Pythagoras' Theorem

 

The Boy Next Door

The boy next door
I just adore him
So I can't ignore him
The boy next door

If you adore something, then you can’t ignore that something!

In checking on the internet, I am not the first engineering student who could not get his head around the concept of ignoring the imaginary portion of solutions involving AC currents. I was always taught that ignoring something does not make that something go away. I could not bring myself to ignore the imaginary portion, so I ignored electrical engineering. In hindsight, maybe I should have not ignored anything.

The solution for a hypotenuse in Euclidean geometry, Pythagoras’ Theorem, is c=√(a²+b²) which is true because cos²(x)+sin²(x)=1.  But this is only true on a flat surface.  The solution on a spherical surface is cos(c/R)=cos(a/R)*cos(b/R) where R is the radius of that spherical surface, and the solution on a hyperbolic surface is cosh(c)=cosh(a)*cosh(b).  But cosh(i*x)=cos(x)+i*sin(x).  This means that the hypotenuse on a hyperbolic surface can be restated, rotated by 90 degrees, since cosh(x) = cosh(ix) rotated by 90 degrees,  as 

cosh(c/R)-i*sin(i*c/R)=cosh(a/R)*cosh(b/R)
                                           -i*cosh(a/R)*sin(i*b/R)
                                           -i*cosh(b/R)*sin(i*a/R)
                                          +sin(i*a/R)*sin(i*b/R).

The limit as R→∞ because sin(0)= 0, is

Cosh(c)-i*sin(i*0)=cosh(a)*cosh(b)-i*cosh(a)*sin(i*0)-i*cosh(b)*sin(i*0)+sin(i*0)*sin(i*0)

Because cos²(x)+sin²(x)=1, it is also true that sin(x)=√(1-cos²(x)). Thus all three formulae for the different surfaces are the same, and Pythagoras’ Theorem is merely the case of ignoring the imaginary components when R→∞.  This is also why, when a²+b² is negative, the solution to Pythagoras’ Theorem becomes imaginary. They said on the Chiffon Margarine TV commercial when I was growing up, ”It’s not nice to fool Mother Nature!”.  It is apparently not nice to ignore her either!

Conservatives

 

Life Begins at Forty

Conservative or sporty, it's not until you're forty
That you learn the how and why and the what and when
In the twenties and the thirties you want your love in large amounts
But after you reach forty, it's the quality that counts

Can we take back the word conservative.

I am well past forty, but I don’t think I am the opposite of sporty. Nothing should ever be defined by being an opposite. Saying that conservatives own the libs, tries to say that everyone who is not a liberal must be a conservative. I am not sure that is the case. Both Liberals and old time Conservatives believe in government. It used to be that Conservatives also believed in limited government, because the sovereign in the US Constitution is the People, but the government must be composed of individuals, People, might be well intention, but the road to you-know-where is paved with good intentions. Conservatives also believe in Lord Acton’s maxim that “Power corrupts, and absolute power corrupts absolutely.”  For both reasons, conservatives believe that government should be limited, so as to best avoid well intentioned but misguided actions, and because the less power the government has, the less corrupt it is likely to be.

But being in favor of limited government does NOT mean being in favor of no government. Especially when those in favor of no government really mean that they only support themselves and are in favor of government when the government agrees with them, or they control the government. It is the difference between geometric and exponential behavior. Approaching zero, but never getting to zero is exponential behavior. Eventually reaching zero is geometric behavior. Conservatives have been deceived into thinking that since they believe in limited government they are the allies of those who believe in no government. It is possible to support mercy, show tolerance, and support pluralism without favoring no government. Conservatives used to have a cautious regard for the impact on the future, “First, do no harm”, not no consideration of the future, “Après nous, la deluge.”  There is a difference between cautious action and no action. A conservative used to jokingly be called a liberal who got old, moved to the suburbs, and took out a mortgage. In reality conservatives can be any age. An election contest between conservatives and liberals should be about representing all of the people, not winning against liberals so that you can rule the people.

