scrape_r_rational/data/cache2/4i17l4.md

[Q][D] I need better math to make this work.

• Author: u/None *

• URL: https://www.reddit.com/r/rational/comments/4i17l4/qd_i_need_better_math_to_make_this_work/

• Score: 0

• Created: 2016-05-05T18:20:32

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u/alexanderwales [+5] Time flies like an arrow (32 minutes later)

The odds of rolling twelve sixes once is (1/6)^12 which is:

1/2,176,782,336

The odds of doing it ten times in a row is (1/2,176,782,336)^10 which is:

1/2,388,636,399,360,109,977,557,402,041,718,133,080,829,429,159,844,757,507,642,063,199,359,529,632,522,467,783,435,119,230,976

Which you might notice is a large number (~2 trigintillion).

If you want to use "virtually certain if done a quadrillion times" then something closer to "six sixes three times in a row", since the odds of rolling six sixes three times in a row is:

1/101,559,956,668,416

Or approximately one in a hundred trillion.

u/None [+1] (42 minutes later)

Thank you very much. I think it would fit better with the larger numbers, though. Do you agree?

EDIT: Oh wow, you must be the guy of "The Metropolitan Man" and "Branches of the tree of time". Chapeau.

u/alexanderwales [+2] Time flies like an arrow (55 minutes later)

I think it works better with larger numbers, but you'll need a way to contextualize them, since few people have an intuitive grasp on very large numbers.

What you'd instead want is something like ... let's say that you roll a die for every atom in the observable universe (10^80 or so) every second for three million years (10^14 or so universe-rolls). That gives you the odds of getting your twelve sixes ten times in a row an average of once. And also gives the reader a better handle on the immensity of the odds.

u/lsparrish [+4] (2 hours later)

Since we have a sample of one (i.e. one tree of life with a single common point of origin), it's hard to say how low of a chance is consistent with reality. If the chance is extremely low, that helps explain the Fermi paradox.

u/None [+1] (4 hours later)

We have a sample of one planet, not of one chemical process. In fact, we are pretty familiar with chemical processes and how they work, and we can get a feeling of how much variables are at play and how many events are needed for a molecule of a certain complexity to form, since we already have the amino acids formation rates from the Miller experiment and such. If we take for example amino acids and nucleotides as the basic structures, and we eyeball a "molecular complexity value" for these molecules, and a "minimal complexity necessary for self replication value", ve can get a feeling of how much events we need to get a self replicating molecule of adequate complexity in nature, and all this taking into account no other molecules that the ones we have on Earth, thus very likely accepting lower odds than in reality.

u/Anakiri [+5] (2 hours later)

My first advice would be to not do whatever you are doing. You are invoking tribalism for what appears to be no good reason - though of course it may make more sense in context.

If you must defend Our Side's (evolutionists? Do we call ourselves that?) righteous and true process of abiogenesis against Their Side's silly and misguided foolishness... still don't, because abiogenesis is a chemical process. Just like any other chemical process, the statistical effects only dominate way far out on the tails of the graph - functionally never, because there are many Avagadro's numbers of trials to make the graph really sharp. If you put the same ingredients in the same environment you'll get the same result. I would only feel comfortable talking about chance when talking about multiple planets, and their probability of starting in the right place.

If you must talk about chance, then you are misleading your audience into thinking that your numbers mean anything, when you actually pulled them out of thin air, annoying both of the tribes you are invoking.

If you must have your numbers, I recommend not using any numbers that break your calculator if you don't have to. You don't need to go to such extremes to demonstrate your point, and phrasing it as x number of y number of die rolls is unnecessarily dense. The chance of winning the lottery is, let's say, 1/10,000,000. Earth has 160,000,000 random tickets. Now Earth's chance of not winning the lottery is 1/10,000,000. You'd need to look through, on average, ten million Earths to find one without life.

With the relationship between probability and number of trials plainly revealed, a creationist will now object. They will say that you are misrepresenting the numbers, and Earth does not have that many tickets relative to the odds. They will say that it's more like rolling 120 sixes in a mere quadrillion tries. You will have no defense against that claim, because their made-up numbers are not necessarily worse than your made-up numbers, and you will make Our Side look foolish. Only proceed if that is your intention.

u/None [+1] (15 hours later)

Just like any other chemical process, the statistical effects only dominate way far out on the tails of the graph - functionally never, because there are many Avagadro's numbers of trials to make the graph really sharp.

Risking to sound condescending, and also risking the ire of moderators, since I'm definitely in the wrong subreddit for this discussion, no.

