What is an order-of-magnitude estimate? Enrico Fermi described this type of estimation by using it to estimate the number of piano tuners in San Francisco. By estimating the population of San Francisco, the percentage of people who own a piano, the percentage of people who get their piano tuned each year, the length of time that it takes a tuner to tune a piano (including an allowance for transportation time to and from the location), and similar information, we can make an order-of-magnitude estimate of the number of piano tuners in San Francisco. “Order of magnitude” refers to a multiplier of 10 between each number; 1000 is an order of magnitude larger than 100 and two orders of magnitude larger than 10. From an estimate like this, we can say that there are about 50 piano tuners in San Francisco (probably more than 5, and not as many as 500). We can’t say for sure whether there are 40, 50, or 60.
We can use an order-of-magnitude estimate like this one to evaluate the approximate probability of the formation of the first genetic information. Standard macroevolutionary theory teaches that the first genetic information was formed as RNA (ribonucleic acid) by the random polymerization of the four different types of nucleotides that compose RNA (adenine, cytosine, guanine, and uracil; hereafter abbreviated A, C, G, and U). These random polymerizations are said to have taken place on the surface of certain types of clay, which can be shown in laboratory tests to catalyze (or speed up) the random polymerizing of RNA (and ultimately the formation of the first genetic information). The assumptions we will make in this order-of-magnitude estimate will err on the side of favoring the macroevolutionary scenario; thus, if our probabilities are infinitesimally small, we will be justified in questioning its viability.
Here are the assumptions we will make:
- We are trying to produce the genome of a typical bacterium (6,000 base pairs, which means 6,000 nucleotides matching in a row)
- We will assume that if we can get one strand right, that the other will automatically complement it. This happens easily, even outside living creatures.
- Excess nucleotides will always be present (never mind where they came from–we’ll assume they are not the limiting factor. They must also be produced frequently, since cytosine has a comparatively short half-life.)
- The Earth’s entire surface is covered with some clay that promotes polymerization (such as montmorillionite clay–a current favorite).
- These nucleotides are allowed to polymerize throughout the Earth’s history, estimated by macroevolutionary geologists at 4.5 billion years (recall that this is unreasonably generous, since it leaves no time for higher forms of life to evolve).
- We will assume that there are a billion different viable forms of the bacterial RNA (to allow plenty of room for different species to arise, and also to allow plenty of room for polymorphisms; note that it is estimated that there are only 0.002 to 0.1 billion species of all kinds in the world today, including hundreds of thousands of insect species).
- For added generosity, let’s assume that there are a billion planets in the universe that have this setup (it will increase the odds that one planet will get a set of bacterial RNA)
- Let’s also assume that there are a billion universes with this same setup (macroevolutionary cosmologists and physicist postulate their existence in order to raise the odds for evolution happening on earth–but they have not been observed!)
Now, let us calculated the probability of getting a given viable bacterial RNA. The odds of getting the first nucleotide correct is 1/4; also for the second nucleotide and beyond. Since each polymerization is independent of the previous one, we multiple the probabilities to get the overall probability. Since the chain is 6,000 nucleotides long, we need to do this 6,000 times. The odds of doing this correctly for a given RNA sequence are (1/4)^6000. This number is too large to be calculated on most calculators, but wolframalpha.com, a search engine which specializes in scientific and mathematical information, calculated it for me: (1/4)^6000 = 1 in 2.3*10^3612. Since it’s difficult to understand how large this number is, I asked Wolfram-Alpha to give the full number. Here it is:
2290593203500326442498254071102877992464615830839054768055123450544313 3851077403791573877586580573186350995335624442848376566408900340661545 7341269160953934651531316272895970961099648619548663674165694428394886 9330648470173371350813320809268809952407079715398039210502009557335794 3662055666767306385538495087529677470990968153918788613785751389005221 2385415364000233552517923094155148081278364846747449615787812522617139 5342006341679075520576304970776016746818912261453204962575441115371836 9447156895505073882545721273943517481650733405401933044529879802965087 4661803072896341035911246341091848324390496868908539422798829655406361 3709807896975047594167461331023628146001054998291892885044803396603840 7878196527044715747436853386831577880020356214741210341558715729680198 0525189824097250230848812002387365002027283572275248844963488736471394 3526031912848227248826190464847696594892838239669305251912416877251755 3390869295245378359828370235435165885369163710464894220310701508827933 3805264299792599815801920922903898158871712892609715338272913453162186 5313978608581541705515982751534447133263250347818367765137031003609793 8897585753779083035010667766548311999605347475370343426743825340005381 0997864187276609708209309038066394442278969691365489002023222850825449 7953096787063044370098338492177314930216742550624871750833859476679189 5095680602732346712939153259990811489391303284206503760197305419615240 9217301646404793801369143966718432036059811187775136277557250792266837 4235979682286834034089138475154767372727122932222887885208321879666030 5975797728877829876864681599425995732540887496009877581583503399859516
