# Explaining the Drake Equation on a smaller scale

So me and my friend were planning a video to explain the Drake Equation (within a time limit of 5 minutes), and we needed some help. This video is aimed at explaining the concept to an age group between 13-18 years, and having gone through loads of articles, we felt that a lot of the common audience would not be able to comprehend the concept.

So our question was, can we take the Drake Equation and try to explain it with maybe a real life example and on a smaller scale? It is an incredibly interesting equation and we felt like doing a good job of explaining it to a common teenager.

Thanks!

• I think you may not be giving these kids enough credit. I don't think the premise of that equation is something that is too complex for kids of that age. I'd suggest taking a look at youtube videos which explain this concept to see how they do it. – zephyr Oct 4 '16 at 12:35
• I agree with @zephyr, I don't think an every day example will do you much good here. You can think of any number of examples which use the same logic ("How many piano tuners are there in NYC?"), but in the end: the Drake Equation is quite straightforward and should not be too difficult for teenagers to grasp, and at any rate an every day example would not necessarily be easier to understand. – user1991 Oct 4 '16 at 13:04
• it's hard to imagine anything simpler than the Drake equation. it's just ...... a few fractions. – Fattie Oct 4 '16 at 16:03
• I guess you could make an "everyday example" along the lines ... "Here's the population of North America. Now, how many have cellphones? .. of those, how many have Android cellphones? .. of those, how many have Samsung Android cellphones? ..." just to indicate how you can 'fraction down" something. – Fattie Oct 4 '16 at 16:22
• I don't think the Drake equation is conceptionally hard to understand for 13-18 yr olds as it's really basic maths that you learn at age 7 or 8; the big problem is (as many other have said) that we have no good data how big the different terms are. So I think your video should more usefully try to explain or visualise those uncertainties rather than the equation as such. – Stephan Matthiesen Feb 19 at 12:46

Just scribble a rectangle on a piece of paper, and say "there are 100 billion stars in our galaxy"....

Then, color off (let's say) 1/3 of the rectangle, and say "only one third of those are the sort of star that could have life, so that's blah billion"

Then, color off (say) 9/10ths of that box, and say "we believe about 90% of those have planets - so that's blah billion"

Then, color off (say) 1/20th of that box, and say "of those with planets, it seems that about 1 in 20 have Earth-like planets. Now we're down to blah billion..."

and so on.

(Note: the Drake equation has a number of fairly silly terms relating to "nuclear war!", which were added as political sops in that era; suggest ignore these unless you want to sound 90 years old!)

So just scribble a box or draw a line on a piece of paper ... or maybe use "a bag of marbles" as the other answer suggests.

Just BTW there is in fact an entire documentary (I noticed it on "Netflix") called "The Drake Equation" which does exactly what you say...

.. it is not really very good as I remember. I think the guy simply draws a line in the ground, to do the "fractions" demo, you know? (ie, they just erase more and more of the line). It doesn't need to be more complicated than that.

It's worth noting that the Drake equation simply points out:

(i) if you multiply those three or four fractions together, you get the number of civilizations in the galaxy. Which is self-evident.

but, the whole point is

(ii) we have utterly no clue - not even vaguely - what most of the fractions are,

You could say it's a written formula, which, helps clarify our thinking on, something we are utterly clueless about. So rather than just vaguely saying "we're utterly clueless," we can speak more clearly about the nature of our cluelessness!

although interestingly,

(iii) very admirably, the issue of "How many stars have planets?" ... one could say that issue has been somewhat settled these very years, as we speak - that's great.

• Thank you so much! This is perfect and I'll definitely credit you for this in thew video :) – Aman Bhargava Oct 5 '16 at 15:46
• lol no need for any credit, you have enough to do :) good luck... – Fattie Oct 5 '16 at 15:49

As the Drake identity (it's not an equation) is just a trivial exercise in combinatorics, I'd suggest the simplest, most commonly used model in combinatorics: The urn.

You have a number N of balls in an urn. Those represent the stars in the galaxy. Of those only a fraction is green, the rest is red. Green signifies "has planet", red "doesn't have a planet". You take the fraction of green ones that then host a planet in it's habitable zone and so on, for every characteristic the Drake identity describes.

In the end you just count how many balls with all desired characteristics on them you've taken out of the urn, relative to the total number of balls in the urn.

If you write the corresponding fractions in your video side-by-side with the undesired balls disappearing, it should increase the understandability further.

• The idea of "has planet" stars being few is a bit dated. I would go so far as to say that based on our current understanding "doesn't have a planet" would be an anomaly. – called2voyage Oct 4 '16 at 14:16
• @called2voyage: I was intentionally not going into any details for estimates of the actual numbers, only showing what thinking lies behind multiplying a bunch of factors together. Which is most probably the Drake identity OP is familiar with. – AtmosphericPrisonEscape Oct 4 '16 at 14:19
• Not to be pedantic (however I feel somewhat justified since you made the point), but the Drake Equation is indeed an equation and not an identity. An equation is not a stringent mathematical object, it's merely something which expresses equality between two things. And in fact, all identities are equations. An identity is simply an equation which is true for all values of all variables. The Drake equation is not an identity because one could easily plug numbers into the equation to make it not true. For example, set all right hand variables to zero and all left hand variables to 1. – zephyr Oct 4 '16 at 14:35
• It's also not a "trivial exercise in combinatorics". It's just a basic algebraic equation. Multiplying numbers doesn't put it in the realm of combinatorics. – zephyr Oct 4 '16 at 14:38
• @AtmosphericPrisonEscape By stringent I meant the requirements to be considered an equation are not strict. Essentially the only requirement is that the expression must express equality between two things. As such, any statement of equality, regardless of how trivial or in need of solving it may be, is an equation. Using your definition, 1 = 1 wouldn't be an equation, when it most certainly is. At they very least it certainly isn't an identity. – zephyr Oct 4 '16 at 14:46