Time Doesn’t Exist: A mathematical introspective

Chris Stakutis   978 764 3488     Octorber 2013   CTO www.concordsoftwareandexecutiveconsulting.com

Introduction

How often have we thought: What was before the beginning of time.  Or, what is after the end of time? These are natural questions from any of us, including our 3 year old children. Turns out, the question is ludicrous because it is all from a “view”, a framework, that simply is irrelevant. Let’s explore this through a variety of life and mathematical views.

Views and frameworks

When you think through a problem, or a situation, do you essentially talk to yourself (quietly)? Do you use your native language such as English?  You actually think within the framework of the environment you were prescribed.  Seems natural enough.  However, not all languages have the same idioms or expressions or even values. Some aspect (or “view”) that you have or observe might be simply impossible for another civilization to understand or “see”.

We have often heard the expression “lost in translation”. While we can attempt to translate each word in a sentence to any language, the meaning could be completely lost because of different frameworks (frames of reference, cultural experiences, beliefs, etc).  Aside from locality of any experience, differences (seafood vs steak or drum vs opera), the language itself exerts a framework that on one hand can propel a civilization and on the other completely dis-allow the group to “see” or understand something.  Hence why the question “what was before the beginning of time” might soon to be understood to be nonsensical. Let’s explore.

Roman numerals

Numbers and mathematics are a complete invention of human society (and not all that old). We invented numbers. They are not real and we are about the only “thing” on the planet that uses them (although there is some evidence that animals can do rudimentary counting -- a mother cat, for example, can count her kittens, although it is unclear if it is pictorial or discrete).

Think of how many 1,000’s of years our brethren survived and thrived and couldn’t communicate to one another let alone count or do math. As they evolved, and trade came into being (because it is more efficient to focus on a specific crop/product and then trade with others) there needed to be some accounting mechanism.  Vertical scratches on walls, or sticks lined up, could express a quantity of sorts.  This was perhaps the beginning of math and Roman Numerals.  

It was very simple and clever. More sticks (or vertical scratches) meant more product. But gosh, if you get to a lot of them, it is unwieldy. So they introduced a series of other symbols as shorthand to represent chunks-of-sticks.  The focus was on fewer horizontal symbols to express a quantity, hence the creative “subtract from adjacent symbol if higher value” (e.g. IV means 1 less than 5. Cool).

This was a framework. It allowed a certain kind of commerce and trade to advance. Life was good--math was born.  People thought in terms of vertical lines, “V” and “X” symbols.  These aren’t anything real, just a representation that helped us understand something: quantity.

Turns out, Roman Numerals are in part the reason for the fall of the Roman Empire. Why? Because you can’t do columnar math on roman numerals. Think of it...you can’t line-up two roman numeral numbers and “add” them.  It just doesn’t work.  In fact you can’t add them in any fashion without reverting back to your fingers and toes (let alone multiply, divide, square root, etc).

Enter: the Arabic system.  Ten symbols per position, and now you can do columnar math (as well as multiply and divide and so on). This was a HUGE advancement in commerce, in engineering, and even calculating someones age. Huge advancement in our evolution.

The point? While roman numerals propelled civilization to new levels, it also couldn’t answer to certain tasks and proved a limiting way to view collections and quantities. A new system improved on those deficiencies...but who knows if that numbering system solves every problem. Frameworks help put perspective on abstract concepts, but can also limit our ability to accomplish or even “see” things beyond them.

Color

I used to like to play a mind exploring game with my young children and their friends. Close your eyes...and now...picture a color you have never seen before.  Go ahead, please try.

You can’t, I assure you.  Whatever color you think you might be imagining if I were to ask you to describe it, you’d describe it based on colors we all know (hence, it already exists). We are simply incapable of thinking of a new color because our framework doesn’t allow for it--much the same way the romans simply couldn’t do columnar math.  

But think about computers and color.  When you see a color pixel on the screen, do you think inside the computer there are three trays of red/green/blue that spit just the right mixture into the dot on the screen?  No.  To a computer, a color is a number.  You put a number in “cell” in the computer and then some color guns/diodes decide how much of certain wavelengths to spray on the screen. Color is a number.  A number--at least in the computer framework.  Guess what? It doesn’t care what number you put in there. While maybe we can only distinguish 255 variations of Blue, you can put 10,445 into that cell...and that’s still a color!!! Pause, think about that.  The framework is different. Your computer can see colors you can not even conceive.

Imaginary Numbers

Back to math.  Math is artificial--it doesn’t exist in a nature (aside from cats counting kittens)-- it is a perspective or framework we have created. Let’s go through some examples.

