# Please critique my theory-compare Drake's equation

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#### newtonian

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Critique and comments on my theory (i.e. my version)<br /><br />P = TxRxA<br /> <br />Where P = the upper limit of chemical reaction products in our universe since our universe began - 10^122<br /> <br />T = the time alloted for chemical reactions to proceed (in this case, the age of the universe) - 10^18 seconds<br /> <br />R = the upper limit of rate of chemical reactions - 10^24 per second is, of course, an overestimate.<br /> <br />A = the upper limit of atoms available for chemical reactions to proceed, less than 10^80 in our universe.<br /> <br />The extention of this theory to specific probabilities for specific reaction products is of course also part of my theory. <br /> <br />The next step: C is less than P.<br /> <br />C being the number of statistical proteins produced or any other specific reaction product.<br /> <br />C is also less than P divided by B [e.g. 10^122 divided by 10^112 = 10^10]<br /> <br />Where B is the predicted probability of C: 10^112<br /> <br />C divided by T = G<br /> <br />Where G is the predicted rate of formation of C during T.<br /> <br />10^10 statistical proteins divided by 10^10 years = one per year.<br /> <br />The law of large numbers also applies to my theory.<br /><br />In word form (Newtonian style): the larger the number of trials, also the larger the number of steps to the target chemical reaction product (e.g. a statistical protein) makes the predicted probability more certain. <br /><br />Critique is welcome, as are any comments.<br />Of course, the upper limits in the above calculation can be applied to many things, including the search for earth-like planets.<br /><br />And it can be incorporated into Drake's equation as a upper limit factor.<br />

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#### newtonian

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Wow - 38 views and no responses! I'll help you all along a little. <br /><br />Consider the independent but relevant Drake's equation by Frank Drake (reproduced roughly):<br /><br />N= R* Fp ne f-omega fi fc L<br />Of course, Drake goes way beyond my simple theory, and it is very difficult to put numbers to his formula for the number (=N) of detectable intelligent civilizations in the Milky Way.<br /><br />Since my theory deals with upper limits rather than the actual numbers, it is much easier to find an accurate result.<br /><br />Still, I would appreciate critique of the tentative numbers I have posted for the factors in my theory formula.<br /><br />And also where you would put it as a factor in Drake's equation.<br />

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#### mooware

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So tell us what numbers you come up with, what they mean and what you are trying to prove with this calculation.<br /><br />

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#### newtonian

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mooware- What am I trying to prove? <br /><br />Answer: The truth, whatever that turns out to be.<br /><br />To be more specific: <br /><br />Drake's equation tries to determine the number of detectable intelligent civilizations in Milky Way- he seems to assume by chance, despite the obvious skewing factor that intelligent civilizations could create life with a much higher probability than would be the chance formation of life represented in his equation.<br />My equation or formula also assumes chance formation, specifically chance combinations.<br /><br />There are many applications of my theory, but I zeroed in on one for the sake of simplicity:<br /><br />Trying to determine the upper limit of rate of formation of statistical proteins [by chance] in our universe since our universe began.<br /><br />In my next post I will zero in on one factor at a time and both explain why I punched in the specific numbers I did for upper limits, and also try to post a plausible estimate for the actual most likely number, which would be like a mean between upper and lower limits - but far more complex than that.<br /> <br />Meanwhile, study my first post. I did post numbers for the factors already.

