Tag Archives: Mathematics

Conway’s Game of Life

This will become an Index to posts on Conway’s Game of Life.

Lwss_smallIntroduction:  Like Hinduism, Conway’s Game of Life played a large role in undoing the religious thinking that permeated my thinking in my early 20s.  When we leave anything behind, we often do if for many ‘reasons’ — not a few of which we were blind to.  As I have written about religion the past four years, I have seen some of those invisible players in my life.  Conway’s Game of Life was one of them.

Question to Readers:  What are some of the invisible players you have discovered years after leaving something?

Conway Life Links:

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Prayer Amplifier App (It doesn’t work)

I was inspired by xkcd’s recent comic and did this little imitation by changing the subject to “Prayer” — I thought it fit perfectly.  I also freely borrowed a few commentor’s avatars — thank you.

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The Divine Proportion

Euclid of Alexandria, in his “Elements” (300 BC), gave us the first clear definition what he called “The Extreme and Mean Ratio” but what was later raised to loftier levels and called “The Golden Ratio” and  “The Divine Proportion”.

The ratio actually has two Greek letters used to symbolize it:  phi (φ) is more commonly used and is named after “Phidias”– a Greek sculptor (more on that later).  But professional mathematicians often use tau (τ) because “tau” is the first letter in “tomi” which means “the section” in Greek.

Phi is a fascinating irrational number.  I am enjoying Mario Livio’s book “The Golden Ratio” which I will use as fodder for a few posts.  But first, I thought I’d get readers a little invested with an exercise!

Help Euclid find the spot, “C”, on the line segment AB that fulfills the equation to its right.  In other words: What point do you think creates “The Divine Proportion”?

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Math, Logic & Rhetoric

Last updated Oct 2013

This is an index of posts concerning Math.

Luck & Randomness

Conway’s Game of Life

Phi: The Divine Proportion

Math and the Religious Mind

Number Theory

Computer Programs

Rhetoric & Logic

Where Fallacies Live

The Reification Fallacy

Logical Fallacies & Rhetorical Tricks

Whack-a-Creationist

Study Logic and its Limitations

The Ecological Fallacy

Dawkins’ Relevance Fallacy

Demons & Classifying Fallacies

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Math & the Religious Mind: Intro

Introduction:

We all have buttons that, when pushed, can stop us from thinking clearly and can polarize dialogues making them useless, if not destructive.  On Triangulations I discuss highly polarizing topics: religion, philosophy, politics, lifestyles and more.  On most my posts I try to relate those topics to habits of our minds.  But on many posts, buttons get pushed, the points I intend to make are often lost and threads get side-tracked.  Of course, some of that is simply due to my bad writing or bad ideas. 🙂

Anyway, I thought I’d experiment with some posts on Mathematics with an emphasis on how our “Religious Mind” relates to Mathematics (“Math” in American English, “Maths” in British English — don’t want to push buttons right from the start!).

Hopefully there will not be too many readers who are emotionally attached to theories of math or to numerology.  So discussing Math may be a fun way to approach the same issues of Mind using a more neutral subject.

Related Posts:  Math & the Religious Mind: an index post

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Types of Numbers

Numbers_Square

Above is a diagram I made to illustrate the common number types.  There apparently is no agreement on the definition of “number” and the meaning has changed over the centuries.  I will be using this diagram to assist in other posts on Math & the Religious Mind.  Let me know if your favorite type of number is not on the chart.  Meanwhile, go ahead, I dare you, find a better chart than this one out there on the web! 🙂

Related Posts:  Math & the Religious Mind: an index post

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Infinity is not a Number

Thinking about infinity as a real (albeit, large) number is a common error.  I think it springs from the same habits of mind that creates many religious concepts.  The temptation of the mind to concretize abstractions is what forms this mathematical error and likewise, many religious superstitions.  Our minds are not comfortable with nebulosity.

