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## Algebra (all content)

### Course: Algebra (all content)>Unit 11

Lesson 31: Logarithmic scale (Algebra 2 level)

# Logarithmic scale (with Vi Hart)

Vi Hart and Sal talk about how we humans perceive things nonlinearly. Created by Sal Khan.

## Want to join the conversation?

• Why is this video in Pre-Calculus? :D
• The scale it uses is logarithmic in a way. Logarithms are part of pre-calculus.
• They say we think in logarithmic scale, but it seems to me from the video, we tend to think linearly about things that are in fact logarithmic. Am I just thinking about this the wrong way?
• You're not thinking about it the "wrong way." Go back to where they give the piano. All humans naturally think of pitch in a logarithmic scale without realizing it. With each octave we actually have a doubling of the sound frequency, however, when we are listening to the notes being played one after another we think of them incrementing in equally spaced intervals because that's how we're taught to think of numbers for the purposes of counting and basic math.

When it comes to a certain force pressing up on our skin it's the same way. A German physician by the name of Ernst Weber, who is considered one of the principle founders of experimental psychology was the first to notice this.

The reason you feel that you think linearly is because we naturally count objects as 1, 2, 3, 4, 5, 6, etc and since we think of each thing we count as distinct, we think of there being an equal distance between each number on the number line. As a result, we base all our mathematics on this. However, the fact that our thinking is not quite like that becomes apparent when we're dealing with large numbers. Sal and Vi show this at around when she asks him how far apart 1,000 and 1,000,000 are on a number line. As it turns out, in our minds, the distance between numbers gets smaller as we count to higher and higher numbers. For example, 2 is twice as big as 1, and there appears to be a huge difference between the two numbers, however, there doesn't seem to be as big of a difference between 20 and 21, even though, we increment by the exact same amount as we did from 1 to 2 to get from 20 to 21.
• I love, love, love Khan Academy, but this video needs a take-two.
• what does this have to do with pre calculus?
• Logarithmic functions and scale.
• Hello Vi and Sal. I needed a little clarification please. So...am I correct in thinking that a logarithmic scale is based on the relativity of where you are making a calculation from?

It occurred to me when you were using your speaking example. When we are asked to speak louder, we speak louder relative to how loud we were initially talking. If I am talking at a 2 and am asked to speak louder, then I might speak at a 4. If I'm again asked to speak even louder, then I wouldn't adjust based on my original volume (which was at a 2), I'd adjust based on the current 4 to perhaps an 8, because that was still perceived as not loud enough. In that sense, the volume increases exponentially based on the current relative "state?"
• Where is this video catagoized under? Is it only under News and Noteworthy?
• Look at the upper bar and it says "Precalculus."
• Who is Vi Hart?
(1 vote)
• She's a math YouTuber who worked with Khan Academy for a while.