Normal II

 

The First Commandment

I am the lord, I am your God.
I am the Lord, the only God.
I am the Truth, I am the Life
I am the Way, the only Way.
You shall have no other gods before me.

Do YOU believe in the commandments?

"I am the Lord your God, you shall have no other gods before me”.  Kind of definitive isn’t it. There is  “God” vs. “no God”, but there is NOT“Good” vs. “Evil”.  That would imply that there are two gods.  Thus the choice is between 0, “No God” and 1, “God”, not between -1, “Evil” and 1, “Good

And that makes all of the difference mathematically.  Before a “Come to Jesus Moment”, μ, when you are saved, you can be 0, but you can not be -1.  This requires that the mean of choice, μ, is 0.5, not 0.0; the median of choice, CDF(μ) is 50%, not 100%; and the mode of choice is also 50%, not 100%.

There is also the problem that those who believe in Good vs. Evil also seem to believe that there is no variance, whose square root is standard deviation.  If we live in a universe where the choices are 0 and 1, then the range of choices, the difference between the mean and the actual choices, s, is 0.5. If random events follow a logistics distribution, a hyperbolic secant squared distribution, then the variance, σ², is s²π²/3, which means that the square root of the variance, σ, is s*π/√3 and the universe of random events is  hyperbolic.  If s =.5, then this means that the standard deviation, σ, is .5*π/√3=0.9069.  In a normal distribution (a mathematical term, not a judgmental term) the choice which ordinarily happens at the mean can happen as early as μ-3*σ and as a late as μ+3*σ and its cumulative choice, CDF, would be 1 at infinity and 0 at negative infinity.  While it is true that having a standard deviation of 0 also has a CDF of 0 at -∞ and a CDF of 1 at +∞, but having a variance of zero does not satisfy the 68/95/99 rule and is thus NOT normal.

Reality TV

 

Tryin' To Make It Real, Compared To What?

I love the lie and lie the love
A-Hangin' on, with push and shove
Possession is the motivation
That is hangin' up the God-damn nation
Looks like we always end up in a rut (everybody now!)
Tryin' to make it real, compared to what? C'mon baby!

REALity TV, compared to what?

With the WGA on strike, the broadcast TV networks are getting set for a fall season with lots of Reality TV. At least that is what they, and a former president who was a Reality TV star, call it. A better name is UNSCRIPTED, because it is anything but REAL.

I once had the opportunity to attend a taping of Deal or No Deal, a reality TV game show. I wish it was in the first two seasons when Meghan Markle was a briefcase model, because that would make a better story, but it was in a later season. What you see on TV is anything but what is real.

What was broadcast on the TV screen was the unexpected appearance of the loved ones of the contestants in the audience. In reality, the people in those seats were removed and the loved ones were seated for just that shot. The contestant was so excited and hyper when the cameras were rolling. When the cameras stopped, that hyper, excited contestant sat passively and did not move. The one-hour show which was broadcast became a 4-hour ordeal to record, and when those originally in the audience started leaving, the remaining audience members were herded into their empty seats so only shots with no empty seats would be shown on camera. What you see is NOT what is real. What you see is what the producers want you to see.

Public Goods

 

Return To Sender

Return to sender, address unknown
No such number, no such zone
We had a quarrel, a lover's spat
I write I'm sorry, but my letter keeps coming back

Th US Postal Service will return to sender, but an email site?

I have an email address that my family ghosted. It was so inundated with spam, etc., that it became easier to just move to another company and another email address. But that original email address is still active all of these years later. And it is the email address that is on file with my college. I only found this out when I had to go back to that email site (I had to be verified by the company offering that email that I was who I said I was). In doing so I found hundreds of old emails from my college.

The college knows my post office address. When I move or change that address, mail gets forwarded for a time and then eventually it is retuned to sender. I am well aware of this because when my late father moved to a nursing home, he received forwarded letters for a time, but the sender eventually received a return to sender note.

