*Robert James Matthys*

- Published in print:
- 2004
- Published Online:
- January 2010
- ISBN:
- 9780198529712
- eISBN:
- 9780191712791
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198529712.003.0008
- Subject:
- Physics, History of Physics

The traditional plot of a clock's time error versus time is far superior to the Allan variance for showing a pendulum clock's time performance. The Allan variance is admittedly a universal and ...
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The traditional plot of a clock's time error versus time is far superior to the Allan variance for showing a pendulum clock's time performance. The Allan variance is admittedly a universal and statistically more accurate measure of a clock or oscillator's random frequency and time variations (that is, variance), because it is averaged over multiples of each time interval. However, it is a whole curve on a graph instead of being just a single memorable number, and its value is drastically reduced by the short time span it is able to cover. The variance, however, can be used to generate an oscillator's ‘root mean square (rms) time error versus time’ curve, a curve that is much easier to understand. But the rms time error's equally short time span also drastically limits its value to the clockmaker.Less

The traditional plot of a clock's time error versus time is far superior to the Allan variance for showing a pendulum clock's time performance. The Allan variance is admittedly a universal and statistically more accurate measure of a clock or oscillator's random frequency and time variations (that is, variance), because it is averaged over multiples of each time interval. However, it is a whole curve on a graph instead of being just a single memorable number, and its value is drastically reduced by the short time span it is able to cover. The variance, however, can be used to generate an oscillator's ‘root mean square (rms) time error versus time’ curve, a curve that is much easier to understand. But the rms time error's equally short time span also drastically limits its value to the clockmaker.

*Don S. Lemons*

- Published in print:
- 2017
- Published Online:
- January 2018
- ISBN:
- 9780262035903
- eISBN:
- 9780262338745
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262035903.003.0002
- Subject:
- Physics, History of Physics

In the middle ages (550-1510 CE) scientific knowledge was consolidated and translated, first from Greek and Latin into Arabic and Syriac and then from Arabic and Greek into Latin. Alhazen (1020 CE) ...
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In the middle ages (550-1510 CE) scientific knowledge was consolidated and translated, first from Greek and Latin into Arabic and Syriac and then from Arabic and Greek into Latin. Alhazen (1020 CE) was an important Arabic speaking scholar who made important contributions to a theory of vision and of refraction. Oresme and the school of Oxford scholars were the first (1360 CE) to describe uniform acceleration graphically. Leonardo De Vinci was a prolific inventor and user of informative diagrams – one of which describes the cause of “earthshine” (1520 CE).Less

In the middle ages (550-1510 CE) scientific knowledge was consolidated and translated, first from Greek and Latin into Arabic and Syriac and then from Arabic and Greek into Latin. Alhazen (1020 CE) was an important Arabic speaking scholar who made important contributions to a theory of vision and of refraction. Oresme and the school of Oxford scholars were the first (1360 CE) to describe uniform acceleration graphically. Leonardo De Vinci was a prolific inventor and user of informative diagrams – one of which describes the cause of “earthshine” (1520 CE).

*Manfred Eigen*

- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780198570219
- eISBN:
- 9780191748974
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570219.003.0004
- Subject:
- Physics, History of Physics

So far, our discussion has mainly been concerned with inanimate matter. Only in Chapter 3 did we notice what is missing in “information” if “meaning” is excluded. A phenomenological theory of the ...
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So far, our discussion has mainly been concerned with inanimate matter. Only in Chapter 3 did we notice what is missing in “information” if “meaning” is excluded. A phenomenological theory of the generation of “meaningful information” is given in this chapter and in Chapter 5. If we are dealing with genetic sequences, making use of four classes of symbols (referring to the four nucleotides used in nucleic acids), a sequence including n positions has 4n different possibilities. The sequence space is then a point space including 4n points, one for each possible sequence. The distances between any two sequences of this length corresponds to the number of positions occupied by different symbols. A value parameter is introduced which finally determines the population structure. The mutant spectrum appears in the form of a rather dissipated “cloud” that has one or several value maxima, a fact that is due mainly to the presence of “neutral sequences” (i.e. sequences of equal fitness value). The theory confirms formally Darwin’s result. However, the interpretation is completely different from the one generally encountered. Under normal conditions there is no fittest single individual. Rather, fitness is a property of a population, expressed by an eigenvalue of a matrix to which contribution is made by all the individuals present. Since we are dealing with coupled differential equations, the linear case can be expressed by the matrix of rate coefficients. However, according to a mathematical theorem by Perron and Frobenius, only the largest eigenvalue of the matrix is stable. To this we can assign the term “fittest”. The theory uncovers many surprising details. It also unifies the mechanisms of origin and evolutionary adaptation, both referring to different regions in the solutions of the same system of coupled differential equations. Some mathematical details can be found in the Appendices, including contributions from Peter Richter and Peter Schuster.Less

So far, our discussion has mainly been concerned with inanimate matter. Only in Chapter 3 did we notice what is missing in “information” if “meaning” is excluded. A phenomenological theory of the generation of “meaningful information” is given in this chapter and in Chapter 5. If we are dealing with genetic sequences, making use of four classes of symbols (referring to the four nucleotides used in nucleic acids), a sequence including n positions has 4^{n} different possibilities. The sequence space is then a point space including 4n points, one for each possible sequence. The distances between any two sequences of this length corresponds to the number of positions occupied by different symbols. A value parameter is introduced which finally determines the population structure. The mutant spectrum appears in the form of a rather dissipated “cloud” that has one or several value maxima, a fact that is due mainly to the presence of “neutral sequences” (i.e. sequences of equal fitness value). The theory confirms formally Darwin’s result. However, the interpretation is completely different from the one generally encountered. Under normal conditions there is no fittest single individual. Rather, fitness is a property of a population, expressed by an eigenvalue of a matrix to which contribution is made by all the individuals present. Since we are dealing with coupled differential equations, the linear case can be expressed by the matrix of rate coefficients. However, according to a mathematical theorem by Perron and Frobenius, only the largest eigenvalue of the matrix is stable. To this we can assign the term “fittest”. The theory uncovers many surprising details. It also unifies the mechanisms of origin and evolutionary adaptation, both referring to different regions in the solutions of the same system of coupled differential equations. Some mathematical details can be found in the Appendices, including contributions from Peter Richter and Peter Schuster.