undermine carnap 's distinction existence questions internal framework external philosophy fiction problem empty names debate existence 's status property come relative obscurity limelight perennial issues free possible worlds philosophy time new life breathed analytic view metaphysics studying phenomenal human concepts rather making claims noumenal world style often blurs philosophy language introspective psychology compared system building


university press crane farkas k ''metaphysics guide anthology'' oxford university press gale richard ''the blackwell guide metaphysics'' oxford blackwell gay peter ''the enlightenment interpretation'' vols new york ww norton company harris e e ''the foundations metaphysics science'' london george allen unwin harris e e ''the restitution metaphysics'' new york humanity books heisenberg werner atomic physics causal law ''the physicist 's conception nature'' koons robert c pickavance timothy h ''metaphysics fundamentals'' wiley blackwell le poidevin r


al eds ''the routledge companion metaphysics'' new york routledge loux j ''metaphysics contemporary introduction'' rd ed london routledge lowe e j ''a survey metaphysics'' oxford oxford university press tuomas e tahko ''an introduction metametaphysics'' cambridge cambridge university press reading benovsky jiri ''meta metaphysics metaphysical equivalence primitiveness theory choice'' springer bliss ricki j miller eds forthcoming ''the routledge handbook metametaphysics'' routledge kim jaegwon ernest sosa eds ''metaphysics anthology'' blackwell philosophy anthologies kim jaegwon ernest sosa eds ''a companion metaphysics''


malden massachusetts blackwell neil manson robert w barnard eds ''the bloomsbury companion metaphysics'' bloomsbury raven michael j ''the routledge handbook metaphysical grounding'' routledge external links http wwwbritannicacom ebchecked topic metaphysics metaphysics encyclop dia britannica http wwwuclacuk philosophy lpsg london philosophy study guide offers many suggestions read depending student 's familiarity subject http wwwuclacuk philosophy lpsg l mhtm logic metaphysics


'''metaphilosophy''' sometimes called '''the philosophy philosophy''' investigation nature philosophy ref name lazerowitz subject matter includes aims philosophy boundaries philosophy methods ref name joll ref ref name marsoobian ref thus philosophy characteristically inquires nature reality objects possibility knowledge nature truth metaphilosophy self reflective inquiry nature aims methods activity makes kinds inquiries asking ''is'' philosophy sorts questions ask might pose answer


philosophy traced back least far works ancient greeks ancient indian nyaya relationship philosophy philosophers consider metaphilosophy subject apart philosophy beyond ref name griswold others object idea ref name heidegger timothy williamson argues philosophy philosophy automatically part philosophy philosophy anything else ref name williamson nicholas bunnin jiyuan yu write separation first second order study lost popularity philosophers find hard observe distinction ref name bunnin ref evidenced


synonyms sometimes seen distinct morris lazerowitz claims coined term 'metaphilosophy' around used print ref name lazerowitz see also internet encyclopedia philosophy article nicholas joll http wwwieputmedu con meta sh b contemporary metaphilosophy ref lazerowitz proposed metaphilosophy 'the investigation nature philosophy' ref name lazerowitz earlier uses found translations french term derived greek word ''meta'' beyond ''philosoph a'' love wisdom term 'metaphilosophy' used paul moser ref name moser ref sense 'second order' fundamental undertaking


philosophy manner suggested charles griswold ref name griswold usage considered nonsense ludwig wittgenstein rejected analogy metalanguage metaphilosophy ref name wittgenstein ref expressed martin heidegger ref name heidegger philosophers treat prefix ''meta'' simply meaning ' nowiki ''about'' nowiki ' rather referring metatheoretical 'second order' form philosophy among rescher ref name rescher ref double ref name double ref others williamson prefer term '' nowiki 'philosophy philosophy''' instead 'metaphilosophy' avoids connotation 'second order' discipline looks philosophy instead denotes something part


wittgenstein wrote metaphilosophy sense metatheory philosophy c broad distinguished critical speculative philosophy subject matter philosophy relations special sciences ''introduction scientific thought'' curt ducasse ''philosophy science'' examines several views nature philosophy concludes philosophy distinct subject matter appraisals ducasse 's view among first described 'metaphilosophy' henri lefebvre ''m taphilosophie'' argued marxian standpoint favor ontological break necessary methodological


approach critical social theory whilst criticizing louis althusser 's epistemological break subjective marxism represented fundamental theoretical tool school marxist structuralism paul moser writes typical metaphilosophical discussion includes determining conditions claim said philosophical one regards meta ethics study ethics form metaphilosophy well meta epistemology study epistemology ref name moser topics many sub disciplines philosophy branch 'metaphilosophy' ref name edwards however topics within 'metaphilosophy' cut across various subdivisions philosophy consider fundamentals important


sub disciplines mentioned cognitivity systematicity methodology historicity self reference self application immanence non immanence disagreement diversity primacy practical philosophy good bad philosophy expertise ends philosophy death philosophy anti philosophies philosophy assertion philosophy exposition philosophy style philosophy literature literature philosophy philosophical beauty philosophy science philosophy related fields activities philosophy argument philosophy wisdom philosophy metaphilosophy philosophy folk philosophy 'primitive' life philosophy philosophers philosophy pedagogy aims philosophers eg existentialists pragmatists think philosophy ultimately


practical discipline help us lead meaningful lives showing us relate world around us others eg analytic philosophers see philosophy technical formal entirely theoretical discipline goals disinterested pursuit knowledge sake ref name pdp ''penguin dictionary philosophy'' ref proposed goals philosophy include discovering absolutely fundamental reason everything investigates making explicit nature significance ordinary scientific beliefs unifying transcending insights given science religion ref name mp ''mastering philosophy''


anthony harrison barbet ref others proposed philosophy complex discipline different dimensions boundaries defining philosophy boundaries problematic nigel warburton called notoriously difficult ref name ptb ref straightforward definition ref name mp interesting definitions controversial ref name ocp ref bertrand russell wrote ref bertrand russell ''the wisdom west'' p agreement philosophy involves general fundamental topics ref name pdp ref name odp ref clear agreement series demarcation issues including first order second order investigations authors say philosophical


inquiry second order concepts theories presupposition subject matter thinking thinking generally second order character ref name oxfordcne ref philosophers study rather use concepts structure thinking however ''oxford dictionary philosophy'' warns borderline 'second order' reflection ways practicing first order discipline always clear philosophical problems may tamed advance discipline conduct discipline may swayed philosophical reflection ref name odp philosophy empirical science argue philosophy distinct science


questions cannot answered empirically observation experiment ref name simons ref ref name gutting ref analytical philosophers argue meaningful empirical questions answered science philosophy however schools contemporary philosophy pragmatists naturalistic epistemologists argue philosophy linked science scientific broad sense term preferring see philosophical reflection continuous best practice field intellectual enquiry ref name odp philosophy religion argue philosophy distinct religion


philosophers use answer philosophical questions recently philosophers cast doubt intuition basic tool philosophical inquiry socrates contemporary philosophy language ''rethinking intuition'' various thinkers discard intuition valid source knowledge thereby call question 'a priori' philosophy experimental philosophy form philosophical inquiry makes least partial use empirical research especially ''opinion polling'' order address persistent philosophical questions contrast methods found analytic philosophy whereby say philosopher sometimes begin appealing


intuitions issue form argument intuitions premises however disagreement experimental philosophy accomplish widespread several philosophers offered criticisms one claim empirical data gathered experimental philosophers indirect effect philosophical questions allowing better understanding underlying psychological processes lead philosophical intuitions analytic philosophers like timothy williamson rejected move 'armchair' philosophy ie philosophical inquiry undergirded intuition construing 'intuition' believe misnomer merely referring common


cognitive faculties one calling question 'intuition' one would say harboring skeptical attitude towards common cognitive faculties consequence seems philosophically unappealing williamson instances intuition instances cognitive faculties processing counterfactuals subjunctive conditionals specific thought experiment example question progress prominent question metaphilosophy whether philosophical progress occurs whether progress philosophy even possible even disputed notably ludwig wittgenstein whether genuine philosophical problems actually exist opposite also


paperback ''philosophische untersuchungen'' ''philosophical investigations'' translated gem anscombe external links https webarchiveorg web http wwwblackwellpublishingcom journalaspref site ''metaphilosophy'' journal published blackwell peter suber http wwwearlhamedu peters courses meta topicshtm metaphilosophy themes questions personal list


greek mathematician euclid holding calipers rd century bc imagined raphael detail ''the school athens'' '''mathematics''' greek label none lit knowledge study learning translit th includes study topics numbers arithmetic number theory ref name oed ref formulas related structures algebra ref name kneebone ref shapes spaces contained geometry ref name oed quantities changes calculus analysis ref name latorre ref ref name ramana ref ref name ziegler ref general consensus exact scope epistemological status ref name mura ref ref name runge ref mathematical activity consists discovering proving pure reasoning properties abstract objects objects


either abstractions nature natural numbers line modern mathematics abstract entities defined basic properties called axioms proof consists succession applications deductive rules already known results including previously proved theorems axioms case abstraction nature basic properties considered true starting points theory consideration result proof called ''theorem'' contrary physical laws validity theorem truth rely experimentation correctness


