Ch1 -
Estimating cars in US. Immediate family - 3 people, 3 cars. So, US population 330 million, so 330 million cars.
*A rough estimate is often good enough.
*The more you know, the better your estimates.
One person one car seems too much. Young people, old people, those using public transport etc. So let’s say more than half, two thirds or three quarters of population → 200 to 250 million. Checked Google, real value close enough.
*Refine your estimate if necessary.
*Independent estimates should be similar.
Consensus is a good sign, unless everyone is making the same error.If two independently created estimates are significantly different, however, something is awry and at least one of them is wrong.
How many miles does a typical car get driven a year? Let’s say 20 miles to work one side. That’s 200 miles in a week, and 10000 miles in a 50 week year.
*Too big and too small tend to average out.
How Long does it last?
..10 years.
How Many Cars are sold each year?
If there are 250 million cars and each lasts 10 years, then one tenth of them, or about 25 million, must be replaced each year.
*This is an example of a kind of conservation law: a car that reaches the end of its life will generally be replaced by a new one. Of course that assumes a steady state.
Conservation: what goes in must come out.
How Much does it cost to own a car?
*Multiplication, division and approximate arithmetic are good enough.
Most of the time, you can get a value by looking it up, but you will be much better offif, before you resort to a search engine, you makeyour own estimate. It won’ttakelong and you’ll quickly get good at it. Practice will arm you for a lifetime of being wary about what people are telling you.
Some unit conversions and their approximations for estimating..
Ch2 -
About 1 oil barrel - 42 gallons
US reserve would last 3 months, not 260 years!
News often mistake numbers, million for billion, barrel for gallon and so on.
We can figure out by having some basic numeric sense of these numbers. Even if our estimate is wrong, it can’t be wrong by a factor of a 1000.
So, first need to know some real facts.
Second, don’t need to be very accurate in estimations to make sense of something.
Third, we can reason backwards from conclusions to assumptions and given data. If some number is claimed to be correct—for instance, the petroleum reserves will last 250 years—what are the implications of that? If the implications are nonsensical or plain impossible, that means there must be some mistake, and we can backtrack to figure out what might have gone wrong.
Fourth, we can look for consistency among independent computations or sources. If there are multiple ways to arrive at value, the different values should be reasonably close to each other; if they’re not, something is awry.
Ch3 -
Words like million, billion and trillion have no intuitive meaning to most people, myself included, and thus we tend to treat them as synonyms for “big,”“really big,”and “really really big.”
Sep 2008 US financial crisis,
“So divide 200 million adults 18+ into 425,000.00.”
Lol, it’s $425.
“So what’s point? We Are all number numb. And, very few people, even really smart folks rarely do the math.”
Since big numbers don’t carry enough intuitive meaning, we need to cut them down to size, to bring them into a range where there’s decent chance of understanding them.
What’s my share?
One good way to reduce large numbers like the national debt or the cost of a corporate takeover to human scale is by expressing them as the amount per person or per family.
*Ask yourself “Could I afford it personally?” That’s Often a valuable corrective.
Basically, never take big numbers or big visualisations at face value. Do the math, be it approx estimates.
Visualizations of big numbers are a mixed lot. Some work well, but in many cases they simply replace an unintuitive number by a similarly unintuitive image, like a pile of tires or a trip to the moon.
Ch4 -
To put everyone on the same footing,
kilo is one thousand,
mega is one million,
giga is one billion, and
tera is one trillion.
If you want to future-proof yourself as technology advances, the rest of the sequence is peta, exa, zetta and yotta. Each one is 1,000 times bigger than the previous one.
milli, micro, nano, and pico, which are one thousandth, one millionth, one billionth, and one trillionth. These are most often applied to lengths and times, like millimeters and nanoseconds.
When they are too many zeroes or words like million million trillion, it’s better to switch to exponents and do the math.
Ch5 -
“Americans receive almost two million tons of junk mail daily.”
Poor mailman, that would be 26 pounds every day just for me and my wife. Abby’s value is clearly too high.
Get the units right!
Think about how we reasoned through this. Convert the big number in the original statement into a smaller number that represents its individual effect on us. If that number is clearly wrong, think about what might have been wrong with the original statement, and work through some of the possible errors to see whether a simple change could explain the original and thus lead to a more likely answer.
Ch6 - Dimensionality