THE ULTIMATE METAL COUNT

[Frustration]

30 minutes ago, IlstrawberrySeed said:

Silver is a fabrial metal? Is that confirmed or just implied as in the WoB?

I wasn't just referring to silver, there are more than 10 metals and their alloys that work, meaning there are over 20, compared to Allomancy's 16.

[alder24]

14 minutes ago, Frustration said:

I wasn't just referring to silver, there are more than 10 metals and their alloys that work, meaning there are over 20, compared to Allomancy's 16.

Why? I always assume the base 16 metals are the fabrial metals that can be used, because they are the same metals, they have similar effect to those allomatic ones, and Cosmere has a general thing for metals. And plus all god metals and their alloys. So the number of allomantic metals is the same for use in fabrials.

[Frustration]

15 minutes ago, alder24 said:

Why? I always assume the base 16 metals are the fabrial metals that can be used, because they are the same metals, they have similar effect to those allomatic ones, and Cosmere has a general thing for metals. And plus all god metals and their alloys. So the number of allomantic metals is the same for use in fabrials.

Silver has uses throughout the cosmere, but not in allomancy.

[alder24]

1 minute ago, Frustration said:

Silver has uses throughout the cosmere, but not in allomancy.

But silver isn't use in fabrials.

[Frustration]

4 minutes ago, alder24 said:

But silver isn't use in fabrials.

Source?

[alder24]

16 minutes ago, Frustration said:

Source?

For now I should add. Look again at the metals used in Fabrials. They are the same as in allomancy, and have similar effects of pushing and pulling. And this WoB:

Spoiler

Questioner

Quick question on aluminum. Why does it affect other forms of Investiture?

Brandon Sanderson

When I was building the cosmere, I just had to build certain themes into it, and metal was one of those. And the metals have kind of a Spiritual integrity, and Spiritual component, that if I can get into Dragonsteel explaining why, you'll get your kind of origins.

Questioner

And that's why, in Warbreaker, metals are different with Awakening, and stuff.

Brandon Sanderson

And even in Roshar, the cages that you're building for fabrials, once you start to figure out how those metals affect it, you'll be like, "Oh wait, that makes sense!" And these are just across the cosmere.

And if you want an in-world answer, it has to do with stuff in Dragonsteel. But really, the answer is, I was building this and I'm like, "I just want this to be a theme. So I'm just going to give this Spiritual component to metals." So it works in Mistborn, and it works all across everything.

LTUE 2020 (Feb. 15, 2020)

 

[MangoBoi101 he/him]

60th Post (im closing in on 10786 fast)

can you guys please tell me what a fabrial is? I feel left out of something that I should understand but I dont.

[IlstrawberrySeed]

1 hour ago, MangoBoi101 said:

can you try?????

The formula that made the 19thousand digit number was the culmination of months of filling zink at work and tapping it later. I will work on this, but it is unbeleavably complex for something that sounds so innocent. The problem is that the number of fuerochemical effects is based on the number of hemalurgic effects, and vice versa, so it isn't simply a formula, but multiple with a decent number of unknowns mixed in. Alomancy relies on both the number of F and H effects. Oh, and it relies on what materials each metal has, and what other metals those can be apart of, and wether charged impurities (such as .1% iron, fuerochemically charged, in otherwise pure copper) due to effects. I wouldn't expect fuerochemical charge to effect fuerochemical charge, but who knows about F for H, H for F, or H for H, and of course it has effects for Allomancy.

1 hour ago, Frustration said:

I wasn't just referring to silver, there are more than 10 metals and their alloys that work, meaning there are over 20, compared to Allomancy's 16.

I don't see why he couldn't be referencing shardmetals. If silver isn't confirmed, I am going to operate under the idea that the number of fabrical medals are the same as the number of metals in the metalic arts.

13 minutes ago, MangoBoi101 said:

can you guys please tell me what a fabrial is? I feel left out of something that I should understand but I don't.