I can't seem to find an appropriate paper on the internet, but when you carry out a reaction between two compounds, or elements even, the starting materials are never exactly pure, and not every atom combines in the expected way, so other compounds are made that you didn't want (that you can predict, yes, but that's another story).

This inaccuracy is amplified over and over when dealing with more than two compounds and elements in a constant change of state such as in nature, I guess that there is a tendency for similar molecules to find themselves in the same general spot, but there's anyway a continuous mixing and bonding and breaking of things.

In this context randomness is dominant because of the continuous shift of conditions and concentrations, so I don't agree at all with your argument of "functionally never" dominant statistical effects.

And about the tribalism thing, I would of course use different tones to address an extremist, someone who never thought about the matter, someone with a general idea but with a weak certainty and someone searching for clarity. This is a tone calibrated for the Rational Subreddit, where I thought the abiogenesis position was generally shared.

u/Anakiri [+1] (a day later)

No worries, I've never really agreed with the mods on that point. Even if I did, subthreads are open season - discuss whatever comes up. And, your thread's been deleted. As far as I'm concerned, we're not in any subreddit at all anymore. Go nuts!

You are correct that "Every atom does exactly what you want" is way far out on the tail of the graph, on the opposite side as "No atom does exactly what you want". The sharp peak is at "X% of atoms do exactly what you want". That percent does compound as you look at reacting the results of previous reactions. But there are so many atoms that it doesn't make much sense to talk about it like a probability to me. I don't think I disagree with your point. I'm basically saying that when you try to combine atoms together more than 10^(25) times, you are, in practice, guaranteed to get millions and billions of every possible result.

I'm saying that it's so guaranteed that it is misleading to even talk about it in terms of probability. As narfanator mentioned, you're talking about "atmospheric pressure turns off because brownian motion lines up just right" as if it's something to even seriously consider. Yes, technically, there is a probability of that happening, and there is a probability of life not forming from a mixture that could have formed life, but I think even humoring those notions is muddying your intuition pump. It is ineffective writing.

And that's the real problem here. I never thought you were asking for help crafting a debate with a real creationist, or else I would have just told you you're in the wrong place. I thought you were mentioning them for no reason. You're right, everyone here is fully on board with abiogenesis and evolution and heliocentrism. We all love to sneer at the silly little creationists. You have succeeded in making me feel superior to someone who isn't present, and you've got me thinking about how stupid they are. Why did you make me feel that? How does that feeling help your point? Why are you distracting me with that when you're trying to teach me?

You've just primed to me identify as an evolutionist, so I put on my scientist hat. You've told me that I should care about truth and accuracy - then you immediately start making up numbers! You told me pay attention to things like that, so I immediately notice that making up different numbers leads to a different conclusion. You are undermining your own argument!

I'd really recommend that you just stick with the birthday paradox or something.

u/None [+1] (a day later)

I don't think I disagree with your point. I'm basically saying that when you try to combine atoms together more than 1025 times, you are, in practice, guaranteed to get millions and billions of every possible result.

Which is exactly what I'm saying.

I'm saying that it's so guaranteed that it is misleading to even talk about it in terms of probability.

And I agree, my intention was to arrange a metaphor to help make this clear to someone who doesn't have a good picture of any of this points in their minds. Some people don't think about certain things that don't influence their everyday lives, and they can be lead to certain conclusions because they lack fitting models of how some things happen. What I think you misunderstood from my text is the audience that it is addressed to, which is to say someone who fancies increasing their knowledge if the explanation is good and clear enough. Coincidentally, I think this description suits a large share of many first world country populations.

For example, in the United States (which I don't live in, but which I take interest in seeing as they're the most powerful country in the world and they are the people that vote for the person who takes the choices that will definitely affect my country in the long run, not to mention that 95% of their policies are applied here too after a couple of years) only 32% of the population is a supporter of the naturalistic explanation for the origin of species, and I think that giving the other rest better instruments for understanding is a worthwhile project for my free time. I could also leather-bind books, but that is boring to do every day.

We all love to sneer at the silly little creationists. You have succeeded in making me feel superior to someone who isn't present, and you've got me thinking about how stupid they are.

You're mistaking my terror for some need of feeling superior.

but I think even humoring those notions is muddying your intuition pump. It is ineffective writing.

I agree that could be the case. I lack writing experience.

You've told me that I should care about truth and accuracy - then you immediately start making up numbers!

That is the reason I asked what I believe to be critical thinking people to help me out with the math. This wasn't supposed to be an advertisement to my writing skills, this was supposed to be a "hey guys this thing doesn't make sense with these numbers, do you happen to know a way in which they would make more sense?".

