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JJ
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Replying to Avatar Gigi

> One luminary clock against the sky

> Proclaimed the time was neither wrong nor right.

>

> —Robert Frost, *Acquainted with the Night* (1928)

> Time is still the great mystery to us. It is no more than a concept;

> we don't know if it even exists...

>

> —Clifford D. Simak, *Shake­speare's Planet* (1976)

Time is money, or so the saying goes. It follows that money is also

time: a repre­sen­ta­tion of the collec­tive economic energy stored by

humanity. However, the link between time and money is more intri­cate

than it might seem at first. If money requires no time to create, it

doesn't work as money very well, or not for long. More profoundly, as we

shall see, keeping track of things in the infor­ma­tional realm always

implies keeping track of time.

As soon as money goes digital, we have to agree on a *defin­i­tion of

time*, and herein lies the whole problem. You might think telling the

time is as easy as glancing at whatever clock is nearby, and you would

be right when it comes to everyday tasks. But when it comes to

synchro­nizing the state of a global, adver­sarial, distrib­uted

network, telling the time becomes an almost intractable problem. How do

you tell the time if clocks can't be trusted? How do you create the

concept of a singular time if your system spans the galaxy? How do you

measure time in a timeless realm? And what is time anyway?

To answer these questions, we will have to take a closer look at the

concept of time itself and how Bitcoin makes up its own time: block

time — more commonly known as *block height*. We will explore why the

problem of timekeeping is intimately related to keeping records, why

there is no absolute time in a decen­tral­ized system, and how Bitcoin

uses causality and unpre­dictability to build its own sense of now.

Timekeeping devices have trans­formed civiliza­tions more than once. As

Lewis Mumford pointed out in 1934: "The clock, not the steam-engine, is

the key-machine of the modern indus­trial age." Today, it is again

a timekeeping device that is trans­forming our civiliza­tion: a clock,

not computers, is the true key-machine of the modern infor­ma­tional

age. And this clock is Bitcoin.

## Keeping Track of Things

> Let the child learn to count things, thus getting the notion of

> number. These things are, for the purpose of counting, consid­ered

> alike, and they may be single objects or groups.

>

> —David Eugene Smith, *The Teaching of Elemen­tary Mathe­matics* (1900)

Very broadly speaking, there are two ways to keep track of things:

physical tokens and ledgers. You can either use real-world artifacts

directly, e.g., give someone a sea shell, a coin, or some other tangible

*thing*, or you can repli­cate the state of the world by writing down

what happened on a piece of paper.

Imagine you are a shepherd and want to make sure that your whole flock

returned home. You can put a collar on each sheep, and as soon as

a sheep returns home, you simply remove the collar and hang it up in

your shed. If you have one hanger for every collar, you will know that

every sheep returned safely as soon as all hangers are filled. Of

course, you can also count them and keep a list. However, you will have

to make sure to create a new list every time you start counting, and you

will also have to make sure not to count a single sheep twice (or not at

all).

Money is essen­tially a tool to keep track of who owes what to whom.

Broadly speaking, every­thing we have used as money up to now falls into

two categories: *physical* artifacts and *infor­ma­tional* lists. Or, to

use more common parlance: tokens and ledgers.

![]()

It is impor­tant to realize the inherent differ­ence of these

categories, so let me point it out explic­itly: The first

method — a physical token — *directly* repre­sents the state of

things. The second one — a ledger — *indirectly* reflects the state

of things. Each comes with advan­tages and disad­van­tages. For example,

tokens are physical and distrib­uted; ledgers are infor­ma­tional and

central­ized. Tokens are inher­ently trust­less; ledgers are not.

In the digital realm — no matter how intensely marketing gurus try to

convince you of the opposite — we can only use ledgers. It is an

*infor­ma­tional* realm, not a physical one. Even if you call a certain

kind of infor­ma­tion a "token," it is still a malleable piece of

infor­ma­tion, written down on a hard drive or some other medium that

can hold infor­ma­tion, effec­tively rendering it an infor­ma­tional

record.

