Monday, March 29, 2021

Vitamin D

This is Joseph

There seems to be an odd discussion of micronutrients that suggest that large doses are beneficial. I first encountered this via Linus Pauling who posited large benefits to large doses of vitamin C. Now people are positing that vitamin D might help versus covid-19 infections. Now, it is clear that vitamin malnutrition is horrible and it is possible that large doses of vitamins are helpful but I want to do an analogy for why I am pretty sure that there needs to be a high level of evidence. Consider these two paragraphs:

Adequate levels of vitamin D are essential to human health. There are many places where inhabitants may have low levels of vitamin D due to environmental issues and this may adversely impact human health (muscle weakness, pain, fatigue and depression are bad). Therefore, it is clear that the more vitamin D we can get people to consume the better.

Adequate levels of macronutrients (calories) are essential to human health. There are many places where inhabitants may have low levels of macronutrients (calories) due to environmental issues and this may adversely impact human health (starvation is bad). Therefore, it is clear that the more macronutrients (calories) we can get people to consume the better.

Obviously, while starving in bad, overeating isn't ideal either. I am always a bit amazed that the default conversation for appropriate intake of micronutrients is not "adequate intake" and not "more is better". Like there is no reason to presume that macro and micro-nutrients necessarily work the same, but one is amazed that the assumption that they are so completely different is so common. 

Friday, March 26, 2021

AstraZeneca dust-up

 This is Joseph

Statement from AstraZeneca was titled (emphasis mine):

AZD1222 US Phase III trial met primary efficacy endpoint in preventing COVID-19 at interim analysis

Gave results of:

79% vaccine efficacy at preventing symptomatic COVID-19

100% efficacy against severe or critical disease and hospitalisation

Comparable efficacy result across ethnicity and age, with 80% efficacy in participants aged 65 years and over

Statement from NIAID

Late Monday, the Data and Safety Monitoring Board (DSMB) notified NIAID, BARDA, and AstraZeneca that it was concerned by information released by AstraZeneca on initial data from its COVID-19 vaccine clinical trial. The DSMB expressed concern that AstraZeneca may have included outdated information from that trial, which may have provided an incomplete view of the efficacy data. We urge the company to work with the DSMB to review the efficacy data and ensure the most accurate, up-to-date efficacy data be made public as quickly as possible.

Full results from AstraZeneca:

76% vaccine efficacy against symptomatic COVID-19

100% efficacy against severe or critical disease and hospitalisation

85% efficacy against symptomatic COVID-19 in participants aged 65 years and over 

So a few points. One, the data was from the interim analysis, even though it was definitely out of date at the time of publication. Still, it was one of two reportable numbers. Noah Haber discusses this here, including noting that the protocol is publicly available

Two, the media framing looks terrible. Unless the results are misreported, the interim analysis was 3% high in the overall and 5% low in the over 65 participants. These are small changes and kind of average out, given that efficacy in over 65 year old participants was a concern because of under-participation in the earlier AstraZeneca trials. But this framing seems excessive:

Federal officials were taken aback by the board’s allegations. One said the way that AstraZeneca handled the results was the equivalent of “telling your mother you got an A in a course, when you got an A in the first quiz but a C in the overall course.” Another said the disclosure by the board would inevitably hurt the company’s credibility with U.S. regulators.

I am not sure I would consider the two reports materially different. Certainly, I do not see them as being the difference between an A and C (probably I would call them both B's, compared to other trials and the degree of change between them). Since they were doing frequentist statistics, looking at numbers between the two prespecified analyses seems like a bad plan (p-hacking concerns arise). That said, why is the analysis plan not Bayesian? 

That said, unless these numbers are false in some way, how is this a major change? 

Finally, why doesn't the United States just give up on approving AstraZeneca and agree to allow it to be exported. It is pretty clear that US regulators have decided that they aren't interested in the product but the export restriction is blocking shipping it to other places that could actually use it. Why not be honest, say they won't need it (they don't) and allow it to be exported to other places across the globe who are desperate for vaccines. Isn't it in everybody's best interests to reduce variants by increasing resistance to covid-19 infections globally? 

How is this the best plan? 

Thursday, March 25, 2021

Repost: I wonder where Republicans got the idea that they could get away with using false claims about election fraud to justify voter suppression

 TUESDAY, MAY 3, 2016

Context only counts if it shows up in the first two dozen paragraphs

The New York Times has a good piece on the impact of voter ID laws but I do have a problem with a few parts (or at least with the way they're arranged).

