The Temperature Addition Paradox – Mind Your Decisions

This is an intriguing paradox about Celsius and Farenheit that has confused many people. We all know that 0°C is equal to 32°F. So then we can conclude 0° + 0° = 64°F. A viral meme alleges that teachers are confused and angry about this one!

Clearly the conclusion is wrong. So what’s the problem?

As usual, watch the video for a solution.

Temperature Addition Paradox!

Or keep reading.
.
.

“All will be well if you use your mind for your decisions, and mind only your decisions.” Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon.

.
.

.
.
.
.
M
I
N
D
.
Y
O
U
R
.
D
E
C
I
S
I
O
N
S
.
P
U
Z
Z
L
E
.
.
.
.
Answer To Viral Meme Celsius Farenheit

(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).

We know that C and F are related by the formula:

°F = (9/5)°C + 32

Think about a thermostat that is set to 68°F. This is equivalent to 20°C, so it is true that;

68°F = 20°C

Now imagine we say something like, “Turn the thermotat up by 1 degree.” The thermostat would then read 69°F, and that is equivalent to ~20.6°C

69°F ≈ 20.6°C

So 1 degree F is about 0.6°C. (It is exactly 5/9 degrees C).

Now let’s imagine the thermostat was set to centigrade, and it read 0°C. That is equal to 32°F.

0°C = 32°F

Now imagine we say something like, “Change the thermotat up by 0 degree C.” The thermostat would still read 0°C, and that is equivalent to 32°F

0°C ≈ 32°F

So now we can see what is going on. When we say to “add” a number of degrees, we are not adding a quantity of degrees. We are adding a CHANGE in the temperature. So let’s go to our equation:

°F = (9/5)°C + 32

We can use the Δ (change) operator on both sides to see how a change in F affects C. We get:

Δ°F = Δ(9/5)°C
or
Δ(5/9)°F = Δ°C

So now we return to the original problem. We do have the true equation:

0°C = 32°F

Now if we want to “change” the left side by 0°C, we need to add Δ0°C on the left hand side. Since Δ0°C = Δ0°F, we then add Δ0°F to the right hand side.

0°C + Δ0°C = 32°F + Δ0°F

The left hand side has a sum of 0, and the right hand side has a sum of 32. so we get:

0°C = 32°F

This is the very same equation we started with, but at least it is a true equation! So obviously adding 0 degrees Centigrade the correct way did not lead to the wrong conclusion 0C + 0C = 64F.

So the new version of the meme will look like this:

References

Temperature scales
https://en.wikipedia.org/wiki/Fahrenheit#/media/File:Thermometer_CF.svg

Nest thermostat (CC BY-SA 2.0)
https://en.wikipedia.org/wiki/Smart_thermostat#/media/File:Nest_Diamond_Thermostat.jpg
https://creativecommons.org/licenses/by-sa/2.0/

Delta Temperature Conversion
https://ecostruxure-building-help.se.com/bms/topics/show.castle?id=5239&locale=en-US&productversion=1.8

https://www.reddit.com/r/learnmath/comments/son1ws/0_plus_0_is_64/

https://www.reddit.com/r/math/comments/auywq/what_is_0_degrees_celsius_0_degrees_celsius/

https://news.ycombinator.com/item?id=1610354

https://math.ucr.edu/home/baez/torsors.html

https://www.reddit.com/r/maths/comments/q5f02q/im_actually_really_confused_mathematically_can/

https://www.reddit.com/r/memes/comments/zqspq3/wait_a_minute/