The Most Important Number You Don’t Know

Numbers are a big part of life. Numbers can be lots of things to us: interesting, important, familiar, etc. We all know lots of numbers. This post is about the most important number you don’t know.












Account balances.


Numbers are a part of life.

Numbers You May Know

Numbers can be interesting and familiar…

…3.1416, aka, pi, which is the ratio of a circle’s circumference to its diameter.

…10100 (1o to the 100th power), also known as “Googol,” the inspiration for the name of the world’s number-one search engine, Google.

…1.618, the “golden ratio” that describes perfect proportions.

…911, the number we call in an emergency.

…7, the world’s most popular “favorite number.”

These are a few of the numbers you may know.

Numbers You Absolutely Know

Then there are numbers you most certainly know…

…your birth date.

…the birth date of your spouse or significant number

…the birth dates of your children.

…the phone number of your spouse or significant number.

Important Numbers

Numbers can be important. There are numbers that are likely very important to you…

…your social security number.

…your bank account number.

…the PIN number of your ATM.

…your income.

…the balance in the mortgage on your home.

…the balance in your savings account.

Of course, there are many other numbers in the world, the vast majority of which don’t mean that much to you, and which likely aren’t very important.

The Most Important Number You Don’t Know

And then there is this number: 10^10^123 – 10 to the 10 to the 123rd power – aka “the Penrose Number.”

Odds are good you’ve never encountered that number before.

I had never hear of it before stumbling across it a handful of days ago.

And when I discovered that number and understood its potential significance, I was floored.

My mind was blown, and my thinking forever changed.

That number – 10^10^123, or the Penrose Number – is very likely the single most important number that you don’t know.


Before I continue, please allow me to share some caveats up front:

– I am not a scientist.

– I am not a mathematician.

– While I do have a decent command of numbers (I’m a CPA with a degree in Accounting from Michigan State University), the larger issues that support what I’m going to say here are way beyond my simplistic understand of such things.

But that doesn’t matter, because this post is not about “the science” behind the Penrose Number.

This post is about what we can infer from the Penrose Number, and how that might affect our view of things.

Lots of things.

Maybe, everything.

And to understand what we can infer from the Penrose number, you also don’t need to have any background in cosmology, or physics or mathematics.

All you need to be is objective, reasonable, logical and open-minded.

If you are those things, I would respectfully ask you to continue reading.

If you’re not, cut your losses and quit now, because a primary purpose of this post is to expand your knowledge and, maybe, alter your view of things a little bit.

And if you’re not objective, reasonable, logical and open-minded, you may not be open to such expansion.

Still Here?

If you’re still reading, let’s continue on with our exploration of the Penrose Number, its potential significance and why I think it is very likely the most important number you don’t know. Here are the key things to understand up front:

About Roger Penrose

The Penrose Number is named after Roger Penrose. According to Wikipedia, Penrose is:

An English mathematical physicist, mathematician,  philosopher of science and Nobel Laureate in Physics. He is Emeritus Rouse Ball Professor of Mathematics at the University of Oxford, an emeritus fellow of Wadham College, Oxford and an honorary fellow of St John’s College, Cambridge, and of University College London (UCL).

Penrose was awarded the 2020 Nobel Prize for Physics three weeks ago, in early October 2020.

Penrose was a close friend of Stephen Hawking, the famous English theoretical physicist, cosmologist, and author who was director of research at the Centre for Theoretical Cosmology at the University of Cambridge at the time of his death in 2018.

Exactly as with Hawking, Penrose was deeply interested in the origins of the universe, and moves in circles that included the likes of Hawking and others like him.

It is within that larger context that the Penrose Number was conceived, and also within which it gained notice and recognition.

The Context

You’re probably familiar with the Big Bang Theory. According to

The Big Bang Theory is the leading explanation about how the universe began. At its simplest, it says the universe as we know it started with a small singularity, then inflated over the next 13.8 billion years to the cosmos that we know today.

Per the Big Bang Theory, the universe came into existence as a result of a set of very specific, precise conditions and occurrences.

One of those conditions was something called “initial entropy.”

Entropy is the degree of “thermodynamic disorder” in a closed system like the universe (it’s not essential that you understand this point; so, if you don’t, no worries; just keep reading).

Those initial entropy conditions had to be absolutely perfect in order for the universe to develop as it did.

The Penrose Number

This is the context in which Penrose enters the discussion.

Penrose wondered about these questions:

What “initial entropy” conditions had to have existed in order for the universe to have been created in accordance with the Big Bang Theory, and for that universe to then ultimately be supportive of life coming into existence randomly?

What are the odds that those exact conditions could have existed at the time of the Big Bang?

The Penrose Number is his scientifically-based-and-calculated estimate of those odds.

According to Penrose, the odds against such an occurrence were on the order of 10 to the power of 10123 to 1, or 10^10^123, aka, the Penrose Number.

Gaining Perspective on the “Odds Against” the Penrose Number

As you’ve probably already surmised, those odds are infinitesimally nanoscopic (if that’s not a word, it is now).

