From xkcd, of course. The title is “Conditional Risk” which is a morphing of “Conditional Probability” into the current situation.
I love watching lightening storms. But the most adventuresome I get while doing that is setting on my front step.
Category Archives: Technology
Fun with statistics
I can’t say why I needed to know but lets just say I have been a little distracted recently as I have been working on a problem. It turns out I could map my problem into the German tank problem.
I had actually kind of pulled an equation out of the air and proclaimed (to myself), “this looks and feels right”. But I needed something more than my gut telling me that. It turns out for a uniform distribution (which, for the most part, my problem is) the best estimate of the true population size based on a limited sample of the population numbers is:
N = m + m/k – 1
Where ‘N’ is the population estimate, ‘m’ is the largest serial number of the samples you have and ‘k’ is the number of samples you have.
This could be used, presuming the serial numbers are sequential, to estimate the number of iPhones or Androids sold. This is far, far, from my application but still a fun application of statistics.
In my application I could substitute in an expression for ‘m’ which made my problem identical to the German tank problem. After rearranging the resulting equation I came up with the exact equation I had, essentially, pulled out of the air!
I’m still marveling at the implications of that result. In a few days I have a meeting with people who may or may not be thrilled to know that much of the work they have done for the past couple of years is bogus and that I have the solution to make it all better.
Quote of the day—Steve Ballmer
I kiss the ground you walk on.
Steve Ballmer
September 10, 2010
Windows Phone 7 Ship Party 
[Click the pictures to see a higher resolution version.
He also said his trademark, “I love this company.” at the top of his lungs:
He also talked about how important Window Phone 7 is to the company and how much he appreciated all the hard work and how much he really loves his Windows Phone 7 phone.
It is a really nice phone. I took three of them to the Boomershoot site this weekend and did some tests. With one of them I was able to pick up a Wi-Fi signal from an ordinary Linksys router from 1090 meters away. The other two were picking up signal from over 600 meters away. Try that with your iPhone.—Joe]
Al Gore, you’ve doomed us all!
Over the last few months on my twice monthly visits to Idaho there has been a bunch of wind turbines being erected near the Rye Grass rest area on I-90. When Barb came west on Tuesday of this week to visit me in my bunker she told me she stopped and took pictures of the turbines. “They look like something out of a science fiction movie”, she said.
Wow! It just so happens that on my return trip last Sunday I also took some pictures:
Of course all this reminded me of something else:
Quote of the day–Terry Myerson
Today is the day that the Windows Phone team has been driving towards, and we’re very excited to say that we’ve reached the biggest milestone for our internal team – the release to manufacturing (RTM) of Windows Phone 7! While the final integration of Windows Phone 7 with our partners’ hardware, software, and networks is underway, the work of our internal engineering team is largely complete.
Windows Phone 7 is the most thoroughly tested mobile platform Microsoft has ever released. We had nearly ten thousand devices running automated tests daily, over a half million hours of active self-hosting use, over three and a half million hours of stress test passes, and eight and a half million hours of fully automated test passes. We’ve had thousands of independent software vendors and early adopters testing our software and giving us great feedback. We are ready.
Terry Myerson
September 1, 2010
Windows Phone 7 – Released To Manufacturing
[If you climb high enough on my work food chain you will find Myerson.
I can’t vouch for the exact numbers but they sound about right. We have some amazing automation. And if you think the half-million hours of active self-hosting is implausible think again. I first used a Windows Phone 7 about a year ago and started carrying one as my primary phone early this year. When I went on vacation to Missouri last May I took three (the rest were loaned out to co-workers for testing) of them with me and used them for navigation (I’m on the “Location Team”), traffic, lots of email, web browsing, pictures, video, and of course phone calls. Everyone I know on the team has a minimum of two phones and some have five. That adds up to a lot of hours. I actually suspect the half million hours is an understatement.
I am more proud of this product than anything I have worked on since Direct X 1.0. In terms of my primary reason for wanting to work for Microsoft (to change the world) this is, by far, my largest contribution.
Technically it is great. It’s not perfect but it is much more than “good enough” to compete. Market acceptance is a question in our minds though.