Stricter Rules for Voter IDs Reshape Races

By MICHAEL WINES and MANNY FERNANDEZ MAY 1, 2016

SAN ANTONIO — In a state where everything is big, the 23rd Congressional District that hugs the border with Mexico is a monster: eight and a half hours by car across a stretch of land bigger than any state east of the Mississippi. In 2014, Representative Pete Gallego logged more than 70,000 miles there in his white Chevy Tahoe, campaigning for re-election to the House — and lost by a bare 2,422 votes.

So in his bid this year to retake the seat, Mr. Gallego, a Democrat, has made a crucial adjustment to his strategy. “We’re asking people if they have a driver’s license,” he said. “We’re having those basic conversations about IDs at the front end, right at our first meeting with voters.”

Since their inception a decade ago, voter identification laws have been the focus of fierce political and social debate. Proponents, largely Republican, argue that the regulations are essential tools to combat election fraud, while critics contend that they are mainly intended to suppress turnout of Democratic-leaning constituencies like minorities and students.
In the third paragraph, we have two conflicting claims that go to the foundation of the whole debate. If election fraud is a significant problem, you can make a case for voter ID laws. If not, it's difficult to see this as anything other than voter suppression. This paragraph pretty much demands some additional information to help the reader weigh the claims and the article provides it...

More than twenty paragraphs later.

Mr. Abbott, perhaps the law’s most ardent backer, has said that voter fraud “abounds” in Texas. A review of some 120 fraud charges in Texas between 2000 and 2015, about eight cases a year, turned up instances of buying votes and setting up fake residences to vote. Critics of the law note that no more than three or four infractions would have been prevented by the voter ID law.

Nationally, fraud that could be stopped by IDs is almost nonexistent, said Lorraine C. Minnite, author of the 2010 book “The Myth of Voter Fraud.” To sway an election, she said, it would require persuading perhaps thousands of people to commit felonies by misrepresenting themselves — and do it undetected.

“It’s ludicrous,” she said. “It’s not an effective way to try to corrupt an election.”

I shouldn't have to say this but, if a story contains claims that the reporter has reason to believe are false or misleading, he or she has an obligation to address the issue promptly. Putting the relevant information above the fold is likely to anger the people who made the false statements, but doing anything else is a disservice to the readers.

Wednesday, March 24, 2021

He came to extend the light of consciousness to the stars and we accused him of having a messiah complex


 

And no, this does not appear to be a joke.

Tuesday, March 23, 2021

There's also a Laffer connection if you follow the links

Cathie Woods,  the founder, CEO, and CIO of ARK Investment Management is probably the most prominent and possibly the most influential of the Tesla bulls. Lots of investors, particularly retail investors, put a great deal of weight in her pronouncements, including this one projection.


That target has inspired some skepticism.


That 300% suggests that Tesla will have to find new worlds to conquer. The report lists insurance as a growth opportunity. If you're up for a lesson in how the insurance industry works, this long but dense thread explains why that ain't happening.
FT Alphaville makes many of the same points.



But the Ark projections haven't been falling entirely on critical ears.


Woods and many other analysts have done very well embracing Tesla, crypto, and all the other disruptors and their defenders invariably resort to "look at the results" arguments when critics question the projections. With that in mind, let's close with this.


Monday, March 22, 2021

E.W. Niedermeyer points out an important paradox with autonomous systems -- if Tesla's FSD didn't suck so much, it would be dangerous

Those who follow Tesla Twitter, particularly from the critical side, have been seeing quite a bit of this.

Here's the entire video.



Road and Track has a painful play-by-play.

But E.W. Niedermeyer explains how a pretty good autonomous driving system would actually be more dangerous.





For an even more disturbing example, check out this from Jalopnik.




Friday, March 19, 2021

When we said drones will revolutionize the industry, we should have been more specific

Go back eight or ten years and take a look at the predictions for drone delivery services. You'll see that we aren't nearly as far along as the optimists expected we'd be, but that doesn't mean drones haven't had a huge impact elsewhere. In fields like entertainment and journalism, camera drones are routinely doing things that had been prohibitively expensive and in some cases simply impossible.










And then there's this industry being disrupted.






