The dictionaries and files can be used together in various ways but the most common use of a dictionary is to count the occurrence of words in a file with some written text. For this tutorial, we created a file "Physics.txt" by copying the entire text on the Wikipedia page "https://en.wikipedia.org/wiki/Physics".
Example 1 Write the program that will ask a user to type the file name and then count the occurrence of each word in the file and save it in the dictionary as a key-value pair. In this example, the key is the word and the value is the number of times the key (word) appears in the text.
Solution: The first step is to write the code that will ask a user to type the file name that will be opened. This will be done using the input function and the string typed by the user will be assigned to the variable name FILE_NAME.
The definition of the FILE_NAME variable will be placed under the while True: command.
Example 1 Write the program that will ask a user to type the file name and then count the occurrence of each word in the file and save it in the dictionary as a key-value pair. In this example, the key is the word and the value is the number of times the key (word) appears in the text.
Solution: The first step is to write the code that will ask a user to type the file name that will be opened. This will be done using the input function and the string typed by the user will be assigned to the variable name FILE_NAME.
FILE_NAME = input("Enter file name:> ")
The next step is to try opening the file name provided by the user. The best approach would be to use while loop with try and except. The document with the name entered by the user will try to be opened under the try command. In case the document is opened the break command will stop the while loop. In case the document with the name provided by the user does not exist the except command will be executed i.e. the output will be "File does not exist. Enter another one." and the while loop will be executed again.The definition of the FILE_NAME variable will be placed under the while True: command.
while True:Now that file is successfully opened we have to create a procedure to count the words in the file. First, we will define an empty dictionary and assign it to a variable named COUNT_WORDS. Then we will create for loop which will "read" the file line by line and convert each line into a list of words i.e. break line into words in list form using split() function. Then the second for loop will be created that will traverse over a list of words and create key-value pair values in dictionary. However, we have to create if-else statement to update or create key-value pair. If the key-value pair does not exist than create key-value pair with value set to 1 since it is first occurence of that word in text. If the key-value pair does already exist than just increase value of key-value pair by 1.
FILE_NAME = input("Enter file name:> ")
try:
FILE_OPEN = open(FILE_NAME, encoding='utf-8')
break
except:
print("File does not exits. Enter another one.")
continue
COUNT_WORDS = {}
for line in FILE_OPEN:
words = line.split()
for word in words:
if word not in COUNT_WORDS:
COUNT_WORDS[word] = 1
else:
COUNT_WORDS[word] += 1
print("COUNT_WORDS = {}".format(COUNT_WORDS))
The entire code is given below.
while True:Output:
FILE_NAME = input("Enter file name:> ")
try:
FILE_OPEN = open(FILE_NAME, encoding='utf-8')
break
except:
print("File does not exits. Enter another one.")
continue
COUNT_WORDS = {}
for line in FILE_OPEN:
words = line.split()
for word in words:
if word not in COUNT_WORDS:
COUNT_WORDS[word] = 1
else:
COUNT_WORDS[word] += 1
print("COUNT_WORDS = {}".format(COUNT_WORDS))
Enter file name:> Physics.txt
COUNT_WORDS = {'Hide': 1, 'WLE': 1, 'Austria': 1, 'Logo': 1, '(no': 1, 'text).svgWiki': 1, 'Loves': 1, 'Earth': 3, 'photo': 1, 'contest': 1, 'during': 7, 'June': 10, '2022:': 1, 'Upload': 2, 'photos': 1, 'of': 461, 'natural': 10, 'heritage': 1, 'sites': 1, 'in': 170, 'Croatia': 1, 'to': 120, 'help': 2, 'Wikipedia': 3, 'and': 324, 'promote': 1, 'nature!': 1, 'Page': 2, 'semi-protected': 1, 'Physics': 45, 'From': 6, 'Wikipedia,': 1, 'the': 498, 'free': 3, 'encyclopedia': 1, 'Jump': 1, 'navigationJump': 1, 'search': 2, 'For': 14, 'other': 21, 'uses,': 1, 'see': 6, '(disambiguation).': 1, 'Not': 2, 'be': 30, 'confused': 1, 'with': 66, 'Physis.': 1, 'Various': 1, 'examples': 3, 'physical': 13, 'phenomena': 12, 'Part': 1, 'a': 117, 'series': 1, 'on': 79, 'Stylised': 1, 'atom': 3, 'three': 4, 'Bohr': 1, 'model': 8, 'orbits': 1, 'stylised': 1, 'nucleus.png': 1, 'The': 70, 'fundamental': 14, 'science': 14, 'IndexOutlineGlossary': 1, 'History': 12, '(timeline)': 1, 'Branches': 4, 'Research': 14, 'icon': 2, 'portal': 5, 'Category': 1, 'vte': 5, 'is': 102, 'that': 65, 'studies': 4, 'matter,[a]': 1, 'its': 18, 'constituents,': 1, 'motion': 14, 'behavior': 2, 'through': 4, 'space': 5, 'time,': 7, 'related': 6, 'entities': 1, 'energy': 12, 'force.[2]': 1, 'one': 19, 'most': 14, 'scientific': 9, 'disciplines,': 1, 'main': 2, 'goal': 1, 'being': 3, 'understand': 6, 'how': 7, 'universe': 7, 'behaves.[b][3][4][5]': 1, 'A': 13, 'scientist': 1, 'who': 12, 'specializes': 1, 'field': 17, 'physics': 132, 'called': 10, 'physicist.': 1, 'oldest': 2, 'academic': 2, 'disciplines': 5, 'and,': 2, 'inclusion': 1, 'astronomy,': 3, 'perhaps': 1, 'oldest.[6]': 1, 'Over': 1, 'much': 10, 'past': 1, 'two': 11, 'millennia,': 1, 'physics,': 43, 'chemistry,': 8, 'biology,': 1, 'certain': 7, 'branches': 5, 'mathematics': 11, 'were': 14, 'part': 5, 'philosophy,': 1, 'but': 19, 'Scientific': 5, 'Revolution': 2, '17th': 4, 'century': 5, 'these': 12, 'sciences': 3, 'emerged': 1, 'as': 60, 'unique': 1, 'research': 17, 'endeavors': 1, 'their': 16, 'own': 2, 'right.