“Infinity” is a mathematical concept used to describe a property of a set.  Apparently there is no agreed upon definition of what a “number” actually is, but here I am using the term to describe the real numbers that non-mathematicians intuitively mean by “number”.  In that sense, Infinity is not a number nor is it a being nor a god.  Infinity is thus an example of how we often unnecessarily concretize the nebulous to feel anchored, secure and in control.

Related Posts:  Math & the Religious Mind: an index post

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25, 35 and the Holy Trinity

In Skepticblog, Michael Shermer just posted a fun article  about his recent run-in with numerology. He tells of an uncomfortable fake interview he had with a proud self-proclaimed Muslim heretic from Kazakhstan who staged the interview with Michael in order to push his Islamic book about the mystical implications of the number 19.  At the end of his article Shermer challenges readers to “employ their own patternicity skills at finding meaningful patterns in both meaningful and meaningless noise with such numbers and numerical relationships….” In Shermer’s terms, “paternity” is the hyper-over-kill ability to see connection and meaning where it doesn’t exist. Coincidentally (hmmmm?), I just recently discovered an miraculous numerical pattern which I am entering in Michael’s challenge.  See if you agree that it is miraculous. Click more to read my inspiring story:
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Hyperbole – word study

We all know what it means to exaggerate.  The word comes from Latin:
ex= “thoroughly” +
aggerare “heap, up” [ad– “toward” + gerere “carry”].

But like many concepts in English we also have a Greek derived word with similar meaning:  “Hyperbole”:  Gk huperbole,  huper, “above” + bole, “throw”.

But “hyperbole” is sometimes just used to mean the same as exaggeration, it is often used to identify an intentional literary or speech device which is not meant to be taken literally.  Thus here are the common definitions of “hyperbole”:

  1. Exaggeration
  2. Intentional Exaggeration
  3. Intentional Exaggeration not intended to be taken literally

As a communication tool, hyperbole can be used in the following ways:

  • To grab attention
  • To emphasize a contrast
  • To deceive

A hyperbole is effective at contrasting one idea against another — it makes their differences clear albeit with gross exaggeration.  This can wake up the listener and help them realize that the speaker is introducing a new paradigm.  Whereas if a speaker uses slow, careful, caveat-laden comparisons and descriptions to contrast two concepts, a listener may not really get their point or may get tired of listening.  “Hyperbole” is a great rhetorical tool.  It makes the contrasting idea easy to remember and often easy to apply.  Such is the simple nature of the human mind.

Well that is all great for the mind ready to be moved.  Nonetheless, if the listener has no desire to be swayed, they may point out the exaggeration of the hyperbole and focus only on its inaccuracies.  They may not forgive the rhetoric.  Hyperbole is a rhetoric tool but it disobeys all sorts of logic rules.   But when the goal of the communication is victory and not truth, a competitor will choose their weapon appropriately.

Finally, some geometry to explain the picture used in this post.  As I said, the etymology of “hyperbole” is:

“Hyperbole”:  Gk huperbole . to huper, “above” + bole, “throw”.

When we throw an object, it follows a certain geometric shape — a parabola which is related to a hyperbola.   “Hyperbola” has the exact same etymology as hyperbole.  While reviewing the definitions of hyperbola and parabola, I found that they and circles and ellipses were simply sections of a cone.  But none of the definitions I found were elegant — none put explained the differences in these shapes in clear, yet concise terms.  So I will offer Sabio’s elegant definition of Conic Sections below:

Four geometric figures are determined by the intersection of a (non-vertex) plane with the sides (nappes) of a cone.  The figure types are determined by the acute angle formed by the plane and the cone’s axis.

Hyperbola = 0 degrees (parallel axis) to degree of Nappe Angle
Parabola = degree of Nappe Angle
Ellipse =  degree of Nappe Angle to 90 degrees
Circle = 90 degrees (perpendicular to axis)

Note: for simplicity I limited to planes which do not include the vertex of the cone.  Otherwises Lines and a Point must be included as possible conic sections.

Math folks, please help me if I have erred.   Others, if you have read this far, let me know what you think about the literary tool of hyperbole.

triangle_end_tiny
See other “Word!” posts, here.

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