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Showing posts with label Mathematics. Show all posts
Showing posts with label Mathematics. Show all posts
Wednesday, February 26, 2025
What Everyone Gets Wrong About Gambling on Sports
"Do you think it still counts as gambling if you're guaranteed to win? Do you think it would be a net positive to society if 100% of sports bettors used tools to gain an edge? Do you think I should have kept this story to myself? Do you ever get nervous?"
Tuesday, May 7, 2024
Math Education: It's Not Easy
"Dr. Jo Boaler is a leading math education expert and one of the writers of the California Mathematics Framework, a set of guidelines focused on improving equity in California's math classrooms. We first talk about her upcoming book, Math-ish, and the beauty of pursuing more "ish" in our lives. Then, we discuss a recent anonymous complaint that was filed with Stanford University, accusing Dr. Boaler of misrepresenting research to serve her own agenda."
Dr. Jo Boaler Tried To Improve Math Education. Then An Anti-woke Mob Came For Her
Click on the link below for an example of a new approach to mathematics education that is not well-received in some academic circles:
Sunday, September 10, 2023
A "Knotty" Subject (But Not Pornography)
"There is an entire branch of math simply devoted to knots – and it has changed the world. We’ll rope you in."
Click on the link below for a fascinating look at a subject that relates to not only math but also chemistry, biology, and physics:
Sunday, October 23, 2022
Math Education: How Much Is Needed And What Type?
One of the controversies in education is the amount and type of mathematics education needed in middle and high school. Click on the links below for examples of current thinking on the matter:
“We hear on all sides that we’re not teaching enough mathematics — you know, that the Chinese are running rings around us,” Hacker says. “I’m suggesting we’re teaching too much mathematics to too many people. … I would say everybody doesn’t have to know calculus. If you’re going to become an aeronautical engineer, fine. But most of us aren’t. It’s a bit like saying everybody should learn Arabic because they may need it someday.” (https://www.sciencefriday.com/segments/how-much-math-should-everyone-know-show-your-work/)Thursday, September 30, 2021
Mathematics: Primary Or A Language Of Nature
There is much discussion in mathematics, philosophy, and science circles regarding the reality of mathematics. Click on the links below for a sample:
Thursday, May 13, 2021
A Mathematical Speculation Of Infinity
"If there's a hotel with infinite rooms, could it ever be completely full? Could you run out of space to put everyone? The surprising answer is yes -- this is important to know if you're the manager of the Hilbert Hotel."
Click on the link below for a unique way of presenting the concept of infinity:
Wednesday, January 27, 2021
Another Example Of The Difficulty Of Explaining Consciousness
"In this video I talk about a few approaches to mathematically describe consciousness and its shortcomings. I also briefly talk about what such studies could one day be good for."
Sabine Hossenfelder is a physicist who addresses the controversial topics within physics not only with knowledge but with discernment regarding the line between evidence and hypothesis. This video is a good example of her qualifications:
Monday, November 25, 2019
Math And Logic Are Formal Sciences
Let's put Mathematics and Logic in proper relationship to Science:
"Formal science is a branch of science studying formal language disciplines concerned with formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, game theory, systems theory, decision theory, and theoretical linguistics.[1] Whereas the natural sciences and social sciences seek to characterize physical systems and social systems, respectively, using empirical methods, the formal sciences are language tools concerned with characterizing abstract structures described by symbolic systems. The formal sciences aid the natural and social sciences by providing information about the structures the latter use to describe the world, and what inferences may be made about them." (link)
"Formal sciences – branches of knowledge that are concerned with formal systems. Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the real world, but instead with the properties of formal systems based on definitions and rules." (link)
"All of science relies heavily on the existing abstract frameworks of mathematics and logic to interpret and describe the evidence it analyzes and ultimately to express its conclusions. Put simply, science uses mathematics and logic as scaffolding to construct predictive models, using empirical evidence as building materials. In this way, all branches of science are concerned with these fields, but no branch of science is directly concerned with advancing them.