The ledger-like nature of all digital infor­ma­tion is the root cause of

the double-spend problem. Infor­ma­tion never repre­sents the state of

the world *directly*. Further, the movement of infor­ma­tion implies

copying. Infor­ma­tion exists in one place, and to "move" it, you have

to copy it to another place and erase it at its origin. This problem

doesn't exist in the physical realm. In the physical realm, we can

actually move things from A to B. The infor­ma­tional realm doesn't have

this property. If you want to "move" infor­ma­tion from list A to list

B, you have to copy it from A to B. There is no other way.

Another way to think about it is in terms of unique­ness. Physical

tokens are unique compos­ites of atoms whose assembly is not easily

replic­able. Pure infor­ma­tion does not have this property. If you can

read the infor­ma­tion, you can also copy it perfectly. Practi­cally

speaking, it follows that physical tokens are unique, and digital tokens

are not. I would even argue that "digital token" is a misnomer. A token

might repre­sent secret infor­ma­tion, but it will never repre­sent

unique, singular, uncopy­able infor­ma­tion.

This differ­ence in proper­ties shows that there really is no way to

"hand over" infor­ma­tion. It is impos­sible to pass on a digital token

like you would pass on a physical one since you can never be sure if the

original owner destroyed the infor­ma­tion on his end. Digital tokens,

like all infor­ma­tion, can only be spread, like an idea.

> ... if you have an apple and I have an apple, and we swap

> apples — we each end up with only one apple. But if you and I have

> an idea and we swap ideas — we each end up with two ideas.

>

> —Charles F. Brannan (1949)

Physical tokens — what we call physical bearer assets, or

"cash" — are free from this dilemma. In the real world, if you hand me

a coin, your coin is gone. There is no magical dupli­ca­tion of the

coin, and the only way to give it to me is to physi­cally hand it over.

The laws of physics do not allow you to double-spend it.

While double-spending does exist in the non-digital realm — George

Parker, a con artist who famously "double-spent" the Brooklyn Bridge and

other landmarks comes to mind — it requires elabo­rate decep­tion and

gullible buyers. Not so in the digital realm.

In the digital realm, because we are always dealing with

*infor­ma­tion,* double-spending is an *inherent* problem. As everyone

who ever copied a file or used copy-and-paste knows, infor­ma­tion is

something that you can copy *perfectly*, and it is not bound to the

medium that hosts it. If you have a digital photo­graph, for example,

you can copy it a million times, store some copies on a USB stick, and

send it to thousands of different people. Perfect copies are possible

because infor­ma­tion allows for flawless error correc­tion, which

elimi­nates degra­da­tion. And to top things off, there is virtu­ally no

cost to dupli­ca­tion and no way to tell what the original was.

Again: when it comes to infor­ma­tion, copying is all there is. There

simply is no way to *move* digital infor­ma­tion from A to B.

Infor­ma­tion is always *copied* from A to B, and if the copying process

was successful, the original copy of A is deleted. This is why the

double-spending problem is so tricky. Absent of a central authority,

there is no way to move *anything* from A to B in a trust­less manner.

You always have to trust that the original will be deleted. A natural

side-effect is that, when it comes to digital infor­ma­tion, it is

*impos­sible* to tell how many copies are in existence and where these

copies might be.

Because of this, using digital "tokens" as money can not and will never

work. Since tokens derive their relia­bility from being hard to

repro­duce as a result of their unique physical construc­tion, this

advan­tage disap­pears in the digital realm. In the digital realm,

tokens cannot be trusted. As a result of the nature of infor­ma­tion's

intrinsic proper­ties, the only viable format for digital money is not

a token but a ledger — which brings us to the problem of time.

## Tokens Are Timeless, Ledgers Are Not

> For the things seen are tempo­rary, but the things unseen are

> everlasting.

>

> —Paul of Tarsus, *Corinthians* 4:18b

When it comes to physical tokens, the time of a trans­ac­tion does not

matter. You either have the coins in your pocket, or you don't; you can

either spend them, or you can't. The simple act of posses­sion is the

only prereq­ui­site for spending. The laws of nature take care of the

rest. In that sense, physical tokens are trust­less and timeless.

When it comes to ledgers, physical posses­sion falls to the wayside.

