Difference between revisions of "Singularity"
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==Mathematical Context== | ==Mathematical Context== | ||
| − | One of the more complex functions which is visible in the laboratory is fluid-flow formulae which can be made to operate in regions where singularities occur. In the years leading up to 2023 researchers found singular solutions to the Euler equation. Now we have a proof that | + | One of the more complex functions which is visible in the laboratory is fluid-flow formulae which can be made to operate in regions where singularities occur. In the years leading up to 2023 researchers found singular solutions to the Euler equation. Now we have a proof that true singularities occur in specially constructed geometries. Basically the researchers created a boundary between two stable regimes where the singularity was maintained. In these cases neither the mathematics nor the computer simulations are powerful enough to show there actual behavior.<ref>Don Monroe, ''Computer-Assisted Proofs take on Fluid Flow'' '''CACM 66''' No. 8 (2023-08) pp. 12-14</ref> Continuous mathematical solutions can only work in the spaces between the infinitely large and the infinitely small. |
==Human Context== | ==Human Context== | ||
Revision as of 13:22, 3 August 2023
Full Title or Meme
A Singularity is an artifact of continuous mathematical functions that can be taken to the limit, whether very small or very large.
Mathematical Context
One of the more complex functions which is visible in the laboratory is fluid-flow formulae which can be made to operate in regions where singularities occur. In the years leading up to 2023 researchers found singular solutions to the Euler equation. Now we have a proof that true singularities occur in specially constructed geometries. Basically the researchers created a boundary between two stable regimes where the singularity was maintained. In these cases neither the mathematics nor the computer simulations are powerful enough to show there actual behavior.[1] Continuous mathematical solutions can only work in the spaces between the infinitely large and the infinitely small.
Human Context
Von Neumann was deeply aware of the accelerating pace of progress and the profound implications of this progression for humanity's future, which brings us to the fifth key idea of the information age. A year after von Neumann's death in 1957, fellow mathematician Stan Ulam quoted von Neumann as having said that "the ever accelerating progress of technology and changes in the mode of human life give the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue." This is the first known use of the word "singularity" in the context of human history.[2]
References
- ↑ Don Monroe, Computer-Assisted Proofs take on Fluid Flow CACM 66 No. 8 (2023-08) pp. 12-14
- ↑ John von Nuemann, The Computer & the Brain Yale Univ Press (1958) ISBN 9780300181111
