Visualising Numbers

I thought of something a while ago; and I only managed to experiment with it recently. We all write down and read numbers in the same way (depending on how your culture learns to read and write). For example, I am English speaking and therefore read left to right; knowing that ‘0’ is a place-holder etc. and we write long division/multiplication etc. in similar acceptable defined ways.

The difference comes in when an individual visualises numbers in their mind. I know this sounds strange (and you’re probably visualising a sheet of paper with numbers written on it from left to right; and thinking ‘there’s nothing significant about that’).

However, there is something significant about how we visualise numbers in our minds. Forget the piece of paper, and forget about what numbers look like when you read and write. Close your eyes and count from 1 to 10 in your head. What did that sequence visually look like in your mind? Now think of the entire series of numbers between 1 to 100. What does that gap look like? How is the sequence laid out or filled? I asked a few of my friends to draw exactly how they visualise numbers in their minds – this was the outcome:

Me – Dr Slater:

Dr Slater Visualising Numbers

Dr Slater Visualising Numbers

For some reason; I stack groupings of numbers in zig-zag formation in my mind (going up then right). Initially, with smaller numbers, the separator stack will be a series of ‘teen numbers. As place holder groups get larger, I stack groups of similar 10s together (thousands go together, ten thousands stack together etc. where every subsequent stack is a zig or a zag in the overall counting sequence).

Dr Slater Summary Visualising Numbers

Dr Slater Summary Visualising Numbers


This chick is crazy (in my opinion), because trying to immerse myself in how she visualises numbers in her mind causes my eye to twitch. She initially counts left to right in groups of 10s, but then eventually her sequence snakes between groupings of 10s (she starts counting right to left).

Nomti Visualising Numbers

Nomti Visualising Numbers


Ryan is very practical and straightforward in the way his mind visualises numbers. He counts left to right and stacks groups of 10s together going down. His mind is largely uncluttered by crazy sequences like mine. If you tell him to visualise just one number; he will only have nearby milestone numbers surrounding that number (to give it context in the overall numerical sequence).

Ryan Visualising Numbers

Ryan Visualising Numbers


Danny is similar to me in that there will be at least one stand-alone sequence before he starts stacking 10s of numbers (going down).

Danny Visualising Numbers

Danny Visualising Numbers

Some of you are probably bored or weirded out by me wanting to visualise numbers in my mind. I can reason with that – I also find numbers kind of boring. However, there has to be some deep interesting explanation as to why we all visualise numbers differently in our minds (and this is what truly intrigues me). The way in which each of us visualises numbers probably has a profound output in determining an individual’s analytical capabilities and problem solving abilities. For example; IQ tests usually determine how a person’s mind works (well or not), and not necessarily what you know (it’s not general knowledge or memory based etc.). Based on how I visualise numbers; you might think my mind is cluttered and poorly organised; and therefore my mind does not work well (low IQ). There is no admissible evidence to prove this link in my theory, but I do have hap-hazard thoughts!

Is there an expert in any relevant field related to this who can shed some light on this? Thanks guys!

✘ Hack It! ✘

12 thoughts on “Visualising Numbers

  1. Interesting. I tried several times to visualize numbers in my mind, but instead of anything like what you got, I kept changing the number instead of having them laid out in order.
    No matter how I try to visualize a bunch of numbers, I never have more than one in my mind at once. Maybe it’s just because it’s late at night, or maybe I’m just odd, I’m not sure.
    Very interesting post, it sure got me thinking.

    Liked by 1 person

  2. I’m no expert, but the Ancient Sumerians started it off, by counting wheatsheafs, slaves, etc., and recording the result on clay tablets, after they found they didn’t have enough fingers and toes. They wrote from right to left, which may be why we have the smallest numbers on the right, getting larger (in multiples of ten) to the left. At first they had no zero, but the people on the Indus Plain were more advanced (and more imaginatively abstract), and that allowed the decimal (or sexadecimal) system to go riot. Negative numbers came next, and the Greeks and Arabs performed wonders, the latter inventing Algebra, where you don’t need any numbers at all!
    Have you tried counting in binary (0’s and 1’s)? This also goes from right to left, but I doubt if our computers see it that way. And just think; everything you are doing right now is being expressed in terms of “to be, or not to be!”.

