Tom Chavez

Just as a small insect rushes into a fire, Hiraṇya Kaśipu attacked Narasiṁha. Sri Narasiṁha easily captured the great demon, who could not be pierced even by a thunderbolt of Indra, just as Garuḍa might capture a great snake.

Garuda is the avian carrier of Lord Viṣṇu. He is very big in Thailand, Indonesia and other Asian countries. But I digress.

Al Peffley

Single Person Transportation in the world of 2020:

Hitachi Personal Vehicle Prototype

Colibri Single Person Rechargeable Electric Car (pretty cool color and body shape, huh?)

We've come a long way, baby!

I LIKE this 1962 vintage vehicle (and even owned one in a former life ):

A John Delorean "masterpiece"...it was a classy-looking, high performance 389c.i. Catalina in simply elegant styling.
 

Gregg Wilson

I rest my case.

Al Peffley

I once owned a '56 Chev two-tone lime green and black sedan with a 301c.i. engine in it, but never a '57. My favorite '57 model was the Bel Air 2-door post sedan in black or black with a white top. Bob Keller (thanks for supplying his last name, Rich) had a fast '57 2-door post that he modified for drag racing and drove around Burien in the mid 60's. I always liked the sedan's looks over the hardtop models (less interior chrome and fewer water leaks.)

This classic '57 2-door sedan "Gasser" was auctioned off at Barrett-Jackson a few years ago for big bucks.

The car brings back good memories of hot August nights at Alki Point, HCC parties, and cruising the Seward Park loop. I think Ronnie Joors (his parents owned the Blockhouse Restaurant next to the Spanish Castle on old Highway 99) also had a '57 Chev and someone in our class that lived in Normandy Park. I think Ronnie died tragically in a fire while he was sleeping at rental house across from the Alki Point beach.

This was George Brower's '57 Bel Air 2-door sedan (photo taken by me at his farm, only months before he passed away - RIP, my very good friend):

Tom Chavez

Hiraṇya Kaśipu’s Demise

Hiraṇya Kaśipu flailed his limbs all around, very much afflicted at being captured by Narasiṁha. In the doorway of the assembly hall Narasiṁha placed the demon on His lap, and eviscerated him with the nails of His hand.

Narasiṁha’s mouth and mane were sprinkled with drops of blood, and his eyes burned with anger. Garlanded with intestines from Hiraṇya Kaśipu’s abdomen, Narasiṁha resembled a lion that has just killed an elephant.

Hiraṇya Kaśipu was not killed by any living entity in the universe, but by Viṣṇu himself in the form of an avatar, descended from the spiritual sky. He was not killed by any weapon but by the sharp nails of Narasiṁha.

He was killed neither indoors nor outdoors, but in the doorway of the palace. He was not killed during the day or night, but at twilight. And he was not killed on the ground, in the water or in the sky but on the lap of Narasiṁha.

Tom Chavez

Prahlād is Crowned King

After the mess was cleaned up and order restored, Narasiṁha spoke to Prahlād, “My dear Prahlād, I am very pleased with you. It is my pastime to fulfill everyone’s desires. You may ask from Me any benediction you like.”

Prahlād smiled and said, “My dear Lord, I am born of a demoniac family and am naturally inclined to material enjoyment. Kindly do not tempt me with those illusions which create bondage to birth and death.”

Narasiṁha said, “My dear Prahlād, a devotee like you never desires material opulences, either in this life or in the next. However, I order you to become king of the demons. It doesn’t matter that you are in the material world. Always think of Me, for I am the Supersoul in everyone’s heart.”

Prahlād said: “O Lord, because You are so merciful, I ask for one benediction. My father, due to ignorance, was inimical toward You, falsely thinking that You killed his brother. I wish that he be excused for his atrocious activities.”

Narasiṁha replied: “My dear Prahlāda, your father has been purified. Because you were born in this family, the entire dynasty has been purified. Wherever devotees decorated with all good qualities appear, that place and dynasty, even if condemned, are purified.”

Narasiṁha spoke to Brahmā: "My dear Lord Brahmā, as it is dangerous to feed milk to a snake, it is dangerous to give benedictions to demons, who are by nature ferocious and envious. I warn you not to give such benedictions to any demon again."

