1159: Countdown

For the countdown previously found in the header text, see Countdown in header text.

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Countdown

Title text: For all we know, the odds are in our favor.

Explanation

The comic shows a seven segment display (aka calculator-style numbers) with a countdown. Black Hat explains that it is a countdown, maybe to a supervolcano eruption. However, an unfortunately placed picture blocks view of the full display. Due to the form of a seven-segment display, the first digit could be 0, 6, or 8, and five digits are completely blocked by the picture. Cueball is worried and asks him to move the picture, but Black Hat lazily or teasingly refuses to move it.

He has already teased that he doesn't know what the countdown is for. His reply can either be understood as if he does not know which one of the (seven potential) supervolcanos it is counting down to, or to which other cataclysmic event it is a countdown for (such as a meteor strike or global nuclear war for instance - it could also just be a general Doomsday Clock). Since it seems to be Black Hat's countdown, it is safe to assume that he knows both what it counts down to and when it stops, but he just likes to mess with peoples' minds.

The fully visible part starts at 2409, and based on the pace of the scene, it seems to be in seconds. Thus, it is unclear when the eruption might occur. If the obscured digits are '899 999', there's another 2.85 million years to go. On the other hand, if they are all 0s, it could be as soon as 45 minutes.

The choice of the picture is probably also interesting. The image is distorted enough that you can imagine it as being two very different images.

1. It could depict a setting sun either reflecting in an ocean or with a river (possible also a lake) running out of the picture. But if it is a sun it is not very circular, although there do appear lines to indicate it is shining. This could maybe be explained with atmospheric interference.
2. Alternatively it depicts an exploding volcano, a mountain with lines away from it to indicate the explosion or the eruption, and lava flowing away from it or collecting in lakes.

In either case, it could make sense. If it is a volcano, the supervolcano clock makes sense. On the other hand, we are talking about the possible end of the world as we know it, so the sun setting upon humanity could be a great metaphor.

The title text: "For all we know, the odds are in our favor" could imply the assumption that since we can't see the digits behind the picture, we can treat them as random. If so, chances are only 1 in 300 000 they are all zeros. However, because of statistical principles such as Benford's law, the digits are not entirely random.

In an alternative view, the strip is not about pondering at distributions of digits on an oracle countdown. It's more of a grim view of our natural disaster prediction capabilities. As they say – the question is not if it will happen but when it will happen. "Move the picture" would mean investing in research and warning systems - that would correspond to shifting the picture to the left. If we disregard the 40 minutes, but instead think of it as an arbitrary interval of interests, minuscule as we folks have them, say - one's lifetime; or grimmer yet - some term of office. Because, hey, year after year passes and no apocalypse has been observed - the empirical odds are low indeed. An interesting question is what we would use the knowledge of the timing of our impending doom, if it is an event we can do nothing about, such as stopping a supervolcanic eruption or a large asteroid with a direct impact course on Earth. Would we not have lives more happily for our remaining years, how few that might be, while not knowing... On the other hand, if the event is something we might prevent given enough time to plan (and the funding resources such knowledge would ensure), then it may have saved us if we moved the picture just in time!

Using a countdown theme for comic #1159 could be a subtle joke, as 11:59/23:59 is one minute to midnight (on the Doomsday clock!).

Supervolcanos were also referenced in the title text of 1053: Ten Thousand and it is the subject of in 1611: Baking Soda and Vinegar.

Transcript

[Black Hat is sitting with his laptop on a desk when Cueball, standing behind him, looks up on the wall and asks him about the large digital countdown timer with red numbers which is hanging high up on the wall. It has a white frame around the black display with the red numbers. Most of the left part of the counter is covered by a framed picture that hangs on a string attached to a nail above the counter. The picture depicts either a setting sun reflecting in an ocean or an exploding volcano with lava flowing away from it. The picture does not block the left-most part of the frame around the counter, and it is also possible to see the two left-most lines of the first digit on the countdown, so they are both turned on. This proves that the numbers go all the way to the left end. The next five digits are covered by the picture. Then one digit is only partly covered, as only the two most left lines are not visible. From the visible lines, it is though clear that this digit shows a 0. The next seven digits are fully visible, giving eight discernible digits.]

00002409

Cueball: What's that?

Black Hat: Countdown.

