Everything Machine

How Smart Are You

Intelligence is the ability to think like another. So let's see how smart you are, as I show you how stupid I am.

The Logical Fallacy

Math (properly played) is a Logic Puzzle. And Logic is an Axiomatic System. It works by taking assumptions (axioms) and following them where they lead. But the first assumption in any Axiomatic System is that such an Axiomatic System works.

Well, no. Strictly speaking that doesn't have to be the first assumption, at all.

God -> Logic ≠ Logic -> God

There is no Logical (Game Playing) reason why God should not pre-date and overpower Logic (that Logic exists at God's whim) or conversely God only exists to the extent such a Being can be Constructed according to the Logical Rules in place. I mean, you can argue that one is True and the other is False, but both are Equally Valid Logical Constructions, depending upon one's assumptions.

Want To Play A Game?

So, Logic is not as straightforward as some would have it. And by extension, Logic doesn't mean the same thing from one person to the next. In a Logical Construction, we can include such things as:

• Logic
• The Law of The Excluded Middle
  • X = Y
or
X ≠ Y

    • This is an assumption.
• X = X
  • This is, also, an assumption.
• God
• Faith
  • Sect
• Math
• Euclidean
  • Non-Euclidean
• Deterministic
  • Stochastic
    • Welcome to Quantum Physics

It's a game of picking and choosing and setting relative priorities.

I mean, sure. One cascading array of choices may reflect Reality better than another. But proving such a thing is impossible from within such an Axiomatic System... meaning, it's impossible to prove using only Logic and never resorting to Faith.

Belief

Everything is Faith Based.

Everything is Personal Opinion.

Feel free to disagree. But then, as The Dude (who has been known to abide) might say, "Yeah. Well. That's just, like, your opinion, Man."

Moving On

But's that's all preamble. It's not why we have all gathered here, today.

Can We Compress The Universe?

The main idea (along with many lesser side tangents), which sparked this rant, has to do with Quantum Physics, Information Theory, and Data Compression.

The claim was made that The Universe could be Compressed in such a way that multiple copies of The Universe could be stored within The Universe.

Um, no.

Bits Of Entropy

Now, I did not read the raw documentation, so I may well be responding to a Straw Man. But, hey. That's OK. And even a Straw Man is deserving of some consideration. So, how did one (or could one) come to the above stated conclusion?

1. The Universe is composed of Matter & Energy.
2. Matter & Energy exist (and/or can exist) in various states of Order & Disorder.
3. These States of Order & Disorder can be assigned Numeric Values.
• Higher States of Disorder corresponding to Higher Numbers.
• These Numbers being intended to correlate with the amount of Information that is required to Replicate State.
• I may have to cover what is meant by all this in much greater detail.
  • But for now, that will have to wait.
4. The number which corresponds to The Universe As It Is is significantly less than the Theoretical Maximum Number for the amount of Matter & Energy present in The Universe.
5. Ergo Sum: The Universe could be reconfigured to store multiple copies of itself.

Mathematically, it is sound, as I am sure the numbers work out.

Logically, it is not, for a variety of reasons.

Type Mismatch

At the most basic, there is an error in comparing Types.

To wit, This Universe, Our Universe, The Universe we all know and love can be assigned two Numbers:

1. The first corresponds to the amount of Information that This Universe Actually Contains.
2. And the second representing the amount of Information This Universe could Theoretically Contain.

But In Reality, both Numbers must be equal, because for A Universe (Any Universe) to contain more information that it presently holds, Said Universe would have to become a Different Universe.

Thus, This Universe cannot hold more information than it does.

Anything else is just playing games with words.

I Give You The Moon

For example, suppose we were to store a copy of The Moon in The Moon: somehow Compress the Information that makes up The Moon (I really should get to the issue of Compression before too terribly long) and store that Information within some lesser part of The Moon.

First (if we did such a thing), clearly The Moon is not as it was.

New Moon ≠ Old Moon

And Second, if it were possible to store a copy of The Moon in only half of The Moon (or any other lesser part of The Moon), then it follows (by the Logic I am choosing to use, so make of it what you will) we would, also, be able to make a copy of that copy (and a copy of that copy (and a copy of that copy (and a copy of that copy (for as long as we like)))), handily reducing the amount of The Moon that is required to store a Copy of The Moon to an arbitrarily small size.

