Ancient Indian Medicine

Ancient Indian Medicine Some examples of divinely caused diseases - Rudra: shooting arrows to cause acute pains o “The arrow that Rudra cast upon thee, into (thy) limbs, and into thy heart, this here do we now draw out away from thee. From the hundred vessels which are distributed along thy limbs, from all of these do we exorcise forth the poisons . Adoration be to thee , O Rudra, as thou castesth (thy arrow); adoration to the (arrow) when it has been placed upon (the bow); adoration to it as it is being hurled; adoration to it when it has fallen down!” - Fire demon & evil spirit Takman: “Whether thou art flame, whether thou art heat, or whether from licking chips (of wood) thou hast arisen, Hrudu by name art thou, O god of the fiery , do thou feel for us, and spare us, O Takman! To the cold Takman, and to the deliriously hot, the glowing, do I pay homage . - In ancient Indian medicine (earlier medical thinking) we find this notion that many diseases are divinely caused due to sins or particularly deity being offended and the patient having a remedy to that offense to make amends to that particular deity. - We have another deity causing disease by shooting arrows - We have an example of it being helpful when trying to restore health to your patient to name what is causing the illness, in this case its Rudra - Call the deity by name and ask it to leave o “From all of these do we exorcise forth the poisons .”  We are calling up on this deity and ask that all the poisons and illnesses from the patients to be removed - The next few lines are important with adoration put onto Rudra - The metaphorical arrow that is causing the disease was removed by preya and incantation so we have a lot of reputation - In this medical culture we have this notion of sending illness either directly through a deity or through a demon - We have an example of a demon or an evil spirit causing disease in the form of the fire demon & evil spirit called Takman - “Whether thou art flame, whether thou art heat, or whether from licking chips (of wood) thou hast arisen o Based off this we cannot determine what the name of the demon causing the illness o This is to cover the practitioners bases and make sure that “Takman” is causing the disease o Translation: Just to be on the safe side, whether you do this or whether you do that, please be nice to us and leave us alone - In this medical verdict we know that tackman is a demon or being that is known to cause various kinds of fever

o We see that quite often in medical cultures if certain diseases are very prevalent like fevers or skin conditions and the diseases that have to do with the area people live and where that culture is located and we have deities directly associated with that particular ailment (illness) and they will be the first being called upon for help in curing that disease Slide 2 – Continued - Demon-like version of Takman o “Homage to the deliriously hot, the shaking, exciting, impetuous (Takman)! Homage to the cold, to him that in the past fulfilled desires! May the Takman that returns on the morrow, he that returns on two successive days, the impious one, pass into this frog !” - We have the same thing when dealing with a “Takman” like demon - This is a charm which almost turns into a prayer - Lets look at it as a mix between a charm or an incantation (spell) and a prayer - And again tribute is paid to tackman and tackman needs to be driven out of the patient and transferred into an animal o Taking the disease out of a living thing and passing it on to another living thing - Important to pay homage to the supernatural being because we do not want to piss off a god or a demon that is bad news - Showing obedience and asking the being to remove itself form the body of the patient and passing into a different living thing in this case a frog - Frogs are commonly used in ancient medicine Supernatural healing - Mountain plant kushtha for fever: - Prayer conveys magic power to fight disease o “Thou art born upon the mountain, as the most potent of plants, come hither, O Kushtha, destroyer of the Takman, to drive out from here the Takman ! Thou art born of the gods, thou art Soma’s good friend. Be thou propitious to my in- breathing and my out-breathing, and to the eyes of mine! Superior O Kushtha is thy name; ‘superior’ is the name of thy father. Do thou drive out all disease, and render the Takman devoid of strength! Pain in the head, affliction in the eye, and ailment of the body, all that shall the Kushtha heal - a divinely powerful remedy forsooth!” - Putting a prayer on the magical plant to fight off the disease - Calling directly upon the plant of the things - We are naming the plant which gives the plant more power and naming it the most potent of plants and calling upon the plant to come and destroy the fever (Takman)

