Landmark Numbers and Bad Number Analogies 

A year is about pi-ty million seconds. Not thirty million, not forty million, but pi-ty million. :)

Matt: "We'll stand a double-decker bus apart." *stands 0.8 double-decker buses apart*

they're clearly less than a bus apart.

Overheard at a planetarium show in Seattle: If the Earth were the size of a grain of sand... It would be really small.

So if everyone lost five pounds, the NHS would save less than a pound per person. Imperial units and currency units are confusing.

Once the stack of dollar bills was brought up I got flashbacks to Tom Scott driving for hours.

"Is 4 a lot?" "Depends on the context. Dollars? No. Murders. Yes."

I love the phrases "don't engage your emotional reaction" and " no one is trying to help you understand, they want you to hurry up and feel something"

My least favourite number analogy - when a reporter tells you that something weighs 10 kilos and then feels that they have to put it in simple terms by adding "that's the same as 10 bags of sugar"...

milli-Helen - sufficient beauty to launch a single ship

American List of Preferred Measurements (4th edition): Imperial Driving Minutes (for distance) Olympic Swimming Pools Football Fields Empire State Building School Busses Your own Feet/Steps Coca Cola Bottles Whales Washing Machines Metric

As a programmer I find it very useful to remember that a day has a bit less than 100k seconds (86400 seconds to be exact), so when someone says that "there are millions of events every day" you can just convert it to "there are tens of events every second", which is really not that much for computers.

When people use analogies like "this will stretch to the moon in back x times", the point is not to give anyone an intuitive sense of *how* big something is, just that it's really really big. It's pretty much equivalent to saying, "there are as many ___ as grains of sand on a beach" or "there are as many ___ as there are atoms in the universe". They are kind of like fake landmarks, things that you don't appreciate the actual size of, but you know they are big. The same thing happens on small scales too. "Smaller than a human blood cell", "smaller than the HIV virus" I actually learned the other day that modern transistors in computers are smaller than a human blood cell and the HIV virus. Lol. I don't know how small those things are, but I know they're very tiny, and the idea that we make transistors that small is insane. It at least gave me the sense that we really are reaching a limit of how small we can make transistors

My favorite part of this book is how the dialogue between you two demonstrated that you need YOUR OWN landmark numbers, not someone else's. Every time he'd say his intuitive amount, you'd do it differently and have your own intuitive amount, but you could still talk because it made sense to you both.

That last point was incredible. "No one wants you to understand. They want you to hurry up and feel something."

The phrase “24/7/365” always hits my eardrums awkwardly. There are 24 hours in a day. Then there are 7 days in a week. So my brain is expecting the next corollary to be 52, as in the number of weeks to a year. But instead, this popular phrase jumps back to days again! I think “24/7/52” would make more sense in a short list of quantities meant to convey the listener’s attention from the duration of a day to that of a year. Right then. End rant. Cheers! -Phill, Las Vegas

My go-to for understanding the height of something is 1 story ≃ 10 feet ≃ 3 meters. For example, the Falcon 9 rocket is 230 feet high, which doesn't tell me much. But that's the height of a 23 story building, which I understand right away, and it also happens to be about the height of the building I live in.

One thing I keep in mind are various odds to put chances into perspective: Coin flip - 50% Rolling a one on one die - 16% Rolling a 20 on a 20-sided d&d die - 5% Rolling a 12 on two dice ~ 3% Flipping heads 10 times in a row - 0.1% (1 in 1,000) Flipping heads 20 times in a row - 0.0001% (1 in 1,000,000) When people say "It was only a 10% chance of rain and it's pouring, weather man screwed up", I use the rolling a 1 analogy. When people say there is only a 3% chance of dying to Covid, I ask how often they rolled a 12 in monopoly. Chances of winning the powerball lottery? (1in 300 million), roughly equal to flipping heads 28 times in a row.

To paraquote Brian David Gilbert, a classic naval hit point is the number of 14" shells you can withstand. So all living creatures have 1 HP.

When I was a teenager, my dad reminded me that you only get about 2000 weekly wages in your life to try to get me to budget.

