If homeopathy is the idea that the effect of some solution in water becomes more effective the more it is diluted then at least when it is mainly water, and further diluted that is nonsense. I know something about water: Most important and not commonly known is that the formulae is xH2O where x is a spectrum of integers. I.e. because the two protons have given up their electrons to a large extent to the oxygen atom, it is negative and they are positive charge centers. Also they are both on the same side, 105 degrees in angular separation, so H2O has a permanent electric dipole. Thus it can and does form chains or "polymerize." These chains are constantly breaking and reforming - why x is a distribution, not a fixed integer. The higher the temperature the smaller the average value of x is. The chains become quite long (average x is in the double digits, I think) below 4C. So the jumble of these chains is sort of like a random jumble of increasingly longer spaghetti pieces - the void spaces occupying an increasing fraction of the volume as water cools below 4C - why, unlike not polar liquids it gets lighter before becoming a solid.
Water has no mechanism for "memory" of what substance may have been present before in solution. To the extent that homeopathy is based on the false assumption that water "remembers" it is NONSENSE. But the placebo effect can make it appear to work - same as the placebo effect of sitting on two dimes will work for those who believe that improves their arthritis. Etc.
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Allopathic (conventional western style medicine) usually has demonstrable effects to support its use for treating certain diseases, at least FDA approved medicines; However, there are still serious problems with it. The first being that the diagnostic procedures are not always correct - so you may be treated for a disease you do not have, and generally this will to some extent damage you. Then there is the possibility that there is some delayed side effect - the deformed children (now in the 40s) of thalidomide being the extreme case but surely hundreds of lesser cases exist. (In the courts now is Votix probably production of many deaths.)
I try to stay away from all medicines and even places like clinics where sick people are found. I often state that my body (yours too) is smarter than all the doctors in the world combined. Thus do not take aspirin to reduce mild fevers, antihistamines for my allergies, etc. I have on two or three occasions (once every 30 or so years) taken anti-biotic, but only after allowing my body (immune system) to try to kill the invading organism on its own for several days. While I have great faith in my body's defense that evolution as provided, I do recognize that evolution has been perfecting the attack skills of the bacteria also. Thus sometimes it is necessary to suddenly change the environment on them to one their ancestors never saw. Unfortunately their descendents will soon have seen most of these man-made anti bacterial agents as we feed them to cows etc. prophylactic etc. and very few behave as I do - they get anti-biotics several times each year.
Avurvedic and herbal/ traditional medicines of other regions.
I do not know much about these, but am sure some have real merit. Humans are fantastically good "collective correleators" All societies evolve and compete - Darwinian survival makes the medical wisdom they develop a net benefit although it can contain some aspect that are destructive. Most of these medicines are probably with little effect other than then placebo effect. Fortunately, modern scientists are finally realizing that some of these traditions and agents, which nature developed and man adventuresome ignorant men discovered are probably better than anything yet to come from some bio-chemical or biological drug company. One I do use is Mountain Arnica - it does seem to be every effective in aiding minor injuries heal. I also drink occasionally a tea (Mata Leon) and use a natural sweetener (Now commercially available as "Stevita") both of which have been used by Indians of Brazil for thousands of years. (I consider sugar, something man's insulin system did not evolve to cope with as it is only a few hundred year old, to be a slow acting posion.)
There was an extensive study in England many years ago on the common cold. Many paid volunteers stay hours in a cold damp room each day for week or so (I forget exact details). The scientist concluded that does not cause one to catch a cold. They may be correct, but my money is on the collective unconscious correlative ability of millions of people as reflected in the very name "cold" and the general belief that these conditions do promote the catching of colds. True, many widely held beliefs are wrong. (My favorite example is not the "flat Earth" as few believe that now. I prefer the false belief that most still do hold that the "moon is orbiting the Earth" when in fact it has only a tiny wobble as it orbits the sun that makes it 13 times each year slightly less than 1 AU from the sun and 13 times slightly more than 1AU instead of an exactly elliptically orbit about the sun.)