On Visualising Time

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. 

Haha, these silly humans still use digits!

"Ha-ha-ha, these silly humans still use digits!"

 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.

This is soft of what the last fifty years looks like in my head (Click to enlarge)

This is an approximation of what the last fifty years looks like in my head (Click to enlarge)

 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.

On Invention

There was a special Primetime program on RTE on Wednesday dedicated to the country’s economic predicament. The first half was heavy with the doom and gloom that has become so prevalent on the TV here.  A set of interviews with unemployed brickies and couples in negative equity, followed by a panel discussion, where the main participant from what I could see was George Lee’s ever more deeply furrowed brow.  However, to second half tried to be a little more upbeat, and the presenter,  Mark Lyttle, went out in search of some optimism and hope, exploring roads out the current mess.   The key message thrown forward was that a “Smart economy” (Knowledge Economy is so 2008) of innovation and invention would be required.  Several companies were profiled, and there was a discussion on how to drive invention in the country.

And who were these innovative companies?  NTR,  Creganna and Steorn.  Apparently NTR, of West-Link fame, have bought a company in Arizona developing solar Stirling engines, which while innovative, is only going to fatten the company’s coffers further, but not drive any real employment in Ireland.  It is still an improvement on gouging commuters for a living.  Creganna are a positive story, an indigenous producing innovative and viable biomedical products in an industry in which Ireland can compete.  The country badly needs more companies like it. 


Saviours of the economy?

 This brings me to Steorn.  Initially I laughed out loud about how we were pinning our hopes on a company that claims to have invented a perpetual motion machine.  Now while I am almost 100% sure that they are either a) not very good at taking correct measurements or b) a bunch of chancers and the whole thing is a continuous PR exercise to loosen gullible investor’s wallet, I tried to take something positive from it in these pessimistic times.  And there are some elements of the story I like.

Firstly, we need people challenging the so-called Laws of Physics, whether they are complete crackpots or people conducting legitimate research.  The term Laws of Physics has always made me uncomfortable.  It gives off the impression to the general public they are gospel, set in stone, some sort of platonic forms.  Whereas all they are in reality are base scientific rules we have learned from empirical evidence.  All the evidence we have found so far fits the rule, but we can never proves it is true.  The only thing we can do it possibly falsify them, and then come up with and new and improved rule.  Newton’s Law of Gravity becomes Einstein’s Law of General Relativity and so on.  And while this does not happen very often, it is no harm to have people continually pounding away at the foundations of science, just to make sure they are as solid as we think they are.

And then there is how Steorn claim to have invented the technology – Serendipity.  Accidentally discovering a perpetual motion machine while developing an anti-fraud device for a cash machine?  In this case it seems a little too big a leap to be credible.  But serendipity is the key to almost every great invention.  It is not too be confused with plain luck.  Louis Pasteur probably put it best when he said”In the fields of observation, chance favours only those minds that have been prepared”.  After the show, I talked to my dad about this idea and he reminded me of an invention of his own that came about from serendipity.  Working away in the UCD veterinary lab in the early 1960s, he was trying the concentrate the level of antibodies in a blood serum using a centrifuge.  He accidentally spun a test tube from the freezer than had not fully defrosted.  Along with noticing his mistake, he also noticed that some thick liquid that collected at the bottom resembled concentrated serum.  He tested it and found it was indeed concentrated serum.  Somehow, spinning half frozen serum was more successful than the regular method.  After a few more experiments, fine-tuning the temperature and centrifuge speed, he submitted a letter to Nature magazine,  “A Freezing-thawing Technique for Concentrating Antibodies in Serum”  outlining his method, although at this stage he did not know the exact underlying mechanism, merely that it worked.

Back in the 1960s, scientists only read journals in libraries, and without photocopiers, they would mail the authors for reprints.  My mum pulled out a dusty old bag that had been stored up in their attic, which contained over five hundred letters from laboratories and universities around the world that had been sent to my dad asking for reprints of the published letter.   Looking online, many biological and medical science papers in the 1960s cite my dad’s letter in Nature, with one Russian scientist referring to it in his 1966 paper as “McErlean’s Method of Concentration”.  Eventually a chemist wrote to him proposing the mechanism, and they fine-tuned the process further.  Essentially,  the ease at which serum is removed is due the to the fact that the water freezes first and the substances suspended or dissolved therein are trapped in the lattice work of ice crystals in a concentrated form and are removed by centrifugal force.  If the temperature is too high, the water doesn’t freeze, too low and everything gets frozen.  He never patented the idea, and it simply became standard laboratory practice over the years, his association with the idea fading from view.   He also managed to recover salts from solution using the same method, and it occurred to him later it could possibly be used as another method for de-salination of seawater.

Alexander Fleming was not very tidy

Unlike in this picture, Alexander Fleming's lab was apparently an untidy disorganised mess. If he had been tidy, we mightn't have antibiotics today

Serendipitous discoveries seem to be most prevalent in medicine, biology and pharmacology.  Possibly the two biggest weapons we have in fighting diseases, antibiotics and vaccination, were discovered accidentally by Alexander Fleming and Edward Jenner.  Fleming’s sloppiness meant fungus managed to grow on a sample he had forgotten about, and Jenner happened to be working in a rural community where cowpox and cow maids could be observed, something not possible if he had be working in an urban laboratory.  There was an rural myth about cowmaids being immune to smallpox and he was able to join the dots.  Another newer invention, reminiscent of Jenner’s, is that of this years Young Scientist winners, two 13-year-old boys from Cork, John O’Callaghan and Liam McCarthy.  They developed a cheap test for measuring the level of infection in dairy cows, by investigating a belief that infected milk visibly thickened when a drop of washing up liquid was added.  I doubt the initial person who spotted this deliberately added a drop of washing up liquid, and I doubt the two enterprising boys would have investigated and developed it further had they not lived on dairy farms, heard about the belief, and worried about the financial effects of undetected infection.

The bottom line to all this is we can try and plan a “Smart Economy”, but pouring money from a government venture capital funds into start-up companies and continuing billions in funding through SFI to heavily directed university research programs will not necessarily produce any immediately useful innovation.  Forced innovation has a very poor record. Instead, we need to focus on creating an army of prepared minds rather than a handful of PhDs, an army who are taught to question their everyday work, whether they are milking cows or designing anti-fraud systems for ATM machines.  And eventually someone, somewhere will eventually have a “That’s weird” moment, realise their mistake or result wasn’t a necessarily a bad one, and go on to discover something game changing.  And creating prepared, questioning minds starts well before university or industry, in a school system that promotes thinking, not learning things by rote, and practical application,  not repetitive homework.  And it would also help if we stopped being gloomy, downbeat and seeing failures before they happen.  And if they do happen, they are not always a bad thing.