A fabrial is a piece of magitech from the stormlight archive. It consists, in part, of a gem filled with magic and a cage made of metal. The metal is one of the 2-3 primary variables determining what the fabrial does.

[Frustration]

14 minutes ago, alder24 said:

For now I should add. Look again at the metals used in Fabrials. They are the same as in allomancy, and have similar effects of pushing and pulling. And this WoB:

  Reveal hidden contents

Questioner

Quick question on aluminum. Why does it affect other forms of Investiture?

Brandon Sanderson

When I was building the cosmere, I just had to build certain themes into it, and metal was one of those. And the metals have kind of a Spiritual integrity, and Spiritual component, that if I can get into Dragonsteel explaining why, you'll get your kind of origins.

Questioner

And that's why, in Warbreaker, metals are different with Awakening, and stuff.

Brandon Sanderson

And even in Roshar, the cages that you're building for fabrials, once you start to figure out how those metals affect it, you'll be like, "Oh wait, that makes sense!" And these are just across the cosmere.

And if you want an in-world answer, it has to do with stuff in Dragonsteel. But really, the answer is, I was building this and I'm like, "I just want this to be a theme. So I'm just going to give this Spiritual component to metals." So it works in Mistborn, and it works all across everything.

LTUE 2020 (Feb. 15, 2020)

 

Well, we happen to have a Nickel-Silver allloy that may just have effects on Fabrials

Spoiler

In Raboniel's dagger, mentioned in this sheet

I unfortunetly don't have the time to translate it right now, but it's there

 

12 minutes ago, IlstrawberrySeed said:

I don't see why he couldn't be referencing shardmetals. If silver isn't confirmed, I am going to operate under the idea that the number of fabrical medals are the same as the number of metals in the metalic arts.

Whenever he's ased about allomantic metals he always refers to there being sixteen of them, Shardmetals are outside the standard boundaries.

[MangoBoi101 he/him]

what do those words mean? I cant understand any of this, What Are ShardMetals!?!?!

[alder24]

God metals. Atium, Lerasium, Harmonium etc.

[MangoBoi101 he/him]

ohhh Ok that makes sense now thx

whats the final number/ incomprehensible bunch of spam?

[IlstrawberrySeed]

1 hour ago, MangoBoi101 said:

ohhh Ok that makes sense now thx

whats the final number/ incomprehensible bunch of spam?

On 1/6/2023 at 9:10 AM, IlstrawberrySeed said:

I calculated it before I read this thread, and also found a number with over 19 thousand digits. specifically:

  Reveal hidden contents

1703000440845819495232211498826217387880651654234288706375264427654259950622864735126080211248793345885882499191471173704549506974800990768539080410047314974790285591128898849771395136526491288784771662739127591984635421115693596133866512122552479424153332692450206555865977185024738482023927225175670829147011207405785073086045008593498777015381312822111629060840176525377740024794852220211275604882442032563267202694981686725066322255817269851426266929814738178104627084224157511998182215511729271705334363922251312388300387113065279523166031375748338380136483369589803899737982832930300044265908118498656757226153572217669725058225411083516214652635178541050164212882339834233953587903176923904512434011177072398434732489598734565964102115299732307918059555491368823831816156532145268924220962343341131145563289628535311803777546651319440233703488970968262934184175483516143200020520669150791525864394433551364913659090036632701767934987206514995289611543463446360863419186475959220112429210558620024237679820534437580626935544307801826686580604582369092120104213946118527344684390394698880287432016933470544970268303565581960735212460849787199997728218665647888879527333539735619535652502942960924201152000426512199150088889576693580679001688435182595156544661640635218790456906298487681187605076246002919809156047667355064140963156762316556402605756660554449872023582062655628155226230235350149994526637792224757350133092452682736980649341586487745542464322692750879221798089457906215770187149419674078797787742916255014547340159190498951929258290678808361725200192042571370901534806056324187650828773819773399322968220320632324818122792787642288412013201338062645387472024405100155864839373832923863892016973692583673224779680827633085354381147591592647127061524221890666108845219233298950581190557078406506745835510852946811831428120381970215759944388736225697786900504607549434504378805953385555984963596679205363905190016615886704812507551314274602476427301290444014956618686845464664249236937479467844350019579622222383866938173793618087210558941894612418402703592988526291865793734872302693898101489198919389181267823669688430447561093061992287055306362887587022619120754585976110855008605157128964712584571962523095031617028126218248396945464366806812596411810277368317092450027613380151371405870903822532212257080317906869902388464998546700900420003527905512445360791903814552317964400390352370099079464877969613148562143845389409828965593525882490282058715527231817829663747197841113895920276217591977571983381089041984736724378504344786283369567850366513734457023232401871259203302481900510954099323085717675315536021191632879697001092832517020023325125772667541981568793013266449564459966248197923227503176468358289439978729193848435962532199287780411792492897398541703696853071421923020207961622617880515269926661218876118990240539535243175628857740501070168595559332392470839687112821253635074762698192753757518192195006230348663941947644796808764655392564648667754775771617197294853729140229552878513973502163843491515402722054747526936939175672258574011308138273153692281945028240735201980691333759888690042813146840610906638246706377622754608724178361697616075395015081759366052893948367621917190890733122548703649416395595701028723509905851452269696656255918910604682143591811318225019789664698468517224442551517842328817545153413853808542864053916259831737281029530043549808511962895343277801832642273822561204350302133910008430549323110848484539602739629126874814354328960224237319695356048624076281366499594041199867024897670768771349709081218482845998857895458685680546163197855410111229863738224838883163224017017456489280143393963824681468072524252625342248821305667063044437302555239943311891555270556894888710560284495131481865948906038850356047524632285171188702412806218543693817984804280592783697300762541120854306528618713211090842397129497465677603521066169762540772212993630110229568460844016969021064649686339806649327536755885147813166980422966660508591202953332601406274804910880447144042119735339023235114528649848912321876963969411696669623860276116043050140863382704022427044970088487295268508087178994553437083890107511250355519954658185997051418244051276201067291093372646356472862089520445823934276745167163522709149299317283746214196329481147837145658227414567884905612486755825409880518753318075182223589858301036518086254932470312034432386119234967232448548397871868187443088722075811316573279205626483179587070366708941057940866118726108271632022509961738569262124326820537804321969472024470610300912704256593807526911391758154710840071848178821981950782924099785176047439889590796483532025772644614310240311833475125146716020837831761287564964258937447766824508095891702587408518161167078313306860827044432332450785308856702717256754644738368526248080681992620091700695779016619925566858834405688487154186459154976750159605035154333831657692509655840360953195510675