And thereby, packing an Infinity of Angels onto the Head of a Pin.

But then, Real World Compression doesn't work that way.

So, yeah. Maybe it is time to talk about compression.

Digital Compression Of Data

The Digital Compression of Data works by:

1. Discovering Order
2. Finding Rules for that Order
3. Replacing said Order with said Rules
• Via Substituting
• This is the compression step.
4. Repeating Until No Order Remains

Static, Random Noise, and a Fully Compressed System all look the same. They look like Heat Death. They look like Un-Ordered Chaos.

Symbolic Expression Of Reality

Data Compression works great on Word Strings, because Word Strings have highly stylized rules and use Repetitive Letters, Words, and Phrases.

Painting A Pretty Picture

The size of the Data Set doesn't matter. It's really easy to Compress Well Ordered Data. A Black Square Measuring 10,000x10,000 Pixels is only marginally harder to describe (and therefore Compress, as Compression and Description are synonyms in this context) as a similar White Square Measuring 1x1 Pixels.

Though, if we take a moment to consider the original question. I think it would be ludicrous to imagine we could store anything (say, a smaller White Square) in the original Black Square (however massive it might be) without altering the Original Black Square.

Take A Picture It Will Last Longer

A Book contains Information. This Information is easy to Compress. We used to do this by taking Photographs of The Pages, a technique known as Micro-Filming. And now, these same Books tend to be Digitized. But in both processes, all that is being saved are The Words. If one wants to save The Book (itself), one needs to save The Book.

Eh, that's probably not clear.

Words are Words. And Books are Books. And if one wants to have an Exact Copy of a Book down to the Aged Binding, Mouldy Pages, and Fading Lettering, one needs to store a lot more Information than just The Words on The Page.

The Problem Of Equivalence

I would argue (posit, theorize, hypothesize, and/or state unequivocally) that the only way to make an Exact Copy of a Book is to make an Exact Copy of Said Book; and that one cannot Compress the Information contained within a Physical Object any more than it already has been.

Reality is already Compressed.

Seriously, if God Doesn't Play Dice, as (I believe) Einstein once famously quipped, then I'm pretty sure He Doesn't Waste Bandwidth, Either, as a lesser known blogger (being yours truly) has recently just written.

Steady State

I question whether I believe in Quantum Mechanics. Certainly, until a few months ago, I thought it was utter hogwash. But before we get to the Quantum side of things, let me explain the alternative: Non Quantum Mechanics. If Quantum Mechanics says there is a point at which things can no longer be divided, Non Quantum Mechanics disagrees; and rather, holds that Bits of Matter (by whatever name, even if they are only fields of energy) exist in Exact Positions in Space with Unlimited Precision. And the same holds true for their Energy Levels, Clock Cycles, and all the rest.

In short, even if Humans are unable to know Position & Energy (absolutely and/or past a certain level of precision), Position & Energy Exist in The Universe specifically and with Unlimited Precision.

Thus, to make a Copy of a Book that is a True Copy of that Book (down to the last Electron Spin and Quantum State) then one has to make a Copy of that Book. And No Compression is Possible, because there is no Order to be found (i.e. there are no overlapping or repeating patterns) in data that is never the same and is infinitely distant (in a Dimensional Sense) from one Bit of Data to the next.

Essentially, Compressing a non-repeating un-predictable randomly-chosen (please, call it a transcendential) number is not possible.

But Quantum

Of course, if one does not believe that Steady State hogwash (and why should one, especially since I use Steady State to refer to a cluster of phenomenon), Quantum Physics does make things easier.

Quantum means Quantifiable. It's like the opposite of an Infinity of Values, as I just got done describing in the preceding section.

In other words, a Quantum System only exists (can only exist) in a Finite Number of States and cannot be sub-divided any further than:

• Quanta of Time
• 10^-43 seconds
• Quanta of Space
• 10^-35 meters
• Quanta of Energy
• ???

Thus both 10^-44 seconds or 10^-36 meters are not meaningful constructs. 10^-43 seconds is as short as Time goes. It cannot be divided any further. 10^-44 seconds is not in-between seconds. It simply does not exist.