Prahlād performed the ritualistic ceremonies for his father and then Lord Brahmā enthroned Prahlād as king of the demons. The kingdom would be eventually handed down to Prahlād’s son and grandson, while Prahlād was still alive.

During the reign of Prahlād’s grandson, named Bali, another avatar of Viṣṇu descended to trick Bali out of the heavenly kingdom in order to return it to the demigods. But that is another story. 

According to the Vedas, the Supreme Lord descends innumerable times into the universe, on various planets, to counteract the demons, to save the pious, and to restore the principles of dharma.

Many avatars and pastimes are described in Śrīmad-Bhāgavatam, sometimes called the ‘Biography of God’. An English edition of this ancient classic is available in 18 volumes from the Bhaktivedanta Book Trust, with original Sanskrit, translations, and purports.

Gregg Wilson

The good ol' times:

Good ol' times in 1956, 1957, 1958:

We lived in Milwaukee and I got to follow the Braves. We would bicycle every so often down to the park; sit in the right field bleachers; and watch and talk to Hank Aaron. He was polite and quiet. But when he came to bat, you held your breath. He was all business and would likely hammer it out of park. We knew he go farther than Babe Ruth. And he did. The home run king.

Got tired of blabbing about the virus.

Al Peffley

I was back east on a business trip and was lucky to see Cal Ripken play two games which were his last two when he retired. After each game he signed autographs for children until the last kid left the ballpark. He loved kids and donated a lot of time supporting youth programs. He was also a humble man with a big heart. He made the most amazing play on a third base line drive I have ever seen by an infielder. He jumped about three feet straight up off the ground, caught the hot ball on the tip of the glove's web, spun in mid air while transferring the ball to his throwing hand, and threw a bullet ball exactly to the first baseman to make the second out. It was accomplished with smoothness, perfect motion, and preciseness with perfect body coordination. What extraordinary talent for a senior player!

Tom Chavez

Tom Chavez

Journey to Infinity—Historical Background—Is Infinity Real?

Over thousands of years people have debated whether infinity and infinitesimals (smaller than anything, but bigger than nothing) actually exist.

Around 450 BC, Zeno introduced paradoxes arising from infinitely dividing time, space and physical particles. These paradoxes made folks skeptical about ‘infinitesimals’ for millenia.

Aristotle argued that there is no infinite, only a ‘potential infinity’. If you take the biggest number ever and add 1, you get a bigger number. This can go on as long as you like, but you never get to infinity.

Euclid proved that there is no end to prime numbers, but he also considered them only ‘potentially’ infinite, since you can never get to all of them.

Around 50 BC Lucretius argued that a finite universe must have a boundary. An object thrown at the boundary would go right past it since nothing lies beyond the boundary to stop the object. Therefore space must be infinite.

In the 5th century St. Augustine argued for an infinite God capable of infinite thoughts. He wrote, “Who are we mere mortals to dare presume to limit God’s knowledge?”

Thomas Aquinas, in the 13th century, argued,“Any set is specified by the number of things in it. No number is infinite, for number results from counting through a set. So no set can actually be infinite.” 

Giordano Bruno in 1584 published ’On the infinite universe and worlds’. He was brought before the Inquisition and tortured, but refused to recant, and was therefore burned at the stake in 1600. Infinity defied ecclisiastical authority. 

The teaching of infinitesimals was banned in Jesuit Colleges in 1649. In 1665 Isaac Newton developed infinitesimal calculus, but substituted the word ‘fluxion’ for ‘infinitesimal.’ He prudently did not publish his work.

In the 1700s, George Berkeley ridiculed Newton’s ‘fluxions’: “They are neither finite quantities, nor infinitely small, nor yet nothing. May we not call them ghosts of departed particles?”

David Hume argued that space and time are not infinitely divisible; there is a minimum size which you can’t further subdivide. 

Immanuel Kant argued that infinity can’t exist because it can’t be perceived. The influential mathematician, Carl Friedrich Gauss, argued that ‘infinite’ is not to be taken literally, because infinity is never permissible in mathematics.

By the 1800’s the question remained: is infinity real, a metaphor, or just a fiction of imagination?

