The Official MathGeek Blog

The Mathematical Atlas

The Mathematical Atlas is a gateway to modern mathematics.  It is a collection of short articles designed to provide an introduction to the areas of modern mathematics and pointers to further information, as well as answers to some common or not so common questions. The material is arranged in a hierarchy of disciplines, each with its own index page.   My favorite quote so far: "Measure theory is a meeting place between the tame applicability of real functions and the wild possibilities of set theory."  Exactly!  To see some of those wild possibilities, click here.

NameVoyager

Here is a very cool link that shows the popularity of names as a function of a time. The graph below, for example, shows that the name "Eric" was most popular in the early seventies but has inexplicably dropped off since that time. 

   

The Goat Problem

Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does.

The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors.

After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch?  More...

The Antikythera Mechanism

More than a hundred years ago an extraordinary mechanism was found by sponge divers at the bottom of the sea near the island of Antikythera. It astonished the whole international community of experts on the ancient world. Was it an astrolabe? Was in an orrery or an astronomical clock? Or something else? For decades, scientific investigation failed to yield much light and relied more on imagination than the facts. However research over the last half century has begun to reveal its secrets. It dates from around the 1st century B.C. and is the most sophisticated mechanism known from the ancient world. Nothing as complex is known for the next thousand years. The Antikythera Mechanism is now understood to be dedicated to astronomical phenomena and operates as a complex mechanical "computer" which tracks the cycles of the Solar System.  More...

Rice swaps print for digital press

(From News.com) Rice University said Thursday that it will introduce the country's first all-digital academic press after a 10-year hiatus from publishing a print peer-review journal.

The Texas university plans to use an open-source publishing platform, called Connexions, so that professors can author scholarly works with text and multimedia files like audio, animations and referential hyperlinks. With the system, works can be printed on-demand.  More...

Welcome to MathGeek.com!

Prime Number Posters!

For years Perfectly Scientific Inc. has been producing high quality posters of the largest currently known prime number. Each poster is printed on thick glossy paper and measures 29 inches by 40 inches. Framed and unframed posters dating back to June of 1999 are available for purchase. Prices vary, as each new prime tests the limits of the technology necessary to print these high-resolution posters. The digits are very clear, but unless you have very, very good eyesight, you will need one of their watchmaker's loupes or an equivalent magnifier to read the digits.  More...

The Moonstick

A moonstick is a slide rule moon phase calendar.  It replaces a conventional moon phase chart or moon phase calculator.  The moonstick can determine the moon phase for any date, past (8000 years), present, or future (8000 years).  It can also perform a variety of "advanced searches" (for example, "On what dates this year are there new moons?  How long until there is a full moon on Halloween?").  The moonstick automatically recognizes all leap years and leap centuries, all time zones, the calendar adjustment of 1582, and years "BC".  The moonstick produces results accurate to 1½ hours in approximately 10 seconds. More...