718994481419900386340083729330365302375501930795110350347735094843536087041223770559807765421594630912836133025009502460259896156817628327574046354406618919761206977328824363709265303070771058558968871494883457608427185589382017425636649493186121363311593980247511771901306403932378800341170821596966585801717797690231362304854882466610759852270401820358452043375384238307308623489363608558998344170043053851178459905200221405285406668964138615456466709174150007601779298544114528167384427939933896653571358939418548967930116982614627014485004375544843033456909088750603901992022898757293011153452579652261368498814768403537876207148570564152651650007723586401237947142392922551039888919431051208872184894817325204363732349767668303118720943956021426498067173909794566411632176675991554323064071373429935627724583479775465894047739445925262588058327982274894093765385611136875082104359931374177964703265990795695808049477250686572614443413125450984384129784989963274461231444283823745456910814312993398827640193738405609840609763234243998495755846599151896883312760034840831536063189070687117669493092284202517211251395970571320068880609854680710903302048283546161331325938975459180140594587624544068372215105749835798625073431311778970489230602412187603306683315693233384207134287779219703254545571665683629041937802879290756237212147770910510553273977345911189338439504772821208459083972724037672117102859650257159599540029606764966010751108736760503720746525784114347583910736767936409659912335749341547697013161077775821609759996213043368052829980500432215590840241379476081277946541190994617195649856759337134278802104881213295695065621704673472266763127622581967367923661252205172559872942957583566988304303172333385975830453382671682326935563134989570040657409894487894854662668820939947378353269407524302326630976833815930610350758384758575450188846059579999870568210710429190561320249127371217666965819498208757448898768306170905901139189882398731007346203597529659317230691971061118685879816919410876849604416430589770490421148846716106341304463774135802540463798087284558132493287238899015826000708101206019971727748622926810297817213808270342815869889291280705061281239925090385814915450609786020560632983298595422325475210253365306187092836080553439946695149580348140165109182224346150068743143082053525309449348196264686449533275695287344274235174145326567381930654049714642192669610406866970683084520492102303683940833496822897119580294032370951245177449997020876267306458190716292022537755631304803031225898803772334863118502844027577901912401178073885997967848814842480133568100254031204709378659647406435746203771488804977685604200675832965429562271190223218917662494950900445189259144754598570847918653736666894394874297783291666366165115527477620590834553763126209403886441942380299813753696009320617063438153644404825797732895782697488101376521867275118976357052752123433505481091954577453702421880153873786597068526193612839320180581534510869653599972453880556074178216593001885012217222451555749106585187499080489688018368750274337374913027282146778317981722488746018082597433388818994500370654617748731371811930599448461939127659057502513150423055116884795245024385599257548740454763976509071409056824280438197477988088812373399647010925725497163295026487369510425963286481655571677265423058000782755626804151041583533823853845560266380162474274801275179888549860106059427415768869367461460113038109411672176378237563144578915272582296225031525298547431119606527078736404370600230939395727799601929353008123878744044515213844383775846406169381781253545535493730418802507021656318923841210600902570544579339814058962560814267059965160416140684700861209076320977160172145220448530853066788489445630065631429501500324996833674234904345259577296317811041606578246748857654677805438997557879473913645302234281965013531053109300079222212940426097238905051078896464564760530126370520176441731413908470126323840451120537001528149417108201208734944674660250634149611312989271727211363097827611556266591249038930714001311514527848392411860507035139018306123894184236223472981428040870230184411804755290608199497957533087504726756442782271291830951458033018899386809388016798159490928062947332865418494882623195243913705101303456142829184069412334310451448567512975093019652927124171031123352156885232984429121978216161866044520882640099068020157580103413365175131820789678702749993217216425187754883054769937116581814989535885594170336433170640987160791702165441107106178873524048371838175194261873997126132670139437941526002942247657780976740352589271647743100889960284061438540964710921525936481480555149383346714995188549165109425801052322317454439271645314413042881935831789224238157327260717473160979671148890104648181637566860496873620011361464798998685526806539454808774692723887599835499334381180930541360017920355383575927655725674263829500713688330445687989688573627076961172233202533478489585202631355881950618954