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#### thalion

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Disclaimer: I'm neither a chemist nor a statistician.<br /><br />I think your formula is too inclusive. You're tacitly including interactions between all the elements in the cosmos. If it's life as we know it that we're worried about, we should only be concerned with the "big four": carbon, nitrogen, hydrogen, and oxygen. There is a large, but probably not infinite number of ways that these atoms can combine. Let's not forget as well, that the proportion of these elements has not been constant throughout the age of our universe, which would affect the numbers in your formula.<br /><br />Finally, proteins are very large, complex molecules, even more so than DNA/RNA itself; the factor of their complexity seems to be missing from the formula. If you're working from raw probability, with no other considerations, the statistical likelihood of a protein spontaneously assembling is vanishingly small. It's like asking what the probability is that, somewhere in the universe, there is a spontaneously-assembled--assuming pure chance controls what does and doesn't form--graham cracker copying machine with protractinium sheets of paper.<br /><br />The assumption of pure probability is, IMO, a dead-end with respect to the origin of life. The entire reason we believe that the origin of life is discoverable is because we believe that molecules behave in predictable ways that make certain configurations more likely than others in different circumstances.<br /><br />Second, different reactions are possible under different conditions. The spontaneous assembly of a simple sugar is much more probable in a concentrated solution than it is in deep space. With this in mind, one should take into account the likelihood of the combinations occurring in different environments.

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#### mooware

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<font color="yellow">"Answer: The truth, whatever that turns out to be"</font><br /><br />Mee thinks you've already come to a conclusion of what the truth is. Otherwise, I have a suspicion, you wouldn't have come up with this type of formula. <br /><br />So, what is it, and how do your numbers prove it?<br /><br />

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#### bobw

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<blockquote><font class="small">In reply to:</font><hr /><p>R = the upper limit of rate of chemical reactions - 10^24 per second is, of course, an overestimate.<p><hr /></p></p></blockquote> <br /><br />I think that number is outlandish and your assertion that it is an obvious overestimate is pulled out of thin air along with almost everything else that I have read which was written by you.<br /><br />The space shuttle main engines burn 17000 gallons/minute of liquid oxygen; that's 283.333 gallons/second. LOX has a density of 1141 kg/m^3. 1 gallon = .0037584 cubic meters so the space shuttle burns 1.064878 X 1141 = 1215.025 kg/sec of oxygen. At 16 grams/mole there are 75939.0625 moles of atomic oxygen combining with the same number of moles of molecular hydrogen each second in the shuttle engines. As I'm sure you recall, a mole is 6.02 X 10^23 atoms. I would call each molecule of water formed an individual chemical reaction, wouldn't you? <b>That means that each second while the shuttle main engines burn there are 4.57153 X 10^28 chemical reactions per second !</b> <br /><br />This dwarfs your estimate of the upper limit of reaction rates for the whole universe. I just don't know any way to critique your post other than to say that whoever wrote it doesn't have a clue. I suppose that's an ad-hom. I can't take anything you write seriously. Sorry, kids learn this stuff in high school chemistry classes all over the country. <br /><br /><blockquote><font class="small">In reply to:</font><hr /><p>And it can be incorporated into Drake's equation as a upper limit factor. <p><hr /></p></p></blockquote><br /><br />Yeah, right. <div class="Discussion_UserSignature"> </div>

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#### bobw

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I don't know. 10^24 just struck me as wrong because there are six times that many molecules in 180 grams of water. Well, all the "of course", "certainly", and "obviously" gets on my nerves, too. <div class="Discussion_UserSignature"> </div>

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#### paleo

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The number of chemical reactions is irrelevent. Take whatever number you come up with and multiply it by a million or reduce it by a million. It is meaningless unless you can show a relationship to the formation of life. The same with all the other variables.<br /><br /> We don't know how life formed on Earth so we can't say what variables need to come together to form life. We don't know if other variables can lead to life. <br /><br /> Your "In word form (Newtonian style): the larger the number of trials, also the larger the number of steps to the target chemical reaction product (e.g. a statistical protein) makes the predicted probability more certain."<br /><br /> This means nothing without a base line. 'makes the predicted probability more certain' can mean makes it more likely to happen twice instead of once in a quadrillion or can mean can make it more likely 999 times out of a thousand.<br /><br /> All the predictions about the frequency of life in the universe is a bunch of hooplah until we understand the mechanism of the origin of life. Otherwise, all predictions are a house of cards built on a house of cards. <br /><br /> Please, however, keep speculating. It's one of those topics that gets the gray matter turning over.