reasoning though experimentation often useful discovering new theorems interest mathematics widely used science modeling phenomena enables extraction quantitative predictions experimental laws example movement planets predicted high accuracy using newton 's law gravitation combined mathematical computation independence mathematical truth experimentation implies accuracy predictions depends adequacy model describing reality inaccurate predictions arise means model must improved changed


mathematics wrong example perihelion precession mercury cannot explained newton 's law gravitation accurately explained einstein 's general relativity experimental validation einstein 's theory shows newton 's law gravitation approximation still accurate everyday life mathematics essential many fields including natural sciences engineering medicine finance computer science social sciences areas mathematics statistics game theory developed direct correlation applications often grouped name applied mathematics mathematical areas developed


independently application therefore called pure mathematics practical applications often discovered later ref name wigner fitting example problem integer factorization goes back euclid practical application use rsa cryptosystem security computer networks mathematics human activity far back written records exist however concept proof associated mathematical rigour first appeared greek mathematics notably euclid 's ''elements'' mathematics developed relatively slow pace renaissance algebra infinitesimal


calculus added arithmetic geometry main areas mathematics since interaction mathematical innovations scientific discoveries led rapid increase rate mathematical discoveries end th century foundational crisis mathematics led systematization axiomatic method turn gave rise dramatic increase number mathematics areas fields applications witness mathematics subject classification lists sixty first level areas mathematics areas mathematics abacus simple


calculating tool used since ancient times renaissance mathematics divided two main areas arithmetic devoted manipulation numbers geometry devoted study shapes also pseudo science numerology astrology clearly distinguished mathematics around renaissance two new main areas appeared introduction mathematical notation led algebra roughly speaking consists study manipulation formulas calculus shorthand ''infinitesimal calculus'' ''integral calculus'' study continuous functions model change relationship


varying quantities variables division four main areas remained valid end th century although areas celestial mechanics solid mechanics often considered mathematics considered belonging physics also subjects developed period predate mathematics divided different areas probability theory combinatorics later became regarded autonomous areas end th century foundational crisis mathematics resulting systematization axiomatic method led explosion amount


areas mathematics mathematics subject classification contains first level areas areas correspond older division four main areas case number theory modern name higher arithmetic geometry however several first level areas geometry name commonly considered belonging geometry algebra calculus appear first level areas split several first level areas first level areas exist th century example category theory homological algebra computer science


various parts mathematics notable example fermat 's last theorem stated pierre de fermat proved andrew wiles using among tools algebraic geometry specifically scheme theory category theory homological algebra another example goldbach 's conjecture asserts every even integer greater sum two prime numbers stated christian goldbach remains unproven despite considerable effort view diversity studied problems solving methods number theory presently split several subareas include analytic


number theory algebraic number theory geometry numbers method oriented diophantine equations transcendence theory problem oriented geometry geometry arithmetic one oldest branches mathematics started empirical recipes concerning shapes lines angles circles developed mainly need surveying architecture fundamental innovation elaboration proofs ancient greeks sufficient verify measurement say two lengths equal property must ''proved'' abstract reasoning previously proven results theorems basic properties considered self evident


basic subject proof postulates principle foundational mathematics elaborated sake geometry systematized euclid around bc book ''elements'' resulting euclidean geometry study shapes arrangements constructed lines planes circles euclidean plane plane geometry three dimensional euclidean space euclidean geometry developed without change methods scope th century ren descartes introduced called cartesian coordinates major change


paradigm since instead defining real numbers lengths line segments see number line allowed representation points using numbers coordinates use algebra later calculus solving geometrical problems split geometry two parts differ methods synthetic geometry uses purely geometrical methods analytic geometry uses coordinates systemically analytic geometry allows study new shapes particular curves related circles lines curves defined either graph functions whose study led differential geometry


avoiding different treatment intersecting parallel lines affine geometry study properties relative parallelism independent concept length differential geometry study curves surfaces generalizations defined using differentiable functions manifold theory study shapes necessarily embedded larger space riemannian geometry study distance properties curved spaces algebraic geometry study curves surfaces generalizations defined using polynomials topology study properties kept continuous deformations algebraic topology use


topology algebraic methods mainly homological algebra discrete geometry study finite configurations geometry convex geometry study convex sets takes importance applications optimization complex geometry geometry obtained replacing real numbers complex numbers x xsvg elliptic curve file hyperbolic trianglesvg triangle paraboloid file torussvg torus file mandel zoom satellitejpg fractal algebra algebra may viewed art manipulating equations formulas diophantus century al khowarazmi th century two main precursors algebra first one solved relations unknown natural numbers equations deducing


new relations getting solution second one introduced systematic methods transforming equations moving term side equation side term ''algebra'' derived arabic word used naming one methods title main treatise quadratic formula expresses concisely solutions quadratic equations algebra began specific area fran ois vi te introduced use letters variables representing unknown unspecified numbers allows describing consisely operations


done numbers represented variables th century algebra consisted mainly study linear equations called presently linear algebra polynomial equations single unknown called ''algebraic equations'' term still use although may ambiguous th century variables began represent things numbers matrices modular integers geometric transformations operations operate often generalizations arithmetic operations dealing concept algebraic structure introduced consist


set whose elements unspecified operations acting elements set rules operations must follow scope algebra evolved becoming essentially study algebraic structures object algebra called ''modern algebra'' abstract algebra latter term still used mainly educational context opposition elementary algebra concerned older way manipulating formulas rubik 's cube study possible moves concrete application group theory types algebraic structures properties useful often fundamental


many results presently calculus refers mainly elementary part theory analysis commonly used advanced parts analysis subdivided real analysis variables represent real numbers complex analysis variables represent complex numbers presently many subareas analysis shared areas mathematics include multivariable calculus functional analysis variables represent varying functions integration measure theory potential theory strongly related probability theory ordinary differential equations partial differential equations numerical analysis mainly devoted computation computers solutions ordinary


partial differential equations arise many applications mathematics discrete mathematics mathematical logic set theory subjects belong mathematics since end th century period sets considered mathematical objects logic although used mathematical proofs belonged philosophy specifically studied mathematicians study infinite sets georg cantor mathematicians reluctant consider collections actually infinite considered infinity result endless enumeration cantor 's work offended many mathematicians considering actually infinite sets also


showing implies different sizes infinity see cantor 's diagonal argument existence mathematical objects cannot computed even explicitly described example hamel bases real numbers rational numbers led controversy cantor 's set theory period appeared various areas mathematics former intuitive definitions basic mathematical objects insufficient insuring mathematical rigour examples intuitive definitions set collection objects natural number used counting point


shape zero length every direction curve trace left moving point etc origin foundational crisis mathematics eventually solved mainstream mathematics systematize axiomatic method inside formalized set theory roughly speaking mathematical object defined set similar objects properties objects must example peano arithmetic natural numbers defined zero number number unique successor number zero unique


predecessor rules reasoning nature objects defined way philosophical problem mathematicians leave philosophers even many mathematicians opinions nature use opinion sometimes called intuition guide study finding proofs approach allows considering logics sets allowed deducing rules theorems proofs etc mathematical objects prove theorems example g del 's incompleteness theorems assert roughly speaking every theory contains natural numbers theorems true provable larger theory


aspects computer science contributed turn expansion logical theories applied mathematics applied mathematics concerns mathematical methods typically used science engineering business industry thus applied mathematics mathematical science specialized knowledge term ''applied mathematics'' also describes professional specialty mathematicians work practical problems profession focused practical problems ''applied mathematics'' focuses formulation study use mathematical models science engineering areas mathematical practice past practical applications motivated development mathematical theories


became subject study pure mathematics mathematics developed primarily sake thus activity applied mathematics vitally connected research pure mathematics statistics decision sciences applied mathematics significant overlap discipline statistics whose theory formulated mathematically especially probability theory statisticians working part research project create data makes sense random sampling randomized experiments design statistical sample experiment specifies analysis data data becomes available reconsidering data


experiments samples analyzing data observational studies statisticians make sense data using art modelling theory inference model selection estimation estimated models consequential predictions tested new data statistical theory studies decision problems minimizing risk expected loss statistical action using procedure example parameter estimation hypothesis testing selecting best traditional areas mathematical statistics statistical decision problem formulated minimizing objective function like expected loss cost specific constraints


example designing survey often involves minimizing cost estimating population mean given level confidence ref name raoopt ref use optimization mathematical theory statistics shares concerns decision sciences operations research control theory mathematical economics ref name whittle ref computational mathematics computational mathematics proposes studies methods solving mathematical problems typically large human numerical capacity numerical analysis studies methods problems analysis using functional analysis approximation theory numerical analysis broadly includes study approximation discretisation special focus rounding errors


numerical analysis broadly scientific computing also study non analytic topics mathematical science especially algorithmic matrix graph theory areas computational mathematics include computer algebra symbolic computation style border px solid ddd text align center margin auto cellspacing px px px px px px px game theory fluid dynamics numerical analysis optimization probability theory statistics cryptography px px px px px px mathematical finance mathematical physics mathematical chemistry mathematical biology mathematical economics control theory history history