And the above Depth of Information must be stored for The Breadth of The Universe:

• 10⁸⁰ atoms
• 10¹¹ light years diameter
• i.e. 10²⁷ meters in diameter

{These are very rough numbers.}

Now, on first blush, it does look like the number of Atoms vastly outshines the rest of the Data Points; and as such, they could be used to Store the required Information handily. But this is only at first blush.

On second blush, I'm think the true math goes something along the lines of:

10263 * 1035 / 1080 = 1033

And that means the Information Spread between Atoms is 10³³, which is pretty darn large, making the Data pretty darn Sparse. Meaning, there's a lot of ground each Data Point (each Particle) is expected to cover.

But there is Order in The Universe. So by definition (i.e. drawing from the relative parts of Information Theory and that sort of thing), The Universe (the Theoretical Bits of Information it contains) can be Compressed.

So, I'm thinking the limiting factor is Quantum Space, which at 10^-35 (which can be thought of as 10³⁵ possibilities per meter) is completely dwarfed by the number of Data Points involved: i.e. Atoms, at 10⁸⁰. Which means, there is plenty of room for Compression.

So sorry.

I was wrong.

I felt convinced that when I actually looked at the numbers, Quantum Space would be more important than (would squash-out the significance of) the Data Holding Points (i.e. the Atoms). But as it turns out, that's not the case.

Thus, as a Valid Statement in Information Theory: A Universe Our Size Could Hold Several Times Our Universe's Compliment of Information.

Or restated, A Universe With The Same Mass As Ours But In Heat Death Would Contain ?x Times More Information Than Ours.

It's not Usable Information. But I have no belief anyone was ever claiming such a thing.

But then again, as I've said many times before, "Ya can't keep a Good Rant down."

So, I'm not about to stop there.

Split The Difference

To clarify my position (if this does any such thing), if Our Universe only consisted of two Atomic Particles (or The System we wanted to Compress only consisted of two Atomic Particles), no Compression would be possible as the Dimensional Space we would need to cover (the Set of Possibilities) would be so vast that we would need those two Particles in their full Native State to Store their own Information. But as the number of Storage Points (i.e. Particles) increases to the point where it dwarfs the Set of Possibilities (The Size of Space for starters, being the Size of The Universe in Plank Units), compression is indeed possible.

As a simpler example, it is fairly difficult to Compress the Letter String 'AB'. But I think we all could find a way to Compress 'ABABABABAB'.

Of course, I'm not backing down one iota from my conviction that this is just a Word Game.

But as long as we all understand that we are simply Playing Games, I think we can increase our Theoretical Level of Compression quite a bit further.

Steady State / Quantum State

I view Energy Fields as Continuous. Whereas in the world of Quantum Mechanics things are more Discrete.

So, like, where I would give a Particle essentially Infinite States, Quantum Mechanics says there are only a handful. And this Handful of States act like Letters, Words, or Phrases (in a Book or other bit of Writing) when it comes to Compression.

10⁸⁰ Atoms in 10² Quantum States reflects 10⁸² Bits of Information Uncompressed. But Compressed, it reflects something along the lines of 10⁸⁰ Bits of Information just by extracting the Order contained within those repetitive Quantum States.

Essentially, there are so few Quantum States compared to Atoms (Particles, whatever) that it is Theoretically Possible to Save the Quantum State Information for almost nothing. I mean, it's not. But rather than being a big number it comes out being a very small (basically insignificant) number.

Uncompressed: 1080 * 102 => 1082

Compressed: 1080 + 102 => 1080


So really, what I am saying is that rather than only being able to fit a Few Compressed Universes into Our Universe, I wonder why the claim wasn't for several Billion Trillion Gazillion more.

Saving State

In the Land of Computers, we Save Programs all the time. We Save them. And then, we Run them. A Saved Program is different from a Running Program. A Running Program has State, the Registers in the CPU have Value, all the Variables have been Assigned, and so on and so forth.

Two Identical Programs with the Same State using Normal (Non-Quantum) Computers will ALWAYS yield the Same Result. Essentially (as I am defining it), State is all that goes into a Program (it's all of the Inputs). So if a Program would Yield a Different Outcome for the Same Input, The State must be different. And like I said, for a Normal (Non Quantum) Computer that's ALWAYS the case, as anything which would cause the Program to Yield a Different Result is by definition part of State. And with that qualification, I'll let you guess the difference between a Normal Computer and a Quantum Computer.