You recall square root, right? Square root of 25 is 5.  It means find a single number that multiplied by itself gets to the desired number.  Square root of 9 is 3.  This turns out to be VERY important in mathematics and engineering and building airplanes, bridges, computers, and everything else.  But what is the square root of -9?  There are no two identical numbers you can multiply and get to -9.  It’s impossible (because of our framework).  And that stops a lot of practical mathematical operations (beyond the scope here, but in intense math calculations such situations commonly arise).

So what did our friendly mathematicians do? They invented“ imaginary” numbers. Can you believe that? They decided that while maybe you can’t totally have a two identical numbers that multiply to a negative value, you can at least introduce a symbol to represent that number and define mathematical rules on that symbol and hope in the end the symbol just goes away (normal math reduction type of tasks, like how X-over-X such as X/X evaluates to just “1”, and it really doesn’t matter what if any transient value X had).  So the square root of -9 is “3i” (lowercase letter i because it is cute for an imaginary number).  The use and definition is like anything else in algebra (essentially means Three Times Three Times i,.  Thus all the normal math rules apply for adding and multiplying with one caveat -- any “i” that is squared gets to be replaced with -1.  So… 3 times 3 times i becomes 3-i-squared or 9 times -1 which is -9.  Voila, done!

The point?  Our numbering system simply couldn’t conceive of the square root of a negative number.  This elegant solution is somewhat simplistic because it introduced a new temporary symbol to solve a systemic problem, but it worked. The real point is that different systems, or frameworks, have limitations.  We invent hacks to work around the true inefficiencies.

Pi...so irrational

Let’s look at more numbers. We know what Pi is: it represents the relationship of the circumference of a circle to its diameter (an extremely important relationship in all aspects of engineering).  So what’s the big deal? How do you calculate it? You can’t. At least not accurately.

If you had a perfect circle and a perfect measuring tape, maybe you could get reasonably close (in fact, the relationship/ratio is roughly “3”...or slightly more accurately “3.14”).  Pause for a moment on Pi, and let’s look at irrational numbers in general.

Early traders realized that sometimes you sell a “half of a crate of bananas”.  Fractions were born!  You could perfectly represent “half” by a ratio:  “one over two” e.g. ½.  You can similarly represent ⅓.  After all, a ratio is just an expression of division.  But can you divide 3 into 1? No, you can not. It repeats forever...it never ends, never ever never.  In one numbering system, fractions, has a framework that perfectly represents this quantity but the decimal framework just can’t do it.

Yet the decimal system rules the world and carries huge efficiencies, especially in complex math and computers.  So, guess what our mathematical friends do about the relationship of a circle’s circumference to its diameter? Yep, once again, they invented a symbol and defined operations on that symbol.  We all know the symbol as Pi.  Just like “X” in algebra or “i” in imaginary numbers, we can do a ton of math treating it simply as a symbol and then at the end worry about substituting a close approximation of it’s value (if you used 3 instead 3.14159… the error could be disastrously skewed at the end of a  complex calculation--translation: the bridge would collapse or the car would crash).

The point?  Once again, our numbering system, our framework, simply can’t conceive of numbers that go on forever with no terminal value. A different view (or framework) can bandaid that problem but all these examples point out that our numbering system really isn’t right to answer many life tasks (although it is handy enough to get us through).

Back to Time

We invented Roman Numerals. We invented imaginary numbers. We invented Pi.

We also invented Time -- and for the same reason: to help us get through problems.

In the same way asking “what is the square root of -9” makes no sense, so too does asking what was before the beginning of time. The framework isn’t right to respond to such questions and in the right framework such questions would not arise.  Would you ever ask “how high is purple”? Makes no sense.  Asking what is before the beginning of time makes no sense similarly.

There are many other books and visionaries about how time doesn’t exist.  A prevailing thought is that Time and Distance are actually the same thing.  Can you imagine that? (Like imagining a different color?).  We invented the concept of time because it helps us to understand certain kinds of useful math (your age, hours worked, etc) much like imaginary numbers and Pi and colors that only a computer can see.

Frameworks allow us to propel our civilization. They put some sense around concepts that are difficult to understand, and then allow us to do operations on those concepts (add them, do commerce, etc).  But they also limit us from seeing a completely different framework or universe.

I’m not capable of understanding a universe that doesn’t have time, but then again, I can’t imagine the color 12,337, yet my computer can.

© 2014 Chris Stakutis is an independent consultant, author, and software creator available to help your business.