Tag Archives: math

Betelgeuse: Schrödinger’s Star

21 Tuesday Jan 2020

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Much Ado About Something

Some astronomers are taking a dim view of the fading light of Betelgeuse. Many are trying to dampen down reports of the star’s demise while not ruling out the possibility. The reality of science is that no one knows what is happening.

What are you doing, Betelgeuse?

A Funny Thing Happened On the Way to a Supernova

Betelgeuse is the hot topic in astronomy because it has been dramatically dimming or ‘fainting’ [SEE Graph 1.0.] In a period of three months, it has dropped from being the eleventh brightest star in the night sky to the twenty-third brightest. This fainting spell is significant because when a star goes supernova it rapidly collapses prior to the event.

Astronomers Edward Guinan, Richard Wasatonic (Villanova University,) and Thomas Calderwood (AAVSO) posted a notice on December 8th of the fainting of Betelgeuse that helped raise awareness of the event. The news media became aware of it and by late December the fainting of Betelgeuse was trending in public speculation of a spectacular doom for Betelgeuse.

Graph 1.0 – Betelgeuse fainting is historic (2018 to current)

A 645-Year-Old Notice

Because of the distance between Earth and Betelgeuse, we wouldn’t know of a supernova event until approximately 645 years after it happens. Our first indication would likely be through a sudden increase in neutrinos. The visual confirmation would occur a few hours later.

If Betelgeuse has gone supernova within the past ≈645 years, then an astronomer could say that Betelgeuse has both gone supernova and has not gone supernova. The delay creates a Schrödinger’s cat scenario. The truth is unknowable.

But astronomers remind us that it may be 100,000 years of more until Betelgeuse makes a stellar spectacle of itself and then abruptly ends its role of marking Orion’s armpit. Their impreciseness of the future of the star is due to a lack of observations of the behavior of progenitor stars (stars that end their life as a supernova) in the years, months, weeks, and days just prior to a supernova.

Betelgeuse is the armpit of Orion

Why Don’t Astronomers Know?

It’s been over 400 years since a star in the Milky Way was observed after it went supernova. That event, like almost every other supernova observation, occurred after the star exploded. Rarely have astronomers been forewarned of an impending explosion and in those cases, the warning has been a matter of hours prior to the event.

To make an accurate prediction of a supernova, we must have data to create a theoretical model of behavior preceding the collapse of the star. The model must be created by using mathematical formulas based on observable data. Without the math, a prediction is just an opinion.

In science, “We don’t know,” is the motivation to discover the truth, even if the truth contradicts the desires and opinions of the majority. At the core of every legitimate scientist is an unwavering desire to offer facts and not mislead others. Astronomers can’t, and shouldn’t, attempt to predict a supernova. “We don’t know,” is the correct answer and the general public has to accept that answer.

Unfortunately, most humans don’t like not knowing. Religions like to give absolute answers to questions even if the answer is unknown or even if it is 100% wrong. A scientist and/or scholar is governed by a higher power of truth. For scientists, not knowing the answer is what makes the process discovery so satisfying. 

The End of the Faint?

In the past week observations of the fainting of Betelgeuse have leveled off. This may indicate that Betelgeuse is about to begin increasing in brightness. It may also indicate the fainting is pausing, or it may indicate that there is no pause and next week astronomers will see a continued drop in brightness. No one knows. 

Graph 2.0 – Is the dimming leveling off in mid-January? (OCT 2019 to current)

My Answer To the Question

I am not a scholar in the field of astronomy so I can state my opinion about the situation. My opinion is that at some time in the past 645 years, Betelgeuse has gone supernova…and it hasn’t.

You have to love Schrödinger.

Why Are There 360 Degrees in a Circle?

19 Monday Mar 2018

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Everyone knows there are 360 degrees in a circle. Why? A circle could have a 1,000° which would make a half circle equal 500° and a quarter circle 250°. Who chose the number 360? Was there a vote? Who do we blame? Inquiring minds want to know!

Two circles getting in each other's way

2017 Total Solar Eclipse from Canyon City, OR

As it turns out there are at least two reasons we use 360° as the number to define a complete circle. One reason has to do with astronomy and the other with mathematics.