4751217086975807460294738428018338592485796034133919973077413533686949 1956368516611377674237208178041919106870280789033916144099126661387307 7526600578045242253024373178584527824852295057513761093944464722805553 9117717164315059230286413698788578331540178223949579078165011005988727 4595946783100447198954930537574190738099064718222518825147478490657161 1675484975233339688122794911475119965635459462447339289782867275308572 1621023943443062014490727808446685389294420571986970601078764950034180 6904790181420256733072612769503473201816461274039931292984401423199725 4340930170763466037725337419662914359959934881352713101312534635085302 3203781630211532813886686430142939639476747185671316635043595580465472 5436951706056632361702749907044372801683830358699136529946432620564283 9343150405350488810175472025383807889192539392721103826349328251385543 8169772823869564875140655788823474751813846542682825520838131006911762 5217360239526199430454346435033842859303165451350797675107176380424351 2718983930779120937657434512013867455548820224148073627378623609980111 1130760640189547044207203761774747082024351686619800395756958410106080 4661356296500120146645677141557786648630936176345539004262109110167208 9100758253488015840017224071067971558665492397885347660725631381708401 9127947685341853735187972127773344945050773031895050404703449225069038 7355696568657085290734466234786952456543122517479114466613670208736084 2313671545657762822696089905680216827990227867450866967383478161022109 0005418907699377867277059648206586073751433641713011744511704016132334 9063389003771777472580944833242545989973822564674460973839015552175709 6422261937569234096692347902063011590763830494478011352558782053282752 6432990876482679910153249074963538068771014944040060242262380449774268 2401904233153226013937331725013335198352712395550422922110105171367715 4198166625001314304274403493877643127657624870317305687566284108475166 0001324414350620739304183073837766897250290371164996773381894357892372 5532823256616542654631382911359993958629376.
Wait, though! We’re not done yet. That number hasn’t been adjusted for all our generous assumptions. Let’s do that now. We have assumed that there are a billion different viable forms of this DNA, on a billion planets, in a billion universes. This makes 10^27 different simultaneous possible opportunities for our first RNA to have been produced. This means that we need to divide our probability of roughly 1*10^3612 by 1*10^27. The odds of that first RNA forming are now reduced to 2.3 × 10^3585. But we still have 4.5 billion years, or 141,912,000,000,000,000 (141 quadrillion, or 1*10^17) seconds to do it in. How many polymerizations would need to be happening per second on Earth? We divide our answer by this number of seconds and find that our probability has now decreased to only 1.6 × 10^3568. How many polymerizations per second per square centimeter of Earth? The earth’s surface area can be shown to be about 5 *10^18 cm2 (its radius is about 6.8 *10^6 meters). Dividing our previous probability by this amount, we find that we would require about 1× 10^3549 polymerizations per second per cm2 on Earth and all other Earth-like planets included in this analysis, simply to develop the first bacterial chromosome(s).
Researchers observering the polymerization of nucleotides on Montmorillonite clay have not noticed speeds in excess of 1 nucleotide per thirty minutes (in laboratory environments designed to facilitate the process).  This indicates that the current model does not provide an even remotely probable model for the origin of life–bacterial or otherwise.
Just to clarify this, let us apply the same reasoning we have previously used to the development of the human genome. Although developments after the first bacterium appeared would have been more complex, most of them would still have been by random single nucleotide mutations. This means that our probabilistic calculations can provide a rough estimate of the probability that the human genome arose by random genetic mutation. The human genome consists of 2.3*10^9 base pairs. The probability that this genome would arise by random mutation is 1 in 4^2300000000, or 1.133218×10^1384737980. It’s hard to describe how big this number is. I was going to copy and paste it into a separate document, but it is about 10^10 digits long. If we could put 1000 digits on a page, it would take about ten million pages to hold the number. It should be clear from our previous calculations that the generous assumptions we made to the standard model are inadequate to allow for the development of the first genetic material by random polymerization and mutation. In the face of these facts, it seems difficult to believe that this first step in the macroevolutionary process could have taken place. Thoughtful observers must continue to search for more viable explanations. Further posts will consider this subject in greater detail, drawing on evidence from a variety of disciplines.