The Essence of Mathematics -- Contrasts

Three quotations found at MathNexus...

The essence of mathematics is exact truthfulness.
 - Ellery W. Davis, Mathematical Supplement of School Science, 1903

The essence of mathematics is accuracy.
 -Walter Bagehot, The Works of Walter Baghot, Travelers Insurance Company, 1891

The esssence of mathematics lies precisely in its freedom.
 - Georg Cantor, Mathematische Annalen, 1883

Any surprise that only Cantor is famous?

I have twice mentioned Paul Lockhart and his essay A Mathematician's Lament.

One of my December holiday presents was his new "math textbook" named Measurement.

It is truly a delightful book, everything that I hoped that Lockhart would some day write.  It is unlike any math textbook, but I know of no way to describe better other than to say it is what his Lament yearns for and would have made Cantor happy while being heretical to Davis and Bagehot.

(Not that Lockhart's ways to play with measurement are inexact or inaccurate, but that is not the essence of why or how he or Cantor do math.)

The Seventh Voyage of Sinbad

Health and projects have kept me from blogging, but tonight I will make time to fix that.  How about a movie review?

Smiley has been interested in learning about kinds of monsters.  He is pretty good about inventing new ones for the stories he tells me.  But he still wants to know what ideas other people have already established.

I finally found a great book to help satisfy his need: Dragons, Dragons by Eric Carle.  (It was reviewed by my wife's friend Sarah.)  Not as exhaustive as the old Barlowe's Guide to Extraterrestrials I enjoyed as a kid, but much more appropriate to Smiley's kindergarten age.

Then I serendipitously saw this DVD at the library.

What great monsters!  Both boys are loving this movie.

The film is a classic of Harryhausen's animation that I had never heard of.  It is one of the few films to score 100% at Rotten Tomatoes.  It is indeed a fun romp guaranteed to cause smiles.

I think they cyclopses are the true stars of the film.

But the best actress is clearly Kathryn Grant, who plays the princess. I had never heard of her, despite her other identity as Bing Crosby's wife.

Her lines are just as hokey as anyone else's.  But she also has the responsibility of acting old-fashioned feminine.  She remains genuinely cheerful and supportive, whether cursed by a shrinking spell, rescuing Sinbad or being rescued by him, or climbing into a magic lamp hoping to meet a young genie.

Brave Sinbad and wicked Sokurah are both wooden in comparison.  The men in the movie treasure the princess but never objectify her, and she runs with that dynamic to let the cheesy Hollywood love she shares with Sinbad highlight how daring and sweet can be very complimentary.

Shopping for Magic Stuff

When I started playing Pathfinder, the only rulebooks were the Core Rulebook and a bestiary.

The game provided a simplified and sane collection of "best of the game" D&D 3.5E rules for folks who wanted to keep playing that.

Players did not have as many options, but they were more-or-less balanced and sensible options all collected in one place for easy reference.

Since then, Pathfinder has jumped the shark.  It now has so many rulebooks that there is no point to owning them.  A player or GM needs to search through all the books to see all of the options for a situation.  This is best done online.

The same "too many books, too many broken combinations of options" problem that Pathfinder was created to fix has returned.

(The latest example is an eleventh level Half-Elven Oracle with Eldritch Heritage in the Arcane Bloodline who uses Paragon Surge to temporarily get Improved Eldritch Heritage or Expanded Arcana.  This character has nearly instant access to every Wizard and Cleric spell up to fifth spell level.)

The setting of Golarion also moves farther and farther from my kind of fantasy setting.  The world has increasingly dysfunctional economics because of how much wealth PCs are expected to gain.

As someone who grew up playing AD&D, even the idea of a "magic item shop" seems silly.  A lot of the fun of AD&D was finding creative ways to use the wacky assortment of strange items you found in dungeons.

In Pathfinder, adventurers instead sell (for half price) the items they will not be using daily and with that money the party Wizard crafts (for half price) more practical but boring magical equipment.

Now Pathfinder has an entire book devoted to magic item shops!

Perhaps I am too critical.  Maybe the book actually makes magic item shops someplace where Golarion's adventurers buy stuff, instead of only selling items there to get the gold the party Wizard needs for his crafting.