Whoever is in control of the ledger needs to make sure that things are

*in order*. What is other­wise given by physical laws, namely that you

can't spend money that you don't have and you can't spend money that you

have already spent previ­ously, has to be enforced by man-made rules. It

is these rules that govern the orderly opera­tion and mainte­nance of

a ledger, not physical laws.

Moving from physical laws to man-made rules is the crux of the matter.

Man-made rules can be bent and broken, physical laws not so much. For

example, you can't simply "make up" a physical gold coin. You have to

dig it out of the ground. You can, however, absolutely make up a gold

coin on paper. To do this, you simply add an entry to the ledger and

give yourself a couple of coins. Or, in the case of central banks,

simply add a couple trillion with a few computer keystrokes. (Fancy

finan­cial people call this "Rehypoth­e­ca­tion," "Fractional Reserve

Banking," or "Quanti­ta­tive Easing" — but don't be fooled, it's all

the same: making up money.)

To keep ledgers and those who manip­u­late them honest, regular,

indepen­dent audits are required. The ability to account for every

single entry in a ledger is not a luxury. Auditors need to be able to go

over the books — backward in time — to keep ledgers honest and

functioning. Without reliable timestamps, verifying the internal

consis­tency of a ledger is impos­sible. A mecha­nism to estab­lish an

unambiguous order is essen­tial.

Without an absolute sense of time, there is no way to have a defined

order of trans­ac­tion. And without a defined order of trans­ac­tions,

the rules of a ledger can not be followed. How else can you make sure

how much money you actually have? How else can you make sure that things

are *in order*?

The distinc­tion between tokens and ledgers highlights the neces­sity

for keeping track of time. In the physical realm, coins are timeless

artifacts that can be exchanged without oversight. In the digital realm,

coinstamping requires timestamping.

## Centralized Coinstamping

> Time: a great engraver, or eraser.

>

> —Yahia Lababidi (b. 1973)

The common way to solve the double-spending problem — the problem of

making sure that a digital transfer only happens once — is to have

a central list of trans­ac­tions. Once you have a central list of

trans­ac­tions, you have a single ledger that can act as the sole source

of truth. Solving the double-spending problem is as easy as going

through the list and making sure that every­thing adds up correctly.

This is how PayPal, Venmo, Alipay, and all the banks of this

world — including central banks — solve the double-spending problem:

via central authority.

> The problem of course is the payee can't verify that one of the owners

> did not double-spend the coin. A common solution is to intro­duce

> a trusted central authority, or mint, that checks every trans­ac­tion

> for double-spending. \[...\] The problem with this solution is that

> the fate of the entire money system depends on the company running the

> mint, with every trans­ac­tion having to go through them, just like

> a bank.

>

> —Satoshi Nakamoto (2009)

It is worth pointing out that Satoshi didn't manage to make

infor­ma­tion non-copyable. Every part of bitcoin — its source code,

the ledger, your private key — can be copied. All of it can be

dupli­cated and tampered with. However, Satoshi managed to build

a system that makes rule-breaking copies completely and utterly useless.

The Bitcoin network performs an intri­cate dance to decide which copies

are useful and which aren't, and it is this dance that brings scarcity

into the digital realm. And like with every dance, a temporal measuring

stick is required to dictate the rhythm.

Even a central­ized ledger can only solve the double-spending problem if

it has a consis­tent way to keep track of time. You always need to know

who gave how much to whom and, most impor­tantly: *when*. In the realm

of infor­ma­tion, there is no coin-stamping without time-stamping.

> It must be stressed that the *impos­si­bility of associ­ating events

> with points in time* in distrib­uted systems was the unsolved problem

> that precluded a decen­tral­ized ledger from ever being possible until

> Satoshi Nakamoto invented a solution.

>

> —Gregory Trubet­skoy (2018)

## Decentralized Time

> Time brings all things to pass.