360 Degrees? Blame the Babylonians

The Greeks are partly responsible for defining the numerical value for a circle, but really it was the Babylonians. It may even be farther back than the Babylonians, but someone erased their hard drive and now we will never know.

Apparently, the Babylonians loved the number ’60.’ They created a number system using Base 60 (we use Base 10.) The number 60 is amazing because it can be divided into so many factors. 60 can be divided evenly by 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. Since the Babylonians loved 60, the fact that a circle can be divided into six equilateral triangles made 360 the best option for defining the numerical value of a circle.

We don’t actually know if it was the Babylonians, but we do know that several prominent Greek mathematicians used 360° as the numerical value for a circle. It is written…in Greek of course.

Star Gazers In a 360 Days

But long before the Babylonians, it was obvious to anyone who looked up at the sky at night that the stars followed a circular pattern through the year. If one noted the position of a star or constellation on a particular night and time, next year that star would be in the same place on the same day and time.

The elapsed number of nights for a full circle? About 360. Anyone who tracked the stars would have noted that the circular pattern of the stars resumed after about 360 days.

The reason we have 360° is most likely because of the speed at which the Earth rotates, (once every 24 hours,) and there are approximately 360 rotations (days) in a year.

Metric Circles?

Believe it or not, there were attempts to make circles metric. It didn’t take. There are some uses for it, but the 360° value is more accepted ‘around’ (that’s a joke) the world.

Common Core: Are You A Good Switch Or A Bad Switch? Part III

25 Wednesday Mar 2015

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PART III:  An Answer to the Question:  Good? or Bad?

Implementation of Common Core/US News and World Report

Implementation of Common Core

THE VERDICT
In the past year significant political forces have targeted Common Core. The protests have been at near hysterical levels in many communities around the country. The complaints about Common Core are as follows:

  • Standards create a factory-like environment that attempt to put all students in one ‘box.’
  • Teachers focusing on test scores, not educational achievement
  • Parents don’t understand math methods
  • United States history under Common Core is un-American because it includes both positive and negative aspects of the history of our country
  • A belief that parents should define school curriculum, not the school, district, state, or federal government
  • A belief that President Obama is behind the implementation of Common Core and other conservative conspiracy theories

Many of the issues have been generated by conservative voices after a push by Republicans during the past election cycle to ignite anger and votes against public education. Almost all of the complaints would have occurred from any attempt to improve and refine American educational techniques, especially when those improvements involve standardization for all American schools.

If you believe that setting minimum standards in reading, writing, and math is bad, then Common Core is bad. If you believe that children in your community should graduate with similar skills to other students around the country, then Common Core is good. If you believe that a high school degree should be the end of a person’s education, then Common Core is bad. If you believe that every student should receive an education that would prepare them for college, then Common Core is good.

THE REAL PROBLEM
Despite the politicizing of Common Core, there is a real issue in implementing any change in education. Funding.

Any business that seeks to upgrade or improve their methods knows that there is a real cost to any change. Yet, even smart business people seem to forget that to improve our educational system requires a major funding commitment. It takes money to research and establish new programs. It takes money to train school districts, principals, and teachers. It takes money to create new teaching materials, and it takes money to educate parents.

What Common Core is missing is the funding needed to make it a success. Until we can accept the fact that a commitment to education requires a commitment to funding, then we will continue using 20th educational techniques in a 21st century world. America’s efforts to update our educational system will cost money and Common Core is a victim of a society that has abandon quality education because it costs too much.

THE HYSTERIA OF THE LOUDEST VOICES
Unfortunately, Common Core lost a lot of support in the past twelve months. Much of that was due to the political rhetoric during last year’s campaigns, but some teachers are also pulling back support. This is not surprising. As parents become more vocal in opposition, few teachers are willing to oppose parent sentiment even if they are wrong.

Common Core is not a perfect educational system, but it does attempt to better prepare America’s children for a higher level of achievement. Most of the real issues can be resolved with better funding. Just as a school built in the 1950’s is no longer relevant for 2015, education methods of the pre-information era are not relevant today. Our population is continuing to increase and the skills our children must have to thrive as adults are going to advance. Education is going to be expensive, but if we don’t pay now, we will pay more later.