Tom Chavez

Covid-19 News: Young People More Susceptible

Young adults and children appear to be increasingly contracting Covid-19 in the United States, according to a new study. Half of those who had tested positive for Covid-19 in Washington state by early May were aged under 40, significantly more than at the initial stage of the outbreak

Epidemiologist Judith Malmgren and her team at the University of Washington analyzed data from all 22 testing laboratories across the state. They found that young people had become more susceptible to the virus since early March.

While new cases have been declining in Washington state, the proportion of children and young adults confirmed with Covid-19 rose from 20 per cent on March 1 to 50 per cent early this month.

And there was “no decline in cases” in the 0 to 19 age group, Malmgren said in the paper. In contrast, the incidence of the disease among people aged 60 and older fell by 55 per cent from the peak of cases.

In Brazil, doctors have said that half their patients were young, and many were dying – 15 per cent of deaths in the country were people aged under 50, which was 10 times the proportion in Europe, The Washington Post reported.

The situation was worse in Mexico, with nearly a quarter of deaths among people aged between 25 and 49, according to health authorities.

Hydroxychloroquine Looking Worse with Time

Hydroxychloroquine has no benefit on hospitalized patients and could raise the risk of heart problems and death, according to a study of nearly 100,000 cases, based on data from 671 hospitals on six continents, and published in the medical journal The Lancet on Friday.

The paper assessed the cases of 96,032 hospitalized patients, of whom 14,888 were treated with hydroxychloroquine, chloroquine, or a combination of the drugs with a class of antibiotics called macrolides.

The study was conducted by researchers from Harvard Medical School, health data firm Surgisphere, University Hospital of Zurich, the University of Utah and the HCA Research Institute.

All 14,888 people treated with the chloroquine regimens were given the medication within 48 hours of being diagnosed with Covid-19 and were not on mechanical ventilation when they started the treatment.

While the control group had a mortality rate of 9.3 per cent, the treatment groups had the death rate ranging from 16.4 per cent to 23.8 per cent.

In addition, the patients in the treatment groups reported a much higher percentage of heartbeat abnormalities known as de-novo ventricular arrhythmia.

< Both reports from South China Morning Post, Hong Kong >

Tom Chavez

Journey to Infinity — Simple Sets

In 1840 the mathematician Bernard Bolzano published ‘Paradoxes of the infinite’ in which he argued that infinity actually exists. He introduced the idea of infinite sets.

Georg Cantor developed that idea and changed the whole course of mathematics. 

A set is a collection of things, called ‘elements.’ The elements can be anything. A set may be defined by words, like “the set of all humans.” The ‘elements’ of this set include all people. 

Mathematicians often use brackets to indicate a set. For example, {  } is a set of three apple symbols.

Cantor needed a way to compare sets. He defined equality between sets as follows:

Definition: Two sets are equal if each element in both sets can be mapped to one and only one element in the other set. This is called a 1-to-1 mapping, or a 1-to-1 map.

When we count the elements in {  }, we create a 1-to-1 mental ‘map’ between  {  } and the set {1, 2, 3} of the first three counting numbers. 

Here are three examples of mappings (indicated by arrows) between a set of numbers and a set of mangos, showing equal and unequal sets:

A. The element 1 is mapped to two mangos. This is not 1-to-1, so the sets are unequal.

B. The element 4 is not mapped. But each element should be mapped, so these sets are unequal.

C. Each element in each set is mapped to one and only one element in the other; therefore they are equal sets.

Two sets are equal if there is a one-to-one mapping between them. If you understand this, then you are ready for the counter-intuitive insanity of infinity!

Al Peffley

Tom - I did not see anywhere in your medical therapy trial reports that zinc was used in concert with the drug on patients at the onset of the Chinese virus infection process. The drug will NOT help a patient after they lose too many lung cells and bacteria begins to complete the fatal respitory system damage on vulnerable humans.

This is another MD's view of the ongoing death toll reports and why some Richard Horton endorsed actions by US governors have not been successful, except to damage Americans' way of cutural life, the US economy, the judgement calls of our sitting President, and our God-granted individual freedoms described in the Bill of Rights:

https://www.americanthinker.com/articles/2020/05/cooking_the_books_on_covid19_deaths.html

and another specialist MD's field experience is discussed in this article here:

https://www.americanthinker.com/articles/2020/05/killing_off_a_pandemic_is_engineering_not_science.html

I have read that the current Editor in Chief of The Lancet, Richard Horton, seems to have a bad case of "TDS". The international general medical journal has a major editorial staff office in Beijing (besides an US editorial office in New York, and headquarters in London.) Horton has admitted that he believes that, "... politics and health...the two go hand-in-hand." (https://www.telegraph.co.uk/news/health/news/11112930/Lancet-hijacked-in-anti-Israel-campaign.html - see last paragraphs of article).

