Hello.  Good morning.

Aaahhh, doesn’t that feel better?  Now I can use my standard Thursday blog post opening phrases, because today is, in fact, Thursday.  It’s the 21st of November, the third Thursday of the month, so in the USA you only have seven shopping days until Thanksgiving.

Speaking of Thanksgiving, since next Thursday is that holiday, I probably will not be writing a blog post then.  It is one holiday on which our office is always closed.  We will be open on so-called Black Friday, but I can’t guarantee that I’ll write a post on that day.

Of course, in principle, I cannot guarantee that I’ll write anything at all ever again after this post.  I may not even survive to post this entry*‒I am in the back seat of a Lyft, on the highway (I-95) of the East Coast of the US, so goodness knows there’s a non-zero chance of a fatal accident.  I would even wish for one, but I know such a thing would involve harm and possibly death to other, more innocent, people.

Also, of course, wishes don’t actually directly affect reality‒thank goodness.  Imagine if even one percent of wishes came true as wished.  The world would be thoroughgoing chaos…and not in a good way.  I tend to say of wishes that “If wishes were horses, then we’d all be hip deep in horse shit,” but it would be even more terrifying if wishes worked.

The “if‒then” character of the wishes saying (my version or the more SFW one that involves beggars riding) often makes me think of lines of computer code in some generic programming language, like:

If wishes==horses then execute beggars.ride

Or maybe 

If wishes==horses then horseshit_level = “hip deep”

I wonder what that would look like in machine language.  Or, I wonder what it would look like in straight binary.  Really, though, I know part of the answer to the latter piece of wondering:  it would look, to the naked eye, like a random string of ones and zeros, perhaps the tally of some very long record of flipping a coin and marking heads as 1 and tails as 0 (or vice versa).

Actually, of course, given a binary-based computer language, one can literally generate every possible computer program just by flipping an ever-increasing number of coins.  Or, to be honest, one can do it just by counting in binary:  0, 1, 10, 11, 100, 101, 110, 111, 1000…

This is why, if memory serves, computer science people and information theory people say that every program can literally be assigned (and described by) a number.  You could express that number in base ten if you wanted, to make it a bit more compact and familiar to the typical human.  Or, if you want to be more efficient and make conversion easier, you can use hexadecimal.  This is easier because a base-sixteen number system is more directly and easily converted to and from binary, since 16 is a power of 2 (2 to the 4th).

Even the human genome, or any genome in fact, could be fairly readily expressed in binary.  The DNA code is a 4 character language, so it wouldn’t take too much work to make it binary, however you wanted to code it.  Then, each person’s genome would have a single, unique number.  That’s kind of interesting.

It would be a bit unwieldy as an ID number, of course.  The human genome is roughly 3 billion nucleotides long, which means it would be roughly 6 billion binary digits (AKA bits).  And since every ten bits is roughly a thousand in base 10 (2^10 is 1024, which is very close to 10^3, aka 1000) then 6 billion bits should be roughly 2 billion decimal digits long (a bit less), which is much, much larger than the famously large number, a googol**.

It’s a big number.  This should give you at least some idea of just how unique each individual life form is at a fundamental level.  There are so many possible genomes that the expected time until the final heat death of the universe is unlikely to be long enough to have a randomly created duplication within the accessible cosmos.

Of course, within an infinite space‒which is the most probable truth about our universe as far as we can tell‒one will not only have every possible version that can exist, but will have infinite copies of every possible version.  Infinity makes things weird; I love it.

Of course, just as with the making of computer programs by simply counting in binary, the vast majority of genomes would not code for any lifeform in any kind of cellular environment, using any given kind of transcription code you might want (the one on Earth, found in essentially all creatures, uses three base pairs to code for a given amino acid in a protein, but that’s not all that DNA does).  Similarly, most of the counted up programs would not run on any given computer language platform, because they would not code for any coherent and consistent set of instructions.

But even so, you would still, eventually, get every possible working program, or every possible life form in any given biological system if you could just keep counting.

On related matters, there are things like the halting problem and so on, but we won’t get into that today, interesting though it may be (and is).

It’s quite fascinating, when one is dealing with information theory (and computer science) how quickly one encounters numbers so vast that they dwarf everything within the actual universe.

Mind you, the maximum possible information‒related to the entropy‒carried within any bounded 3-D region is constrained by the surface area (in square Planck lengths) of a black hole with that size event horizon.  For our universe, roughly 96 billion light years across, I think that’s something like 10 to the 124th bits, or at least it’s that many Planck areas.  That’s quite a bit*** smaller than the number of possible genomes, though I have a sinking feeling that I’m underestimating the number.

And information, at least when instantiated, has “mass” in a sense, and the upper limit of the amount of information in a region of spacetime is delineated by the Bekenstein entropy description.  So there’s only so many binary strings you can generate before you turn everything into a black hole.

Something like all that, anyway.

I may have been imprecise in some of what I said, but when you’re dealing with very large numbers, precision is only theoretically interesting.  For instance, we**** have found Pi to far more than the number of digits needed to calculate the circumference of the visible universe down to the Planck length.  It would require only about 40 digits of Pi to get to that precision to the size of a hydrogen atom, and those are only about 10^25 Planck lengths across, so we wouldn’t expect to need much more than 65 digits of Pi to get that precise, but let’s be generous and use 100 digits.

How many digits of Pi have actually been “discovered” by mathematicians?  Over 105 trillion digits.  Talk about angels dancing in the heads of pins!  It’s literally physically impossible, according to the laws of quantum mechanics, even to test whether that number precisely defines the ratio of any given circle to its diameter by measuring it.  One cannot, in principle, measure finely enough.

Still it just goes to show that mathematics is vastly larger in scope than any instantiated, superficial reality.  Information is deeper than one might think…so to speak.  But, then, so are minds themselves, vastly deeper.

As Idris/the TARDIS asked in Doctor Who, Series 6, episode 4, “Are all people like this?  So much bigger on the inside?”  Yes, Idris, I suspect they are, even those people we don’t like and feel the urge to denigrate.

That’s enough for today, I think.  I’ve achieved nothing, really, other than write a Thursday blog post, but then again, that’s all I meant to do.  I hope you have among the better half of all the vast number of possible days available to you.

TTFN

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*If you’re reading this, though, I clearly did survive.  I have mixed feelings about that.

**How much larger?  Soooo much larger that if you subtracted a googol of something from 10^1,800,000,000 of something, you would not change it to any extent measurable even by the most precise instruments humans have ever created.  And a googol is already something like 10 to the 19th times as large as the total estimated number of protons and neutrons in the accessible universe.

***No pun intended.

****Actually, I had nothing to do with it; it’s just the sort of “royal we”***** kind of thing everyone uses when discussing the accomplishments of humanity as a whole.

*****Not to be confused with royal wee.  That’s the sort of weird, niche thing one might find for sale in mason jars on the dark web.  Be careful if you’re into such things.  I wouldn’t buy it unless you’re sure of the source, so to speak.