We are always dreaming

Take a large pot of water and leave it out in sub-freezing temperatures for a few days. It will turn into a block of ice.

Now take that pot of water and put it on the stove and crank up the flame. Before long, it will start to boil.

Let it cool for a few hours at room temperature and it will resume its familiar liquid form.

If you drop a live fish into liquid water it will swim around and do fishy things.

Things would not go so well if you drop a fish onto a block of ice. Fish are not good skaters.

And if you drop a fish into boiling water…well, the fish will not be very happy.

Think about these states of water as metaphors for how your brain works. A block of ice is a dead brain. A pot of boiling water is a brain having a seizure. Water at room temperature is a normal brain.

The fish represents consciousness.


Liquid brain

There is a constant low level of electrical activity among neurons (like water molecules bouncing off of each other, doing the Brownian dance). Intrinsic random neuronal activity is the norm – it keeps a low fire burning all the time. In a sense, the brain has a pilot light.

A bit of randomness is helpful for keeping the mind creative and open to new ways of thinking – consciously and unconsciously. Like the ever-present force of natural selection that curates random mutation in genetic evolution, there are dynamical structures in the brain that permit more meaningful, useful energy to percolate from the random background.

Command and control

The majority of the brain’s activity is unconscious. At every second of your life a vast army of dynamical structures are buzzing around, managing the low-level mechanisms of multi-sensory input, attention, memory, and intent. These structures are vast, short-lived, and small. And they are entirely inaccessible to the conscious mind.

The command and control area of the brain is located at the front-top of the neocortex. The signature of consciousness is a network of relatively stable, large-scale dynamical structures, with fractal fingers branching down into the vast network of unconscious structures. The buzz of the unconscious mind percolates and fuses into something usable to the conscious mind. It offers up to the conscious mind a set of data-compressed packets. When the command and control center relaxes, we experience wandering thoughts. And those thoughts wander because the brain’s pilot light provides constant movement.

These ideas are derived from Dehaene’s Consciousness and the Brain.

Surrender to dreaming

When we start falling asleep, the command and control center begins to lose its grip. The backdrop of randomness sometimes makes its way past the fuzzy boundary of our consciousness – creating a half-dreaming state. Eventually, when consciousness loses out, all that is left is this random, low-level buzz of neural activity.

But dreaming is obviously not totally random. Recent memories have an effect…and of course so do old but powerful memories. The physical structure of the brain does not permit total randomness to stay random for very long. Original randomness is immediately filtered by the innate structure of the brain. And that structure is permeated with the leftovers from a lifetime of experience.

So here’s a takeaway from recent neuroscience, inspired by the findings of Stanislas Dehaene: WE ARE ALWAYS DREAMING. That is because the unconscious brain is continually in flux. What we recognize as dreaming is merely the result of lifting the constraints imposed by the conscious mind – revealing an ocean – flowing in many directions.

The unconscious brain can contribute to a more creative life. And a good night’s sleep keeps the conscious mind out of the way while the stuff gathered in wakefulness is given a chance to float around in the unconscious ocean. While in the ocean, it either dissolves away or settles into functional memory – kicking out an occasional dream in the process.


Pi is Meaningless

Ladies and Gentlemen. Introducing…a completely random series of numbers:

 3.11037 55242 10264 30215 14230 63050 56006 70163 21122 01116 02105 14763 07200 20273 72461 66116 33104 50512 02074 61615

Those are the first 100 digits of Pi in base 8.

“Base 8?” you screech. “Why base 8”.

Why not? We humans use base 10 because (scientists conjecture) we have ten fingers, and our ancestors used them to learn how to count. Having five digits at the end of each appendage is common in most animals we are familiar with.


But if the octopus had become the dominant species on Earth, and developed complex language, math and the internet (underwater), it is quite likely that it would have come up with a base 8 number system.


Therefore, octopuses would celebrate Pi Day by reciting its digits in base 8.

Or not.

Maybe they would think Pi is boring.

Like me.


No I’m not an octopus. And no, that’s not me. But it’s cute, don’t you think?

