The Reference Frame

Friday, June 15, 2012
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George Musser's occult musings on Erik Verlinde's entropic gravity

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Among the editors of Scientific American whose names I can recognize, George Musser is the most reasonable one.

The relevance of this babe will be clarified below.

Nevertheless, I still find his reasoning and approach to questions to be largely incompatible with the scientific discourse. He has just started a new SciAm blog named Critical Opalescence and dedicated the first article to Erik Verlinde's entropic gravity and related (and unrelated) efforts to transform everything we think about gravity and cosmology:
Is Dark Matter a Glimpse of a Deeper Level of Reality?
Just to remind you, Erik Verlinde conjectured two years ago that the gravitational force results from the desire of the system to reduce its entropy. However, gravity cannot be entropic because entropic forces inevitably lead to irreversible behavior (while the distance between the Earth and the Sun oscillates back and forth) and the interference patterns would be broken if there were very many microstates whose number depends on the distance, a point that was independently made by Archil Kobakhidze of Melbourne.

Erik Verlinde has said many other things in recent years. Many of them seem unrelated to the (wrong) claim about gravity's being an entropic force. He wants to return to some (medieval) steady state cosmology, reject the existence of dark matter as well as dark energy, but there is no paper about these topics that would make sense and that would offer an alternative explanation of the relevant cosmological observations.

But I want to discuss Musser's article – and why I consider his general framework to evaluate science pretty much unsatisfactory. He's a fine guy, don't get me wrong; I just think that he's not trying to solve problems in the scientist's way. We hear that two years ago, he exchanged lots of e-mails about Verlinde's divine inspirations. How did he feel about it?
I don’t think I’ve ever been so flummoxed by physicists’ reactions to a paper. Mathematically it could hardly have been simpler—the level of middle-school algebra for the most part. Logically and physically, it was a head-hurter. I couldn’t decide whether it was profound or trite.
In these sentences, you may see that Musser is trying to reach conclusions by looking at other people's reactions. He has never been similarly "flummoxed" because he isn't terribly experienced, not even in his "sociological" approach to science. What we're talking about in this context is a physicist who has done nontrivial contributions to physics in his life but at some moment, he loses his mind and becomes obsessed with ideas that demonstrably don't make any sense. And maybe, some time later, he realizes why these ideas are preposterous but because he has already received tens of millions of dollars for that idea, he doesn't find enough integrity to admit that the ideas were wrong and worthless from the beginning.

For the former reason, namely Verlinde's previous contributions, many physicists try to be even more polite than they are when they talk about other pseudoscientists; still, the latter reason makes it clear that the fair treatment of this proposal should match the treatment of any other pseudoscientist who claims to have superseded Einstein and others. This tension between the emperor's nice clothes from the past and the emperor's new kind of clothes (the naked ones) is making the physicists react in bizarre way and journalists may be flummoxed.

But it's surely not the first time when the physicists had to deal with such a transition of their colleague. Gerard 't Hooft was arguably the Ayatollah of theoretical physics some decades ago, his contributions have been priceless, and he's still incredibly bright. But at some moment, he jumped on the research of things that didn't make sense – I am specifically talking about the totally meaningless attempts to reformulate quantum mechanics as deterministic hydrodynamics – and if he's dedicating his intellectual life to this stuff for a decade, one should perhaps notice that the current 't Hooft is someone else than the previous one. Gerard 't Hooft remains a great name but that can't prevent us from seeing that most of his writings in the recent 10 years have been pure BS.

I could give you a dozen of other examples although none of them would be as prominent as that of Gerard 't Hooft. So this is a situation that theoretical physicists know rather well; Musser was only flummoxed because he is an outsider. But he continues:
The theorists we consulted said they couldn’t follow it, which we took as a polite way of saying that their colleague had gone off the deep end. Some physics bloggers came out and called Verlinde a crackpot.

For those who know Verlinde, that label hardly fits.
The last sentence above suggests that the claim that Verlinde's work on entropic gravity is worthless crap is somewhat correlated with the question whether one knows Verlinde in person or not. But in science, it's not correlated and it mustn't be correlated. If a theory disagrees with the experiment, then it's wrong. This simple statement is the key to science. It doesn't matter how beautiful the guess is, how smart the author is, what his name is – if it disagrees with the observations, it's just wrong. Go to 0:40-1:00 to hear these basic principles of science in the audio form.

