TOWARDS UNIFYING HOMEOPATHY AND CONVENTIONAL MEDICINE

The periodicity of wave functions

Depicting the Vf, remedy, and remedy torque as wave functions, implies a certain periodicity in their properties and behaviour. Such periodicity can indeed be exhibited by the Vital Force in its expression of symptoms; their strength varying according to periodic modalities, such as the time of day, etc.
Interestingly, there is some experimental evidence that biologically active substances at different serially diluted potencies will have periodic effects on their substrates. For example, Schiff reports alternating effects of different ultra-diluted potencies of anti-immunoglobuline E (aIgE) on the decoloursation of stained basophils, in most cases when the aIgE had been diluted and agitated beyond molecular existence:⁶⁷ some potencies enhance decolourisation while others retard it. Schiff claims this as evidence for the water memory effect.

Accordingly, k₂ values determine the periodicity of the Vf and remedy wave functions. As this constant is also associated with remedy potency (inversely proportional to material dose), it is interesting to investigate the possible effects of very low remedy k₂ values on the periodicity of ?_Rx.

From the previous section, we know that at low k₂ values, the remedy wave function approximates to ?_Rx » cos k₂?S₂. Now, the cosine function can be represented algebraically as the power series:-⁶⁸

cos x = 1 – x²/2! + x⁴/4! – x⁶/6! +….(-1)ⁿx²ⁿ/(2n)!                             3

As x becomes very small, the values of the higher powers of x effectively vanish. Therefore, for small x, equation 3 approximates to :-

cos x » 1 – x²/2!                           4

Similarly, for small values of k₂, the remedy wave function, ?_Rx approximates to:-

?_Rx » 1 – [k₂?S₂]²/2!                 5

Equation 5 is no longer a periodic: it is now a parabolic function (see steep and shallow white curves in figure 4: the steepness is determined by the value of k₂).

Figure 4. Plots of the real part of equation 2 (?_Rx = cos k₂?S₂: k₂ = 1; black curve: k₂ = 0.075; shallow grey curve), and equation 5 (?_Rx » 1 – [k₂?S₂]²/2!: k₂ = 1; steep white curve: k₂ = 0.075; shallow white curve).

Thus, for small values of k₂, the shallow grey (equation 2) and white (equation 5) curves in figure 4 are virtually indistinguishable. Only as k₂ grows does the difference between the grey and white curves become apparent. This theoretical finding may help illustrate essential differences between the homeopathic and the conventional medical approaches to the action of remedies.

The effect of remedy potency

Homeopathic philosophy maintains that a remedy becomes more potent the more it is diluted and succussed.⁶⁹ This means that even at only moderate potencies (greater than 12c and 24x), homeopathic remedies possess little or no molecules of the original material substance, yet a remedy of higher potency should have a more profound effect on the Vf than one of lower potency.

The conventional medical approach to the action of remedies predicts otherwise: the less of the remedy’s material substance is actually present, the weaker its effect in curing the disease (in conventional medicine, the idea of an all-pervading Vital Force is considered moribund: its nearest equivalent is the homeostatic immune system). This could be represented in figure 4 by the grey curve, i.e., equation 5. Its parabolic shape means it crosses the x axis only once, after which it never returns, regardless of the value of k₂. However, its response to a remedy at low k₂ (or potency, in this case in a material dose) approximates to the extended white curve in figure 4. Thus, the form of the remedy function ?_Rx shown in equation 5 could be said to represent the predictions of conventional medicine concerning the effect of highly diluted remedies, i.e., that the weaker the drug dose in material terms, the less effect the drug has on the homeostatic immune system. However, the form of the remedy wave function ?_Rx in equations 1 and 2 represents the predictions of homeopathy, i.e., ultra-highly diluted remedies can still affect the Vital Force.