Ayurveda - Natural system of medicine: Ayur “life”, veda “science/ knowledge” - Disease: imbalance/ stress in one’s consciousness - Lifestyle interventions & natural therapies to restore balance (body-mind-spirit- environment) - Important concepts: universal interconnectedness, body’s constitution ( prakrit ), life forces ( doshas ) are the primary bases of Ayurveda medicine - Cyles of nature underpin human life & health - Goals: eliminate impurities, reduce symptoms, increase resistance to disease, reduce worry, increase harmony using herbs, plants, oils, common spices Ø Practitioners to balance these elements Ø Usage of herbs, plants and oils and common spices are used extensively - Ayurveda is still practiced today Ayurveda: Theories - 5 basic elements: fire, water, air, earth, ether - 3 humours: bile, phlegm, wind (produced by blood & body using food) - BALANCE! - 3 doshas (forms of energy in the body): pitta (fire), kapha (earth), vata (air/wind) - The humors can cause problems when they are out of balance - The 3 humors correspond with the 3 doshas - Pitta which acts as fire and is related to fire temperament intelligence activity and is associated with the digestive system and seen as the cause of inflammation and heart burn - Kapha acts as earth and water related to growth and salility and calm and is also associated with the torso and the cause of obesity and diabetes - Vata acts like air or wind and is related to imagination and creativity, associated with respiration and circulation and is the cause of constipation/anxiety 8 branches of Ayurveda - 4th c BCE (epic Mahābhārata) - These 8 branches were formalized as: Ø Internal Medicine Ø Surgery Ø Ears, eyes, nose, throat issues Ø Pediatrics Ø Toxicology Ø Purification of the reproductive organs Ø Health and longevity Ø Psychiatry & spiritual healing - The existence of rational way of thinking about medical views doesn’t mean that supernatural views stop existing

- Ancient India has many different beliefs and have coexisted with each other - Other people still believe in the gods and held onto the belief of supernatural causes of diseases Samhita on anatomical knowledge of Ayurveda practitioners - Practitioners of Ayurveda: 360 human bones - Samhita: 300 bones (books of surgical science) o 120 in the extremities o 117 in pelvic area, sides, back, abdomen, breast o 63 in neck etc. o Samhita tells us how these totals are empirically verified mainly by looking at a dead body Superiority of Salya-Tantrum - This is different from what we have seen with Greek medicine which had a strong version to human dissection - Greeks had a big taboo on filing a dead body - With Indian medicine knowing the human anatomy is important - Anyone who wants to have the knowledge of the human anatomy needs to have first hand experience by preparing a dead body and carefully observing what they can see - Studying butchered animals and comparing it to human anatomy does not work out that well - Greek medicine also deals a lot with different metaphors - Anatomy is of the upmost importance for good and proper treatment of patients and doesn’t seem to be a huge taboo on dissecting human beings

o supernatural and rational can coexist - there seems to be evidence for scholarly discussion In ancient Indian medicine based on the text of sushruta Let f(n) and g(n) be functions with positive values for every n ≥ 0. Assume that f(n) is (g(n)), so there are constants c ’ > 0 and n ’ 0 ≥ 1 such that f(n) < c ’ g(n) for all n ≥ n ’ 0 .Which of the following is a correct proof that f(n) + g(n) is O(g(n))? A) f(n) + g(n) <= c x g(n) for all n ≥ n 0 , for c = 1 and n 0 = 1 B) f(n) + g(n) ≥ c x g(n) for all n ≥ no, for c = 1 and n 0 = 1 C) f(n) + g(n) <= c x g(n) for all n ≥ n 0 , for c = c ’ + 1 and n 0 = n ’ 0 D) f(n) + g(n) <= c x g(n) for all n ≥ n 0 , for c = c ’ and n 0 = n ’ 0 E) None of the above is a correct proof because we do not know whether g(n) is O(f(n)) Consider a hash table of size M that stores kM keys, where k is not a constant. Assume that the hash function has O(1) time complexity and it maps keys uniformly across the entire table, and that separate chaining is used to resolve collisions (hence, every linked list of the hash table has the same length). What is the tightest order of the worst case time complexity of the remove (key) algorithm invoked on this hash table (Hint. What is the worst case?) A) O(1) time B) O(n) time C) O(k) time D) O(M/k) time E) O(kM) time Algorithm traverse(r) Input: Root r of a binary tree. if r is a leaf then return the value stored at r else { a  traverse(r.leftChild) b  traverse(r.rightChild) if a < b then return a + b else return a – b } According to the definition of order or "big Oh', which of the following is a correct proof for 2n 2 + 5n is O(n 3 )? A)2n 2 + 5n < n 3 for all n > 1. B)2n 2 + 5n ≥ n 3 for all n ≥ 2. C)2n 2 + 5n ≤ cn 3 for all n ≥ n 0 , where c = n and n 0 = 1. D)2n 2 + 5n ≤ 2n 3 for all n ≥ 3. E) None of the above is a correct proof, because 2n 2 + 5n is not O(n).