Thursday, March 18, 2021

The story is "Tesla has one message for customers and investors, and another one for legal authorities." The meta-story is that the bastion of conventional wisdom is telling this story.



Regardless of where it's reported, this is big news (and potentially grounds for one hell of a class action lawsuit). Still, it's worth noting that highly skeptical coverage of Tesla and Musk is no longer limited to a few voices in the wilderness like Lopez of Business Insider and Hiltzik and Mitchell of the LA Times.

From Axios:

Tesla recently told California regulators that the "Full Self-Driving" beta software it's testing with select customers doesn't make them autonomous — nor will it any time soon.

Why it matters: The company is charging $10,000 extra for the not-really-self-driving, might-arrive-someday addition to its standard Autopilot adaptive cruise-control and lane-keeping feature.

  • Meanwhile, CEO Elon Musk is selling investors on the notion that its full self-driving tech will enable Teslas to become money-generating robotaxis.

Our thought bubble: Tesla has one message for customers and investors, and another one for legal authorities.

Catch up quick: Legal transparency website PlainSite this week released a year's worth of correspondence between Tesla lawyers and the California Department of Motor Vehicles, which regulates autonomous vehicles.

  • The agency had been pressing Tesla for details about the technology's evolving capability since late 2019 while reminding the company that it does not have a permit to deploy autonomous vehicles in California.

Wednesday, March 17, 2021

I love LA... Penultimate Snow

Last week and this past Monday, the weather included some late winter storms, very probably the last of the year. The snow line got down to twenty-five hundred feet. To put that in perspective, the highest point in the city of LA is just over five thousand feet and highest point in the county is just over over ten. 

My standard joke about LA is that we have all the weather you could want; we just drive to it, so this weekend, I headed up the Angeles Crest not far from my place to catch the last snow of the season. Next year, when traveling won't feel so risky, I'll get a cabin and do some hiking. For now, though, these views will have to hold me.






Tuesday, March 16, 2021

Vaccine nuance

This is Joseph.

Are all covid-19 vaccines precisely equal? No. Should you care very much which one you get? Also no. This seems like a contradiction until we think it through. 

Prior to the reporting of any phase 3 trials, the pre-specified efficacy for a useful vaccine was often cited as 50%. Here is an NPR story discussing this prior to Pfizer results. It is worth noting, as Bill Miller states, that even a weak vaccine likely reduces severity:

"That's certainly the case with the influenza vaccine," Miller adds. "People who get the vaccine may still get the flu, but, for the most part, their disease is milder than if they hadn't had the vaccine."

So how do the US vaccines stack up to this standard? For the trial endpoints, Pfizer is 95%, Moderna is 94%, and Johnson and Johnson is 72%. Even the lowest efficacy vaccine is almost exactly at the 75% Dr. Fauci pre-specified as what he was hoping for, even if he was unsure it was realistic.  Further, there are other trade-offs between the vaccines, including price, storage requirements, or number of doses. The lower efficacy option has better storage properties, is cheaper and is only a single dose. The newer vaccines that might yet be approved also look good, AstraZeneca is 70% and Novavax is 89%, so there are a growing number of options far more effective than the pre-specified level needed for a useful vaccine. 

Based on this, there are only safe and effective options available in the United States. I suppose that there might be some customer preferences, but everything is safe and works, based on the trial data. 

So what can real world evidence add? 

Well, we can try to find rare side effects. There was some concern about the AstraZeneca vaccine (not available in the US) and blood clots, at least until people noticed that the rate was lower than would be expected by chance. One of the sanest voices in the pandemic points out that this might be lower than by chance:

Professor Sir David Spiegelhalter, a statistician from the University of Cambridge, urged caution over the decision to pause the AstraZeneca vaccine rollout in some countries, saying it could be doing "more harm than good".

But it is important to monitor for problems. For example, if there were big ones with the Pfizer vaccine then you'd expect Israel to have noticed by now. Spoiler: there weren't any.

We can also measure the population level effects on disease. So we know that the AstraZeneca (AZ) vaccine appears to reduce population rates of hospitalization by 95%, which was higher than that seen post-vaccination by Pfizer, at 84% (this was based on 1.14 million vaccinations in Scotland) -- although this was mostly comparing single dose Pfizer to single dose AZ (results could differ after 2 doses). Both vaccines are mitigating the human cost of the pandemic, which is the reason the pandemic was a crisis to begin with. 

