How Do We Know What We Think We Know?

Rene Descartes Etching
Rene Descartes shocked the world by asserting “I think, therefore I am.” In the mid-seventeenth century that was blasphemy! William Holl/

9 May 2018 – In astrophysics school, learning how to distinguish fact from opinion was a big deal.

It’s really, really hard to do astronomical experiments. Let’s face it, before Neil Armstrong stepped, for the first time, on the Moon (known as “Luna” to those who like to call things by their right names), nobody could say for certain that the big bright thing in the night sky wasn’t made of green cheese. Only after going there and stepping on the ground could Armstrong truthfully report: “Yup! Rocks and dust!”

Even then, we had to take his word for it.

Only later on, after he and his buddies brought actual samples back to be analyzed on Earth (“Terra”) could others report: “Yeah, the stuff’s rock.”

Then, the rest of us had to take their word for it!

Before that, we could only look at the Moon. We couldn’t actually go there and touch it. We couldn’t complete the syllogism:

    1. It looks like a rock.
    2. It sounds like a rock.
    3. It smells like a rock.
    4. It feels like a rock.
    5. It tastes like a rock.
    6. Ergo. It’s a rock!

Before 1969, nobody could get past the first line of the syllogism!

Based on my experience with smart people over the past nearly seventy years, I’ve come to believe that the entire green-cheese thing started out when some person with more brains than money pointed out: “For all we know, the stupid thing’s made of green cheese.”

I Think, Therefore I Am

In that essay I read a long time ago, which somebody told me was written by some guy named Rene Descartes in the seventeenth century, which concluded that the only reason he (the author) was sure of his own existence was because he was asking the question, “Do I exist?” If he didn’t exist, who was asking the question?

That made sense to me, as did the sentence “Cogito ergo sum,” (also attributed to that Descartes character) which, according to what Mr. Foley, my high-school Latin teacher, convinced me the ancient Romans’ babble translates to in English, means “I think, therefore I am.”

It’s easier to believe that all this stuff is true than to invent some goofy conspiracy theory about it’s all having been made up just to make a fool of little old me.

Which leads us to Occam’s Razor.

Occam’s Razor

According to the entry in Wikipedia on Occam’s Razor, the concept was first expounded by “William of Ockham, a Franciscan friar who studied logic in the 14th century.” Often summarized (in Latin) as lex parsimoniae, or “the law of briefness” (again according to that same Wikipedia entry), what it means is: when faced with alternate explanations of anything believe the simplest.

So, when I looked up in the sky from my back yard that day in the mid-1950s, and that cute little neighbor girl tried to convince me that what I saw was a flying saucer, and even claimed that she saw little alien figures looking over the edge, I was unconvinced. It was a lot easier to believe that she was a poor observer, and only imagined the aliens.

When, the next day, I read a newspaper story (Yes, I started reading newspapers about a nanosecond after Miss Shay taught me to read in the first grade.) claiming that what we’d seen was a U.S. Navy weather balloon, my intuitive grasp of Occam’s Razor (That was, of course, long before I’d ever heard of Occam or learned that a razor wasn’t just a thing my father used to scrape hair off his face.) caused me to immediately prefer the newspaper’s explanation to the drivel Nancy Pastorello had shovelled out.

Taken together, these two concepts form the foundation for the philosophy of science. Basically, the only thing I know for certain is that I exist, and the only thing you can be certain of is that you exist (assuming, of course, you actually think, which I have to take your word for). Everything else is conjecture, and I’m only going to accept the simplest of alternative conjectures.

Okay, so, having disposed of the two bedrock principles of the philosophy of science, it’s time to look at how we know what we think we know.

How We Know What We Think We Know

The only thing I (as the only person I’m certain exists) can do is pile up experience upon experience (assuming my memories are valid), interpreting each one according to Occam’s Razor, and fitting them together in a pattern that maximizes coherence, while minimizing the gaps and resolving the greatest number of the remaining inconsistencies.

Of course, I quickly notice that other people end up with patterns that differ from mine in ways that vary from inconsequential to really serious disagreements.