0:05 Curiously enough, the only thing that went through the mind of the bowl of petunias as it fell was "Oh no, not again"

This made me think of a pod cast I've been listening to, The British History Podcast. That includes a historic number metaphor. Anglo-Saxons talked of land in Hides. One Hide is 120,000 m^2. To leave it there no one would really understand it. However a Hide was "enough land to support a family ". So when Kings dole out 20,000 hides of land you know, almost intuitively, that's a lot! Or a peasant who dies and leave 1 hide to split between his sons is poor.

Correct me if I made a mistake here, but on data storage: A Lorum Ipsum .txt file of 140 000 words is about a megabyte. "Ready Player One" by Ernest Cline is 136048 words. So a tome like that is ~1 megabyte. I know what a large book looks like. A hundred megabytes is a well stocked bookcase of 100 such books. I know what a filled book case looks like. Ten such bookcases is a row of bookcases in a library, and thus a gigabyte. I know what a library row looks like. A floor in a library is maybe ten rows, so 10 GB on a library floor. I know what library floor looks like. A huge library with 12.8 floors filled with books (and 0.2 for the lobby and coffee corner) is equivalent to the 128 GB usb stick dangling from my keychain. I've never been to a library that size, though they probably exist.

The dreaded 'width-of-a-human-hair' analogy.

I've been listening to Tim Harford on More or Less for over 10 years and never seen his face. I assumed he was just a disembodied voice that had possessed a microphone at the BBC. Watching Tim walk and talk like he is a normal person was somehow deeply unsettling.

I love the extra animations in this video. Kudos to the editor and animator.

This reminds me of one of my data visualization pet peeves: different sized circles to represent different quantities. For example, one circle represents 100 of something and a circle with twice the radius represents 400 of that thing, BUT people don’t intuitively get that twice the radius means four times the amount. Area increasing with the square of length is not an intuitive idea for many people, and this style of visualization helps nobody, except maybe the graphic designer

reminds me of the "give every person a million bucks" tweet

This video is approximately 0.6 Matt Subscriber Milliseconds long.

I always say that if somebody reports an absolute number, it's because the percentage is insignificant, and vice versa.

In Melbourne, Australia, everything to do with volume is measured relative to the Melbourne Cricket Ground as being "enough to fill X MCGs". Especially when the papers want to contextualise large construction projects

If the Earth had a diameter of 1 foot, then the moon would be one double-decker bus away, and would be the size of a softball.

1 ton = 1 m³ of water ≈ 13 people

I always calculate app prices in 1 Euro/Pound/Dollar cheeseburgers from your fast food joint of choice. Like if an app is 2.99, I think "Would this app bring me as much joy as three cheeseburgers?"

When it comes to understanding excessive wealth I use “minimum wage years” as landmark number. For example, Jeff Bezos’ net worth is about 13 million minimum wage years. Homo Sapiens appeared 200 000 years ago, dinosaurs disappeared 65 million years ago - somewhere in between those two lies the order of magnitude of time a single human would have to work to acquire (and reasonably spend) such amount of wealth ...

"isn't a double decker just very intuitive?" Someone is very Londoncentric over there. I've never seen one of those in my life

I've heard that six inches is a hotly contested measurement for a lot of guys.

Mine really just shows how insane some of the numbers in physics are, in particular the relative strength between the four fundamental forces. The Strong Force is the strongest at 10^38 times stronger than gravity. Electromagnetism is next at 10^36 times stronger than gravity and 1/137 the strength of the strong force (as far as I remember). The weak force is 10^25 times stronger than gravity or 1/10,000,000,000,000 (10 trillion) the strength of the strong force. But 10^38 is beyond our normal understanding of number, which is where the "landmark" number comes into play (it still doesn't make any reasonable sense): If gravity is the energy given off by a 1W light bulb in one second (1 joules), then the strong force is the energy given off by the sun (3.8 × 10^26 watts) for 10,000 years (~1.2 x 10^38 joules).