I know Erik Verlinde rather well, in person, and so do most of the people who have politely suggested that he has gone off the deep end. And I am actively aware of lots of his nontrivial previous work (having co-discovered some of it), and so are the other folks. But this personal familiarity can't have any impact on our ability to realize that the paper doesn't agree with the experimentally known physics of gravity. Science is or must be meritocracy, not nepotism. Maybe a better term for the nepotist science that Musser implicitly suggests could be "crony science".

Let me accuse George Musser of misunderstanding this basic point by demagogically suggesting that the criticism of Verlinde's claims arises because people don't know the author. Quite on the contrary, it's mostly the people who know him well who realize that the paper is bunk; many of the people who are true outsiders are ready to be impressed by the paper. Musser's suggestions are upside down.

Also, Musser says:
He is a brilliant theorist, and the amount of discussion his paper provoked suggested that most of his colleagues saw something in it.
This is just a bizarre way of arguing. The first sentence is an ad hominem appraisal that simply isn't tolerable in science. One may be used to claiming that someone is brilliant but if this person looks at the brilliant person's particular paper that self-evidently fails to be brilliant – it's actually stupid – he must adjust his opinions about the paper according to the most complete observations.

Concerning the claim that "most colleagues saw something in it", it's a bizarre claim, too. First, I don't know how Musser decided that the people who see something in the paper represent a "majority". I accuse Musser of making this "fact" up – it's the kind of activism-journalism, making claims up that are probably wrong but that can't be easily verified, in order to distort the readers' opinions in a specific direction – and perhaps even push other people towards an agreement with this would-be majority.

I am not aware of any truly serious theorists who have written followup papers on that proposal – and only two or three "marginal" examples. There's no evidence that the proposal works – and no evidence that competent people think that it works.

Musser tells us that he met Verlinde, Verlinde has doubled his bets, and the attitude of experts hasn't changed.
One told me: “There are a lot of ideas he’s bringing together in an interesting way, but it’s a little hard for us to decipher, so I’m withholding judgment.” All he has really done, though, is take a general sentiment among string theorists and follow it to its logical conclusion.
The quote is very, very polite, indeed, although the point of the quote isn't hard to decipher. I am very doubtful whether similarly excessively polite appraisals are constructive. As far as I can say, the modern world is drowning in kilotons of superstitions and bad science that became widespread partly because certain people whose job was partially to separate the weeds from the crap have been polite and failed in this job of theirs.

The last sentence – one by Musser – is simply incorrect. There is nothing in string theory that would indicate that gravity is an entropic force. Quite on the contrary, the entropy of various configurations – such as a pair of nearby cold heavy orbiting neutron stars – may be explicitly calculated in string theory and the entropy (or at least the contribution that would depend on the distance) is zero.

Holography doesn't imply that the entropy of gravitating objects depends on the distance, not even vaguely or spiritually.

The general holographic insights imply that the event horizons (and therefore black holes) carry the Bekenstein-Hawking entropy; this fact may be applied to distant cosmic horizons as well so the bulk dynamics may be encoded by degrees of freedom on the surface. But none of these things suggests that a pair of neutron stars carries a huge entropy that would depend on the distance. If we use a holographic description of the system associated with a distant holographic screen, the maximum entropy or the number of degrees of freedom will depend on the geometry of the distant screen, not on internal details such as the distance between the neutron stars.

And indeed, one may also present proofs that are independent of string theory and that imply that a distance-dependent entropy of such a binary star would lead to inconsistencies with the basic observed properties of gravity. To summarize, the claim that the entropic gravity follows from – or has anything to do with – string theory is simply a lie. No such relationship exists.

Musser rightfully says that it's hard to reconcile GR and QM; some intuition has to be modified; spacetime is probably emergent, and so on. However, saying that "spacetime is emergent" is something totally different than saying that "a pair of neutron stars carries a huge distance-dependent entropy" (or that "there is no dark matter", among other things). There is a lot of processes that take place in the vacuum (virtual particles appearing and disappearing – but one may use different descriptions of the same thing). The vacuum is "composite" and has a complicated structure. It knows about everything that can be created in it. But none of these insights changes the fact that the entropy of the vacuum has to be strictly zero. The vacuum state must be a unique quantum mechanical state in the Hilbert space. If the entropy were nonzero, the entropy_density/flux four-vector would pick a privileged reference frame in the spacetime. That would conflict with the special theory of relativity.