PREVIOUSLY:  Part I:  A Primer in American Education 
                            Part II:  What is Common Core?

Common Core: Are You A Good Switch Or A Bad Switch? Part II

25 Wednesday Mar 2015

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PART TWO: What is Common Core?

Cartoon in Chicago Tribune about parent reaction to Common Core

Cartoon in Chicago Tribune about parent reaction to Common Core

The Third Generation of Standardized Education
The basic premise of the George W. Bush (43rd President) administration’s No Child Left Behind (NCLB) mandate was that reading, writing, and math are fundamental to all learning. This is a sound concept; however, these basic skills cannot supplant other subjects traditionally taught in K-12 schools, nor can they be isolated from those subjects. Our society, both business and personal interactions, require an adequate understanding of a wide variety skills and knowledge that exceed the basic skills of reading, writing, and math.

Common Core is an attempt to refine the concept of NCLB by creating standards for all schools that focus on reading, writing, and math, but it also folds these skills into other subjects that impact personal success in the 21st century. Common Core emphasizes teaching methods and outcomes, but leaves it to the State, school district, and school on how to incorporate the program into the curriculum.

Why Some Parents Dislike Common Core Math
Some of the methods adopted by Common Core have angered parents and politicians. In particular, the approach to teaching math. The math issue centers on bewildered parents who don’t understand the revised math teaching methods and why equations seem to be more complicated than when they attended school. The assumption by parents is that whatever they were taught is good enough for their children; however, that is not necessarily true.

Almost every adult in this country was taught that the symbol for a number (e.g.; ‘7’) was everything we needed to know about the number that it represents. We were taught to memorize how the symbol ‘7’ multiplied by the symbol ‘9’ equals the symbol ’63.’ That teaching method does not mean that the student understands that ‘7,’ ‘9,’ and ’63’ are symbols representing a group of objects. 

This is a subtle, but important understanding in math functions. The equation ‘7 x 9 = 63,’ means that we are taking a group of seven objects, adding eight more groups of seven, and determining the total of objects. That is much more complicated than just memorizing that 7 x 9 = 63, but it helps us realize that multiplication is a shortcut to manually counting out 63 objects individual, rather than grouping them.

The weakness of memorization of relationships between symbols also creates confusion as a student moves into higher mathematical equations. In algebra, geometry, and calculus the numeral symbols become less relevant. For example, X = (X+1) and Y = (X-3) can be confusing because ‘X’ stands for EVERY number.

The Credit Card Example
A man is given ten credit cards, but he is NOT told that each credit card represents an amount of money in the bank and, that if used, the money is replenished the next day. He is told how to use each credit card. One card is to buy gas, one to use at the grocery store, etc. Today, he’s at the gas station and it so happened that two of his friends are already there. He decides to pay for his friend’s fuel, which they appreciate. They go on their way, but when he tries to pay for his fuel, the credit card is declined. He didn’t understand that the card represented a limited amount of money, he just assumed it could be used for any amount of fuel. That is similar to how math has been taught in the past. We may have known what to do with the numbers (symbols,) but we may not have fully understood that numbers are just symbols.

Good News, Bad News
Parents objections to the new math teaching methods are a good sign that our children are gaining a deeper understanding of mathematics than their parents did in school; however, parents need to be able to assist their children with homework.¹ This means parents need to be taught the new methods, but few if any schools have developed programs to teach parents because there is no funding available to accomplish the task.

Who Came Up With the Common Core Math Techniques?
Despite the belief that Common Core math techniques were invented in the past few years, the techniques were modeled off educational programs in certain Asian countries where they have been more successful at preparing students for college. In 2009, a coalition of State Governors and Educators worked together to build an educational program that would serve as a ‘best practices’ guide for American schools, which was the birth of Common Core.

NEXT:  Part III:  An Answer to the Question – Good? or Bad?
PREVIOUSLY:  Part I:  A Primer in American Education 

¹Most studies indicate that students perform better when parents are involved in their children’s education. At the very least it indicates to the child that their parents place a high value on becoming educated.