mathematics seen ever increasing series abstractions evolutionarily speaking first abstraction ever take place shared many animals probably numbers realization collection two apples collection two oranges example something common namely quantity members evidenced tallies found bone addition recognizing count physical objects prehistoric peoples may also recognized count abstract quantities like time days seasons years babylonian mathematical tablet plimpton dated nbsp bc evidence


complex mathematics appear around nbsp babylonians egyptians began using arithmetic algebra geometry taxation financial calculations building construction astronomy oldest mathematical texts mesopotamia egypt nbsp bc many early texts mention pythagorean triples inference pythagorean theorem seems ancient widespread mathematical concept basic arithmetic geometry babylonian mathematics elementary arithmetic addition subtraction multiplication division first appear archaeological record babylonians also possessed place value system


used sexagesimal numeral system still use today measuring angles time archimedes used method exhaustion approximate value pi beginning th century bc pythagoreans greek mathematics ancient greeks began systematic study mathematics subject right around bc euclid introduced axiomatic method still used mathematics today consisting definition axiom theorem proof book ''elements'' widely considered successful influential textbook time greatest mathematician antiquity often held


archimedes c bc syracuse developed formulas calculating surface area volume solids revolution used method exhaustion calculate area arc parabola summation infinite series manner dissimilar modern calculus notable achievements greek mathematics conic sections apollonius perga rd century bc trigonometry hipparchus nicaea nd century bc beginnings algebra diophantus rd century ad numerals used bakhshali manuscript dated nd century bc nd


century ad hindu arabic numeral system rules use operations use throughout world today evolved course first millennium ad india transmitted western world via islamic mathematics notable developments indian mathematics include modern definition approximation sine cosine early form infinite series page al khw rizm 's ''algebra'' leonardo fibonacci italian mathematician introduced hindu arabic numeral system invented st th nbsp centuries indian mathematicians western world golden age islam


especially th th nbsp centuries mathematics saw many important innovations building greek mathematics notable achievement islamic mathematics development algebra achievements islamic period include advances spherical trigonometry addition decimal point arabic numeral system many notable mathematicians period persian al khwarismi omar khayyam sharaf al n al early modern period mathematics began develop accelerating pace western europe development calculus isaac newton gottfried leibniz th century revolutionized mathematics leonhard


euler notable mathematician th century contributing numerous theorems discoveries perhaps foremost mathematician th century german mathematician carl gauss made numerous contributions fields algebra analysis differential geometry matrix theory number theory statistics early th century kurt g del transformed mathematics publishing incompleteness theorems show part consistent axiomatic system powerful enough describe arithmetic contain true propositions cannot proved mathematics since greatly extended fruitful interaction mathematics science


one gets know hence also study science word mathematics came narrower technical meaning mathematical study even classical times adjective ''math matik s'' meaning related learning studious likewise came mean mathematical particular ''math matik khn '' meant mathematical art similarly one two main schools thought pythagoreanism known ''math matikoi'' time meant learners rather mathematicians modern sense latin english around term ''mathematics'' commonly meant astrology


sometimes astronomy rather mathematics meaning gradually changed present one resulted several mistranslations example saint augustine 's warning christians beware ''mathematici'' meaning astrologers sometimes mistranslated condemnation mathematicians ref name boas ref apparent plural form english like french plural form less commonly used singular derivative goes back latin neuter plural cicero based greek plural ''ta math matik '' used aristotle nbsp bc meaning roughly things mathematical although plausible english


borrowed adjective ''mathematic al '' formed noun ''mathematics'' anew pattern ''physics'' ''metaphysics'' inherited greek english noun ''mathematics'' takes singular verb often shortened ''maths'' north america ''math'' ref name maths http oedcom view entry maths ''n'' http oedcom view entry math ''n '' ''oxford english dictionary'' line version ref philosophy mathematics general consensus exact definition epistemological status mathematics ref name mura ref name runge aristotle defined mathematics science quantity definition prevailed th century however aristotle also noted focus


quantity alone may distinguish mathematics sciences like physics view abstraction studying quantity property separable thought real instances set mathematics apart ref name franklin ref th nbsp century study mathematics increased rigor began address abstract topics group theory projective geometry clear cut relation quantity measurement mathematicians philosophers began propose variety new definitions ref name cajori ref great many professional mathematicians take interest definition mathematics consider undefinable ref name mura even consensus


whether mathematics art science ref name runge say mathematics mathematicians ref name mura three leading types three leading types definition mathematics today called logicist intuitionist formalist reflecting different philosophical school thought ref name snapper ref severe flaws none widespread acceptance reconciliation seems possible ref name snapper logicist definitions early definition mathematics terms logic benjamin peirce science draws necessary conclusions ref name peirce ref ''principia mathematica'' bertrand russell alfred north whitehead


advanced philosophical program known logicism attempted prove mathematical concepts statements principles defined proved entirely terms symbolic logic example logicist definition mathematics russell 's mathematics symbolic logic ref name russell ref intuitionist definitions intuitionist definitions developing philosophy mathematician l e j brouwer identify mathematics certain mental phenomena example intuitionist definition mathematics mental activity consists carrying constructs one ref name snapper peculiarity intuitionism rejects


math strictly weaker statement math p math ref name sep p ref formalist definitions formalist definitions identify mathematics symbols rules operating haskell curry defined mathematics simply science formal systems formal system set symbols ''tokens'' ''rules'' tokens combined ''formulas'' formal systems word ''axiom'' special meaning different ordinary meaning self evident truth used refer combination tokens included given formal system


shall certainly admit system empirical scientific capable tested experience mathematics shares much common many fields physical sciences notably exploration logical consequences assumptions intuition experimentation also play role formulation conjectures mathematics sciences experimental mathematics continues grow importance within mathematics computation simulation playing increasing role sciences mathematics several authors consider mathematics science rely empirical


evidence ref name bishop ref ref name nickles ref ref name pigliucci ref opinions mathematicians matter varied many mathematicians feel call area science downplay importance aesthetic side history traditional seven liberal arts others feel ignore connection sciences turn blind eye fact interface mathematics applications science engineering driven much development mathematics one way difference viewpoint plays philosophical debate whether mathematics ''created''


art ' 'discovered'' science practice mathematicians typically grouped scientists gross level separated finer levels one many issues considered philosophy mathematics inspiration pure applied mathematics aesthetics mathematics arises many different kinds problems first found commerce land measurement architecture later astronomy today sciences pose problems studied mathematicians many problems arise within mathematics example physicist richard feynman invented path integral formulation quantum mechanics using combination mathematical reasoning


physical insight today 's string theory still developing scientific theory attempts unify four fundamental forces nature continues inspire new mathematics mathematics relevant area inspired applied solve problems area often mathematics inspired one area proves useful many areas joins general stock mathematical concepts distinction often made pure mathematics applied mathematics however pure mathematics topics often turn applications eg number theory cryptography remarkable fact even purest mathematics


often turns practical applications physicist eugene wigner named unreasonable effectiveness mathematics ref name wigner ref philosopher mathematics mark steiner written extensively matter acknowledges applicability mathematics constitutes challenge naturalism philosopher mathematics mary leng fact physical world acts accordance dictates non causal mathematical entities existing beyond universe happy coincidence ref name mathematics reality ref hand anti realists connections acquired among mathematical things mirror connections acquiring among


objects universe happy coincidence ref name mathematics reality areas study explosion knowledge scientific age led specialization hundreds specialized areas mathematics latest mathematics subject classification runs nbsp pages several areas applied mathematics merged related traditions outside mathematics become disciplines right including statistics operations research computer science mathematically inclined often definite aesthetic aspect much mathematics many mathematicians talk ''elegance''


mathematics intrinsic aesthetics inner beauty simplicity generality valued beauty simple elegant proof euclid 's proof infinitely many prime numbers elegant numerical method speeds calculation fast fourier transform g h hardy ''a mathematician 's apology'' expressed belief aesthetic considerations sufficient justify study pure mathematics identified criteria significance unexpectedness inevitability economy factors contribute mathematical aesthetic mathematical research often seeks critical features


mathematical object theorem expressed characterization object features prize examples particularly succinct revelatory mathematical arguments published ''proofs book'' popularity recreational mathematics another sign pleasure many find solving mathematical questions social extreme philosophers continue find problems philosophy mathematics nature mathematical proof notation language rigor leonhard euler created popularized much mathematical notation used today mathematical notation use today invented


th century mathematics written words limiting mathematical discovery euler responsible many notations use today modern notation makes mathematics much easier professional beginners often find daunting according barbara oakley attributed fact mathematical ideas ''abstract'' ''encrypted'' natural language unlike natural language people often equate word ''cow'' physical object corresponds mathematical symbols abstract lacking physical analog mathematical symbols also highly


encrypted regular words meaning single symbol encode number different operations ideas mathematical language difficult understand beginners even common terms ''or'' ''only'' precise meaning everyday speech terms ''open'' ''field'' refer specific mathematical ideas covered laymen 's meanings mathematical language also includes many technical terms ''homeomorphism'' ''integrable'' meaning outside mathematics additionally shorthand phrases ''iff'' belong mathematical jargon


