Probability of immortality ad God s existece. A mathematical perspective Jesús Sáchez Idepedet Researcher, Bilbao, Spai Email: jesus.sachez.bilbao@gmail.com https://www.researchgate.et/profile/jesus_sachez64 ORCID 0000-0002-563-895 Copyright 209 by author Abstract What are the probabilities that this uiverse is repeated exactly the same with you i it agai? Is God iveted by huma imagiatio or is the result of huma ituitio? The ituitio that the same laws/mechaisms (evolutio, stability wiig probability) that have created somethig like the huma beig capable of self-awareess ad cotrollig its surroudigs, could create a beig capable of cotrollig all what it exists? Will be the characteristics of the ext uiverses radom or ted to somethig? All these questios that with differet shapes (but the same essece) have bee asked by huma beigs from the begiig of times will be developed i this paper. Keywords Die of ifiite faces, immortality, existece of God.. Itroductio I this paper, it will be commeted the possibilities of God existece ad the possibilities of repeatig whatever makes you be you agai. For that, we will start with the die of ifiite faces, showig that the mathematics tell us that the possibilities that this world is repeated as it is or at least that you are repeated as you are really high (if ot, uavoidable). All the possible cosequeces of this will be developed. Also, it will be commeted that the possibilities that the differet uiverses evolutio ted to somethig are also high. For that, we will take ito accout the law that stability wis over probability, meaig that the most stable solutio (i a world of ifiite possible modificatios) always wis idepedetly of the improbable it is. I the ed, the cocept of God i humaity ad how it is related to the above will be commeted.
J. Sáchez 2. The die of ifiite faces If you throw a die of 6 faces, you will get a first umber. If afterwards, you throw the same die of 6 faces ifiite times, we kow by experiece that somewhe, you will get the same first umber agai. Ad, i fact, the mathematics tells us the same. The followig equatio (do ot worry, you will see oly two equatios i this paper) cofirms it. Pr = 6 + 5 6 6 + 52 6 2 6 + + 5 6 6 = 6 ( + 5 6 + 52 6 2 + + 5 6 ) = 6 ( 5 = 6) 6 6 5 6 = = () 6 6 Above equatio makes the sum of the possibilities of gettig a certai umber, each time you throw a die. Each term represets the probability of gettig a certai umber, if you have ot got it i the previous throws. To sum all the terms, it is used the geometric series sum []. The total sum is whe (the umber of times you throw the die) teds to ifiity. This meas, there are 00% possibilities that i the ed (after havig throw the die ifiite or less times) you will get the umber you wat (or repeat ay rolled umber). This is obvious, but the issue starts ow. We kow that this happes if the die has 6 faces, but what would happe if the die has ifiite faces? The questio is, if we roll a die of ifiite faces, we will get a umber (whichever you wat from to ifiity). If I roll the die agai, ifiite times, will I ever repeat this umber eve if the die has ifiite faces? I fact, this ca be calculated. Secod (ad last) equatio: Pr = + ( )2 + 2 = ( ) = + + ( ) = ( ) ( + = = (2) ( )2 ( ) + + + 2 ) The process followed is the same as before, but istead of 6 faces, we put faces. Surprisigly, the result is the same, eve whe (the umber of the faces of the die ad also the umber of times I throw it) teds to ifiity. The possibilities are 00% that I will repeat the umber eve with a die of ifiite faces. This has importat philosophical cosequeces, as we will see i the followig chapters. 2
J.Sáchez 3. Probabilities of ew uiverses to happe We do ot kow much about whatever is outside the uiverse, the laws or mechaisms that work there. But, we ca ifer some thigs: There is a law, process, mechaism (as you wat to call it) that had led to this uiverse to happe. With the available iformatio, there is othig that tell us that it caot happe agai (the creatio of other uiverses whether they are differet, similar or equal to this oe). Regardig the secod statemet. The alterative to that oe is that it exists a limit to the umber of uiverses that could be created. A kid of fuel to create uiverses that whe it is fiished, more uiverses caot appear. The problem with this, is that whatever law or mechaism that allowed this fuel to exist i the first time, there is othig that tell us, that could ot allow ew fuel to appear agai. Ad we are i a circle of the same reasoig, makig the secod statemet true agai (but i a secod level). 