In fact, the human mind cannot even grasp just how tiny those odds are. To help provide some perspective on just how small those odds are:

– 10123 is written as a 1 followed by 123 zeros. And the Penrose Number is 10 to the power of 10123 to 1.

– 10123 is so large that there is no name for it.

– 10123 is greater than the total number of atoms (which is thought to be 1079) believed to exist in the entire universe.

– In Penrose’s book The Emperor’s New Mind: Concerning Computers Minds, and the Laws of Physics, Penrose wrote this (emphasis added):

One could not possibly even write the number down in full in the ordinary denary (decimal) notation: it would be 1 followed by 10123 successive 0’s. Even if we were to write a 0 on each separate proton and on each separate neutron in the entire universe – and we could throw in all the other particles for good measure – we would fall far short of writing down the figure needed.

Reading that quote from Penrose is what ultimately blew my mind and reframed much of my thinking as it relates to the Big Bang Theory.

Just stop and think – really stop and think – about what Penrose said: the odds of the initial entropy conditions being exactly what they had to be in order to create a universe that would ultimately be supportive of life to come into existence randomly are so huge that the number of zeros you’d have to write down in order to express those odds is greater than the number of atoms in the entire universe.




My Brain Broke

My brain almost breaks trying to understand the magnitude of those odds.

Ever since I became aware of it, I can’t get the Penrose Number out of my head.

It’s like a song – the worst (or best, I can’t decide) ear worm of all time – that just keeps playing over and over, on a seemingly infinite loop, in my mind.

My brain WANTS to grasp this…but it just isn’t smart enough or complex enough to do so.

A significant challenge inherent in all of this is that the human mind simply cannot think in these terms and on this scale.

And when we encounter things we cannot readily process mentally, we tend to dismiss them.

Another Attempt at Perspective

Because of that, I spent the better part of a day trying to come up with some analogy that I thought the average person might understand (or that I might understand, for that matter).

I even posted this on Facebook, hoping someone with a PhD in Mathematics might be able to help me out.

Calling all math geniuses… I am trying to calculate the the odds of rolling snake eyes 10 times in a row (with a pair of dice, obviously) as a percentage of the “Penrose number.” Or, even better, I’m trying to articulate this relationship in lay terms, e.g., “the odds of rolling snake eyes 10 times in a row are a trillion trillion trillion trillion times more likely than the Penrose number.” Thanks in advance to anyone smart enough to answer this question…

In response, a person I know named Ron Mazier, who has a degree in Economics from Texas A&M and is a former lecturer at Tulane University, offered this:

So more precisely the Penrose number is 10^10^121.5 times less likely than snake eyes 10X.

It’s hard to compare. At first, I thought 10^10^123 was equal to 10^1230, but nope that’s only 10 to the power of 10 with 3 zeros. Penrose is 10 to the power of 10 with 123 zeros. Think about this: What’s the chance of picking one in a million? That’s 10^6. The chance of pulling that 200 times in a row is 10^1200 (6×200); a little over 10^10^3. Now you have to repeat those 200 pulls 41 days (3 x 41 = 123) in a row to get the Penrose number, I think. Pull one in a million 200 times a day for 41 days.

Later, he added this:

I think my estimate is still way too small. Pulling 1 in a million 200 times for 41 days is only 10^(6x200x41) or 10^49200 which is less than or 10^100000 or 10^10^5. I’ll need another cup of coffee.

Allow me to summarize what Ron said…

The odds of you:

…winning a “one in a million” sweepstakes…

200 times per day

…for 41 days in a row

…would be 10^10^5.

And that is not even close to the odds against one of the foundational assumptions of the Big Bang Theory as expressed by the Penrose number.


Winning a one in a million sweepstakes 200 times per day for 41 straight days…and that’s not even close to what we’re talking about here?


Initial Entropy Was Just One of Many X Factors

But wait, there’s more.

The phenomenon to which the Penrose Number applies (initial entropy conditions) is just one of many instances/conditions/X factors that had to happen EXACTLY as they did in order for the universe to have come into existence, and for that universe to be ultimately supportive of life.

Here are two additional quick examples of other such X factors:

Explosive power of Big Bang precisely matched to power of gravity; density precisely matched with critical density 

Per A Case Against Accident and Self-Organization, for the universe to form, the force of gravity had to match precisely the explosive force of the Big Bang. The matching had to be to the remarkable precision of one part in 1055213. If the rate of expansion was reduced by only one part in a thousand billion, the matter in the universe would have collapsed back to a singular point after a few million years.

One part in a thousand billion.

And, remember, this is separate and distinct from the Penrose Number.

In other words, AFTER you beat the ((10 to the power of 10123) to 1) odds of the Penrose Number, you then have to somehow end up with the one in a thousand billion precision of the force of gravity exactly matching the power of the Big Bang.

Resonance precision required for existence of carbon, a necessary element for life

Another thing that had to be perfect in order for a universe that would ultimately be supportive of life to come into existence randomly: the formation of carbon, which has to exist in sufficient quantities to support life.

