I've been thinking of how you can talk to people about exponential growth

[captain queeg]

Most people know the thing about putting a penny in the bank and having it double every so many weeks/months/years how you'd be rich sometime in the future. Maybe using that idea, it’s like a payday loan at 30% daily interest. Not sure they’d understand a daily rate. Maybe a very high annual rate compounded daily. A graph maybe. But I think they’d just not believe it. And we really don’t know the rate of spread, it’s certainly going to be high for awhile due to idiots not believing and taking precautions.

[jayfish]

1. Think No Longer.

[crickets]

7. I remember that commercial, and thought of it today as well.

Easy, obvious, and somebody ought to be making public health announcements along these lines right now. Jerome Adams is our current Surgeon General (had to look it up) and is, AFAIK, doing fuck all to promote public awareness and safety.

https://en.wikipedia.org/wiki/Jerome_Adams

During the COVID-19 outbreak, Adams asserted on CNN’s State of the Union with Jake Tapper that he’d seen no indication that people who want to be tested for the virus cannot be. [24] During the same interview with Jake Tapper of CNN Adams stated that “The president (aged 73) sleeps less than I do and he’s healthier than I am" [25].

[jayfish]

8. Then You Might Also Remember...

[crickets]

12. I do! I look forward to the day I can find that picture funny again. nt

[flibbitygiblets]

34. This! A simple commercial explains it perfectly.

Change the "tell two friends" to "infect two people", and include a running total at the bottom, along with % of people living in the US.

[intrepidity]

2. Tell them to talk with you in three weeks

and compare notes then about where we are today vs in three weeks.

Then they'll understand.

[Ms. Toad]

16. Not so sure about that . . .

based on my experience trying to explain exponential growth to someone on DU who says they are an engineer. (Paraphrasing - A line has to become really really steep, with a slope greater than 2 before it becomes exponential. )

[intrepidity]

19. My point is that in three weeks, they will have witnessed it

I haven't done the math specifically, but based on what I'm seeing today, in three weeks things are going to be so very glaringly different.

[Ms. Toad]

24. Depending on the formula you use -

200,000 -1.4 million (the former is power curve based on more data; the latter is an exponential curve based on data after the multiplier took hold).

But my point was they may not accept it even then.

I was running approximately the same numbers in China. Using those numbers (talking about exponential growth) I predicted the number of infected, and the number of dead - and about 3 weeks out was within 3 days of predicting the date the death toll would exceed SARS. This was in a conversation with someone who predicted it would NEVER exceed SARS - and the comment in my last post about slope came from the same person AFTER the exponential growth in China.

So - seeing the numbers will not necessarily convince them.

[intrepidity]

43. Yeah, I've seen many of your posts on the topic over the past month

I know you know what you're talking about.

[Ms. Toad]

44. I'm not an epidemiologist -

but I can run the numbers (and make decent guesses about things that make what I'm seeing accurate, or not so)

[intrepidity]

45. Yep. nt

[Girard442]

3. You might try pennies on a checkerboard.

You know, 1 on the first square, 2 on the second, 4 on the third, 8 on the fourth, and so on. Most people imagine by the time you're done, you have a bucket of pennies or so.

[customerserviceguy]

5. Great idea

Put it into dollars and cents, and it will make sense.

[Blue_true]

15. Good idea. But exponential change is much steeper than your

example. Maybe 1 on the first square, 7 on the second, 120 on the third, 1300 on the forth, ect. If you have that many pennies.

[Girard442]

20. Actually, the total number of pennies on the board is (2 raised to the power n) - 1

Where n is the number of squares covered.

1 : 1
2 : 3
3 : 7
4 : 15
etc.

Which is pretty much the definition of exponential growth. If you raised the number of pennies on each square by a factor of 10, faster, but still exponential. Faster than exponential is combinatorial, but that isn't what we're seeing.