>

> —Aeschylus (525 BC -- 456 BC)

Time and order have a very intimate relation­ship. As Leslie Lamport

pointed out in his 1978 paper *Time, Clocks, and the Ordering of Events

in a Distrib­uted System*: "The concept of time is funda­mental to our

way of thinking. It is derived from the more basic concept of the order

in which events occur." Absent a central point of coordi­na­tion,

seemingly intuitive notions of "before," "after," and

"simul­ta­ne­ously" break down. In the words of Lamport: "the concept of

'happening before' defines an invariant partial ordering of the events

in a distrib­uted multi­process system."

Phrased differ­ently: Who should be in charge of time if putting someone

in charge is not allowed? How can you have a reliable clock if there is

no central frame of refer­ence?

You might think that solving this problem is easy because everyone could

just use their own clock. This only works if every­one's clock is

accurate, and, more impor­tantly, everyone plays nice. In an

adver­sarial system, relying on individual clocks would be a disaster.

And, because of relativity, it does not work consis­tently across space.

As a thought exper­i­ment, imagine how you could cheat the system if

everyone was in charge of keeping the time for themselves. You could

pretend that the trans­ac­tion you're sending now is actually from

yesterday — it just got delayed for some reason — thus, you would

still have all the money that you've spent today. Because of the

asynchro­nous commu­ni­ca­tion that is inherent in every decen­tral­ized

system, this scenario is more than a theoret­ical thought exper­i­ment.

Messages do indeed get delayed, timestamps are inaccu­rate, and thanks

to relativistic effects and the natural speed limit of our universe, it

is anything but easy to tell apart the order of things absent of

a central authority or observer.

> Who's there? Knock knock.

>

> —An Asynchro­nous Joke

To better illus­trate the impos­si­bility of the problem, let's look at

a concrete example. Imagine that you and your business partner both have

access to your company bank account. You do business all over the world,

so your bank account is in Switzer­land, you are in New York, and your

business partner is in Sydney. For you, it is January 3^rd^, and you are

enjoying a beautiful Sunday evening at your hotel. For her, it's Monday

morning already, so she decides to buy break­fast using the debit card

of your shared bank account. The cost is \$27. The avail­able balance is

\$615. The local time is 8:21 am.

At the same time, you are about to pay for your stay with another debit

card linked to the same bank account. The cost is \$599. The avail­able

balance is \$615. The local time is 5:21 pm.

![]()

So it comes to be that — at exactly the same moment — you both swipe

the card. What happens? (Dear physi­cists, please excuse my use of "the

same moment" — we will ignore relativistic effects and the fact that

there is no absolute time in our universe for now. We will also ignore

that the concept of synchro­nous events doesn't really exist. Bitcoin is

compli­cated enough as it is!)

The central ledger at your bank will probably receive one trans­ac­tion

before the other one, so one of you will be lucky, the other not so

much. If the trans­ac­tions happen to arrive in the same

*tick* — let's say in the same millisecond — the bank would have to

decide who gets to spend the money.

Now, what would happen if there was no bank? Who decides who was the

first one to swipe? What if it wasn't only you two, but hundreds or even

thousands of people coordi­nating? What if you didn't trust those

people? What if some of those people are trying to cheat, e.g., by

setting their clocks back so that it looks like they spent the money

a couple of minutes earlier?

> A time-related tool \[is\] needed to estab­lish a canon­ical ordering

> and to enforce a unique history in the absence of any central

> coordi­nator.

>

> —Giacomo Zucco, [*Discov­ering

> Bitcoin*](https://bitcoinmagazine.com/articles/discovering-bitcoin-a-brief-overview-from-cavemen-to-the-lightning-network)

> (2019)

This problem is *precisely* why all previous attempts of digital cash

required a central­ized registry. You always had to trust someone to

correctly identify the order of things. A central­ized party was

required to keep the time.

Bitcoin solves this problem by re-inventing time itself. It says no to

seconds and yes to blocks.

## Keeping the Time, One Block at a Time

> Time's glory is to calm contending kings,

> To unmask false­hood and bring truth to light,

> To stamp the seal of time in aged things,

> To wake the morn and sentinel the night,

> To wrong the wronger till he render right;

>

> —William Shake­speare, *The Rape of Lucrece* (1594)

All clocks rely on periodic processes, something that we might call a

"tick." The familiar *tick-tock* of a grand­fa­ther's clock is, in

essence, the same as the molec­ular-atomic buzzing of our modern Quartz

and Caesium clocks. Something swings — or oscil­lates — and we simply

count these swings until it adds up to a minute or a second.

