The Hidden Mathematics Of Drug Testing

Imagine the following scenario:

There exists a drug test that is 99% accurate on both drug users and non-drug users; If 100 drug users are tested, 99 will test correctly positive and 1 will incorrectly test negative. If 100 non-drug users are tested, 99 will correctly test negative and 1 incorrectly positive (false positive).

Now, imagine a group of 1000 people, (workers, welfare recipients, whatever) whose rate of drug use is 0.5%. One individual from this group is chosen at random and tested. The test is positive. Most people would say that the probability of that individual being an actual drug user is 99%. The test is 99% accurate, right?

Wrong

The probability that the tested person is really a drug user is ~33%. In other words, it is more likely the person is not a drug user, even though the "99% accurate" test was positive. At first, this may sound implausible. But it's not. Why?

The absolute number of non-drug users is much larger than users. The number of false positives (0.995%) outweighs the number of true positives (0.495%).

Substituting real numbers;

1000 individuals are tested
There should be 995 non-users and 5 users.
From the 995 non-users, 0.01 × 995 ≃ 10 false positives (1% of the 995)
From the 5 users, 0.99 × 5 ≃ 5 true positives (99% of 5)
The total of all positives, 10+5 = 15. Of these 15 positive results, only 5, about 33%, are genuine.

This is just one of many cases where mathematics is misused in public policy.  Politicians and self-righteous people can claim "We should drug test population x, the tests are 99% right! Very few people will be falsely accused!" As I have demonstrated above, this is simply not true.
The same kind of misuse of mathematics is used in DNA sampling also, with literal life and death consequences. See Misused Mathematics of DNA Sampling.

Why Dave Ramsey is Wrong (Dave Ramsey Lie #1)

Many financial "gurus" like Dave Ramsey advise their clients to "Buy and Hold"; buy investments regardless of current market conditions and hold them for a long period. My personal favorite flavor of Buy and Hold is Dollar Cost Averaging where you pretend you didn't overpay for a particular investment.
Other advisers say to invest in actively managed portfolios with the (poorly thought out) idea of beating the market. Still others recommend investing in indexes that attempt to follow one or more of the popular markets and take advantage of the market's positive bias.

They are ALL wrong

They are wrong because they are either intentionally dishonest, or more likely, willfully ignorant.

 

What does a hedge fund manager do?

 

Imagine someone has a million dollars in stock. They want to protect their million dollars. So they "hedge" their million by buying an investment whose value is inverse to their stock. They could buy a Put option on their stock, and if the stock goes down, the option goes up. They can exercise the option and gain roughly the amount they lost on the stock. But the option itself has a cost. The hedge fund manager conducts these transactions for the stockholder, and in many cases they are the "Market maker"; the one who sells the stockholder the option.

This scenario IS a Zero Sum Game. Someone gains, someone loses. It sounds like a bad deal for the stockholder (it is), but more importantly, it's a very dangerous game for the hedge fund. Sooner or later,  hedge funds collapse. 
In the real world, hedging is not limited to options, futures, and futures option. The Now Even Bigger too-big-to-fail firms create derivative instruments so complex even they can not decipher them at times.*

The Financial Sector

 

There is no doubt some people make money in the financial sector. We all hear of the success stories. But we seldom hear of the millions who lose. That's just human nature, the winners are celebrated and the losers are forgotten. But the winners all have one thing in common - they have an edge or angle. Where does the wealth of the multi-billionaire hedge fund managers come from? Does it come from growth? Added Value? No, the majority comes from the losers. That isn't to say the economy is Zero-Sum; it isn't. But economic growth can not account for all of the wealth accumulated by the top winners.

The Unpredictable Market

 

The US stock market has dropped in excess of 40% five times in the last 80 years. None of these declines were predicted mathematically. In fact, According to the models used by financial advisors, those declines were impossible. Impossible as in even one of them could not happen in billions of years. But they happened. I explore the reasons why in other posts.

As a result of this phenomenon most (all?) successful managers destroy more wealth than they have ever created.  

This wealth destruction happens because investors entrust successful managers with more money as they become more successful. The few managers who make money do so not because they are highly competent, but because they are simply lucky with favorable timing.

Why Dave Ramsey and most all other so-called experts are wrong.

  

Financial experts fail their clients by not taking into account or informing their clients of the true nature of risk. Whatever their favorite advice, they always discount risk. They happily plod along, advising their naive clients, and some of them make outstanding returns. Then something like Black Monday happens and all the gains they previously made are wiped out. But, the expert shrugs his shoulders and says that's life, no one could have seen that coming. 