[Blue_true]

22. Your example was of a straight line of slope 2. nt

[Ms. Toad]

25. No it is not.

It is an exponential growth.

1 penny (2^0) on the first squre
2 pennies (2^1) on the second square
4 pennies (2^2) on the third,
8 pennies (2^3) on the fourth, etc.

Please (1) calculate the number of pennies on the 64th square and (2) provide the linear formula (y=2x+b) that will accurately calculate the number of pennies on any given square. and (3) prove your point by calculating the number of pennies on square 37 using your linear formula.

It is really inappropriate for an engineer to misinform others on the board (who may not have a math background) about basic middle shcool math. Please provide the formula, or stop misinforming people.

[Blue_true]

27. I have gone through this with you before. I don't have an inclination

to revisit that.

[Ms. Toad]

28. Prove your point -

Give me the precise linear formula (y=2X+b) that accurately calculates the number of pennies on each square. All you have to do is figue out an appropriate "b." Then calculate the number of pennies using your formula that woudl be on square 37.

I guarantee that you cannot do it, becase it is NOT linear.

[Blue_true]

32. The original post that I responded to was calling linear data exponential,

it was not. Now numbers have been changed. Why doesn't the person simply admit to not thinking the original post through?

[Ms. Toad]

36. That data is exponential. Not linear.

1=2^0
2=2^1
4=2^2
8=2^3
16=2^4

The EXPONENT is one less than the square.

They are not wrong - you are.

To prove your point, give me the linear formula, with a slope 2 (y=2x+b) that generates the series (y) 1, 2, 4, 8, 16 for squares (x) 1, 2, 3, 4, and 5.

You can't do it, because it is not linear. There is not a single value for b that will generate the series in the original post.

[caraher]

26. No it isn't

I've graphed it for you on Desmos

[Blue_true]

30. The numbers that you had in your original post were not the numbers

that you graphed. I responded to your original post when this started. That you create a graph that uses adjusted data is somewhat pointless, why can't you just come out and say that your original example was not a good one?

[caraher]

31. I'm somebody else

Maybe the person you were arguing with changed their numbers - sorry if they did. Or maybe you replied to the wrong post earlier.

I got the numbers from Girard442's post #20, which does not appear to be edited. It said, when I saw it,

Where n is the number of squares covered.

1 : 1
2 : 3
3 : 7
4 : 15
etc.

Which is pretty much the definition of exponential growth. If you raised the number of pennies on each square by a factor of 10, faster, but still exponential. Faster than exponential is combinatorial, but that isn't what we're seeing.

[Blue_true]

33. If you are someone else, I was not originally responding to you.

Yes, your example is exponential, the post that I responded to had straight line data that the person was calling exponential.

[Ms. Toad]

41. It's not straight line data.

It's the same exponential curve, less 1 (which governs only where it crosses the y-axis). Shifting where an exponential curve crosses the y axis does not make it a line.

[Blues Heron]

35. No it's an exponential curve

the final square has 2^64 pennies on it.

184,467,440,737,096,000,000 give or take

[Ms. Toad]

37. 263 - but definintely exponential

The number of pennies on each square is 2^(n-1), where n is the square number.

9,223,372,036,854,775,807 pennies on square 64.

I've been banging my head against the wall with the "no- it's linear with a slope 2" argument since mid-January.

[Blues Heron]

39. missed it by that much!

I knew I'd be off by either a zero or a doubling heh

[Ms. Toad]

42. The trick is to figure out what exponent you need for the first square

1=2^0, so if you are on square 1, you have to subtract one from the square number to get the exponent.

But yes - you doubled one too many times and landed on square 65

[Ms. Toad]

38. You've got the parentneses in the wrong place

It's 2^(n-1), which generates the series 1, 2, 4, 8, 16.

[eShirl]

4. video game

[global1]

6. I'll Always Remember The Disney Example Of A Nuclear Chain Reaction Using Ping Pong Balls And.....

mousetraps. One ping pong ball thrown into a surface with other ping pong balls setting on mousetraps and in no time a chain reaction - much like exponential growth of this virus.