Skipping past all the details to cut to the chase, Astrophysicist Sir Fred Hoyle calculated the odds inherent in the formation of carbon.

What he discovered was so shocking – because the odds against that specific process working the way it had to work in order to form carbon were so extreme – that it made him question his personal spiritual orientation.

Quoting from A Case Against Accident and Self-Organization:

By his own admission, Hoyle’s atheism was dramatically disturbed when he calculated the odds against these precisely matched resonances existing by chance. Hoyle wrote:

A common sense interpretation of the facts suggests that a superintellect has monkeyed with physics, as well as with chemistry and biology, and that there are no blind forces worth speaking about in nature. The numbers one calculates from the facts seem to me so overwhelming as to put this conclusion almost beyond question.

In other words, the results of his own research were so shocking to Hoyle that it made him rethink his position on the existence of a higher power…because the odds were so overwhelmingly against the process of carbon formation working in the manner that it does.

There are a number of additional instances where the odds of something happening within the chain of events necessary in order to create a universe that would ultimately be supportive of life to come into existence randomly are so extreme as to be virtually impossible, but you get the gist.

A Practical Perspective

If I’ve confused you with the way I’ve presented this so far – and that is entirely possible, and, if that’s the case, I apologize – let’s consider this from a slightly different perspective.

Let’s forget about all this science for a moment and take a fresh look at things from a more practical perspective.

If the odds of a theory – any theory, it doesn’t matter which one – being correct are 1 in 100, how much confidence do you have in that theory?

Those aren’t great odds, but that’s certainly possible, right?

How about 1 in 1,000?

Sure, that theory could still be correct, but it makes you wonder, doesn’t it?

How about 1 in 1,000,000?

I believe most people would have a hard time believing any theory with such odds against.

How about 1 in 1,000,000,000?

One in a BILLION? I have to believe most people would scoff at the idea that any theory with such low odds could be correct.

How about 1 in 1050?

Less Than Zero

In the world of probability theory, 1 in 1050 is considered “zero probability.” It’s hard to imagine anyone believing in any theory with such long odds against.

How about 1 in 10 to the power of 10123?

Again, that’s the Penrose Number, and it is a TRILLION TRILLION TRILLION times less likely than the “zero probability” odds – 1 in 1050 – of the prior example.

A trillion trillion trillion times less than the number considered zero in the world of probability theory!

In short, the Penrose Number tells us that the “accidental” or “coincidental” creation of our universe is, from a mathematical, probability and statistical perspective, a literal impossibility.

And THAT leads us, finally, to the purpose of this post.

The Point

The Penrose Number is the most important number you don’t know (or didn’t know, until now) because it’s representative of the fact that science may not have all the answers after all…

…about the origins of the universe.

…about the origins of life.

…about the origins of YOU.

If the odds of just one of the many components of the Big Bang Theory being correct are 1 in 10 to the power of 10123, what does that say about the veracity of that theory?

Most of us have accepted the Big Bang Theory as the explanation for the creation of the universe, and, by extension, the explanation for the creation of life itself.

We do so because that’s what we were taught in school, and because there doesn’t seem to be another viable explanation.

We also accept the Big Bang Theory as correct because – let’s be honest – most of us really don’t care that much about such things.

We’re all busy and distracted by the daily concerns of life: earning a living, feeding our families, having a roof over our head, trying to enjoy life a little before it’s over, etc.

We don’t care that much about science, or physics, or astronomy or cosmology.

But what if “the science” is wrong?

Not Even About Science

Further, this really isn’t even about science.

It’s about the implications of science being right or wrong, and the potential domino effect that may have on our thinking about a whole host of other very important things, like:

– Where we came from.

– How we got here.

– The true meaning and purpose of life.

What if you’re struggling – exactly as I am – to accept the Big Big Theory as fact now that you understand the massive, overwhelming odds against it being an accurate explanation for the creation of, well, everything?

Parting Thoughts

What then?

To be clear, I don’t purport to have the answers.

I’m a nobody, a no one, a zero.

But I will say this: the Penrose number was probably the most important number you didn’t know before today.

Will it be the most important number you know going forward?

That will be for you to decide.

Impact on Penrose

As a final comment, I’ll leave you with this, which is a quote from Penrose.

I cited this quote earlier, but I omitted the first sentence in that initial reference. I am repeating that quote, but this time in its entirely, with the first sentence added back in (emphasis added):

This now tells how precise the Creator’s aim must have been, namely to an accuracy of one part in 10 to the 10123rd power. This is an extraordinary figure. One could not possibly even write the number down in full in the ordinary denary notation: it would be 1 followed by 10123 successive 0’s.” Even if we were to write a 0 on each separate proton and on each separate neutron in the entire universe – and we could throw in all the other particles for good measure – we would fall far short of writing down the figure needed.

Exactly as with Hoyle before him, it appears Penrose’s own discovery may had had an impact on his overall philosophical and spiritual orientations.

That is, Penrose’s discovery of the Penrose Number may have changed the way he looked at everything.

How will the discovery of the Penrose Number affect you?