Homeopathic dilutions
Homeopathy
involves a process known by practitioners as "dynamisation" or
"potentisation" whereby a substance is diluted
with alcohol or distilled water and then vigorously
shaken in a process called "succussion". Insoluble solids, such as quartz and oyster shell, are diluted by grinding them with lactose (trituration).
The founder of homeopathy, Samuel Hahnemann (1755 — 1843) believed that the process of succussion activated the "vital energy" of the diluted substance, and that successive dilutions increased the "potency" of the remedy.
The idea is considered a pseudoscience, because at common dilutions, no atoms of the original material are likely to remain.
It is illogical that a process of dilution would arrive at a higher potency.
There is not enough water on earth to produce the highest homeopathic dilutions from one molecule.
Potency scales
Several potency scales are in use in homeopathy. Hahnemann created the centesimal or "C scale", diluting a substance by a factor of 100 at each stage. The centesimal scale was favored by Hahnemann for most of his life.
A 2C dilution requires a substance to be diluted to one part in one hundred, and then some of that diluted solution diluted by a further factor of one hundred. This works out to one part of the original substance in 10,000 parts of the solution.
A 6C dilution repeats this process six times, ending up with the original material diluted by a factor of 100−6=10−12.
Higher dilutions follow the same pattern.
In homeopathy, a solution that is more dilute is described as having a higher potency, and more dilute substances are considered by homeopaths to be stronger and deeper-acting remedies.
The end product is often so diluted that it is indistinguishable from the dilutant (pure water, sugar or alcohol).
Hahnemann advocated 30C dilutions for most purposes (that is, dilution by a factor of 1060). In Hahnemann's time it was reasonable to assume that remedies could be diluted indefinitely, as the concept of the atom or molecule as the smallest possible unit of a chemical substance was just beginning to be recognized.
We now know that the greatest dilution that is reasonably likely to contain one molecule of the original substance is 12C, if starting from 1 mole of original substance.
This bottle contains arnica montana (wolf's bane) D6, i.e. the
nominal dilution is one part in a million (106).
Some
homeopaths developed a decimal scale (D or X), diluting the substance to ten
times its original volume each stage. The D or X scale dilution is therefore half that of the same value of the C scale; for example, "12X" is the same level of dilution as "6C".
Hahnemann never used this scale but it was very popular throughout the 19th century and still is in Europe. This potency scale appears to have been introduced in the 1830s by the American homeopath, Constantine Hering. In the last ten years of his life, Hahnemann also developed a quintamillesimal (Q) or LM scale diluting the drug 1 part in 50,000 parts of diluent. A given dilution on the Q scale is roughly 2.35 times its designation on the C scale. For example a remedy described as "20Q" has about the same concentration as a "47C" remedy.
Potencies of 1000c and above are usually labelled with Roman numeral M and with the centesimal 'c' indicator implied (since all such high potencies are centesimal dilutions): 1M = 1000c; 10M = 10,000c; CM = 100,000c; LM (which would indicate 50,000c) is typically not used due to confusion with the LM potency scale.
The following table is a synopsis comparing the X and C dilution scales and equating them by equivalent dilution. However, the homeopathic understanding of its principles is not explained by dilution but by "potentisation", hence one can not assume that the different potencies can be equated based on equivalence of dilution factors.
|
X Scale
|
C Scale
|
Ratio
|
Note
|
|
1X
|
—
|
1:10
|
described as low potency
|
|
2X
|
1C
|
1:100
|
called higher potency than
1X by homeopaths
|
|
6X
|
3C
|
10−6
|
|
|
8X
|
4C
|
10−8
|
|
|
12X
|
6C
|
10−12
|
|
|
24X
|
12C
|
10−24
|
Has a 60% probability of containing one molecule of
original material if one mole of the
original substance was used.
|
|
26X
|
13C
|
10−26
|
|
|
60X
|
30C
|
10−60
|
Dilution advocated by Hahnemann
for most purposes: on average, this would require giving two billion doses
per second to six billion people for 4 billion years to deliver a single
molecule of the original material to any patient.
|
|
400X
|
200C
|
10−400
|
|
|
Note: the "X scale" is
also called "D scale". 1X = 1D, 2X = 2D, etc.
|
|||
The problem of homeopathic dilution
Serial
dilution of a solution results, after each dilution step, in fewer
molecules of the original substance per litre of solution. Eventually, a
solution will be diluted beyond any likelihood of finding a single molecule of
the original substance in a litre of the total dilution product.