reason special notation technical vocabulary mathematics requires precision everyday speech mathematicians refer precision language logic rigor mathematical proof fundamentally matter rigor mathematicians want theorems follow axioms means systematic reasoning avoid mistaken theorems based fallible intuitions many instances occurred history subject level rigor expected mathematics varied time greeks expected detailed arguments time isaac newton methods employed less rigorous problems


inherent definitions used newton would lead resurgence careful analysis formal proof th nbsp century misunderstanding rigor notable cause common misconceptions mathematics today mathematicians continue argue among computer assisted proofs since large computations hard verify proofs may erroneous used computer program erroneous hand proof assistants allow verification details cannot given hand written proof provide certainty correctness long proofs


million dollar reward currently one problems poincar conjecture solved see also international mathematical olympiad list mathematical jargon outline mathematics lists mathematics topics mathematical sciences mathematics art mathematics education national museum mathematics philosophy mathematics relationship mathematics physics science technology engineering mathematics notes references wwwascdorg ref ref name devlin devlin keith ''mathematics science patterns search order life mind universe'' scientific american paperback library ref bibliography reading nbsp translated expanded version soviet


mathematics encyclopedia ten volumes also paperback cd rom http wwwencyclopediaofmathorg online formal sciences main topic articles


metaphilosophy ethics '''meta ethics''' study nature scope meaning moral judgment one three branches ethics generally studied philosophers others normative ethics questions one ought act applied ethics practical questions right behavior given usually contentious situations normative ethics addresses questions evaluating specific practices principles action meta ethics addresses questions ''is'' goodness tell good bad seeking understand

Humanities Philosophy Ethics Meta-ethics


assumptions underlying normative theories another distinction often made normative ethics involves first order substantive questions meta ethics involves second order formal questions theorists argue metaphysical account morality necessary proper evaluation actual moral theories making practical moral decisions others reason opposite premises suggest studying moral judgments proper actions guide us true account nature morality meta ethical questions according richard garner bernard rosen three kinds meta ethical problems three general questions ref name garner rosen ref


meaning moral terms judgments moral semantics asks meanings words 'good' 'bad' 'right' 'wrong' see value theory nature moral judgments moral ontology asks questions whether moral judgments absolute relative one kind many kinds etc may moral judgments supported defended moral epistemology asks questions know something right wrong garner rosen say answers three basic questions unrelated sometimes answer one


strongly suggest perhaps even entail answer another ref name garner rosen meta ethical theory unlike normative ethical theory attempt evaluate specific choices better worse good bad evil although may profound implications validity meaning normative ethical claims answer three example questions would normative ethical statement moral semantics '''moral semantics''' attempts answer question meaning moral terms judgments answers may implications answers two


questions well cognitivist theories ''cognitivist'' theories hold evaluative moral sentences express propositions ie 'truth apt' 'truth bearers' capable true false opposed non cognitivism forms cognitivism hold propositions true including moral realism ethical subjectivism opposed error theory asserts erroneous moral realism moral realism ''robust'' sense cf moral universalism minimalist sense holds propositions ''robust'' mind independent facts facts person group 's subjective opinion


g e moore holds objective ''irreducible'' moral properties property 'goodness' sometimes intuitive otherwise ''a priori'' awareness moral properties moral truths moore 's open question argument considered naturalistic fallacy largely responsible birth meta ethical research contemporary analytic philosophy ethical subjectivism ethical subjectivism one form moral anti realism holds moral statements made true false attitudes conventions people either society individual


god approve right non god beings obedience divine view criticized plato ''euthyphro'' see euthyphro problem retains modern defenders robert adams philip quinn others like ideal observer theory divine command theory purports universalist despite subjectivism error theory error theory another form moral anti realism holds although ethical claims express propositions propositions false thus statement murder morally wrong statement murder morally permissible false according


error theory j l mackie probably best known proponent view since error theory denies moral truths error theory entails moral nihilism thus moral skepticism however neither moral nihilism moral skepticism conversely entail error theory non cognitivist theories non cognitivist theories hold ethical sentences neither true false express genuine propositions non cognitivism another form moral anti realism forms non cognitivism also forms expressivism however mark timmons terrence horgan distinguish two allow possibility cognitivist forms


expressivism non cognitivism includes '''emotivism''' defended j ayer charles stevenson holds ethical sentences serve merely express emotions ayer argues ethical sentences expressions approval disapproval assertions killing wrong means something like boo killing '''quasi realism''' defended simon blackburn holds ethical statements behave linguistically like factual claims appropriately called true false even though ethical facts correspond projectivism moral fictionalism related theories '''universal prescriptivism''' defended r hare holds moral statements function like universalized imperative


sentences killing wrong means something like n't kill hare 's version prescriptivism requires moral prescriptions universalizable hence actually objective values spite failing indicative statements truth values per se centralism non centralism yet another way categorizing meta ethical theories distinguish '''centralist''' '''non centralist''' moral theories debate centralism non centralism revolves around relationship called thin thick concepts morality thin moral concepts good bad right wrong thick moral concepts courageous inequitable dishonest


sides agree thin concepts general thick specific centralists hold thin concepts antecedent thick ones latter therefore dependent former centralists argue one must understand words like right ought understanding words like unkind non centralism rejects view holding thin thick concepts par one another even thick concepts sufficient starting point understanding thin ones non centralism particular importance ethical naturalists


late th early st centuries part argument normativity non excisable aspect language way analyzing thick moral concepts purely descriptive element attached thin moral evaluation thus undermining fundamental division facts norms allan gibbard r hare simon blackburn argued favor fact norm distinction meanwhile gibbard going far argue even conventional english mixed normative terms terms neither purely descriptive purely normative could develop


nominally english metalanguage still allowed us maintain division factual descriptions normative evaluations moral ontology '''moral ontology''' attempts answer question nature moral judgments amongst believe standard morality opposed moral nihilists two divisions universalists hold moral facts principles apply everyone everywhere relativists hold different moral facts principles apply different people societies moral universalism moral universalism '''universal morality''' meta ethical position


system ethics universal ethic applies universally intelligent beings regardless culture race sex religion nationality sexuality distinguishing feature source justification system may thought instance human nature shared vulnerability suffering demands universal reason common among existing moral codes common mandates religion although argued latter fact moral universalism may distinguish gods mortals moral universalism opposing position various forms moral relativism universalist


theories generally forms moral realism though exceptions exists subjectivist ideal observer divine command theories non cognitivist universal prescriptivism r hare forms moral universalism include '''value monism''' common form universalism holds goods commensurable single value scale '''value pluralism''' contends two genuine scales value knowable yet incommensurable prioritization values either non cognitive subjective value pluralist might example contend life nun


life mother realize genuine values universalist sense yet incompatible nuns may children purely rational way measure preferable notable proponent view isaiah berlin moral relativism moral relativism maintains moral judgments origins either societal individual standards single standard exists one objectively assess truth moral proposition meta ethical relativists general believe descriptive properties terms good bad right wrong


stand subject universal truth conditions societal convention personal preference given set verifiable facts societies individuals fundamental disagreement one ''ought'' based societal individual norms one cannot adjudicate using independent standard evaluation latter standard always societal personal universal unlike example scientific standards assessing temperature determining mathematical truths moral nihilism moral nihilism also known ethical nihilism meta ethical view nothing intrinsic moral value


example moral nihilist would say killing someone whatever reason intrinsically neither morally right morally wrong moral nihilism must distinguished moral relativism allow moral statements intrinsically true false non universal sense assign static truth values moral statements insofar true statements known moral nihilists moral skeptics forms moral nihilism non cognitivist vice versa though notable exceptions universal prescriptivism semantically non cognitive substantially universal moral epistemology '''moral epistemology'''


study moral knowledge attempts answer questions may moral judgments supported defended moral knowledge possible one presupposes cognitivist interpretation moral sentences morality justified moralist 's knowledge moral facts theories justify moral judgements epistemological theories moral epistemologies posit moral knowledge somehow possible including empiricism moral rationalism opposed moral skepticism amongst hold moral knowledge gained inferentially basis sort non moral epistemic process opposed ethical


rational process individualist ethical subjectivism holds moral facts merely personal opinions may known introspection empirical arguments ethics run ''is ought'' problem asserts way world ''is'' cannot alone instruct people ''ought'' act moral rationalism moral rationalism also called ethical rationalism view according moral truths least general moral principles knowable ''a priori'' reason alone prominent figures history philosophy defended moral rationalism plato immanuel kant


perhaps prominent figures history philosophy rejected moral rationalism david hume friedrich nietzsche recent philosophers defended moral rationalism include r hare christine korsgaard alan gewirth michael smith moral rationalist may adhere number different semantic theories well moral realism compatible rationalism subjectivist ideal observer theory non cognitivist universal prescriptivism entail ethical intuitionism ethical intuitionism view according moral truths known ''without'' inference view core


hare https wwwgutenbergorg ebooks ''groundwork metaphysics morals'' immanuel kant https webarchiveorg web http homesprynetcom owl ethicshtm essays philosopher michael huemer meta ethics especially intuitionism http wwwmoralbalancecom english ch html ''relativity theory ethics'' j j mittler ethics metaphilosophy


