*repeated addition (multiplication as 'scaling', from Keith Devlin):*

**NOT****http://www.maa.org/devlin/devlin_01_11.html**

Multiplication is **NOT** repeated addition (multiplication as 'scaling', from Keith Devlin):

**http://www.maa.org/devlin/devlin_01_11.html**

Nice quick introduction to several classic paradoxes here:

http://www.popgive.com/2010/06/brain-twisting-paradoxes.html

http://www.popgive.com/2010/06/brain-twisting-paradoxes.html

Richard Wiseman's prior-Friday Christmas problem here:

**http://tinyurl.com/2bqgj2b **(has problem & answer)

If you want to read the problem without the answer being immediately given go here (and get a bonus video in addition, as well):

**http://tinyurl.com/2fbgtlp**

If you want to read the problem without the answer being immediately given go here (and get a bonus video in addition, as well):

Another interesting post from RJ Lipton here:

http://rjlipton.wordpress.com/2010/12/26/unexpected-connections-in-math

This time on the "beauty and power" of "unexpected connections" in mathematics, where findings or knowledge from areas that seem to have little overlap, are conjoined to produce yet newly useful knowledge or proof. This can happen in other areas of science, but is an especially integral underlying part of modern mathematics with its complex, almost unwieldy proofs, going forward.

The post starts off with reference to illustrious mathematician and economics Nobel-Prize winner John Nash (famous to lay folks from the book and movie "**A Beautiful Mind**"), before delving into some more abstract and technical discussion.

Mathematics, full of surprise and beauty, signifying much.

http://rjlipton.wordpress.com/2010/12/26/unexpected-connections-in-math

This time on the "beauty and power" of "unexpected connections" in mathematics, where findings or knowledge from areas that seem to have little overlap, are conjoined to produce yet newly useful knowledge or proof. This can happen in other areas of science, but is an especially integral underlying part of modern mathematics with its complex, almost unwieldy proofs, going forward.

The post starts off with reference to illustrious mathematician and economics Nobel-Prize winner John Nash (famous to lay folks from the book and movie "

Mathematics, full of surprise and beauty, signifying much.

The new Reuben Hersh/Vera John-Steiner book, "**Loving and Hating Mathematics: Challenging the Myths of Mathematical Life**" should be available in stores very shortly:

http://www.amazon.com/Loving-Hating-Mathematics-Challenging-Mathematical/dp/0691142475

[**Addendum:** just received a review copy of the above volume in mail so will have more to say about it perhaps sometime after the Holidays.]

And a rough draft (pdf download) of yet another book for lay people on the Riemann Hypothesis is available here (Barry Mazur co-author):

**http://wstein.org/rh/**

http://www.amazon.com/Loving-Hating-Mathematics-Challenging-Mathematical/dp/0691142475

[

And a rough draft (pdf download) of yet another book for lay people on the Riemann Hypothesis is available here (Barry Mazur co-author):

Hat tip to "Grey Matters" for directing me to this 2008 hour-long PBS 'NOVA' episode on fractals, entitled "**Hunting the Hidden Dimension**":

**http://www.pbs.org/wgbh/nova/physics/hunting-hidden-dimension.html**

Sol's usual array of interesting math links for this week at Equalis Community Blog here:

**http://www.equalis.com/members/blog_view.asp?id=565749**

(if you don't find at least one link there interesting to you, better check to see if you still have a pulse ;-))

And if you haven't yet finished holiday-shopping for all your math-geeky friends, Denise had several suggestions here:

**http://letsplaymath.net/2009/12/22/have-a-mathy-christmas/**

(if you don't find at least one link there interesting to you, better check to see if you still have a pulse ;-))

And if you haven't yet finished holiday-shopping for all your math-geeky friends, Denise had several suggestions here:

growth in interest in prime numbers and number theory:

**http://tinyurl.com/22juwgm**

growth in interest in arithmetic, not so much:

**http://tinyurl.com/25km6aq**

growth in interest in arithmetic, not so much:

I don't comprehend all these hourly designations, but some of you probably will (...worth a chuckle):

**http://www.beaverdam.k12.wi.us/bd/content/mathclock%20withnumbers.jpg**

...and here a prime number watch:

**http://tinyurl.com/2uop37u**** **

And finally a watch based on, of all things, the Sierpinski Triangle:

http://tinyurl.com/2fqolo5

(Perhaps some people just have too much time on their hands! ;-)

...and here a prime number watch:

And finally a watch based on, of all things, the Sierpinski Triangle:

http://tinyurl.com/2fqolo5

(Perhaps some people just have too much time on their hands! ;-)

From "Mathematics Rising" blog:

"...mathematics is not built entirely on logic. It lives somewhere between thought-governed ideal realities and physical realities created by the senses. As such, it may be able to provide its own unique view of cognition itself. It may be said that cognitive processes unfold themselves into mathematical insights."

