Zero and Infinity

My Hero, Zero

You're here,

And nobody really knows

How wonderful you are.

Why we could never reach the star,

Without you, Zero, my hero,

Zero, how wonderful you are.

When we talk about zero or infinity, we should understand what is meant by these terms.

Zero is not just the smallest number.  It is the smaller than the smallest number that can be imagined.  The smallest observable length is the Planck Length, which is  1.62× 10-35 meters.  At the speed of light, it would take  3.34 times 10-9 seconds.  Zero length is even shorter than this length. Zero time is even shorter than this time.   

At the other extreme, infinity is not just the largest number, It is larger than the largest number that can be imagined.  If the Planck length is the smallest observable number, then the inverse of the Planck length, is 6.17 times  1034 meters, which is 1.7 times 1020 light years.  This also means that  it would that it would take 1.7 times 1020  years to travel this distance  at the speed of light.  An infinite length is even large than this length, and infinite time is larger than this time.

Zero and infinity are necessary for mathematics.  But just because something is a large number it does not mean that it is infinite.  Even if something is a small number, it is still greater than zero.  Whenever we deal with large or small numbers it is important to remember this.

Strategy and Tactics II

 

Love and Marriage

Love and marriage, love and marriage

They go together like a horse and carriage

This I tell you brother

You can't have one without the other.

Some things just go together.  But we shouldn't overemphasize one at the expense of the other.

Strategy and Tactics are often used in discussing military affairs.  If we lose every battle, we can’t expect to win the war, but according to the familiar adage  we don’t want to “win the battle (e.g. have a tactical victory) but lose the war (e.g. have a strategic defeat).”  There are those battles that are too costly to win,  i.e. Pyrrhic victories.  There are also strategic retreats where the battle may be lost in order to fight again and win the war. 

Pearl Harbor might have been a tactical victory for the Japanese, but it led to their strategic defeat. Dunkirk is remembered not as a tactical victory by the British, but as a strategic retreat that was an important part of the British victory in WWII. 

Planning, which is merely another name for strategy, is different than operations, which is merely another name for tactics.  They have different goals and time frames.  But both are needed.  It would be a mistake to have an operational success today, that leads to a long-term planning failure in the future.  Both planning and operations are needed in a successful organization.  You can’t have one without the other.

It's Relative

 

How Deep is the Ocean?

And if I ever lost you

How much would I cry?

How deep is the ocean?

How high is the sky?

Are large numbers useful?

Large numbers can be useful, if people understand the difference between relative and absolute values.  A large number by itself is an absolute measure  A large number in comparison with another large number is a relative measure.  To avoid confusion, an effort should be made to state something using both measures, and see if the perception changes.

The vaccination program for  COVID-19 was opened to persons over 65 in Massachusetts on February 18, 2021.  At that time, Governor Baker announced that this would open the vaccination to over one million people.  He further announced that 70,000 appointments would be available beginning on that date.

70,000 sounds like a large number and in absolute terms it is a large number.  However in relative terms it is 70,000 appointments for 1 million people or 7% of the eligible population.  That doesn’t sound so large.

Similarly if we hear that Tiffany’s is having a 50% percent off sale, it sounds like a great deal. But if stated in absolute terms, a $10,000 necklace is on sale for $5,000, that absolute number might only be a good deal if a person can afford that $5,000.

It is useful to state numbers as both relative and absolute values before making a judgement.  This might lead to different judgements being made.

Climate Change

 

Stormy Weather

Don't know why

There's no sun up in the sky

Stormy weather

Since my man and I ain't together

Keeps raining all of the time

There is a difference between weather and climate.

At this moment, there is artic weather in Texas.  Is this evidence that the climate in Texas is cooling, not warming?  Hardly.  Climate is the average of weather over a long period of time. If the weather is colder than is normal now, but has been hotter than normal on previous days, it is an indication that the weather is more variable, not that the climate is colder.  The time period matters.  If the only evidence is from the now, then yes Texas is experiencing Artic conditions.  However climate is about more than the weather right now.

Those who confuse climate with weather are ignoring both the evidence and the definitions. Just as a failure to convict by a supermajority at the February 2021 impeachment hearing should not be confused to be a finding of innocence by a majority at that same impeachment hearing.  Since some of the votes for acquittal were made on constitutional jurisdiction grounds, e.g. the public statements of Sen. McConnell, it can not be claimed that even the vote at impeachment trial was a verdict of innocence.  Even though the Senate apparently voted on the constitutional jurisdiction issue on February 9^th, at least some of the votes for acquittal were not based on the evidence but on constitutional jurisdiction grounds. Those might have voted guilty on the article of impeachment based solely on the evidence.  Additionally since the Senate also took an oath to impartially hear the evidence, and some Senators were either not impartial, or did not even pretend to listen to the evidence, then whether there was a supermajority of impartial Senators on the evidence, not the jurisdiction, was not determined.  