4. What makes you be you At this stage of huma kowledge, we still do ot kow what makes you be you. The oly thig we kow is: Everythig poits to that the huma cosciousess is a emerget pheomeo that appears because of the iteractios of the euros i the brai. Whether it is a physical process directly attached to the euros or it is a emerget process that could be reproduced replicatig these iteractios i other physical systems (i this era, typically semicoductors, but could be whatever other system) we will see that is irrelevat for our purpose. 5. Radomess of how the ext uiverse will be Regardig the radomess of the possibilities, we have two optios: The die that decides how the ext uiverse will be is umodifiable. This meas, the possibilities of the ext uiverse to be the way it will be, do ot deped o previous uiverses ad do ot chage. It is a perfect umodifiable radom decisio. The die that decides how the ext uiverse will be, has memory, depeds o previous results. The possibilities (the faces of the die), chage every time you throw it. It is ot a perfect radom decisio. If the secod optio is correct, we have agai two optios: 3
J. Sáchez The modificatios of the die are chaotic. This meas, they do ot coverge to a defiitive fial die. The faces of the die chage cotiuously every time you throw the die, ad the chages of the die themselves are radom. With the possibility eve, that at some poit the die is exactly the same as it was before aother throw. This situatio is completely radom, ad it is idistiguishable from the situatio of the umodifiable die for our purposes. The reaso is that we will always fid a face of the die (a solutio for the ext uiverse) that ca be ifiitely similar (with as much decimals you eed) to the oe you wat to repeat. This has bee clearly studied i chaotic systems, where the shapes of the results ca be repeated ad ifiitum eve if they are ot exactly the same. But they ca be repeated with the ecessary precisio eeded. [2] Figure 2. Retro-style chaotic Madelbrot set performed i a 8-bit MSX machie. The modificatios of the die preset a evolutio. The die coverges to a fial state. The laws of evolutio (survival of the most stable solutio) apply ad the shapig of the die is ot radom aymore, it coverges to a fial state. The secod optio (ad what evolutio meas) will be commeted i the last chapters. At this stage, we will focus i the first optios. The die presets a perfect radomess every time you throw it. 6. Ca it appear a uiverse exactly equal like this? Or is it eve ecessary that this occurs to repeat yourself There are two possibilities: It is possible that a uiverse exactly like this appears agai. 4
J.Sáchez It is ot possible that a uiverse like this appears agai (because the iformatio that cotais is ifiite ad caot be reproduced exactly the same agai). The secod optio could be disregarded because the uiverse is ot ifiite ad for sure all the iformatio cotaied i it is fiite ad ca be reproduced. But ayway, it is ot eve ecessary that this last setece is true for our purpose. Eve, if the uiverse caot be repeated exactly as it is, we do ot eed it. The oly thig we eed is that whatever thig that has to be repeated for you to be you agai, is ideed repeated. This meas, a uiverse, where appears a beig with the same cofiguratio of euros at a specific time/state. Or a uiverse with a system that reproduces exactly the iteractios (with aother physical system) of your curret euros so the emerget pheomeo of you appears agai. The issue is that a lot of uiverses ca appear i-betwee, ad we do ot mid, we will ot be there. The oly thig eeded is that oe uiverse appears that reproduces whatever system that creates the emerget pheomeo that is you. Ad oce that uiverse fiishes, it will appear a lot of ew uiverses util oe i which you appears agai. I fact, this priso of eteral repetitio has bee proposed already by may philosophers beig the most famous Nietzsche ad his Eteral retur [3]. 7. Immortality So, accordig previous chapters the mathematics tells us that is very probable (ad if the assumptios are correct, eve almost uavoidable) that you appear agai somewhere i aother uiverse (exactly the same as this or eve differet) agai, cotiuously. Ok, it is ot the immortality you wated. You will ot remember aythig of whatever you (whatever you meas) did i other places. You will just always be, as the uiverses will be repeated util you appear agai but with o memories or ay coectio to whatever you have doe before. But, yes, you will always be awake if that is your questio. You will die ad be awake cotiuously. It is ot the best form of immortality you dreamt, right? Let s move to the ext topic, ad the we will recap. 8. Probability versus stability () Imagie a pool full of balls of a lot of differet colors. There are thousads of balls i the pool. Imagie that there are these two laws for these balls: If oe hudred balls of the same color are i cotact cotiuously (formig a sake), they will be joit, formig a permaet sake ad caot be separated agai. The balls that do ot fulfill the previous poit keep beig completely free ad ca be moved with o restrictio. 5