(snip)

Horton and his fellow staff's latest political rants can be read here:

1. The Lancet (16 May 2020). "Reviving the US CDC". The Lancet. 395 (10236): 1521. doi:10.1016/S0140-6736(20)31140-5. [Sorry, for some reason this hyperlink does not work; please use Reference 3's hyperlink below to read this article.]
2. Ensor, Josie (15 May 2020). "The Lancet urges Americans to vote out Trump over coronavirus handling". Telegraph Media Group Limited.
3. https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(20)31140-5/fulltext

Hardly objective journalism for The Lancet, is it? I am sure some authors in The Lancet's articles are objective scientists who stick to accurate medical study criteria, well-documented assumptions and ground rules, and validated lab test techinques and processes as reported the journal. Mr. Horton is an academia "honorary professor", but I don't see any actual MD field work experience in his online bio's. He has worked for the UN and the WHO. He is also a climate change activist. America is not the CCP (yet). Horton has surely politicized a respected medical journal over the responses to the Chinese COVID-19 virus.

Tom Chavez

Al, the editor did not write the article. It is not my intention to mix politics and science. If it is any consolation, India is still using Chloroquine products as a preventative, not a cure. Of course, they manufacture most of the world's supply. Let's see how that turns out. Truth and oil will eventually come to the surface.

I don't know about zinc, but I do know this. Sunshine is good for your health!

Sunshine creates vitamin D when it interacts with your skin. You can overdose on vitamin D supplements, but if your skin generates too much vitamin D, the sunshine breaks it down. So you can't overdose via sunshine.

It is reported that people who have low vitamin D are the ones who suffer most from COVID-19.

Also, it is reported that sunshine quickly kills Covid-19 viruses. 

Let's soak up the rays and be happy and healthy!

Tom Chavez

Journey to Infinity — the Inexhaustible Counting Numbers

Between 1874 and 1884 Cantor developed formal set theory, which became a foundation of modern mathematics. Cantor demystified infinity, but most of his contemporaries misunderstood and deprecated his work.

The set of all counting numbers, N = {1, 2, 3, … , n-1, n, n+1, …}, is an infinite set. The three dots ( … ) represent the numbers we know are there, but can’t physically write down.

Now let’s make a new set containing every hundredth counting number, like this: N100 = {100, 200, 300, … , (n-1)hundred, n-hundred, (n+1)hundred, …}.

Out of every hundred elements in N, only one is in N100. It seems that N has 100 times as many elements as N100, and should be 100 times bigger. But the sets N and N100 are actually equal!

Below is a 1-to-1 mapping between N100 (top set) and N (lower set):

For example, suppose n is 23. Then “n mapped to n-hundred” means 23 is mapped to 2300. Similarly, 2300 is mapped to 23. In this way each element in both sets is mapped to one and only one element in the other set. Therefore, the two sets are equal!

This shows that 1/100 of the elements of N form a set equal to N. In fact, if you just take every millionth, billionth or gazillionth element, you still get an equal-sized infinite set! This is the inexhaustible nature of infinity!

The mathematician Dedekind appreciated Cantor’s work. Dedekind rejected Galileo’s view that the whole cannot be the same size as the part. Dedekind defined an infinite set simply as a set which has the same size as part of itself.

Even the tiniest fractional part of an infinite set can equal the whole set. Amazing! Take the biggest number you like, divide it into infinity, and the result is still infinity.

Of course, if you form a finite set from the elements of an infinite set, it is not equal to the infinite set.

Al Peffley

This is a pretty good description of Cal Ripken, Jr. and his career - https://en.wikipedia.org/wiki/Cal_Ripken_Jr.

Cal Ripken Sr. was a baseball coach and a great mentor to his son. They started the Cal Ripken Baseball League together that still is operating today.