[c]': 1, 'intersects': 1, 'many': 13, 'interdisciplinary': 2, 'areas': 6, 'research,': 4, 'such': 24, 'biophysics': 1, 'quantum': 19, 'boundaries': 1, 'are': 54, 'not': 22, 'rigidly': 1, 'defined.': 1, 'New': 6, 'ideas': 6, 'often': 9, 'explain': 4, 'mechanisms': 2, 'studied': 4, 'by': 54, 'sciences[3]': 1, 'suggest': 1, 'new': 18, 'avenues': 1, 'philosophy.': 2, 'Advances': 1, 'enable': 1, 'advances': 4, 'technologies.': 1, 'example,': 11, 'understanding': 6, 'electromagnetism,': 3, 'solid-state': 3, 'nuclear': 11, 'led': 5, 'directly': 1, 'development': 10, 'products': 1, 'have': 17, 'dramatically': 1, 'transformed': 1, 'modern-day': 1, 'society,': 1, 'television,': 1, 'computers,': 2, 'domestic': 1, 'appliances,': 1, 'weapons;[3]': 1, 'thermodynamics': 3, 'industrialization;': 1, 'mechanics': 20, 'inspired': 1, 'calculus.': 1, 'Contents': 2, '1': 13, '1.1': 1, 'Ancient': 7, 'astronomy': 10, '1.2': 1, 'Natural': 7, 'philosophy': 8, '1.3': 1, 'Medieval': 5, 'European': 6, 'Islamic': 5, '1.4': 1, 'Classical': 12, '1.5': 1, 'Modern': 14, '2': 5, 'Philosophy': 9, '3': 2, 'Core': 2, 'theories': 17, '3.1': 1, '3.2': 1, '3.2.1': 1, 'Fundamental': 4, 'concepts': 5, 'modern': 13, '3.3': 1, 'Difference': 2, '4': 6, 'Relation': 3, 'fields': 14, '4.1': 1, 'Prerequisites': 2, '4.2': 1, 'Application': 2, 'influence': 4, '5': 3, '5.1': 1, 'method': 4, '5.2': 1, 'Theory': 9, 'experiment': 6, '5.3': 1, 'Scope': 2, 'aims': 6, '5.4': 1, '5.4.1': 1, 'Nuclear': 8, 'particle': 18, '5.4.2': 1, 'Atomic,': 5, 'molecular,': 6, 'optical': 8, '5.4.3': 1, 'Condensed': 12, 'matter': 27, '5.4.4': 1, 'Astrophysics': 5, '5.5': 1, 'Current': 5, '6': 1, 'See': 6, 'also': 23, '7': 5, 'Notes': 2, '8': 2, 'References': 2, '9': 2, 'Sources': 2, '10': 6, 'External': 2, 'links': 4, 'Main': 16, 'article:': 11, 'word': 3, '"physics"': 1, 'comes': 2, 'from': 69, 'Greek:': 1, 'φυσική': 1, '(ἐπιστήμη),': 1, 'romanized:': 1, 'physikḗ': 1, '(epistḗmē),': 1, 'meaning': 1, '"knowledge': 1, 'nature".[8][9][10]': 1, 'Egyptian': 3, 'evident': 1, 'monuments': 2, 'like': 9, 'ceiling': 1, "Senemut's": 1, 'tomb': 1, 'Eighteenth': 1, 'Dynasty': 1, 'Egypt.': 1, 'Astronomy': 2, 'sciences.': 4, 'Early': 3, 'civilizations': 1, 'dating': 2, 'back': 2, 'before': 5, '3000': 1, 'BCE,': 1, 'Sumerians,': 1, 'ancient': 6, 'Egyptians,': 1, 'Indus': 1, 'Valley': 1, 'Civilisation,': 1, 'had': 10, 'predictive': 1, 'knowledge': 6, 'basic': 8, 'awareness': 1, 'motions': 3, 'Sun,': 1, 'Moon,': 1, 'stars.': 1, 'stars': 3, 'planets,': 1, 'believed': 1, 'represent': 1, 'gods,': 1, 'worshipped.': 1, 'While': 2, 'explanations': 3, 'for': 60, 'observed': 4, 'positions': 2, 'unscientific': 1, 'lacking': 1, 'evidence,': 1, 'early': 9, 'observations': 5, 'laid': 1, 'foundation': 2, 'later': 5, 'found': 6, 'traverse': 1, 'great': 2, 'circles': 1, 'across': 2, 'sky,[6]': 1, 'which': 33, 'however': 1, 'did': 1, 'planets.': 1, 'According': 1, 'Asger': 1, 'Aaboe,': 2, 'origins': 2, 'Western': 4, 'can': 10, 'Mesopotamia,': 1, 'all': 13, 'efforts': 2, 'exact': 2, 'descended': 1, 'late': 2, 'Babylonian': 1, 'astronomy.[11]': 1, 'astronomers': 2, 'left': 1, 'showing': 1, 'constellations': 2, 'celestial': 3, 'bodies,[12]': 1, 'while': 9, 'Greek': 6, 'poet': 1, 'Homer': 1, 'wrote': 2, 'various': 4, 'objects': 6, 'his': 12, 'Iliad': 1, 'Odyssey;': 1, 'provided': 7, 'names,': 1, 'still': 3, 'used': 13, 'today,': 3, 'visible': 3, 'Northern': 1, 'Hemisphere.[13]': 1, 'has': 16, 'Greece': 1, 'Archaic': 1, 'period': 2, '(650': 1, 'BCE': 1, '–': 20, '480': 1, 'BCE),': 1, 'when': 11, 'pre-Socratic': 1, 'philosophers': 2, 'Thales': 2, 'rejected': 1, 'non-naturalistic': 1, 'proclaimed': 1, 'every': 1, 'event': 2, 'cause.[14]': 1, 'They': 2, 'proposed': 3, 'verified': 1, 'reason': 2, 'observation,': 2, 'hypotheses': 1, 'proved': 1, 'successful': 1, 'experiment;[15]': 1, 'atomism': 1, 'was': 35, 'correct': 1, 'approximately': 1, '2000': 1, 'years': 3, 'after': 2, 'it': 15, 'Leucippus': 1, 'pupil': 1, 'Democritus.[16]': 1, 'articles:': 4, 'Middle': 1, 'Ages': 1, 'medieval': 2, 'world': 9, 'Roman': 2, 'Empire': 2, 'fell': 1, 'fifth': 1, 'century,': 6, 'this': 18, 'resulted': 2, 'decline': 1, 'intellectual': 1, 'pursuits': 1, 'western': 1, 'Europe.': 2, 'By': 5, 'contrast,': 1, 'Eastern': 1, '(also': 3, 'known': 10, 'Byzantine': 2, 'Empire)': 1, 'resisted': 1, 'attacks': 1, 'barbarians,': 1, 'continued': 1, 'advance': 2, 'learning,': 1, 'including': 7, 'physics.[17]': 1, 'In': 17, 'sixth': 1, 'Isidore': 1, 'Miletus': 1, 'created': 3, 'an': 29, 'important': 10, 'compilation': 1, "Archimedes'": 2, 'works': 5, 'copied': 1, 'Archimedes': 1, 'Palimpsest.': 1, 'Ibn': 10, 'Al-Haytham': 1, '(Alhazen)': 1, 'drawing': 1, 'al-Haytham': 2, '(c.': 1, '965–c.': 1, '1040),': 1, 'Book': 8, 'Optics': 5, 'I,': 2, '[6.85],': 2, '[6.86].': 1, 'II,': 3, '[3.80]': 1, 'describes': 2, 'camera': 4, 'obscura': 2, 'experiments.[18]': 1, 'sixth-century': 1, 'Europe': 1, 'John': 4, 'Philoponus,': 2, 'scholar,': 1, 'questioned': 1, "Aristotle's": 5, 'teaching': 1, 'noted': 3, 'flaws.': 1, 'He': 2, 'introduced': 2, 'theory': 23, 'impetus.': 2, 'scrutinized': 1, 'until': 3, 'Philoponus': 4, 'appeared;': 1, 'unlike': 1, 'Aristotle,': 1, 'based': 2, 'verbal': 3, 'argument,': 1, 'relied': 1, 'observation.': 1, 'On': 2, 'wrote:': 1, 'But': 4, 'completely': 1, 'erroneous,': 1, 'our': 4, 'view': 4, 'may': 7, 'corroborated': 1, 'actual': 2, 'observation': 4, 'more': 8, 'effectively': 1, 'than': 7, 'any': 3, 'sort': 1, 'argument.': 1, 'if': 5, 'you': 4, 'let': 2, 'fall': 1, 'same': 5, 'height': 3, 'weights': 2, 'times': 4, 'heavy': 1, 'other,': 4, 'will': 6, 'ratio': 2, 'required': 1, 'does': 1, 'depend': 2, 'weights,': 1, 'difference': 3, 'time': 5, 'very': 12, 'small': 4, 'one.': 1, 'And': 3, 'so,': 2, 'considerable,': 1, 'is,': 4, 'us': 2, 'say,': 2, 'double': 1, 'there': 3, 'no': 5, 'difference,': 2, 'or': 21, 'else': 1, 'imperceptible': 1, 'though': 1, 'weight': 1, 'means': 3, 'negligible,': 1, 'body': 2, 'weighing': 4, 'twice': 1, 'other[19]': 1, "Philoponus'": 1, 'criticism': 1, 'Aristotelian': 3, 'principles': 1, 'served': 1, 'inspiration': 2, 'Galileo': 5, 'Galilei': 2, 'ten': 2, 'centuries': 2, 'later,[20]': 1, 'Revolution.': 1, 'cited': 1, 'substantially': 1, 'arguing': 1, 'flawed.[21][22]': 1, '1300s': 1, 'Jean': 1, 'Buridan,': 1, 'teacher': 1, 'faculty': 1, 'arts': 1, 'at': 24, 'University': 17, 'Paris,': 1, 'developed': 5, 'concept': 1, 'It': 4, 'step': 1, 'toward': 2, 'inertia': 1, 'momentum.