Abstraction Quote by Keith Devlin
“The human brain finds it extremely hard to cope with a new level of abstraction. This is why it was well into the eighteenth century before mathematicians felt comfortable dealing with zero and with negative numbers, and why even today many people cannot accept the square root of minus-one as a genuine number.”
About This Quote
Source Interview: The Math Factor, 2015
Human cognition resists high abstraction, making concepts like zero or imaginary numbers hard to accept.
In simple terms: Our brains struggle with abstract ideas.
Key Takeaway
Simplify and visualize abstract concepts.
Themes
education
mathematics
cognition
Mood
thoughtful
inquisitive
Type
educational
inspirational
When to use this quote
- teaching math
- designing curricula
- public science communication
- software UI for abstract data
Key Concepts
psychology
number theory
learning theory
Questions to Reflect On
- How can you make abstract ideas concrete?
- What analogies help grasp complex concepts?
A Different Perspective
Some abstractions become intuitive with cultural exposure over time.
![“That this subject [of imaginary magnitudes] has hitherto been considered from the wrong point of view and surrounded by a mysterious obscurity, is to be attributed largely to an ill-adapted notation. If, for example, +1, -1, and the square root of -1 had been called direct, inverse and lateral…” quote by Carl Friedrich Gauss](https://sms4smile.com/quotes/img-quotes/acb/carl-friedrich-gauss-9412_adapted_that-this-subject-of-imaginary-magnitude_3134596.jpg)
![“This is all so silly,' said Diko. 'Who cares about what's real and what isn't real? [...] And as for our own history, the parts that will be lost, who cares if a mathematician calls us dirty names like "unreal"? They say such slanders about the square root of minus two as well.” quote by Orson Scott Card](https://sms4smile.com/quotes/img-quotes/652/orson-scott-card-134_math-humor_this-is-all-so-silly-said-diko-who-cares_903746.jpg)
![“I saw the first one [video with Hans Rosling ] when he did - I think it was his first one - in 2006, a TED Talk. And for the first time in my life, I thought here's someone who can take statistics that most people regard as dull and boring and bring it alive.” quote by Keith Devlin](https://sms4smile.com/quotes/img-quotes/f8c/keith-devlin-19829_alive_i-saw-the-first-one-video-with-hans-rosl_101875.jpg)
![“Hans Rosling typically would go into the room, and he would ask the audience questions. Often they had to answer them with clickers or raising their hands or something. We get [data] wrong because 50 years ago that wasn't the case and because we haven't had these graphics we don't realize that…” quote by Keith Devlin](https://sms4smile.com/quotes/img-quotes/740/keith-devlin-19829_answers_hans-rosling-typically-would-go-into-the_518165.jpg)
![“Some of the justifiable critiques has been by - been so successful in telling this story, you know, there's a danger of saying, oh, well, you know, we don't need to worry about this because that's absolutely not the case. What [Hans] Rosling is doing is showing us an overall global trend, which in…” quote by Keith Devlin](https://sms4smile.com/quotes/img-quotes/3dd/keith-devlin-19829_bad-thing_some-of-the-justifiable-critiques-has-be_763450.jpg)
![“In fact, we tend to think things have been getting much worse. In fact, over the last 50 years, almost everything in the world on a global scale has got better. And the way that Hans [ Rosling] did this - it was very good.” quote by Keith Devlin](https://sms4smile.com/quotes/img-quotes/473/keith-devlin-19829_facts_in-fact-we-tend-to-think-things-have-bee_1076728.jpg)
![“In fact, when you try to use [Hans Rosling] data to predict the future, all sorts of problems arise. But what it does do is say, hey, just catch your breath a minute and see what's really been going on. We do have reason to feel good about the fact we've made progress.” quote by Keith Devlin](https://sms4smile.com/quotes/img-quotes/1a8/keith-devlin-19829_arise_in-fact-when-you-try-to-use-hans-rosling_1084549.jpg)
