Wednesday, November 22, 2023

Prosperity Gospel

 

Money (That’s What I Want)

Money don't get everything, it's true What it don't get, I can't use Now give me money, (That's what I want) That's what I want

Is the love of money good for you?

“My kingdom is not of this world”. John 18:36

It is easier for a camel to pass through the eye of a needle, than for a rich man to enter into the kingdom of heaven.  Matthew 19:24

So how can these words be reconciled with the Prosperity Gospel, which is the fast-growing theologically conservative movement frequently associated with evangelicalism and charismatic Christianity. It emphasizes believers' abilities to become rich in this world through devotion and positive confession.  Does Jesus wish to punish those believers in the Prosperity Gospel, by making them rich in this world, or did those believers have a “Come to Satan” moment?

Saturday, November 18, 2023

Continuing Resolutions

 

I Think It’s Gonna Rain Today

Lonely, lonely
Tin can at my feet
Think I'll kick it down the street
That's the way to treat a friend
Bright before me the signs implore me
To help the needy and show them the way
Human kindness is overflowing
And I think it's going to rain today

Continuing Resolutions are Congress’s way of kicking the can down the street.

MAGA Mike Johnson’s innovation in Continuing Resolutions is a laddered approach, which was making two Continuing Resolutions, which each fund approximately half of the Government and expire respectively on January 19, 2024 and February 2, 2024.  Uh, as Steve Colbert observed in his Late Night monologue, isn’t this merely dividing the can in half and kicking both halves down the street.

The old joke goes

“A man had offended the king and was sentenced to death. He fell to his knees before the king and implored, "Oh your majesty! Spare me but for one year, and I will teach your horse to talk!" The king was amazed and granted his wish.

The man's close friend and brother upbraided him, saying, "Why did you make such an absurd promise?"

The man shrugged and replied, "In a year, the king may die. In a year, I may die. In a year, the horse may talk!"

I've got some facts for MAGA Mike.  This horse is NEVER going to talk. Tomorrow may be another day and you might not want to think of unpleasant facts until tomorrow, but “Frankly, Scarlett, I don’t give a damn.”  Kicking the can down the street only moves the can, it does not make the can go away.  Running out the clock, hoping that you or the king may die, is the coward's way.  Deal with the can.  THAT is the way to treat a friend.

Children

 

Fortunate Son

Some folks are born silver spoon in hand
Lord, don't they help themselves, Lord?
But when the taxman come to the door
Lord, the house lookin' like a rummage sale, yeah

It ain't me, it ain't me
I ain't no millionaire's son, no, no
It ain't me, it ain't me
I ain't no fortunate one, no

 I am my father’s son, but I am NOT my father.

The Hunter Biden controversy, Biden impeachment, and the Trump New York civil fraud trial are examples of competing world views.  Are children and their property, the property of their parents? OR are parents wards/stewards of their children, and their property, until they become adults? If you believe that children are NOT property, then whatever Hunter Biden may, or may not, have done as an adult has no relevance to President Biden.  If you believe that children are property, then their net worth is your net worth, and one of the admissions that Ivanaka Trump made at the Trump civil fraud trial is that former President Trump guaranteed loans with the net worth of property that was his children’s.

So these issues expose competing world views.  Are children property of their parents?  Or are children merely wards of their parents until they attain adulthood?  The Jewish faith has an answer to this in the Bar/Bat Mitzvah ceremony where the child proclaims, “Today I am a Man ( gender neutral)”.  The Roman Catholic and many Christian faiths have an analogue in the Confirmation ceremony.  You can NOT be a Man ( even if you "smoke the same cigarettes as me. I can’t get no satisfaction”)  if you are the property of another, including your parent’s.

Tuesday, November 14, 2023

Growth Rates

 

What Kind of Fool Am I

What kind of fool I am
What kind of mind is this
An empty shell
A lonely cell in which
An empty heart must dwell

What kind of growth is this?

It is common to express growth in terms of a Compound Annual Growth Rate, CAGR.  Savings accounts, loans, mortgages, inflation, and the Gross Domestic Product of the economy are often expressed this way.  This implicitly assumes that growth is geometric and follows the formula: 

Future= Base *(100%+CAGR)^(periods, years, between future and base).

This is considered a marked improvement over assuming a simple growth rate:

Future=base * (Period, years, between future and base)*(100% + simple growth rate).

The compound rate is also called a geometric growth rate.  It assumes a constant, but non-negative, growth rate (first derivative).  A problem with continuous growth is that it can surpass an absolute amount in the future.  An equally valid growth rate is exponential growth.  It is more commonly encountered as radioactive decay with a half life. For growth, the mirror of decay, the rate is often expressed as a doubling period.  Exponential growth will approach an absolute but will never exceed it.  It thus has a variable, not a constant, growth rate (first derivative).  This is consistent with a constant rate within an exponential function.