An acquittal in the O.J. Simpson case did not mean that O.J. Simpson could not be found guilty later either in civil court or the court of popular opinion.  A finding depends on the evidence, regardless of what the conditions are now, and on the definitions.  Absence of evidence is NOT evidence of absence. An acquittal is NOT a finding of innocence.  Cold weather is NOT a finding of a colder climate.

Third Parties II

 

It Takes Two

It takes two, baby
It takes two, baby,
To make a dream come true
It just takes two 

It may take two, but what if there are more than two? 

A decision has to be made on: who serves in a government; who is served by a government; and who, and at what amount, is taxed by a government.  This presumes that there is a government, but those who advocate for no government need to explain whom will provide the benefits supported by a government. (We The People ….and all that jazz😉). 

Those who serve in, control, government need not include all members of society.  The US Constitution excludes persons from serving in certain offices based on their place of birth or age. ( e.g. a President must be a natural born citizen over 35 years old.)  Those served by the government need not be limited to those who can serve in the government  (e.g. spotted owls may be served by government, but no one expects them to serve in government).  Those who are taxed by the government need not be authorized by that government. ( e.g. The IRS estimates that about 6 million unauthorized immigrants file individual income tax returns each year. Research reviewed by the nonpartisan Congressional Budget Office indicates that between 50 percent and 75 percent of unauthorized immigrants pay federal, state, and local taxes.)

A political party must make decisions about whether it supports inclusive or exclusive government.  (e.g. who serves in, is served by, and/or is taxed by, government.) A political party must make a decision as to whether it supports a limited or a strong government.  ( the support for NO government by a political party, who are vying to run a government, is a non sequitur.)  While these decisions are continuous not binary, let’s assume that they are only binary.  Then there are potentially four groups of people.  The problem is that the US government by supporting single-ballot plurality-rule elections that are structured within single-member districts tends to favor a two-party system. That is Duverger’s Law.  Since there are potentially at least four groups, and only two parties, two groups may not find a party to represent them.

This dynamic might explain the tension that exist in society today.  Four groups are vying for the control of only two parties. Either groups agree to exist within a party, or they exclude themselves from any party.

 

Lies Count

 

Lies, Lies 

Lies, lies
I can't believe
A word you say
Lies, lies
Are gonna make
You sad someday

Someday, you're gonna be lonely

But you won't find me around

Lies, lies, breaking my heart 

Can we always tell when we are being told lies? 

Mark Twain popularized the phrase “There are three kinds of lies: Lies, damn lies, and statistics”.  Statistics are hard to understand and while they are not lies themselves, if they are misunderstood, then they can become lies. 

A problem with statistics is that most of us do not understand the difference between absolute and relative amounts, and when to use each.  If we hear that vaccines have been administered to 10 million people, but we live in a country with a population of 330 million, while 10 million is a large absolute amount it is only 3% of the population, which is a small relative amount.  When we hear that the price of something is 50% off, that is its relative amount, but the absolute amount is still 50% of the original price, which still might be more than we can, or should, spend. 

A way to better use these statistics is to convert a relative amount into an absolute amount, or vice versa, and see if these new values change the opinion which the statistic was supporting.  If the opinion remains the same, then statistics didn’t lie.  If the opinion does change, then statistics were being used to lie. Lies might not count, but liars can count.

Third Parties

 

The Party’s Over

The party's over, it's time to call it a day.

They've burst your pretty balloon, 

And taken the moon away.

It's time to wind up the masquerade,

Just make your mind up,

The piper must be paid. 

If those leaving the Republican Party form a third party, what will happen? 

Duverger’s Law explains why there are only two parties in the United States.  There may be third parties at any given point in time, but eventually there will only be two parties.  The interesting question  is who will leave the Republican Party and form a third party, and whether that third party eventually becomes the alternative to the Democratic Party. 

Those Republicans who opposed Donald Trump have threatened to leave, or are being pushed out, to form a new center right party.  Those who support Donald Trump have threatened to leave and form, what they are calling, a Patriots Party.   Who leaves, and/or who gets absorbed into another party, eventually will determine what happens in the long term.  Those who support the existing caste system, oppose immigration, and have a narrow view of whom government should be supporting, will not likely find a home in the Democratic Party.  They are the Trump supporters who currently are in the Republican Party.  The “Never Trumpers” might see a place as a conservative wing of a Democratic Party, but if the Republican party is dominated by Trump supporters, then they have to decide whether to continue to be included in that party.  If neither of these groups see a place in the Democratic Party, the less influential group is likely to simply stop supporting any party and no longer vote.  

In any event, if the current divisions continue in the Republican Party, then eventually the dominant group will become the Republican Party or its replacement, and the losers may no longer vote, have a party to represent them.  It is too early to say if that group will be those who believe in limited but inclusive government or those who believe in exclusive government, if there is to be any government at all. There are two binary decisions: Limited or strong government; inclusive or exclusive government. This defines four possible groups but we can only support a two party system.  Some group has to be left out of the party.