I coached Little League (as an Infield Assistant Coach) for a few years when my son played Renton Little League baseball. I did not stick with the sport beyond Little League play as a catcher and church league mens softball teams. The Renton Little League team's Head Coach was a former Baltimore Orioles pitcher that played briefly with Cal when he was first drafted by the Orioles. I personally don't like the City of Baltimore's local government "culture". However, Baltimore still has some exceptional ball players, a lot of fans' team loyalty, great vendors at games with good food offerings, and a beautiful baseball stadium. I worked for the Army and DARPA at the Aberdeen RDEC for three years on the FCS Program before I retired from Boeing. Rural Maryland has beautiful scenery with agricultural and fishing industries. It has good food and a lot of conservative patriot farmers (unlike much of the Baltimore urban ghetto culture.) I liked Cal's quiet home town. I enjoyed going to eating places in Havre de Grace for a tasty supper near the Aberdeen Army base after work. Bel Air, Maryland, (west of Aberdeen) also was the home of an old-fashioned road house diner that served the best (and largest) crab cakes, loaded with crab meat, that I have ever eaten. I like eating at old-fashioned road diners. The established road diners are places where the older waitresses call you " 'Hon ", when they take your order. It makes me smile.

Gregg Wilson

Al,

When the Milwaukee Braves won the World Series in 1957, the town went crazy - in a good sort of way.

We returned to Burien in August, 1958. The Braves were once again in the World Series. My Dad came to my junior high. He announced that he was a doctor, I was his son, and I was very sick. Took me home so I could watch the World Series on television. But the Braves lost.

Oh, yeah, I was really sick!

Gregg Wilson

I am astounded at the political officials (president, governors, congressmen) who are in power but think they have everything under control. And, of course, the experts who have contradicted themselves constantly.

Not so.

We could probably have weathered this coronavirus without shutting the country down, destroying the economy, wiping out God knows how many businesses, and commanding people to stay in their homes, and having 40 million people lose their jobs. Having governments forcibly shut down small businesses that try to open, arresting the owners or massively fining them - has added fuel to the fire.

Promoting plastic gloves, face masks, keeping a safe distance, not touching your face, and washing hands would have been sufficient.

Now we have riots - destructive -in a number of cities because of the murder of a black man in Minneapolis? That was the tip of the iceberg. Putting 10s of millions of businesses out of business and 10s of millions of people out of work is the real cause of the riots.

"The natives are restless."

Usually I expect commentators on Fox News to be rational. But I listened to Tucker Carlson tonight declare that if these people would simply stop and think, there would be no problem. He doesn't have an effing clue.

Tom Chavez

The Core Problem

Gregg, I’ve not seen protest signs against epidemic controls. I see “I Can’t Breathe,” “No Peace Without Justice” and “George Floyd” everywhere.

The United States was founded on a principle that “all men are created equal; endowed by their Creator with certain unalienable rights..."

Unfortunately, certain contradictions have created bad karma.

European immigrants forcibly took lands from indigenous peoples, and then passed laws that it is illegal to take others’ lands by force. Where was the equality?

Slave traders brought Africans for brutal exploitation. Where was the equality?

After the Civil War various systems of favoritism and prejudice have continued. 

Today varieties of white supremacists, Nazis, anti-communists, anti-socialists, anti-immigrants, anti-Muslims, anti-Christians, abortionists, antifa, etc., want to privilege parts of society above others. 

What does “all men are created equal mean?” Certainly we are not equal on physical, mental or intellectual levels. 

I see society analogously to a living body. My body has a huge variety of cells: brain, muscle, bone, skin, nerve, liver, etc., etc. 

All those cells are living individuals, and I am like the lord of the body. All those cells serve and depend upon me. I also serve and depend upon them. I want cooperation with those cells to help me achieve my goals. 

Suppose some cells declare ‘independence’: “There is no owner or lord of this body, let us exploit the bodily resources and do as we like.” They become cancer or cause weakness and disease.

The cells are not independent. If I leave the body, all those cells will die. While I’m alive, all the cells are equal in my eyes. I need my heart, my skin, all those parts. Each has its duty and function.

Sometimes the cells fight one another, like an auto-immune disease. That is what is going on now in our larger society—faction against faction. We are diseased, and we are our own worst enemies.