I thought this was clearly stated in the original post, but I also think I often fall victim to the illusion of transparency.

u/Anakiri [+1] (2 days later)

You're mistaking my terror for some need of feeling superior.

I don't think you need to feel superior. I think you do feel superior. And rightly so! Creationists are scary because of how much political power they wield, while being so astonishingly, willfully stupid and anti-intellectual. Your tone is dripping with well-earned condescention towards them. They deserve it... but by making me feel all of that, you're distracting from your lesson.

"hey guys this thing doesn't make sense with these numbers-"

The problem isn't the numbers. Even if the math worked, I would still notice that made up arbitrary math to support your argument, rather than allowing your argument to follow from undeniable math. It smells fishy. You are trying to save an argument that is flawed at its core.

If your point is that coincidences happen more than you might naively expect, then use the birthday paradox. With only 23 people in a room, there's a 50% chance that two of them share a birthday. There are only 22 chances that any one else shares a birthday with you. But there are then 21 chances that somebody other than you shares a birthday with Person 2, and then 20 chances that someone other than you two shares a birthday with Person 3. By the time you're done, there are 253 chances of a match, at 1/366 probability each. Lesson: Don't confuse the chance of something happening to you with the chance of something happening at all.

If your point is that big numbers make probabilities into virtual certaities, then ask why the sun is still shining. If the sun's core is hot enough to fuse hydrogen, why hasn't it consumed all of its hydrogen at the speed of gravity? Alternatively, why isn't it flickering as it blasts its fuel away from the fusion zone? Answer: Because the chance of two protons fusing when they collide in the sun's core is only around 1/10,000,000,000,000,000,000,000,000,000. It's only that high because of quantum tunneling. (Feel free to check my math!) But the sun is very, very big, so its particles keep winning that lottery at a rate that is steady and predictable enough for life on Earth to exist, while only affecting a small portion of the sun at a time. Lesson: this isn't a thought experiment, you owe your life every day to the certainty of improbable things over large numbers of trials.

u/None [+1] (3 days later)

The problem isn't the numbers. Even if the math worked, I would still notice that made up arbitrary math to support your argument, rather than allowing your argument to follow from undeniable math.

Keeping in mind that this is a thought experiment and not a scientific paper, would you care to elaborate on this sentence? As I replied to Isparrish:

we are pretty familiar with chemical processes and how they work, and we can get a feeling of how much variables are at play and how many events are needed for a molecule of a certain complexity to form, since we already have the amino acids formation rates from the Miller experiment and such. If we take for example amino acids and nucleotides as the basic structures, and we eyeball a "molecular complexity value" for these molecules, and a "minimal complexity necessary for self replication value", ve can get a feeling of how much events we need to get a self replicating molecule of adequate complexity in nature, and all this taking into account no other molecules that the ones we have on Earth, thus very likely accepting lower odds than in reality.

This was in the original text for context. Maybe I should have added it here also... Anyway, it's not like there is no possible math that one could think of to approach the necessary number of events to get a self-replicating molecule, and actually that number should be way, way lower than what my thought experiment uses (because, as ZeroNihilist pointed out: "if every atom on the planet (~1.33e50) attempted that once a millisecond since the universe began (~4.3e20) there would still only be a ~0.0000024% chance that it would ever have occurred"). If even an amazingly and unnecessarily high number as mine becomes virtually certain with enough repetitions, then a relatively smaller number as the one necessary to get a naturally occurring self-replicating molecule should be child's play for the planet.

But this you already know, of course. The problem, apparently, is that my suggestion was too unlikely. A better one would be one that falls in the range of "if every atom on earth had one ten thousand interactions per millisecond since four billion years ago, this event would have happened seven times" or something.

Your tone is dripping with well-earned condescention towards them.

Even if I agree that they earned condescension, I really didn't mean to sound condescending. Reading again now, I think that I can picture how the way I wrote may sound off, and you pointing it out helped me figure out the problem. So thank you for that.

u/None [+0] (3 hours later)

With the relationship between probability and number of trials plainly revealed, a creationist will now object.

Doesn't matter, a creationist wouldn't see evolution even if you smacked them on the head with it. This is supposed to be an "intuition pump" to help visualize the concept of "happened by chance".

I do think that your lottery example could be better suiter for the job, though.

u/None [+2] (5 hours later)

You could really try to show a little less condescension. It's unhelpful. I agree with your points in a vague sort of way, but this is not the place for them and the tone you use just makes me cringe. Take it to /r/atheism if you want pats on the back, or /r/debatereligion if you actually want to develop it.

u/None [+1] (14 hours later)

So that is the subreddit that I was looking for! Thank you!

