FrozenPatriot sends this remediation for those (like me) who stopped learning when the maff got hard:
A long time ago, in an ancient land, there lived a very wise man who was the Vizier in the court of a great Sultan.
Many prosperous years passed and the great Sultan died leaving his young son, the prince, heir to the throne. Lacking both wisdom and experience, the prince started spending like a fool. Thus, the wise Vizier decided to teach the brash prince a lesson.
The Vizier convinced the prince to hold a great contest of wits for any who would enter. As a reward, the prince decided to give the winner whatever he asked, boasting of his great wealth and being under the illusion that it was essentially endless. Naturally, the Vizier won the contest and asked the prince for his prize: a single grain of wheat to place on his chessboard.
“What?! Just a grain of wheat! Are you insulting my wealth?”, scorned the prince.
“Certainly not, your majesty!” the Vizier exclaimed. “I am not yet finished. I also wish to receive double the amount of wheat each day until each square of the chessboard is satisfied, so on the first day you give me one grain of wheat on the first square, on the second day you double it on the second square (giving me two grains), on the third, you double it again on the third square (giving me four grains), and so on, until the chessboard is filled.”
“I thought you were so wise,” the young prince scoffed, “and that you would ask for something more substantial. Regardless, if this is your wish, you shall have it.”
So on that day the Vizier received his first prize — a single grain of wheat. On the second day he received 2 grains, on the third 4 grains, and the young prince couldn’t help himself making fun of the Vizier.
On the sixth day, the Vizier received 32 grains of wheat. On the eighth day — the end of the first row — he received a mere 128 grains. On the sixteenth day — the end of the second row and 25% through the progression — his reward was 32,768 grains. (2-3 bushels)
Less than nine weeks later, how many grains had the Vizier received?
The prince could not satisfy the reward because there’s not enough wheat on earth — 18,446,744,073,709,551,615 (18.4 quintillion or 18.4 million-trillion) grains!
Strikingly, this much wheat would cover all the land on earth to a depth of over 14 inches!
Study the number progression in this table (posted on WRSA’s dropbox for brevity).
That’s the power of exponential growth. The graph of the first two rows of the chessboard (16 spaces) looks like this:
The x-axis (along the bottom) shows the day and the y-axis (along the left) shows number of kernels of wheat. The top right point accounts for 2-3 bushels on the 16th day.
Because the last couple points dwarf the first few so severely, it’s helpful to look at the graph with a logarithmic scale on the left side (y-axis), like this:
As you can see by studying the the y-axis, the scale changes as you go higher. Logarithmic scales are useful for showing small and large numbers on the same chart. Because time is easily understood in linear terms, we will not change the x-axis to logarithmic.
Now, let’s add an exponential trend line to the first chart:
The black line shows typical exponential growth. Note that R2 = 1 above. This means the data points all fit perfectly along the line (1.0 = 100% accuracy). Anything less than 1 indicates the data doesn’t perfectly fit the line, but real-world data usually isn’t perfect.
Now, look at the same line on a log scale:
The black line becomes straight!
What’s my point?
Straight lines on log scales mean exponential growth.
Now, let’s look at some real-world data:
The blue dots are real data points (the top right point was recorded Monday, October 27th), and the black line is an exponential approximation of the data. In this case, R2 = 0.9748 (or 97.48% accurate) which is quite good. Let’s look at the same data with a log scale:
The blue dots follow the straight black line quite well, yes? This indicates the data is following a trend of exponential growth.
The real-world data presented in the two graphs above are, of course, the official number of world-wide Ebola cases, according to the World Health Organization (WHO). The x-axis (along the bottom) is the number of days since the outbreak began last March. As of today, October 31st, it’s around 15,000 and reliably doubling roughly every three weeks. As most of us know, the WHO freely admits their official numbers are low (due to misdiagnosing, not reporting cases, death before tests can be run, etc.) and that the actual total is 2.5 – 3 times higher — i.e. 35,000 – 45,000 cases today.
Am I saying this trend will continue forever? Of course not — but only because I’ve temporarily misplaced my crystal ball… Granted, there are differences between the West and West Africa – namely that we don’t kiss dead bodies during days-long funerals (Ebola concentration increases for several days after death and the dead are currently among the most common sources of new cases). In addition, most of us probably wouldn’t stone to death and dispose in septic tanks the bodies of aid workers who come to help us (which happened), although if we find ourselves at the point which aid workers need to venture to FUSA to stop Ebola, who’s going to come? …and how and why would they get to your neighborhood?
All that being said, clearly nothing has slowed it down so far.
If you’re curious what this trend looks like when projected into the future, here it is.
Disclaimer: past performance does not guarantee future results.
Also, please don’t let this influence your 2016 Independence Day party planning. Yet.
This is the same data set as above, with the trend line extending to an intersection with earth’s population. To those who say projecting (extrapolating) this data is meaningless, I largely agree and would have granted you the same in July with 1000 cases, while discussing extrapolating to 15,000 cases by Halloween. (RUBBISH, say you!) That said, the trend line extension above is still purely an exercise in curiosity.
As with physics, economics, and chemistry, math just is. Math does not have an agenda. Math does not vary with political whims or income levels or normalcy bias. If you disagree with the mathematical analysis above (except for the extrapolation), please don’t shoot the messenger or dismiss it.
If you disagree, simply prove the information above wrong using math, because that’s how math is disproved.
If you don’t believe that established trends generally tend to continue, give your written reasons below as to why not?
Be specific and show your work.
What external force will change this trajectory?
Perhaps you’ve located my crystal ball and can inquire in my absence. Are Westerners somehow different?
“It’s never happened before, so it just can’t!”
Very science-y. You might have a future as a globull warmist.
American healthcare is the best in the world?
I agree that it is. However it’s been finely honed for car crashes and chainsaw accidents and heart attacks, not 8-21 day viral hemorrhagic fevers with R0=2 and CFR=0.7.
Aesop and Doc Grouch have done outstanding work explaining this and I thank and commend them to the highest degree for spending their time freely contributing within their sweet spot. CA (our gracious host) has also given selflessly within his sweet spot, as have countless others within theirs, all of them deserving our laud and thanks (each of you has mine).
I happen to understand applied math (BS and MS in Electrical Engineering), and I’m willing to come forth from the among the readership and contribute where I can. I’m not telling you what to do, or how to plan, or when to act — I’m just presenting the math, and the math just is.
Venturing outside what I know and can prove, I HOPE the above extrapolation is wrong (who among us doesn’t?), that this just burns itself out, and that I can go on living life with my family without another thing to consider and for which to plan.
However — as most WRSA regulars already know — hope is not a strategy.