'''mass deacidification''' term used library information science one possible measure degradation paper old books called slow fires goal process increase ph acidic paper large scale although acid free paper become common large body acidic paper still exists books made cheaper simpler production methods acidic paper especially exposed light air pollution high relative humidity yellows becomes brittle time mass deacidification alkaline agent deposited

Applied science
Library and museum studies
Mass deacidification


used mass deacidification treatment single item deacidification wei t'o products available wei t'o associates inc matteson usa bookkeeper csc booksaver papersave wei t'o also available hand held sprays goals results library congress expected ideal mass deacidification treatment neutralize acidic paper add alkaline reserve produce ph value evenly distributed throughout book cause damage adhesives inks dyes cause odor change color


library congress team scientists centre de recherches sur la conservation des documents graphiques early mid nineties bookkeeper produced ph ref name loc csc book saver gives ph wei t'o gives papersave gives ph studies also found processes adverse cosmetic side effects bookkeeper left palpable residue clamp marks covers caused colored inks rub ref name loc csc book saver left white powdery deposit books papersave caused


formed association research libraries arl barrow also invented aqueous process neutralize acid paper depositing alkaline buffer would retard rate decay ref name ritzenthaler ritzenthaler ''preserving archives manuscripts'' ref addition barrow 's original method non aqueous nbsp employing organic solvents nbsp vaporous nbsp library congress' dez diethyl zinc treatment nbsp methods achieving results researched attempt reduce time labor cost requirements ref name ifla pillete r http wwwiflaorg iv ifla papers e pilettepdf mass deacidification preservation option libraries ''world library information congress th ifla general


pilot plant mass deacidification using process constructed nasa tested books provided library congress however discovered dez removed one deacidification runs pooled bottom chamber probably remained within plumbing dez violently flammable comes contact either oxygen water vapor vacuum chamber could opened remove books within eventually explosives used rupture suspect plumbing


suspicions presence residual dez confirmed subsequent fire destroyed plant book double fold nicholson baker discusses failure nasa program great length chemical company akzo made later attempts refining process though risks fire explosions reduced better process design damage odours remained problem end akzo decided process viable commercial proposition shut research end adoption costs deacidification adopted major research


libraries library congress new york public library clear many archives particularly united states followed suit whereas european national archives tested deacidification techniques united states' national archives records administration nara pioneered aqueous technique improved upon barrow 's chosen invest preservation dollars elsewhere ref name ritzenthaler chief nara document conservation laboratory defended lack mass deacidification program pointing differences library archival collections example noting many


papers coming nara higher quality library collections archives receive records federal government agencies least years old time acidic paper already irrevocably weakened limited resources might best applied elsewhere climate control archives' twenty year preservation plan emphasis maximum benefit greatest number records though dated several sources estimate costs suitability deacidification treatment studies conducted harry ransom humanities research center


general state archive netherlands found dez method properly used might particularly applicable archival materials estimated deacidification costs excluding transportation handling early per volume library congress received million appropriations deacidify books using bookkeeper commercial method evaluate alternative methods actual cost per book finally recent cost comparison reformatting options per volume yielded microfilming scanning minimal indexing based new york public library project deacidification ref


name ifla see also preservation library archival science ''double fold'' paper pulp paper preservation survey foxing references external links https wwwlocgov preserv pubsdeachtml library congress' links mass deacidification publications http wwwcci iccgcca publications cidb view document easpxdocument id canadian conservation institute 's study evaluating commercial deacidification processes http wwwclirorg pubs reports sparks sparkshtml council library information resources report technical considerations choosing mass deacidification process preservation library archival science


'''molecular biology''' branch biology seeks understand molecular basis biological activity cells including molecular synthesis modification mechanisms interactions ref name cell ref ref name ref study chemical physical structure biological macromolecules known molecular biology ref name ref molecular biology first described approach focused underpinnings biological phenomena uncovering structures biological molecules well interactions interactions explain observations classical biology ref name ref term molecular biology used physicist william astbury development

Natural science
Biology
Molecular biology


dna material microorganisms plants animals ref name molecular biology simply study biological molecules interactions rather also collection techniques developed since field 's genesis enabled scientists learn molecular processes ref name ref one notable technique revolutionized field polymerase chain reaction pcr developed ref name pcr reaction amplifies small quantities dna used many applications across scientific disciplines discussed later central dogma molecular biology describes process


dna transcribed rna translated protein ref name molecular biology also plays critical role understanding structures functions internal controls within individual cells used efficiently target new drugs diagnose disease better understand cell physiology clinical research medical therapies arising molecular biology covered gene therapy whereas use molecular biology molecular cell biology medicine referred molecular medicine history molecular biology molecular biology sits intersection biochemistry genetics


basic composition dna known contains four bases known adenine guanine thymine cytosine bases chemical composition x ray crystallography done maurice wilkins rosalind franklin dna structure proposed james watson francis crick watson crick proposed dna structure austrian born scientist erwin chargaff proposed theory rule today known chargaff 's rule stated number adenine thymine guanine cytosine equal proportion ref name chargaff 's rule chargaff 's


rule stated dna ''from species organism stoichiometric ratio of'' purine ''and pyrimidines ie g c specifically amount of'' guanine ' 'should equal to'' cytosine ''and amount adenine equal to'' thymine'' pattern found strands dna '' ref name field genetics arose attempt understand molecular mechanisms genetic inheritance structure gene gregor mendel pioneered work first wrote laws genetic inheritance based studies


scitable url http wwwnaturecom scitable topicpage discovery dna structure function watson access date website wwwnaturecom language en ref discovered unique substance studying components pus filled bandages noting unique properties phosphorus containing substances another notable contributor dna model phoebus levene proposed polynucleotide model dna result biochemical experiments yeast erwin chargaff expanded work levene elucidated critical properties nucleic acids first sequence nucleic acids varies across species second total concentration purines adenine guanine always equal total concentration pyrimidines cysteine thymine ref name auto


known chargaff 's rule james watson francis crick published double helical structure dna ref name ref using x ray crystallography work done rosalind franklin maurice wilkins watson crick described structure dna conjectured implications unique structure possible mechanisms dna replication ref name j watson f h c crick awarded nobel prize along maurice wilkens proposing model structure dna ref name time pass k marcker frederick sanger


discovered peculiar amioacyl trna ecoli called n formyl methionyl trna explained molecule play role special mechanism chain elongation awarded second nobel prize discovering complete sequence nucleotides single stranded dna f bacteriophages ref name demonstrated gene encodes protein three sequential bases gene 's dna specify successive amino acid protein thus genetic code triplet code triplet called codon specifies particular amino acid furthermore


shown codons overlap dna sequence encoding protein sequence read fixed starting point use conditional lethal mutants bacterial virus fundamental advances made understanding functions interactions proteins employed machinery dna replication dna repair dna recombination assembly molecular structuresdiagrammatic representation watson crick 's dna structure angle description dna structure fgriffith experiment diagrammatic representation experiment


fredrick griffith encountered virulence property pneumococcus bacteria killing lab rats according mendel prevalent time gene transfer could occur parent daughter cells griffith advanced another theory stating gene transfer occurring member generation known horizontal gene transfer hgt phenomenon referred genetic transformation griffith addressed ''streptococcus pneumoniae'' bacteria two different strains one virulent smooth one avirulent rough smooth strain glistering appearance owing presence type specific polysaccharide


polymer glucose glucuronic acid capsule due polysaccharide layer bacteria host 's immune system cannot recognize bacteria kills host avirulent rough strain lacks polysaccharide capsule dull rough appearance presence absence capsule strain known genetically determined smooth rough strains occur several different type ii iii etc r r ii r iii etc respectively subtypes r bacteria differ antigen type produce ref name hershey


chase experiment hershey chase experiment confirmation dna genetic material cause infection came hershey chase experiment used ''ecoli'' bacteriophage experiment experiment also known blender experiment kitchen blender used major piece apparatus ''alfred hershey'' ''martha chase'' demonstrated dna injected phage particle bacterium contains information required synthesize progeny phage particles used radioactivity tag bacteriophage 's protein coat radioactive sulphur dna radioactive phosphorus two different test


tubes respectively mixing bacteriophage ''ecoli'' test tube incubation period starts phage transforms genetic material ''ecoli'' cells mixture blended agitated separates phage ''ecoli'' cells whole mixture centrifuged pellet contains ''ecoli'' cells checked supernatant discarded ''ecoli'' cells showed radioactive phosphorus indicated transformed material dna protein coat transformed dna gets attached dna ''ecoli'' radioactivity seen onto bacteriophage 's dna mutated dna


passed next generation theory transduction came existence transduction process bacterial dna carry fragment bacteriophages pass next generation also type horizontal gene transfer ref name relationship biological sciences schematic relationship biochemistry genetics molecular biology following list describes viewpoint interdisciplinary relationships molecular biology related fields '''''molecular biology''''' study molecular underpinnings biological phenomena focusing molecular synthesis modification mechanisms interactions '''''biochemistry'''''


study chemical substances vital processes occurring living organisms biochemists focus heavily role function structure biomolecules proteins lipids carbohydrates nucleic acids '''''genetics''''' study genetic differences affect organisms genetics attempts predict mutations individual genes genetic interactions affect expression phenotype researchers practice techniques specific molecular biology common combine methods genetics biochemistry much molecular biology quantitative recently significant amount work done using computer science