There is the possibility that just as equation 5 is an approximation to equation 2, so the predictions of conventional medicine are not so much in contradiction to homeopathy but might represent an approximation of much wider ranging implications concerning the effects of remedies at different dilutions, as predicted by homeopathy. If so, it might be possible to construct from basic principles a mathematical metaphor of conventional medicine’s homeostatic immune system that delivers similar predictions as the approximated form of the remedy wave function ?_Rx represented by equation 5. Again, this comes with the proviso that there are as yet no rigorous mathematical proofs or lemmas for the use of such inherently physical ideas in these essentially biomedical/therapeutic contexts.

A mathematical metaphor for the homeostatic immune system

Conventional medicine has no concept of an all-pervading Vital Force. In homeopathy, the goal of treatment is to help the Vital Force to throw off the disease (e.g., as in the Vf gyroscopic metaphor). In contrast, conventional medicine recognises a homeostatic immune system but its drug regimes are less concerned with supporting it and more concerned with alleviating symptoms. In homeopathy, this is believed to be the cause of conventional drug side-effects, as the Vital Force reacts against the drug’s initial suppression of symptoms.⁶¹

This line represents n, the totality of symptoms expressed by Is: those to the right are disease symptoms, while those to the left are remedy ‘side-effects’.

Figure 5. Force diagram metaphor for the homeostatic immune system Is disturbed by disease and remedy.

This situation in conventional medicine is represented simplistically by figure 5. Here, a disease ‘vector’ (Dx) acts on a homeostatic immune system ‘vector’ (Is) by ‘deflecting’ it through angle ?. A drug ‘vestor’ is then prescribed (Rx) to alleviate symptoms, correcting the original angle of deflection, only to produce side-effects, and a deflection in the opposite direction by angle ?. might be simply represented in terms of a mathematical metaphor based on a force diagram (figure 5). The box below gives a simplified mathematical derivation of the action of a homeostatic immune system under these circumstances.

We see a close mathematical correspondence between equations 5 and 9 if ? (in the above box) bears a similar relationship in conventional medicine to the expression of drug side-effects by the homeostatic immune system, as k₂S₂ and k₂?S₂ in homeopathy have to the expression of and changes in secondary symptoms by the Vital Force and the curative remedy respectively. Thus, the mathematical metaphors used to represent the Vf and the homeostatic immune system approximate for very low drug potency (i.e., for values of k₂ << 1 when a remedy/drug exists in material molecular form), suggesting that homeopathy and conventionalmedicine should predict similar outcomes for the effects of remedies/drugs given in material doses. Only when the remedy is becoming ultra-diluted, and according to these metaphors do the predictions of conventional medicine and homeopathy diverge.

Conclusions

The aim of this paper has been to show that a perceived similarity in discourse between homeopathy’s concept of a Vital Force and quantum theory’s notion of a wave function, could be the starting point for a much needed rapprochement between conventional medicine and homeopathy.

As others have pointed out,^{72, 73} however, such correspondences are not yet grounded in rigorous mathematical proofs or lemmas. Particularly, more detailed treatments are needed to flesh out the meaning of wave functions and hypothetical spaces used in therapeutic contexts, so that macro-entanglement of patient, practitioner and remedy can indeed be treated as if it were a generalised quantum system. Such elaboration will hopefully appear in later papers. Meanwhile, further development of a simple mathematical metaphor of the Vital Force as a quantised gyroscope, provides insights into the action of the curative homeopathic remedy over a large potency range.

This metaphor depicts the Vital Force and the curative remedy as periodic wave functions. It turns out that at low potency (i.e., the remedy is at a physical material dose), they approximate in such a way as to lose their periodicity and therefore deliver predictions concerning the effects of highly diluted remedies that are in line with those of conventional medicine, i.e., they should have little or no effect.

