Wikipedia:Reference desk/Archives/Mathematics/2016 December 15

= December 15 =

Help me, Obi-Wan Kenobi. You're my only hope!
At User:Guy Macon/sandbox I present some figures about WMF spending. This is for a Signpost editorial I am working on.

My problem is the phrase "No organization can sustain that sort of spending growth on a long-term basis. If we do manage to keep it up, in the year ???? we will be spending more than the $3.7 trillion dollars the US government spent last year." I am having a bit of a problem deciding what to replace that "????" with. I did some rough calculations based on my eyeballing a curve fit and I get different answers depending on slight variations on where I place the curve. I think I have ran past my "good enough for engineering" math abilities on this, and need to ask someone who knows what they are doing to look at the problem. --Guy Macon (talk) 16:51, 15 December 2016 (UTC)


 * Remark: any trend, extrapolated linearly, eventually passes every bound. If that's the most convincing argument you can assemble to support your position, it's a crappy position.  Rather than asking for help with complicated arithmetic, you should find a better argument.  (I have not thought about the issue enough to have an opinion about whether the position you're advocating is reasonable or not.)  --JBL (talk) 17:46, 15 December 2016 (UTC)
 * IMO, the point that linear growth is unsustainable is often overlooked, and bears repeating for emphasis, especially in less mathy circles. Remember not everyone has a PhD in math, nor even undergrad math experience ;) Also, the growth looks more exponential to me anyway. SemanticMantis (talk) 18:19, 15 December 2016 (UTC)


 * One way to extrapolate the spending would be to find the best fitting exponential function, as described here . Using a linear fit, as Linear_least_squares_(mathematics), would give a different estimate. Using yet another model, e.g. logistic regression, the 3 trillion mark would never be met. SemanticMantis (talk) 18:26, 15 December 2016 (UTC)


 * I support what JBL wrote. This is an internet classic (at least among some circles); the TL;DR is that since the world is finite, human activity will eventually stop, hence assumptions like "3% GDP" cannot hold forever. But that is a misleading reasoning, because if the tipping point is in a million years, probably other limits will kick in (e.g. thermonuclear war). The point you make depends on the value of ????: if it is in three years, then something will happen, if it is in 2516, that is not a huge problem. While it is reasonable to fit the trend, determine ??? and then deduce the point you want to make, the inverse process of knowing which point you want to make and then going after data that is supposed to prove it is wrong. Cognitive dissonance kicks in, etc.
 * Now to the math anyways. How to extrapolate a trend depends a lot on what the "trend" is. Since there is, to the best of my knowledge, no Theory of WMF Spending that governs what the curve in the next future should look like, nothing is really more plausible than anything else; because of kitchen sink regression, complicated functions will likely fit the curve better (no matter whether they actually are closer to the Fundamental Function of WMF Spending), so one should prefer simple fits. My lying eyes tell me that the period 2009-2015 looks fairly close to a straight line, the regression would be around $$Spending(year) = $8.5m*(year-2008)$$. That means we reach the $4.7trillion point in 435,000 years (give or take). That far in the past is about when Neanderthal and Homo erectus lineages diverged . And of course, that far in the future, the US government will spend quite a bit more (optimist's view) or quite a bit less (pessimist's view) but probably not as much.
 * Of course, this absurd result means the trend will likely change in that time period. But then, as you took a comparison target ($4.7t) that is about 10,000 times the highest current datapoint (~$52m), any extrapolation is bound to be fantaisist. That would be like measuring your kid in the morning, then in the evening, detecting the (sub-millimetric) difference, and deducing their height in ten years' time (10 hours*10000 = 11 years, for whoever cares). You might get lucky and fall on a reasonable values, but the odds are you will not. Tigraan Click here to contact me 19:05, 15 December 2016 (UTC)

Hmmm. It appears that I am not expressing myself clearly. I was trying to fit an exponential growth curve to the data and as a argumentum ad absurdum show that WMF spending cannot continue to grow exponentially for more that X years without Wikipedia becoming larger that the US government. I think its a good argument, especially considering that I have already encountered several people who actually do think we can keep up our present exponential spending growth forever. I thought about getting fancy and saying "by year X WMF donations would eat up the entire income of everyone in the country".