J. Sáchez Ok, whe we start the experimet how may sakes do you thik there will be i the pool? It is clear, oe. It is very difficult (if ot almost impossible) that 00 balls with the same color are i cotiuous cotact. The most probable solutio is that the balls are radomly distributed, ad o sakes exist. Now, let s apply high vibratio (a big eergy sufficiet to chage the distributio of the balls radomly) to this pool. Ad let s apply it durig a log time (millios of years or more, as much as you wat). What we are doig is to allow the distributio of balls to be modified cotiuously (eergy ad time are the properties that huma beig associates to this uiverse to uderstad the possibility of modificatios, but the importat thig here is that we let the system of balls to be modified cotiuously idepedetly of the way we do it). Let s focus o the pool agai. After a billio years of vibratio, how may sakes of balls will be i the pool? Exactly, a lot, almost all the balls will belog to a sake (probably we will have less tha 00 of each color that do ot belog to a sake). Why? Because there is a law that supersedes ay other laws regardig probability or ad-hoc laws we wat to impose. I a world where ifiite modificatios are possible, stability wis over probability, it does ot matter which improbable it is. The most stable solutio always wis over the most probable solutio (if all the ifiite possible solutios are tested at least oce, -this meas, they are permitted ifiite modificatios util we get to the stable oe-). The issue here is with the first law of balls. If you read it agai, you will read a permaet sake that caot be separated agai. This is the poit, it is ifiitely stable solutio. Oce you are there eve by chace, you caot escape. You oly have to have the chace, eve if it is oly oce. 9. Probability versus stability (2) I am ot reivetig the wheel here. This has bee tested by ature cotiuously, leadig to the laws of evolutio of survival of the fittest. The most importat poit of the evolutio theory is that it works radomly. You oly eed to create chages radomly ad the most stable (or fittest oe) will oe will wi. What are the possibilities that a complex orga as a eye appears from a buch of atoms? Noe. What has happeed i reality? It has appeared. Why? Because it was the most stable solutio for certai beigs to cotrol their surroudigs usig the electromagetic waves that were all aroud. What are the possibilities that a buch of atoms creates self-awareess? Noe. But it has 6
J.Sáchez appeared. It was the most stable solutio for certai beigs to have the will to survive ad replicate (yes, these are us!). It does ot matter how complicate, improbable, impossible is somethig to appear. It will appear if it is the most stable solutio. You oly eed ifiite (meaig a lot, but evetually happeig) modificatios util it happes. Ad i the world outside this uiverse (the world that has the laws that have let this uiverse or other uiverses to happe), it seems that the possibilities of modificatios, are ifiite as commeted i poit 3. 0. Evolutio of the die The other solutio commeted for the die, was that it evolved to somethig. With which law? Clearly, as commeted, the law of stability. If it teds to somethig, it will ted to the most stable solutio. If it does ot ted to somethig, as we have commeted i poits 5 ad 6, the result is eteral repetitio (ad its associated ifamous immortality). What is the most stable solutio for the die? Not to chage aymore. The immutability, to have oly oe face. To get to a solutio where the die is ot eeded (or is ot throw) to be throw aymore, as the most stable solutio/uiverse has bee achieved.. God So, yes, what is God i this perspective? The best, the most defiitive immutable solutio. The defiitive covergece. The best of the possible optios. But, the importat questio is, where are we i all of this? Is this somethig that will be happeed somewhe i the future that does ot affect us? Is the God of the religios really participatig i this world or is it a just a cocept of the perfectio iveted by the huma beig that evetually could happe whe oe of us are here? 2. Cocept of God From the most atheistic poit of view, God is a ivetio of the huma beig to aswer to the questios they do ot have a aswer, or they fear. I the begiig where does the rai come from? Now, how was the uiverse created, or is there a life after death? We have see i this paper that God, istead, could be result of the huma ituitio. Meaig that somehow, the huma beig has had the feelig that the same mechaisms that have brought us -as self-awareess beigs- here (evolutio laws i the ed) would lead to aother eve more perfect solutio/beig. As it could ot put this feelig i a ratioal perspective it has bee always led to emotioal or mystic coceptios. The idea od God as the result of uavoidable perfectio has already bee proposed by 7
