributed to space, but no substance or state of motion can be attributed to that "aether" (aether = curved space-time).[B 13][A 19][9]
In another paper of 1924, named "Concerning the Aether", Einstein argued that Newton's absolute space, in which acceleration is absolute, is the "Aether of Mechanics". And within the electromagnetic theory of Maxwell and Lorentz one can speak of the "Aether of Electrodynamics", in which the aether possesses an absolute state of motion. As regards special relativity, also in this theory acceleration is absolute as in Newton's mechanics. However, the difference from the electromagnetic aether of Maxwell and Lorentz lies in the fact, that "because it was no longer possible to speak, in any absolute sense, of simultaneous states at different locations in the aether, the aether became, as it were, four dimensional, since there was no objective way of ordering its states by time alone.". Now the "aether of special relativity" is still "absolute", because matter is affected by the properties of the aether, but the aether is not affected by the presence of matter. This asymmetry was solved within general relativity. Einstein explained that the "aether of general relativity" is not absolute, because matter is influenced by the aether, just as matter influences the structure of the aether.[A 20]
So the only similarity of this relativistic aether concept with the classical aether models lies in the presence of physical properties in space. Therefore, as historians such as John Stachel argue, Einstein's views on the "new aether" are not in conflict with his abandonment of the aether in 1905. For, as Einstein himself pointed out, no "substance" and no state of motion can be attributed to that new aether. In addition, Einstein's use of the word "aether" found little support in the scientific community, and played no role in the continuing development of modern physics.[B 11][B 12][B 13]

Westmiller said...

Glenn writes:
"... Bryant (2008) claims that they calculated the data wrong by mistreating Wavelength as if it were Length. Otherwise, they would have gotten the expected 30 km/s. What is your opinion of this?"

I exchanged a flurry of emails with Steven Bryant regarding his work on MM87. Although I agree with Steven's noted mathematical error, I pointed out an assortment of errors in his own revisions. Ultimately, he was persuaded by my explanation of the MM87 experimental error and said he would have to revisit his analysis from scratch. With his assistance, I've written an article discussing the contradiction and the probable cause of the minute signal reported by MM, which has not yet been published.

"... our atmosphere produces little friction between air and soil.

Agreed: the atmosphere is captured in the gravity well of Earth (note that the Earth's rotation is slowed by the gravitational effects of the Moon), so any friction is miniscule. However, aether is theorized to be in a universally fixed position, totally independent of any earth motion. In order for aether to be "entrainted" (captured in the motion), Earth must "push it out of the way" in order to move in orbit (even if the aether is more dense closer to Earth), which must produce friction.

Your citation of Miller is correct, but the key words are "... the observed velocity of the drift is smaller than had been expected ...", specifically one-hundredth of the anticipated result: 0.0789 km/s.

Miller thought he found a "non-zero" result for aether drift relative to the cosmos, not earth orbit, in the direction of the constellation Dorado. Apparently, he wasn't aware of the fact that Dorado is the Southern Ecliptic Pole of Earth's orbit (think of the earth orbit as a gyroscope, with the bottom axis pointing "South"). Since there is a tiny wobble in the ecliptic, that's probably what he detected.

The tiny variation of incidental values at higher altitudes may be a result of lower or less variable temperature. However, note that MM87 asserted a larger value of 0.197 km/s at Cleveland altitude [650'] than Miller found at Mount Wilson altitude [5,712'], so it's an inverse relation, if it exists at all.

"Remember that energy, much less a 'packet of quanta energy,' cannot exist."

Agreed, but that's how Einstein described his photon. It was not a particle, it was a wave. He simply ignored the fact that his energy wave required kinetic motion in a medium. The Copenhagen Compromise may have been political, but it was just an agreement to disagree on the nature of light: it's a particle and a wave.

As the Wiki citation notes, Einstein was anxious to avoid a conflict with his friend (Lorentz), who insisted on an aether medium. So, Einstein didn't deny an aether, he simply claimed to have eliminated any mathematical need for the proposition. He did that by borrowing a frivolous ratio from Oliver Heaviside and inserting it into his Special Relativity equation, so that the aether (whether it existed or not) could never be detected.

Glenn Borchardt said...

Bill:

Thanks again for the comments.

You wrote:

“However, aether is theorized to be in a universally fixed position, totally independent of any earth motion.”

[Yes, this was the theory that MM87 was trying to test. There are other much better theories. The one I favor is that aether, like everything else, is in continual motion per the Fourth Assumption of Science, inseparability (Just as there is no motion without matter, so there is no matter without motion).]

“In order for aether to be "entrain[n]ed" (captured in the motion), Earth must "push it out of the way" in order to move in orbit (even if the aether is more dense closer to Earth), which must produce friction.”

[This doesn’t happen because the aether is the distal portion of Earth’s vortex as we explain in "Universal Cycle Theory: Neomechanics of the Hierarchically Infinite Universe."]

