Variance II

 

Don’t Fence Me In

I want to ride to the ridge where the west commences
Gaze at the moon till I lose my senses
I can't look at hobbles and I can’t stand fences
Don't fence me in.

But what if the fence is very, very distant?

A fence limits the outcomes of events. In the universe of random choices there are limits. Those limits are very, very large. For example there are estimated to be between 10⁷⁸ to 10⁸² atoms in the universe. Each of these atoms can have as many as 100⁺ electrons. Each of these electrons can be in random, quantum locations. It is such a large number that for all practical purposes the human mind treats this as an infinite number. But the choices still exist and there is a finite, although very, very distant “fence.” 

In a logistics, sech squared, distribution the parameters are the mean, µ, and s, the range of the choices. The variance, σ², in a logistics distribution is s²π²/3, which means that σ=sπ/√3, and s=√3σ/π,  The variance in a logistics distribution also follows the 68/95/99 rule of normal distributions. In fact at µ+3σ there are 99.97% of the outcomes in a normal distribution. Since in a normal distribution, such as the logistics distribution, the median is also µ and the median by definition is 50% of all outcomes, then, with rounding, 2µ=(µ+3σ) or σ= µ/3, which means that s= µ/√3π. It is thus not possible for there to be no fences, a variance of zero, unless the mean is also zero. In a simple binary choice, yes/no, 1/0, the mean, µ, is 0.5 and the variance, σ², is thus .03.  The mean, µ, is by definition n/2, where n is the number of observations in the sample, thus the variance is  n²/36. As noted above the variance in a universe with more than 10¹⁰⁰ , also known as googol, where do you think the name google comes from, choices will be very, very large but it will still exist. Unless there are no choices, s=0, then the variance can not be zero. Just because you can’t see the fence because it is very far away, doesn’t mean that the fence is not there.

Climate Change II

 

Here Comes The Rain Again

Here comes the rain again
Falling on my head like a memory
Falling on my head like a new emotion

There is a difference between rain and climate.

“Everybody talks about the weather, but no one ever does anything about it.” – Mark Twain.

That is because weather, including rain, is a random event, but climate is a long-term trend. To put it in statistical terms: weather follows a random probability distribution, but climate is the variance that describes the range within which those random weather events can occur. And maybe that can help inform the whole climate change debate. Just because we can’t always control random weather events, maybe we can influence the variance within which those events can occur. Being able to influence climate does not mean that anyone is claiming the ability to influence individual weather events. It is like setting up the house rules at a casino. If it is an honest casino, then each game is a random event that occurs within those house rules.

Saying that there is a concern about climate changes, is saying that there is a  concern about the house rules, NOT that anyone is under the illusion that they can control each random game.

Preclearance

 

It's Been A Long, Long Time

Kiss me once, then kiss me twice
Then kiss me once again
It's been a long, long time

How long is a long, long time?

This is not a silly question. The Supreme Court in Shelby v. Holder ruled that the preclearance requirement of the Voting Rights Act was no longer valid because

“Our country has changed, and while any racial discrimination in voting is too much, Congress must ensure that the legislation it passes to remedy that problem speaks to current conditions.” 

It is true that while governments might have illegally discriminated in the past, no individual currently in government is being charged with that discrimination. Uh…... that is NOT what the Law says. Preclearance does not mean a government can not change their rules, only that governments who have exhibited a pattern of discrimination in the past must preclear those rule changes before they are implemented.

The fact that individuals currently alive do not discriminate does not change the fact that the governments in the past had discriminated. In a few weeks, on July Fourth, we will celebrate the anniversary of the signing of the Declaration of Independence. I guess because no one alive today signed that Declaration we should not celebrate. In November we will celebrate Thanksgiving to commemorate an autumn feast by the Pilgrims. But since no one is alive who was at that feast, then I guess that any celebration is misplaced.  The same goes for Christmas, Passover, etc. Since no one was alive who was present at those events, the religions should not celebrate them. I also guess that the Armenians have forgiven the Turks because no one was alive who forced the march into the desert, and the Irish Catholics must be imagining the parades that Irish Protestants march to commemorate the Battle of the Boyne since none of the marchers were at that Battle. The point is that nations, religions, cultures, etc. exist far longer than the individuals who are currently in those groups. Saying that the group has done good or bad does not mean in any way that the current members have done good or bad. The group may last longer than any individual in that group. If the remedy is being applied to the group, the fact that the individuals in that group have changed is irrelevant. A long, long time to an individual of a group may not be a long, long time to that group.