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#### paleo

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A side note on the number of reactions. That went over my head in the original posting. A lesson that these big numbers are often more 'adjectives' than actual mathematical representations of reality.<br /><br /> Leave off a zero in describing the number of stars in the universe and nobody will blink. Not even most astronomers. What you've done in effect is reduced the size of the Universe (all existence) by 10 times. Quite a monumental achievement considering your not god.<br /><br /> We should be pitbulls when it comes to questioning numbers that are used as the premise for further theory building.

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#### newtonian

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Thalion - Thank you. Excellent points and I agree.<br /><br />However, remember, I was trying to calculate the upper limit. Anything which lowers the limit obviously does not challenge the higher limit.<br /><br />Of course, for a statistical protein to form at the predicted probability of 10^112 against assumes a primordial soup of suitable molecules only.<br /><br />That is clearly not the condition of most of the mass of our universe - nor could it be. <br /><br />I agree that the upper limit should be many powers of 10 lower than 10^122 - in fact, I agree it is "vanishly small." The problem is that "vanishly small" is not a number!<br /><br />Note also the difference between the number of ways atoms can combine with the number of combinations that can actually occur in the finite period of time (the age of the universe) and the finite number of atoms (compare the mass of the universe).<br /><br />The number of ways atoms can combine is not constrained by time and mass - see the difference?<br /><br />Now, I agree the big 4 are most important. However, do you know any life form that uses only the big 4?<br /><br />I am quite sure other elements, like Phosphorus, are required.<br /><br />I agree that probability alone cannot acount for life, and that our universe is fine tuned to favor life, both the creation and the sustaining of life as we know it.<br /><br />However, that is not part of my theory, as you correctly note.<br /><br />My theory must indeed by modified by the degree of fine tuning we find in our universe as continued study of chemistry in our universe reveals.<br /><br />We do, however, already have a massive amount of observational evidence in the field of chemistry - we are certainly not in the dark as to how the basic molecules which have been discovered in space react or what the probability of various reaction products in various environments are.<br /><br />Frankly, it seems more likely to me that our earth was seeded with building blocks of life that are the

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#### newtonian

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crazyeddie - Yes, scientists sometimes formulate the theory without sufficient proof.<br /><br />Or sufficient critique. Which is why I asked for critique.<br /><br />Now if I object to your saying I am subjective, is that objective or on the subject? <br /><br />How I love the English language!<br /><br />Seriously, do you have some alternate numbers you would like to postulate for any of the factors in my theory equation? Or in Drakes equation?

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#### newtonian

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crazyeddie - You are zeroing in on an important factor, but your question avoids it. You posted:<br /><br />Are you talking about the total number of actual chemical reactions that have taken place, or the total potential number?<br /><br />In fact, my theory is giving an upper limit to the highest possible number of chemical reactions (and products) that could potentially have taken place. <br /><br />My theory is not stating the highest possible number of chemical reaction combinations period- the potential is limited by the factors of time, mass, and speed limit for reaction time.<br /><br />I'm still learning Drake's equation - I don't know yet how to factor P into it.<br />

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#### newtonian

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a_lost_packet - This is only the first packet of response - since I'm short on time.<br /><br />And that's the point, our universe has had limited time- so, no, I am NOT supposing that an infinite number of permutations will be achieved in a finite period of time!<br /><br />I do not actually believe life is inevitable, I do not believe our universe is that fine tuned. <br /><br />However, I am not closed minded on just how fine tuned our universe is. <br /><br />That being said, fine tuning effects only one side of the equation: the probability of the end product, in my specified example that would be a statistical protein.<br /><br />Fine tuning does not effect the other side of the equation, the upper limit of possible chemical reaction products formed in our universe since our universe began.<br />Alas, I lack the time to examine those links now, hopefully tonight.<br /><br />Now, unlike Drake's equation, the factors in my equation are not so difficult to determine.<br /><br />Do you feel a specific number I factored in to the equation is higher than it should be?<br /><br />I tried to make the numbers as generous as possible to be sure I had stated an upper limit.<br /><br />It is my opinion further study will lower the upper limit to below 10^122.<br /><br />Though I love discussion and welcome it, I am really looking for actual numbers to factor in- i.e. alternate from what I stated.<br /><br />Thank you for your response and links.