techniques bioinformatics computational biology molecular genetics study gene structure function among prominent sub fields molecular biology since early branches biology informed molecular biology either directly studying interactions molecules right cell biology developmental biology indirectly molecular techniques used infer historical attributes populations species fields evolutionary biology population genetics phylogenetics also long tradition studying biomolecules ground


molecularly biophysics ref name tian ref techniques molecular biology dna animation molecular cloning transduction image molecular cloning used isolate transfer dna sequence interest plasmid vector recombinant dna technology first developed 's technique dna sequence coding protein interest cloned using polymerase chain reaction pcr restriction enzymes plasmid expression vector plasmid vector distinctive features origin replication multiple cloning site mcs selective marker usually antibiotic resistance additionally upstream mcs promoter


regions transcription start site regulate expression cloned gene plasmid inserted either bacterial animal cells introducing dna bacterial cells done transformation via uptake naked dna conjugation via cell cell contact transduction via viral vector introducing dna eukaryotic cells animal cells physical chemical means called transfection several different transfection techniques available calcium phosphate transfection electroporation microinjection liposome transfection plasmid may integrated genome resulting stable transfection may remain independent


genome called transient transfection ref name cell ref dna coding protein interest inside cell protein expressed variety systems inducible promoters specific cell signaling factors available help express protein interest high levels large quantities protein extracted bacterial eukaryotic cell protein tested enzymatic activity variety situations protein may crystallized tertiary structure studied pharmaceutical industry activity new drugs


protein studied polymerase chain reaction polymerase chain reaction pcr extremely versatile technique copying dna brief pcr allows specific dna sequence copied modified predetermined ways reaction extremely powerful perfect conditions could amplify one dna molecule become billion molecules less two hours pcr many applications including study gene expression detection pathogenic microorganisms detection genetic mutations introduction mutations dna pcr technique used introduce restriction enzyme sites ends


dna molecules mutate particular bases dna latter method referred site directed mutagenesis pcr also used determine whether particular dna fragment found cdna library pcr many variations like reverse transcription pcr rt pcr amplification rna recently quantitative pcr allow quantitative measurement dna rna moleculesagarose gel borate buffer cast gel tray gel electrophoresis left gel electrophoresis technique separates molecules size using agarose polyacrylamide gel ref name ref technique one


principal tools molecular biology basic principle dna fragments separated applying electric current across gel dna backbone contains negatively charged phosphate groups dna migrate agarose gel towards positive end current ref name proteins also separated basis size using sds page gel basis size electric charge using known gel electrophoresis proteins stained page gel using coomassie blue dye bradford assay


bind coomassie blue minutes protein dye complex stable hour although 's recommended absorbance readings taken within minutes reaction initiation ref name concentration protein bradford assay measured using visible light spectrophotometer therefore require extensive equipment ref name method developed marion bradford enabled significantly faster accurate protein quantitation compared previous methods lowry procedure biuret assay ref name unlike previous methods bradford assay


susceptible interference several non protein molecules including ethanol sodium chloride magnesium chloride ref name however susceptible influence strong alkaline buffering agents sodium dodecyl sulfate sds ref name macromolecule blotting probing terms ''northern'' ''western'' ''eastern'' blotting derived initially molecular biology joke played term ''southern blotting'' technique described edwin southern hybridisation blotted dna patricia thomas developer rna blot became known ''northern blot'' actually n't use term southern blotting


named inventor biologist edwin southern southern blot method probing presence specific dna sequence within dna sample dna samples restriction enzyme restriction endonuclease digestion separated gel electrophoresis transferred membrane blotting via capillary action membrane exposed labeled dna probe complement base sequence sequence dna interest southern blotting less commonly used laboratory science due capacity techniques pcr detect specific dna


sequences dna samples blots still used applications however measuring transgene copy number transgenic mice engineering gene knockout embryonic stem cell lines ref name tian northern blotting northern blot diagram northern blot used study presence specific rna molecules relative comparison among set different samples rna essentially combination denaturing rna gel electrophoresis blot process rna separated based size transferred membrane probed


labeled complement sequence interest results may visualized variety ways depending label used however result revelation bands representing sizes rna detected sample intensity bands related amount target rna samples analyzed procedure commonly used study much gene expression occurring measuring much rna present different samples assuming post transcriptional regulation occurs levels mrna reflect proportional


levels corresponding protein produced one basic tools determining time conditions certain genes expressed living tissues western blotting western blot technique specific proteins detected mixture proteins ref name western blots used determine size isolated proteins well quantify expression western blotting proteins first separated size thin gel sandwiched two glass plates technique known sds page proteins


gel transferred polyvinylidene fluoride pvdf nitrocellulose nylon support membrane membrane probed solutions antibodies antibodies specifically bind protein interest visualized variety techniques including colored products chemiluminescence autoradiography often antibodies labeled enzymes chemiluminescent substrate exposed enzyme allows detection using western blotting techniques allows detection also quantitative analysis analogous methods western blotting used directly stain specific proteins live cells tissue sections ref


name ref eastern blotting eastern blotting technique used detect post translational modification proteins proteins blotted pvdf nitrocellulose membrane probed modifications using specific substrates microarrays dna microarray printed hybridization target probe dna microarray collection spots attached solid support microscope slide spot contains one single stranded dna oligonucleotide fragments arrays make possible put large quantities small micrometre diameter spots single slide spot dna fragment molecule


complementary single dna sequence variation technique allows gene expression organism particular stage development qualified expression profiling technique rna tissue isolated converted labeled complementary dna cdna cdna hybridized fragments array visualization hybridization done since multiple arrays made exactly position fragments particularly useful comparing gene expression two different tissues healthy cancerous tissue also one


measure genes expressed expression changes time factors many different ways fabricate microarrays common silicon chips microscope slides spots micrometre diameter custom arrays arrays larger spots porous membranes macroarrays anywhere spots given array arrays also made molecules dna allele specific oligonucleotide allele specific oligonucleotide aso technique allows detection single base mutations without need pcr gel electrophoresis short


nucleotides length labeled probes exposed non fragmented target dna hybridization occurs high specificity due short length probes even single base change hinder hybridization target dna washed labeled probes n't hybridize removed target dna analyzed presence probe via radioactivity fluorescence experiment molecular biology techniques control must used ensure successful experimentation molecular biology procedures technologies continually developed older technologies abandoned example


advent dna gel electrophoresis agarose polyacrylamide size dna molecules typically determined rate sedimentation sucrose gradients slow labor intensive technique requiring expensive instrumentation prior sucrose gradients viscometry used aside historical interest often worth knowing older technology occasionally useful solve another new problem newer technique inappropriate see also references reading external links


specialist midwife '''midwifery''' health science health profession deals pregnancy childbirth postpartum period including care newborn addition sexual reproductive health women throughout lives many countries midwifery medical profession special independent direct specialized education confused medical specialty depends previous general training professional midwifery known midwife cochrane review concluded women offered midwifery led continuity models care women

Applied science
Medicine and health
Midwifery


encouraged ask option although caution exercised applying advice women substantial medical obstetric complications ref name sandall review found midwifery led care associated reduction use epidurals fewer episiotomies instrumental births decreased risk losing baby weeks' gestation however midwifery led care also associated longer mean length labor measured hours ref name sandall main areas midwifery pregnancy first trimester trimester means three months normal pregnancy lasts nine months


three trimesters ref name medlineplus first trimester screening varies country women typically offered urine analysis ua blood tests including complete blood count cbc blood typing including rh screen syphilis hepatitis hiv rubella testing ref name medlineplus additionally women may chlamydia testing via urine sample women considered high risk screened sickle cell disease thalassemia ref name medlineplus women must consent tests carried woman 's blood pressure height weight measured past pregnancies family social medical history discussed


women may ultrasound scan first trimester may used help find estimated due date women may genetic testing screening syndrome diet exercise common disorders pregnancy morning sickness discussed ref name medlineplus ref image shows progression pregnancy three trimesters second trimester mother visits midwife monthly often second trimester mother 's partner birth companion may accompany midwife discuss pregnancy issues fatigue heartburn varicose veins


common problems back pain blood pressure weight monitored midwife measures mother 's abdomen see baby growing expected lab tests ua cbc glucose tolerance test done clinically indicated ref name medlineplus ref third trimester third trimester midwife see mother every two weeks week every week weight blood pressure abdominal measurements continue done lab tests cbc ua may done additional testing done


risk pregnancies midwife palpates woman 's abdomen establish lie presentation position fetus later engagement pelvic exam may done see mother 's cervix dilating ref name medlineplus ref midwife mother discuss birthing options write birth care plan childbirth labor delivery illustration normal head first presentation membranes ruptured cervix fully dilated newborn rests caregiver checks breath sounds midwives qualified assist normal vaginal delivery complicated deliveries


handled health care provider training childbirth divided four stages '''first stage labor''' first stage labour involves opening cervix ref name ref early parts stage cervix become soft thin thus preparing delivery baby ref name first stage labour complete cervix dilated full cm ref name first stage labor mother begins feel strong regular contractions come every minutes last