So how does this all link together? All of the evidence suggests all of the vaccines are good. Scotland's real world evidence muddies the waters as to the precise rank ordering (as it is unlikely that the populations being vaccinated were terribly different) but that doesn't change the underlying message: none of the vaccines is showing concerns as to safety or efficacy. I would gladly be randomized to any of the three US available options or to AZ. Even if it was done with a biased die. 

Finally, if I did have to do any sort of prioritization then I would do it via focusing on high risk populations. Give the mRNA vaccines to older and minority groups, who suffer more from the disease. Focus the adenovirus vaccines on the young and high SES crowd. That said, vaccines in arms is the most important variable and every person vaccinated does make the community, as a whole, safer. 

Looking at Mar 15 data, you would rather be the US (21% with 1+ dose), Israel (57% with 1+ dose), or the UK (37% with 1+ dose) and not somebody like Canada (4.7% with 1+ dose). And the number of doses given is vastly more important than the type of vaccine used, provided it is one of the five above with extensively reported phase three clinical trial data. 

Monday, March 15, 2021

If David Wallace-Wells was all that concerned about vaccine hesitancy, maybe he shouldn't have promoted the myth of a West Hollywood autism epidemic

 I've been meaning to do an in-depth thread on David Wallace-Wells -- the issues of climate change, megafires and global pandemics are far too serious to let this clown lead the discussion -- but until then, here's another reminder that DWW has absolutely no credibility on vaccine hesitancy. 

What If Herd Immunity Is Out of Reach? [emphasis added]

A few months ago, these developments might have suggested the true endgame of the pandemic was in sight—and indeed the likely vaccination of 100 million or more by late spring does suggest a dramatic change in the country’s experience of the disease, with those vaccinated feeling safe from hospitalization and death and the disease in retreat. But thanks to a combination of higher herd-immunity estimates, stubbornly high vaccine “hesitancy,” and the arrival of new coronavirus variants that render existing vaccines less effective, the second year of the American pandemic is beginning to look less like a page-turning, book-slammed-shut bang and more like a long and indefinite whimpering into the future — in which many are protected but the disease, undefeated, still circulates, perhaps forever. That the coronavirus would become endemic, like the common cold, has always been one possible outcome, though less appealing than true elimination. The arrival of new variants has made that kind of near-term future, with enduring reservoirs of virus throughout the country, seem less appealing still.

Who do we know with a history of spreading anti-vaxxer talking points?


Tuesday, July 18, 2017

David Wallace-Wells, autism and bad science

David Wallace-Wells has been catching a lot of flack (most of it richly deserved) for his recent New York Magazine article on climate change. It is a hugely troubling sign when the very scientists you were claiming to represent push back against your article.

This controversy illustrates a larger problem with science reporting at the magazine. We already have a post in the queue discussing the neutral-to-credulous coverage of topics ranging from homeopathy to magic crystals to Gwyneth Paltrow's goop empire. The Wallace-Wells piece takes things to another level and goes in a very different but arguably worse direction. Rather than giving bad science a pass, he takes good science and presents it so ineptly has to do it a disservice.

I am not going to delve into that science myself. The topic has been well covered by numerous expert and knowledgeable writers [see here and here]. The best I could offer would be a recap. There are some journalistic points I may hit later and I do want to highlight a minor detail in the article that has slipped past most critics, but which is perfectly representative of the dangerous way Wallace-Wells combines sensationalism with a weak grasp of science.

Other stuff in the hotter air is even scarier, with small increases in pollution capable of shortening life spans by ten years. The warmer the planet gets, the more ozone forms, and by mid-century, Americans will likely suffer a 70 percent increase in unhealthy ozone smog, the National Center for Atmospheric Research has projected. By 2090, as many as 2 billion people globally will be breathing air above the WHO “safe” level; one paper last month showed that, among other effects, a pregnant mother’s exposure to ozone raises the child’s risk of autism (as much as tenfold, combined with other environmental factors). Which does make you think again about the autism epidemic in West Hollywood.


No, David, no it doesn't.

I want to be painstakingly careful at this point. These are complex and extraordinarily important issues and it is essential that we do not lose sight of certain basic facts: by any reasonable standard, man-made climate change is one of the two or three most important issues facing our country; the effect of various pollutants on children's mental and physical development should be a major concern for all of us; high ozone levels are a really bad thing.