120551496122587166256751335254446251860188784844580322343749828316217518310638607072817867756664625749983455043836615625318599911311823249977153839517445055458149183872645630750899383074151568618770994812877510401469646518688767173566776496947386902469032724529136122106038563101185567212597474656752028831566069955362538994145768075136221700901532224614061746299845990325713916732064658325077837924009677749138546390402739148348562710313274898053557157245761797329164671752652951003349221194211082259940092126725304802379714455664111765537115175417181444319270845849730391390571626778907870731733845058989355531525870418354493273835762851223036531370787482452875473352417455045650538874644529334834833107206424099786318961499498540538746421115149068508341979688820786717315277937186938097789593371858758594906026991566086417884548817037195195938095092031772600544499294394156685675325822428775333377107946359611337724651089533803933963741304546060605044616950309023329991158483353044610936515212336924544306527063095868024749839008566409077530703739514186624752777512085805696939668573866951589000789066557738514834889544386014794021708655803254632542058558385948891818854777885724606622296296206629484191561054490377482793305842905490160259830220278158302176726636045397926303990399607979366875367095156795295387700996917284284939337826827738848420146853916783081613621099632401587235913127104731602619467148313022990199828069472127940606698918362274748561614549022000567713597470302467054125213029842594548335683641543349160709054524828983480300553252456974794369584040516187887545707211224744703843531792200866670212119827924398062944386705995595705122653875819727377999615137507606946625894694476829249000423073759760896793814286621216531360534445368490081765844439533499407690009377976669907411275522646568942166659042085016282293242169565439076944429994983486270660371900562994699215873354248325470352714523999498137597047626359715006628374120563864240467939465894888572563268740878222253271436804390135076041589650517173204578057495915647214586563558706140935850024232605673609721189632988991153428261192845054806033558767321864920776278272391493113506770461710602308741833383560297999667814938649119035862626609363079031710287249731356391711122338124545934502223534750763308008234500737120203433670130849610158103732061152520769772520913842493300559655220831904079499722138070678540630999396695571196269335183473214404062137670153904319221797087044428029688946929317587331140675236900358874419548918873760779483614925177550022251092220568882620709158937003936634097475585099434109863931026057740975832036269588583551899671599498883346638821879030434781112552893813345276286920113536228332522910813234819515980480416970858722273044085671857550771526601303463058274419281605525355966778116441466991504851544472141998864615882414896258415112726933282605071512611795448123841507170089577777591790538545049160101473252678595370433288148845776777069661757099297828586743662720760185492386667251040175879848278221675245617711024620172694032347374706878712504874067027373577065573639014957584340311122202769432666177334517778930631129022091900807163748840841517553698393510377912208467959415639397286211491027617025948583577002941737851135978705161860917147588138320643857259381234398878039463183983147079240985264316321705406918095694658774351744373238906069920976986971880427863764393207147906764322836559175284132205344941216830221790448174767291058719956654320018456239251838140806960889886312113128221368149861176113262943674368915975591457296093680034939589940357950647073370794083845368478991904569307059688743410257568970507409322785793479724874736745996373624280623274975305675432942622605160244783966095262082455702595443683128607628212709234250204394930337144831115095937211011553704821264739013639764111094472899563232351436734301990769980815579112392263547036015768829139791801940868583656200212379024053122812718010622998904889774163186255444635427478146869379836134957733854936725586873483448127836557005750065843013249203976093907879645372195773415516938930359337805428094626350142616359028259516412007141468196801992099044659104437389571134506702971606445528570554041652276179307303838272877405198381814280580098897487702651987731262049266876949428039429648973551933471960274333688420051588142282997640657012867780491926216441478363860047087693191977637666178888755107336405369883893866011245884600770341273975008581564121558813915334438237170032814815424578033351196940035182731456171267987890156091617549320305575723092624547177611662514819857305875791105310485671679663975406081340410272788268899660476974066798933129242899319211251918062571804856645475129727755585714964098178278752796888301309431695271423089612282824292105290393279016323003304381545387927487659565310248910375835052031480159704344224035172036415420050096503804768966372682178995181559019348844310648558108714135461633660776175464375183735165314801454