[23]': 1, 'scholarship': 1, 'inherited': 1, 'Greeks': 2, 'Golden': 1, 'Age': 1, 'further,': 1, 'especially': 2, 'placing': 1, 'emphasis': 1, 'priori': 2, 'reasoning,': 1, 'developing': 3, 'forms': 3, 'method.': 1, 'way': 5, 'pinhole': 2, 'notable': 2, 'innovations': 1, 'optics': 3, 'vision,': 2, 'came': 4, 'scientists': 1, 'Sahl,': 1, 'Al-Kindi,': 1, 'al-Haytham,': 2, 'Al-Farisi': 1, 'Avicenna.': 1, 'work': 14, 'Kitāb': 2, 'al-Manāẓir),': 1, 'written': 4, 'he': 11, 'conclusively': 1, 'disproved': 1, 'idea': 1, 'about': 8, 'up': 4, 'theory.': 2, 'book,': 2, 'presented': 2, 'study': 19, 'phenomenon': 2, '(his': 1, 'thousand-year-old': 1, 'version': 2, 'camera)': 1, 'delved': 1, 'further': 2, 'into': 6, 'eye': 2, 'itself': 1, 'works.': 2, 'Using': 1, 'dissections': 1, 'previous': 1, 'scholars,': 1, 'able': 3, 'begin': 1, 'light': 7, 'enters': 1, 'eye.': 1, 'asserted': 1, 'ray': 1, 'focused,': 1, 'explanation': 2, 'projected': 1, 'wait': 1, '1604.': 1, 'His': 2, 'Treatise': 1, 'Light': 1, 'explained': 1, 'obscura,': 1, 'hundreds': 1, 'photography.[24]': 1, 'seven-volume': 1, '(Kitab': 1, 'al-Manathir)': 1, 'hugely': 1, 'influenced': 3, 'thinking': 1, 'visual': 1, 'perception': 1, 'nature': 9, 'perspective': 1, 'art,': 1, 'both': 7, 'East': 1, 'West,': 1, '600': 1, 'years.': 1, 'Many': 3, 'scholars': 2, 'fellow': 1, 'polymaths,': 1, 'Robert': 1, 'Grosseteste': 1, 'Leonardo': 1, 'da': 1, 'Vinci': 1, 'René': 1, 'Descartes,': 1, 'Johannes': 1, 'Kepler': 2, 'Isaac': 2, 'Newton,': 1, 'debt.': 1, 'Indeed,': 1, "al-Haytham's": 4, 'ranks': 1, 'alongside': 1, "Newton's": 5, 'title,': 1, 'published': 1, '700': 1, 'later.': 1, 'translation': 1, 'huge': 1, 'impact': 1, 'it,': 2, 'build': 2, 'devices': 1, 'replicated': 1, 'those': 4, 'built,': 1, 'this,': 2, 'inventions': 1, 'eyeglasses,': 1, 'magnifying': 1, 'glasses,': 1, 'telescopes,': 1, 'cameras': 1, 'developed.': 2, 'showed': 1, 'appreciation': 1, 'proper': 1, 'relationship': 1, 'between': 10, 'mathematics,': 2, 'theoretical': 8, 'experimental': 10, 'physics.': 12, 'Sir': 1, 'Newton': 4, '(1643–1727),': 1, 'whose': 6, 'laws': 12, 'universal': 6, 'gravitation': 2, 'major': 3, 'milestones': 1, 'classical': 17, 'became': 1, 'separate': 1, 'Europeans': 1, 'quantitative': 2, 'methods': 7, 'discover': 2, 'what': 5, 'now': 5, 'considered': 4, 'physics.[25][page': 1, 'needed]': 2, 'Major': 3, 'developments': 2, 'include': 8, 'replacement': 1, 'geocentric': 1, 'Solar': 6, 'System': 2, 'heliocentric': 1, 'Copernican': 1, 'model,': 3, 'governing': 1, 'planetary': 1, 'bodies': 6, '(determined': 1, '1609': 1, '1619),': 1, "Galileo's": 2, 'pioneering': 1, 'telescopes': 1, 'observational': 1, '16th': 1, 'Centuries,': 1, 'discovery': 8, 'unification': 1, '(that': 1, 'would': 8, 'come': 4, 'bear': 1, 'name).[26]': 1, 'calculus,[d]': 1, 'mathematical': 14, 'change,': 1, 'solving': 4, 'problems.[27]': 1, 'thermodynamics,': 3, 'electromagnetics': 1, 'greater': 2, 'Industrial': 2, 'needs': 1, 'increased.[28]': 1, 'comprising': 1, 'remain': 2, 'widely': 1, 'everyday': 2, 'scales': 2, 'travelling': 1, 'non-relativistic': 1, 'speeds,': 1, 'since': 4, 'they': 8, 'provide': 1, 'close': 1, 'approximation': 2, 'situations,': 1, 'relativity': 11, 'simplify': 1, 'equivalents': 1, 'scales.': 4, 'However,': 3, 'inaccuracies': 2, 'high': 4, 'velocities': 1, '20th': 7, 'century.': 2, 'also:': 1, 'special': 7, 'Max': 4, 'Planck': 4, '(1858–1947),': 1, 'originator': 1, 'Albert': 5, 'Einstein': 4, '(1879–1955),': 1, 'photoelectric': 2, 'effect': 4, 'revolution': 1, 'began': 1, "Einstein's": 4, 'relativity.': 3, 'Both': 2, 'due': 1, 'situations.': 1, 'predicted': 3, 'varying': 1, 'speed': 8, 'light,': 2, 'could': 3, 'resolved': 1, 'constant': 2, "Maxwell's": 1, 'equations': 3, 'electromagnetism;': 1, 'discrepancy': 1, 'corrected': 2, 'relativity,': 4, 'replaced': 2, 'fast-moving': 1, 'allowed': 5, 'light.[29]': 1, 'Black-body': 1, 'radiation': 1, 'another': 3, 'problem': 3, 'excitation': 1, 'material': 2, 'oscillators': 1, 'possible': 3, 'only': 5, 'discrete': 3, 'steps': 1, 'proportional': 1, 'frequency;': 1, 'along': 3, 'complete': 1, 'predicting': 1, 'levels': 1, 'electron': 3, 'orbitals,': 1, 'taking': 1, 'over': 3, 'scales.[30]': 1, 'Quantum': 15, 'pioneered': 1, 'Werner': 2, 'Heisenberg,': 2, 'Erwin': 2, 'Schrödinger': 5, 'Paul': 2, 'Dirac.[30]': 1, 'work,': 2, 'fields,': 2, 'Standard': 10, 'Model': 4, 'derived.[31]': 1, 'Following': 1, 'properties': 4, 'consistent': 3, 'Higgs': 7, 'boson': 1, 'CERN': 2, '2012,[32]': 1, 'particles': 15, 'standard': 2, 'others,': 1, 'appear': 3, 'exist;': 1, 'however,': 1, 'beyond': 4, 'Model,': 3, 'supersymmetry,': 2, 'active': 4, 'area': 3, 'research.[33]': 1, 'Areas': 1, 'general': 4, 'field,': 2, 'probabilities': 1, 'groups.': 1, 'ways,': 1, 'stems': 1, "Thales'": 1, 'first': 8, 'attempt': 1, 'characterize': 1, 'matter,': 5, "Democritus'": 1, 'deduction': 1, 'ought': 1, 'reduce': 1, 'invariant': 1, 'state,': 1, 'Ptolemaic': 1, 'crystalline': 1, 'firmament,': 1, 'book': 5, '(an': 1, 'attempted': 1, 'analyze': 1, 'define': 1, 'philosophical': 4, 'point': 1, 'view),': 1, 'advanced': 1, 'nature.': 3, '18th': 1, 'century.[e]': 1, '19th': 4, 'realized': 1, 'discipline': 1, 'distinct': 2, 'Physics,': 2, 'rest': 1, 'science,': 3, 'relies': 1, '"scientific': 1, 'method"': 1, 'world.[35]': 1, 'employs': 1, 'reasoning': 2, 'well': 2, 'posteriori': 1, 'use': 8, 'Bayesian': 1, 'inference': 1, 'measure': 2, 'validity': 4, 'given': 2, 'theory.[36]': 1, 'answered': 1, 'questions': 1, 'philosophers,': 1, 'raised': 1, 'questions.': 1, 'Study': 1, 'issues': 2, 'surrounding': 2, 'involves': 2, 'determinism,': 1, 'metaphysical': 1, 'outlooks': 1, 'empiricism,': 1, 'naturalism': 1, 'realism.[37]': 1, 'physicists': 9, 'implications': 2, 'instance': 1, 'Laplace,': 2, 'championed': 1, 'causal': 1, 'determinism,[38]': 1, 'Schrödinger,': 4, 'mechanics.[39][40]': 1, 'physicist': 2, 'Roger': 2, 'Penrose': 5, 'been': 6, 'Platonist': 2, 'Stephen': 1, 'Hawking,[41]': 1, 'discusses': 1, 'Road': 2, 'Reality.[42]': 1, 'Hawking': 2, 'referred': 1, 'himself': 1, '"unashamed': 1, 'reductionist"': 1, 'took': 1, 'issue': 1, "Penrose's": 1, 'views.