But the suggestion that ozone levels are causing an autism epidemic in West Hollywood is both dangerous and scientifically illiterate. You'll notice that I did not say that suggesting ozone levels cause autism is irresponsible. Though the study in question is outside of my field, the hypothesis seems reasonable and I do not see any red flags associated with the research. If Wallace-Wells had stopped before adding that last sentence, he would've been on solid ground, but he didn't.

Autism is frightening, mysterious, tragic. This has caused people, particularly parents facing one of the worst moments imaginable, to clean desperately to any explanation that might make sense of their situation. As a result, autism has become a focal point for bad science, culminating with the rise of the anti-vaccination movement. There is no field where groundless speculation and fear-mongering are less welcome.

So, if ozone and other pollutants may contribute to autism, what's so bad about the West Hollywood claim? For that, you need to do some rudimentary causal reasoning, starting with a quick look at ozone pollution in Southern California.

Here are some pertinent facts from a 2015 LA Times article:

EPA Administrator Gina McCarthy selected a limit of 70 parts per billion, which is more stringent than the 75 parts-per-billion standard adopted in 2008 but short of the 60-ppb endorsed by environmentalists and health advocacy groups including the American Lung Assn. The agency’s science advisors had recommended a limit lower than 70 -- and as low as 60.

...


About one-third of California residents live in communities with pollution that exceeds federal standards, according to estimates by the state Air Resources Board.


Air quality is worst in inland valleys, where pollution from vehicles and factories cook in sunlight to form ozone, which is blown and trapped against the mountains.


The South Coast air basin, which includes Los Angeles, Orange, Riverside and San Bernardino counties, violated the current 75-ppb ozone standard on 92 days in 2014. The highest ozone levels in the nation are in San Bernardino County, which reported a 2012-2014 average of 102 parts per billion.


Now let's look at some ozone levels around the region. West Hollywood, it should be noted, is not great.





But just over the Hollywood Hills, the situation is even worse.



Go further inland to San Dimas and the level is even higher…






Higher still in Riverside ...






Though still far short of what we find in San Bernardino.



If you look at autism rates by school district and compare them to ozone levels, it is difficult to see much of a relationship. Does this mean that ozone does not contribute to autism? Absolutely not. What it shows is that, as with many developmental and learning disabilities, the wealthy are overdiagnosed while poor are underdiagnosed. It is no coincidence that a place like Santa Monica/Maibu (a notorious anti-vaxxer hotspot) has more than double the diagnosis rate of San Bernardino.

The there's this from the very LA Times article by Alan Zarembo that Wallace-Wells cites [emphasis added]:

 Irva Hertz-Picciotto, an epidemiologist at UC Davis, suspects that environmental triggers such as exposure to chemicals during pregnancy play a role. In a 2009 study, she started with a tantalizing lead — several autism clusters, mostly in Southern California, that her team had identified from disability and birth records.

But the hot spots could not be linked to chemical plants, waste dumps or any other obvious environmental hazards. Instead, the cases were concentrated in places where parents were highly educated and had easy access to treatment.

Peter Bearman, a sociologist at Columbia University, has demonstrated how such social forces are driving autism rates.

Analyzing state data, he identified a 386-square-mile area centered in West Hollywood that consistently produced three times as many autism cases as would be expected from birth rates.

Affluence helped set the area apart. But delving deeper, Bearman detected a more surprising pattern that existed across the state: Rich or poor, children living near somebody with autism were more likely to have the diagnosis themselves.
Living within 250 meters boosted the chances by 42%, compared to living between 500 and 1,000 meters away.

The reason, his analysis suggested, was simple: People talk.
They talk about how to recognize autism, which doctors to see, how to navigate the bureaucracies to secure services. They talk more if they live next door or visit the same parks, or if their children go to the same preschool.

The influence of neighbors alone accounts for 16% of the growth of autism cases in the state developmental system between 2000 and 2005, Bearman estimated.

In other words, autism is not contagious, but the diagnosis is.





Friday, March 12, 2021

This is getting dumb

This is Joseph

Matt Yglesias commenting on the NYT:


Also noted by Alex Tabbarok

AZ has on the order of 50 million doses nearly ready to go and can produce in the US around 25 million doses a month so over a year that production is worth over $100 billion to the world economy, far higher than the modest cost of production! Instead of idling this capacity we should expand it even further as part of a plan to vaccinate the world.