No one could have seen that coming. 

And that's exactly the point. Because they can not properly quantify the risk, they ignore it. Because of this omission, investors are guaranteed to always lose unless their execution timing is exactly right. We know that is impossible. 

This exact phenomenon has been recurring over and over since markets have were invented. And it will continue.

There is a better way. 


* This was an aspect of the so-called Housing Bubble in 2008. Investment banks fraudulently created derivatives so complex they could not decipher them. The government stepped in, and they nor the contractors they brought in could not decipher them. In the end, taxpayers paid off the investment banks and their insurance companies the amount they claimed to have lost. A real-life example is a poker game, where one person wins all the money on the table. Then the government comes in and repays all the losers whatever they claimed to have lost -with no proof.

Diagram of Reality

Reality

 

The Regions

The Intersection

The point where the 4 triangles meet represents the here and now. This point moves forward as  a result of the effects of time. The point moves side to side as a result of the effects of energy.

The Past

All possible past events are represented here. All possible paths to the Intersection are included. This area is 2 dimensional in the diagram because Time and Energy have no effect here.

The Impossible

The Impossible regions represent events in space and time that were never possible (below the Intersection) and will never be possible (above the Intersection)

All Possible Futures

This area is the most complex. It is curved in 2 dimensions to account for Entropy and Chaos.

The Centerline

The Intersection (The “here and now”) is moved forward by Time and tends to follow the Centerline (due to the effects of Entropy) towards Chaos.

  

The best way to understand the diagram is imagine that the Intersection represents you, right now. All of the possible events in your past are represented by the Past triangle. Events that could have been but weren’t are located in the white Past area. Things that could never have occurred are shown by the portion of the two Impossible triangles below the horizontal centerline going through the Intersection. The parts of the Impossible triangles above the horizontal centerline represent events that can never be.

Time moves you forward (Up on the diagram) towards chaos. You must expend energy to move the Intersection away from the Centerline and away from Chaos. Events become increasingly unlikely as you move from the Centeline towards the Impossible. This is shown by the increased shading on either side of the Centerline.

The Future section of the diagram is curved to account for Entropy. Entropy opposes efforts to to move away from the Centerline. In other words, Time and Entropy conspire to move you along to Chaos.

It is important to keep in mind that the diagram is dynamic, constantly moving forward (UP)

The Implications

There truly are things that are impossible. Most people know this instinctively but have never thought much about it. Time prevents us from going backwards to any event, whether the event really happened or just could have happened. Time actually creates the Impossible by constantly erasing the possible. All events below the horizontal centerline, actual, possible and impossible  are forever off limits. 

Events in the Impossible region above the horizontal centerline are also truly impossible. No amount of energy input can get you from the Intersection to a point in the Impossible region because Time is constantly erasing the possibility. You just can’t get there fast enough so to speak.

Energy is the key element. Without the constant input of energy to oppose entropy the Intersection is moved along by time to the chaos point. 
In fact, if not for energy, Reality and Time cease to exist.

Violin - Installing Strings the Right Way

Violin - Installing Violin Strings Correctly

Peg slippage is a very common problem with violin  players. Before you use peg dope, (and take a very real chance of making the problem worse) be sure your strings are installed correctly. Properly installed strings can prevent most instances pf peg slippage, and as a matter of fact, many professional violin players never use peg compound.

Make sure the peg isn't excessively worn

The hole where the string goes through should be more than 1/3 the distance from the hole to the inner side of the pegbox on the side opposite the side the peg goes in from. If the peg has worn so that the hole is less than about 1/3 of the distance to the pegbox wall, it will be impossible to wrap the string correctly. 

 Replacing Tuning Pegs

Procedure

Insert the string so that no more than 3-4mm is out the opposite side. Wind the string once around the protruding length on the opposite side from the peg.

Then guide the string within about 2mm of the inner pegbox wall on the side the peg goes in from. Left for the G and D strings, Right for the A and E strings.

Continue to tighten the string, keep the string very close or barely touching the pegbox wall. 

Remember to keep an eye on the bridge!

As the strings are tightened it will tend to lean forward.
Periodically check it and straighten it when necessary

Summary

The peg, of course, is tapered, and wrapping the string up the taper, tends to pull the peg inward, keeping it tight. Also, if the last couple of wraps actually press between the previous wraps and the pegbox wall, this will also pull the peg in.