In my humble opinion, the core problem is not racism, economic hard times, or pandemic. If we citizens are united in common cause, we can overcome any problem.

The core problem is that we are losing sight of our Creator and becoming an antagonistic chaos of selfish interests.

Our real equality is on a spiritual level; we are all creatures of the Creator, including other species. If we all cooperate to please our Creator, there will be harmony and blessings from above. If we exploit and kill other living entities, we suffer the reaction.

If we follow spiritual principles, the economic, socio-political, medical and other problems can be soon resolved. We can start by cultivating truthfulness, cleanliness, austerity, and mercy. By all our individual actions we create the society we live in.

Gregg Wilson

Tom,

Would you preach this philosophy to a rabid retard, who - having set fire to a police van - is now jumping up and down on the police van roof and is angry happy?

I have a better solution. In August, 1968, our artillery battalion - 800 strong - was ordered to suit up, collect our M14 rifles with bayonets, 80 rounds of thirty calibre ammunition in four magazines. We were told that we would board Air Force transports, fly to Chicago, and go in on the streets to stop a riot. Marching order, bayonets fixed, locked and loaded with ammo. We would clear the streets by force.

They, the rioters, were probably told we were coming. They quickly settled with truce. Our planes landed, refueled, and we were flown back to Camp Pendleton.

Seems to have worked.

Tom Chavez

Gregg, force is required to keep order in society as well as to protect society from outside enemies. Everyone should act with integrity. It should be part of our civic education. 

I like the Vedic philosophy from India, the oldest and longest running civilization (although it has almost disappeared). They had a saying:

“The sage advises, once. The king commands, once. And the daughter is given away in marriage, once.”

The sage is supposed to be in the mode of goodness with pure saintly consciousness. The king/president is in the mode of passion and hence very active. 

The king’s command should be obeyed. He is authorized to use force. If the threat of force suffices, as in the case you experienced, that’s good.

Some people influenced by the mode of ignorance are, as you put it, “rabid retards”. Others are cunning and dishonest. An ignorant thief may steal from a rail car, but an educated thief may steal the whole railroad.

The goal for society is to lift unproductive or counterproductive people out of ignorance. They are also part of society and, if possible, should be rehabilitated. 

In Vedic society a murderer was punished by death. The philosophy was that if he were not executed, he would have to suffer the karma of being murdered in his next life.

I also like the wisdom of ancient Chinese civilization. A friend sent me an interesting Chinese saying this week: “A boy gets money and then becomes degenerate; a girl becomes degenerate and then gets money.”

Tom Chavez

Journey to Infinity—Not all infinities are created equal

The real numbers are more complicated than the counting numbers. They may be represented as a number line which includes positive and negative counting numbers, zero, and everything in between. The real numbers are expressed with decimal expansions. This diagram shows the expansions around zero.

As you zoom in you see more and more real numbers. They are ‘dense’. Between any two counting numbers, no matter how far apart, there are only a finite number of other counting numbers, but between any two real numbers, no matter how close, there is an infinity of other real numbers.

The infinity of real numbers is greater than the infinity of counting numbers. Cantor proved this, using a reductio ad absurdum proof. This method of proof assumes the opposite of what you want to prove, and then shows that the assumption leads to a contradiction.

Cantor assumed that all the reals between 0 and 1 could be mapped 1-to-1 with the counting numbers, which would mean they were infinities of equal size. Such a mapping is shown below.

Assuming that every real number between 0 and 1 is in this list, Cantor created a new number, x, as follows. 

The red diagonal (above) runs through the 1st decimal place of the 1st number, the 2nd decimal place of the 2nd number and, in general, the nth decimal place of the nth number. Change each digit under the red diagonal according to the following rule. Add +1 to the digit, unless it is a 9, in which case change it to a 0. 

In the mapping above, the digit in the 1st decimal place of the 1st number, 3, becomes 4 for the 1st decimal place of x. The digit from the 2nd decimal place in the 2nd number, 6, becomes a 7 for x’s 2nd digit.  From the nth number the digit in the nth decimal place, 9, becomes a 0 in the nth decimal place of x.

The new number x is now different from the 1st number in the 1st decimal place, different from the 2nd number in the 2nd decimal place and, in general, different from the nth number in the nth decimal place.

