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!
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Comments (14)
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! 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?
This is great. I guess this is the way we were trained to memorize. I see my numbers just like yours. I did some googling and found information on number forms and number mapping. My husband sees his numbers differently. He sees them in 10′s down straight lines next to each other. I wonder if the above map is the “common” way people see it. If not, how come I see my numbers mapped out just like yours?
Also, how do you see your months? BTW, my husband visualizes specific dates and events in an organized time-line form. For example, he visutalizes in a number map/form when WWII was taking place.
LOOK UP NUMBER FORMS AND SYNESTHESIA ON WIKIPEDIA. Some people see numbers in color as well.
Thank you, Fanny! Yes, the Number form wikipedia entry seems to match. I had not found this before.
You are the first person who tells me you see them the same way. I think there must be a number of different common patterns.
As for the months of a year, I see them in a slightly illogical way as well: Starting in January the months are lined up in a straight line up to September. September is the “corner month”, which means that after September it turns left to October. After October, November turns left again and the months now continue in opposite direction compared to all the early months in the year. December follows November in a straight line, and – oddly – connects in a left turn again with the January of the next year (closing the cycle). The strange thing here is the imbalance of the month layout: 9 months into one direction, left turn, and then just 2 months in the opposite direction.
The days of the week are also forming a circle, but this must be quite common (with the weekend days going in opposite direction to the week days).
How do you see your months and weeks?
I see the months of January to June straight down then turning right for July and August. September is a little tilted and then October is slightly lower than September. November then is slightly higher than October and then right below it is December. It’s all in a form that can fit in box style. I hope this makes sense.
My weeks are Mon – Friday straight across slightly tilting down. Then Saturday and Sunday are slightly tilted to the right.
Are you doing research? This is so interesting.
There is a difference in our numbers. When I think of 1000, it takes a slight turn to 10K. Then it’s straight up tilting towards the left. When it hits 100K, it turns right straight up to 1 Million….then the Trillion, etc. is just the word.
Yes, I can imagine it a little bit. There should be a site where it is easy to draw up these kind of patterns and compare them
This is SO interesting. Your map is fascinating! I would love to do one but don’t know how other than to draw it out.
My numbers go from 1, in a straight line up, to 29, then 30 starts to the left beside 20, goes up to 39, then 40 starts the same as 30 and so on…at 100 the straight line goes up again to 129, and then the same, 130 to the left beside 120, and so on…at 1000, 100,000, 1 million, that’s when they all switch to the straight line up to 29 (1000 to 29,000, etc)..it’s this huge map that goes upward and to the left. I’ve always thought this was probably so bizarre and illogical of me.
Anne, I would love to find a site to map this.
Am going to look up “number forms and number mapping” and “SYNESTHESIA” right now!
And how interesting the way some people see months! That is so crazy. I’m boring and just see them in a straight line going down like a calendar, basically.
ps – now that I’m trying to picture it, I realize I have exceptions…I would think 100 would start to the left of 90, but it actually kind of floats around 99, and goes up from there. I think something also happens at 100,000, but I can’t quite explain it or really even see it properly to begin with.
Thank you! It’s amazing to find other people who also find this interesting. There really should be an app somewhere to draw up these kind of maps.