# Math does not need to be cited or sourced

Is one in two hundred men a descendant of Genghis Khan?

The OP is simply trying to establish a mathematical basis for the credibility of the assertion in the question -- a "back of the envelope" math check to see if it's possible at all.

While it is not a complete answer, it is a useful answer and adds to our understanding of the question using mathematics.

One does not need to "cite" or "reference" mathematics, because.. well, that is insane. Either the math is credible and sensible, or it isn't. We aren't in the business of proving that 1 = 1.

• – Sklivvz Aug 14 '11 at 10:00
• incorrect, this is highly specific to math. – Jeff Atwood Aug 14 '11 at 10:03
• Logic is as robust as math (logic is even a part of math). There is no reason why math based answers should be privileged over logic based ones. – Suma Aug 14 '11 at 19:00
• "Common sense is the collection of prejudices acquired by age eighteen." - Albert Einstein – Sklivvz Jan 26 '12 at 21:25
• The OP isn't "Math". He's created a model without and basis or validation. – Dave Hillier Mar 13 '12 at 21:57
• @Suma, right, that's in the same category. The important thing is that it's (given sufficient analytical skills) self-evident and self-contained; no universe could ever exist in which it was not correct. – Paul Draper Oct 2 '15 at 4:57

• Assuming that the average "generation" is 30 years
• an average Genghis Khan's descendant will be in their 25th generation
• Assuming that in each generation, for each Genghis Khan descendant there are two of their children that will intermarry with someone that is not a Genghis Khan's descendant

Any of the above are not mathematics; they are assumptions and if they were to be used in a mathematic formula to justify an answer then they need to be treated as any other claim and are required to be referenced.

Math's is credible and sensible. But you need to justify the equation chosen and also the variables used. Grabbing any arbitrary formula and input variables to justify a point is insane!

If only I could use that sort of math to justify my next pay rise.

• The answer shows the formula which is used. It is easy to take different numbers, if you think 25 years per generation is a better value, etc. – user unknown Aug 23 '11 at 20:39
• @user - That's the point, it has nothing to do with who thinks what amount is better as a generation. We should be basing figures on something factual, not what each of us 'feels' is good. – going Aug 24 '11 at 2:29
• I don't say I feel it is good. You can give a lower and a reasonable upper bound, and the more investigation you make, the closer you may come to a real value. But getting values for the year 1300 will not be so easy. Sometimes you don't have a better way than speculation. The method, to provide a simple way to calculate the number is not entirely wrong, but it is too simple. The number of descendants in the population gets more and more saturated over time - this would be an interesting question for a more advanced mathematical model. But as attempt to find an upper bound, it isn't useless. – user unknown Aug 24 '11 at 6:15
• But this site is not for speculation. If anything the site should be anti speculation. The same with the lottery question I have mentioned elsewhere: we are not here to discuss the situation we are here to provide facts. – going Aug 24 '11 at 8:15
• I'm sorry, which lottery question? How is it related? However: If you don't derive a question from a study at hand, you always have to fit an answer to the question, which is mostly a process which involves speculation. Is cycling better for the environment: Just a CO2-question? How heavy is the user, how heavy is the car involved? What amount of gasoline does it need? What food does the worker eat - speculation, guessing, estimation. – user unknown Aug 24 '11 at 8:47
• definitely fair points about assumptions in the math – Jeff Atwood Jan 26 '12 at 23:06
• I really don't get what the problem is here. One possible (valid) refutation of an claim is to demonstrate (via logic/math, using reasonable premises) that a certain conclusion isn't even remotely plausible. The disputed answer to the Genghis Khan question is merely a counter-demonstration of that idea, i.e., that the ballpark number of descendants in the original claim is plausible (or isn't crazily implausible, I suppose). – BradC Oct 4 '12 at 21:17

The math itself does not need any reference, if it is trivial enough for lay people to follow, which I think is the case in the answer you mention. Though in most cases I would at least expect a Wikipedia link for the specific formula used if it is something beyond basic high school mathematics. In this case I suspect that there are established formulas for population genetics that one could use.