Future=base*(100% +exp(rate* period, years, between base and future))

where exp() is the exponential function.

Over the short term, less than 20% of the periods to the absolute, there is virtually no difference between exponential and compound growth.  Exponential growth is higher than compound growth, but less than 5% higher, over the medium term, 20% to 83% of the periods to the absolute.  It is only in the periods near the absolute ( 83% to 100% of the periods to the absolute), that the exponential growth becomes significantly larger.  However unlike compound growth, its future value will never exceed the absolute amount.

It's Relative III

 Dead Man's Curve

(Dead Man's Curve) is no place to play
(Dead Man's Curve) you'd best keep away
(Dead Man's Curve) I can hear 'em say
Won't come back from Dead Man's Curve

If the universe is curved, what does that do to randoneess and choices?

Variance is the dispersion of the data, X,  in a statistical distribution. Mathematically its formula is

Var(X)=∑ (pi*(xi))2 for i =1 to n variables

The variance is traditionally defined as the square of a parameter of a random distribution,  σ2, where σ is also known as the standard deviation, SD.  The other parameter of a random distribution, µ, the mean, which is equal to the median of a normal distribution, is

µ=∑ pi(xi)*xi for i=1 to n variables.

However it is not correct to say that the variance, which is the square of the standard deviation, SD, can be solved by Pythagoras’ formula. This is only true on a flat surface.  In fact on a flat surface, rather than a summation, this should be expressed as a product as

SD(X)=cos-1(∏ cos(pi(xi))) for i=1 to n variables.

On a flat surface, this is identical to  

SD(X)=√( (pi(xi))2 for i =1 to n variables or √( (xi))2/n).

That Bessel’s correction, n/(n-1), is necessary for the SD is an indication that the surface is not flat.

On a spherical surface, the formula should be

SD(X)=R*cos-1(∏ cos(pi(xi)/R)) for i=1 to n variables.

Here R is the radius of the spherical surface.  As R approaches infinity, e.g. the sphere become very large compared to any pi(xi), this becomes identical to the formula for a flat surface.

On a hyperbolic surface, the formula should be

SD(X)=cosh-1(∏ cosh(pi(xi))) for i=1 to n

The variance, σ2, of a random logistics distribution, where the parameters are µ and s, is s22/3.  Because this is the summation of a square, it is correct to say that σ2=s22/3, but it is NOT correct to say that because of this s=σ√3/π.  This is only true for a flat surface.

If the surface is hyperbolic, then the correct formula is

s=cosh-1(cosh(σ√3/π))

Because cosh-1(x)=ln(x±√(x2-1)), cosh2(x)-sinh2(x)=1, cosh(x)=½*(ex+e-x), and sinh(x)= ½*(ex-e-x), this can be expressed as

s=ln(cosh(σ√3/π) ±√( cosh2(σ√3/π)-1))

s=ln(cosh(σ√3/π) ± sinh(σ√3/π))

s=ln(½*(eσ√3/π +e-σ√3/π± ½*(eσ√3/π -e-σ√3/π))

s= σ√3/π ± σ√3/π= 2* σ√3/π or 0

This is because the variance, the square of the standard deviation, is a summation, NOT a single variable.

Only if the surface is flat is it true that s=σ√3/π.

This means that the random normal logistics distribution, the hyperbolic secant distribution,  

PDF = (1/(4s))*sech2((x-µ)/2s); CDF = ½*tanh((x-µ)/2s)+ ½

can be expressed in terms of the parameters µ and σ as

PDF = (π /(8* σ√3))*sech2(π *(x-µ)/(2* σ√3)); CDF = ½*tanh( π *(x-µ)/(2* σ√3))+ ½.

When the standard deviation, σ, is π/(4√3) then this simplifies to

PDF = ½*sech2(x-µ); CDF = ½*tanh(x-µ)+ ½ which is identical to saying that  s=½.

In this case, when x=µ, then the PDF is 50% and the CDF is also 50%. If π is the absolute, and negative numbers are not allowed, then, according to Pearson’s Second Coefficient of Skewness, µ=π/2.  If s=½, then σ2=(½)2π2/3=0.822467.

If the universe is hyperbolic, as proposed by Mabkhout (Mabkhout, 2012), the absolute is defined as π, x is an absolute measurement which means that 0 is an absolute zero, numbers x<0 are not defined, AND the universe is random, then if the universe is normal, it has both a mean and a variance which can be expressed in terms of its absolute. That universe also allows choice, s=½, where there is one choice: the absolute or absolute zero.

