Click on the image to zoom in on the design.

Engineers, mathematicians, and physicists all love the Fourier transform. When we hear about the Transformers movie, we keep thinking about Fourier Transformers, with Oscilloscope Prime leading the noble Autocorrelationbots against the nefarious Decepticonvolutions. Look heroic (and nerdy) with our Oscilloscope Prime math shirt!

The Fourier transform converts functions of time into their frequency components. In other words, it expresses the function as a superposition of a continuum of complex waves of pure frequencies.

If you clap your hands near a piano, how will this excite the strings? You can imagine sustaining a single note on a flute near a piano, and this might resonate with just the string at that frequency while leaving most of the other strings of the piano largely unaffected. The Fourier transform says that the clap can be viewed as a superposition of many flutes playing different pitches at different amplitudes. If we understand how the piano reacts to each flute, then we can understand the reaction to the clap.

Convolution is a natural but complicated operation. The convolution of two probability distributions is the distribution of the sum of independent random variables with those distributions. When you multiply two numbers, you convolve the digits, and then carry. If the digits are small enough, then there are no carries and you only have to convolve the digit string. When you multiply 1011 by 203, you get the convolution 205233. The Fourier transform of the convolution of f and g is the pointwise product of the convolutions of f and g. While convolution is a complicated operation on functions, it is simple on their Fourier transforms.

Noise such as static in an audio recording or scratches on a photograph may affect primarily the higher frequencies. To improve the signal-to-noise ratio, one approach is to dampen the higher frequencies relative to the lower ones. To do this, we can convolve with a function g whose Fourier transform is 1 on low frequencies, and 0 on high frequencies. Since the Fourier transform applied twice returns the original function multiplied by -1, we can find this useful g by taking the Fourier transform of a function which is 1 when -1< t < 1, and 0 outside this interval. The Fourier transform of this function is the function sinc 2x, so convolving with a sinc function is one way to reduce noise.

Our picture of Oscilloscope Prime shows a rectangular wave displayed on his oscilloscope form, and its Fourier transform, a sinc function displayed on his chest. This math shirt can be purchased via our nerdy shirt site.

Click on the image above to zoom

To us, nerdiness means appreciation and understanding of science, mathematics, and technology. We nerds appreciate the beauty of art and nature, but also the elegance of powerful ideas. We think the world becomes more wondrous and more interesting as we understand more of it.

Sometimes nerdiness is expressed professionally, but you don’t have to be a scientist to enjoy science, as shown by the strong popularity of the Discovery Channel, NOVA, and other programs aimed at the interested public. We’re big fans of some areas of science we didn’t study in school.

There is a negative connotation to nerdiness in society, which associates weaknesses to every strength. Attractive people are assumed to be stupid. Strong people are assumed to be clumsy. Intellectuals must be antisocial and weak. These stereotypes are sometimes right, and sometimes wrong. We celebrate the positive aspects of nerdiness, and reject the negative connotations as wishful thinking of the insecure.

In some parts of the English-speaking world, nerd carries the good meanings, and geek carries the bad. In other parts, the reverse is true. To us, a geek is more specialized while a nerd is more general, and both are positive.

We’ve designed a special Nerd Pride shirt featuring the (visible) electromagnetic spectrum. The electromagnetic spectrum is a familiar sight from physics texts from elementary school through graduate school, since light is the most important tool we have for investigating the world. Coincidentally, rainbow flags have been used by numerous movements (indigenous peoples, cooperatives, peace/anti-nuclear, gay/lesbian/bi/transgender, etc.), often to symbolize pride in diversity or hope. As wonderful as we find Weird Al Yankovic’s “White and Nerdy” song, nerds are found in all colors, in all walks of life, and with all educational backgrounds.