The molar limit
If one begins with a solution of 1 mol/L of a
substance, the 10-fold dilution required to reduce the number of molecules to
less than one per litre is 1 part in 1×1024 (24X or 12C) since:
6.02×1023/1×1024
= 0.6 molecules per litre
Homeopathic dilutions beyond this limit (equivalent
to approximately 12C) are unlikely to contain a single molecule of the original
substance and lower dilutions contain no detectable amount. ISO 3696 (Water for
analytical laboratory use) specifies a purity of ten parts per billion, or
10×10−9 - this water cannot be kept in glass or plastic containers
as they leach impurities into the water, and glassware must be washed with hydrofluoric
acid before use. Ten parts per billion is equivalent to a homeopathic
dilution of 4C.
Analogies
Critics and advocates of homeopathy
alike commonly attempt to illustrate the dilutions involved in homeopathy with
analogies. The high dilutions characteristically used are often considered to
be the most controversial and implausible aspect of homeopathy.
1 bottle of poison in Lake Geneva
Hahnemann is reported to
have joked that a suitable procedure to deal with an epidemic would be to empty
a bottle of poison into Lake Geneva, if it could be shaken 60 times.
1 Pinch of salt in the
Atlantic Ocean
One example given is that 12C solution
is equivalent to a "pinch of salt in both the North and South Atlantic
Oceans", which is approximately correct.
1/3 of a drop in all the
waters of the Earth
One third of a drop
of some original substance diluted into all the water on earth would produce a
remedy with a concentration of about 13C.[13][14]
Duck liver 200C in the
entire observable Universe
A popular homeopathic treatment for the
flu is a
200C dilution of duck liver, marketed under the name Oscillococcinum.
As there are only about 1080 atoms in the entire observable universe, a dilution of one molecule
in the observable universe would be about 40C. Oscillococcinum would thus
require 10320 more universes to simply have one molecule in the
final substance.
Swimming pool
Another illustration of dilutions used
in common homeopathic remedies involves comparing a homeopathic dilution to
dissolving the therapeutic substance in a swimming pool.
One example, inspired by a problem
found in a set of popular algebra textbooks, states that there are on the order
of 1032 molecules of water in an Olympic-size swimming pool and
if such a pool were filled with a 15C homeopathic remedy, to have a 63% chance
of consuming at least one molecule of the original substance, one would need to
swallow 1% of the volume of such a pool, or roughly 25 metric tons of water.
30C: 1 ml in 1,191,016 cubic
light years
Yet another illustration: 1 ml of
a solution which has gone through a 30C dilution is mathematically equivalent
to 1 ml diluted into 1054 m3 - a cube of water
measuring 1,000,000,000,000,000,000 (1018) metres per side,
which is about 106 light years. When spherical, then it would be a ball of
131.1 light
years in diameter. Thus, homeopathic remedies of standard potencies
contain, almost certainly, only water (or alcohol, as well as sugar and other
nontherapeutic ingredients).
Proposed explanations
Homeopaths maintain that this water
retains some "essential property" of the original material, because
the preparation has been shaken after each dilution. Hahnemann believed that
the dynamisation or shaking of the solution caused a "spirit-like"
healing force to be released from within the substance. Even though the
homeopathic remedies are often extremely diluted, homeopaths maintain that a
healing force is retained by these homeopathic preparations.
Dilution debate
Not all homeopaths advocate extremely
high dilutions. Many of the early homeopaths were originally doctors and
generally used lower dilutions such as "3X" or "6X", rarely
going beyond "12X". The split between lower and higher dilutions
followed ideological lines. Those favoring low dilutions stressed pathology and
a strong link to conventional medicine, while those favoring high dilutions
emphasised vital force, miasms and a spiritual interpretation of disease. Some products with
both low and high dilutions continue to be sold, but like their counterparts,
they have not been conclusively demonstrated to have any effect beyond the
placebo effect.
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