For large pendulum clocks, these swings are long and easy to see. For

smaller and more special­ized clocks, special equip­ment is required.

The frequency of a clock — how often it ticks — depends on its

use-case.

Most clocks have a fixed frequency. After all, we want to know the time

*precisely*. There are, however, clocks that have a variable frequency.

A metronome, for example, has a variable frequency that you can set

before you make it tick. While a metronome keeps its pace constant once

it is set, Bitcoin's time varies for each tick because its internal

mecha­nism is proba­bilistic. The purpose, however, is all the same:

keep the music alive, so the dance can continue.

| Clock | Tick Frequency |

| --------------------------|-----------------------------------------|

| Grandfather's clock | ~0.5 Hz |

| Metronome | ~0.67 Hz to ~4.67 Hz |

| Quartz watch | 32768 Hz |

| Caesium-133 atomic clock | 9,192,631,770 Hz |

| Bitcoin | 1 block (0.00000192901 Hz* to ∞ Hz**) |

\* first block (6 days)

\*\* timestamps between blocks can show a negative delta

The fact that Bitcoin is a clock is hiding in plain sight. Indeed,

Satoshi points out that the Bitcoin network as a whole acts as a clock,

or, in his words: a distrib­uted timestamp server.

> In this paper, we propose a solution to the double-spending problem

> using a peer-to-peer distrib­uted timestamp server to generate

> compu­ta­tional proof of the chrono­log­ical order of trans­ac­tions.

>

> —Satoshi Nakamoto (2009)

That timestamping was the root problem to be solved is also apparent by

examining the refer­ence at the end of the Bitcoin whitepaper. Out of

the eight refer­ences in total, three are about timestamping:

- *How to time-stamp a digital document* by S. Haber, W.S.

Stornetta (1991)

- *Improving the efficiency and relia­bility of digital time-stamping*

by D. Bayer, S. Haber, W.S. Stornetta (1992)

- *Design of a secure timestamping service with minimal trust

require­ments* by H. Massias, X.S. Avila, and J.-J. Quisquater

(May 1999)

As Haber and Stornetta outlined in 1991, digital time-stamping is about

compu­ta­tion­ally practical proce­dures that make it infea­sible for

a user — or an adver­sary, for that matter — to either back-date or

forward-date a digital document. Contrary to physical documents, digital

documents are easy to tamper with, and the change doesn't neces­sarily

leave any tell-tale signs on the physical medium itself. In the digital

realm, forgeries and manip­u­la­tions can be perfect.

The malleable nature of infor­ma­tion makes time-stamping digital

documents an elabo­rate and sophis­ti­cated process. Naive solutions do

not work. Take a text document, for example. You can't simply add the

date at the end of the document since everyone — including

yourself — could simply change the date in the future. You could also

make up any date in the first place.

## Time is a Causal Chain

> In an extreme view, the world can be seen as only connec­tions,

> nothing else.

>

> —Tim Berners-Lee, *Weaving the Web* (1999)

Making up dates is a general problem, even in the non-digital realm.

What is known in the kidnap­ping world as "Authen­ti­ca­tion by

Newspaper" is a general solution to the problem of arbitrary timestamps.

![]()

This works because a newspaper is hard to fake and easy to verify. It is

hard to fake because today's front page refers to yester­day's events,

events that could not have been predicted by the kidnapper if the

picture would be weeks old. By proxy of these events, the picture is

proof that the hostage was still alive on the day the newspaper came

out.

This method highlights one of the key concepts when it comes to time:

*causality*. The arrow of time describes the causal relation­ship of

events. No causality, no time. Causality is also the reason why

crypto­graphic hash functions are so crucial when it comes to

timestamping documents in cyber­space: they intro­duce a causal

relation­ship. Since it is practi­cally impos­sible to create a valid

crypto­graphic hash without having the document in the first place,

a causal relation­ship between the document and the hash is intro­duced:

the data in question existed first, the hash was gener­ated later. In

other words: without the compu­ta­tional irreversibility of one-way

functions, there would be no causality in cyber­space.