Take it to /r/atheism if you want pats on the back

Talk about condescending. My "condescension" was at least unintentional.

u/ZeroNihilist [+2] (an hour later)

The chance of getting 12 sixes from 12 dice is (1/6)^12 = 1/(6^12) ~= 4.6e-10, i.e. 0.000000046%.

The chance of doing so 10 times in a row is (1/6^12)^10 = 1/(6^120) ~= 4.2e-94, which is an absolutely minuscule number.

The odds of achieving this from 1 quadrillion independent sequences of 10 rolls of 12 dice (because the maths is easier for independent trials) is 1 - (1 - 1/(6^120))^1e15 ~= 4.2e-79, which is also incredibly unlikely.

For reference, if every atom on the planet (~1.33e50) attempted that once a millisecond since the universe began (~4.3e20) there would still only be a ~0.0000024% chance that it would ever have occured.

The big problem is that you're effectively looking for a sequence of 120 rolls with 1/6 probability each, and there are:

2388636399360109977557402041718133080829429159844757507642063199359529632522467783435119230976

possible outcomes, of which only one is correct.

To make the numbers work out, you'd need a total of around 18 dice rolls required for success (e.g. 2 rolls of 9 dice, 6 rolls of 3 dice, 1 roll of 18 dice) from 1 quadrillion trials. That gives a 99.995% chance of observing at least one success.

u/None [+1] (an hour later)

So that's way higher than what is actually required to get the first self-replicating molecule.

u/narfanator [+2] (2 hours later)

+1 to Anakiri's comment

What you really want to look at are the maths and physics behind things like temperature and pressure, as well as (as Anakiri points out) chemical reactions. These are cases where a massive series of stacked probabilities becomes certain enough to have simple equations predicting them.

To use your word, you will virtually always experience atmospheric pressure, because the likelihood of the brownian motion lining up in just the right way to remove that pressure just isn't going to happen.

Also, to reiterate Anakiri, avoid telling people on the internet they're wrong. It generally doesn't work. People are generally "smart" - as in, they have a process by which they go from information about the situation to conclusions - and I think it might actually be harder to convince them that the process they use to do that is wrong (or yielded incorrect results). What you want to do (I think) is add information to the situation they're thinking about, and then they can do their process and (maybe) achieve different results. Belief-in-belief still applies.

u/None [+1] (4 hours later)

As I replied to Anakiri, it's more of a thought experiment than an argument in itself.

u/blazinghand [+2] Chaos Undivided (4 hours later)

Hmm, so debating with creationists is not a super good use of time, in terms of "convince this person that they're wrong and you're right" since most of these discussions are not held in good faith. In general, though, as long as it's reasonably possible that somewhere in the universe there is intelligent life, you can talk about the anthropic principle (introduced briefly by SMBC here) to explain why it's not super unreasonable that there's life, even if it is unlikely.

The basic thing you could say is, yeah, there are tons of planets with no life. By definition, though, there aren't people on a planet without life philosophizing about life.

In a universe in which life is incredibly unlikely and only a small number of stars have it, every living intelligent creature will be in a situation that say the following: "Wow, the planet I'm on is surprisingly, unusually good for intelligent life! this is an awfully suspicious coincidence!" So, it is technically true that life is fairly unlikely to take root on any particular planet, but it happened to take root on the planet on which we live. However, the fact that this is true doesn't imply something strange is going on. This is just what things look like if you assume life happens very rarely, but does still happen. This is just how the world appears.

As a, like, more meta-level piece of advice, though: don't spend time arguing with creationists or evolutionists if at all possible. Why? Most people don't have these discussions in order to learn new things. They're doing this to try to win, and it becomes abrasive. People on both sides may also find this sort of discussion upsetting. Usually a good way to go about it, if possible, is to say something like "I respect your beliefs, even if we don't agree on everything" and your friends should (probably) extend you the same courtesy. If you have religious family and you are not religious, don't share this fact with them until you are financially independent.

u/PeridexisErrant [+1] put aside fear for courage, and death for life (8 hours later)

From the sidebar:

Do not post scenarios for discussion, requests for someone to write a story, or brainstorming threads. Authors get one exemption after each published chapter or equivalent.

u/None [+1] (15 hours later)

Sorry. This wasn't supposed to be any of that, though.

u/PeridexisErrant [+2] put aside fear for courage, and death for life (15 hours later)

Given that this is not Rational Fiction, it belongs in the off-topic thread (fridays), or in another sub.

u/None [+1] (15 hours later)

Duly noted. Sorry again.

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