Most of the people I associate with are engineers. We understand the technology but not people who are different from us. Will this phone be compelling for non-engineers? I’m sure I can configure one such that my wife (who always insists she just wants “a simple phone, nothing more”) can and would use it as a phone, camera, and for occasional navigation but I’m not so sure she would be interested in spending the money on one if I didn’t “twist her arm”. In many ways it is simpler to use than her current phone. Son James (also a software developer working at Microsoft) will get one. I’m not so sure about his girlfriend. I think my daughters and their spouses will give very serious consideration to one. But how does this translate into the market at large? I think it will be at least “good”. With a little bit of luck and a lot of awesome Microsoft marketing (I’ve seen some “concept ads” that look really good) it will do great.
We have some “ship parties” (not really my thing but it is nice to see others have a good time) in the next few days then we have to deliver on the next version. Yesterday I took care of four bugs on our next deliverable so don’t think we are sitting around to see how well this version does before deciding what to do next.—Joe]
All the easier to strip search you
So. You thought you could avoid those intrusive airport technological strip searches by not flying on a commercial plane? You thought they were just were doing that to “other people”? You thought it was okay to look the other way as your Fourth Amendment rights were violated when you flew on an airplane. It was all in the name of “safety”, right?
Via Andy Greenberg (via an email from Chet), coming to your neighborhood soon:
Gee, I wonder why they didn’t show any people in that video? Oh! Andy has some pictures of that too:
That is through vehicles. I would expect the walls of your home will be just as revealing. Imagine what you look like when you are just walking down the sidewalk.
Expect lots of “security sweeps” for the womens basketball and volleyball tournaments. We can’t be too careful with our precious women at risk.
The phrase “concealed means concealed” now means nothing. And since we let them get away with it at airports what’s so special about a public street now? Some terrorist could kill just as many people at the convention center as they could on an airplane. So why shouldn’t the convention center have the same security theater as the our airplanes?
I’ve pointed this out before but what Pastor Martin Niemöller said about the Nazi’s and what Sebastian observed, “What goes around comes around.” is very true.
You play a very risky game when you make exceptions to fundamental principles.
They say ‘Big Brother’–I say ‘Party Time’
Other bloggers say:
- Mad Rocket Scientist (Real damn scary)
- Robb Allen (Depressing quote of the day)
- Linoge (So how does one nominate organizations for the Big Brother Awards?)
I say it’s Party Time.
There are many, many other options. Here is just a very small sample:
If I could get some custom made they would say “TSA = A Security Theater”.
Big Brother wants to spends millions on technology that can be defeated by $20 worth of plastic you can by online.
I have had mine for several years. Do you have yours?
Real Men…
…and women should have available, and know how to use, either a micrometer or a good caliper that reads in thousandths of an inch and/or hundredths of a millimeter. I don’t see how a person could get through life without one. They’re cheap and they last a long time. A set of hole gauges and snap gauges is good also, but the calipers are essential.
That’s in my book.
Jeff Cooper wrote about some other things;
Before the young man leaves home, there are certain things he should know and certain skills he should acquire, apart from any state-sponsored activity. Certainly the youngster should be taught to swim, strongly and safely, at distance. And young people of either sex should be taught to drive a motor vehicle, and if at all possible, how to fly a light airplane. I believe a youngster should be taught the rudiments of hand-to-hand combat, unarmed, together with basic survival skills. The list is long, but it is a parent’s duty to make sure that the child does not go forth into the world helpless in the face of its perils. Shooting, of course, is our business, and shooting should not be left up to the state.
Or something like that. I recall he had learning to handle a motorcycle in there too.
My son took it upon himself to row a boat across Hood Canal a few weeks ago without telling anyone. We saw him heading over, until he disappeared from sight.
I was miffed. That is, until I remembered some of the crazy things I did at that age (16) like piloting a canoe (two canoes, four people) up one side of Priest Lake in Idaho, by moonlight, and then navigating up the channel to Upper Priest Lake by starlight (after moondown) then landing and setting up camp on a low cliff. We figured flashlights were for sissies, back then. Nowadays I carry one. Must be getting soft.
But I digress. Being able to measure the difference between .678″ and .710″ can be pretty important, and it’s not complicated. This sort of thing comes up often while talking to customers. Most of them have the tools and the skill, but a disappointing minority do not.
