People who know me very well can tell that this has always been a favorite topic of mine. It’s about the way I see numbers. The thing is, in my mind the numbers from 0–20 look like this:
It’s not about the shape of a particular number (a single number doesn’t really have a shape), but about the path the numbers take when put together. For example, isn’t it odd that after passing 10, there is this strange corner, where you have to “turn left” to go on?
And the map changes as soon as you “zoom out”:
The patterns are repeated on each level. So, for example, the numbers from 101–200 look pretty much the same as from 1–100, so do the ones from 1,000–100,000 and so on.
But zooming out even more (not that you need this very often), there is this funny loop towards infinity:
And I use these maps in my everyday life.
Two examples:
When I have to add up 25 and 8, I am picturing the 25 on my map and, in a way, “jump to the 33″, perhaps in two hops (first 30, then 33). And when I give the result, I have a sense of “where” it is.
When I want to spend money on something that costs, say, 30 Euros, I first position that price on this map and then make an intuitive judgement on whether that is a good deal or not. The same positioning happens when I think of how old someone is.
So, it’s really an implicit way to navigate through the numbers space – it’s always there.
I know that there are completely different (and probably smarter) ways to deal with numbers. So, I’d be really interested in
- Whether you see numbers in a particular way at all?
- If so, how do you see them? Could you draw them on a map? Would it look very different from mine?
Also, there’s probably research on this (I haven’t found it yet). So, if anyone would be able to point me to related studies, or wants to send me a picture of their own number mind map, i’d highly appreciate that!
Comments (5)
I don’t know, I’ve always thought I visualise the numbers on an infinite line, but I’ll have to think about it again now! That’s fascinating, especially in the context of trying to help my primary-school kids who are just starting out in maths, to see patterns and not be scared of the numbers!
Hi Phil,
Thanks for your reaction! Yes, I also think it’s fascinating. For example, someone once told me that she would see them in a “zig zag” pattern (turning points at 10, 20, etc.), which probably comes from counting with fingers.
I guess knowing more about how these memory maps usually work (or what alternative navigation systems there are) could help in teaching. I’ll let you know if should come across relevant material.
I don’t think I see them in a certain place, but I always look for patterns in numbers. My birth date is 28-9-82 (dd-m-yy), which is a palindrome and the earlier comments here were written on my birth day.
When I was little and I couldn’t sleep I tried to make sums of the numbers of my digital clock radio. I tried combining the first three numbers to get the last one. For example 21:24: The last number is 4 and can be reached by 21+2. After a while this wasn’t much of a challenge any more so I calculated further than the current time and tried to find the next time where the sum wasn’t possible 5=2+1+2, 6=2(1+2), 11:27 isn’t possible any more. Later I was looking for the time where the first three numbers could make all possible last number (2-3+1=0, -2+31=1, -2+3+1=4, 2+31=5, 231=6, 23+1=7, 2(3+1)=8, 2^3+1=9) and there are others. Then I wanted to know how many timestamps in a 24 hour clock radio could make such a sum and how many couldn’t. I still don’t know…
I’m also very interested in the formula of Euler. He managed to combine all the strange math symbols in one simple formula: e^(i*pi)=-1. Isn’t this wonderful?
So I’m not sure I see numbers in a specific pattern, but I’m sure I see patterns in specific numbers!
I noticed some *s (star-signs) are missing in my previous post. I’m not sure why some of them are included and some of them are not, but I think you can see where they need to be…
Thanks, Jan! This is interesting.
So you seem to have an intuitive understanding of numbers and the math behind them? No visualization at all? Or are there on some kind of infinite line?