In order to expand on this conclusion, another simple metaphor was proposed, in which the conventional medical notion of a homeostatic immune system was treated as a simple force vector, Is, deflected by disease and remedy vectors. Thus, disturbance one way elicits symptoms of disease, while the disturbance the other way elicits symptoms of the remedy, i.e., ‘side-effects’. The mathematical treatment of this simple metaphor generates a solution whose interpretation is conventional medicine’s conclusion concerning the lack of efficacy of highly potentised substances. This, however, is the same conclusion drawn from the Vital Force gyroscopic metaphor when it is approximated.

Parallels could be drawn here with the relationship between Newtonian and Einsteinian mechanics: the latter delivers the former when it is suitably approximated to velocities much smaller than light.⁴⁴ Thus Newton does not contradict Einstein: rather Newtonian mechanics is an approximation of Einsteinian mechanics, applicable at low velocities only. Similarly, it could be that there is no contradiction between conventional medicine and homeopathy: rather conventional medicine may perhaps be better understood as an approximation of homeopathy when remedies are given at low potencies in material doses. Thus, although only a preliminary metaphor based on several admittedly unproven assumptions, more sophisticated mathematical treatments than the ones presented here might in the future provide a platform for the possible unification of conventional medicine with homeopathy. Given the increasing scepticism being directed at homeopathy, it would indeed prove ironic if conventional medicine turned out to be a subset of a much broader paradigm that included homeopathy. “Graecia capta Romam victricem captum subducit” – “Captured Greece leads conquering Rome captive.”⁷⁴ One should always dream….

ACKNOWLEDGEMENTS

The author wishes to express his deep gratitude to Ms Barbara A Drillsma-Milgrom for all her help, encouragement, patience, forbearance and inspiration in the preparation of this manuscript.

†This is part 10 in a series of papers entitled Patient-Practitioner-Remedy (PPR) entanglement.

‡Address: Department of Chemistry, Imperial College London, South Kensington, SW7 2AZ, UK; e-mail: l.milgrom@ic.ac.uk

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FIGURE LEGENDS

Figure 1. Schematic of the Vf gyroscope: a real gyroscope in 3-D space precesses around the z-axis sweeping out gradually increasing ‘orbits’ in the x-y plane. The metaphorical Vf gyroscope precesses in fixed quantised ‘orbits’ as shown and the y and z axes are complex. Symptoms are observed along the real x axis.

Figure 2. View of the Vf gyroscope in figure 1, looking down the imaginary iz axis.

Figure 3. Plots of the Vital Force wave function, ?_Vf = 2Acosk₂S₂ (black curve), the remedial torque, d?_Vf/dS₂ = -2Ak₂sink₂S₂ (white curve), and the combination, ?_Vf + d?_Vf/dS₂ = 2Acosk₂S₂ – 2Ak₂sink₂S₂ (grey curve), where A = 1, and (a), k₂ = 0.5; (b), k₂ = 1; and (c), k₂ = 2. Note how as k₂ increases, so do the frequencies of the wave forms, and the grey curve peak amplitude and position with respect to the black and white curves: at low k₂ the grey curve is like the black curve, while at high k₂ the grey curve is more like the white curve. (reference 64).

Figure 4. Plots of the real part of equation 2 (?_Rx = cos k₂?S₂: k₂ = 1; black curve: k₂ = 0.075; shallow grey curve), and equation 5 (?_Rx » 1 – [k₂?S₂]²/2!: k₂ = 1; steep white curve: k₂ = 0.075; shallow white curve).

Figure 5. Force diagram showing the homeostatic immune system Is disturbed by disease and remedy.

Figure 6. Plots of the real part of equation 2 for k₂ = 1 (?_Rx = cos k₂?S₂; black curve), equations 5 and 9 (k₂?₂ » ?: k₂ = 1; steep white curve: k₂ = 0.005; shallow white curve), and equation 7 (k₂?₂ » ?: k₂ = 1; steep grey curve flattening to 0: k₂ = 0.005; shallow grey curve). Note how compared to equation 2, equation 7 goes to 0