Read the entire post on the essence of mathematics here:

**http://mathrising.com/?p=335**

"...mathematics is not built entirely on logic. It lives somewhere between thought-governed ideal realities and physical realities created by the senses. As such, it may be able to provide its own unique view of cognition itself. It may be said that cognitive processes unfold themselves into mathematical insights."

Read the entire post on the essence of mathematics here:

Interesting geeky story of Google planting Mensa-like problem in an ad and rewarding solver:

**http://tinyurl.com/27v3mgq**

Just a little quickie recursive brain workout for starters:

1. The third sentence here is true.

2. This is the second sentence here.

3. The fourth sentence here is false.

4. The sixth sentence here is true.

5. The first sentence in this list is true.

6. The first and last word in this sentence is "the."

Is sentence #5 true or false???

Meanwhile, plenty of fun stuff at Sol's latest "Wild About Math" entry for the Equalis Community blog:

http://www.equalis.com/members/blog_view.asp?id=565749&post=116258

1. The third sentence here is true.

2. This is the second sentence here.

3. The fourth sentence here is false.

4. The sixth sentence here is true.

5. The first sentence in this list is true.

6. The first and last word in this sentence is "the."

Is sentence #5 true or false???

Meanwhile, plenty of fun stuff at Sol's latest "Wild About Math" entry for the Equalis Community blog:

http://www.equalis.com/members/blog_view.asp?id=565749&post=116258

Mark Chu-Carroll at his blog, "Good Math, Bad Math," often posts examples of mathematical 'crackpottery' that come his way, but recently posted about an argument for why everyone's favorite number *Ï€*, should really be substituted with another value tau, *Ï„*, the equivalent of 2*Ï€*, and why this would all make sense in so many ways (tau is based on the radius of a circle, instead of the diameter-basis for pi). And yes, it's a serious argument:

**http://tauday.com/**

Many agree with the logic and reasoning of the assertions in favor of 'tau,' but... well... changing centuries of routine use of pi (and making obsolete all those 'I Love*Ï€* ' t-shirts) , is of course another matter altogether.

Many agree with the logic and reasoning of the assertions in favor of 'tau,' but... well... changing centuries of routine use of pi (and making obsolete all those 'I Love

I've recently been reading a lot of interesting posts, playing with numbers, over at "The World of Trotter Math," especially many recent ones on prime numbers:

**http://trottermath.net/wordpress/**

Upon researching to learn more about the site's proprietor I suddenly discovered his name was Terry Trotter and he passed away in 2004. I don't know who keeps the blog running, but thank you whoever is responsible.

A further-interesting tribute to Mr. Trotter is here:

**http://www.guardiansofdarkness.com/GoD/trotter.html **

Upon researching to learn more about the site's proprietor I suddenly discovered his name was Terry Trotter and he passed away in 2004. I don't know who keeps the blog running, but thank you whoever is responsible.

A further-interesting tribute to Mr. Trotter is here:

Entertaining post (including lots of links) today from Jonathan Farley of The Guardian:

**http://tinyurl.com/27qmk42**

For today's amusement, a paradox quoted directly from Martin Gardner's "**The Jinn From Hyperspace**":

"Now for a final paradox. There is a certain event that I guarantee will or will not take place during the next ten minutes. You are absolutely incapable of predicting correctly whether it will or won't occur. I don't mean that it's unlikely you can predict it. I mean it is logically impossible to predict it!

"You don't believe it? Then do the following. If you think the event will occur write "Yes" inside the blank rectangle below. If you think it won't happen, write "No" inside the rectangle.

"If you predicted correctly, I'll send you a million dollars.

The event is: You will write "No" inside the rectangle."

As Gardner might say, "Gotcha!"

This is just one of many paradoxes entangled with self-reference and classic problems of causation/prediction when dealing with human language and logic.

"Now for a final paradox. There is a certain event that I guarantee will or will not take place during the next ten minutes. You are absolutely incapable of predicting correctly whether it will or won't occur. I don't mean that it's unlikely you can predict it. I mean it is logically impossible to predict it!

"You don't believe it? Then do the following. If you think the event will occur write "Yes" inside the blank rectangle below. If you think it won't happen, write "No" inside the rectangle.

"If you predicted correctly, I'll send you a million dollars.

The event is: You will write "No" inside the rectangle."

As Gardner might say, "Gotcha!"

This is just one of many paradoxes entangled with self-reference and classic problems of causation/prediction when dealing with human language and logic.

...and also creative mathematicians:

nice storyline from "CTK Insights" on 3 young people who bucked the more mundane (and expected) answer on an IQ test to start with Pascal's Triangle and end up with "The Rascal Triangle":

**http://tinyurl.com/29opquv**

(a clear case of thinking-outside-the-triangle)

nice storyline from "CTK Insights" on 3 young people who bucked the more mundane (and expected) answer on an IQ test to start with Pascal's Triangle and end up with "The Rascal Triangle":

(a clear case of thinking-outside-the-triangle)

six is so sexy... "Trotter Math" introduces us here (in a re-post of info from over 10 years ago!) to "sexy primes":

**http://trottermath.net/wordpress/sexy-primes/**

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