282972570042548742121490877216292023688920158075863820215974473120268462916668453892452107772959141878009133136994285044707119402754805474319232853358651610290643475041242914408049004397026307766339893099046135989787651649812065439107421758124282025611311767237698602907340380277975173595460626500709052326477171352103486576814421213998489118180895337006898945987368128526838668683795224142203413958117451477819770137576199565288528066559438936026275195473684380585638634519625214123509610054245123545478291983481022571145317775527425228468185455227025885255614572844749917287310490497549172872653933323108064922209217834829179860386679968797408969363747829515262692844583248439099382910443719280649441872255513228536881582307598328741712389035856549752988121269834975446968374700935234266019200777288924937388644003396676073098886902749037462443145492113136142885793977649420358557281171727707106812680691597464053572782428200498741320732662483590504409074836824946206856961508834133493340786681092772956376013557707806862185219798752371502068467711021745217341319934016740922373797867491945223665879600781427941265428490201487756740465353619725291572935853986317335748156472451354490986658064961408598516704944458206153617604174362195701730892407406798858140065812475186636434204452136375413679200771213230649533451795565312271352866768748627938873487229200285650861300861202252388350623574384028556814717539132720035986834886431230086489662321413535189017626019016059800002523646654128427643270452891469095406253277102700113357733470200781829642800253272619987641889021213308155161480157867724775740028071961510279458376684463628912685720278354731082105670988324724173107135582315381871029162038061868957159733629628284838745272509661469331226625498948561354402709140414236852279849104700907091984145974015807552361864556218948508429439395621320757851098916028374233152191189290415858090278360329613524098773707398821866862577626760558684168979631805790655928050732556873181939305889846780525589357193845214791490032585878566567348138183392411271968416369490774268946610883914863295933331181012378989940279261861854835761544313371119941672555689951597967147455139201875111722760815896632277910702778302100545065994897575808372911767057292494945128170767555235090497501012961967316642111254760483837706529514480704030037505847706543197409623446394349622886077003435190606946135987608112830872282584644039319465958151541381953032755656103328478555736923361106108591635386818430571124568557994812790461322011566468158590529965918131579139843531743895322907572369809150359597122360913951656808965217127368717028838322917946633054594763737319974012487778122768439863655127382690497319940369473573757861126498527887356414394732806348514462512466442546990268868596124796314761366534228975387101553048173328857814999435767765203506417742477577394852979515843492036912277648477454102452161024985446492960696644671079263716477400193002520949547527197742723822883079835455406240224290755939028892868405041116074073349468392707236498551452385588929522218524189583611974850746355507125475917646478294309161384619603412645528616254809851448674889970209178547374604868252591438316441850857827017019273147705439811463442457542034323047902821724139296980319361289944148468106303421544559247437539312468659377396899051563295868886630349655362408935745131880647354970059593789400925021956667293570087634893640323654582432667422257524814332180802735461245165878113930129085770964038704600350036881724759980314111187225396020543914236297114577324229582013674140443820009464461448254750833838407799108332133190793212863477812292307991029773757777595190283418025209662019253919290819583215766702953139786557623906004731792356349938510380685609570662142930763704244937941709458010002582441329483385218407899336697102393022759982325801674839131066009845081489096287448785326229541240406492094176651988063456183931842003121570047882608596018151492667174818836588587808876720099304572182237924291983069847495938180790960110087031030464588210894038524823194257913529147904780385566957509535269643828427038520309671928305550577890039136044730485817554182823943424084221551440892780729923124670678591193873085891672291750075109141946798022876967135909580292283598716555601972127141604722475653223648099268670550744546412307231189245685275719876636299605907718010974645898515932660233032459872028037449700136537800646731923546137956111548136141609250718405236167891787563414633775512480356425307724636943397586361387056716692537649451532284980769031160892248674727664670752381422647020078668053193457841822244396534776645144889700327413727835162338611131452170747771965095944685418085632137983265380823706973466730790665861111480442801916773276149532864470107781519816909244225571728659793537771132361322017462934429588998398185553797090512666473351106484693097739093442745909005351770095558912702909494779358119610369087924487746108801614885287497115198612832255