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#### newtonian

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bobw - Thank you for that excellent post, albeit you forgot to multiply!<br /><br />You fundementally misunderstand the reaction limit.<br /><br />Each atom can only react with each other atom 10^24 times per second. I have given the limit for one atom only. Your example involves many atoms.<br /><br />See your error?<br /><br />If you have 10,000 atoms involved in the reaction, of course you can have 10^28 reactions per second as an upper limit.<br />Your example involves way more atoms than that!<br /><br />According to your own posted numbers, one mole of oxygen contains way more than one atom! <br /><br />To get the total upper limit reaction products in your reaction example, you have to multiply as follows:<br /><br />6x10^23 x 75,939 x 2 (oxygen times hydrogen atoms) x 10^24 (reaction speed limit per atom). That is over 10^52!<br /><br />That would give you the upper limit of chemical reaction products per second with that number of atoms involved.<br />Remember, my limit on reaction speed gives the chemical reaction speed limit for one atom - not 10^29 atoms! <br /><br />The reactions on that shuttle are way lower by at least 28 zeros (28 powers of 10) than my stated speed limit!<br /> <br />The upper limit is not out of thin air, btw. It is based on the amount of time it takes light (a photon) to cross the nucleus of an atom. <br /><br />Feel free to post another estimate for reaction time speed limit - I am certainly open minded on the subject.

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#### newtonian

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crazyeddie - This is my theory. I developed it quite independently, although I later found similar theories elsewhere.<br /><br />This happens in science - it is actually quite common.<br /><br />It is also irrelevant. The relevant point is whether I have actually posted a valid upper limit or not. <br /><br />Its that simple!

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#### newtonian

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bobw - simply:<br /><br />P=TxRxA<br /><br />You got T correct: 1 second.<br /><br />But you didn't multiply R by A- you missed the number of atoms (A) multiplied by R - the reaction rate upper limit.<br /><br />P = 1 (second) x 10^29 atoms x 10^24 reactions per second.<br /><br />P= 10^53 (estimate) reaction product limit; well above the actual reactions you cited, i.e. 10^28+.

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#### newtonian

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paleo - I did not post an estimate on the number of stars in the universe.<br /><br />P=TxRxA<br /><br />A is the number of atoms in our universe (an over-estimate), not the number of stars.<br /><br />I posted an estimate of the number of atoms in the universe - 10^80 amu give or take a power of 10 (one power of ten is ten times). <br /><br />The number of stars is about 100-200 billion stars per galaxy times 100 to 200 billion galaxies.<br /><br />One billion= 1,000,000,000 = 10^9<br /><br />100 billion = 2 more zeros = 2 more powers of 10 = 10^11<br /><br />Multiplying = adding the exponents<br /><br />10^11 x 10^11 = 10^22.<br /><br />So, perhaps there are 4 x 10^22 stars in our universe.<br /><br />Atoms is astronomically higher than this number - hence my estimate of 10^80 amu.<br /><br />BTW- the smallest atom, hydrogen, is about 1 amu. Other atoms have considerably more mass - see the periodic table of elements.<br /><br />If you wish to post an alternate estimate for the mass of our universe - please do so.<br /><br />By all means, question the numbers. <br /><br />Remember, I am trying to give an overestimate, so that the result, P, is a real upper limit.

