Tag Archives: economics

Romancing the Sphere

Some may find this unique table helpful in understanding spheres.

Beyond the purely mathematic, this fully symmetrical regime may also find application in physics, sociology, ontology and economics.

Note: Using the diametric mode for calculations (mentally or on paper) can be quicker than employing the formal (radial) convention, especially when working with hyper-dimensional domains, exponential growth scenarios, or when one is in need of an easier way to factor between domains of differing dimensionality.

Diametric dimensionality

If you would like a personal, complimentary copy of this chart in PDF format (8.5″x11″ – but infinitely scalable) use the form below. Comments optional.
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Notes:

All versions since 2004 have reflected the much needed repair of the broken symmetry found in the 0-sphere definition under the prevailing n-sphere generalisation.

If you prefer the formal mode for transforms between exterior and interior space, simply use •r/d instead of •D/2d.

If you’re a student, check with your professor before applying these principles in your work. If you are the professor, just use your best judgement …and maybe get a second faculty opinion. 😉

Jan. 19, 2011 – Image updated from 2004 version to new 2011 version.

Jan. 22, 2011 – Minor aesthetic changes; image updated.

Jan. 23, 2011 – Diametric ext values adjusted by -1; image updated.

Oct. 26, 2011 – Minor text/aesthetic changes; explicatory notes added.

Dec. 28, 2011 – Declared dimensions as a single-character variable (d);
image not updated — use request form below for most current version.

Jan. 10, 2012 – Image updated.

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Bubble Trouble

200px-Nouriel_Roubini_05Nouriel Roubini discusses the dangers associated with the current market asset bubble leveraged in large measure by short positions on a declining US dollar.

“In 2005 Roubini said home prices were riding a speculative wave that would soon sink the economy. Back then the professor was called a Cassandra. Now he’s a sage.”
— Fortune magazine, 2008

Mother of all carry trades
faces an inevitable bust

By Nouriel Roubini

Since March there has been a massive rally in all sorts of risky assets – equities, oil, energy and commodity prices – a narrowing of high-yield and high-grade credit spreads, and an even bigger rally in emerging market asset classes (their stocks, bonds and currencies). At the same time, the dollar has weakened sharply, while government bond yields have gently increased but stayed low and stable.

This recovery in risky assets is in part driven by better economic fundamentals. We avoided a near depression and financial sector meltdown with a massive monetary, fiscal stimulus and bank bail-outs. Whether the recovery is V-shaped, as consensus believes, or U-shaped and anaemic as I have argued, asset prices should be moving gradually higher.

But while the US and global economy have begun a modest recovery, asset prices have gone through the roof since March in a major and synchronised rally. While asset prices were falling sharply in 2008, when the dollar was rallying, they have recovered sharply since March while the dollar is tanking. Risky asset prices have risen too much, too soon and too fast compared with macroeconomic fundamentals.

So what is behind this massive rally? Certainly it has been helped by a wave of liquidity from near-zero interest rates and quantitative easing. But a more important factor fuelling this asset bubble is the weakness of the US dollar, driven by the mother of all carry trades. The US dollar has become the major funding currency of carry trades as the Fed has kept interest rates on hold and is expected to do so for a long time. Investors who are shorting the US dollar to buy on a highly leveraged basis higher-yielding assets and other global assets are not just borrowing at zero interest rates in dollar terms; they are borrowing at very negative interest rates – as low as negative 10 or 20 per cent annualised – as the fall in the US dollar leads to massive capital gains on short dollar positions…

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Also: Check out our article “The Current State of Currency” (April 2, 2009)

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Filed under Economy, Reason