One may similarly prove that one can't get huge entropy differences for neutron stars at different distances. If the entropy would be much higher for one distance than another distance, it would only be possible to increase (or decrease) the distance; the other motion would violate the second law of thermodynamics. This is the simplest way to see that the distance-dependent entropy is just wrong. It's not deep or mysterious or a topic for discussions that should last for decades, it's a trivial question that can and should be answered in a few seconds. Verlinde's claims are just wrong regardless of his name. A competent physicist must be able to see so.

Needless to say, Musser – and Verlinde himself – doesn't actually discuss any physical experiments or thoughts experiments that are relevant for the question whether gravity could be an entropic force. Of course that the conclusion from many of them is No, it cannot.

They don't discuss irreversibility and any other thermal phenomena even though the conjectured relevance of thermodynamics (due to entropy, a key concept of thermodynamics) is what this idea claims to be all about; they don't discuss neutron interference in gravitational fields or any other inherently quantum phenomena even though Verlinde's claims are presented as ramifications of holography and holography vitally depends on quantum mechanics. They have an agenda, to promote the idea that Verlinde's ideas are important and one must at least pay lip service to them, if not accept them. But they're wrong and they're not important and serious physicists no longer waste a minute with thinking about what Erik Verlinde may have wanted to say in 2010. It was just wrong.

Erik Verlinde has also said many weird things about cosmology. Inflation is bad, much like dark energy and dark matter; steady state cosmology and some unspecified version of MOND that is mysteriously connected with the entropic gravity – well, as far as I can see, only by the person who emits both kinds of fog – are supposed to be cherished. But there isn't even a paper on these cosmological things – not even a manifestly wrong paper such as the 2010 paper on entropic gravity – so a scientist simply can't say anything here.

Musser also exposes us some psychology of the dark matter denial.
They have never detected the material directly, though, and for something that is supposed to be so overwhelmingly dominant, dark matter has a puzzlingly subtle effect. The anomalous motions occur only in the unfashionable outskirts of galaxies. Stars and gas clouds out there move faster than they should, but don’t do anything truly wacky—it is as if the gravitational field of the visible galaxy were simply being amplified.
The first sentence is just bullshit. Dark matter's strength of (non-gravitational) interactions doesn't have to be fundamentally any weaker than the same quantity for neutrinos, particles whose reality is very clear to us. It's just normal that in physics, different types of objects display very different degrees of visibility, by many – often dozens of – orders of magnitude. Dark matter must be heavier than neutrinos which is why it's harder to produce it in the lab today but once you produce it, there's no reason to think that its interactions should be dramatically weaker than those of neutrinos.

But even if the interactions had to be even weaker for a theory of dark matter to be compatible with all the data, it wouldn't mean any problem. Quantities in fundamental physics simply span many orders of magnitude. There's absolutely nothing wrong about the situation in which the dominant component of the matter is very weakly interacting. Any feeling that it's wrong is just a layman's feeling or prejudice, something that science simply can't pay attention to. The dark matter theory can't be ruled out by similar pseudo-arguments and the detailed theories aren't even unnatural in the technical sense so there's just no justification for complaints here.

The whining that the anomalous effects only occur in the outskirts of galaxies is irrational, too. This is an observational fact – Newton's laws without extra matter work OK for the Solar System and slightly longer distances which are still much shorter than the galactic radius but they start to break down at the galactic scale – and dark matter, MOND, or any other theory that would try to explain these facts simply has to agree. Much like dark matter, MOND also shows its muscles in the outskirts of the galaxy – when modifying the forces between objects whose distance is comparable to the galactic radius. You may declare this property "unnatural" but it's nevertheless a property that has been observed in Nature so the right adjective is surely "natural". It should better be natural in a correct theory of Nature, too. And good enough models of dark matter indeed make all these patterns technically natural!

One must also object to Musser's claim that it's mysterious why the matter in the outskirts isn't doing weirder things than just those that you expect from amplified gravity. There's nothing mysterious in physics (physics including dark matter or physics that is independent of dark matter) about this fact. The reason behind this fact is that electromagnetism and gravity are known to be the only two long-range forces in Nature and electromagnetism drops down more quickly for very long distances because the charge is neutralized and the residual forces follow a more quickly decreasing power law. So it's guaranteed that the very long-distance effects of any new object or any new term in the laws must be explainable by a (modified) gravitational field. Musser's attempt to use this well-understood fact against dark matter is totally illogical and wrong.