[43]': 1, 'Further': 2, 'information:': 2, 'Outline': 1, 'Though': 1, 'deals': 5, 'wide': 2, 'variety': 1, 'systems,': 1, 'physicists.': 1, 'Each': 1, 'experimentally': 3, 'tested': 2, 'numerous': 1, 'adequate': 1, 'instance,': 2, 'accurately': 2, 'objects,': 1, 'larger': 1, 'atoms': 4, 'moving': 2, 'less': 1, 'light.': 5, 'These': 5, 'continue': 1, 'today.': 1, 'Chaos': 1, 'theory,': 13, 'remarkable': 1, 'aspect': 1, 'mechanics,': 10, 'discovered': 3, 'original': 32, 'formulation': 3, '(1642–1727).': 1, 'central': 3, 'tools': 1, 'specialised': 1, 'topics,': 1, 'physicist,': 1, 'regardless': 1, 'specialisation,': 1, 'expected': 1, 'literate': 1, 'them.': 2, 'statistical': 3, 'includes': 2, 'traditional': 1, 'topics': 1, 'recognised': 1, 'well-developed': 1, 'beginning': 1, 'century—classical': 1, 'acoustics,': 1, 'optics,': 2, 'electromagnetism.': 1, 'concerned': 11, 'acted': 1, 'forces': 6, 'divided': 3, 'statics': 1, '(study': 3, 'subject': 4, 'acceleration),': 1, 'kinematics': 1, 'without': 4, 'regard': 1, 'causes),': 1, 'dynamics': 4, 'affect': 3, 'it);': 1, 'solid': 1, 'fluid': 1, '(known': 1, 'together': 2, 'continuum': 1, 'mechanics),': 1, 'latter': 1, 'hydrostatics,': 1, 'hydrodynamics,': 1, 'aerodynamics,': 1, 'pneumatics.': 1, 'Acoustics': 1, 'sound': 5, 'produced,': 1, 'controlled,': 1, 'transmitted': 1, 'received.[44]': 1, 'Important': 1, 'acoustics': 2, 'ultrasonics,': 1, 'waves': 3, 'frequency': 1, 'range': 2, 'human': 3, 'hearing;': 1, 'bioacoustics,': 1, 'animal': 1, 'calls': 1, 'hearing,[45]': 1, 'electroacoustics,': 1, 'manipulation': 1, 'audible': 1, 'using': 5, 'electronics.[46]': 1, 'Optics,': 3, 'infrared': 1, 'ultraviolet': 1, 'radiation,': 4, 'exhibit': 1, 'except': 1, 'visibility,': 1, 'e.g.,': 1, 'reflection,': 1, 'refraction,': 1, 'interference,': 1, 'diffraction,': 1, 'dispersion,': 1, 'polarization': 1, 'Heat': 1, 'form': 1, 'energy,': 4, 'internal': 2, 'possessed': 1, 'substance': 1, 'composed;': 1, 'relationships': 1, 'heat': 1, 'energy.': 1, 'Electricity': 1, 'magnetism': 1, 'single': 5, 'branch': 4, 'intimate': 1, 'connection': 2, 'them': 3, 'century;': 1, 'electric': 4, 'current': 1, 'gives': 1, 'rise': 1, 'magnetic': 5, 'changing': 1, 'induces': 1, 'current.': 2, 'Electrostatics': 1, 'charges': 1, 'rest,': 1, 'electrodynamics': 1, 'charges,': 1, 'magnetostatics': 1, 'poles': 1, 'rest.': 1, '{\\displaystyle': 3, '{\\hat': 2, '{H}}|\\psi': 2, '_{n}(t)\\rangle': 4, '=i\\hbar': 2, '{\\frac': 2, '{\\partial': 2, '}{\\partial': 2, 't}}|\\psi': 2, '}{\\displaystyle': 1, '}': 1, 'G_{\\mu': 2, '\\nu': 6, '}+\\Lambda': 2, 'g_{\\mu': 2, '}={\\kappa': 2, '}T_{\\mu': 2, '}}{\\displaystyle': 1, '}}': 1, 'Founders': 1, 'Concepts': 3, 'Scientists': 3, 'Categories': 1, 'generally': 1, 'normal': 1, 'scale': 6, 'under': 2, 'extreme': 1, 'conditions': 1, 'large': 4, 'scale.': 1, 'atomic': 10, 'smallest': 1, 'chemical': 1, 'elements': 1, 'identified.': 1, 'elementary': 5, 'even': 5, 'smaller': 1, 'units': 2, 'matter;': 1, 'high-energy': 3, 'because': 8, 'extremely': 2, 'energies': 1, 'necessary': 3, 'produce': 1, 'types': 1, 'accelerators.': 1, 'scale,': 1, 'ordinary,': 1, 'commonsensical': 1, 'notions': 2, 'space,': 2, 'longer': 2, 'valid.[47]': 1, 'chief': 1, 'present': 1, 'different': 3, 'picture': 2, 'approximates': 1, 'continuous,': 1, 'subatomic': 2, 'level': 1, 'complementary': 1, 'aspects': 3, 'description': 5, 'phenomena.': 3, 'take': 1, 'place': 1, 'frame': 1, 'reference': 1, 'respect': 1, 'observer;': 1, 'absence': 1, 'gravitational': 1, 'gravitation.': 1, 'find': 3, 'applications': 3, 'physics.[48]': 1, 'Causality': 1, 'Covariance': 1, 'Action': 1, 'Physical': 16, 'Symmetry': 1, 'interaction': 2, 'Statistical': 2, 'ensemble': 1, 'Wave': 1, 'Particle': 8, 'domains': 2, 'laws,': 1, 'lie': 1, 'explicit': 1, 'applicability.': 1, 'Solvay': 1, 'Conference': 2, '1927,': 1, 'prominent': 1, 'Einstein,': 1, 'Planck,': 2, 'Hendrik': 1, 'Lorentz,': 1, 'Niels': 1, 'Bohr,': 1, 'Marie': 1, 'Curie,': 1, 'Dirac': 1, 'Loosely': 1, 'speaking,': 1, 'describe': 3, 'systems': 5, 'length': 1, 'slower': 1, 'Outside': 1, 'domain,': 1, 'do': 6, 'match': 2, 'predictions': 4, 'mechanics.': 3, 'contributed': 1, 'framework': 1, 'absolute': 1, 'spacetime': 1, 'accurate': 2, 'components': 1, 'speeds': 1, 'approaching': 1, 'others': 1, 'probabilistic': 1, 'notion': 1, 'interactions': 9, 'Later,': 1, 'unified': 3, 'General': 3, 'dynamical,': 1, 'curved': 1, 'spacetime,': 1, 'highly': 1, 'massive': 3, 'large-scale': 1, 'structure': 3, 'well-described.': 1, 'yet': 1, 'descriptions;': 1, 'several': 3, 'candidate': 1, 'gravity': 1, 'This': 7, 'parabola-shaped': 1, 'lava': 1, 'flow': 1, 'illustrates': 1, 'application': 6, 'physics—in': 1, 'case,': 1, 'law': 4, 'falling': 1, 'bodies.': 1, 'Mathematics': 7, 'ontology': 1, 'chemistry': 3, 'cosmology.': 2, 'provides': 1, 'compact': 1, 'language': 3, 'order': 4, 'advocated': 1, 'Pythagoras,[49]': 1, 'Plato,[50]': 1, 'Galileo,[51]': 1, 'Newton.': 3, 'uses': 1, 'mathematics[52]': 1, 'organise': 1, 'formulate': 1, 'results.': 1, 'results,': 3, 'precise': 1, 'estimated': 1, 'solutions': 1, 'obtained,': 1, 'made': 8, 'confirmed': 2, 'negated.': 1, 'results': 4, 'experiments': 11, 'numerical': 1, 'data,': 1, 'estimates': 1, 'errors': 1, 'measurements.': 1, 'Technologies': 1, 'computation': 1, 'computational': 1, 'research.': 4, 'distinction': 2, 'clear-cut,': 2, 'always': 2, 'obvious,': 1, 'Ontology': 1, 'prerequisite': 1, 'mathematics.': 3, 'ultimately': 1, 'descriptions': 1, 'real': 2, 'world,': 1, 'abstract': 1, 'patterns,': 1, 'world.': 2, 'Thus': 1, 'statements': 4, 'synthetic,': 1, 'analytic.': 1, 'contains': 3, 'hypotheses,': 1, 'theories.': 3, 'logically': 1, 'true,': 1, 'must': 2, 'data.': 1, 'obvious.': 1, 'Its': 3, 'mathematical,': 1, 'physical.[53]': 1, 'problems': 6, 'start': 2, '"mathematical': 2, 'situation"': 1, '(system)': 1, 'law"': 1, 'applied': 8, 'system.': 1, 'Every': 1, 'statement': 3, 'hard-to-find': 1, 'meaning.': 1, 'final': 1, 'solution': 1, 'easier-to-find': 1, 'meaning,': 1, 'solver': 1, 'looking': 1, 'for.[clarification': 1, 'Pure': 1, 'science).': 1, '"the': 1, 'science"': 1, 'geology,': 1, 'biology': 1, 'constrained': 1, 'physics.