5:05 - I’m obsessed with the way he rattles off “double decker bus”

When they talk about the overweight citizens of the UK losing weight to save 100 million pounds, the population they used was for everyone in the UK. Shouldn't it just be the overweight populus to determine how much losing 5 pounds would save the government on a per person basis?

Maybe this is not a so-good comparison, since most people don't have either an intuitive notion of how fast light is or how fast a computer is, but I really like this fact that I came up with: light travels around 10 cm during one CPU clock cycle (roughly one operation, let's say). When you know that electricity is a little slower than light, it makes you think about the length of all those connections between computer components, and how slow everything is compared to a CPU.

My favorites are found in astronomy: - An astronomical unit (AU) is the average distance from the earth to the sun. It's a very handy comparison to give a sense of scale when things are between 1/4 and 100 AUs. - A lightyear is how far light travels in a year. At first, this one seems unintuitive. But consider this: once you measure things that big, there is no sense of scale that your brain can really comprehend. With the lightyear, you at least know how far back in time you're seeing something (when something is 4.2 lightyears away, you're seeing it's state 4.2 years ago). And since so many things in astronomy are measured in lightyears, we get good comparative numbers. So the closest star is about 4 LY away, the other side of our galaxy is about 100,000 LY away, and the closest galaxy is about 2.5 million LY away. Since we measure them all in LY, it's easy to compare and get a sense of relative scales.

"Double-decker buses are such a brilliant and intuitive unit of distance!" Literally anyone who isn't British: (Visible confusion)

My most used landmark number is a "work year" is around 2000 hours. (40 hrs/wk x 50 weeks). An article I read years and years ago tried to scare people about an education gap between countries, and said that U.S. students were "only" given 1500 hours of homework a year (on top of time already spent in school), while it was ~2500 hours a year for European students, and ~3500 hours a year for Japanese students. Since every one of these numbers is ridiculous right out of the gate, I knew I could ignore the rest of the article. And of course the most important reason this landmark is valuable: looking at your various Steam "time played" metrics and having an existential crisis about what you're doing with your life...

Two things I'm surprised were not mentioned: 1. The Smoot. 2. Pi seconds is approximately a nanocentury.

Matt Parker: "All numbers are my friends." Me: "Except tau, right?"

the one that drives me the most crazy is (in the states, at least) when news broadcasts try to express how high up something is by comparing it to a building of certain number of stories. For instance, if something fell 150 feet they always say 'thats like falling from the top of a 15 story building.,' as if typical floors were 10' high. I can tell you as an architect that number is off by 30-60%. Most buildings built in the last few decades are anywhere from 14' -16' per floor, or sometimes more. So falling 150 feet is actually more like falling from a 10 story building. I get why they do it, just like stated in the video, its more about an emotional response than a useful reference....but still.

The last part about "first understand things and then eventually get angry about it" is probably the best life I have ever heard.. Absolutely wonderful

"By all means get excited or get angry, but first understand what's happening. [...] The reason that so many of the comparisons we see are unhelpful is because no one is trying to help you understand, they want you to hurry up and feel something." Incredible

One metric that I like to use is hourly wage. If I want to make a non-essential purchase, I think about how long I would need to work to afford that thing. So if I wanted to buy a new tv for $500, and if I made $20/hour(not taking taxes and such into account), that would cost me 25 hours.

In Ireland distances (between towns especially) are given in time, while it is up to the person receiving the information to know whether the person giving it drives or takes the bus. Here in the house we measure temperature in cats. "It was cold last night, there were 7 cats on my bed."

The length of a double-decker bus is roughly one femtolightyear.

Length: Radius of Earth ~ 6000 km Circumference of Earth = 40000 km (this is more-or-less exact, because it was the original definition of a meter) Weight: Human ~ 70 kg Time: 52 weeks in a year 250 working days in a year 2000 working hours in a year Density: Water = 1 kg/l (all living things have approximately this density) Metal ~ 10 × water (except aluminium = 3 and gold and lead = 20) Speed: Sprinter ~ 10 m/s Sound ~ 300 m/s Light = 3×10^8 m/s

To help if you're finding it difficult to picture somewhere the size of Wales (standard UK unit for rainforest etc) according to latest research, it is the size of 2,861,974 football pitches (probably not taking account of topography)

Loved this video, great conversation.

