Hartley (unit)
Units of information |
Information-theoretic |
---|
Data storage |
Quantum information |
The hartley (symbol Hart), also called a ban, or a dit (short for "decimal digit"),
If base 2 logarithms and powers of 2 are used instead, then the unit of information is the shannon or bit, which is the information content of an event if the probability of that event occurring is 1⁄2. Natural logarithms and powers of e define the nat.
One ban corresponds to ln(10)
Though there is no associated
History
The term hartley is named after Ralph Hartley, who suggested in 1928 to measure information using a logarithmic base equal to the number of distinguishable states in its representation, which would be the base 10 for a decimal digit.[5][6]
The ban and the deciban were invented by
Good argued that the sequential summation of decibans to build up a measure of the weight of evidence in favour of a hypothesis, is essentially Bayesian inference.[7] Donald A. Gillies, however, argued the ban is, in effect, the same as Karl Popper's measure of the severity of a test.[8]
Usage as a unit of odds
The deciban is a particularly useful unit for
Odds corresponding to integer decibans can often be well-approximated by simple integer ratios; these are collated below. Value to two decimal places, simple approximation (to within about 5%), with more accurate approximation (to within 1%) if simple one is inaccurate:
decibans | exact value |
approx. value |
approx. ratio |
accurate ratio |
probability |
---|---|---|---|---|---|
0 | 100/10 | 1 | 1:1 | 50% | |
1 | 101/10 | 1.26 | 5:4 | 56% | |
2 | 102/10 | 1.58 | 3:2 | 8:5 | 61% |
3 | 103/10 | 2.00 | 2:1 | 67% | |
4 | 104/10 | 2.51 | 5:2 | 71.5% | |
5 | 105/10 | 3.16 | 3:1 | 19:6, 16:5 | 76% |
6 | 106/10 | 3.98 | 4:1 | 80% | |
7 | 107/10 | 5.01 | 5:1 | 83% | |
8 | 108/10 | 6.31 | 6:1 | 19:3, 25:4 | 86% |
9 | 109/10 | 7.94 | 8:1 | 89% | |
10 | 1010/10 | 10 | 10:1 | 91% |
See also
Notes
- ^ This value, approximately 10⁄3, but slightly less, can be understood simply because : 3 decimal digits are slightly less information than 10 binary digits, so 1 decimal digit is slightly less than 10⁄3 binary digits.
References
- exists as well.)
- ISBN 978-3-11011700-4. (320 pages)
- LCCN 79-90567.
- ^ "IEC 80000-13:2008". International Organization for Standardization (ISO). Retrieved 2013-07-21.
- Bell System Technical Journal. VII (3): 535–563. Retrieved 2008-03-27.
- ISBN 0-486-68210-2.
- ^ MR 0548210.
- MR 0055678.
- Good, Irving John (1985). "Weight of Evidence: A Brief Survey"(PDF). Bayesian Statistics. 2: 253. Retrieved 2012-12-13.