Math

Police Violence

datadan Uncategorized ,

Once again two young black men are dead because of “arrest-related death”

Here are the stats for arrest related deaths 2003-2009: http://www.bjs.gov/content/pub/pdf/ard0309st.pdf

Of the many numbers that stood out to me were the fact that “accidental” deaths for young men of color were higher than their white counterparts. More damning is the fact that because

White population ~ 63.7%  Black non-hispanic population 12.2%  Source Wiki

White population deaths (2003-2009) = 2026  Black non-hispanic deaths = 1529

12.2/63.7 = x/2026 ==> x=388

So if things were proportional and equal 388 Black non-hispanic people should have been killed.

But 1529 were.  How much greater is this number?

1529/388 =3.94

3.94 times greater

So Black non-hispanics are 4 times more likely to have an arrest related death when accounting for population

If we do the same for white and non-white

36.3/63.7 = x/2026 ==> x=1155

So if things were proportional and equal 1155 non-white people should have been killed.

But 2787 were.  How much greater is this number?

2787/1155 = 2.4

2.4 times greater.

So if you are non-white you are 2.4 times more likely to have an arrest related death.

What the HELL, When will this change!

 

I wonder:

*What about years 2010-2015?

*Arrest-Deaths assumes equal chance of contact.  However people of color are more likely to have police encounters does this again increase likelihood of Arrest-Death encounters.

 

 

Propane tank frost – The ideal gas law.

datadan Outdoor Education , ,

While camping, a parent observed this phenomenon:

propane_tank

 

Here is a pretty good explanation from the Wardburner.

Here was my thinking process:

  1. The area around the base was cold enough to cause water in the atmosphere to change from gas to solid.
  2. What was causing the metal at the base to become colder?
  3. The canister was being used.  The Heat at the top was “pulling” the heat up through the opening therefore causing a temperature differential.
  4. I also posited it was specific to propane. This phenomenon doesn’t happen with Oxygen tanks.

I was wrong of course.

  1. Stored inside the canister is liquid propane.
  2. As it is used, it moves from liquid state to gas state.
  3. The regulator restricts the flow of the gas to a usable level
  4. FTAM351FOVXP019.MEDIUM
  5. The regulator only delivers constant pressure.
  6. To move from liquid to gas requires energy (Phase change)
  7. It draws in heat from the surrounding metal.  This metal then draws heat from the atmosphere, which causes any moisture around the metal to condense and freeze.
  8. PV=nRT\, is the ideal gas law for

  9. P is the pressure of the gas

  10. V is the volume of the gas

  11. n is the amount of substance of gas (also known as number of moles)

  12. R is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant.

  13. T is the temperature of the gas

T = PV/nR

P and V are going down, so PV is getting smaller.  n is going down as well, but R is fixed.  Thus to maintain balance T must be dropping as well.  But are PV getting smaller than the value of n?

Also, why does it happen at the bottom and not any where else?

Problem Solvers

datadan Uncategorized , ,

According to Polya:

“The difference between experienced and inexperienced problem solvers is that inexperienced problem solvers don’t know hwat to do when they don’t know what to do.”

He outlined

First principle: Understand the problem

This seems so obvious that it is often not even mentioned, yet students are often stymied in their efforts to solve problems simply because they don’t understand it fully, or even in part. Pólya taught teachers to ask students questions such as:

  • Do you understand all the words used in stating the problem?
  • What are you asked to find or show?
  • Can you restate the problem in your own words?
  • Can you think of a picture or a diagram that might help you understand the problem?
  • Is there enough information to enable you to find a solution?
  • Do you need to ask a question to get the answer?

Second principle: Devise a plan

Pólya mentions (1957) that there are many reasonable ways to solve problems. The skill at choosing an appropriate strategy is best learned by solving many problems. You will find choosing a strategy increasingly easy. A partial list of strategies is included:

  • Guess and check
  • Make an orderly list
  • Eliminate possibilities
  • Use symmetry
  • Consider special cases
  • Use direct reasoning
  • Solve an equation

Also suggested:

  • Look for a pattern
  • Draw a picture
  • Solve a simpler problem
  • Use a model
  • Work backward
  • Use a formula
  • Be creative
  • Use your head/noggen

Third principle: Carry out the plan

This step is usually easier than devising the plan. In general (1957), all you need is care and patience, given that you have the necessary skills. Persist with the plan that you have chosen. If it continues not to work discard it and choose another. Don’t be misled, this is how mathematics is done, even by professionals.

Fourth principle: Review/extend

Pólya mentions (1957) that much can be gained by taking the time to reflect and look back at what you have done, what worked and what didn’t. Doing this will enable you to predict what strategy to use to solve future problems, if these relate to the original problem.

There are 10 key strategies:
-Working backwards
-Finding a pattern
-Adopting a different point of view
-Solving a simpler, analogous problem
-Considering extreme cases
-Making a drawing
-Intelligent guessing and testing
-Accounting for all possibilities
-Organizing data
-Logical reasoning

Here is a link with some good examples:

problem_solving

the-art-of-problem-solving-vienna-2-06

Problems to use these 10 techniques.