an equation.........................

 

Einstein wrote an equation that says that R is equivalent to the energy of matter.  That is to say: space curves where there is matter.  That is it.  The equation fits into half a line, and there is nothing more.  A vision—that space curves—became an equation.

     But within this equation there is a teeming universe.  And here the magical richness of the theory opens up into a phantasmagorical succession of predictions that resemble the delirious ravings of a madman but all have turned out to be true.

-Carlo Rovelli, Seven Brief Lessons on Physics

Never bet against Big Al..........................

 

    via

Important facts..............................

15.  Two 12-inch pizzas have less pizza than one 18-inch pizza.

-more fun here              math here

believe......................

     "You don't believe in reason," Sharpe let the conversation veer away from the painful subject of the Count of Mouromorto's loyalty.

     "Reason is the mathematics of thinking, nothing more.  You don't live by such dry disciplines.  Mathematics cannot explain God, no more can reason, and I believe in God! Without Him we are no more than corruption.  But I forget. You are not a believer."

Bernard Cornwell, Sharpe's Rifles

Competition................

       One area where all American steelmakers could maintain absolute, almost religious agreement was on the topic of British steel.  British steelmakers were more efficient, and as a result, their rails were cheaper even than Carnegie's.  As with the iron industry before, the Americans' collective strategy was equally simple: tariffs.  Congress complied.  The tariff on a ton of imported British steel started at $28 per ton.  Given that Carnegie's first-ever order was fulfilled at $68 per ton, the British would have had to sell steel at $40 per ton, with overseas shipping included, to pay the tariff and match the price in the market.  In an era without a personal income tax or corporate income taxes, the federal government relied on duties and tariff generated income for a significant portion of its revenue . . .

      Even Carnegie, with all his competitive, Darwinian pride, granted that tariff protection "has played a great part in the development of manufacturing in the United States." . . . But laissez-faire capitalism it was not.  The invisible hand of Adam Smith's free market was accompanied by the guiding hand of government policy.

-Bhu Srinivasan, Americana: A 400-Year History of American Capitalism

Hey, it could happen...................

 

Fun with math.........................

more fun here

Nuttiness..........................

Two wee excerpts from this post at the National Review:  Professor:  Learning Math Can Cause 'Collateral Damage' to Society

“Reasoning without meanings provides a training in ethics-free thought,” Paul Ernest writes in “The Ethics of Mathematics: Is Mathematics Harmful?” — a chapter of his book The Philosophy of Mathematics Education Today.

“Money and thus mathematics is the tool for the distribution of wealth,” he writes. “It can therefore be argued that as the key underpinning conceptual tool mathematics is implicated in the global disparities in wealth.”

If academics were as interested in the creation of wealth as they are in the distribution of wealth, the world could be a much nicer place.   Talk of wealth distribution without talk of wealth creation always reminds me of this line from my favorite Ten Years After song:

Tax the rich, feed the poor, till there are no rich no more

Then what?

Quiz time..............................

Years back, Marilyn vos Savant had a quiz column in which a question was: “Two bugs in a jar reproduce, doubling their number every minute. The jar is full in an hour. How long does it take to half fill the jar?”

-extracted from here 

Savoring............................

I have............................

            via

Columbus makes a few mistakes....

     The diameter of the spherical Earth had been calculated accurately by the Greek Eratosthenes in the second century BC, and his calculation was still widely known in the time of Columbus.  Though no European foresaw what lay in wait for Columbus, since all thought mistakenly that the  Ocean Sea, empty of land, was much larger than it was, almost all who could read and had looked into the subject understood that Columbus was seriously underestimating the overall size of the Earth.*
     Columbus, basing his calculations on inaccurate assumptions, theorized that the east coast of Asia could be reached by a European ship within a few weeks of its leaving port.  The actual circumference of the Earth is about 40,000 kilometers, whereas Columbus assumed it to be closer to 25,000 kilometers.  Compounding his mistake was his misreading - in a Latin translation - of a renowned ninth-century Persian astronomer, Ahmad ibn Muhammad ibn Kathir al-Faghani, known in the West as Alfraganus.  The Persian's correct measurements were given in Arabic miles, which Columbus assumed to be the same as Roman miles.  In actuality, Roman miles are about 25 percent shorter than Arabic ones.  Had the Ocean not held the Americas and the vast sea been empty of land between Europe and Asia, Columbus and his crew, heading west, would have perished in the deep and never been heard from again.  This had indeed been the fate of several earlier (and well-known) attempts.

-Thomas Cahill,  Heretics and Heroes

*No one who knew anything thought the Earth was flat.  This was an anti-Catholic fable created by a nineteenth-century Frenchman named Jean Antoine Letronne and disseminated widely to English speakers by Washington Irving in his unreliable biography of Columbus.

Beware......................

.............................................of mathematical optimization.

The problem with models...........................

.....................................(beside the fact they involve mathematics):

What economists call "models" are interpretive frameworks.  They are presented mathematically, with proofs that connect initial assumptions to ultimate predictions.  However, the predictions are not falsifiable.  The models' predictions hold only when other things are equal, and other things are never equal.

-Arnold Kling,  Specialization and Trade:  A Re-Introduction to Economics

So, you're telling me now............

................that my college degree is worthless?   The history major in me quickly learned (by watching a significant percentage of the freshmen football players flunk calculus) that studying higher math might interfere with my college career.  Forty-three years after graduating I haven't had the need for any math beyond what I learned in high school algebra and geometry.  Your experience may vary.

Fun with math......................

via

The wiki for Euler's Identity is here, just in case you're curious.

Wouldn't you love to come up with a sentence like "Also, as a pragmatic matter it's very useful for shutting down emotional conversations that occur while gazing upon the vault of heaven in a mystic coalescence of wonder and fear"?   Genius.

Math even I can understand................

If A is success in life, then A = x + y + z. 
Work is x, play is y and z is keeping your mouth shut.

-Albert Einstein

Raise your hand..................

..................if you have ever "flipped" a Monopoly board because of the "obnoxious" behavior of one of your game mates.  Hmm.  Okay, raise your hand if any of your game mates has ever "flipped" the Monopoly board on you. 

                Interesting post here (Crazy Math Fact #8 out of 9) about whether all spaces on a Monopoly board should be considered "equal".  Note the fine print at the bottom of this slide:

Spoiler alert (too late):

thanks Craig

Mathiness............................

..............If everybody who bought a lottery ticket for tonight's monster Powerball drawing took the time to read this, our nation would be way smarter, and probably way more prosperous.

About cleverness.........................

"In the last 30 yeas the field of investment banking had been transformed from a field that was dominated by people who were good at meeting clients at the 19th hole, to people who were good at solving very difficult mathematical problems that were involved in pricing derivative securities."
-Larry Summers

      Yet these cleverer people managed things less well - much less well - than their less intellectually distinguished predecessors.  Although clever, they were rarely as clever as they thought, or sufficiently clever to handle the complexity of the environment they had created.  Perhaps the ability to meet clients at the nineteenth hole is more relevant to making good investments than the ability to solve very difficult mathematical problems.

-John Kay, as excerpted from Other People's Money:  The Real Business of Finance