![]()

With this causal building block in place, one can come up with schemes

that create a chain of events, causally linking A to B to C and so on.

In that sense, secure digital timestamping moves us from a timeless

place in the ether into the realm of digital history.

> Causality fixes events in time. If an event was deter­mined by certain

> earlier events, and deter­mines certain subse­quent events, then the

> event is sandwiched securely into its place in history.

>

> —Bayer, Haber, Stornetta (1992)

It goes without saying that causality is of the utmost impor­tance when

it comes to economic calcu­la­tions. And since a ledger is nothing but

the embod­i­ment of economic calcu­la­tions of multiple cooper­ating

partic­i­pants, causality is essen­tial for every ledger.

> We need a system for partic­i­pants to agree on a single history

> \[...\]. The solution we propose begins with a timestamp server.

>

> —Satoshi Nakamoto (2009)

It is fasci­nating that all of the puzzle pieces that make Bitcoin work

did already exist. As early as 1991, Haber and Stornetta intro­duced two

schemes that make it "diffi­cult or impos­sible to produce false

time-stamps." The first relies on a trusted third party; the second,

more elabo­rate "distrib­uted trust" scheme, does not. The authors even

identi­fied the inherent problems of trusting a causal chain of events

and what would be required to rewrite history. In their words, "the only

possible spoof is to prepare a fake chain of time-stamps, long enough to

exhaust the most suspi­cious challenger that one antic­i­pates."

A similar attack vector exists in Bitcoin today, in the form of a 51%

attack (more on that in a later chapter).

One year later, Bayer, Haber, and Stornetta built upon their previous

work and proposed to use trees instead of simple linked lists to tie

events together. What we know as *Merkle Trees* today are simply

efficient data struc­tures to create a hash from multiple hashes

deter­min­is­ti­cally. For timestamping, this means that you can

efficiently bundle multiple events into one "tick." In the same paper,

the authors propose that the distrib­uted trust model intro­duced in

1991 could be improved by carrying out a recur­ring "world champi­onship

tourna­ment" to deter­mine a single "winner" who widely publishes the

resulting hash somewhere public, like a newspaper. Sounds familiar?

As we shall see, it turns out that newspa­pers are also an excel­lent

way to think about the second ingre­dient of time: unpre­dictability.

## Causality and Unpredictability

> Time is not a reality \[*hupostasis*\], but a concept \[*noêma*\] or

> a measure \[*metron*\]...

>

> —Antiphon the Sophist, *On Truth* (3rd century AD)

While causality is essen­tial, it is not suffi­cient. We also need

*unpre­dictability* for time to flow. In the physical realm, we observe

natural processes to describe the flow of time. We observe a general

increase in entropy and call that the arrow of time. Even though the

laws of nature seem to be obliv­ious in regards to the direc­tion of

this arrow in most cases, certain things can't be undone, practi­cally

speaking. You can't unscramble an egg, as they say.

Similarly, entropy-increasing functions are required to estab­lish an

arrow of time in the digital realm. Just like it is practi­cally

impos­sible to unscramble an egg, it is practi­cally impos­sible to

unscramble a SHA256 hash or crypto­graphic signa­ture.

Without this increase in entropy, we could go forward and backward in

time willy-nilly. The sequence of Fibonacci Numbers, for example, is

causal but not entropic. Every number in the sequence is caused by the

two numbers that came before it. In that sense, it is a causal chain.

However, it is not useful to tell the time because it is entirely

predictable. In the same way that a kidnapper can't simply stand in

front of a calendar that shows the current date, we can't use

predictable processes as proof of time. We always have to rely on

something that can't be predicted in advance, like the front page of

today's newspaper.

Bitcoin relies upon two sources of unpre­dictability: trans­ac­tions and

proof-of-work. Just like nobody can predict what tomor­row's newspaper

will look like, nobody can predict what the next Bitcoin block will look

like. You can't predict what trans­ac­tions are going to be included

because you can't predict what trans­ac­tions are going to be broad­cast

in the future. And, more impor­tantly, you can't predict who will find

the solution to the current proof-of-work puzzle and what this solution

will be.