2:11 I love that detail of that text on the bus and behind the fence

Sign in Greggs: "Please keep 2 metres apart - that's about 15 sausage rolls"

my favourite approximation I used in my physics degree all the time was that the number of seconds in a year is about pi * 10^7

In PE the teacher asked us to write on a scale of 1-10 how good we thought we were at badminton, so he could make fairer teams. I proudly wrote π next to my name.

Everybody should see this... Such useful information. Thank you! Awesome video!

I was in college in the 1980s and we rated how good-looking girls were in milliHelens. As in, "If Helen of Troy's face could launch 1000 ships, how many ships could Brenda's face launch?" Electrical engineering nerds; no wonder we didn't have girlfriends.

"I want to do it safely" *get rolled over by a bus*

Not exactly a landmark NUMBER so to speak but this talk of breaking things down into things you understand to grasp things you don't understand is my favorite way of explaining things. And one I was using even ended up on the back of a product (Wifi Modem) and it made me smile when I saw it. Explaining how channels work in your modem by comparing channels to lanes on a road and data packets to cars, the more lanes you have, the more cars you can fit comfortably without slowdown. Again, not exactly what you're talking about, but definitely in the same vein of teaching, and I love all of it.

One category that I think sometimes gets overlooked but can be very useful are some basic senses of sizes for computer data. It helps really get a handle on, for example "how much better is a 100 Mb/s internet connection than a 1 Gb/s connection?" So here are a few to get a sense of size: 1 byte: A text file with one character in it 1 kilobyte: A text file with about a paragraph of text 1 megabyte: A text file with about 400 pages of text OR a picture from a 5MP camera (iPhone from 2010) 2.5 megabytes: A picture from a 12MP camera (iPhone from 2020) 5 megabytes: About 4 minutes of MP3 audio 1-2 gigabytes: A movie at standard definition 3-5 gigabytes: A movie at high definition 1 terabyte: An HD movie collection with about 300 films

As a Welshman my favourite is multiples of the size of Wales when describing geographical areas.

Didn't even mention the classic football field analogy

I have a bunch of these! (Note: I'm rounding A LOT here; many of them are off by factors of two or three or four; it's mostly an order-of-magnitude thing, except when I happen remember a more specific value.) I didn't remember all of them and had to check a bunch to make this list. Anyway, here: *Miscellaneous:* Number of stars in the galaxy ~ 100 billion Number of galaxies in the universe ~ 1 trillion Number of atoms in a cell ~ 100 trillion Number of cells in a human ~ 100 trillion *Money* (note that GDP/person is average income): Bezos (richest person) net wealth (including illiquid assets) ~ 200 billion US deficit (what gets added to the debt every year) ~ $1 trillion more/year US government spending (federal, state, & local) ~ $10 trillion/year Total US debt ~ $20 trillion US GDP ~ $20 trillion/year ($60,000/person/year) US GDP growth ~ 2.5%/year, so around $500 billion more/year GWP (Gross World Product) ~ 100 trillion/year (~$10,000/person/year) Average income of the bottom billion or so ~ $1/day, or ~$500/year Average income of someone born into the bottom billion after they move to the US, if they're allowed ~ $10,000/year *People:* NYC population ~ 10 million UK population ~ 50 million Nigeria population ~ 200 million America population ~ 330 million (~1/3 of a billion) Europe population ~ 750 million India population ~ 1 billion China population ~ 1 billion Africa population ~ 1 billion People living under $2/day ~ 1 billion Asia population ~ 4 billion World population ~ 8 billion *INTERLUDE* | Here's a use-case combining *money* and *people:* If you took all of Bezos's money, you can pick 1 of the following to do: * Abolishing all taxes & fully fund the US governments (with 0 deficit) for 1 week * Keep all taxes & fully fund the US governments (with 0 deficit) for 2 months * Pay 1% of existing US debt * Give every American (including hundreds of thousands of ex-Amazon employees) a one-time $500 check * Give the poorest billion a one-time $200 check (about doubling their yearly salary for one year (except those that used to work somewhere in Amazon's supply chain)) * Give everyone a one-time $25 check (Note that, of course, you couldn't actually do this; like all billionaires, most Bezos's wealth is purely theoretical because it's shares of stock (in this case Amazon). So you'd need to liquidate a lot of Amazon's shares, but doing so would crash the value of Amazon shares. That's why Bezos can't actually buy $200 billion worth of _stuff_ even if he wanted to. But for the sake of the argument, this is what the scales of the numbers are.) Moving on... *Length:* Earth's radius ~ 10,000 kilometers (10 thousand km) Moon's orbit radius ~ 100,000 km (100 thousand km) Sun radius ~ 1,000,000 km (1 million km) Earth's orbit radius = *1 Astronomical Unit (AU)* ~ 100,000,000 km (100 million km) Pluto's orbit _diameter_ ~ 100 AU ~ 10,000,000,000 km (10 billion km) Oort cloud diameter ~ *1 light-year* ~ 100,000 AU Distance to closest solar system (Alpha Centauri) ~ 4 light-years Diameter of Milky Way ~ 100,000 light-years Distance to closest galaxy (Andromeda) ~ 1,000,000 light-years Diameter of the observable universe ~ 100,000,000,000 light-years