[Same picture, but Cueball is looking at Black Hat. The counter counts down.]

00002400

Cueball: To what?

Black Hat: Supervolcano, I think. I forget which one.

[Cueball looks up again for about 18s (between 2nd and fourth image) - beat panel.]

00002396

[Cueball looks at Black Hat again.]

00002382

Cueball: Maybe we should move that picture?

Black Hat: Too hard to reach. It's probably fine.

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Discussion

If you assume (with nothing else known), that large numbers have a probability about reciprocal to themselves to ensure a sum/integral of 1, the digits not being zeroes is extremely unlikely.

Whether black hat guy thinks a supervolcanoe eruption is a favourable event or being spared from one is not made entirely clear. Sebastian --178.26.121.97 08:56, 11 January 2013 (UTC)

I warmly recommend the article harmonic series (mathematics). ;-) --131.152.41.173 13:30, 11 January 2013 (UTC)

You are right, the harmonic series is divergent. However, the maximal number of digits - which can be possibly displayed - is finite. Which distribution would you suggest? Sebastian --178.26.121.97 19:35, 11 January 2013 (UTC)

Sebastian, do you know the specific name of the statistical principle you're invoking? I agree, but St.nerol does not, and he has a quick tendency to remove things. One part of it is that you don't know the magnitude of a number, exponential distribution is a more appropriate model than linear. Another part is about the unlikelihood of the middle digits being zero. - Frankie (talk) 21:37, 11 January 2013 (UTC)

Benford's law is about the probability of certain first digit(s). Sebastian --178.26.121.97 22:34, 11 January 2013 (UTC)

Hmm... "Benford's law also concerns the expected distribution for digits beyond the first, which approach a uniform distribution". I missed that the first time I read the article. Okay, that covers the essential parts of the argument. - Frankie (talk) 19:43, 12 January 2013 (UTC)

Come on now Frankie, I'm doing my best. I was just too quick to think that the claim was just another of these casual confusions about probability that non-math people have from time to time. (You know, I haven't rolled a 6 for some time, so now the chances must be pretty high...) I hadn't heard about this very counter-intuitive Benson-principle before, but found this page helpfylly explanatory.

So, I trust you on this. What I don't understand is, how do we know that Benfords law can be applied to this particular 14 digit number? The time left to an eruption? Also, how could a calculation of the actual probabiliy of the preciding digits being zero or anything else be made? – St.nerol (talk) 22:52, 12 January 2013 (UTC)

What is more important for this comic than the Benford's law itself, is its underlying condition that many naturally existing numbers are lognormally distributed. And not uniformally distributed. Under that premise we can try do hypothesize about the odds of leading zeroes. Sebastian --178.26.121.97 00:28, 13 January 2013 (UTC)

The initial timer is a physical quantity, therefore scale invariant, and created by a lognormal distribution (first random experiment). Now there are two possibilities: -- a) BHG specifically got a 14-digit display for the countdown (with the first digit according to Benford's law of course) and the initial timer 14 digits wide. b) The initial timer value possibly was much smaller and it could have been any number which fit on the display. -- Cueball comes in. The shown timer is uniformally distributed within the range below the initial timer (second random experiment). Because of the visible zeroes a) does not seem to be likely and b) would be true, specifically b) with the hidden digits being zero, as the shown zeroes are very unprobable with all large timer values, and the short timer actually is quite probable (lognormal distribution). Is this a valid way to argue for probabilities? Sebastian --178.26.121.97 00:55, 13 January 2013 (UTC)

It seems legit, but I can't tell, really. But we have no concrete estimation yet (maybe that's too hard). Do you really think that this phenomenon is so strong so that (from the 1 in 30000) it makes the probability for four zeroes higher than for all the other 29999 possibilities together? –St.nerol (talk) 08:45, 13 January 2013 (UTC)

Another effect is that if the initial counter was small to begin with, it is quite unprobable (with only one supervolcanoe eruption) that Cueball comes in during the run of the counter. I will try to do a calculation example to compare the possibilities with reasonable assumptions. Sebastian --178.26.121.97 08:52, 13 January 2013 (UTC)

I restructured the last part somewhat. Hope that I didn't screw anything up, and if so, fix it! And it would be very nice if you could also add some more explanation of the math involved! –St.nerol (talk) 19:36, 13 January 2013 (UTC)