In contrast to the kidnap­per's newspaper, however, proof-of-work is

physi­cally linked to what happened *directly*. It is not just a record

of an event — it is the event itself. It is the proba­bilistic

direct­ness of proof-of-work that removes trust from the equation. The

only way to find a valid proof-of-work is by making a lot of guesses,

and making a single guess takes a little bit of time. The proba­bilistic

sum of these guesses is what builds up the timechain that is Bitcoin.

By utilizing the causality of hash-chains and the unpre­dictability of

proof-of-work, the Bitcoin network provides a mecha­nism for

estab­lishing an indis­putable history of events witnessed. Without

causality, what came before and what came after is impos­sible to tease

apart. Without unpre­dictability, causality is meaning­less.

What is intuitively under­stood by every kidnapper was explic­itly

pointed out by Bayer, Haber, and Stornetta in 1992: "To estab­lish that

a document was created after a given moment in time, it is neces­sary to

report events that could not have been predicted before they happened."

![]()

It is the combi­na­tion of causality and unpre­dictability that allows

the creation of an artifi­cial "now" in the other­wise timeless digital

realm. As Bayer, Haber, and Stornetta point out in their 1991 paper:

"the sequence of clients requesting time-stamps and the hashes they

submit cannot be known in advance. So if we include bits from the

previous sequence of client requests in the signed certifi­cate, then we

know that the time-stamp occurred after these requests. \[...\] But the

require­ment of including bits from previous documents in the

certifi­cate also can be used to solve the problem of constraining the

time in the other direc­tion, because the time-stamping company cannot

issue later certifi­cates unless it has the current request in hand."

All the puzzle pieces were already there. What Satoshi managed to do is

put them together in a way that removes the "time-stamping company" from

the equation.

## Proof of Time

> *Causa latet: vis est notis­sima.*

> The cause is hidden, but the result is known.

>

> —Ovid, *Metamor­phoses*, IV. 287 (8 AD)

Let us recapit­u­late: to use money in the digital realm, we have to

rely on ledgers. To make ledgers reliable, unambiguous order is

required. To estab­lish order, timestamps are neces­sary. Thus, if we

want to have *trust­less* money in the digital realm, we must remove any

entity that creates and manages timestamps and any single entity that is

in charge of time itself.

It took a genius like Satoshi Nakamoto to realize the solution: "To

imple­ment a distrib­uted timestamp server on a peer-to-peer basis, we

will need to use a proof-of-work system similar to Adam Back's

Hashcash."

We need to use a proof-of-work system because we need something that is

native to the digital realm. Once you under­stand that the digital realm

is infor­ma­tional in nature, the obvious conclu­sion is that

compu­ta­tion is all we have. If your world is made of data,

manip­u­la­tion of data is all there is.

Proof-of-work works in a peer-to-peer setting because it is

*trust­less*, and it is trust­less because it is discon­nected from all

external inputs — such as the readings of clocks (or newspa­pers, for

that matter). It relies on one thing and one thing only: compu­ta­tion

requires work, and in our universe, work requires energy and time.

## Bridging Times

> I know it works for me.

> As we cross the bridge — the burning bridge —

> With flames behind us,

> We front the line.

> It's you and me, baby, against the world.

>

> —Kate Bush, *Burning Bridge* (1985)

Without proof-of-work, one would always run into the Oracle problem

because the physical realm and the infor­ma­tional realm are eternally

discon­nected. The markings on your list of sheep aren't your sheep, the

map is not the terri­tory, and whatever was written in yester­day's

newspaper isn't neces­sarily what happened in the real world. In the

same manner, just because you use a real-world clock to write down

a timestamp doesn't mean that this is actually what the time was.

Put bluntly, there simply is no way to trust that data repre­sents

reality, except if the reality in question is inherent in the data

itself. The brilliant thing about Bitcoin's diffi­culty-adjusted

proof-of-work is that it creates its own reality, along with its own

space and time.