[54]': 1, 'Similarly,': 1, 'role': 2, 'linking': 1, 'properties,': 1, 'structures,': 1, 'reactions': 2, "(chemistry's": 1, 'focus': 3, 'molecular': 3, 'distinguishes': 1, 'physics).': 1, 'Structures': 1, 'formed': 1, 'exert': 1, 'electrical': 2, 'each': 3, 'characteristics': 1, 'substances,': 1, 'bound': 1, 'conservation': 1, 'mass,': 2, 'charge.': 1, 'industries': 1, 'engineering': 6, 'medicine.': 1, 'Applied': 4, 'implemented': 1, 'acoustic': 2, 'reflecting': 1, 'diffuser': 1, 'screw,': 1, 'simple': 1, 'machine': 1, 'lifting': 1, 'Experiment': 1, 'laser': 1, 'term': 4, 'intended': 2, 'particular': 2, 'use.': 1, 'An': 5, 'curriculum': 1, 'usually': 4, 'few': 1, 'classes': 1, 'discipline,': 1, 'geology': 2, 'engineering.': 2, 'differs': 1, 'designing': 1, 'something': 1, 'particular,': 4, 'rather': 2, 'conducting': 1, 'aim': 1, 'technologies': 2, 'problem.': 1, 'approach': 2, 'similar': 3, 'people': 2, 'working': 1, 'accelerator': 1, 'might': 2, 'seek': 3, 'better': 6, 'detectors': 1, 'heavily': 1, 'statics,': 1, 'subfield': 1, 'building': 1, 'bridges': 1, 'static': 1, 'structures.': 1, 'control': 3, 'concert': 1, 'halls;': 1, 'similarly,': 1, 'creates': 1, 'devices.': 1, 'makes': 1, 'realistic': 1, 'flight': 1, 'simulators,': 1, 'video': 1, 'games,': 1, 'movies,': 1, 'critical': 2, 'forensic': 1, 'investigations.': 1, 'With': 2, 'consensus': 1, 'change': 2, 'things': 3, 'ordinarily': 1, 'mired': 1, 'uncertainty.': 1, 'origin': 2, 'earth,': 1, 'reasonably': 1, "earth's": 2, 'temperature,': 2, 'rate': 1, 'rotation,': 1, 'function': 1, 'allowing': 1, 'extrapolate': 1, 'forward': 1, 'backward': 1, 'so': 3, 'predict': 2, 'future': 3, 'prior': 1, 'events.': 1, 'allows': 1, 'simulations': 1, 'drastically': 1, 'technology.': 3, 'considerable': 1, 'interdisciplinarity,': 1, '(e.g.,': 1, 'econophysics': 1, 'sociophysics).': 1, 'Physicists': 3, 'test': 4, 'methodical': 1, 'compare': 1, 'conclusions': 1, 'drawn': 1, 'observations,': 1, 'logical,': 1, 'unbiased,': 1, 'repeatable': 1, 'way.': 1, 'To': 1, 'end,': 1, 'performed': 1, 'determine': 1, 'invalidity': 1, 'theory.[55]': 1, 'concise': 1, 'relation': 1, 'expresses': 1, 'principle': 1, 'some': 4, 'gravitation.[56]': 1, 'Theoretical': 3, 'Experimental': 4, 'astronaut': 1, 'fall.': 1, 'Lightning': 1, 'Theorists': 2, 'develop': 4, 'models': 2, 'agree': 2, 'existing': 4, 'successfully': 1, 'experimentalists': 2, 'devise': 1, 'perform': 2, 'explore': 2, 'Although': 2, 'separately,': 1, 'strongly': 1, 'upon': 2, 'other.': 1, 'Progress': 1, 'frequently': 1, 'defy': 1, 'theories,': 1, 'prompting': 1, 'intense': 1, 'applicable': 1, 'modelling,': 1, 'generate': 1, 'testable': 2, 'predictions,': 1, 'inspire': 1, '(and': 1, 'equipment).[57]': 1, 'interplay': 1, 'phenomenologists,': 1, 'complex': 3, 'relate': 2, 'theory.[58]': 1, 'historically': 1, 'taken': 1, 'philosophy;': 1, 'electromagnetism': 2, 'way.[f]': 1, 'Beyond': 1, 'universe,': 4, 'hypothetical': 2, 'issues,[g]': 1, 'parallel': 1, 'universes,': 1, 'multiverse,': 1, 'higher': 1, 'dimensions.': 1, 'invoke': 1, 'hopes': 2, 'theories;': 1, 'then': 2, 'consequences': 1, 'making': 1, 'predictions.': 1, 'expands,': 1, 'expanded': 2, 'by,': 1, 'involved': 2, 'design': 3, 'equipment': 1, 'accelerators': 1, 'lasers,': 1, 'whereas': 1, 'industry,': 1, 'resonance': 2, 'imaging': 1, '(MRI)': 1, 'transistors.': 1, 'Feynman': 7, 'explored': 1, 'theorists.[59]': 1, 'modeling': 1, 'quantitative.': 1, 'Here,': 1, 'path': 1, 'modeled': 2, 'calculus': 4, 'behavior:': 1, 'purview': 1, 'covers': 1, 'phenomena,': 1, '(such': 1, 'quarks,': 1, 'neutrinos,': 1, 'electrons)': 1, 'largest': 3, 'superclusters': 1, 'galaxies.': 1, 'Included': 1, 'composing': 1, 'things.': 1, 'Therefore,': 1, 'sometimes': 1, '"fundamental': 1, 'science".[54]': 1, 'occur': 2, 'terms': 4, 'simpler': 1, 'Thus,': 2, 'connect': 2, 'observable': 1, 'humans': 1, 'root': 2, 'causes,': 1, 'causes': 1, 'together.': 1, 'Chinese': 2, 'rocks': 1, '(lodestone': 1, 'magnetite)': 1, 'attracted': 1, 'invisible': 2, 'force.': 1, 'magnetism,': 2, 'rigorously': 2, 'knew': 1, 'amber,': 1, 'rubbed': 1, 'fur': 1, 'cause': 2, 'attraction': 1, 'two.[60]': 1, 'electricity.': 1, '(electricity': 1, 'magnetism).': 1, 'revealed': 1, 'just': 2, 'force—electromagnetism.': 1, 'process': 1, '"unifying"': 1, 'continues': 1, 'weak': 1, 'force': 2, 'electroweak': 1, 'interaction.': 1, 'ultimate': 1, '(theory': 1, 'everything)': 1, 'why': 1, '(see': 2, 'section': 1, 'below': 1, 'information).[61]': 1, 'Contemporary': 1, 'broadly': 1, 'physics;': 3, 'condensed': 7, 'atomic,': 1, 'astrophysics;': 1, 'Some': 1, 'departments': 1, 'support': 1, 'education': 1, 'outreach.[62]': 1, 'Since': 1, 'individual': 2, 'become': 2, 'increasingly': 2, 'specialised,': 1, 'today': 2, 'entire': 1, 'careers.': 1, '"Universalists"': 1, '(1879–1955)': 1, 'Lev': 1, 'Landau': 1, '(1908–1968),': 1, 'worked': 1, 'multiple': 1, 'rare.[h]': 1, 'subfields': 1, 'employ,': 1, 'shown': 2, 'following': 1, 'table.': 1, 'Field': 2, 'Subfields': 1, 'astrophysics,': 4, 'Astroparticle': 1, 'phenomenology': 1, 'electrodynamics,': 2, 'chromodynamics,': 1, 'Electroweak': 1, 'Effective': 1, 'Lattice': 1, 'Gauge': 1, 'Supersymmetry,': 1, 'Grand': 1, 'Unified': 1, 'Theory,': 1, 'Superstring': 1, 'M-theory,': 1, 'AdS/CFT': 1, 'correspondence': 1, '(gravitational,': 1, 'electromagnetic,': 1, 'weak,': 2, 'strong),': 1, 'Elementary': 3, 'particle,': 1, 'Spin,': 2, 'Antimatter,': 1, 'Spontaneous': 1, 'symmetry': 1, 'breaking,': 1, 'Neutrino': 1, 'oscillation,': 1, 'Seesaw': 1, 'mechanism,': 1, 'Brane,': 1, 'String,': 1, 'gravity,': 1, 'everything,': 1, 'Vacuum': 1, 'Atomic': 4, 'Molecular': 2, 'Chemical': 2, 'Photonics': 1, 'information': 4, 'Photon,': 1, 'Atom,': 1, 'Molecule,': 1, 'Diffraction,': 1, 'Electromagnetic': 2, 'Laser,': 1, 'Polarization': 1, '(waves),': 1, 'Spectral': 1, 'line,': 1, 'Casimir': 1, 'Solid-state': 2, 'High-pressure': 1, 'Low-temperature': 1, 'Surface': 1, 'Nanoscale': 1, 'mesoscopic': 1, 'Polymer': 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'Engineering': 1, 'Fluid': 3, 'dynamics,': 1, 'Geophysics,': 1, 'Laser': 1, 'Materials': 2, 'Medical': 1, 'Nanotechnology,': 1, 'Optoelectronics,': 1, 'Photonics,': 1, 'Photovoltaics,': 1, 'oceanography,': 1, 'computation,': 1, 'devices,': 1, 'electronics,': 1, 'Vehicle': 1, 'simulated': 1, 'CMS': 1, 'detector': 1, 'Large': 3, 'Hadron': 3, 'Collider,': 1, 'featuring': 1, 'appearance': 1, 'boson.': 1, 'constituents': 2, 'them.