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  3. I think how we’re taught maths and culture makes a difference to how we visualise it. It fascinates me how some cultures only have a 1, 2 and many. Maths is a language and the symbols and structures we are taught effects our ability to visualise and communicate with it. One day I was sitting in programming class and the teacher explained the process by which we may work out a sum in our heads as if we all do it in the same way. In that moment I had a realization that I hadn’t been taught right and had been doing it wrong my whole life. Some people stumble across better methods for mental arithmetic without even trying or realizing it. That’s when I decided to buy some books on speed mathematics to try and re-learn how to solve certain problems in a more effective way.

    A while back I also decided to ask my boyfriend to explain his thought processes to me while doing a Suduko, and we both realized that we had very different ways of thinking about the problem. It’s fascinating and yet could drive me crazy trying to get my head around the ways that people may visualize things differently. I’m like Ryan, counting in stacks of 10.

    Liked by 1 person

    • That’s awesome. Thanks for the new insight. I might have to also re-learn maths, because i did very badly at it in school. I know im capable if show the right way that suits my brain. I love Soduko though 🙂 havent played in a while.


      • I think we all develop different ways of thinking it through, and sometimes when we struggle it’s not because we’re incapable of maths, just that we haven’t been taught the right way. I love Suduko too :).

        Liked by 1 person

  4. Interesting post. Here are some things to consider.

    The people’s background, are they usually working with numbers in some sort of occupation ? Why I ask this is because my background is English Literature and communication ( special education & mass media). I do not visualize numbers. Your visualization exercise make my head hurt. 😀

    I think in terms of the names of numbers. For example, if I am memorizing a phone number I will do the following. …..

    879 – 9450 is eight hundred & seventy nine, ninety four, fifty . I will think of it as a line in a poem or song with a rhythm. In terms of memory 879, 94 and 50 are three items to remember.

    Not all people are visual learners. Not all visual learners think in terms of symbols. Get someone to visualize a piece of text, prose or poetry. People who learn lines of poetry or a script do not visualize the lines to remember them.

    One of the things I noticed my fellow teachers in the math department had trouble with was getting student to do math problems ( language based ones) . They would struggle with the students who did not get it. Working with students in Special Ed classes and assisted independent programs, I realized that what was causing the difficulty was “translating” .

    Mathematics is a a language. People who enjoy and work with numbers think in math the way others think in English or French. Math has its own syntax – BEDMAS. People conversant in Math read a math problem and translate into an equation. It is automatic for people fluent in math. Those whoa re not have to go through a translation process .

    While it is true that our English language reads from left to right, a fluent reader does not read every word. Their eyes scan the page making predictions based on their knowledge of the language and content of the message. You slow down & speed up based on how familiar you are with the type of information. You may take in whole lines or jump back and forth processing so rapidly that you are not conscious of what you are doing. The less you know about the content the slower you go.

    Liked by 1 person

    • That’s definitely true, especially the last part about skimming – I do that often when I read. Thanks for the feedback on how you visualise; it makes me realise that all of our minds actually work differently, despite us putting things down on paper similarly. I wish a university could do a large scale test of this on students specialising in different subject matter (as you said above) this will show interesting results and differences.

      Liked by 1 person

  5. It is really interesting to see how everyone thinks about the exact same things so different. I’m jealous of a few people for being able to visualize numbers in such a streamlined pattern, and other forms make my head hurt to try! I’ve always grouped numbers in a more circular or spiral structure, divided into groups of ten. For equations I pluck the numbers out of their respective spiral and I solve the equation in my head just as I would on paper.
    Hat’s off to teachers trying to explain these concepts to children who don’t think the same way the curriculum is taught. There are so many different ways to find the correct solution to a problem, you just have to find the way that makes sense to that child.

    Liked by 1 person

  6. Numbers in my mind are one long unending row that scrolls to where I need it. I noticed everyone had some sort of chunk here and there and just wanted to add my visualization for diversities sake. Interesting article and study of the mind.

    Liked by 1 person

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