I sucked all the bits out of this town
I’m in a small town in central Missouri. I’ve been accessing the Internet via Internet Sharing with my cell phone and that worked well for a while. Then the data transfer rate gradually went to zero. Rebooting the phone and computer didn’t help. I started “borrowing” wireless bandwidth from someone with a SSID of “Linksys” (it is my understanding they are the largest free Internet provider in the country). That went away about two hours ago and I’m back on the cell phone which gives me a few bits every once in a while before drying up.
It’s like I am pumping water from a well and I pulled the water table down below all the intake pipes in the town. I’m mostly sucking air now with just an occasional few spurts of water.
Another indication of the low bit table is that my new phone with the weak cell signal (known issue, we are working on it) runs its battery dead, even while plugged into USB power, trying to sync my email from work.
Until I leave town blogging and email responses will be marginal at best.
Encrypting mobile communication
This is very interesting to me:
More than a million BlackBerry users may have key services in Saudi Arabia and
the UAE cut off after authorities stepped up demands on smartphone maker
Research In Motion for access to encrypted messages sent over the device.BlackBerry’s Messenger application has spread rapidly in the Gulf Arab region
but because the data is encrypted and sent to offshore servers, it cannot be
tracked locally.“Certain BlackBerry services allow users to act without any legal
accountability, causing judicial, social and national security concerns,” the
United Arab Emirates’ Telecommunications Regulatory Authority (TRA) said in a
statement.…
India raised similar security concerns last week, and Bahrain in April warned
against using BlackBerry Messenger to distribute local news. As far back as
2007, France cautioned officials about using the services.Indian security officials were concerned that BlackBerry’s encrypted data
could be used to coordinate acts against the state. They have clamped down on
mobile phone operators in the wake of 2008 attacks that killed 166 people in
Mumbai.
Sure, secure communications can “be used to coordinate acts against the state”. But secure communications can be used to secure the Jews in your attic too.
There is a lot of secure communications that goes on with Windows Phone 7 too. I wonder if any of it will run afoul of repressive government laws.
I may have to write an app for defeating such laws if things progress to far in that direction. It consumes more bandwidth but it’s possible to create communication channels that are essentially invisible while in plain sight and encrypt them as well. I’ve done this before with another app but sort of lost interest when we started winning the gun rights war in this country. I might have to fire up that project again.
TSA blinders
I’ve been wondering when something like this would be publicized and available for sale.
If I had the time and didn’t mind missing my flight I would make myself a set of clothes that were lined with, or made of, aluminized Mylar. I pretty sure it would be hot and uncomfortable but it would also totally block the latest TSA body scanners.
If I had enough money that I didn’t have to work anymore I think I could entertain myself for years making (bigger) fools of the TSA on a weekly basis. Of course some of my jollies might bring commercial aviation to halt for a day or two and then I would feel bad for the hardship I had imposed on all the innocent people trying to travel.
Our universe is a black hole
I’ve been meaning to explain my black hole hypothesis for some time now but there is always something more important to do. But David and Say Uncle posted about it so it’s time I elaborated.
I tried to leave a comment on David’s post last night but the blog software rejected it as spam. David posted my comment in a separate post a few minutes ago. Here is the comment:
Actually my hypothesis was formed almost exactly 1.5 years ago.
See here and here.
I did a little bit of math on the topic but to say my cosmological math is weak would be a gross understatement. What results I did come up with seemed plausible though. That is–the “background radiation left over from the big bang” appears to have a similar temperature to that of the event horizon of a black hole composed of all the matter of our known universe.
I recently listened to the book Parallel Worlds and was surprised and pleased to hear that others had explored the same hypothesis–at least part of it anyway. No mention was made of the direction the black hole being on the time axis. This is a critical component and the easiest thing to prove as being consistent with the known facts.
I will now elaborate further.
My first “Ah hah!” moment was back in February of 2009 and I posted a couple of Tweets about it:
I’m listening to The Black Hole War. This inspired me to explore the hypothesis that our universe is a black hole.
We are rushing toward the singularity at the speed on light on the time axis.
Since then I have made casual references to my hypothesis on my blog (here, and here) and I think a comment or two on other people’s blogs.
Our experience with time dilation and length contraction is the best support for this hypothesis. Starting with the equation for time dilation we can rearrange it as follows (brother Doug pointed this out to me a couple decades ago, I have not read or heard it expressed this way before or since so a great deal of credit, or blame, for inspiring this hypothesis goes to Doug):
DeltaT’ = DeltaT/(SQRT(1 – v2/c2)) Where DeltaT’ is the elapsed time for the moving, at velocity ‘v’, object and DeltaT is the elapsed time for the stationary observer. ‘c’ is the speed of light.