J. Sáchez several philosophers beig Descartes ad Aselm of Caterbury amog them [4][5]. The couterproof towards them has always bee that that there is othig that obliges the reality to create this perfectio, oly because the huma mid is able to imagie it. I this paper, it has bee explaied, that there is o obligatio to be created. It is a probable solutio just followig the laws of ifiite modificatios (expected to be possible i whatever other extra-world that has the mechaisms for this uiverse to appear) ad the law of the most stable solutio to be the wier. Oly two solutios: eteral repetitio with o covergece or defiitive perfect immutable solutio (what has the cocept of God for the huma beig durig ages). I fact, this same explaatio tells us why there is somethig istead of othig. The othig is ustable, whatever possible evet that appears breaks it. Istead, the somethig ca create its mechaisms of survival ad eve replicatio (replicatig uiverses for example) to survive. So, o metaphysics eeded, just logic. It survives the stable solutio (it does ot matter how improbable it is) ot what it is the most probable oly for a certai state of thigs. This meas, if the differet uiverses ad the laws (the die) that creates them ted to somethig, teds to the most stable (ad so immutable) solutio. If ot, to eteral repeatability. 3. But does God have a log white beard? () Eve, if you do ot believe it, this is the most importat questio of this paper. Meaig: is God just a theoretical cocept that will happe whe we are ot here ad that does ot affect our lives at all? Or is it really somethig existig ow that could affect our world? Durig years, it was thought that it was ot possible that a omisciet beig existed ad at the same time, the huma beig had free will. The reaso was clear. If there is a beig that kows what is goig to happe, this meas that the huma beig caot chage it, so it does ot have a real free will (everythig is already writte). The Methodists [6] came up with a solutio. They said that the omisciet beig was able to be i all the times at the same time kowig what happes i every time, but that the huma beig i its ow existece, i its ow view of the world could still take the decisio he/she wats. I put a example. All of us kow that Napoleo made a mistake whe eterig Russia ad it was the start of the ed for him. All that we are here at this time, we kow that. But the thig that we kow it, has affected the decisio of Napoleo? No, we could thik that 8
J.Sáchez he had free will ad that we kow ow the result i other time, ad we are ot affectig his decisio. The Methodists say the same about omisciece. God is everywhere ad at every time (kows that Napoleo made a mistake ad kows the mistakes you have committed, but that does ot mea that you are ot free to do them i your existece ad i your time). 4. But does God have a log white beard? (2) The questio is, if we uderstad God as the defiitive, fial solutio to all the possible modificatios of uiverses existig util arrivig to a perfect immutable solutio, ca it affect our world? I will oly aswer if it is possible or ot, ot of it really does or ot. It could affect our world i a way. The most perfect defiitive solutio, it is uderstood that has the cotrol to all the possible reality wheever or wherever it has appeared. So yes, the same as commeted with the example of the Methodists ad omisciece would apply here. Oce the beig is created it could have cotrol over everythig that has already existed i its ow time, so it could affect. I repeat, I am ot sayig it does, I am sayig the possibility exists. Stroger pushers regardig pre-existece are clearly Pierre Teilhard de Chardi ad Frak J. Tipler. [7][8] You ca see a metaphor of this i the film Iterstellar [9]. There, some beigs have evolved so much that they ca act i the dimesio of time, the same way we ca act, for example, i space dimesios. So, they use this possibility to act i the past to facilitate that their ow evolutio happes. Somethig similar, could happe if a beig capable of cotrollig all what it exists, appear. Apart from the questio of if it affects this world or ot, there is aother oe. I the previous poits I have commeted the ifamous immortality of the eteral repetitios of you (i the same situatios or i other, but completely idepedet oes to the others). Is it possible that the immortality