“Your citation of Miller is correct, but the key words are "... the observed velocity of the drift is smaller than had been expected ...", specifically one-hundredth of the anticipated result: 0.0789 km/s.”

[Reread the quote. It says “10 km/s.”]

“"Remember that energy, much less a 'packet of quanta energy,' cannot exist."

Agreed, but that's how Einstein described his photon. It was not a particle, it was a wave. He simply ignored the fact that his energy wave required kinetic motion in a medium. The Copenhagen Compromise may have been political, but it was just an agreement to disagree on the nature of light: it's a particle and a wave.

As the Wiki citation notes, Einstein was anxious to avoid a conflict with his friend (Lorentz), who insisted on an aether medium. So, Einstein didn't deny an aether, he simply claimed to have eliminated any mathematical need for the proposition. He did that by borrowing a frivolous ratio from Oliver Heaviside and inserting it into his Special Relativity equation, so that the aether (whether it existed or not) could never be detected.”

[As you point out, Einstein was thoroughly confused, just as are the folks who read and think they understand such stuff. Mechanists know that particles, corpuscles, things, microcosms or whatever you want to call them take up xyz dimensions and have location with respect to other things. Motion is what each of those microcosms do. A wave is not a thing. It is the motion of things (e.g., water, air, aether particles). If Einstein studied sound, he would have to proclaim that sound waves were “soundons.”]

Westmiller said...

I'll let our lengthy discussion stand as-is, with a few quibbles:

[... aether ... is in continual motion ...]

It's fine to say it's matter in motion, but you can't evade the questions of what matter in what motion. There is no detectible mass, nor any evidence that it has motion.

[... aether is the distal portion of Earth’s vortex ..]

Vortex theory is interesting, but this phrase implies that aether is created by Earth's motion, which is odd.

[Reread the quote. It says "10 km/s."]

That was the velocity in the direction of Dorado, not earth motion.

[As you point out, Einstein was thoroughly confused ...]

I think he was more frustrated at the failure of MM87 to detect aether. His SR was just a mathematical method of preserving an aether that couldn't be detected.

[... If Einstein studied sound, he would have to proclaim that sound waves were 'soundons.']

LOL. Probably.

Glenn Borchardt said...

Thanks again Bill,

Your comments are in quotes.

I wrote:

[... aether ... is in continual motion ...]

“It's fine to say it's matter in motion, but you can't evade the questions of what matter in what motion. There is no detectible mass, nor any evidence that it has motion.”

[Remember that perfectly empty space and perfectly solid matter are idealizations. Neither could actually exist. All things have properties in between those two ideals. That is inferred when we use The Tenth Assumption of Science, Interconnection (All things are interconnected, that is, between any two objects exist other objects that transmit matter and motion). Those “objects” and the “space” that surrounds them each have the ideal qualities we think of as perfectly empty space and perfectly solid matter. Even here, the space that we assume to be empty still has matter (aether-2?), though it must be deemed less resistant to the motion of more massive objects, such as aether-1. We determine baryonic mass by measuring its response to other things, especially in response to impacts from aether-1, as in gravitation. With The Eighth Assumption of Science, infinity (The universe is infinite, both in the microcosmic and macrocosmic directions), there is no end to the subdivision, just as Aristotle said. The upshot is that, at some point (aether-1, aether-3?), we will never be able to discover “detectible mass, nor any evidence that it has motion.” In a way, we are like the primitives who were unable to detect the mass of nitrogen and oxygen in the air that moved the leaves that surrounded them at every point.]

[... aether is the distal portion of Earth’s vortex ..]

“Vortex theory is interesting, but this phrase implies that aether is created by Earth's motion, which is odd.”

[You would need to read "Universal Cycle Theory: Neomechanics of the Hierarchically Infinite Universe," but all vortices tend to concentrate complexed matter at their centers, with the less-complexed matter being pushed outward (see the video at www.universalcycletheory.com ). There is no “creation” involved whatsoever (Re: The Fifth Assumption of Science, conservation (Matter and the motion of matter can be neither created nor destroyed)). Aether-1, like aether-2, etc. already exists. Where do you think baryonic matter comes from? Thin air? Magic? Creation from nothing?]


[Reread the quote. It says "10 km/s."]

“That was the velocity in the direction of Dorado, not earth motion.”

[Doesn’t make any difference. It there was no aether, the result would have been zero. According to DeMeo (2001), this is why Einstein was so adamant in destroying Miller’s career. After assuming that MM87 proved the absence of aether, Einstein knew that any detection of aether would mean the end of relativity and of his own career.]


[As you point out, Einstein was thoroughly confused ...]

“I think he was more frustrated at the failure of MM87 to detect aether. His SR was just a mathematical method of preserving an aether that couldn't be detected.”

[Boy! That is a new one!

Reference

DeMeo, J., 2001, Dayton Miller's ether-drift experiments: A fresh look: Infinite Energy Magazine, no. 38, p. 72-82.]

Rick Doogie said...

Thanks Bill and Glenn for a great discussion. Many interesting points.