The one I hate most is "it's hotter than the surface of the sun". It's not a particularly impressive temperature, and the saying should rather be "it's cooler than the surface of the sun" because it's the coldest part of the sun.

These "Landmark numbers" are, by their very nature, experience based. I'm from the US, and I have never been to Europe. I've never seen a double decker bus. I'm sure we have them in the US somewhere, but I've never experienced one. Therefore, this reference doesn't mean much to me. Thought I'd throw that in for consideration because I don't "intuitively know how big a double decker bus is". Do you intuitively know how big a full grown Blue Spruce tree is? Most people here in Colorado do.

The landmark number I like the best is that a nanosecond is about a foot as light travels. Or for those uncomfortable with feet, it’s 30cm or a third of a metre. So if I’m sitting six feet from my wife, we’re 6ns apart. 3m from my son, we’re about 9 or 10ns apart. So a microsecond is about 1000 feet, or 300m. I can get an intuitive idea of tiny timescales by relating them to human scale distances at the speed of light.

I really love Tim's podcast, so this was a pleasant surprise

I was going to comment about how some number analogies are not trying to build understanding but rather to make you astounded or dumbfounded, and then I was like "Well, maybe wait to the end of the video to see if they touch on it first". Glad I did, and the last bit was particularly insightful in conjunction with the technique of using landmark numbers, because then I totally understood why one would take issue with analogies meant to inspire awe more than understanding. Your guest (I already forgot their name but youtube isn't gonna let me go check it without losing my comment on my phone haha) is really good at connecting how numbers are used with ethical and social issues, glad they are making the rounds on the maths channels I watch. Good social distancing btw, stay safe Matt

I love the “bowl of petunias” hitchhiker’s reference

"landmark numbers are your friends" * ramanujan stares from the distance with all the integers *

I recently had to do a estimation like that to decide if it was worth upgrading a subscription channel for an extra $6 a month. The upgrade would remove ads, so I did the following calculation: I watch this channel about 2 hours a day. Given the amount of ads it shows, this is 15 minutes of ads per day, so roughly 2 hours per week, 100 hours per year! For $6 a month I free up four whole days of uninterrupted commercial watching per year! Definitely worth it!

That was great. I saw his numberphile on the storks, interesting. Also, loved the RouteMaster

0:56 I think we can all agree that that is actually a *parker* double decker bus away

0:06 “Oh no, not again”

A useful one I know off the top of my head is that the earth is about 24,000 miles in circumference and is therefore spinning at about 1,000 mph. It's handy for being able to kind of guess distances on a map/globe.