SQRT(1 – v2/c2) = DeltaT/DeltaT’
1 – v2/c2 = (DeltaT/DeltaT’)2
1 = (DeltaT/DeltaT’)2 + v2/c2
c2 = c2 (DeltaT/DeltaT’)2 + v2c2 (DeltaT/DeltaT’)2 is the square of a velocity. Hence we could substitute a symbol for this expression. Let’s let ‘t’ = c (DeltaT/DeltaT’).
c2 = t2 + v2
What this says is that as a moving objects velocity, ‘v’, increases the velocity ‘t’ must decrease such that the sum of t2 + v2 remains constant. This gives us time dilation. But what is the less obvious observation is that as ‘v’ goes to zero our velocity in the ‘t’ direction becomes the speed of light. Hence stationary objects in our frame of reference are actually traveling in the ‘t’ direction at the speed of light.
Inside the event horizon of a black hole all objects travel at the speed of light. If they move off of the straight line toward the center of the black hole the sum of their velocity components still must be precisely equal to the speed of light. Hence if they take on a velocity vector perpendicular to the straight line to the singularity they move slower in the direction of the singularity. This is exactly our experience with time. Our time “velocity” decreases when we increase our velocity in any other direction. Hence, I hypothesize that, we are inside the event horizon of a black hole moving toward the singularity which happens to be in the direction of the axis we call ‘time’.
Further support for this hypothesis is length contraction. We know that as the velocity of a moving object increases the observable length (it doesn’t actually contract, only observations of it’s length decrease) of an object decreases. At the speed of light the length of an object is zero (I suspect it actually becomes the Planck length, but this is just a guess on my part). Since we (according to my hypothesis) are traveling at the speed of light on the time axis we can only observe a single instant of time.
Of course the first question that comes to mind is, “When do we get ripped apart by tidal forces and our subatomic components get sucked into the singularity?”
I don’t know the answer to that, but it is something to think about isn’t it?
Have a nice day.
Another step closer to GATTACA
Entire human genome sequencing for $100.
My estimate is that the potential for GATTACA is only another decade away.
Gunnies be Patient
I’ve seen it before and let it go, but today I ran into several variations of, “Once you get the sights adjusted, this gun is very accurate” in different places on gun forums and product reviews.
Serious shooters should know the problem with that assertion, but not all shooters know it. These were shooters making the assertion after all.
Accuracy and sight adjustment (or zero) are not the same thing.
(Joe uses the term “sight angle” or “indicated sight angle” which makes more sense when you think about, which of course he has)
Accuracy is the ability of the firearm system (the gun itself, the ammo and the sighting system) to place shots consistently. The sights could be “off” considerably (bullets impacting far from the point of aim) and that gun is just as accurate as if it were putting your bullets exactly at the point of aim.
The difference is in sight adjustment, but that in itself has nothing to do with accuracy. Accuracy = consistency.
It has been said that “Sometimes the first duty of intelligent men is the restatement of the obvious.” — George Orwell (Thank You, Walter Williams, for pointing that out)
You intelligent men have your assignment, then. Carry on.
My first Windows Phone Seven video
I tried the video camera on my Windows Phone Seven (with a Samsung “Taylor”) with my daughters at lunch today. I’m impressed.
Full disclosure–I’m on the Microsoft Windows Phone Seven team but I had nothing to do with the video or camera portions of the phone.
Video glasses update II
Background post is here.
I picked up my glasses today. I don’t know how long they had been at the P.O. box waiting for me. I don’t check my snail mail very often.
It appears they sent me a brand new pair rather than repairing the old ones.
[shrug]
That works for me.
I’ll be more careful with them from now on.
You can make money without doing evil
Google is famously known for saying you can make money without doing evil. Aside from my belief this statement betrays an unspoken belief that most earning of money is inherently evil, good intentions are not enough.
