It’s Saturday again, as I warned everyone would happen if we didn’t do something to stop it.  Unfortunately, no one appears to have listened, so, well…here we are again.

Of course, as I also warned you all, I am working today, and so, here I am writing another blog post, just like all the others.

Except it’s not quite exactly the same as all the others.  And, given the 1000 or so words per blog post, and the number of possible words there are available, even avoiding random jumbles of characters, the number of possible blog posts that I could write is probably far greater than the number of potential days I have left in any plausible human lifetime…or any plausible universal lifetime short of infinity, probably.

Let’s do some quick and dirty math.

I’m going to estimate very roughly, because I only have vague (but educated) intuitions, but let’s assume I start any given blog post with a choice from a list of maybe twenty words.  That seems like a decent ballpark figure.  After that, there are only a limited number of potential next words that would make any sense and that I might be inclined to use.  I’m going to cull that down to 10 options per each next word, and I’m going to ignore individual word probabilities and predominances relative to other words.  I’m also going to ignore the fact that I often write more than 1000 words per post.  We’re just being quick and dirty here.

So, with 20 first words, then ten to choose from for each next word, if we assumed more or less random sorting among those, we’d have a potential number of blog posts of roughly 20 x 10 to the 999th power, or 2 x 10¹⁰⁰⁰ possible blog posts.  That’s a staggering number of possible posts, each just a thousand words long.

How staggering is it?  Well, the famous number “googol”, is 10¹⁰⁰ (ten to the hundredth power, or 10 times 10 times 10…repeated a hundred times).  It can be written as a 1 followed by 100 zeroes.  That number itself is roughly 10 to the 19th times as large as the number of baryons in the entire visible universe.  In other words, that’s ten billion billion times as many.  That’s more than a billion times the number of people alive on Earth now times the number of baryons in the universe.

But that’s just a googol.  A googol is so small compared to 2 x 10¹⁰⁰⁰ that if you subtracted a googol from 2 x 10¹⁰⁰⁰ the change would be so unnoticeably small that to notice it, one would require a precision far beyond the most precise measurement humans have ever made.  We’re talking about one part in about 10 to the 900th power.  That’s rounding off!

The best we’ve done as far as comparing experiment and theory goes is the magnetic moment of an electron‒or maybe it’s the fine structure constant, I’ll have to check on that (no, it’s the electron one).  That has been measured to agree with theory out to about the 12th decimal place, if I remember correctly.  As Feynman has said, that’s like measuring the distance between NYC and LA to the precision of the width of a human hair (which is far more precise than would in any case be useful or even applicable for such a distance measurement).

Anyway, the point I’m making is that the number of possible blog posts that can be a thousand words long with a few‒admittedly somewhat overgenerous‒constraints is staggering.  If I could write a blog post every Planck time for the rest of the life of the sun* I wouldn’t even make a dent, not a noticeable scratch or scuff in that number.  And you can’t really do more than one quantum event in any given Planck time, if I understand correctly, anyway.

So, I’m not going to run out of possible blog posts any time soon.  Even though I’ve probably overestimated the number of words I’m likely to use following any given previous word‒and I haven’t weighted the odds as would some GPT-like language model that creates text without thinking, based on huge numbers of things other people have written‒it’s still such a huge number that it’s too large really even to contemplate seriously.

And yet, time after weary time, I write blog posts about very similar things, such as my pain and my depression and the fact that I could really use some help from someone.  It’s very boring, I guess.  I apologize.  If you’re looking to diverge very much, I guess my blog might not be the ideal place for you.  But, of course, the huge majority of all possible blogs that would fit my above-listed criteria would be gibberish**, so we don’t want to get too caught up in those numbers.

It’s a bit like thinking about the human genome.  There are, I think, on the order of a billion base pairs in the human genome, and each “slot” has 4 potential nucleotide “letters” (adenine, guanine, cytosine, and thymine) so the number of possible genomes is about 4 to the billionth power, or 2 to the 2 billionth power…and every 2¹⁰ is roughly 10³ (2¹⁰ being 1024),and 2¹⁰⁰⁰ is about 10³⁰⁰ so 2 to the billionth is about…10^27,000,000, if my calculations are correct.  I’m not sure they are, but you get the idea.  It’s a big f*cking number!

Most of these orders of base pairs would not designate a human, nor even anything that could live at all.  So let’s whittle things down in truly draconian fashion and say only 10 to the 90th are potentially viable***.  That’s still far more potential humans than the number of baryons in the visible universe.

I think you can see that we’re never actually going to instantiate that number of humans, since each human is made of a substantial number of baryons…it’s something like 10²⁷, but that’s just a ballpark figure****.  So, unless we find a way to generate a lot of new baryons, and fit them into the visible universe without causing the whole thing to collapse upon itself due to gravitational effects, the whole of actual humanity will always be a sea of unimaginably untapped potential.

I think we all kind of knew that, anyway, didn’t we?

Likewise, the number of actual blog posts I‒or anyone else‒will ever write before the heat death of the universe (assuming that’s the way things end) is embarrassingly negligible.  But we work with what we have.

And speaking of that, I guess I’d better mentally prepare myself for work, since I am already on the train.  I hope you all have a good weekend.  Whatever you do, it will probably be more interesting than anything I’m going to do.  Believe it or not, I find some consolation in that fact.

*It’s about 10⁶⁰ Planck times:  10⁴³ Planck times per second times 60 seconds per minute times 60 minutes per hour times 24 hours per day times 365.25 days per year times about 5 billion years.

**I mean even more so than my actual blog posts are.

***Don’t make the mistake of thinking that’s a reduction by 26,999,910/27,000,000. It’s way more of a reduction than that.  Don’t be fooled by the comparatively small numbers in exponents.  We’re taking a number that was 27 million digits long and making it only ninety digits long.  If you subtracted the second number from the first, it would be such a small change you’d have to look out well past the 26 millionth digit even to see a difference.

****Again, don’t be confused by the relative closeness of the exponents and worry that we’ll run out of baryons soon.  10 to the 27th is vanishingly small compared to 10 to the 81st.  In fact, curiously, 10²⁷ x 10²⁷ x 10²⁷ = 10⁸¹.  Every single gram of hydrogen contains 6 x 10²² atoms, and obviously the number of grams of hydrogen in the universe is waaaaaaaaaaaaaay bigger than that!