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#### newtonian

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paleo- On your other post concerning application to the origin of life.<br /><br />Please note my theory can be applied to many things besides origin of life. And chemical reaction product proportion is relevant, whether a building block of life or not.<br /><br />It can also be applied to the search for earth-like planets.<br /><br />P could be the highest number of planets formed in our universe since our universe began.<br /><br />T would be similar, the age of our universe. You might want to use years rather than seconds as the unit.<br /><br />R would be the rate of planet formation- the fastest time a planet can be formed- clearly much slower than chemical reaction rates, and probably also best expressed in years rather than seconds.<br /><br />A would still be the mass of the universe. However, you would want to use units that would be reasonable for expressing the smallest possible planet mass allowed for an earth-like planet.<br /><br />Of course, more detail would be in Drake's equation, but some of the additional factors would be hard to estimate.<br /><br />ORIGIN OF LIFE<br /><br />As you brought this up, I assume you would be interested in applying my theory to this.<br /><br />As you note, that would be very difficult.<br /><br />I chose a statistical protein because it is simpler.<br /><br />Life requires informational proteins, not mere statistical proteins. <br /><br />And one must define "information."<br /><br />We do not know which came first, btw. Enzymes to catalyze protein formation, or a self-replicating protein or RNA or DNA.<br /><br />Realistically, life requires much more than this. For example, enzymes and receptors fit like a 3-D lock and key, and a key is useless without a lock- etc., etc. <br /><br />It is very complex. Feel free to attempt it- I have chosen to stay simpler.<br /><br />There are a limited number of ways, i.e. chemical pathways, by which a statistical protein can be synthesized. <br /><br />It is a very complex and difficult process.<br /><</safety_wrapper>

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#### newtonian

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a_lost_packet_ - OK, your first link, a thread which I hope to post on, states this on Drake's equation (alas, Nova Origins did not make this clear):<br /><br />The Drake Equation<br /><br />N=R*fp*ne*fl* fi*fc*L<br /><br />R = the average rate of star formation in the galaxy<br />fp = the fraction of suitable suns with planetary systems<br />ne = the mean number of planets that are located within the zone where water can exist as a liquid<br />fl = the fraction of such planets on which life actually originates<br />fi = represents the fraction of such planets on which some form of intelligence arises<br />fc = is the fraction of such intelligent species that develop the ability and desire to communicate with other civilizations<br />L = is the mean lifetime (in years) of a communicative civilization <br />P in my theory would be factored in as an upper limit for ne, sort of. It doesn't fit exactly, so I would propose modifying Drake's equation, as follows, for upper limits:<br /><br />R can remain the same.<br /><br />1. The maximum number of stars that could have earth-like planets with environments suitable for the origin and sustaining of life - or creation and sustaining of life.<br /><br />This could be expressed as a percent of R- say 10%<br /><br />2. The maximum number of such planets per star. This would be multiplied by the percent of R. Say10, hence 10 x 10%=1<br /><br />3. Assume intelligent life could be created on all such planets. That would be an upper limit.<br /><br />4. Assume that intelligent civilizations could exist forever. That would also be an upper limit.<br /><br />5. (out of order) Assume all intelligent civilizations could communicate with us eventually, assuming we also live forever - again an upper limit.<br /><br />OK, say R leads to 10 times the current population of stars: 10^23 stars.<br /><br />f is the maximum number of planets per star. Say 10 planets for one tenth of the stars. All have intelligence and can communicate.<br /><br />Then f beco