And that is the difference between a public service, as provided by the US Postal Service, and a private company providing an email address. A public service can attempt to notify both parties when it is unable to complete a transaction, even when it makes no profit on that notice. A private company can not be expected to notify either party unless it is getting a profit for providing that service. Email addresses provided by a private company may look and feel like a public good, but they are still private goods, and unless those private goods make money they will not be offered. So no incentive to return to sender,

Tolerance III

 

The Rules of the Road

But that's how it goes,
You live and you learn,
The rules of the road.

So what are the rules?

Playing a game means following the rules of that game. There is a branch of study about playing games, Game Theory. It studies, subject to the rules, the best strategy for playing a game. Game Theory has demonstrated that there are different strategies for playing a game with only two‑players, than there is for a game with three-or-more players, (and that does NOT mean that there are not three‑players in most games. There is often an umpire to call balls and strikes, even if that umpire is merely the two players being honorable, and there is probably a league of potential opponents, making all of those games more than two-players). But the rules should only ensure that bad behavior is not rewarded if it is caught, not that there is no bad behavior.

There is a board game called Lie, Cheat and Steal. It is a variation of the Prisoner's Dilemma. The object is to win even if that means lying, cheating, or stealing. The payout matrix for Player One on each move, the rules, where the payout matrix for Player Two is the oposite of this, effectively is:

Player One (rows)/Player Two	Not Lie, Cheat, or Steal	Lie, Cheat or Steal
Not Lie, Cheat or Steal	1	-2
Lie, Cheat or Steal	2	0

But there is a problem for society if this behavior is rewarded. If players Lie or Cheat, then transactions may not take place. If Stealing is allowed, then there is no incentive to ever produce anything because it may be stolen from you. To allow transactions to continue and to encourage production, society would prefer it if the payout matrix for Player One was:

Player One (rows)/Player Two	Not Lie, Cheat, or steal	Lie, Cheat or Steal
Not Lie, Cheat or Steal	1	0
Lie, Cheat or Steal	0	0

The payout matrix would be the same if the a constant were subtracted from every cell, for example, 

	Not Lie, Cheat, or steal	Lie, Cheat or Steal
Not Lie, Cheat or Steal	0	-1
Lie, Cheat or Steal	-1	-1

And that is why society has laws and trials. Those laws are not intended to PREVENT lying, cheating, or stealing. They are intended to NOT REWARD lying, cheating, stealing or other bad behavior, if and when it is caught. The penalties should be large enough such that being caught has to be considered when each player makes their choice.

IOW, dominance, winning at all costs, might be good for one player, but that win is not necessarily good for society. What is good for society, is tolerance, allowing, but not encouraging, any choice, i.e. making each game at least a three-player game. Any law which restricts choice even if that choice is to lie, cheat or steal, is bad, even if it is well intentioned.  But laws can be enacted to prevent rewarding bad choices.

Affirmative Action II

 

Working Class Hero

There's room at the top they are telling you still|
But first you must learn how to smile as you kill
If you want to be like the folks on the hill
A working class hero is something to be
A working class hero is something to be

Should the working class be opposed to Affirmative Action?

I have degrees from two of the Ivy Leagues. But, since I come from a working-class background, I could not afford tuition at either of these Ivy League Universities. I was only able to attend because of merit based scholarships.  I was a National Merit Scholar in high school and properly nerdy enough at my undergraduate college that I earned merit-based scholarships to graduate school.  This must mean that I am FOR a merit-based system and OPPOSED to affirmative action,  correct?  Nothing could be further from the truth.   https://dbeagan.blogspot.com/2022/08/affirmative-action.html

Man is a group animal.  In the words of John Donne, “No Man is an Island”. It is the group that matters, not each individual in that group, whether that group is a club, a college, or a nation.   A merit based system is good for the individual and should be supported, but Affirmative Action is for the group, including every individual in that group, including the working class.