seconds contractions gradually become stronger frequent longer lasting '''second stage labor''' second stage baby begins move birth canal baby moves opening vagina crowns meaning top head seen vaginal entrance one time episiotomy incision tissue opening vagina done routinely believed prevented excessive tearing healed readily natural tear ref name mayo clinic however recent research


must deliver placenta ref name order mother may need push like contractions first stage labour may experience one two ref name midwife may assist mother delivering placenta gently pulling umbilical cord ref name '''fourth stage labor''' fourth stage labor period beginning immediately birth extending six weeks world health organization describes period critical yet neglected phase


lives mothers babies ref name world health organization ref recently babies routinely removed mothers following birth however beginning around authorities began suggest early skin skin contact placing naked baby mother 's chest benefit mother infant early skin skin contact endorsed major organizations responsible well infants ref name medscape ref thus help establish bonding successful breastfeeding midwife carries immediate mother infant assessments infant lies mother 's chest removes


infant observations first breastfeed following birth mother episiotomy tearing perineum sutured midwife regular assessments uterine contraction fundal height ref name maternal newborn care ref vaginal bleeding ref name labor delivery postpartum care ref throughout labor delivery mother 's vital signs temperature blood pressure pulse closely monitored fluid intake output measured midwife also monitors baby 's pulse rate palpates mother 's abdomen monitor baby 's position vaginal examinations indicated


birth deviates norm stage midwife requests assistance multi disciplinary team birthing positions last century women used upright position alternative positions give birth lithotomy position used advent forceps seventeenth century since childbirth progressively moved woman supported experience home medical intervention within hospital significant advantages assuming upright position labor birth stronger efficient uterine contractions


aiding cervical dilatation increased pelvic inlet outlet diameters improved uterine contractility ref name factors influencing maternal positions labor ref upright positions second stage include sitting squatting kneeling hands knees ref name gelis gelis jacues history childbirth boston northern university press ref postpartum period women hospital birth minimum hospital stay six hours women leave medical advice women may choose leave hospital full postnatal assessments conducted daily whilst inpatient frequently needed postnatal assessment includes woman 's


observations general well breasts either discussion assistance breastfeeding discussion lactation suppression abdominal palpation caesarean section check involution uterus check caesarean wound dressing n't need removed check perineum particularly tore stitches reviewing lochia ensuring passed urine bowels open checking signs symptoms dvt baby also checked jaundice signs adequate feeding concerns


baby nursery exam six seventy two hours birth check conditions heart defects hip problems eye problems community community midwife sees woman least day ten mean sees woman baby daily cannot discharge care day ten earliest postnatal checks include neonatal screening test nst heel prick test around day five baby weighed midwife plans visits according health needs mother baby


discharged care health visitor care newborn birth baby receives apgar score least one minute five minutes age score assesses baby five different areas worth points areas colour respiratory effort tone heart rate response stimuli midwife checks baby obvious problems weighs baby measure head circumference midwife ensures cord clamped securely baby appropriate name tags


hospital babies lengths routinely measured midwife performs checks close mother possible returns baby mother quickly skin skin encouraged regulates baby 's heart rate breathing oxygen saturation temperature promotes bonding breastfeeding countries chile midwife professional direct neonatal intensive care units advantage professionals professionals use knowledge perinatology bring high quality care newborn medical surgical conditions midwifery led continuity care clinical


midwifery facilitator training midwives babies student practice midwifery led continuity care one midwives primary responsibility continuity care childbearing women multidisciplinary network consultation referral health care providers different medical led care obstetrician family physician primarily responsible shared care models responsibility may shared midwife obstetrician family physician ref name sandall ref midwife part intimate situations mother reason many say important thing look


labour measured hours increased chances cared labour midwife known childbearing woman increased chances spontaneous vaginal birth decreased risk preterm birth decreased risk losing baby weeks' gestation although appears differences risk losing baby weeks overall difference number caesarean sections trials cochrane review included licensed midwives none included lay traditional midwives also trial included hospital birth ref name sandall history ancient


history woman giving birth birth chair work german physician eucharius r lin icon birth mary detail russia th century ancient egypt midwifery recognized female occupation attested ebers papyrus dates bce five columns papyrus deal obstetrics gynecology especially concerning acceleration parturition action process giving birth offspring birth prognosis newborn westcar papyrus dated bce includes instructions calculating expected date confinement describes different styles


ref however certain characteristics desired good midwife described physician soranus ephesus nd century states work ''gynecology'' suitable person literate wits possessed good memory loving work respectable generally unduly handicapped regards senses ie sight smell hearing sound limb robust according people endowed long slim fingers short nails fingertips soranus also recommends midwife sympathetic disposition although need borne child


highly trained reasonably considered medical specialist concentration midwifery ref name jackson agnodice agnodike gr earliest historical likely apocryphal midwife mentioned among ancient greeks midwives known many different titles antiquity ranging ''iatrin '' gr nurse ''maia'' gr midwife ''obstetrix'' lat obstetrician ''medica'' lat doctor ref name flemming rebecca flemming medicine making roman women oxford oxford university press pp ref appears though midwifery treated differently eastern end mediterranean basin opposed west east women advanced


beyond profession midwife ''maia'' gynaecologist ''iatros gynaikeios'' translated ''women 's doctor'' formal training required also gynecological tracts circulating medical educated circles east written women greek names although women number based facts would appear midwifery east respectable profession respectable women could earn livelihoods enough esteem publish works read cited male physicians fact number roman legal provisions strongly suggest


midwives enjoyed status remuneration comparable male doctors ref name french one example midwife salpe lemnos wrote women 's diseases mentioned several times works pliny ref name jackson ancient roman relief carving midwife however roman west information practicing midwives comes mainly funerary epitaphs two hypotheses suggested looking small sample epitaphs first midwifery profession freeborn women families enjoyed free status several generations attracted therefore


seems midwives servile origin second since funeral epitaphs describe women freed proposed midwives generally valued enough earned enough income able gain freedom known epitaphs certain slave women selected training midwives slave girls may apprenticed likely mothers taught daughters ref name french actual duties midwife antiquity consisted mainly assisting birthing process although may also helped


medical problems relating women needed often midwife would call assistance physician difficult birth anticipated many cases midwife brought along two three assistants ref name towler bramall towler bramall p ref antiquity believed midwives physicians normal delivery made easier woman sat upright therefore parturition midwives brought stool home delivery take place seat birthstool crescent shaped hole baby would delivered birthstool


midwife made initial call whether infant healthy fit rear inspected newborn congenital deformities testing cry hear whether robust hearty ultimately midwives made determination chances infant 's survival likely recommended newborn severe deformities exposed ref name french nd century terracotta relief ostian tomb scribonia attice wife physician surgeon ulpius amerimnus details childbirth scene scribonia midwife relief shows midst


likely received maternity care hired midwives may highly trained possessed rudimentary knowledge obstetrics also many families choice whether wanted employ midwife practiced traditional folk medicine newer methods professional parturition ref name french like lot factors antiquity quality gynecological care often depended heavily socioeconomic status patient post classical history william hunter attending pregnant woman caption notes strenuous fight midwives customary obstetricians


male medical students washing hands properly dissecting cadavers sanitary recommendations ignored acceptance germ theory became widespread argument surgeons dangerous midwives lasted study bacteriology became popular early hospital hygiene improved women began feel safer setting hospitals amount aid ease birth experienced doctors physicians trained new century found great contrast hospital obstetrics practice women homes could


maintain sterile conditions trained help ref name brought bed ref german social scientists gunnar heinsohn otto steiger theorize midwifery became target persecution repression public authorities midwives possessed highly specialized knowledge skills regarding assisting birth also contraception abortion contemporary late th century midwives already recognized highly trained specialized professionals obstetrics however beginning st century medical perception pregnancy childbirth potentially pathological dangerous still dominates western culture midwives work hospital settings also influenced


view although large trained view birth normal healthy process midwives play much larger role care pregnant mothers europe america medicalized model birth still influence countries even though world health organization recommends natural normal humanized birth ref name fortaleza declaration ref midwifery model pregnancy childbirth normal healthy process plays much larger role sweden netherlands rest europe however swedish midwives stand since administer


percent prenatal care percent family planning services sweden midwives sweden attend normal births public hospitals swedish women tend fewer interventions hospitals american women dutch infant mortality rate one lowest rate world deaths per thousand births united states ranked twenty second midwives netherlands sweden owe great deal success supportive government policies ref name lingo ''encyclopediacom'' ref see also afghanistan midwifery project childbirth obstetrics antiquity global library women 's medicine


international confederation midwives obstetrics midwifery maya society references '''notes''' '''bibliography''' craven christa consumer right choose midwife shifting meanings reproductive rights neoliberalism american anthropologist vol issue pp nbsp il montreal kingston mcgill queens university press ford anne r wagner vicki bourgeautt ivy l benoit cecilia davis floyd robbie ed reconceiving midwifery mcgill queen 's university press montreal kingston macdonald margaret work field birth midwifery narratives nature tradition home vanderbilt university press nashville http wwwverloskundigenpraktijkgroningennl obstetricians city groningen reading


litoff judy barrett historical overview midwifery united states ''pre peri natal psychology journal'' https wwwquestiacom library journal p historical overview midwifery united online litoff judy barrett midwives history rima apple ed ''the history women health medicine america encyclopedic handbook'' garland publishing covers historiography solagbade popoola ''ikunle abiyamo bent knees gave birth'' research material scientific historical content based traditional forms african midwifery yoruba west africa detailed within ifa traditional philosophy asefin media publication external links http internationalmidwivesorg international confederation midwives


icm https webarchiveorg web http wwwwhoint pmnch en partnership maternal newborn child health pmnch childbirth maternal health motherhood women 's health