The authority revealed that as well as collecting SSID information (the
network’s name) and MAC addresses (the number given to Wi-Fi devices such as a
router), Google had also been collecting payload data such as emails or web page
content being viewed.“The independent audit of the Google system shows that the system used for
the Wi-Fi collection intentionally separated out unencrypted content (payload
data) of communications and systematically wrote this data to hard drives,” said
Simon Davis from Privacy International.…
Google said the error came after a piece of experimental code written in 2006
was included in the software used by its Street View cars by mistake.However, Davis says Google’s explanation “doesn’t add up”.
“This is complex code and it must have been given a budget and been overseen.
Google has asserted that all its projects are rigorously checked,” said
Davies.“It goes to the heart of a systematic failure of management and of duty of
care.”
I’m not going to say it could never happen at Microsoft but if my experience is any indication it would be a very, very safe bet.
I wrote the original code for an internal application used on Windows Mobile 6.x that has collected millions of SSIDs and BSSIDs (also known as MAC addresses). My officemate wrote the code that gathers the same information on Windows Phone 7. I know what we had to go through in terms of review by peers, lawyers, and management. Privacy was of paramount importance. There was never even a suggestion that connection traffic should be considered “fair game”. The information of the type Google is in trouble for storing on hard drives never even gets into RAM let alone is processed enough to hit persistent storage.
I’m not in a position to say that Google had evil intent but I have trouble imagining what they thought they could do with code that stored information gathered in that way that would not be considered “evil” or at least extremely unethical.
.50 caliber myth
AmericanMercenary, a U.S. army solider, gives us data on the effectiveness of .50 caliber rifle fire on aircraft.
That should put the myth propagated by the VPC and Brady Campaign to rest. At least for rational people.
Trade-offs and goals
If you want to save yourself some time by not read my late night rambling just read three sentences from Say Uncle on this topic.
As an engineer I make a lot of trade-offs. Execution speed and size (assembly language) versus code clarity and development time (high level languages) used to be a big trade-off. Calculating results every time you need them or caching them in RAM is a trade-off (it didn’t use to be that way but today the answer is usually you want to calculate them every time). Do you load everything in RAM for quick access or leave it on disk until you need it? Do you bringing a new hire up to speed or do you do it yourself?
I can whip out some code that will test a hypothesis in a few minutes or an hour and not worry if there is a single comment in it or if it handles a single error condition. To implement that same functionality in a product that literally millions of people will use, sometimes millions of times a day (or even per minute) may take weeks of effort by a team of people. It will involve specifications, design documents, a test plan, manual testing, automated tests, unit tests, code reviews by multiple peers, and alpha/beta testing by thousands or even 10s of thousands of end users. It only takes me a fraction of a second to decide how to proceed when I know the final goal for the task at hand.
Man minutes versus man months of time involved. Two different extremes in the effort involved in implementing, essentially, the same functionality. The difference is in what I was attempting to accomplish.
I’ve been making engineering trade-offs for over 30 years and most of the time it comes pretty easy to me. When my officemate, a very smart person but a fairly new entry into actually producing deliverable code, asks for advice on a trade-off it takes more time for her to ask the question than for me to arrive at the correct answer.
Another example comes from this morning. My boss came into my office and asked, essentially, “Do we ever return an answer of less than ‘X’ for condition ‘B’?” I knew my code didn’t do that directly but there were times when my code got the answer from the server rather than computing it directly and I couldn’t say for certain without checking with the server people. I started to go down that path and explain how the server might come up with a different answer and I barely got started into the fine details when he stopped me. “Let me give you some more context”, he said. The context was he was writing an email with the target audience of upper management who would not care about the fine details. When he asked the question I thought there was some bug that had been reported and he wanted to know if it really was a bug and if so who it should be assigned to. Without knowing what he was trying to accomplish I had made the wrong trade-off. I was giving him more and more detail when he really needed validation of his high level overview.
As a gun lobbying organization the NRA-ILA makes trade-offs too. What they are trying to accomplish is to improve, and in certain worst case scenarios minimize harm to, our specific enumerated right to keep and bear arms. Nearly all other considerations must be given a lower priority.
At the NRA Annual Meetings last month I spent a couple hours talking to a NRA board member. He explained why they had done certain things in the D.C. lawsuit (for the most part I am not at liberty to discuss them) and had avoided the U.S. Supreme Court for decades. The next night (or was it the night after?) I spend time with Alan Gura who had a different view of the NRA contribution to the D.C. lawsuit. It was Gura’s contention that NRA-ILA really knows their stuff in regards to legislation but the same people attempting to handle court battles results in people working out of their area of expertise with less than optimal outcomes. My simple take on the topic was that the NRA was trying to avoid a disastrous loss and Gura was trying to get solid win. They both have our best interests at heart but in certain situations ended up “fighting over the ball” and risked fumbling it for a loss.