Here's a video illustrating that:

I saw that on the Wonderful World of Disney (probably back in the 50's) when I was a kid and never forgot it.

I think it kind of makes the point of exponential spread or growth - basically a chain reaction.

[Volaris]

9. If the american adult population doesnt fucking know how exponents work,

We seriously need to fire betsy devos and give the public education system a shitload of rich people's money, because that's 6th grade math education.

[jayfish]

10. IMO, Math Is Taught Poorly In The US.

It took me three tries with Algebra I before I was able to pass it (A). I had to figure it out myself. From looking at the homework my kids bring home it looks like it's even worse now.

[Volaris]

13. I wont argue with you, I've struggled with it my self.

But even then i understood how necessary a basic understanding of it was and is.

We probably DONT teach it as efficiently as we could, but you worked till you got it, and so did I.

Its exponents. Again, middle school level at its basic understanding.

This shouldnt be this much of a problem in a first world nationstate.

(On Edit): and points on the Tribbles. Live long, and prosper! V

[Nature Man]

21. hint: it's on purpose

[Blue_true]

11. Just say to them that it is a case where they make a small change and get a big

result. Use a hobby that they do, for example gardening, say they plant one more pepper plant than they normally do, but get ten times the number of peppers that they normally get.

[MoonlitKnight]

17. Take away one electronic device, then two....

But an easy way is to ask them to fold a sheet of paper nine times. The thickness grows exponentially, making it impossible.

If you were able to fold it 103 times, the thickness would exceed the observable universe.

[Blue_true]

18. Does the person has enough visualization to grasp your last example?

The first would give a good feel example, the amplifying increase in resistance from the paper for each fold of the paper.

[GulfCoast66]

14. I got thru to a coworker today...

He was carrying on about nothing compared to regular flu. I told him there were 15 less than 2 weeks ago. Around 2000 now. And asked what that means it could be in 2 more weeks. That quieted him down.

But I’m sure I’m the next day or so Hannity will tell him what to think now.

[0rganism]

23. i would go with the "doubling rate" idea

if you're confident in your audience's ability to do basic math, you can note that the length of time to double is roughly 0.70 divided by the growth rate (e.g., a 10% APR leads to doubling in 7 years, and a 7% APR doubles in 10).

[caraher]

29. I teach that a lot

I learned it as the "rule of 70" which is easier for most people to figure because you can just work in percents; so doubling time is 70/(rate in percent) e.g. 10% per year --> doubling in 70/10 = 7 years

[ret5hd]

40. The Wheat and Chessboard Problem (Wikipedia):

https://en.m.wikipedia.org/wiki/Wheat_and_chessboard_problem

The total number of grains equals 18,446,744,073,709,551,615

If each grain was a penny, the total value would be:
$184,467,440,737,095,516.15

Over $180 quadrillion dollars

Yes, quadrillion.

[Ms. Toad]

46. A friend of mine posted this on FB - I think it's helpful

"There’s an old brain teaser that goes like this: You have a pond of a certain size, and upon that pond, a single lilypad. This particular species of lily pad reproduces once a day, so that on day two, you have two lily pads. On day three, you have four, and so on.

Now the teaser. “If it takes the lily pads 48 days to cover the pond completely, how long will it take for the pond to be covered halfway?”

The answer is 47 days. Moreover, at day 40, you’ll barely know the lily pads are there.

That grim math explains why so many people — including me — are worried about the novel coronavirus, which causes a disease known as covid-19. And why so many other people think we are panicking over nothing.

"

It is hard to conceptualize, on Day 40 (when only 1/512 of the pond is covered) that in a mere 8 days the entire pond will be completely covered. But working backwards from the date of full coverage seems to make point more clearly.

[Lars39]

47. Tribbles