I was discussing mathematics with some friends last weekend. One complained they were useless doing numerical calculations in their head, but good at complicated algebraic maths written on paper. Another was the opposite, finding algebra impossible, but able to do long division in their head without any brow scrunching . Which lead me to think whether representing quantities with number or symbols is even close to optimal. To some autistic savants, numbers take on very different qualities. 3 might be green, furry and oval shaped, while 42 is red and narrow. But somehow, by combining green, furry and oval-shaped to red and narrow, another coloured shape forms, maybe brown and smooth, which in turn maps to 45. Somehow, they are able to map numbers into another domain where mathematical operations are incredibly straightforward, which leads to seemingly extraordinary computational abilities.

I get the impression to standard way non-autistic people represent numbers is probably highly sub-optimal for doing easy calculations, and one of these days some aliens are going to discover us and our crazy numerical notation system and have a good laugh, like the robots in the old smash advertisements laughing at how we make mash potatoes. Numbers are quite abstract and something we have difficult visualizing in our mind’s eye, particularly when trying to see them long-multiplied in our heads. All this lead me to think about another abstract quantity, Time. I am fascinated about how we visual it in our heads. We know it moves in one direction, and between the time-lines in history school-texts and talk of it as a the fourth dimension in modern physics, it is often portrayed as a very linear concept. Yet quantities like days and years, based on the circular motions of the planet, can also give it a circular feel. So clocks representing the hour of the day have been represented by a circle, but for some reason annual calendars are not. I have always found this strange, because in my own head, the year is a flat ring. When planning the year’s holidays on airlines websites or discussing project time lines in work, I don’t find calendars with group of weeks clumped into months an easy way of understanding dates and planning different events. Listed below are the different time quantities, along with how I visualise them in my head.

**Seconds** – No fixed image, but they are a linear concept. I tend to just count them like I do numbers.

**Minutes and Hours** – A circular concept, the second and minute hands of the clock hanging on the wall in my parents kitchen.

**Days**- Two loops of the hour hand of the same clock.

**Weeks**- A linear image, it is a narrow band I stand on, where I can look in either direction at future or past weeks. The weekdays are flat, but the weekends are elevated, sort of like mini mountain ranges. There is also a slight curvature of the band, related to my year visualisation.

**Months** – Don’t really visualise these at all.

**Years **- The year is a flat ring, but horizontal, not vertical like the hanging clock. My viewpoint is like I am standing on the present, and I can look forward or backwards around the disc into the future or previous months. This image is very much at odds with how years are represented in calendars and planners.

**Decades to Millennia** - Back to linear again, I visualize this as a reel of tape. Probably the best way to describe it is like a reel of old film negatives. Because when I move through the decades, I fill the tape with images relevant to the time period. The tape also has a peculiar shape. The future is higher than the past, and for some reason it loops around itself between the 1970s and 1990s. Elsewhere it is reasonably straight, although different decades have different slopes. I have tried to do a rough sketch in the picture below.

**Beyond Millenia** – No fixed image.

When planning time-related activities, using the visualizations above, I run into problems when I move from something visualised as circular to something more linear. In planning an event over two days, like a weekend, I constantly switch from a linear view to a circular one and visa versa. Neither is comfortable. But once the event becomes longer than a few days, I resort completely to the linear view. The same thing happens when planning events over a few years. Each year is a circle, but my decades image is strictly linear.

I would be intrigued to find out how other people visualize time. Somewhere there must be a guy who gets around the phase transition from circular days and linear weeks by inventing a sort of spiral shape, like a spring. While I have thought about using that image, unfortunately the clay is already too well set in my now thirty-something brain.

Another interesting aspect about my images of time is how three dimensional they all are. While the basic lines and circles may be two dimensional, in my head, I am actually standing on the them, and their surfaces have curves and bumps. The strangest curve is the loop in the decades just before the millennium. While the decades can be stretchy, slowing meander upwards, this is the only time they ever loop. This time period corresponds to my childhood and teenage years. I would like to redraw the diagram in another thirty years if I am still around. Perhaps there will be more loops in what now looks like a flat future, the time line getting tangled as I move through the years and fill it with everyday events. I’m sure sure someone like Freud or Jung has already written a book on this sort of stuff.

However we imagine the passage of time in ours heads, we are giving it a visual form that is doesn’t really have in the real world. But it greatly aids our understanding, enabling us to chop it into usable quantities, to map it to underlying time dependant processes like to rotation of the earth around the sun, and to easily understand where different events lie relative to each other. With all my talk of time looping and stretching, it might sound like some sort of high end relativistic physics is going on in my head. But alas those sorts of concepts are something I never really got my head about fully, giving up on about page 35 of Stephen Hawking’s “A Brief History of Time” many years ago. But I often think there must be an easier way to visualize time that makes understanding that sort of physics easy. Perhaps somewhere there is an autistic savant that has visualized a solution to the Einstein field equations. But his particular solution has no actual symbolic representation, it just resembles a yellow wedge of mouldy cheese.