But what needs to be cited here are the facts that are used, the average number of children and the average generation length. In this case the numbers used seem to be very conservative and unlikely to exaggerate the result, but in general such facts should be sourced. It is far too easy to get the results you want with such calculations by fudging those numbers.

The bigger problem I see with this answer is the extremely simplistic model used, the author mentions the problems with it but provides no estimate on the error these simplifications could have on the result. I suspect that this specific model is too simplistic to be really useful, but I don't really know how big the error in this model is.

Following the math is not the problem, assessing the validity of the model and the facts/constants used in it is the hard part. And that part should be referenced.

• ok, rather than using edits to add passive-aggressive notes to the top of the post, why not edit in references to "average # of children" and "average generation length"? The post was 11 hours old and already it's getting converted to community wiki and crazy warnings slapped on it? Why not just a comment asking the author to politely provide citations for a few of the numbers? – Jeff Atwood Aug 14 '11 at 10:13
• We did in fact (see my first comment on the question) – Sklivvz Aug 14 '11 at 10:17
• @skl no, the comment said nothing even CLOSE to "But what needs to be cited here are the facts that are used, the average number of children and the average generation length. In this case the numbers used seem to be very conservative and unlikely to exaggerate the result, but in general such facts should be sourced. It is far too easy to get the results you want with such calculations by fudging those numbers." – Jeff Atwood Aug 14 '11 at 10:32
• @Jef Sure, but the link did point to a meta question we put together on purpose because we can't be reasonably expected to have the "math is not enough without the facts" argument every time. The OP did not even ask for specifics, they simply ignored the comment. – Sklivvz Aug 14 '11 at 10:36
• @skl the OP indeed did engage in the comments -- try reading them -- but the initial comment was a boilerplate "read this generic link to 5 pages of discussion", not the clear call to action that the above paragraph of Fabian's post is. – Jeff Atwood Aug 14 '11 at 10:52
• @Jef he did engage in the comments, but not regarding sources. Mods would have explained better if he had any specific question, however it looks like he didn't read the meta post linked. – Sklivvz Aug 14 '11 at 11:06
• @Jeff In this specific case I don't think the specific numbers are the biggest problem of the answer, but the too simple model itself. I suspect that a realistic model would not be purely exponential, but assuming limited mobility of the Khan descendents, more and more Khan descendents would marry among themselves. Plugging better data into a flawed model won't help. – Mad Scientist Aug 14 '11 at 11:47
• @fabian it's a "back of the envelope" calculation. I agree it is not a COMPLETE answer, but it was not intended to be. See en.wikipedia.org/wiki/Back-of-the-envelope_calculation -- "The defining characteristic of back-of-the-envelope calculations is the use of simplified assumptions." I find these helpful to demonstrate, with math and simplified calculations, if the claim could be even possible. "In these notes Weisskopf used back-of-the-envelope calculations to calculate the size of a hydrogen atom, a star, and a mountain, all using elementary physics." – Jeff Atwood Aug 14 '11 at 11:58
• @Jeff A "back of the envelope" calculation only works if you have an idea on how large the effect of your simplifications is. You need to be able to reason why your simplifications are valid, in this case the author of the answer assumes a purely exponential function. An exponential function is extremely sensitive to small changes in the input data, that is not a good starting point for a back of the envelope calculation. The amplification of any small error is just too large in this case for my taste. – Mad Scientist Aug 14 '11 at 12:25
• @fabian fine, but criticizing the back of the envelope calculation belongs in the comments. I could similarly say that some study you referenced in support of your answer had a flawed model as well; that does not mean your answer is invalid and should be cwiki and have a canker sore notice placed on it within 24 hours. Particularly if the author said up front that this was a back of the envelope exercise to demonstrate not a final answer, but a "do the math and physics say this is even possible?" reality check. Such things are the very BASIS of all science. – Jeff Atwood Aug 14 '11 at 12:37
• @Fabian: in this specific case, I would not assume that Khan's descendants have limited mobility since the Mongols campaign reaches almost all Asia, parts of Russia and Europe. I agree that the model have a lot of simplification (like any other models), and it would be better to use logistic function to model the problem, but I would not pretend to know how to use logistic function, and given that the original paper claims is just 0.5%, the logistic and exponential function (which is easier to calculate) would not deviate much yet. – Lie Ryan Aug 14 '11 at 13:05
• @Lie Ok but your answer is still not addressing the question. – Sklivvz Aug 14 '11 at 16:17