[63]': 1, 'addition,': 1, 'accelerators,[64]': 1, 'detectors,[65]': 1, 'computer': 2, 'programs[66]': 1, '"high-energy': 1, 'physics"': 1, 'naturally': 1, 'collisions': 1, 'particles.[67]': 1, 'Currently,': 1, 'described': 3, 'Model.[68]': 1, 'accounts': 1, '12': 2, '(quarks': 1, 'leptons)': 1, 'interact': 1, 'via': 1, 'strong,': 1, 'electromagnetic': 2, 'forces.[68]': 1, 'Dynamics': 1, 'exchanging': 1, 'gauge': 1, 'bosons': 1, '(gluons,': 1, 'W': 1, 'Z': 1, 'bosons,': 1, 'photons,': 1, 'respectively).[69]': 1, 'predicts': 1, 'boson.[68]': 1, 'July': 8, '2012': 3, 'CERN,': 2, 'laboratory': 1, 'announced': 1, 'detection': 1, 'boson,[70]': 1, 'integral': 1, 'mechanism.': 1, 'nuclei.': 1, 'commonly': 1, 'power': 1, 'generation': 1, 'weapons': 1, 'technology,': 1, 'medicine': 1, 'imaging,': 1, 'ion': 1, 'implantation': 1, 'materials': 2, 'engineering,': 1, 'radiocarbon': 1, 'archaeology.': 1, '(AMO)': 1, 'matter–matter': 1, 'light–matter': 1, 'molecules.': 1, 'grouped': 1, 'interrelationships,': 1, 'similarity': 1, 'used,': 1, 'commonality': 1, 'relevant': 1, 'All': 1, 'classical,': 1, 'semi-classical': 1, 'treatments;': 1, 'treat': 1, 'microscopic': 2, '(in': 1, 'contrast': 1, 'macroscopic': 3, 'view).': 1, 'shells': 1, 'atoms.': 1, 'focuses': 2, 'activities': 2, 'control,': 1, 'cooling': 1, 'trapping': 1, 'ions,[71][72][73]': 1, 'low-temperature': 1, 'collision': 1, 'effects': 1, 'correlation': 1, 'dynamics.': 1, 'nucleus': 1, 'hyperfine': 1, 'splitting),': 1, 'intra-nuclear': 1, 'fission': 1, 'fusion': 1, 'multi-atomic': 1, 'structures': 1, 'external': 1, 'Optical': 2, 'tends': 1, 'realm.': 1, 'Velocity-distribution': 1, 'data': 2, 'gas': 1, 'rubidium': 1, 'atoms,': 1, 'confirming': 1, 'phase': 2, 'condensate': 1, 'matter.[74][75]': 1, '"condensed"': 1, 'phases': 4, 'whenever': 1, 'number': 2, 'system': 1, 'strong.[76]': 1, 'familiar': 1, 'solids': 1, 'liquids,': 1, 'arise': 1, 'bonding': 1, 'atoms.[77]': 1, 'More': 1, 'exotic': 1, 'superfluid[78]': 1, 'condensate[79]': 1, 'low': 1, 'superconducting': 1, 'exhibited': 1, 'conduction': 1, 'electrons': 1, 'materials,[80]': 1, 'ferromagnetic': 1, 'antiferromagnetic': 1, 'spins': 1, 'lattices.[81]': 1, 'contemporary': 1, 'Historically,': 1, 'grew': 1, 'out': 1, 'subfields.[82]': 1, 'apparently': 1, 'coined': 1, 'Philip': 1, 'Anderson': 1, 'renamed': 2, 'group—previously': 1, 'theory—in': 1, '1967.[83]': 1, '1978,': 1, 'Division': 2, 'Solid': 1, 'State': 2, 'American': 10, 'Society': 5, 'Matter': 6, 'Physics.[82]': 1, 'overlap': 1, 'nanotechnology': 1, 'engineering.[76]': 1, 'cosmology': 2, 'deepest': 1, 'visible-light': 1, 'image': 1, 'Hubble': 2, 'Ultra-Deep': 1, 'stellar': 2, 'structure,': 1, 'evolution,': 1, 'Because': 1, 'broad': 1, 'subject,': 1, 'astrophysicists': 1, 'typically': 1, 'apply': 2, 'physics.[84]': 1, 'Karl': 1, 'Jansky': 1, '1931': 1, 'radio': 2, 'signals': 1, 'emitted': 1, 'initiated': 1, 'astronomy.': 2, 'Most': 1, 'recently,': 1, 'frontiers': 1, 'exploration.': 1, 'Perturbations': 1, 'interference': 1, 'atmosphere': 2, 'make': 1, 'space-based': 1, 'infrared,': 1, 'ultraviolet,': 1, 'gamma-ray,': 1, 'X-ray': 1, 'formation': 3, 'evolution': 2, 'plays': 1, 'cosmological': 2, "Hubble's": 1, 'expanding,': 1, 'diagram,': 1, 'prompted': 1, 'rival': 1, 'steady': 1, 'state': 1, 'Bang.': 1, 'Bang': 3, 'success': 1, 'nucleosynthesis': 1, 'cosmic': 2, 'microwave': 1, '1964.': 1, 'rests': 1, 'pillars:': 1, 'principle.': 1, 'Cosmologists': 1, 'recently': 1, 'established': 1, 'ΛCDM': 1, 'dark': 7, 'matter.': 1, 'Numerous': 1, 'possibilities': 1, 'discoveries': 1, 'anticipated': 1, 'emerge': 1, 'Gamma-ray': 2, 'Telescope': 1, 'upcoming': 1, 'decade': 1, 'vastly': 1, 'revise': 1, 'clarify': 1, 'universe.[85][86]': 1, 'potential': 1, 'tremendous': 1, 'next': 1, 'years.[87]': 1, 'evidence': 2, 'composed': 1, 'weakly': 1, 'interacting': 1, 'particles,': 1, 'complementing': 1, 'Collider': 2, 'underground': 1, 'detectors.': 1, 'IBEX': 1, 'already': 2, 'yielding': 1, 'astrophysical': 1, 'discoveries:': 1, '"No': 1, 'knows': 1, 'creating': 1, 'ENA': 1, '(energetic': 1, 'neutral': 1, 'atoms)': 1, 'ribbon"': 1, 'termination': 1, 'shock': 1, 'solar': 3, 'wind,': 1, '"but': 1, 'everyone': 1, 'agrees': 1, 'textbook': 1, 'heliosphere—in': 1, "System's": 1, 'enveloping': 1, 'pocket': 1, 'filled': 1, "wind's": 1, 'charged': 1, 'plowing': 1, 'onrushing': 1, "'galactic": 1, "wind'": 1, 'interstellar': 1, 'medium': 1, 'shape': 2, 'comet—is': 1, 'wrong."[88]': 1, 'List': 3, 'unsolved': 3, 'diagram': 1, 'signed': 1, 'R.': 4, 'P.': 3, 'Feynman.': 1, 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'geocentric': 1, 'Solar': 6, 'System': 2, 'heliocentric': 1, 'Copernican': 1, 'model,': 3, 'governing': 1, 'planetary': 1, 'bodies': 6, '(determined': 1, '1609': 1, '1619),': 1, "Galileo's": 2, 'pioneering': 1, 'telescopes': 1, 'observational': 1, '16th': 1, 'Centuries,': 1, 'discovery': 8, 'unification': 1, '(that': 1, 'would': 8, 'come': 4, 'bear': 1, 'name).[26]': 1, 'calculus,[d]': 1, 'mathematical': 14, 'change,': 1, 'solving': 4, 'problems.[27]': 1, 'thermodynamics,': 3, 'electromagnetics': 1, 'greater': 2, 'Industrial': 2, 'needs': 1, 'increased.[28]': 1, 'comprising': 1, 'remain': 2, 'widely': 1, 'everyday': 2, 'scales': 2, 'travelling': 1, 'non-relativistic': 1, 'speeds,': 1, 'since': 4, 'they': 8, 'provide': 1, 'close': 1, 'approximation': 2, 'situations,': 1, 'relativity': 11, 'simplify': 1, 'equivalents': 1, 'scales.': 4, 'However,': 3, 'inaccuracies': 2, 'high': 4, 'velocities': 1, '20th': 7, 'century.': 2, 'also:': 1, 'special': 7, 'Max': 4, 'Planck': 4, '(1858–1947),': 1, 'originator': 1, 'Albert': 5, 'Einstein': 4, '(1879–1955),': 1, 'photoelectric': 2, 'effect': 4, 'revolution': 1, 'began': 1, "Einstein's": 4, 'relativity.': 3, 'Both': 2, 'due': 1, 'situations.': 1, 'predicted': 3, 'varying': 1, 'speed': 8, 'light,': 2, 'could': 3, 'resolved': 1, 'constant': 2, "Maxwell's": 1, 'equations': 3, 'electromagnetism;': 1, 'discrepancy': 1, 'corrected': 2, 'relativity,': 4, 'replaced': 2, 'fast-moving': 1, 'allowed': 5, 'light.[29]': 1, 'Black-body': 1, 'radiation': 1, 'another': 3, 'problem': 3, 'excitation': 1, 'material': 2, 'oscillators': 1, 'possible': 3, 'only': 5, 'discrete': 3, 'steps': 1, 'proportional': 1, 'frequency;': 1, 'along': 3, 'complete': 1, 'predicting': 1, 'levels': 1, 'electron': 3, 'orbitals,': 1, 'taking': 1, 'over': 3, 'scales.