This uses false premises, specifically in alloying with shardmetals, and number of shardmetals a shard can have.

@MangoBoi101, a formula using 2 variables is metals * E<n=1, metals> possible charges of the metal

The problem is that this means the number of effects is either infinite, or finite because metals-charges overlap.

[Firesong she/her]

I know this is quite a necro, but I have a question to ask. 

How exactly did we get this number, the 10^19729 one? I know combinatoric formulae and tried using them in several ways to try and get this number, but I just, can't get to even one-centillionth of it. Can someone actually show the work behind it, so that I can see if it actually makes any sense. 

I could only get 65535 if order doesn't matter, and 5.6874039553×10^13 if it does matter. 

If you add allomantic metals, then it rises to 7.1526377254×10^35 if order matters, and 4.294967295×10^9 if it doesn't. But would technically be less as this includes a lot of combining alloys with a metal that they already contain. And it also assumes that mixing together non-god allomantic metals makes another viable allomantic metal. 

I even went absurd and added Feruchemical and Hemalurgic metals to it as well, and made order matter, and still got 3.4491444203×10^89. Even more extreme, I counted alloying something with itself as a different metal, and got 4.0027434866×10^115. 

So, how did you get something with almost 20,000 zeroes?

Edited July 20, 2023 by Firesong

[Underwater_Worldhopper he/him]

On 2/28/2023 at 8:09 PM, Frustration said:

Well, we happen to have a Nickel-Silver allloy that may just have effects on Fabrials

  Hide contents

In Raboniel's dagger, mentioned in this sheet

I unfortunetly don't have the time to translate it right now, but it's there

The page itself says that it does not affect the gemstone. Silver could affect Fabrials, but so far as we know, it does not.

[Firesong she/her]

2 hours ago, Underwater_Worldhopper said:

The page itself says that it does not affect the gemstone. Silver could affect Fabrials, but so far as we know, it does not.

Yeah, we don't fully understand that dagger yet, like, we know how it uses Raysium to siphon Investiture into a gem. But the alloy being specified makes me think it has some importance to the way it works. 

[Underwater_Worldhopper he/him]

1 minute ago, Firesong said:

Yeah, we don't fully understand that dagger yet, like, we know how it uses Raysium to siphon Investiture into a gem. But the alloy being specified makes me think it has some importance to the way it works. 

The specificity is indeed a little suspicious, but so far we have nothing explicit.

[Frustration]

On 7/20/2023 at 5:18 PM, Firesong said:

I know this is quite a necro, but I have a question to ask. 

How exactly did we get this number, the 10^19729 one? I know combinatoric formulae and tried using them in several ways to try and get this number, but I just, can't get to even one-centillionth of it. Can someone actually show the work behind it, so that I can see if it actually makes any sense. 

I could only get 65535 if order doesn't matter, and 5.6874039553×10^13 if it does matter. 

If you add allomantic metals, then it rises to 7.1526377254×10^35 if order matters, and 4.294967295×10^9 if it doesn't. But would technically be less as this includes a lot of combining alloys with a metal that they already contain. And it also assumes that mixing together non-god allomantic metals makes another viable allomantic metal. 

I even went absurd and added Feruchemical and Hemalurgic metals to it as well, and made order matter, and still got 3.4491444203×10^89. Even more extreme, I counted alloying something with itself as a different metal, and got 4.0027434866×10^115. 

So, how did you get something with almost 20,000 zeroes?

Detailed explanation can be found here:

On 6/21/2021 at 5:54 PM, mathiau said:

I assure you that calculation makes sense and have a firm mathematical backing. My previous explanation on the other hand maybe not

 

So, first we want the number of different possible God we can create, this is because Ettmetal is not an alloy of Lerasium and Atium but something both different and Allomantically viable and we have no reason to believe the fused Shard of Mercy, Cultivation and Devotion or any other would be different

Number of Gods with one Shard : 16=16!/1!(16-1)!

Number of Gods with two Shard, I take two Shards among the sixteen without regard for order : 16=16!/2!(16-2)! (=120)

Number of Gods with two Shard, I take three Shards among the sixteen without regard for order : 16=16!/3!(16-3)!

...

Number of Gods with fifteen Shards, I take fifteen Shards among the sixteen without regard for order : 15!/15!(16-15)! (=16)

Number of Gods with one Shard, I take fifteen Shards among the sixteen without regard for order : 16!/16!(16-16)! (=1)

So the number of Gods is Σ_k=1^16 (16!/k!(16-k)!) which is equal to Σ_k=1^16 (16!/k!(16-k)!)- 16!/0!(16-0)!