'''mechanical engineering''' engineering branch combines engineering physics mathematics principles materials science design analyze manufacture maintain mechanical systems one oldest broadest engineering branches mechanical engineering field requires understanding core areas including mechanics dynamics thermodynamics materials science structural analysis electricity addition core principles mechanical engineers use tools computer aided design cad computer aided manufacturing cam product lifecycle management design analyze manufacturing plants industrial equipment machinery heating cooling systems transport systems aircraft watercraft robotics medical devices

Applied science
Engineering and technology
Mechanical Engineering


weapons others branch engineering involves design production operation machinery mechanical engineering emerged field industrial revolution europe th century however development traced back several thousand years around world th century developments physics led development mechanical engineering science field continually evolved incorporate advancements today mechanical engineers pursuing developments areas composites mechatronics nanotechnology also overlaps aerospace engineering metallurgical engineering civil engineering electrical engineering manufacturing engineering chemical engineering


industrial engineering engineering disciplines varying amounts mechanical engineers may also work field biomedical engineering specifically biomechanics transport phenomena biomechatronics bionanotechnology modelling biological systems history application mechanical engineering seen archives various ancient medieval societies six classic simple machines known ancient near east wedge inclined plane ramp known since prehistoric times wheel along wheel axle mechanism invented mesopotamia modern iraq th millennium bc lever mechanism first appeared around


years ago near east used simple balance scale ref name paipetis ref move large objects ancient egyptian technology lever also used shadoof water lifting device first crane machine appeared mesopotamia circa bc ref name paipetis earliest evidence pulleys date back mesopotamia early nd millennium bc sakia developed kingdom kush th century bc relied animal power reducing tow requirement human energy reservoirs form hafirs developed


ad improved water clock invented seismometer jun ad invented chariot differential gears medieval chinese horologist engineer su song ad incorporated escapement mechanism astronomical clock tower two centuries escapement devices found medieval european clocks also invented world 's first known endless power transmitting chain drive islamic golden age th th century muslim inventors made remarkable contributions field mechanical technology al jazari one wrote famous ''book ingenious devices'' presented many mechanical


designs al jazari also first known person create devices crankshaft camshaft form basics many mechanisms th century important breakthroughs foundations mechanical engineering occurred england continent dutch mathematician physicist christiaan huygens invented pendulum clock first reliable timekeeper almost years published work dedicated clock designs theory behind england isaac newton formulated newton 's laws motion developed calculus would become mathematical basis physics


newton reluctant publish works years finally persuaded colleagues edmond halley gottfried wilhelm leibniz also credited developing calculus time period early th century industrial revolution machine tools developed england germany scotland allowed mechanical engineering develop separate field within engineering brought manufacturing machines engines power first british professional society mechanical engineers formed institution mechanical engineers thirty years civil engineers


formed first professional society institution civil engineers european continent johann von zimmermann founded first factory grinding machines chemnitz germany united states american society mechanical engineers asme formed becoming third professional engineering society american society civil engineers american institute mining engineers first schools united states offer engineering education united states military academy institution known norwich university rensselaer polytechnic


institute education mechanical engineering historically based strong foundation mathematics science education archimedes' screw operated hand could efficiently raise water animated red ball demonstrates degrees mechanical engineering offered various universities worldwide mechanical engineering programs typically take four five years study depending place university result bachelor engineering beng bachelor science bsc bs bachelor science engineering bsceng bachelor technology btech bachelor mechanical engineering bme bachelor applied science basc


degree emphasis mechanical engineering spain portugal south america neither bs btech programs adopted formal name degree mechanical engineer course work based five six years training italy course work based five years education training order qualify engineer one pass state exam end course greece coursework based five year curriculum requirement 'diploma' thesis


specialisations degree takes four years full time study achieve ensure quality engineering degrees engineers australia accredits engineering degrees awarded australian universities accordance global washington accord degree awarded student must complete least months job work experience engineering firm similar systems also present south africa overseen engineering council south africa ecsa india become engineer one needs engineering degree like btech diploma engineering


engineer 's degree master 's engineer 's degrees may may include research doctor philosophy includes significant research component often viewed entry point academia engineer 's degree exists institutions intermediate level master 's degree doctorate coursework standards set country 's accreditation society intended provide uniformity fundamental subject material promote competence among graduating engineers maintain confidence engineering profession whole engineering programs us example required abet show


students work professionally thermal mechanical systems areas specific courses required graduate however may differ program program universities institutes technology often combine multiple subjects single class split subject multiple classes depending faculty available university 's major area research fundamental subjects required mechanical engineering usually include mathematics particular calculus differential equations linear algebra basic physical sciences including physics chemistry statics dynamics strength materials solid mechanics materials engineering composites thermodynamics heat transfer energy conversion


hvac fuels combustion internal combustion engine fluid mechanics including fluid statics fluid dynamics mechanism machine design including kinematics dynamics instrumentation measurement manufacturing engineering technology processes vibration control theory control engineering hydraulics pneumatics mechatronics robotics engineering design product design drafting computer aided design cad computer aided manufacturing cam mechanical engineers also expected understand able apply basic concepts chemistry physics tribology chemical engineering civil engineering electrical engineering mechanical engineering programs include multiple semesters mathematical classes including calculus advanced mathematical concepts including differential equations partial


differential equations linear algebra abstract algebra differential geometry among others addition core mechanical engineering curriculum many mechanical engineering programs offer specialized programs classes control systems robotics transport logistics cryogenics fuel technology automotive engineering biomechanics vibration optics others separate department exist subjects mechanical engineering programs also require varying amounts research community projects gain practical problem solving experience united states common mechanical engineering students complete one internships studying though typically mandated


team professionals specialized fields like mechanical drafting designing prototyping printing cnc machines specialists mechanical engineers design oversee manufacturing many products ranging medical devices new batteries also design power producing machines electric generators internal combustion engines steam gas turbines well power using machines refrigeration air conditioning systems like engineers mechanical engineers use computers help create analyze designs run simulations test machine likely work license regulation engineers may seek license state provincial


national government purpose process ensure engineers possess necessary technical knowledge real world experience knowledge local legal system practice engineering professional level certified engineer given title professional engineer united states canada japan south korea bangladesh south africa chartered engineer united kingdom ireland india zimbabwe ''chartered professional engineer'' australia new zealand ''european engineer'' much european union us become licensed professional engineer pe engineer must pass comprehensive fe fundamentals engineering


exam work minimum years ''engineering intern ei '' ''engineer training eit '' pass principles practice pe practicing engineer professional engineer exams requirements steps process set forth national council examiners engineering surveying ncees composed engineering land surveying licensing boards representing us states territories uk current graduates require beng plus appropriate master 's degree integrated meng degree minimum years post graduate job competency development peer reviewed project


report become chartered mechanical engineer ceng mimeche institution mechanical engineers ceng mimeche also obtained via examination route administered city guilds london institute developed countries certain engineering tasks design bridges electric power plants chemical plants must approved professional engineer chartered engineer licensed engineer instance may prepare sign seal submit engineering plans drawings public authority approval seal engineering work public private clients requirement


written state provincial legislation canadian provinces example ontario quebec 's engineer act countries australia uk legislation exists however practically certifying bodies maintain code ethics independent legislation expect members abide risk expulsion salaries workforce statistics total number engineers employed us roughly million mechanical engineers largest discipline size median annual income mechanical engineers us


workforce median income highest working government lowest education total number mechanical engineering jobs projected grow next decade average starting salary bachelor 's degree subdisciplines field mechanical engineering thought collection many mechanical engineering science disciplines several subdisciplines typically taught undergraduate level listed brief explanation common application subdisciplines


unique mechanical engineering others combination mechanical engineering one disciplines work mechanical engineer uses skills techniques several subdisciplines well specialized subdisciplines specialized subdisciplines used article likely subject graduate studies job training undergraduate research several specialized subdisciplines discussed section mechanics mohr 's circle common tool study stresses mechanical element mechanics general sense study forces effect upon matter typically


engineering mechanics used analyze predict acceleration deformation elastic plastic objects known forces also called loads stresses subdisciplines mechanics include statics study non moving bodies known loads forces affect static bodies dynamics study forces affect moving bodies dynamics includes kinematics movement velocity acceleration kinetics forces resulting accelerations mechanics materials study different materials deform various types stress fluid mechanics study fluids react forces kinematics study motion


bodies objects systems groups objects ignoring forces cause motion kinematics often used design analysis mechanisms continuum mechanics method applying mechanics assumes objects continuous rather discrete mechanical engineers typically use mechanics design analysis phases engineering engineering project design vehicle statics might employed design frame vehicle order evaluate stresses intense dynamics might used designing car 's engine evaluate forces