[30]': 1, 'Quantum': 15, 'pioneered': 1, 'Werner': 2, 'Heisenberg,': 2, 'Erwin': 2, 'Schrödinger': 5, 'Paul': 2, 'Dirac.[30]': 1, 'work,': 2, 'fields,': 2, 'Standard': 10, 'Model': 4, 'derived.[31]': 1, 'Following': 1, 'properties': 4, 'consistent': 3, 'Higgs': 7, 'boson': 1, 'CERN': 2, '2012,[32]': 1, 'particles': 15, 'standard': 2, 'others,': 1, 'appear': 3, 'exist;': 1, 'however,': 1, 'beyond': 4, 'Model,': 3, 'supersymmetry,': 2, 'active': 4, 'area': 3, 'research.[33]': 1, 'Areas': 1, 'general': 4, 'field,': 2, 'probabilities': 1, 'groups.': 1, 'ways,': 1, 'stems': 1, "Thales'": 1, 'first': 8, 'attempt': 1, 'characterize': 1, 'matter,': 5, "Democritus'": 1, 'deduction': 1, 'ought': 1, 'reduce': 1, 'invariant': 1, 'state,': 1, 'Ptolemaic': 1, 'crystalline': 1, 'firmament,': 1, 'book': 5, '(an': 1, 'attempted': 1, 'analyze': 1, 'define': 1, 'philosophical': 4, 'point': 1, 'view),': 1, 'advanced': 1, 'nature.': 3, '18th': 1, 'century.[e]': 1, '19th': 4, 'realized': 1, 'discipline': 1, 'distinct': 2, 'Physics,': 2, 'rest': 1, 'science,': 3, 'relies': 1, '"scientific': 1, 'method"': 1, 'world.[35]': 1, 'employs': 1, 'reasoning': 2, 'well': 2, 'posteriori': 1, 'use': 8, 'Bayesian': 1, 'inference': 1, 'measure': 2, 'validity': 4, 'given': 2, 'theory.[36]': 1, 'answered': 1, 'questions': 1, 'philosophers,': 1, 'raised': 1, 'questions.': 1, 'Study': 1, 'issues': 2, 'surrounding': 2, 'involves': 2, 'determinism,': 1, 'metaphysical': 1, 'outlooks': 1, 'empiricism,': 1, 'naturalism': 1, 'realism.[37]': 1, 'physicists': 9, 'implications': 2, 'instance': 1, 'Laplace,': 2, 'championed': 1, 'causal': 1, 'determinism,[38]': 1, 'Schrödinger,': 4, 'mechanics.[39][40]': 1, 'physicist': 2, 'Roger': 2, 'Penrose': 5, 'been': 6, 'Platonist': 2, 'Stephen': 1, 'Hawking,[41]': 1, 'discusses': 1, 'Road': 2, 'Reality.[42]': 1, 'Hawking': 2, 'referred': 1, 'himself': 1, '"unashamed': 1, 'reductionist"': 1, 'took': 1, 'issue': 1, "Penrose's": 1, 'views.[43]': 1, 'Further': 2, 'information:': 2, 'Outline': 1, 'Though': 1, 'deals': 5, 'wide': 2, 'variety': 1, 'systems,': 1, 'physicists.': 1, 'Each': 1, 'experimentally': 3, 'tested': 2, 'numerous': 1, 'adequate': 1, 'instance,': 2, 'accurately': 2, 'objects,': 1, 'larger': 1, 'atoms': 4, 'moving': 2, 'less': 1, 'light.': 5, 'These': 5, 'continue': 1, 'today.': 1, 'Chaos': 1, 'theory,': 13, 'remarkable': 1, 'aspect': 1, 'mechanics,': 10, 'discovered': 3, 'original': 32, 'formulation': 3, '(1642–1727).': 1, 'central': 3, 'tools': 1, 'specialised': 1, 'topics,': 1, 'physicist,': 1, 'regardless': 1, 'specialisation,': 1, 'expected': 1, 'literate': 1, 'them.': 2, 'statistical': 3, 'includes': 2, 'traditional': 1, 'topics': 1, 'recognised': 1, 'well-developed': 1, 'beginning': 1, 'century—classical': 1, 'acoustics,': 1, 'optics,': 2, 'electromagnetism.': 1, 'concerned': 11, 'acted': 1, 'forces': 6, 'divided': 3, 'statics': 1, '(study': 3, 'subject': 4, 'acceleration),': 1, 'kinematics': 1, 'without': 4, 'regard': 1, 'causes),': 1, 'dynamics': 4, 'affect': 3, 'it);': 1, 'solid': 1, 'fluid': 1, '(known': 1, 'together': 2, 'continuum': 1, 'mechanics),': 1, 'latter': 1, 'hydrostatics,': 1, 'hydrodynamics,': 1, 'aerodynamics,': 1, 'pneumatics.': 1, 'Acoustics': 1, 'sound': 5, 'produced,': 1, 'controlled,': 1, 'transmitted': 1, 'received.[44]': 1, 'Important': 1, 'acoustics': 2, 'ultrasonics,': 1, 'waves': 3, 'frequency': 1, 'range': 2, 'human': 3, 'hearing;': 1, 'bioacoustics,': 1, 'animal': 1, 'calls': 1, 'hearing,[45]': 1, 'electroacoustics,': 1, 'manipulation': 1, 'audible': 1, 'using': 5, 'electronics.[46]': 1, 'Optics,': 3, 'infrared': 1, 'ultraviolet': 1, 'radiation,': 4, 'exhibit': 1, 'except': 1, 'visibility,': 1, 'e.g.,': 1, 'reflection,': 1, 'refraction,': 1, 'interference,': 1, 'diffraction,': 1, 'dispersion,': 1, 'polarization': 1, 'Heat': 1, 'form': 1, 'energy,': 4, 'internal': 2, 'possessed': 1, 'substance': 1, 'composed;': 1, 'relationships': 1, 'heat': 1, 'energy.': 1, 'Electricity': 1, 'magnetism': 1, 'single': 5, 'branch': 4, 'intimate': 1, 'connection': 2, 'them': 3, 'century;': 1, 'electric': 4, 'current': 1, 'gives': 1, 'rise': 1, 'magnetic': 5, 'changing': 1, 'induces': 1, 'current.': 2, 'Electrostatics': 1, 'charges': 1, 'rest,': 1, 'electrodynamics': 1, 'charges,': 1, 'magnetostatics': 1, 'poles': 1, 'rest.': 1, '{\\displaystyle': 3, '{\\hat': 2, '{H}}|\\psi': 2, '_{n}(t)\\rangle': 4, '=i\\hbar': 2, '{\\frac': 2, '{\\partial': 2, '}{\\partial': 2, 't}}|\\psi': 2, '}{\\displaystyle': 1, '}': 1, 'G_{\\mu': 2, '\\nu': 6, '}+\\Lambda': 2, 'g_{\\mu': 2, '}={\\kappa': 2, '}T_{\\mu': 2, '}}{\\displaystyle': 1, '}}': 1, 'Founders': 1, 'Concepts': 3, 'Scientists': 3, 'Categories': 1, 'generally': 1, 'normal': 1, 'scale': 6, 'under': 2, 'extreme': 1, 'conditions': 1, 'large': 4, 'scale.': 1, 'atomic': 10, 'smallest': 1, 'chemical': 1, 'elements': 1, 'identified.': 1, 'elementary': 5, 'even': 5, 'smaller': 1, 'units': 2, 'matter;': 1, 'high-energy': 3, 'because': 8, 'extremely': 2, 'energies': 1, 'necessary': 3, 'produce': 1, 'types': 1, 'accelerators.': 1, 'scale,': 1, 'ordinary,': 1, 'commonsensical': 1, 'notions': 2, 'space,': 2, 'longer': 2, 'valid.[47]': 1, 'chief': 1, 'present': 1, 'different': 3, 'picture': 2, 'approximates': 1, 'continuous,': 1, 'subatomic': 2, 'level': 1, 'complementary': 1, 'aspects': 3, 'description': 5, 'phenomena.': 3, 'take': 1, 'place': 1, 'frame': 1, 'reference': 1, 'respect': 1, 'observer;': 1, 'absence': 1, 'gravitational': 1, 'gravitation.': 1, 'find': 3, 'applications': 3, 'physics.