It’s the Thought That Counts

It has been discussed by many that our brains are wired on an evolutionary scale, and that the rapid change of society through technological advances has outpaced us, leaving us with many disconnects between what we see every day and what we can actually handle.  In many ways, we might be happier if we lived in small tribes and were closely surrounded by wilderness, instead of surrounded by brick and cement, drive vehicles and get visual stimuli from computer or television screens.   One aspect of this disconnect, that I find quite intriguing, and I think is central to our ability to understand the world we find ourselves in, is what I call and order of magnitude problem.

Think about early man in those hunter gatherer days.  Counting is a base cognitive skill, important for our survival.  But what is that we might count?  You might count the amount of fruit gathered on any particular day, the number of children, or people.  Such numbers might get you into the 100s.  You might count seasonal cycles.  If you were lucky maybe you had 80 of those to count.  You might count lunar cycles.  Getting you to about 1040.  Even this would require some note making, because this is counting over time, and surely you would not sit there and count something that high.  Such cycles of time were the only things worth keeping track of.  We had no need to measure time beyond that.  No need for small units of time such as a second.  It might make sense to come up with some unit of measurement for distance. Something comparable to arm lengths or hand widths…something we might use to size an animal, measure height of people or spears.  When it came to traveling, you might then simply use something like phases of the moon, or number of diurnal cycles.  Once again such counting would leave numbers small.  Occasionally you might find yourself thinking about numbers in terms of fractions.  Maybe something like half a day, or a quarter of an armlength.  For things very small, you probably would no longer use armlength as your standard, but perhaps finger width.  Such techniques are ones that we still use today.

The reality is that if you think about numbers, you probably won’t get very far.  Now do a little exercise for me.  If you think of the number 1000.  How do you think about it, to picture a 1000 of something?  You might think what a $1000 can buy, but money is a fiction that represents a quantity of stuff you can buy which varies depending on what stuff your buying.  If you wanted to actually count, what would you think about.  Maybe 1000 people in a room.  You might have a sense for how big a group that is.  Chances are you won’t get it exactly.  Go down to a 100 and your chances of picturing 100 things gets better.  Now do 10 of something.  Pretty easy.  Now do 1.  Even easier.  Let’s go down another order of magnitude.  Try to think of something that is 0.1.  Here as we move down an order of magnitude we can no longer count whole things.  So think of 1/10th of a person probably gets a bit graphic, so what are you thinking of to imagine 0.1?  For that you now have to think of some standard.  Maybe a mile, an inch, a meter?  Depending on what you choose, you can do okay.  Now try 1/100th.  Again with the right starting point you might do okay, but even dividing by 100 can be hard for someone without a formal education and once we get to 1/1000th our ability to guess at the meaning of that fraction is severely reduced regardless of our starting point.  So if you are keeping track this puts the human mind, on a good day our brains are capable of somewhat accurately sorting out 5 orders of magnitude (10-2 – 103).  However, if we look at the scale of the universe in size we span 52 orders of magnitude from the plank length to the size of the observable universe (please see this very cool interactive graphic that allows you to explore the different spatial scales of the universe).  In terms of time, our quantum clocks can measure up to 1  ten billionth of a second (10-10) .  Meanwhile we know the universe has been around for about 14 billion years (1015 seconds).  If you don’t have trouble digesting such numbers you are a super genius, because everybody should.  Those are just the extremes, but unless you are within that 5 orders of magnitude range I discussed earlier, it makes little difference.  And this is also important because it means that a million miles, might as well be a billion miles in our head.  However, the difference between those two numbers is meaningful.  In science, to consider two numbers like that the same would be to make a grievous error on the order of 100,000%.

Scientists, through years of working with the numbers that shape our world are often better at dealing with these things, but even scientists tend to use conventions to make numbers easier to manage.  There is a reason why you don’t measure the distance from New York City to Boston in inches.  We have developed different units of measurement for distance.  In the old English system we have inches, feet, yards and miles.  In metric, we have prefixes that span numerous orders of magnitude so that we don’t have to always report distance in meters.  For objects in space in our solar system we might use astronomical units to keep those distances in more manageable numbers.  For things outside our solar system, light years.

                  Image of radar reflectivity.