Violin - Replacing Tuning Pegs

 

Replacing Violin Pegs

Violin pegs become worn, or contaminated and sometimes either stick or will not hold. Replacing pegs can be done by almost any player, but requires some expensive specialty tools and a little practice. 
There are a few things to keep in mind; 

Every peg should be fitted to a particular peg hole. Do not exchange one for another. 
Be very careful when using the peg hole reamer. A destroyed peg costs a couple of dollars, but overzealous use of the reamer can necessitate a pegbox bushing job, which is expensive and not a do-it-yourself procedure.
When applying any kind of pressure to the side of the pegbox, support the opposite side.

Tools and Material

30:1 Peg Hole Reamer
Peg Shaver
Knife
Slot files or small fine tooth file
1mm drill bit (1.5mm will suffice)
Sandpaper (240, 400 and 600 grits)
Peg Compound
Violin pegs

After removing the string(s) and old peg(s), ream the peg holes. Only remove as much material as necessary to true up the holes. There should be a slight ~2 degree tilt upward from the peg side. 
It is helpful to leave the other 3 pegs installed and work on one at a  time. This will help prevent accidentally reaming a hole from the wrong side
Once the hole is true, turn the reamer backwards 2-3 turns to start burnishing the hole 

 

The following photo shows the reamer in the peg hole. Notice the D peg hole is wallowed and the peg has a curve worn in it, rather than the smooth 30:1 taper as when new

Once the peg hole is trued up (removing the least amount of wood from the pegbox as needed), score the new peg with a sharp knife right next to the collar. This will prevent ripout of the collar when shaving the peg.

 Make sure the peg shaver is adjusted properly. Practically all violin pegs are made to a 30:1 taper. Some very, very old instruments were made with a 20:1 taper. If you have one of these rare violins, you should probably think again about replacing the pegs.  
The best way to adjust the peg shave is to loosen the screws retaining the blade, carefully insert the reamer with the cutting edge(s) away from the blade, and adjust the blade accordingly. 

Begin shaving the peg, taking very small cuts to keep the peg perfectly round and to prevent tear-out. 

Check the fit often to avoid cutting the peg too small!

 

Continue shaving the peg and checking the fit until the end of the peg is 40mm from the peg box outer wall. Once the peg is sanded, and doped you will end up with the proper distance of 36-38mm

 Here is an example of the shavings for one peg -

Sand the peg with 240 grit, 400 grit and 600 grit sandpaper in progression. 

After sanding, apply a generous amount of Hindersine Hinderpaste Peg Compound or equivalent. DO NOT use Hill's Peg Compound. You will ruin the peg and seriously contaminate the peg holes in the pegbox. Hill's Peg Compound is a product made to address improper peg maintenance and does not work well even for that. If you don't have access to or cannot obtain Hinderpaste or an equivalent, use ordinary bar soap.

 

For the first application apply the Hinderpaste on the entire shaft of the peg. Turn the peg in the corresponding peg hole pushing the peg in with a small amount of force.

Wipe the peg clean with a clean cloth, and apply more Hinderpaste. After the first application, you will be able to see where the peg contacts the pegbox and apply the compound only to those areas. 
Repeat application of the Hinderpaste compound 3 or 4 times or until the peg turns smoothly in the hole without binding.

The peg will now need to be cut to length. Push the peg into the corresponding hole and mark the excess on the opposite side of the pegbox.
Remove the peg and using a fine-tooth saw, cut off the excess. 

When installed fully, the peg should sit 1mm below the surface of the pegbox. I mark the peg flush and use a 1.2mm kerf Japanese pullsaw, which leaves the correct depth. 
Sand the end of the peg where it was cut, and file and sand a small chamfer on the peg end.

 

With the peg installed, mark a spot 1/3 of the distance from the inside wall of the pegbox to the opposite side, measuring from the side the peg is installed from; from the left for the G and D pegs, and from the right for the A and E pegs.
Cut a small groove in the exact middle of the diameter of the peg, at the 1/3 mark. I use special string slot files, but a regular small, fine file will work. The groove not only helps center the drill bit when drilling the string holes, but it creates a radius for the string where it come out of the hole. 
Make sure the groove is parallel to the peg "handle". In other words, lay the peg flat when making the groove.

 

 Drill a 1 - 1.5mm hole in the center of the groove, all the way though the peg.

 Install the pegs and strings 

The Proper Way To Install Violin Strings