[48]': 1, 'Causality': 1, 'Covariance': 1, 'Action': 1, 'Physical': 16, 'Symmetry': 1, 'interaction': 2, 'Statistical': 2, 'ensemble': 1, 'Wave': 1, 'Particle': 8, 'domains': 2, 'laws,': 1, 'lie': 1, 'explicit': 1, 'applicability.': 1, 'Solvay': 1, 'Conference': 2, '1927,': 1, 'prominent': 1, 'Einstein,': 1, 'Planck,': 2, 'Hendrik': 1, 'Lorentz,': 1, 'Niels': 1, 'Bohr,': 1, 'Marie': 1, 'Curie,': 1, 'Dirac': 1, 'Loosely': 1, 'speaking,': 1, 'describe': 3, 'systems': 5, 'length': 1, 'slower': 1, 'Outside': 1, 'domain,': 1, 'do': 6, 'match': 2, 'predictions': 4, 'mechanics.': 3, 'contributed': 1, 'framework': 1, 'absolute': 1, 'spacetime': 1, 'accurate': 2, 'components': 1, 'speeds': 1, 'approaching': 1, 'others': 1, 'probabilistic': 1, 'notion': 1, 'interactions': 9, 'Later,': 1, 'unified': 3, 'General': 3, 'dynamical,': 1, 'curved': 1, 'spacetime,': 1, 'highly': 1, 'massive': 3, 'large-scale': 1, 'structure': 3, 'well-described.': 1, 'yet': 1, 'descriptions;': 1, 'several': 3, 'candidate': 1, 'gravity': 1, 'This': 7, 'parabola-shaped': 1, 'lava': 1, 'flow': 1, 'illustrates': 1, 'application': 6, 'physics—in': 1, 'case,': 1, 'law': 4, 'falling': 1, 'bodies.': 1, 'Mathematics': 7, 'ontology': 1, 'chemistry': 3, 'cosmology.': 2, 'provides': 1, 'compact': 1, 'language': 3, 'order': 4, 'advocated': 1, 'Pythagoras,[49]': 1, 'Plato,[50]': 1, 'Galileo,[51]': 1, 'Newton.': 3, 'uses': 1, 'mathematics[52]': 1, 'organise': 1, 'formulate': 1, 'results.': 1, 'results,': 3, 'precise': 1, 'estimated': 1, 'solutions': 1, 'obtained,': 1, 'made': 8, 'confirmed': 2, 'negated.': 1, 'results': 4, 'experiments': 11, 'numerical': 1, 'data,': 1, 'estimates': 1, 'errors': 1, 'measurements.': 1, 'Technologies': 1, 'computation': 1, 'computational': 1, 'research.': 4, 'distinction': 2, 'clear-cut,': 2, 'always': 2, 'obvious,': 1, 'Ontology': 1, 'prerequisite': 1, 'mathematics.': 3, 'ultimately': 1, 'descriptions': 1, 'real': 2, 'world,': 1, 'abstract': 1, 'patterns,': 1, 'world.': 2, 'Thus': 1, 'statements': 4, 'synthetic,': 1, 'analytic.': 1, 'contains': 3, 'hypotheses,': 1, 'theories.': 3, 'logically': 1, 'true,': 1, 'must': 2, 'data.': 1, 'obvious.': 1, 'Its': 3, 'mathematical,': 1, 'physical.[53]': 1, 'problems': 6, 'start': 2, '"mathematical': 2, 'situation"': 1, '(system)': 1, 'law"': 1, 'applied': 8, 'system.': 1, 'Every': 1, 'statement': 3, 'hard-to-find': 1, 'meaning.': 1, 'final': 1, 'solution': 1, 'easier-to-find': 1, 'meaning,': 1, 'solver': 1, 'looking': 1, 'for.[clarification': 1, 'Pure': 1, 'science).': 1, '"the': 1, 'science"': 1, 'geology,': 1, 'biology': 1, 'constrained': 1, 'physics.[54]': 1, 'Similarly,': 1, 'role': 2, 'linking': 1, 'properties,': 1, 'structures,': 1, 'reactions': 2, "(chemistry's": 1, 'focus': 3, 'molecular': 3, 'distinguishes': 1, 'physics).': 1, 'Structures': 1, 'formed': 1, 'exert': 1, 'electrical': 2, 'each': 3, 'characteristics': 1, 'substances,': 1, 'bound': 1, 'conservation': 1, 'mass,': 2, 'charge.': 1, 'industries': 1, 'engineering': 6, 'medicine.': 1, 'Applied': 4, 'implemented': 1, 'acoustic': 2, 'reflecting': 1, 'diffuser': 1, 'screw,': 1, 'simple': 1, 'machine': 1, 'lifting': 1, 'Experiment': 1, 'laser': 1, 'term': 4, 'intended': 2, 'particular': 2, 'use.': 1, 'An': 5, 'curriculum': 1, 'usually': 4, 'few': 1, 'classes': 1, 'discipline,': 1, 'geology': 2, 'engineering.': 2, 'differs': 1, 'designing': 1, 'something': 1, 'particular,': 4, 'rather': 2, 'conducting': 1, 'aim': 1, 'technologies': 2, 'problem.': 1, 'approach': 2, 'similar': 3, 'people': 2, 'working': 1, 'accelerator': 1, 'might': 2, 'seek': 3, 'better': 6, 'detectors': 1, 'heavily': 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'way.': 1, 'To': 1, 'end,': 1, 'performed': 1, 'determine': 1, 'invalidity': 1, 'theory.[55]': 1, 'concise': 1, 'relation': 1, 'expresses': 1, 'principle': 1, 'some': 4, 'gravitation.[56]': 1, 'Theoretical': 3, 'Experimental': 4, 'astronaut': 1, 'fall.': 1, 'Lightning': 1, 'Theorists': 2, 'develop': 4, 'models': 2, 'agree': 2, 'existing': 4, 'successfully': 1, 'experimentalists': 2, 'devise': 1, 'perform': 2, 'explore': 2, 'Although': 2, 'separately,': 1, 'strongly': 1, 'upon': 2, 'other.': 1, 'Progress': 1, 'frequently': 1, 'defy': 1, 'theories,': 1, 'prompting': 1, 'intense': 1, 'applicable': 1, 'modelling,': 1, 'generate': 1, 'testable': 2, 'predictions,': 1, 'inspire': 1, '(and': 1, 'equipment).[57]': 1, 'interplay': 1, 'phenomenologists,': 1, 'complex': 3, 'relate': 2, 'theory.[58]': 1, 'historically': 1, 'taken': 1, 'philosophy;': 1, 'electromagnetism': 2, 'way.[f]': 1, 'Beyond': 1, 'universe,': 4, 'hypothetical': 2, 'issues,[g]': 1, 'parallel': 1, 'universes,': 1, 'multiverse,': 1, 'higher': 1, 'dimensions.': 1, 'invoke': 1, 'hopes': 2, 'theories;': 1, 'then': 2, 'consequences': 1, 'making': 1, 'predictions.': 1, 'expands,': 1, 'expanded': 2, 'by,': 1, 'involved': 2, 'design': 3, 'equipment': 1, 'accelerators': 1, 'lasers,': 1, 'whereas': 1, 'industry,': 1, 'resonance': 2, 'imaging': 1, '(MRI)': 1, 'transistors.': 1, 'Feynman': 7, 'explored': 1, 'theorists.[59]': 1, 'modeling': 1, 'quantitative.': 1, 'Here,': 1, 'path': 1, 'modeled': 2, 'calculus': 4, 'behavior:': 1, 'purview': 1, 'covers': 1, 'phenomena,': 1, '(such': 1, 'quarks,': 1, 'neutrinos,': 1, 'electrons)': 1, 'largest': 3, 'superclusters': 1, 'galaxies.': 1, 'Included': 1, 'composing': 1, 'things.': 1, 'Therefore,': 1, 'sometimes': 1, '"fundamental': 1, 'science".[54]': 1, 'occur': 2, 'terms': 4, 'simpler': 1, 'Thus,': 2, 'connect': 2, 'observable': 1, 'humans': 1, 'root': 2, 'causes,': 1, 'causes': 1, 'together.': 1, 'Chinese': 2, 'rocks': 1, '(lodestone': 1, 'magnetite)': 1, 'attracted': 1, 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'Subfields': 1, 'astrophysics,': 4, 'Astroparticle': 1, 'phenomenology': 1, 'electrodynamics,': 2, 'chromodynamics,': 1, 'Electroweak': 1, 'Effective': 1, 'Lattice': 1, 'Gauge': 1, 'Supersymmetry,': 1, 'Grand': 1, 'Unified': 1, 'Theory,': 1, 'Superstring': 1, 'M-theory,': 1, 'AdS/CFT': 1, 'correspondence': 1, '(gravitational,': 1, 'electromagnetic,': 1, 'weak,': 2, 'strong),': 1, 'Elementary': 3, 'particle,': 1, 'Spin,': 2, 'Antimatter,': 1, 'Spontaneous': 1, 'symmetry': 1, 'breaking,': 1, 'Neutrino': 1, 'oscillation,': 1, 'Seesaw': 1, 'mechanism,': 1, 'Brane,': 1, 'String,': 1, 'gravity,': 1, 'everything,': 1, 'Vacuum': 1, 'Atomic': 4, 'Molecular': 2, 'Chemical': 2, 'Photonics': 1, 'information': 4, 'Photon,': 1, 'Atom,': 1, 'Molecule,': 1, 'Diffraction,': 1, 'Electromagnetic': 2, 'Laser,': 1, 'Polarization': 1, '(waves),': 1, 'Spectral': 1, 'line,': 1, 'Casimir': 1, 'Solid-state': 2, 'High-pressure': 1, 'Low-temperature': 1, 'Surface': 1, 'Nanoscale': 1, 'mesoscopic': 1, 'Polymer': 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