You always look like you have happiness in your eyes during the intro. I truly appreciate that.

I'm an astronomy teacher from Israel, and when I teach about the asteroid that ended the dinosaur age I tell them this: The size of the asteroid is about the size of Gush Dan (Tel Aviv Metropolitan Area, 10km). The distance between Tel Aviv and Haifa, and Tel Aviv and Be'er Sheva is about 100km each, which is the radius of the Chicxulub crater. So imagine a rock the size of Gush Dan hitting Earth so hard it makes a hole all the way between Haifa and Be'er Sheva.

One of my pet peeves for bad number analogies is where there is no analogy at all, but just no context ... like when news outlets report things like "Parkershire Council spent £50,000 on stationery last year!" in angry, outraged tones without giving any clue as to how it compares to similar organisations but is clearly aimed at making people think it's a big number.

Thank for sharing ❣🌻

The ending of this video reminds me of that scene in The Rutles mockumentary where Eric Idle has to first fast-walk, then jog, then run, then sprint to keep-pace with the cameraman before running out of breath in the middle of the street!

Tim: Don't get emotional about it. First, try to *understand* it. Matt: *HIS BOOK IS OUT ISN'T THAT EXCITING OH YEAH!*

How much money do you earn, in prime ministers?

In a similar vein, I've always used go-kart rides as a unit of measure to weigh spending money on a thing. An approximate going rate for a ride here in Seattle right now is $20/10 minutes. So if I'm considering spending $100 on something, I ask myself whether I'll get more enjoyment out of it than spending 50 minutes on a go-kart. I consider a go-kart ride to be the peak of/cap on "how much I'm willing to spend per unit of entertainment". What's great about using this unit of measure is it automatically adjusts as you travel, as the cost of 1 ride is generally pinned to 'as much as you can possibly get people to spend'.

Something I remember is the circumference of the earth is 40,000 Kilometers or ~25,000 miles. Puts into perspective the amount of miles I have on my car

In Germany, the calculate areas in "Saarland", the SMALLEST federal state.

I can’t tell if 200 was a serious guess or not. He seems genuinely confident then surprised

Nice Hitchhikers Guide reference! Love it!!!

Great video!

Light can travel around the equator about 7.5 times in one second. I know the equator is still enormous, but it has always felt like a very intuitive way of picturing something otherwise quite astronomical.

For me, one of the most useful landmark numbers is the block. You can intuitively know how far any distance is if you say "it's 20 blocks away". I would guess the average lenght of a block varies from country to country, but where I live (Perú), it's extra helpful because the average lenght is 100 meters, so converting from "blocks" to kilometers is just an order of magnitude.

I use a landmark to convert celsius and fahrenheit, 10c = 50f. Then use the 5/9 ratio to work out the temps from there. 15=59, 20=68, etc I compare "entertainment" purchases (touristy things like mini-golf, ziplines, boat rides, go-karts, etc) to the price of a Movie Ticket (in regards to x amount of dollars for two hours) I now use the book Humble Pi as a landmark book to evaluate the sarcasm in other books.

Spent many hours of my childhood waiting for the school bus where this was filmed - should have spent the time practising my bus length calculations!

ohh so that's why all my (translated) dinosaur books were talking about dubble decker busses even thought those are very rare where I live

I love the conversion rhymes I learned at school 2 and a Quarter pounds of jam weigh about a kilogram. A Litre of water is a Pint and 3 Quarters A Metre is more than a Yard you see, in fact it's about 3 Foot 3 (inches) Since I also know that a litre of water weighs a kilogram I can pick up my (full) water bottle an instantly know what a kilogram feels like. I don't know about anyone else but these things really help me

Subtle "Hitchhiker's Guide" reference in the first 10 seconds, very nice!

I was a cashier at a grocery store, and I would tell my customers their total in pennies. "Alright, your total is 10,704 pennies." ($107.04) The usual response was, "OK... wait! How much?" I became known as The Penny Guy and people started bringing their kids shopping with them because kids would always get bug-eyed in amazement and gawk at how expensive their food was. We would all get a good laugh.