The real question, here, is whether back-of-the-envelope answers should be allowed on Skeptics. I don't think so. To put it bluntly, this is Skeptics, not Speculation.

The problem with back-of-the-envelope calculations is they are very rough estimates. I have no problem, personally, with allowing mathematical estimates on the site, for as long as they are rigorous. Knowing that something is plausible is, as you said, useful information, but this particular answer played it too loose and made it rather large assumptions. So, it got downvoted like a study with a poor methodology would.

• thus downvotes and comments should carry, which is fine. Leaving a canker sore notification on it should not, and will not. – Jeff Atwood Aug 15 '11 at 3:41
• A back-on-the-envelope estimation could prove such a claim wrong, if it would need a generation length of 10 years, 20 female childs per woman and Dchinghis Khan being 5000 years old. If a simple test to disprove such a claim fails, it is an interesting answer, because nobody else has to repeat the attempt. – user unknown Aug 23 '11 at 20:45

I agree with Fabian's post.

Further to that, I think this case is a very good example of why we should be asking for references on this kind of posts.

The post answers the following imaginary question: is it mathematically impossible that the claim is true? A math question and answer. They are off topic here. This is not math.SE.

The real question asks the following: is a specific percentage of the population descendant of Gengis Khan? An historical/biological question, which should have an historical/biological answer. Did GK have enough children and grandchildren to sustain a family tree?

This site is about facts, and not speculation. Math applied to speculation is still speculation, and it's quite disheartening reading meta questions like these coming from none other than you, Jeff. Right or wrong, skepticism is about empirical data and the site is about skeptical answers.

• How does it not address the question? The original question is "Is one in two hundred men really a descendant of Genghis Khan?", the OP is skeptical about the number 0.5% cited in the paper and my answer showed that the number 0.5% that is cited in the paper is certainly plausible and not necessarily exaggerated. While I haven't addressed the issue whether GK does have enough children and grandchildren to sustain a long family tree, there is nothing in S.SE that forbids a partial answer. – Lie Ryan Aug 14 '11 at 18:44
• @Lie: you have shown the 0.5% is plausible (possible), but not that it is true. Showing that is impossible with maths, but can be done with history and genetics research. (I am afraid I am just repeating what Sklivvz said, but I am not sure what other could be said). – Suma Aug 14 '11 at 18:58
• @lie, you haven't even shown that GK has even a single descendant alive today. Let alone being able to address that number in a convincing fashion. – Sklivvz Aug 14 '11 at 19:23
• I can't imagine how you could answer a statistical question without math. And since there is, afaik, no genetic material of Dschingis Khan in a mummy or something left - how could you prove it, show it? Male anchestors are always hard to prove. And do you want to count millions of birth certificates? Did they have birth certificates or something similar 12-hundret-something in asia? – user unknown Aug 23 '11 at 21:22
• @user nobody said you couldn't use math... And not all questions are answerable with facts. When you meet one, saying so is fine (as a comment). – Sklivvz Aug 23 '11 at 21:25
• @Sklivvz: I would leave the question of "whether GK has a single descendant alive to other person", my answer was never intended to be a complete answer. I can calculate, but I can say -- with pride -- that I know none about history nor genetics, so I would not pretend that I do. – Lie Ryan Sep 1 '11 at 8:02
• I think one could compute the probability of GK not having a single descendant alive... – UncleBens Feb 17 '12 at 18:54