The point is:

I don’t understand why people pride themselves on being able to recite the digits of Pi (in any base). It is a waste of valuable gray matter that could be used for something useful.

According to Michael Hartl, “some people memorize dozens, hundreds, even thousands of digits of this mystical number. What kind of sad sack memorizes even 40 digits of π ?”

It has been found that the digits of Pi are indistinguishable from a random sequence of digits, no matter how high you count. If you select any sequence of digits in Pi (like, say, the first 100 digits starting at the billionth digit), you will find no particular bias or pattern. In fact, the likelihood of any digit (or sequence of digits) occurring is statistically flat: evenly-distributed. It’s as random as it gets (although there is no PROOF yet of the “normality” of Pi).

This is why I suggested in a previous blog post that the music in this video:

Screen Shot 2014-12-17 at 9.33.19 AM

…is meaningless. This guy Blake (who is a fine musician) could have just as easily used the digits from a random number generator.

By the way – I now see that there was a legal battle regarding copyright infringement in a case of using Pi as the basis for a melody.

Two unfortunate first-world preoccupations rolled into one.

Instead of fetishizing the digits of Pi (or any irrational number), why not explore the teachable aspects of Pi such as this:


…or this:





…or this:


According to Wolfram,

Screen Shot 2015-03-13 at 7.23.17 PM

What’s interesting is how chaos is formed – whether in an abstract number system or in a natural system. The digits of Pi should be understood as the result of a dynamical process that emerges when we try to find relationships between circularity and linearity. The verb is more meaningful than the noun.


Pi is Random. Stop Trying to Turn it into Music.

I have seen and heard several attempts at turning the digits of Pi into music.

Screen Shot 2014-12-17 at 9.33.19 AM

The highly-flourished music in this YouTube video is well-crafted. But I agree with the way one comment sums it up…

“So basically we’ve learned that any random sequence of numbers will sound reasonably pleasant if interpreted as notes in a major scale…”.

Yes. It is oh so convenient that the digits 1 through 8 can be mapped to the ever-so agreeable, politically-correct notes of the diatonic scale.

Don’t confuse this talented musician’s performance with anything remotely meaningful about the digits of Pi. Because……

Pi is INDISTINGUISHABLE from a sequence of random numbers. Extensive statistical analyses of the first six billion digits have been done to try to find tendencies, frequencies, repetitions, ANYTHING that constitutes a feature or a pattern.



Perhaps there is something in this apparently-random sequence that will someday reveal the existence of an alien intelligence. Yea, right.

Here is Vi Hart’s reaction to some of this musical Pi insanity…

Screen Shot 2014-12-18 at 9.14.19 AM

At least Jim Zamerski has the sense to consider that Pi can be expressed in other bases than 10, for making music. But again, regarding the use of Pi as the raw input into this musical treatment, how much musical content is there?


Personally, I would love to hear the results of a search algorithm that finds segments of Pi that come close to mimicking a famous melody. I have no doubt that “Happy Birthday To You” … using the digit 0 to represent a rest, and the digits 1 through 8 to represent the notes G3 through G4 in the C-major scale … can be found somewhere in Pi.

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Just for fun, I figured out what those digits would be. Here they are:


Sure, it might require wading through billions of digits using a special-purpose pattern-finding algorithm to get statistically close to this exact sequence. But at least the musician would have done some work. And it would be just as original.

What about “Pi Art”?

links-pi-cristianIt’s beautiful.

But meaningless. The digits of Pi are statistically no different than a random sequence of digits. Why not use the golden mean, or e, or the square root of 2? The digits in these irrational numbers are just as meaningless as Pi.

I submit that the best way to get creative over Pi is to think about its real meaning: Pi is the ratio of a circle’s circumference to its diameter. This ratio shows up in some interesting, and sometimes unexpected, situations – like Buffon’s needle:

Screen Shot 2014-12-18 at 10.53.28 AM

I will close with a simple, elegant expression of Pi. It may not be beautiful, but it says it all.