Musser's description is a mixture of layman's prejudices, half-truths, and downright lies. It's just nonsense. Dark matter doesn't have to be right but this kind of a trash talk is nowhere close to be a piece of evidence that dark matter is wrong even if it is wrong – and no evidence that MOND is right even if it is right. Let us discuss one more paragraph about these irrational arguments, a comparison of dark matter with a gorilla:
Consequently, some astronomers and physicists suspect there may be no dark matter after all. If you notice the floorboards in your house are sagging, as if there is too much weight on them, you might conclude there is an 800-pound gorilla in the room with you. You see no gorilla, so it must be invisible. You hear no gorilla, so it must be silent. You smell no gorilla, so it must be odorless. After a while, the gorilla seems so improbably stealthy that you begin to think there must be some other explanation for the sagging floorboards—the house has settled, say. Likewise, perhaps the laws of gravity and motion which led astronomers to deduce dark matter are wrong. “I think dark matter will be a sign of another type of physics,” Verlinde said.
The fairy-tale about the gorilla is surely amusing but its application on dark matter is just wrong. Science actually explains perfectly naturally why dark matter is mute, odorless, tasteless, and invisible, among other things. Dark matter contains no sugar so it's not sweet; no salt, so it's not salty; no other compounds, so it's not bitter; no methane or ammonia so it's not stinking. Its vibrations occur at frequencies much lower than what the human ear may hear, so the dark matter is silent. And so on.

Musser and Verlinde may have managed to prove that our houses are not filled by tons of smelly gorillas jumping around. Such a proof is a great achievement but it is not equivalent to the proof that there's no dark matter. Dark matter doesn't need to be smelly because metabolism isn't necessary for its "survival"; it doesn't have to exchange signals about bananas with other clouds of dark matter because it doesn't depend on eating the bananas etc. So there's really no sensible reason to a priori assume that dark matter is a loud and smelly exhibitionist. Musser's and Verlinde's "arguments" rely on the assumption that everything that is natural in the Universe must look like a gorilla but it simply ain't the case. I think that even many untrained smart kids in the kindergarten know many objects allowed or actively predicted by the laws of physics that are very different from a gorilla.

After a few introductory words about MOND i.e. Modified Newtonian Gravity, we learn
Astoundingly, Verlinde even derived the five-to-one ratio. “I started seeing this as a manifestation of this larger phase space,” he said.
Except that it wasn't possible to write a paper that would make it through the arXiv anti-crackpot filters that would present this five-to-one argument. At this moment, it's just a commercial without any accessible justification and chances are overwhelming that this status will never change.

There isn't any large (whose size is distance-dependent) phase space associated with two non-black-hole objects that orbit each other. But even if you forget about the question whether the claim about such a big phase space could be right, there's something disturbing about the very words chosen in this sentence by Verlinde. Since the mid 1920s, we've known quantum mechanics that superseded phase spaces by the Hilbert spaces. Verlinde deliberately avoids quantum mechanics. Of course, the fact that we talk about Hilbert spaces and not phase spaces is totally essential for anything that is related to holography or any other principles he claims to build upon so it's really indefensible to neglect it if you claim to be finding a deeper meaning of holography.

I am afraid that the very fact that he talks about phase spaces is another piece of evidence that his work has never been addressed to the mature physicists per se and that earning tens of millions of dollars from idiots in various laymen's agencies for wrong but ambitious high-school-level physics pseudoscience has been his plan from the beginning.

Now, after mentioning Sean Carroll's superficial criticism of MOND, Musser promotes MOND by these sentences, among others:
I’m inclined to agree, but one thing gives me pause. MOND manages to account for a wide range of anomalous galactic motions with one simple formula. Even if MOND doesn’t overturn the laws of physics, it has shown that dark matter behaves in a simple way.
This is another untrue commercial. What MOND actually describes in a satisfactory way is just the dependence of a quantity like a velocity on two parameters or so – imagine a galaxy size and the radial distance. The ranges that have been observationally tested aren't too wide so one may fit the dependence on the two parameters by two constants encoding the trend – two exponents in a power law in two variables, if you wish. And both of these new parameters (exponents) had to be adjusted in MOND to give you the right theory. If the dependence or exponents had been different, one could design "another MOND" that would do an equally good job. MOND is just fitting some data – in a way that is almost guaranteed to be possible – while promoting a different paradigm.