Aw, heck.

I might as well just tell you now.

Quantum Computers

Quantum Computers rely on Quantum Effects which are not Deterministic. They are Stochastic. And Stochastic means Probabilistic or Random.

Deterministic: 1 + 1 = 2

Stochastic: 1 + 1 = something, maybe, sometimes

Because it's a whole different type of Math (please see the discussion on Axiomatic Systems above), it has its own Strengths and Weaknesses. A Theoretical Strength would be that a Quantum Computer could have a Register (Memory Bank) so large the entire Solution Set could be loaded at once. And the entire Solution Set could be Queried as a Monolithic Whole more or less along the lines of Are you the Particular Solution in the Solution Set that I am looking for? And the downside is that the Quantum Computer is going to return different Answers to the same question left and right. But, hey. Ask it often enough, and one will typically find that the Solution tends to circle about (hover about, probabilistically pointing towards) the Correct Answer.

And because Quantum Computers will be so fast (a future looking statement if ever there was), it won't hardly matter that the same question has to be asked ten, twenty, or fifty-four million times in rapid succession in order to get a feel for the correct answer.

Saving State

It, also, means that it is impossible to Save The State of a Quantum Computer, as they lack Meaningful State. What they have are Quantum States. But that's the same thing as saying The State of a Quantum Computer is Un-Known, Un-Knowable, Un-Reliable, and subject to change: i.e. from a Classical Perspective, Quantum Computers have no Savable State.

Load the Same Program with the Same Inputs and a Different Result is possible.

And in regards to this ambiguity, it doesn't matter if The Program being loaded is something as simple as 1 + 1 = ? or as complex as The Universe = ?

Sooner or later, you're going to get 42 for both.

Uncertainty Remains

So, what does this mean in regards to the Problem of Compression?

Well (assuming Quantum Mechanics), if one Compresses The Universe and then Uncompresses it, after a single Clock Tick, after the smallest increment in Quantum Time, The Original Universe and The Copy will not be the same.

In fact, since Observation Effects a Quantum System, there is no way to confirm The Copy is accurate even without the passage of time.

So, sure, one can make a Copy of The Universe... maybe, possibly, who knows? But even if one did, The Copy would differ from The Original immediately if not sooner, as we would have no way of knowing if The Copy was exact or not, you know, if there was an Error In Transcription or not.

Archival Quality

Given that a Quantum Universe (is there any other kind) evolves over Time, one might imagine (or certainly, I might imagine) that any Archived Copy would degrade over time due to Quantum Effects, that the Bits Stored in Memory would change over Time due to Quantum effects.

But I think if enough Quantum States were used to Store Each Bit, then some sort of stability could be reached. Certainly, that happens at the Macro Scale of Every Day Life. And I believe such stability could be (and no doubt, will be) achieved close to The Quantum Level: say, by using a thousand Quantum States to store Each Bit, which would be more than enough to store a Copy of The Universe in itself, given the type of Compression that's likely.

It's A Tie

Well, the Winner in any Mental Game such as this is always, hard to say, but I would say it is a tie.

Storing a Copy of The Universe in The Universe itself (but not as itself, which would be The Trivial Case) is Theoretically Possible... but more than a little impractical.

The Universe As A Hard Drive

So, let's recap the discussion and assume for metaphor's sake that The Universe is a Hard Drive. Then, what am I saying?

• The Hard Drive can be Compressed.
• But then, storing The Compressed Information on The Hard Drive, obviously changes The Hard Drive.
• Any Copies Are Useless.
• Fidelity of Transcription cannot be assured.
• Each Copy will behave differently moving forward.
  • So really, are they even Copies of one another?

The Universe as a Book

If Computer Hard Drives are not your thing, perhaps using a Book as a Metaphor would be more to your liking.

• It's easy enough to Copy a Book into a smaller section of itself.
• Just Write in the margins.
• But such an activity tends to change the Reading experience.
• Copying Changes The Words
• As the Words are Read, one will find that they differ from the Words used in a different Copy of the same Book.

Those Crazy Quantums

One final thing I will say about Compression is that Quantum Math does not work the same as Classical Math. And I will not go into that here, as it may well be the subject of my next rant.

Suffice to say, in Quantum Math:

That which is Easy becomes Hard.

And that which is Hard becomes Easy.