I’ve managed to resolve this dilemma by accepting the following conclusion:

Objective reality isn’t.

At first blush, this sounds like ambiguous nonsense. It isn’t, though. To understand it fully, you have to go out and get a nice, hot cup of coffee (or tea, or Diet Coke, or Red Bull, or anything else that’ll give you a good jolt of caffeine), sit down in a comfortable chair, and spend some time thinking about all the possible ways those three words can be interpreted either singly or in all possible combinations. There are, according to my count, fifteen possible combinations. You’ll find that all of them can be true simultaneously. They also all pass the Occam’s Razor test.

That’s how we know what we think we know.

Chaos Piggies

Don Argott’s 2009 film The Art of the Steal led me down a primrose path to some insight about chaos in human interactions.

25 November 2017 – After viewing Don Argott’s 2009 film The Art of the Steal about the decades long history of the Barnes Foundation and its gradual conversion from a private suburban-Pennsylvania art-education institution into a Philadelphia tourist attraction, the first thing I thought about was the Beatles’ song “Piggies.” The second thing I thought about was the chaos of human interractions. That led to an epiphany about the class struggle that has been going on, probably, since long before there were humans around to divide into classes that could struggle.

To understand what I’m talking about, the best place to start is with some general observations about mathematical chaos.

The fundamental characteristic of chaotic systems is that they have limited predictability. That is, while they may seem to evolve along a predictable path in the short run, as time goes on “what happens next” becomes increasingly unpredictable until eventually all bets are off. You can set something up to keep going forever, but if it turns out to be a chaotic system, eventually it comes unravelled.

Another chaos characteristic is what electronics engineers call 1/f noise. It’s called 1/f noise because if you carefully analyze the signal, you find it’s a mixture of waves whose amplitude is inversely proportional to their frequency. It’s found in measurements of everything from ocean waves to solid state electronics. When you see this kind of behavior in virtually anything, it’s a sure sign of chaos.

It turns out that the best way to create a chaotic system is to take kazillions of things all acting independently, then somehow get them to affect each other. In the case of human society, you’ve got kazillions of people all doing their own things independently, but having to work together to get anything done.

Now, let’s look at the Beatles’ song:

“Have you seen the little piggies/Crawling in the dirt?” …

“Have you seen the bigger piggies/In their starched white shirts?” …

Sound familiar? The lyrics are pointing out an observation of 1/f noise. The “little piggies” are analogous to the rapid, high-frequency fluctuations whose effect is swamped by the larger, low-frequency fluctuations represented by the “bigger piggies.”

In other words, the big and powerful few have and outsized effect compared to that of the small and powerless many.


I’m not crediting George Harrison with sufficient insight into mathematical chaos to draw the parallel between it and the social scene he was describing. He was certainly smart enough and interested enough to make the connection, but in 1968 when the song was released chaos theory was not widely enough understood to inform Harrison’s songwriting. Most likely at the time he was simply creating a metaphor in which we now can percieve chaos.

Okay, what has “Piggies” to do with The Art of the Steal?

The thesis of the film is that big, powerful politicians conspired to run roughshod over a group of small, relatively powerless art lovers trying to preserve the legacy of one Dr. Albert C. Barnes, who created the Barnes Foundation in the first place. Supposedly (and we have no reason to doubt it) Barnes hated the big, powerful interests who ultimately got control of his art collection decades after his death.

The lesson I’d like to draw from this whole thing is not quite the lesson the film would like us to draw, which is that the big piggies are bad guys beating up on the good guy little piggies. That’s the usual class-struggle argument.

To me, the good and bad in this tale is a matter of viewpoint. What I’d prefer us to learn is that Barnes’ attempt to create something that would forever function as he wanted it to was fundamentally doomed to failure.

Human society is a chaotic system, so any human organization you set up will eventually evolve in ways you cannot predict and cannot control. That’s Mommy Nature’s way.

If you try to go against Mommy Nature’s way, as Barnes did, Mommie Nature SPANK!