that the religios talk about exist? If the solutio is the covergece, as commeted, yes it could be possible. Agai, I am ot sayig it does, I am just sayig it could be possible. We ca expect that if the fial solutio to all the reality is the most stable ad the best oe, it is better a solutio where the beigs ca keep existig tha a oe without them. Ad eve it is better a solutio with all of them that oly with a part of them as the oes remaiig will cosider better the oe with other oes also icluded, so the solutio should chage agai (it is ot the defiitive oe). These last chapters are the most speculative ad talk oly about possibility or ot, ot about if it is or ot. But, this should ot affect the previous chapters where the possibili- 9
J. Sáchez ties of the differet coclusios are really checked i the most possible scietific way (usig logic ad mathematics). 5. Coclusios Usig logic ad mathematics, we have arrived at the followig coclusios: The possibilities that whatever makes you be you agai are repeated, are very high (if ot uavoidable). Oe of the solutios of the possible ifiite modificatios of uiverses to come, is to evolve to a defiitive stable solutio. If ot, the solutio will be the eteral repetitio, makig above poit eve more probable. The cocept of God as the defiitive stable solutio commeted i the secod poit above, has bee developed ad related to the cocept of God as geerally uderstood. Bilbao, 3th April 209 (vixra-v2). 6. Addedum v2 A last commet Oe of the questios that could appear is the followig? But, why we? How may beigs could exist i all the possible uiverses ad why could we be immortal -i the meaig that our life (or at least what make us be us ) could be repeated ifiite times- ad the rest of possible beigs ot? The aswer is that this ca happe to all the possible beigs (ad i fact to everythig -whatever this meas- that could exist) with o restrictio i the umber of repetitios. Why? Let s go to the Hilbert s paradox of the Grad Hotel [0]. We have a hotel with ifiite rooms ad all of them are occupied. The a ew guest appears. Could we give him a room? The aswer is yes. We could move all the guests to the ext room (the oe i room to room 2, the oe i 2 to 3, the oe i 3 to 4 ). So, we will have the room free agai, ad we could give it to the ew guest. Ad if ifiite ew guests come? We could move the perso that is ow i i room, to the room 2. The perso i room 2, to the room 4. The perso i room 3, to the room 6 ad so o. I that case, the rooms,3,5,7 will be free agai. So, we ca give our ew ifiite guests these rooms. So, what s the meaig of all this? The cocept of completeess that we have i our ituitio does ot work for ifiite thigs. The ifiity ca be complete ad at the same time ca make more space to ew thigs with o restrictio. This meas, it is possible that ifiite beigs exist (i fact, all that is possible could exist at least oce i oe of the ifiite possible uiverse) ad the exist agai ifiite times, as commeted i the paper (chapter 2 ad 3). There is o restrictio to the umber of possible beigs existig ad to the possible times that they exist. Ad the last commet regardig covergece. I the paper, I have commeted that what we usually call God could appear as the result of covergece of the possible solutios, this is, a kid of evolutio. Really, this is ot eve ecessary. If it is possible that God appears (a beig able to cotrol all the reality, all the possible uiverses), oly if it is just a possibility, this meas, it is oe of the faces of the die which is throw whe a ew uiverse is created, it will appear. As commeted i chapters 2 ad 3, if it is possible it 0
J.Sáchez will happe, as the die will be throw ifiite times with all the possible results happeig ifiite times. Ad oce that has happeed, as we cosider it ( God ) a stable solutio, it will remai. But eve, if it is ot stable, it will happe agai ifiite times, as commeted also i chapters 2 ad 3. I fact, this applies to whatever thig/beig that has the possibility to appear, it will evetually appear, as it will be oe of the results of the die that will be throw ifiite times. 7. Ackowledgemets To my family ad frieds. To the umoved mover. 8. Refereces [] https://e.wikipedia.org/wiki/geometric_series [2] Gleick, James (988) Caos, La creació de ua ciecia. Seix Barral, Barceloa, Spai [3] https://e.wikipedia.org/wiki/eteral_retur [4] https://e.wikipedia.org/wiki/re%c3%a9_descartes [5] https://e.wikipedia.org/wiki/aselm_of_caterbury [6] https://e.wikipedia.org/wiki/methodism [7] https://es.wikipedia.org/wiki/pierre_teilhard_de_chardi [8] https://e.wikipedia.org/wiki/frak_j._tipler [9] https://e.wikipedia.org/wiki/iterstellar_(film) [0] https://e.wikipedia.org/wiki/hilbert%27s_paradox_of_the_grad_hotel