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#### newtonian

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a_lost_packet_ - That latter link is interesting - thank you for the link.<br /><br />The first page was disappointing to me, given the buildup that these are eminent scientists.<br /><br />One problem was the skimming over the chemical pathways to RNA, or proteins, or whatever they favor came first.<br /><br />This is basic chemistry, and examining the question in depth by eminent scientists certainly should include this chemistry.<br /><br />For example, no effort was made to specify any chemical pathway to RNA from the building blocks found on asteroids, etc.<br /><br />Water was considered favorable for life.<br /><br />The simple fact of chemistry is that water is the enemy of many steps on chemical synthesis pathways.<br /><br />Put simply, water reacts with many chemicals on synthesis pathways to complex molecules of life.<br /><br />The simplest and most obvious omission is the fact that HCN + H2O often yields HCOOH (formic acid) as a product.<br /><br />These are the specific steps:<br /><br />1. HCN + H2O yields (reversible) H-C-O-NH2 (the NH2 is bound to the C, not the O).<br /><br />HCONH2 is formamide.<br /><br />2. HCONH2 + H2O yields (reversible) HCOOH + NH3<br /><br />HCOOH is formic acid; NH3 is ammonia.<br /><br />Now, there are a number of chemical pathways from this step - a finite and known number of pathways.<br /><br />Assuming HCN passes the water hurdle and goes on to a more complex chemical pathway, you would then need to examine each pathway carefully.<br /><br />Each and every one if you are a careful scientist, btw.<br /><br />One such pathway is HCN to Cyanamide to Dicyandiamide to Amino acids.<br /><br />Consider just the next step: to Cyanamide, which is N-C-NH2<br /><br />Again, water reacts with cyanamide to yield Urea, an evolutionary dead end.<br /><br />This is the reaction:<br /><br />N-C-NH2 + H2O yields H2N-C-O-NH2 (again, the NH2 is bound to the C, not the O.<br /><br />Cyanamide will also transform to Carbodiimide in a reversible reaction. However, Carbodiimide al

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#### newtonian

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stevehw33 - Can you see the flaws in your reasoning?<br /><br />I'll just point out two for now, and let you rethink the rest of your post.<br /><br />1. You posted:<br /><br />"Then he states a bit further on down here, that there are less than 10exp122 reactions going on in the universe. Absurd! There are about 10exp80 protons alone!"<br /><br />OK, since when do protons cause chemical reaction products? <br /><br />You are confusing nuclear reactions with chemical reactions.<br /><br />Chemical reactions involve atoms. There are less atoms than there are protons in our universe.<br /><br />You act as if 10^122 chemical reaction products is an overestimate. Yet your posted figure reduces my estimated upper limit!<br /><br />Remember, I posted 10^80 amu, and then overestimated 10^80 atoms, deliberately. And that is "A" in the equation. You ignore this must be multiplied by R and T to yield the result P. You fail to post any estimate for R or T.<br /><br />BTW- I agree with your estimate of protons in our universe, at least within one power of 10.<br /><br />My estimate, btw, is not armchair philosophizing. It is based on Sir Arthur Eddington's calculations for the mass of our universe. Ever hear of Eddington?<br /><br />Now, are you ready to admit your error and agree that there are less than 10^80 atoms in our universe available for chemical reactions?<br />2. Your second error is factorial! You are confusing the possible arrangement of atoms with the limited number of arrangements that can actually be produced in a finite mass (the human body) in a finite time.<br /><br />You posted:<br /><br />It doesn't take much math to figure out that each chemical interacting with others in the body creates a factorial (!) kind of math. With 30K genes interacting, we get a phenomenal number with millions of zeros after it. That's in one human body!<br /><br />Ah, and how fat is this human body? See your error yet?<br /><br />You are expecting us to swallow that a human body produces 10^1,000

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#### newtonian

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stevehw33- It is sad that you do not have the courage to admit your own errors.<br /><br />Even more sad that you make baseless accusations, and when you are called on it make lame excuses why you can't post any accurate critique.

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#### mooware

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Well, I'm not a mathematician so I can't approach your arguments on that level, nor am I educated enough to converse about chemical reactions. <br /><br />I notice you use the word "fine tuned" in your arguments, as in the universe was fine tuned to support life, etc. etc. Well, couldn't it be that life arose from what was available, rather than having to be fine tuned?<br /><br />

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