This is a wholly inappropriate accusation to make here. If you have a problem, please put it through appropriate channels. No editor has a perfect score, we all slip up because we're all human. lcarsos_a (talk) 23:49, 12 January 2013 (UTC)

Assuming that the middle digits are random, the expected value is 1.53 million years. But: If the display is off-the-shelf, it is probably larger than the largest number actually displayed. Maybe the counter started at 1e8, and the next smaller display had only 8 digits. Maybe we should have a look at the statistical distribution of digits in commercially available LED displays ... 77.88.71.157 08:42, 14 January 2013 (UTC)

Benford's Law does not apply to a countdown timer; the page even lists "numbers assigned sequentially" as a type of distribution that should not be expected to follow it. The comic could have taken place at any of the point in the timer's lifespan with those 9 visible numbers. Unless we attempt to compare actual predicted supervolcano eruption dates (which would be interesting, I will admit) there is no reasonable way to go about this prediction other than the stated 1 in 300,000 chance of it being all zeroes. 108.162.216.111 01:12, 26 February 2015 (UTC)

I don't think there are displays with that many digits. You have to buy several one digit (perhaps four digits) displays and multiplex them together. 23:56, 15 February 2014 (UTC)

"I forget which one" may be a reference to the 7 known supervolcanoes, or it might be to a list published by the Guardian in 2005 of the top 10 existential threats to life on Earth, which went briefly viral. It included a supervolcano eruption, as well as viral pandemic, meteorite strike, greenhouse gases, superintelligent robots, nuclear war, cosmic rays, terrorism, black holes, and telomere erosion [1]

I understand how the hidden numbers could mean that a volcano could either erupt very soon or a very long time. But I don't get why this is a joke. Is there something funnny that I am missing? -- 72.38.90.50 (talk) (please sign your comments with ~~~~)

It's a joke, because a supervolcano eruption would have a major impact on the earth, and Black Hat has a timer that will tell him when one will occur, but he is too lazy to see whether it will happen soon. -- 76.14.25.84 (talk) (please sign your comments with ~~~~)

The title-text may be a reference to the line "May the odds be ever in your favor!" in The Hunger Games. I wonder if this might also be a commentary on the foolishness of assuming that a rare event won't happen anytime soon. gijobarts (talk) 19:54, 12 January 2013 (UTC)

The picture could be somewhat symbolic. It could be a sunset or sunrise, like the would could be about to end or not. 67.194.183.127 06:19, 13 January 2013 (UTC)

Benford's Law has no bearing on what any of the covered digits are except the first, and even then it only weakly applies; it only applies to the FIRST digit of natural numbers, and since we can have leading 0's is really doesn't apply. Furthermore, even if it applied to all the digits, the probability distribution on the covered digits is not affected by the shown digits; that's not how probability works. If I flip a coin 10 times and it's heads all ten times, the probability that the 11th flip is still 50/50. -Mike Powers

Benford's Law shows that with real-life (physical) numbers you cannot just use a 10% probability for each digit. These numbers are not uniformally, but lognormally distributed. That means, there is a smaller tendency to greater numbers than their possible number space would allow. Benford's Law with its relevancy to the first n digits is not directly applicable here, but its general validity contradicts some of the assumptions normally often made. As you see many zeroes in the middle part, the probability is quite high that also the first digits are zero. Here the length of the number has a normal distribution and a short number is about as probable as a long one. And long ones with zeroes in the middle are seldom so it is probably a short number. This would not be the case, if each digit is randomly selected from 0-9. Then the greater probability of longer numbers would cancel out this effect. Sebastian --178.26.121.97 10:07, 3 February 2013 (UTC)

Regarding the independence of the digits: That is conditional probability. We have a probability distribution for the complete number. In nature this is a lognormal distribution (with suitable parameters regarding the scale; that is why the intention to buy a display with certain width is important). That means zero digits are quite common, as short numbers have much weight. With just creating the digits independently you do not get a lognormal distribution. With four zeroes shown only 1/10.000 of the longer numbers are possible any longer, making them much rarer. To begin with they would need a probability of at least 10.000 as high to counter this effect, but they do not have it (with a uniformal distribution they would have it). Sebastian --178.26.121.97 10:25, 3 February 2013 (UTC)