In other words, x is different from every number in the list. Our starting assumption was that this is a complete mapping of all the reals between 0 and 1, but the real number x is missing. The assumption has proven false, because x is not mapped. 

Therefore, there is no 1-to-1 mapping between the counting numbers and the reals between 0 and 1. And if there is no mapping for the reals between 0 and 1, there is certainly no mapping between the counting numbers and all the reals. 

The conclusion is that the reals are a larger infinite set than the set of counting numbers. There are at least two infinities, the countable infinity of the counting numbers, and the uncountable infinity of the real numbers. Not all infinities are created equal.

Gregg Wilson

Tom,

You have this infinity thing all wrong. Chuck Norris counted from 1 to infinity...

TWICE!

Tom Chavez

Good one, Gregg! But Cantor, with ordinal numbers, went a little further than Chuck Norris.

The End of Infinity

An “ordinal number” is a number which indicates order — essentially, first, second, third, etc. Ordinals are defined in set theory but, for simplicity, we can call the smallest ordinal 0. Next comes 1, 2, 3, etc. There’s an ordinal for every natural number.

Cantor passed every finite ordinal and then came to the smallest ordinal greater than every finite ordinal, which he called 𝜔 (omega). He continued to 𝜔+1, 𝜔+2, 𝜔+3, and so on to 𝜔+𝜔, or 2𝜔, which is where Chuck Norris stopped. But Cantor went on to 3𝜔, 4𝜔 and finally to 𝜔^𝜔, or “infinity to the power of infinity.”

But that bored Cantor because even 𝜔^𝜔 can be put in one-to-one correspondence to the counting numbers—it’s still a countable infinity and not a real biggie. If you don’t want to go further down the rabbit hole, stop here. 

Cantor then defined numbers that go beyond ordinals, called cardinal numbers, which refer to the size of sets. The first cardinal number, representing the size of the set of counting numbers, is ℵ0, (aleph null). This is the smallest size infinity.

Any ‘countable’ infinity, any set which can be mapped one-to-one with the counting numbers, has cardinality ℵ0. The next cardinal number is ℵ1, (aleph one).

The real numbers, represented by the real number line, are called the continuum, and their cardinal number is c. Cantor proved that c is greater than ℵ0, that is, c>ℵ0.

Cantor wondered, is there an infinity in between c and ℵ0, or is the infinity of the real numbers the first infinity past the infinity of the counting numbers? In other words, is c equal to ℵ1, or is ℵ1 between c and ℵ0? He could not answer this question.

Cantor guessed that c must be equal to ℵ1, which is called the “continuum hypothesis.” Later, Kurt Gödel and Paul Cohen proved that the continuum hypothesis is independent of the axioms of modern mathematics. We definitely don’t want to go there. 

Cantor went on to show that for any infinite set, the set of all possible subsets (power set) is a larger infinity. This means there is no universal set containing all other sets. There is no largest infinity.

An infinite hierarchy of infinities, each of which is endless, goes onward and upward forever, one greater than the other, without end. No human being can ever understand it all, because “life is finite” in the human body.

Tom Chavez

I Can’t Breathe!

We are supposed to be a society in which all are treated equally with an equal right to “life, liberty and the pursuit of happiness.” 

Why the stark difference between the death rate of caucasians and people of color from the coronavirus? 

Why the different responses toward black people protesting and white people storming government buildings with assault rifles? 

Black people who protest because the police are killing them are called “thugs”. White people, spitting on police, hanging a sitting governor in effigy, are called “good people.”

Children scream while being taken away from parents at the southern border, pleading to have their mommy and daddy back. 

The National Museum of African American History and Culture shows a picture of a black baby ripped from his mother, who is on her knees begging the slave master not to take her child.

Injustice has gone on a long time, not only in slavery but also with Native Americans on reservations, Japanese-Americans in internment camps, and the public school-to-prison pipeline. 

That’s why some people are more concerned about buildings burning than about a man being killed by police on the ground.

See the true equality of all living beings by viewing them as divine sparks of life; not as their temporary and external physical bodies.

The humble sages, by virtue of true knowledge, see with equal vision a learned and gentle brāhmaṇa, a cow, an elephant, a dog and a dog-eater [outcaste].—Bhagavad-Gita 5.19