Simple, yet counterintuitive mathematics | Why numbers don't always mean what you think

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[factsopinionsandinterestin]

Ironically, we intuitively guessed that the guy on the right saved more money on gas, because you wouldn't have asked otherwise...

[TheOnlyJura]

Damn, I can't believe you actually wrapped a cable around the globe just to make this video!

[freakydeaky]

Oh man, the extension cable example made going up a belt size seem so much worse :(

[timchallenge]

Just discovered this channel and I'm hooked!

[jebeda]

The metric measurement for gas consumption is L/100km, so the green car (lower left) gets 9.44 L/100km, and the yellow (top left) gets 6.71 L/100km, thus saving 2.72 L/100km. The grey car (bottom right) gets 29.4 L/100km and the blue car (top right) gets 23.5 L/100km, thus saving 5.8 L/100km if you switch.



Measuring gas consumption in a unit that actually measures CONSUMPTION of gas per amount driven is much more meaningful for these types of comparisons. MPG (or km/L) is not actually a "consumption" but more like a "range" measurement.

[jujeremy]

The first problem shows why measuring fuel efficiency in L/100km is much more useful. Since the units are volume per distance rather than the reciprocal as with mpg, you MULTIPLY your distance by fuel efficiency to compute the volume of fuel consumed. So, if you rephrased this question for someone not using wonky hillbilly units, it would read "One person trades in their 9.4 L/100km car for a 6.7, while the other trades in their 29.4 for a 23.5. Who buys less fuel compared to before?" The answer is then intuitive and obvious.

[HelplessGazellle]

Hey, you should watch your youtube statistics to see if your views go up over the next few weeks. The main thing stopping me from watching your videos is other time commitments. But now that schools/colleges are being canceled, I think a lot of people will have enough free time to watch more of your videos. I know I sure will. Thanks for making great content. Your job is my dream job.

[cerwe]

A mother is 21 years older than her Child. In 6 years, the Child will be 5 times younger than the mother. Where is the father?

[ssifr]

It's amazing how in the third example the original radius doesn't matter at all.

[unclecreepy]

There was a sports show called “Numbers Never Lie” where they used a lot of stats to talk about games and make predictions, etc. But they were wrong so many times because of the simple fact that while numbers never lie, people do. They would constantly misinterpreted or misunderstand the stats and numbers.

This is especially true when dealing with a small sample size where adding 1 or 2 can double the percentage.

[descuddlebat]

Simple intuition for the last ace thing: The probability for a position to contain the last ace is the probability that it contains an ace, times the probability there is no ace after it. The former a constant 1/13 (4 aces / 52 cards), the latter is 1 only if there are no cards after this one.

[stephenkamenar]

the first example is so confusing because the guy on the left IS saving more on gas in terms of percent. He's saving 40% instead of the other guy saving only 25%.
but ofc the guy on the left's gas bill was already so low saving 40% on it doesn't matter that much.
very interesting though, fooled me! o:

[vidhound]

I’ve told people the circumference puzzle before, and once you do the math, you figure out that of course it is the non-intuitive answer. But I also am looking for ways to visualize it that make it more intuitive.

One way that I think makes it easier to picture is if you imagine the earth being a cube rather than a sphere. It is then much easier to picture what adding 6 feet does to the height of the cable, since it gets 1.5 feet on each of its four sides.

[Nwk]

The metric way of expressing fuel economy is in liter/km not km/liter. Converting into those units makes the first exercice not counter-intuitive at all! :)

[stephenkamenar]

the strawberry example is the same as stock prices. if a stock drops 99% vs 98%
the difference in price between the two is 100%. you'd have twice as much $ if it only dropped 98% instead of 99%

[circledline]

Thank god he said he was kidding at 7:47 or else I would've believed him.

[eduardoroman]

La probabilidad de que aparezca un as en la posición nro 52 del mazo es exactamente 1/13, como corresponde a cualquier otro número de las cartas desde el as hasta el rey. En cambio, para que aparezca el ultimo as (o cualquier otro número) en la posición nro 51, la probabilidad ya es algo menor, ya que al 1/13 hay que restarle la probabilidad de que la última carta tambien sea un as. Y así sucesivamente retrocediendo en el mazo, las probabilidades serán decrecientes. Por lo tanto, sí, la posición nro 52 es la más probable para un nùmero de carta determinado, sea este un as, un 2, un 3, un 4, etc etc.

Translated for english speakers:
The probability of an ace appearing in the 52nd position of the deck is exactly 1/13, as corresponds to any other number of cards from ace to king. However, for the last ace (or any other number) to appear in position 51st, the probability is already somewhat lower, since at 1/13 you have to subtract the probability that the last card is also an ace. And so on by backing into the deck, the odds will be decreasing. Therefore, yes, the position 52nd is most likely for a given card number, be it an ace, a 2, a 3, a 4, etc.

[markschultz]

The reason why it doesn't work is because the cost depends on the amount of gasoline burned, which is part of the denominator, so you first have to switch from kilometers per liter to liters per kilometer so that the amount of gasoline burned is in the numerator, then you can do a simple calculation to get the right answer.

[toyfabrik]

Here's some even more counterintuitive maths:
Since he apparently got some 40, 000 km of cable lying around (and he wouldn't have lied to us about the actual lenght of the cable shown in the video??) i did a rough calculation:
Here in Europe, for 100 m of double stranded copper cable, the cheapest variety, the cost would be about 25 € (or 30 Dollars). So it's about 300 Dollars for 1 km of cable.
Multiplied by 40, 000 km, this is about 12 million Dollars worth of cable (!)
All spent for a single YouTube video.
This man is a true hero of the internet! ^^

[digitig]

The way we solved the cable around the Earth one when I was at school was "We're not told the radius of the Earth, so presumably it doesn't matter. That means we can set it to zero, and the answer is simply the radius of the circle whose circumference is the length of the cable."