Intellectual Property

 

You Belong To Me

See the pyramids along the Nile
Watch the sun rise on a tropic isle
Just remember, darling, all the while
You belong to me

But to whom does Intellectual Property belong?

“To promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries;”

US Constitution, Article 1, Section 8

A copyright, ©, is a protection for the seller in a transaction. A copyright licenses the Intellectual Property, IP,  of artists for a defined period before it enters into the public domain. A copyright confers government protection for that Intellectual Property while it is NOT in the public domain. Otherwise that IP could otherwise be copied, without a fee, by the potential buyer. Without this protection, the seller does not have an incentive to produce that Intellectual Property.

A patent is related to a copyright but covers scientific and technical Intellectual Property. Like a copyright, it is for a defined period and is protected by the government during that period.

A trademark, ^TM, is a protection for the buyer in a transaction. A trademark is used to ensure that the good that is being sold is trustworthy.  A trademark may include a word, but it is most probably a stylized symbol which may include a word. A trademark does NOT have a defined period and is valid forever. E.g. one of the oldest trademarks is the Golden Lions of Lowenbrau. By registering that trademark with the government, the government is ensuring that the goods being sold with that trademark can be trusted by the buyer.

Copyrights were originally extended to authors because, under the technology at the time that the Constitution was written, primarily books could be easily copied. The intent is that all creative works can be copyrighted, and that all inventions can be patented.

Artists and inventors are people, not corporations. An artist or inventor can be employed by corporations, but corporations are NOT the People, at least they are not enumerated in the US Census as the People. Corporations are instead chartered by the government. Corporations may be groups of the People, but they are a special entity charted by the government where the assets of the People owning shares in, or employed by, those corporations are protected from liability.

As such, corporations should not be issued copyrights or patents. They are not the People. Copyrights, or patents, can not be created, or invented, by corporations. They can be created, or invented, by the People employed by corporations, but not by corporations themselves. Thus copyrights and patents should be issued only to the artists and inventors. Those artists and inventors can then in turn issue licenses that may give rights, including exclusive rights, to anyone, including corporations, during the period that the government is ensuring its protection.

This is NOT  a trivial issue. For example, a copyright can be issued to the late Walter Elias Disney for Steamboat Willie and that copyright can be passed down to the estate of Walter Elias  Disney during the period of protected ownership. The license to use that copyright, including exclusive use, can be sold to the Disney Corporation, and the Disney Corporation can own the license to the copyright, and whatever terms and restrictions are agreed to in the license between the copyright holder and the receiver of the license, but not the copyright itself.

Thus it becomes a legal matter to whom copyrights, or patents, may be issued. In the case of a book, it is clearly the author. In the case of a song, it may be the composer and the lyricist. In the case of collaborative arts, such as movies, the copyright may name a number of positions ( e.g. producer, director, leading actors, writers, etc.) while excluding others ( e.g. extra and uncredited actors, stunt persons, grips, etc.)  Who can be named on a copyright, or patent, should be a legal matter. The ability to issue of copyrights and patents is a congressional matter, the actual issuance is an executive matter, and disputes about ownership and licensing is a judicial matter. Corporations can license copyrights, or patents, but they can not own copyrights. or patents.

Because corporations have previously been issued copyrights and patents, any changes where copyrights and patents can NO LONGER be issued to corporations would take effect only upon enactment of a new law. At that time, all existing corporate copyrights, or patents, should be considered instead to be exclusive licenses to that corporation by anonymous copyright, or patent, holders. Thus a case of copyright infringement by one corporation against another, would be treated exactly the same but would now be a case of license infringement. Corporations could be sued for license infringement, but they could not be sued for copyright, or patent, infringement because while they could license a copyright, or patent they could not be issued a copyright, or patent.

In the case where there are multiple holders of a copyright or patent, it should take only a two thirds supermajority of those holders to issue a license. This would prevent a single copyright, or patent, holder from being able to block the actions of other holders of that same copyright or patent.

All licenses should require that the copyright, or patent, IP is available during that specified time period. If the IP is not available to others, or is not used by the license holder, during that period, any license would be terminated. Thus corporations could not buy up and prevent patents from being sold or used, and streaming platforms could not delete copyrighted material from their sites, effectively making them unavailable to all other parties.

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 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.