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Resolution of Paradox: a Gateway to Mathematical Progress


Hermann Weyl (1885-1955)

A paradox is a statement that appears to contradict itself, or that is counter-intuitive. The analysis of paradoxes has led to profound developments in mathematics and logic. One of the richest sources of paradox is the concept of infinity. Hermann Weyl, one of the most brilliant mathematicians of the twentieth century, defined mathematics as “the science of the infinite”  [TM192 or search for “thatsmaths” at].

Ever since there has been time to wonder, humankind has been intrigued by the enigma of infinity. The idea has perplexed philosophers and mystified mathematicians for millennia. The Greeks were contemplating infinity from the time of Pythagoras. Head-on confrontation of infinity led to contradictory conclusions; the paradoxes of Zeno are amongst the most noted of these.

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Don’t be Phased by Waveform Distortions

For many years there has been an ongoing debate about the importance of phase changes in music. Some people claim that we cannot hear the effects of phase errors, others claim that we can. Who is right? The figure below shows a waveform of a perfect fifth, with components in the ratio {3 : 2} for various values of the phase-shift. Despite the different appearances, all sound pretty much the same.

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Saros 145/22: The Great American Eclipse

Next Monday, the shadow of the Moon will bring a two-minute spell of darkness as it sweeps across the United States along a path from Oregon to South Carolina. The eclipse is one of a series known as Saros 145. [TM121 or search for “thatsmaths” at].


Saros series 145 recurring every 18 years, 10 days and 8 hours.
[Image from ]

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RT60 and Acoustic Excellence

This week’s That’s Maths column (TM072) [search for “thatsmaths” at] is about architectural acoustics, and about the remarkable work of Wallace Clement Sabine.

Boston Symphony Hall. Image downloaded from website:

Boston Symphony Hall. Image downloaded from BSH.

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2014 in review

2014 annual report of for this blog.

Here’s an excerpt:

The concert hall at the Sydney Opera House holds 2,700 people. This blog was viewed about 37,000 times in 2014. If it were a concert at Sydney Opera House, it would take about 14 sold-out performances for that many people to see it.

Click here to see the complete report.

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