 I think we need to have a very careful reality check. What could possibly be the reason for not allowing the export of the vaccine? People keep pointing out that Astra-Zeneca has not done the paperwork for an emergency use authorization, but what is the point of letting it sit unused when the company would like to export it. 

If it works, why would the United States not want to use it? If it is inferior to current vaccines why should we deny it to countries dealing with large outbreaks? I understand not immediately authorizing it because the US has vaccines with good data already approved but then it should be exportable. I also understand wanting to use it domestically to speed up vaccination rates but then there should be hard questions asked about why the company is not applying to the FDA. 

But the current course of action seems to make no actual sense. What am I missing? What is the value in letting the doses expire due to an export ban? 

Defunding the police

This is Joseph.

I am a big fan of reading history. While I admit I have a Western European and Classical period bias in my reading, it isn't limited to just these periods. Every once in a while you hear an argument that really has no good analogue in how societies have tried things in the past. It doesn't mean that the past is a prison, but that I would like to consider ideas about how to use past ideas as a starting point for current problems.

Whenever I hear about "Defund the Police", I have questions. Now, the same slogan covers a wide range of policies, some of which are extremely good ideas. Militarized police is a step backwards to when the main peacekeepers were military, and that was definitely helped by a town guard that was less violent. You didn't want the same soldiers who sack cities to be keeping the peace in a town or city that you really care about. 

But if it means abolish the police, which occasionally it does, then I want to bring up my favorite example of a society without police: medieval Iceland. It is a very good example and has actually been brought up as a possible model by Libertarians from time to time (see the linked David Friedman article for an example). But it does raise a serious concern for a large society like the United States or Canada -- even in a small and highly interdependent society like Iceland you had a serious problem with blood feuds that eventually led to power imbalances and the fall of the Icelandic Commonwealth.  There does seem to be a huge advantage in a relatively neutral arbiter of the law.

That said, that does not mean that we cannot focus on improving the quality of the police and the strength of civilian governance. Our institutions are what holds a society together and it is an obvious point of improvement to diversify police functions and to find ways to improve policing outcomes. This is an obvious win-win. But I have some bad news -- most of the time the effort to improve a government function requires actual resources. It is quite rare that something is so overfunded that funding cuts actually improve efficiency. 

Thursday, March 11, 2021

The sad part is this actually makes the first one look rational...

It's back...




There was at least an initial logic to the first Gamestop bubble. If successfully executed, it is possible to make a great deal of money out of a short squeeze. This time, however, we are in pure delusional money territory.

“It’s a marathon, not a sprint. Whatever happens resist the urge to sell. The longer we hold the higher it goes,” said @catchme1fyoucan, an Italy-based user of retail trading platform eToro, in a discussion on GameStop.

For many, perhaps most, of the investors this time around, the lesson of the first bubble was exactly the wrong one. They believe they drove the stock up because of the rightness of their cause and the power of their will,  and the only reason it went back down was a loss of faith.

The details of this surge don't do much to help clear things up for us non-believers.

One explanation was a tweet from activist investor Ryan Cohen, who is a major shareholder in GameStop and was appointed as a board member as part of an attempt to reverse the company’s ailing fortunes.

Mr Cohen is known as “Papa Cohen” on the Reddit forum, and is known to have a significant holding in the company. That means that his tweets have a particular pull for those who follow the stock – even if they might be largely incomprehensible to others.

One such tweet was posted by Mr Cohen on Wednesday evening. It showed a McDonald’s ice cream cone and was accompanied by a frog emoji.

Soon after that post, the shares began to surge. It is impossible to say definitively whether there is any connection between the stock price and Mr Cohen’s tweet, but it at least focused new attention on the GME shares.


In case you were wondering if the description leaves something out...


While we don't want to push the analogy too far, we live in a time of movements based on finding hidden messages in cryptic tweets. By the QAnon standard, buying Gamestop at $265 hardly seems crazy at all.

As I type this, it is snowing in the City of Los Angeles

At least in the parts above 2,500 feet. The highest point in the city is just over 5,000 feet so the snow line will cover a lot of square miles, even more in the eastern part of the county. The mountains will be beautiful.