If we have initially the same probability for numbers of digit length 1-14 (about 7%): After looking we (partly) know that digits 1 till 4 are non-zero and digits 5-8 are zero. Then numbers of digit length 1-3 have 0% probability, numbers with digit length 5-8 have 0% probability. Numbers with digit length 9-14 have a probability of 0.01% each and numbers with length 4 have a probability of 99.94%. The results differ with the logarithmic distribution of number length. E.g. with mu=11 digits and sigma=2 digits, the probability of 4 digits is 85%. With mu=12 digits and sigma=3 digits, the probability of 4 digits is 98.3%. With mu=7.5 digits and sigma=4 digits the probability of 4 digits is 99.95%. With mu=12 digits and sigma=2 digits, the probability of 4 digits is 47.64%. Sebastian --178.26.121.97 11:07, 3 February 2013 (UTC)

The 11:59 subtle joke is slightly reinforced as the countdown steps over 2400. Sebastian --178.26.121.97 11:11, 3 February 2013 (UTC)

Could "the odds are in our favour" be a reference to the hunger games? 141.101.98.240 (talk) (please sign your comments with ~~~~)

If you had read all the comments, you would have seen that someone else already thought the same, and nesting your comment below his/hers would make more sense. But that's just me grammar naziing around. 108.162.212.18 00:05, 16 February 2014 (UTC)

I think that it should be mentioned that there is no reliable way to accurately predict volcanic eruptions in the long-term; the best we can do is check current seismic activity to get an idea if it might happen "soon". A countdown clock would either be based on misconceptions that volcanoes follow statistical patterns and therefore based on gambler's fallacy, or would have to be based on future data or magic. That it is mentioned as an "oracle countdown" alludes to this, but I don't think it adequately explains the futility of predicting seismic activity. --141.101.104.17 23:00, 11 December 2014 (UTC)

Just in time by the look of things

Supervolcanic eruptions are signalled not by seismic waves but by tropical storms -from which they seem to draw their power. The steps are missing that fully describe the energy flow. But the sequence is still good, at least for fairly low VEI numbers. The heavy stuff from the 1980's doesn't carry the other data I require: So we wait.

If you are suffering volcano induced trauma, find yourself a planet-wide tropical storm advisory page and check it once every few days. I once met a Japanese couple who were caught in the Kobe disaster. The woman was still very nervous about things but I knew I didn't know enough then to comfort her. Shortly after that or about that time, Mt Untzen erupted, killing the journalists sent there by their lords and stoopids. I asked god to help me understand these things but I was too stupid to listen in those days.

Life is for regrets to blossom in.

I believe the more you learn about something the less you fear it. Unfortunately you have to use Windows to access the Smithsonian archives so if you are reading these comics >>>thataway>>> STOP NOW! (use Listserv or follow me on sci.geo.earthquakes.) I used Google News BEFORE it was clickbait (talk) 20:42, 11 January 2015 (UTC)

There has been some speculation about the picture. Someone noticed that it also closely remembers the very early "comic" (sketch) 4? --Lupo (talk) 14:49, 26 September 2019 (UTC)

For every one time the 6th digit rolls over, you will have one moment when the last eight digits are "00002409". You could assume that the number on the countdown clock started as a 14-digit number, so the 6th digit will roll over at LEAST 100,000 times, and the last 8 digits will read 00002409 at least 100,000 times. Therefore Blackhat is right to be unconcered about the very low probably of the event occuring in the next hour, which makes sense as a way to think about supervolcanos. ~~Waterengineer~~ -- Waterengineer (talk) (please sign your comments with ~~~~)

...just moved and sort-of-signed your comment. Bottom-posting is the standard in Talk (or indent with a(n extra) ":" straight after what you want to reply to...) and using "~~~~" to auto-insert a time-and-dated signature, like I'm doing, is advisible. If you have an account (like you do) you can modify what your .sig text is quite a lot, so "~~Waterengineer~~" can form part of it if you wish. Hope that helps. Please do enjoy your future editing! 172.70.86.68 22:02, 27 January 2022 (UTC)

What if the picture is meant to resemble the landscape from comic #4? I think it looks similar enough to not be a coincidence. 172.68.54.65 07:42, 30 October 2024 (UTC)