(I'm not managing to make clean sum in forum so I'll have to write "sum for k going from 1 to n" by Σ_k=1^n)

Since 0!=1 we have 16!/0!(16-0)!=1. For the Σ_k=1^16 (16!/k!(16-k)!) part we'll use Newton's binomial formula, Σ_k=1^n (a^k*b^(n-k)*n!/k!(n-k)!) =(a+b)^n which gives here

Σ_k=1^16 (1^k*1^(n-k)*16!/k!(16-k)!)=2^16

So the number of Gods is 2^16-1

 

Now the number of viable Godmetal alloy. For this part we made the supposition that if you take any combination of godmetals there'd be a way to alloy them in order to make a viable metal. It is a supposition that can be argued about, in my mind the fact there is more than sixteen viable alloys of Atium suggests this hypothesis is right.

Now for the actual calculation, you do the exact same reasoning as for the number of Gods but you replace every instance of 16 by 2^16-1

 

Is this clearer?

My excuses, I thought you were only looking at r=2 which would be "a big number in an order 2 polynomial" in which case it would made made sense if it was smaller than the exponential of a significantly smaller number

I'm not sure whether you mean you're summing the values for each r or if you're looking at each of them but I guess it doesn't matter since in the former case you get exactly 2^(10^21)-1 and in the latter case you get something of the order of 2^(10^21)/10^5, both of which are is far more than any number said in this thread except the insane 2^(17*(16)!) which we latter all agreed was wrong

May I know the exact context of your calculation? I'm a bit surprised you're obtaining all permutations of the stars with just binomial coefficients. (though it's definitely possible I just didn't understand what you said)

 

[Firesong she/her]

3 hours ago, Frustration said:

Detailed explanation can be found here:

 

Ah, yeah, I forgot to take into account all the different ways a Shard can fuse. 

Also, oh my, 10^10^14. 

I did the math, got 1.849669091121656*10^588 or 1.454313010902972*10^963, depending on if order matters. 

Edited July 22, 2023 by Firesong

[Newly Awakened]

So would you just have a single Misting who can only burn Bavantiun-Atium-Tanavastium-Pewter or would it work like another God metal alloy in the sense that at pewter Misting with enough connection to the Shard can burn the God metal alloyed with the normal metal they can usually burn? Because this WOB 

Spoiler

word_thief

What would happen if a Mistborn ingested the metal of a Shardblade/Plate?

Brandon Sanderson

A Shardblade is Invested. A Mistborn isn't likely to have a tie to that type of Investiture. So probably nothing would happen…

General Twitter 2013 (Oct. 24, 2013)

seems to state that anyone with a Connection to the Shard can burn the God metal, so a Misting with Connection could alloy the metal they burn with any Shard they are Connected to, creating a whole host of possibilities.

[Underwater_Worldhopper he/him]

1 hour ago, Newly Awakened said:

So would you just have a single Misting who can only burn Bavantiun-Atium-Tanavastium-Pewter or would it work like another God metal alloy in the sense that at pewter Misting with enough connection to the Shard can burn the God metal alloyed with the normal metal they can usually burn? Because this WOB 

  Hide contents

word_thief

What would happen if a Mistborn ingested the metal of a Shardblade/Plate?

Brandon Sanderson

A Shardblade is Invested. A Mistborn isn't likely to have a tie to that type of Investiture. So probably nothing would happen…

General Twitter 2013 (Oct. 24, 2013)

seems to state that anyone with a Connection to the Shard can burn the God metal, so a Misting with Connection could alloy the metal they burn with any Shard they are Connected to, creating a whole host of possibilities.

There've been other WoBs that say that the Connection isn't necessary, so it's uncertain whether it's required. There are differing opinions on whether Regular Mistings can burn their adjacent God Metal Alloys because the WoBs have been really unclear about it, but I personally think they should be able to.