I love patterns, even heuristically explained ones, but there's simply no nontrivial pattern that would be more predictive than the input data that had to be adjusted here and that could therefore be used as evidence for MOND. Claims to the contrary are just marketing.

Let me omit a paragraph on the steady state cosmology that Verlinde also promotes – the justifications behind his claims are completely unknown (in literature and/or talks) and the final message without any beef just looks too stupid to deserve more than one sentence on TRF. So let's focus on Musser's final paragraph:
The grander his claims become, the less plausible they seem. Still, Verlinde has captured theorists’ sense that cosmological mysteries signal a new era of physics.
I don't think that the latter claim is right, either. In 1998 or so, cosmology entered a new data-laden era in which it became another high-precision science. That occurred despite the fact that the discipline was so close to philosophy and theology just decades earlier. Dark energy was observed; a theory with dark matter and dark energy explained a huge amount of very accurate observations including WMAP etc.

So the trend in cosmology of the recent decade has been exactly the opposite one than Musser suggests; it was a migration away from mysterious babbling towards quantitative theories with lots of bolts.

The smallness of the dark energy remains a bit mysterious but it doesn't really contradict our models, whether you find the anthropic principle legitimate or whether you believe that there's a more "technical" explanation of the vacuum selection. To summarize, I don't see any evidence whatsoever that there are "cosmological mysteries that signal a new era of physics". Unlike other broad morals sometimes offered to summarize the scientific research, this one is simply not supported by anything that has happened in cosmology – theoretical or experimental – and in quantum gravity or string theory.
The impulse to explain dark matter and dark energy as signatures of a deeper reality, rather than a bolt-on to current theories, arises not only in string theory but also in alternatives such as loop quantum gravity and causal set theory.
Another lie. String theory gives us absolutely no reason to think that dark matter should be more than a "bolt-on" to current theories; quite on the contrary, string theory models overwhelm us with dark matter candidates (LSPs or axions in the big stringy axiverse, to mention the two dominant bolts) and they make effective particle physics theories without any dark matter pretty unnatural. With some disclaimers, the same thing could be said about dark energy, too. Musser's very words "bolt-on" are clearly chosen to sound derogatory (and "not creative") but there exists absolutely no scientific justification for such derogatory remarks.

What loop quantum gravity and causal set theory "say" is completely irrelevant for these scientific questions because these theories are nowhere near the ability to describe related phenomena such as cosmology, certainly not in a deeper and more complete and accurate way than the previous theories such as the classical general relativity.
And if Verlinde is wrong and spacetime really is a root-level feature of our world, what other intuition will have to give way? What other thing that we thought we knew for sure is wrong?
The combination of two questions in the first part of the first sentence is just totally unfair. The claim that "Verlinde is wrong" has nothing to do with the claim that "spacetime is a root-level feature of our world" and they can't be mixed in this way. The spacetime is almost certainly emergent, at least to some extent. But Erik Verlinde has nothing to do with this insight; he didn't make it and he didn't derive it, surely not as the first physicist.

When we say that the spacetime is emergent or doomed, we're certainly not saying that anything that Verlinde has said since 2010 is right. These assertions have nothing to do with each other. If you attributed the fuzzy insight that "spacetime is doomed" to Maldacena or to Witten or to Susskind, you would be inaccurate but your comment would have a true core; if you credit Erik Verlinde with these things, it's just bullshit. In the same way, he hasn't invented the idea that we may try to look for widely believed intuitions that are wrong; science has been doing it from the very beginning, starting with Galileo (if I overlook his semi-scientific predecessors).

So even though Musser's article at least conveys the fact that true experts think that the paper is bunk, it is wrong at so many levels and it is such a flagrant example of "journalistic activism" that I am left utterly disappointed. The quality of science journalism has deteriorated dramatically – and it's much worse for most of Musser's colleagues.

And that's the memo.

Posted by Luboš Motl
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Other texts on similar topics: alternative physics, science and society, stringy quantum gravity

snail feedback (27)
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reader PlatoHagel said...

As I went through the information about Disqus they give descriptive examples of words you can select. A default? I saw the correlation to their example and identified it toward what was appearing here, as you say,"due to abuse, your message didn't appear."

