Amen. This is one reason why I'm awfully glad that Barney Frank is my representative. There are certainly some things I disagree with him about, but he has consistently been a very outspoken critic of the Patriot Act. I heard a debate between him and Viet Dinh (who was a co-author of the Patriot Act) at Wheaton College in Massachusetts this spring that was fantastic.
The most surprising thing to me about the debate was that neither were as strictly ideological or partisan as I would have expected. If anyone is interested, the entire debate is available through the WGBH website at
http://forum.wgbh.org/wgbh/forum.php?lecture_id=18 07
Perhaps the most difficult part in my own work as a mathematician is understanding an area well enough to create meaningful, interesting conjectures. In many cases, the proof falls out immediately. This obviously isn't universally true (e.g. Fermat's Last Theorem), but the mathematicians that I have the most respect for are the ones who are able to see the connections between seemingly unrelated areas and ask the right questions to pull it all together.
As other have said, computing may be able to verify an existing proof, but I think the real creativity and beauty in mathematics is often found in the initial formation of the conjecture.
I think that by grouping the two alcoholic beverages together you are missing the point of the example. There doesn't have to be any connection between the two lowest ranked candidates.
The basic problem is that in an election with 3 candidates (A, B, and C), A can be the winner under strict plurality, B can be the winner under plurality with elimination, but C will beat either A or B in a head-to-head election.
In other words, the voting procedure can have as big an influence on the winner as the voters' preferences! There is a large body of work in voting theory that studies why different procedures give different results.
On a slightly related note, the reason why we only have two "real" choices for president in the US is that our method of voting reinforces the two party system. If we could specify our second (and third and fourth) preferences and these preferences had some impact on the election, then people wouldn't feel like they were throwing their vote away and we could avoid the "a vote for Nader is a vote for Bush" syndrome.
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Amen. This is one reason why I'm awfully glad that Barney Frank is my representative. There are certainly some things I disagree with him about, but he has consistently been a very outspoken critic of the Patriot Act. I heard a debate between him and Viet Dinh (who was a co-author of the Patriot Act) at Wheaton College in Massachusetts this spring that was fantastic.
The most surprising thing to me about the debate was that neither were as strictly ideological or partisan as I would have expected. If anyone is interested, the entire debate is available through the WGBH website at http://forum.wgbh.org/wgbh/forum.php?lecture_id=18 07
Perhaps the most difficult part in my own work as a mathematician is understanding an area well enough to create meaningful, interesting conjectures. In many cases, the proof falls out immediately. This obviously isn't universally true (e.g. Fermat's Last Theorem), but the mathematicians that I have the most respect for are the ones who are able to see the connections between seemingly unrelated areas and ask the right questions to pull it all together.
As other have said, computing may be able to verify an existing proof, but I think the real creativity and beauty in mathematics is often found in the initial formation of the conjecture.
I think that by grouping the two alcoholic beverages together you are missing the point of the example. There doesn't have to be any connection between the two lowest ranked candidates.
The basic problem is that in an election with 3 candidates (A, B, and C), A can be the winner under strict plurality, B can be the winner under plurality with elimination, but C will beat either A or B in a head-to-head election.
In other words, the voting procedure can have as big an influence on the winner as the voters' preferences! There is a large body of work in voting theory that studies why different procedures give different results.
On a slightly related note, the reason why we only have two "real" choices for president in the US is that our method of voting reinforces the two party system. If we could specify our second (and third and fourth) preferences and these preferences had some impact on the election, then people wouldn't feel like they were throwing their vote away and we could avoid the "a vote for Nader is a vote for Bush" syndrome.