I think the people that are upset with the NRA support of Harry Reid don’t really understand the trade-offs involved and what the NRA is trying to accomplish. To best support the members, the gun owning people of this country, they have to play a “chess game” where they can never take back a move, the pieces are clouding in smoke, the playing field is shifting, the rules are only partially known and subject to violation by the individual pieces at any time. Try thinking three or four moves ahead under those conditions and see how well you can do. The NRA plays that game very well. They are experts at it. Sometimes when an expert is at work you will be baffled at the moves they make.
To the simple minded observer if you put a “good conservative” in office you will automatically get support for gun rights, hence you should always give support to “good conservatives”. Even an amateur like me can see far enough ahead to see a problem with that in certain situations. There are trade-offs involved. With a ‘D’ beside his name and lots of seniority Reid has lots of power that someone with an ‘R’ and little (or no) seniority would not have. That is just one trade-off. Another is that in certain jurisdictions a “good conservative” is not electable. The demographics of that district are such that the NRA can curry favor with someone that will be in a position to help us or they can try to defeat them during the election then try to make up with them after the election. Another trade-off is that some people like everything, or most everything, the Democrats offer but support our right to keep and bear arms. To a certain extent I am baffled by both the Republican’s and the Democrats. I really don’t understand (and don’t think they do either) the philosophy behind their politics. My guiding political principles are pro freedom. Each party has something to offer and a lot they want to take away from me in this regard. There are trade-offs in who I vote for.
In the case of Harry Reid an NRA lobbyist said this about him in an email discussion:
I have candidates for office running against pro-gun Dems who expect that NRA is going to endorse them as the pro-gun Republican challenger over the pro-gun Democrat incumbent…and tout all of their other “conservative” positions as proof that they’re the better candidate. They get frustrated with me, but I have to remind them that NRA doesn’t use whether you are pro-Life and small taxes to determine your endorsement or grade — and a large number of our members appreciate that, because they don’t agree with conservatives or Republicans on anything but guns! 😉
Whether they like it or not, Harry Reid has voted with gun owners and NRA 100% and used his position in the Senate to advance gun ownership rights in recent years. The Obama Admin was forced to sign a bill with Guns in Parks because Harry Reid allowed the Amendment. The House is holding up DC voting rights because Harry Reid allowed the DC gun rights amendment to the bill.
If Harry Reid isn’t the Senate Majority Leader, we’d have Chuck Schumer or Dick Durbin — think we’re going to get any of those amendments on bills with THEM in charge? No — it’ll be more Lautenberg crap.
In the eyes of an expert political lobbyist the making of the decision about Reid took less time than it took to write the first sentence of the explanation and it’s clear that is the correct answer for gun owners. Those that try to change the NRA support of Reid risk fumbling the ball to the loss of all of us.
Video glasses update
As I mentioned before I broke my new video glasses while taking them off. I considered just gluing them but decided to call and see if I could purchase a replacement part. I called the number in the user manual for Global One Sales & Distribution (814-669-1953) and was told they would ship me the new part but recommended I send them in for repair. The camera is in that part of the frame and there are wires going back to the processor and memory card. The cost, including shipping back to me is $40. I sent them in for repair.
He asked me how I broke them. I told him and he said I was for the fourth person to break them taking the glasses off while the lanyard was attached. They haven’t had other people break them at all. I advise not using the lanyard. What happened to me was that I tried to take them off with one hand holding on to the frame just in front of my left ear. As I pulled them over my head the lanyard caught on my right ear and the glasses were pulled as if it were a wishbone. The lanyard had a large moment arm (engineer speak for “big lever”) and the frame could not handle the force.
There are a few other things of note here. 1) I could not find a website for “Global One Sales & Distribution”; 2) The phone number 814-669-1953 (a Texas area code) is associated with a Self-Storage facility in Pennsylvania which has the same address as that which I was requested to ship the glasses to; 3) These glasses have more features (via a comment from wizardpc) and cost less than $75 (I paid $239 + tax for mine from Afton Arms who had a booth at the NRA meeting).