Publications by Eric Hall

1. Wise, G. L., and E. B. Hall, Counterexamples in Probability and Real Analysis, Oxford University Press, New York, 1993, (ISBN 0–19–507068–2). (Review)
2. Hall, E. B., Alan Wessel, and Gary Wise, "Some Aspects of Fusion in Estimation Theory," Selected Papers on Sensor and Data Fusion, SPIE Milestone Series, Volume MS 124, edited by Firooz A. Sadjadi, 1996, pp. 62–64 (ISBN 0–8194–2265–7).
3. Hall, E. B. and G. L. Wise, "An Algebraic Aspect of Linear System Theory," IEEE Transactions on Circuits and Systems, Vol. 37, No. 5, May 1990, pp. 651–653.
4. Hall, E. B. and G. L. Wise, "A Curiosum Concerning Discrete Time Convolution," IEEE Trans. on Acoustics, Speech, and Signal Processing, Vol. 38, No. 6, June 1990, pp. 1058–1059.
5. Wessel, A. E., E. B. Hall and G. L. Wise, "Importance Sampling Via a Simulacrum," The Journal of the Franklin Institute, Vol. 327, No. 5, 1990, pp. 771–783.
6. Wise, G. L. and E. B. Hall, "A Note on the Distribution of the Determinant of a Random Matrix," Statistics and Probability Letters, Vol. 11, No. 2, pp. 147–148, February 1991.
7. Hall, E. B., A. E. Wessel and G. L. Wise, "Some Aspects of Fusion in Estimation Theory," IEEE Transactions on Information Theory, Vol. 37, No. 2, pp. 420–422, March 1991.
8. Hall, E. B. and G. L. Wise, "On Optimal Estimation with Respect to a Large Family of Cost Functions," IEEE Transactions on Information Theory, Vol. 37, No. 5, pp. 691–693, May 1991.
9. Wise, G. L. and E. B. Hall, "A Comment on the Finite Memory of Stochastic Processes," IEEE Transactions on Signal Processing, Vol. 40, No. 9, p. 2368, September 1992.
10. Hall, E. B. and G. L. Wise, "A Result on Multidimensional Quantization," Proceedings of the American Mathematical Society, June 1993, Vol. 118, No. 2, pp. 609–613.
11. Wise, G. L. and E. B. Hall, "On Mutual Independence," Statistics and Probability Letters, Vol. 17, No. 5, 1993, pp. 395–398.
12. Hall, E. B., "A Note on the Convergence of Quantizers," Mathematical Problems in Engineering, Vol. 2, pp. 57–61, 1996.
13. Hall, E. B. and G. L. Wise, "Simultaneous Optimal Estimation Over a Family of Fidelity Criteria," Proceedings of the Twenty–First Annual Conference on Information Sciences and Systems, Baltimore, Maryland, March 25–27, 1987, pp. 65–70.
14. Wessel, A. E., E. B. Hall and G. L. Wise, "Some Comments on Importance Sampling," Proceedings of the Twenty–Second Annual Conference on Information Sciences and Systems, Princeton, New Jersey, March 16–18, 1988, pp. 325–329 (invited).
15. Hall, E. B., A. E. Wessel and G. L. Wise, "On Fusion in Estimation Theory," Proceedings of the Twenty–Sixth Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois, September 28–30, 1988, pp. 599–608.
16. Hall, E. B. and G. L. Wise, "Conditioning: A Critical Review," Proceedings of the 23rd Annual Conference on Information Sciences and Systems, Baltimore, Maryland, March 22–24, 1989, pp. 271–276.
17. Hall, E. B. and G. L. Wise, "Some Comments on Filtering in Estimation Theory," Proceedings of the 32nd Midwest Symposium on Circuits & Systems, Urbana, Illinois, August 14–16, 1989, pp. 1162–1165.
18. Hall, E. B. and G. L. Wise, "On an Aspect of Optimal Nonlinear Estimation," Proceedings of the Twenty–Seventh Annual Allerton Conference on Communication, Control, and Computing, Monticello, Illinois, September 27–29, 1989, pp. 692–701.
19. Hall, E. B. and G. L. Wise, "Some Pathologies Associated with Maximum Likelihood Estimation," Proceedings of the Twenty–Fourth Annual Conference on Information Sciences and Systems, Princeton, New Jersey, pp. 11–16, March 21–23, 1990.
20. Hall, E. B. and G. L. Wise, "An Analysis of Convergence Problems in Kalman Filtering which Arise from Numerical Effects," Proceedings of the 33rd Midwest Symposium on Circuits and Systems, Calgary, Alberta, Canada, pp. 315–318, August 12–14, 1990.
21. Hall, E. B. and G. L. Wise, "Some Comments on Stochastic Calculus," Proceedings of the 1991 Conference on Information Sciences and Systems, Baltimore, Maryland, March 20–22, 1991.
22. Hall, E. B. and G. L. Wise, "Some Aspects of Multidimensional Convolution," Proceedings of the 1991 International Conference on Acoustics, Speech, and Signal Processing, Toronto, Ontario, Canada, May 14–17, 1991, pp. 2317–2320.
23. Hall, E. B. and G. L. Wise, "On a Failure of Multidimensional Quantization," Proceedings of the 1991 International Conference on Acoustics, Speech, and Signal Processing, Toronto, Ontario, Canada, May 14–17, 1991, pp. 1921–1924.
24. Hall, E. B. and G. L. Wise, "Decentralized Estimation with Nontraditional Fidelity Criteria and Corrupted Estimates," Proceedings of the 1992 Conference on Information Sciences and Systems, Princeton, New Jersey, March 18–20, 1992.
25. Wise, G. L. and E. B. Hall, "Estimation of a Random Variable Based on Multidimensional Data," Proceedings of the 1992 International Conference on Acoustics, Speech, and Signal Processing, Vol. 3, pp. 317–320, San Francisco, California, March 23–26, 1992.
26. Joudeh, I. and E. B. Hall, "Delay Analysis for Packet Trains in Computer Communications using Single Server Queues," Proceedings of the 1992 National Telesystems Conference, Washington, D.C., May 19–20, 1992, pp. 13-7–13-14.
27. Bienn, M. and E. B. Hall, "Symbol Synchronization over a Frequency Nonselective Fading Channel," Proceedings of the IEEE Wichita Conference on Communications, Networking and Signal Processing, Wichita, Kansas, April 26–27, 1994.
28. Hall, E. B., "On the Modeling of Quantization Effects via Points of Accuracy," Proceedings of the 33rd IEEE Conference on Decision and Control, Lake Buena Vista, Florida, pp. 2522–2523, Dec. 14–16, 1994.
29. Bienn, M. and E. B. Hall, "A Decision Theoretic Approach to Symbol Synchronization over a Frequency Nonselective Fading Channel," Proceedings of the 34th Conference on Decision and Control, New Orleans, Louisiana, pp. 2070–2075, Dec. 13–15, 1995.
30. Hall, E. B., "The Composite Classification Problem in Optical Information Processing," NASA/ASEE Summer Faculty Fellowship Program – 1994, Vol. 1, Richard Bannerot and Donn G. Sickorez, eds., NASA Contractor Report 188410, Grant NGT 44–001–800, July 1995, Chapter 13.
31. Aliyazicioglu, Z. and E. B. Hall, "Optimal Decision for Distributed Detection Systems," Proceedings of the Second World Conference on Integrated Design and Process Technology, Austin, Texas, pp. 121-127, December 1-4, 1996.

Nature's Fundamental Laws May Be Changing

Recent research has found evidence that the value of certain fundamental parameters, such as the speed of light or the strength of the invisible glue that holds atomic nuclei together, may have been different in the past.

"There is absolutely no reason these constants should be constant," says astronomer Michael Murphy of the University of Cambridge. "These are famous numbers in physics, but we have no real reason for why they are what they are."

The observed differences are small — roughly a few parts in a million — but the implications are huge. The laws of physics would have to be rewritten, and we might need to make room for six or seven more dimensions than the four — the three spatial ones, plus time — that we are used to.  More...