Quail Run

Near my grandmother's home is a neighborhood named Quail Run.

When we were visiting her in December, and drove by this intersection for the first time, Smiley was astounded.

"This must be where the fanciest houses are!" he proclaimed.  "They have bushes made of letters, just like in World World!"

Build a Better Battleship

Each week I volunteer in Smiley's kindergarten classroom.  I also help with math in some of the school's fourth and fifth grade classrooms.

Last week I invented a nice version of the game Battleship to help teach about equivalent fractions.

The kids loved it.  Yay!

Wait for the Recession, Then Buy Small-cap ETFs

Victor Liang has noticed that Small-cap ETF funds eventually outperform the overall market, especially if purchased during a recession.

It is an interesting article.  But it has four problems as an investment strategy.

First, the required time-frame of 10+ years makes this strategy viable primarily for how to invest for your kids.  Most investors do not have so many years to wait.

Second, the strategy does not understand or describe its risks.  Investors that want to use this strategy do not know what to do with their other investments to balance its weaknesses and manage overall risk.

Third, it is risky.  The three Small-cap ETF funds are not very old.

• IJR was established in 2000
• VBR was established in 2004
• SLY was established in 2010

Thus the "pattern" of outperforming over a ten-year period has only had time to happen once.  It is a risky bet that the pattern will repeat regularly.

Fourth, it is chasing gains.  Small-cap stocks surged last year.  Because the proposed strategy has such a long-term focus this would not be such a harsh criticism, except for the previous point that the "pattern" is not well-founded.

An Introduction to Investing

At the end of last month I finished back-burner project.  I wrote a series of four essays to introduce people to the stock market.

• How do I know which stocks or ETFs to buy? You can read my strategy for investment picking.
• Once I know which stock or ETF to buy, how do I know when to buy it? You can read my strategy for investment timing.
• For most of my family's savings we use dividend investing.
• I manage my IRA with a certain style of sector investing.

May these be helpful to you or someone you know!

Last year was an easy year to do well in the stock market, because the overall market grew so much.

 

Yet there is still satisfaction from beating the market by 7.5% with my Roth IRA.

(I do not expect the first three accounts to outperform the market, since they contain the commonly recommended mix of stocks and bonds to reduce risk.)

UPDATE: Blerg.  The day I decide to blog this, Google changes the code for their stock graph widgets. The last two essays were much nicer with those working.  Now the graph's images are broken, and the entire widget is a link to Yahoo! Finance.  Perhaps some hacker had fun.

Smiley and Percentages

My father-in-law recently introduced Smiley to the game The Battle for Wesnoth.

One of the game's features is a button that shows the player a battle's possible battle outcomes and their probabilities.  This was the first time Smiley had paid any attention to percentages.

Yesterday, at the San Diego Zoo, he saw a toy that he wanted at a gift shop.  It was a stick that made a whooshing noise when turned upside down, decorated like a giraffe's neck and head.

He had never seen such a toy before.  Nevertheless, he told me, "But Daddy, I have been wanting that toy 70% for 8 days!"

I am not sure what 70% means to Smiley, but it is apparently synonymous with "a whole lot".

2014 New Year's Resolution

"Here is a lesson in creative writing. First rule: Do not use semicolons. They are transvestite hermaphrodites representing absolutely nothing. All they do is show you've been to college."
― Kurt Vonnegut, A Man Without a Country

I do not agree completely with the above quotation.  But I have paid attention since reading it a few months ago.  Usually my writing improves when I break up sentences that contain joined independent clauses.

Cutting those clauses forces me to choose my words with more care.  Surprisingly often, gluing independent clauses with a semicolon or em-dash or a "comma plus conjunction" phrase is legitimate but hinders my clarity.

So my new year's resolution is to join independent clauses as little as possible.

---

 As a case in point, here is my stream-of-consciousness draft of the above:

I do not agree completely with the above quotation, but since reading it a few months ago I have noticed how much my writing improved by breaking up sentences.  I must choose my words with more care when I minimize joining independent clauses―surprisingly often, gluing independent clauses with a semicolon or em-dash or a "comma plus conjunction" phrase is legitimate but hinders clarity.  So my new year's resolution is to join independent clauses as little as possible.