If the universe is hyperbolic and random, then random events do not repeat except on an imaginary plane. Random events may appear to repeat, be cyclical, but it is not in the real surface where the coefficient of the imaginary axis is 0.  I.e., Mark Twain was correct.  History does NOT repeat, but it sure does rhyme.

Mabkhout, S. (2012). The infinite distance horizon and the hyperbolic inflation in the hyperbolic universe. Phys. Essays, 25(1), p.112.

Choices

 

I’m Putting All My Eggs in One Basket

I'm putting all my eggs in one basket
I'm betting everything I've got on you
And, I'm giving all my love to one baby
Lord help me if my baby don't come through

This might be a good strategy in love, but it is NOT a good betting strategy.

We are warned not to put all of our eggs in one basket.  The reason being that if anything happens to that basket, then we will have no eggs.  IOW, Henry Ford’s famous choice for the color of a Model T in the 1920s, “Any color, as long as it is black”, is not a choice at all.  It might have been good for Ford’s assembly process since black paint dried faster, but it was not necessarily good for his customers. The company store in the song Sixteen Tons is also not a choice since you either bought at the company store or did without. In both cases having only one choice is putting all your eggs in one basket.

Having a choice between two things is also not a choice.  Game Theory proves that having at least three choices is necessary, https://dbeagan.blogspot.com/2021/05/tough-but-fair-beats-always-being-nasty.html assuming that the parties/players offering those choices are not colluding.  The song should be “I’m Putting All My Eggs in THREE Baskets”

Saturday, November 11, 2023

Baseball

 

Take Me Out To The Ball Game

Katie Casey was baseball mad,
Had the fever and had it bad.
Just to root for the home town crew,
Ev’ry sou Katie blew.
On a Saturday her young beau
Called to see if she’d like to go
To see a show, but Miss Kate said “No,
I’ll tell you what you can do

 

Take me out to the ball game,
Take me out with the crowd;
Just buy me some peanuts and Cracker Jack,
I don’t care if I never get back.
Let me root, root, root for the home team,
If they don’t win, it’s a shame.
For it’s one, two, three strikes, you’re out,
At the old ball game. 

Next time you sing the chorus, remember the verse!

The American League regular baseball season is 162 games, at least since 1961.  That is what the asterix after Roger Maris’ regular season home run record was all about. The National League increased its season to 162 games in 1962.

An average season since the mid-1960s is  81 wins and 81 losses, a .500 record.  For the standings to be normally distributed, no team can win more than 162 games or lose more than 162 games.  Thus the record has to be such that 81 minus standard deviation/3 ≥0.  That means that the standard deviation of a 162-game season is 81 divided by 3 ≤ 0 or less than 27 games.  The variance is the square of the standard deviation or less than 729.  The team with the best regular season record, before the bias of the playoffs, was 100% the DOMINATE team, but each game was randomly decided, no fixes, so that the CERTAINTY of its being best team is: 68% with a record of 108 and 54; 95% with a record of 135 and 27; and over 99% with a record of 162 and 0.

However, since the introduction of the championship, division, and wildcard playoff series, the league regular season champions might be sitting their best players once the team has clinched a spot in the playoffs, and is no longer trying to win every game at the end of the season. Thus, the playoffs can determine the most DOMINATE team in those playoffs, but the CERTAINTY that this is also the best team can no longer be established.  The regular season is only a means to determine the seeding for the playoffs.

Each playoff series can determine a dominate team for that series, but can not also determine that the DOMINATE team in each series is the BEST team.  In a 3-game series, a team that wins 2 games is dominate but it could have been expected to have a 3-0 or a 2-1 record if all three games had been played.  But the CERTAINTY of the dominate team being the best team is only 34% (it is 88% for a 3-0 record but that is only 12% of the possible outcomes!)   In a 5-game series, a team that wins 3 games can be expected to have a 5-0, 4-1, or 3-2 record.  The winning team has a certainty of being the best team of 38%.   In a seven-game series, a team that wins 4 games can be expected to have a 7-0, 6-1, 5-2, or a 4-3 record.  This is a certainty of 40%.  However, the winner of the wild card or division round was not necessary the higher seed, so if the lower seed wins its certainty should be reduced by being in the previous round. 

The playoffs determine the most DOMINATE team in each series with an odd number of games, but they do not determine the best team with CERTAINTY.  It is the record of the losing team that does that. If the series is stopped after a majority of the wins have been achieved  (e.g. four games in a seven-game series), there is no way to determine what the record would have been in the games which were not played.

That is why the playoffs might be more exciting, but they are not, can not, be certain. If we wanted to be certain, we would have to play ALL of the games. In other words, Play Ball!