Whatever we measure in science can change over large ranges and change at massively different rates.  Change is rarely linear, but very often exponential.  As a result, we might find ourselves dealing with quantities which very over several orders of magnitude.  In my field a good example for this is radar reflectivity.  You may not be familiar with it, but you’ve certainly seen radar images if you’ve paid attention to the weather.  Higher reflectivities indicate bigger drops and faster rain rates.  Lower reflectivities represent light rain or drizzle.  The difference in size between a drizzle drop and a basic rain drops is no more than a factor of 10, but the reflectivities span over 10- 1,000,000.  Thus, meteorologists convert those reflectivity values using decibels.  The decibel system was initially used for sound given the large range of frequency for sound waves, but now is a common tool for expressing values that vary over several orders of magnitude by taking the logarithm (base 10) of the value. This reduces the number to its order of magnitude.  For example, instead of 106 if I take the logarithm with base 10 of that number I get 6.  And 6 is much easier to wrap our heads around than 1,000,000.  I know I’ve gotten kind of technical here with this example, but the point is that nature, as we’re discovering, does not conform to the numbers our brains had to deal with when we evolved.  And most scientists, while they might have some understanding of the microscopic or macroscopic numbers and the wide ranges of values science employs, to objectively analyze and come to some meaningful conclusions we very often have to be able to visually see those numbers between about 0.01 and 1000.

You might say that such numbers make little difference to most of us unless we are in science, but let’s talk about where our everyday lives might be impacted.  First let’s start with the population of the world.  There are 7 billion people.  Try to wrap your head around that number.   Is your soul mate really just one in a billion?  Could such a large group of people create an environmental disaster? How many bodies could certain countries throw at you in a war? About 700 million, globally, live in abject poverty.  Do the numbers seem so voluminous that it’s easier to ignore human suffering, or make you feel defeated before you try?

What about some of the more important educational and scientific controversies that still exist today? Evolution has been happening for several billion years, but many would like to believe that we’ve been around for only 6000 years.  Religious dogma aside, isn’t it possible that part of the reason that some people resist what science clearly demonstrates is because we are talking about a length of time that few can relate to?  The vastness of time threatens to humble us all as blips in a universe far older than we can fathom. And its size and origin similarly attacks our human conceit at being the grandest and cleverest design in a creator’s eye.

                                         The Geologic Time Scale

Vast amounts of people also create vast sums of money.  Billionaires have almost unimaginable wealth that people still commonly believe that can obtain too.  Politicians and media constantly throw large dollar values in our faces to intimidate us.  When one wants to high light wasteful spending we can put point to something costing 100’s of millions of dollars and we shudder at such an amount being wasted.  Forgetting that with 100 million taxpayers, something in the 100’s of millions is costing us a handful of dollars a year.  I have seen the tactic used frequently.  Once again we might on some level realizes that a 100 million, 10 billion, and a trillion dollars are different, but they are all unimaginably large sums of money that in the battle for what’s important and what’s not, they can all be seen as being on equal footing. The idea that public television and radio need to be cut for austerity is quite simply a joke when compared to a 10% increase in defense spending if anybody thinks that’s going to balance the budget.

One might argue that the microscopic matters very little (no pun intended), but I do think an appreciation for that scale is valuable, if for no other reason helping us appreciation the vast variation of scales that make up our known universe.  Scientists often take very small numbers that might exist for pollutants or toxicity in foods or water, and change the unites of those numbers so that they are bigger.  I understand why, because of course we don’t want to underwhelm in those situations, but maybe it’s also a problem that we continue to cater to this limited range of numbers that our minds most easily manage.   It’s probably best to start incrementally, and perhaps a good example of how we can begin is with time.  John Zande over at his blog, The Superstitious Naked Ape, offers up a good first step towards our lack of comfortability with numbers outside of our “sweet spot”.  The start of our counting of years begins with the birth of Christ, but this is a religious and faith based reason to start the counting of the years.  Why not use Thai’s bone which is our earliest evidence of careful astronomical observations of the sun and moon over a 3 ½ year period.   Instead of the year 2017, it would instead be 15,017.

                                                                          Thai’s bone

It might seem like an arbitrary difference, but I think it would give us a better feel for the vastness of time, and a better appreciation for the numbers that shape the universe we’ve come to know.  Since there seems to be little stopping the advance of science in technology, perhaps we better find more ways to help these brains, made for a different time, catch up.