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Without even looking I guarantee that the Periodic Table of Finite Simple Groups is garbage --- there's no way that the space of finite simple groups have the s

by gohrt 10y ago

Without even looking I guarantee that the Periodic Table of Finite Simple Groups is garbage --- there's no way that the space of finite simple groups have the same structure as the space of atoms.

cokernel 10y ago
Here's Ivan Andrus's (the creator's) explanation of it: https://irandrus.wordpress.com/2012/06/17/the-periodic-table-of-finite-simple-groups/ https://irandrus.wordpress.com/2012/06/17/the-periodic-table... It's worth taking a look. (Well, I make no guarantees.)
- srtjstjsj 10y ago
  The author admits to twisting the shape of the table to arbitrarily make it look like the table of elements, even though the only similarity is that both have some sense of 2-dimensionality. The groups table is not "periodic" in any sense. > I also considered the non-classical groups to be “less important” and so there are fewer rows of them to better match the look of the real periodic table. They also have larger orders so it makes sense to include fewer of them on the table. > Since there are no “sporadic” elements, I had to decide what to do with the sporadic simple groups. These are groups that don’t fall into any of the other families. At one point I put them in the upper right corner with a jagged boundary like the non-metals. This made the table resemble the real periodic table, but it had more rows and less columns so it looked rather “thick”. Unfortunately, it didn’t make as much sense from an algebraic point of view, so I placed them where the lanthanides and actinides are found instead. This is slightly misleading, because if enough new elements were to be discovered there would be another row in that section. But you can’t have everything perfect. After all, there are an infinite number of simple groups, and only a finite number of elements.
moscaf 10y ago
Yeh, I know, the idea that mathematics could in any way model reality is garbage.
- srtjstjsj 10y ago
  The rows of the periodic table of finite simple groups -- what do they model?
goldenkey 10y ago
A little silly to speak with such overconfidence considering the only similarity is the "table" paradigm. The actual periodic table is poor for its use anyways, and there have been valid criticisms that call for a more abstract grouping, like a spiral/ring table [1] [2] But in any case, the properties of numbers are intrinsic to the relationship between space and time - the ability to store a number physically [in memory] and then act on it at a later time. You can try to claim that physics transcends mathematics -- but I would argue that the properties of numbers, and hence algebras, are more fundamental than even physical field theories are. [1] http://www.chemistryland.com/CHM130W/03-BuildingBlocks/Chaos/SpiralTable.jpg http://www.chemistryland.com/CHM130W/03-BuildingBlocks/Chaos... [2] https://upload.wikimedia.org/wikipedia/commons/6/6b/The_Ring_of_Periodic_Elements.svg https://upload.wikimedia.org/wikipedia/commons/6/6b/The_Ring...
- deleted 10y ago
  [deleted]

by gohrt 10y ago

Without even looking I guarantee that the Periodic Table of Finite Simple Groups is garbage --- there's no way that the space of finite simple groups have the same structure as the space of atoms.

cokernel 10y ago

Here's Ivan Andrus's (the creator's) explanation of it: https://irandrus.wordpress.com/2012/06/17/the-periodic-table-of-finite-simple-groups/ https://irandrus.wordpress.com/2012/06/17/the-periodic-table... It's worth taking a look. (Well, I make no guarantees.)

srtjstjsj 10y ago
The author admits to twisting the shape of the table to arbitrarily make it look like the table of elements, even though the only similarity is that both have some sense of 2-dimensionality. The groups table is not "periodic" in any sense. > I also considered the non-classical groups to be “less important” and so there are fewer rows of them to better match the look of the real periodic table. They also have larger orders so it makes sense to include fewer of them on the table. > Since there are no “sporadic” elements, I had to decide what to do with the sporadic simple groups. These are groups that don’t fall into any of the other families. At one point I put them in the upper right corner with a jagged boundary like the non-metals. This made the table resemble the real periodic table, but it had more rows and less columns so it looked rather “thick”. Unfortunately, it didn’t make as much sense from an algebraic point of view, so I placed them where the lanthanides and actinides are found instead. This is slightly misleading, because if enough new elements were to be discovered there would be another row in that section. But you can’t have everything perfect. After all, there are an infinite number of simple groups, and only a finite number of elements.

moscaf 10y ago

Yeh, I know, the idea that mathematics could in any way model reality is garbage.

srtjstjsj 10y ago
The rows of the periodic table of finite simple groups -- what do they model?

goldenkey 10y ago

A little silly to speak with such overconfidence considering the only similarity is the "table" paradigm. The actual periodic table is poor for its use anyways, and there have been valid criticisms that call for a more abstract grouping, like a spiral/ring table [1] [2] But in any case, the properties of numbers are intrinsic to the relationship between space and time - the ability to store a number physically [in memory] and then act on it at a later time. You can try to claim that physics transcends mathematics -- but I would argue that the properties of numbers, and hence algebras, are more fundamental than even physical field theories are. [1] http://www.chemistryland.com/CHM130W/03-BuildingBlocks/Chaos/SpiralTable.jpg http://www.chemistryland.com/CHM130W/03-BuildingBlocks/Chaos... [2] https://upload.wikimedia.org/wikipedia/commons/6/6b/The_Ring_of_Periodic_Elements.svg https://upload.wikimedia.org/wikipedia/commons/6/6b/The_Ring...

deleted 10y ago
[deleted]