So if it is a bug(natural default) we will see if it disappears. It is under "moderation selections entitled Blacklist."

How did you get your comments to appear on the side of your blog?

reader Luboš Motl said...

A disqus guy said it was a bug to be eliminated on the blog.disqus.com recent blog about the upgrade. The recent comments widget is installed via Tools in the Dashboard, go to

http://stuxnet-lumo.disqus.com/admin/tools/

where you replace stuxnet-lumo with your shortname.

reader hajoucha said...

Thank you for this update. Disqus seems to work quite well. Also there is an extra bonus, since the side panel "recent disqus comments" now shows which comment is under which blogpost as well (unlike "recent echo comments" panel).

reader hajoucha said...

just a test

reader Luboš Motl said...

Dear hajoucha, it works but I won't put your mailinator e-mail address to a white list because it's temporary and may be later used by others, can't it? So your comments will be waiting for moderation. If you invent an e-mail address that can't be guessed too easily, it may be a different story...

reader Luboš Motl said...

Good, hajoucha, but so far DISQUS has only replaced the built-in Blogger.com comments whose recent comments widget had the article names, too. See

http://motls.blogspot.com/2012/05/recent-slow-bloggercom-comments.html

reader Luboš Motl said...

test depth 5

reader Luboš Motl said...

test depth 6

reader George Christodoulides said...

in the beginning i could log on the google account and post but later it would not let me connect at all from the google account and that was the only twiiter account i have since i don't use it .

reader Luboš Motl said...

Testing new DISQUS comments...

I suppose that $\LaTeX$ doesn't work.

reader Anonymous rat said...

Testing anonymous DISQUS 2012 comments.

reader Nobody at TRF said...

Testing anonymous comments.

reader Luboš Motl said...

Interesting. Here it uses the same dark background color and the same totally white foreground color as the blog itself - colors that have been optimized for maximum visibility. Maybe your monitor brightness and/or contrast is set to be wrong?

Also, press ctrl/+, perhaps several times, to increase the size of everything - magnify not only fonts. I don't know why white-on-black should be less readable than black-on-white, it's actually more readable for me, but the magnification should help.

reader PlatoHagel said...

Test.....I kinda wish my link on side bar would update....site is still lead by science even in face of subjective experience context information. Oh, and thanks of heads up on the use of Disqus... it is being implemented as well.

reader Guest said...

testing

reader Dilaton said...

Cool, now even I can make a slow comment :-)

reader George Christodoulides said...

the google+ account works on this one. i don't have to post as FUNPLAY

reader Luboš Motl said...

Haha, you could have always written your actual name instead of FUNPLAY, couldn't you?

Just to be sure, it's still possible to post under anonymous nicknames here. I won't use, remember, or transmit any e-mail addresses someone fills to DISQUS and I will be able to see unless it's agreed upon by the user.

reader Shannon said...

testing with ipad... Still impossible to download a picture for my avatar :-(

reader James Mayeau said...

Is this where we do the bitching, aiming scorn at things which the Boss has no control over?

reader Guest said...

test with avatar

reader James Mayeau said...

Oh my goodness! That's my real name.

I feel encumbered by a new sense of responsibility for the tone and content of my opinion.

Cats out of the bag.

reader Luboš Motl said...

You may still change it. I will forget it and the number of people who saw it is comparable to two! Or you may create a new account where you fill a different nick as a name, can't you? I would find it a bit unfortunate if your real name were blunting your tiger teeth. Note that Shannon became just Shannon - you wrote it so it showed up, right? ;-)

reader James Mayeau said...

It not like Mooney has a bounty on my head. Anyhow, I figure they'd come for Anthony Watts way before it came to that. ;)

reader PlatoHagel said...

I am not sure Lubos but I think all your gmail respondents are set to blacklist?

reader Luboš Motl said...

Why do you think so? If you mean the message "due to abuse, your message didn't appear", it's a bug of DISQUS 2012 that will be fixed soon. No posters or contacts with a human face are on my blacklist.

reader sandrahelen848 said...

because my teacher asked me to include it in a letter stating ' this is not an event but these are the technicalities were focusing on "..and I really don't understand the word fully.

regards,
sandrahelen848,
http://hvactrainingpro.com/ (This website explains about top hvac training programs and schools)
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