"Formal science is a branch of science studying formal language disciplines concerned with formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, game theory, systems theory, decision theory, and theoretical linguistics.[1] Whereas the natural sciences and social sciences seek to characterize physical systems and social systems, respectively, using empirical methods, the formal sciences are language tools concerned with characterizing abstract structures described by symbolic systems. The formal sciences aid the natural and social sciences by providing information about the structures the latter use to describe the world, and what inferences may be made about them." (link)
"Formal sciences – branches of knowledge that are concerned with formal systems. Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the real world, but instead with the properties of formal systems based on definitions and rules." (link)
"All of science relies heavily on the existing abstract frameworks of mathematics and logic to interpret and describe the evidence it analyzes and ultimately to express its conclusions. Put simply, science uses mathematics and logic as scaffolding to construct predictive models, using empirical evidence as building materials. In this way, all branches of science are concerned with these fields, but no branch of science is directly concerned with advancing them.
"In a similar way, applied fields such as Medicine and Engineering rely heavily on the natural sciences as a framework on which to build, but are not themselves concerned with advancing those fields." (link)
More from Quora: (link)(link)(link)(link)(link)
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The principles underlying mathematics and logic are axiomatic.
More from Quora: (link)(link)(link)(link)(link)
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The principles underlying mathematics and logic are axiomatic.
Sunday, January 28, 2018
The "Wisdom" Of Focusing On Mathematics?
A very interesting counter to the prevailing “wisdom” of the importance
of mathematics. Frankly, how about focusing on science based thinking
instead?
Have you used trigonometry since you were 18?
Have you used trigonometry since you were 18?
Wednesday, June 29, 2016
The Myths in "The Math Myth"
" I kept track of errors, unreferenced claims, and misleading arguments as I read The Math Myth,
and I found so many that I’m halfway tempted to publish an annotated
edition of the book. (I’m not the only one frustrated by Hacker’s many
specious arguments. Mathematician Keith Devlin and math and statistics teacher Amy Hogan, among others, have written posts pointing out other flaws in his arguments and conclusions."
It Doesn’t Add Up
It Doesn’t Add Up
Tuesday, June 21, 2016
Improbability
"We can unconsciously increase the odds of a “rare” event occurring by
post hoc analysis, open ended criteria (wiggle room), and mining large
sets of data. In fact, we are inherently good at doing all of these
things. We might call the overall process pattern recognition. Our
brains evolved to make connections, to see patterns, and then to imbue
them with meaning."
The Improbability Principle
The Improbability Principle
Friday, June 17, 2016
Monday, April 18, 2016
Friday, January 29, 2016
It's Amazing What Was Happening In The Middle East Before - - -
- - - a religion thought it knew everything. Sound familiar?
This ancient Babylonian map of Jupiter just changed history as we know it
This ancient Babylonian map of Jupiter just changed history as we know it
Thursday, January 28, 2016
A Mathematical Look At Grand Conspiracy Theories
"Conspiratorial ideation is the tendency of individuals to believe that
events and power relations are secretly manipulated by certain
clandestine groups and organisations. Many of these ostensibly
explanatory conjectures are non-falsifiable, lacking in evidence or
demonstrably false, yet public acceptance remains high. Efforts to
convince the general public of the validity of medical and scientific
findings can be hampered by such narratives, which can create the
impression of doubt or disagreement in areas where the science is well
established."
Math vs Conspiracies
Math vs Conspiracies
Wednesday, January 27, 2016
Mathematics Education On The Cusp
"The Common Core math standards have been contentious since they were
launched several years ago, with many parents taking to social media to
complain about their kids getting incomprehensible homework. Kids are
now expected, for example, to explain how multiplication works using the
“box” and “lattice” methods. These methods take longer, and are harder
to master at first, but have been shown by some research to be more
effective than the multiply-and-carry method, particularly for kids who
have trouble memorizing things. And while they may be new for this
generation of parents, they have been around since at least the 13th century."
http://www.theatlantic.com/education/archive/2016/01/the-man-who-tried-to-kill-math-in-america/429231/
http://www.theatlantic.com/education/archive/2016/01/the-man-who-tried-to-kill-math-in-america/429231/
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