Consider the following algorithm that given the root r of a tree, it computes the number of nodes that store the value k. The value stored in a node r is denoted as r. value. Algorithm find(r, k) In: Root r of a tree and value k Out: Number of nodes in the tree with root r storing the value k if r is a leaf then { if r.value = k then return 1 else return 0 } else { count + 0 for each child c of r do count <- count + find(c, k) return count } Which of the following statements is correct? A)The algorithm is correct B)The algorithm is incorrect C)The algorithm does not always terminate D)The algorithm is correct but only if the tree is binary E) The algorithm is correct but only if the tree is proper binary Consider the following algorithm or the search problem. Algorithm find(k, A, ini, end) In: Value k, array A, first index ini of A, and last index end of A Out: Position of k in A, or - 1 if k is not in A if ini ≥ end then return -1 else { m  [ ini + end 2 ] if k = A[m] then return m else if k < A[m] then return find(k, A,ini,m - 1) else return find(k, A, m + 1,end) Which of the following statements is correct? A)The algorithm is correct B)The algorithm is incorrect because it might not terminate C)The algorithm is incorrect because the value of m should be [ ini + end 2 ] D)The algorithm is incorrect because it always terminates but sometimes it returns -1 even E)if k is in A The algorithm is incorrect because it always terminates but sometimes it returns an index i of A when k is not in A

Algorithm count (v, T, M): In: Value v, non-full hash table T of size M with hash function h(k) Out: Number of times that value v is stored in the hash table 1. Initialize count to 0 2. Let i = h(v) 3. Let start = i // to keep track of where we started to avoid infinite loops 4. While T[i] is not NULL and count < M: 4.1. If T[i] == v: 4.1.1. Increment count by 1 4.2. Increment i by 1 4.3. If i == M: // wrap around if we reach the end of the table 4.3.1. Set i to 0 4.4. If i == start: // break the loop if we've checked all the positions 4.4.1. Break 5. Return count Consider a hash table of size 7 with hash function h(k) = k mod 7. Draw the contents of the table after inserting, in the given order, the following values into the table: 62, 6, 17, 16, and 7 when double hashing with secondary hash function h'(k) = 5 - (k mod 5) is used to resolve collisions. Here is some information that might help you: 62 mod 7 = 6, 17 mod 7 = 3, 16 mod 7 = 2, 62 mod 5 = 2, 17 mod 5 = 2, 16 mod 5 = 1, and 7 mod 5 = 2. Consider the following algorithm, where r is the root of a proper binary tree with n nodes in which every node u stores a value u.value. A is an array storing m values. Algorithm travel(r, A, n, m) In: root r of a proper binary tree with n nodes, array A storing m values if r is a leaf then { if A[0] < r. value then A [0]  r.value } else { travel(r. leftChild, A, n, m) for i  0 to m - 1 do if A[i] > r. value then A[i]  r.value travel(r.rightChild, A, n, m) A[0] + A[0] + 1 } [4 marks] Ignoring recursive calls, how many operations does the algorithm perform when invoked on a leaf and when invoked on an internal node? Explain. [2 marks] How many calls does the algorithm perform (including the initial call)? Explain. (8 marks] What is the total number of operations that the algorithm performs? What is the order of the time complexity? Explain.

Draw the execution stack up to the moment when the statement marked with asterisks (*) is executed (so stop right after the statement r  r + 1 has been executed. but before the return r statement is executed). The addresses where recursive calls are made are marked with (A) and (B). The first activation record has been drawn for you; the return address OS means that algorithm main is invoked from the operating system. Do not draw the activation records that have been popped out of the execution stack. Consider the following binary search tree. Remove the key 13 from the tree and draw the resulting tree. Then remove the key 2 from this new tree and show the final tree (so in the final tree both keys, 13 and 2, have been removed). You must use the algorithms described in class for removing data from a binary search tree. 6 11 17 9 21 8 13 3 5 2