Does someone have a better way to convince a non-technical audience that exponential spending growth is not sustainable? --Guy Macon (talk) 18:45, 15 December 2016 (UTC)


 * As I wrote above, $4.7t / $52m is too high a value to validly extrapolate, barring theoretical reasons to do so. (If it was close to 1, one could hope that extrapolation is possible, but that would be no proof; but because it is not, such a hope is extremely unreasonable.) If your point is merely to prove that "exponential growth is unsustainable" (if you need that, your reader is probably a child), then the Wheat and chessboard problem is a nice analogy. Tigraan Click here to contact me 19:11, 15 December 2016 (UTC)


 * OK, I am convinced. I will find a better way of making the point that WMF spending cannot grow exponentially forever. Thanks! --Guy Macon (talk) 22:58, 15 December 2016 (UTC)


 * Due to inflation you cannot directly compare dollar spendings in different years. Bo Jacoby (talk) 02:00, 16 December 2016 (UTC).


 * During the period from 2005 to 2015 inflation was between 1% and 3% per year, and the the cumulative inflation for the entire decade was 21.4% -- far less than the increase in WMF spending. --Guy Macon (talk) 18:55, 17 December 2016 (UTC)


 * Yes, the correct way to state it is that "increases in spending can not outpace inflation forever". StuRat (talk) 23:58, 17 December 2016 (UTC)

GAMBLING TRICK
why cant i make a partnership with somebody that he bets "a" and i bet "b" and we split the profits? — Preceding unsigned comment added by 195.60.235.5 (talk) 17:11, 15 December 2016 (UTC)


 * You could, but you'd also be splitting the cost of the bet so you don't gain at all. 🔯 Sir Joseph 🍸 (talk) 18:06, 15 December 2016 (UTC)


 * You might like to read our article on Odds (and Gambling mathematics, Mathematics of bookmaking and the links at Betting strategy for more technical accounts), and do some calculations on your expected "gain".   D b f i r s   19:30, 15 December 2016 (UTC)


 * Presumably the "house" doesn't give you even odds, or they wouldn't make any money. In roulette, for example, you can bet either red or black, and double your bet if you win, but there's also a green 0 and, in American roulette, also a green 00, which are there to skew the odds in the house's favor, so they make a profit. StuRat (talk) 00:00, 18 December 2016 (UTC)


 * If you bet on different outcomes, it is possible to make a profit with the right odds. For example, with only two possible outcomes and odds (c/d), (e/f) you will always be able to do this if (c*e)/(d*f) > 1. (To see this, say you have bet some amounts on each outcome then calculate what your net gain/loss in the event of each outcome.) As StuRat says though, whoever is giving you odds will probably not be giving you odds that are good for this. I have actually written some code that collects odds from one of those sites that compiles betting odds from lots of other sites and I run it from time to time looking at sports that only have a few outcomes. There are a number of cases each time that would give a net profit if the 'right amount' is bet on each outcome, but the potential profit in each case is usually quite a small proportion of the total amount bet, so large amounts of money in total need to be bet for profits not to be very small. There is also the issue that odds change with time so if you were trying to bet in this way you'd have to be quite quick and also that betting sites sometimes input odds into their systems that they don't mean to, so you could have a case where profit looks good but then one betting site realises it has made a mistake and calls all bets on an event void and you're left in the lurch or so to speak.


 * If you wanted to do this I think you'd have to spend a decent amount of time on it, in view of the possibilities of mistakes on your and the oddsmakers' parts and from my experience (as stated above) you'd probably have to bet quite a lot of money to get any significant return. Even with all this annoyingness there is still an element of risk involved, e.g. from betting sites/shops/whoever randomly declaring bets void or even shops closing or the internet going down.


 * Having said all this, if you still want to do this, the mathematics is quite fun to do (IMO) and you'd (hopefully) be making money from oddsmakers, which are in my opinion generally bad. Please feel free to ask more questions about this. I am a rock (and an island) (talk) 17:43, 18 December 2016 (UTC)