Proof-of-work provides a direct connec­tion between the digital realm

and the physical realm. More profoundly, it is the only connec­tion that

can be estab­lished in a trust­less manner. Every­thing else will always

rely on external inputs.

The diffi­culty to mine a new Bitcoin block is adjusted to make sure

that the thin thread between Bitcoin's time and our time remains intact.

Like clock­work, the mining diffi­culty readjusts every 2016 ticks. The

goal of this readjust­ment is to keep the *average* time between ticks

at ten minutes. It is these ten minutes that maintain a stable

connec­tion between the physical and the infor­ma­tional realm.

Conse­quently, a sense of human time is required to readjust the ticks

of the Bitcoin clock. A purely block-based readjust­ment wouldn't work

since it would be completely discon­nected from our human world, and the

whole purpose of the readjust­ment is to stop us ingenious humans from

finding blocks too fast (or too slow).

As Einstein has shown us, time is not a static thing. There is no such

thing as a universal time we could rely upon. Time is relative, and

simul­taneity is nonex­is­tent. This fact alone makes all

timestamps — especially across large distances — inher­ently

unreli­able, even without adver­sarial actors. (This is why timestamps

of GPS satel­lites have to be adjusted constantly, by the way.)

For Bitcoin, the fact that our human timestamps are impre­cise doesn't

matter too much. It also doesn't matter that we have no absolute

refer­ence frame in the first place. They only have to be precise enough

to calcu­late a somewhat reliable average across 2016 blocks. To

guarantee that, a block's "meatspace" timestamp is only accepted if it

fulfills two criteria:

1. The timestamp has to be greater than the median timestamp of the

previous 11 blocks.

2. The timestamp has to be less than the network-adjusted time plus two

hours. (The "network-adjusted time" is simply the median of the

timestamps returned by all nodes connected to you.)

In other words, the diffi­culty-adjust­ment is about keeping a constant

time, *not* a constant level of security, diffi­culty, or energy

expen­di­ture. This is ingenious because good money *has* to be costly

in time, not energy. Linking money to energy alone is not suffi­cient to

produce absolute scarcity since every improve­ment in energy

gener­a­tion would allow us to create more money. Time is the only thing

we will never be able to make more of. It is *The Ultimate Resource*, as

Julian Simon points out. This makes Bitcoin the ultimate form of money

because its issuance is directly linked to the ultimate resource of our

universe: time.

The diffi­culty adjust­ment is essen­tial because, without it, the

internal clock of Bitcoin would tend to go faster and faster as more

miners join the network or the efficiency of mining devices improves. We

would quickly run into the coordi­na­tion problem that Bitcoin sets out

to solve. As soon as the block time falls below a certain threshold,

say, 50 millisec­onds, it would be impos­sible to agree on a shared

state, even in theory. It takes light around 66 millisec­onds to travel

from one side of the earth to the other. Thus, even if our computers and

routers were perfect, we would be back at square one: given two events,

it would be futile to tell which event happened before and which event

happened after. Without a periodic adjust­ment of Bitcoin's ticks, we

would run into the hopeless problem of solving the coordi­na­tion

problem faster than the speed of light. Time is also at the root of the

problem of crypto­graphic insta­bility, which was outlined in Chapter 1.

Cryptog­raphy works because of an asymmetry in time: it takes a short

time to build a crypto­graphic wall and a long time to break it

down — unless you have a key.

Thus, in some sense, proof-of-work — and the diffi­culty adjust­ment

that goes along with it — artifi­cially slows down time, at least from

the perspec­tive of the Bitcoin network. In other words: Bitcoin

enforces an internal rhythm whose low frequency allows ample buffer for

the latency of commu­ni­ca­tions between peers. Every 2016 blocks,

Bitcoin's internal clock readjusts, so that — on average — only one

valid block will be found every 10 minutes.

From an outside perspec­tive, Bitcoin funnels the chaotic mess of

globally broad­cast asynchro­nous messages into a parallel universe,

restricted by its own rules and its own sense of space and time.

Trans­ac­tions in the mempool are timeless from the point-of-view of the

Bitcoin network. Only when a trans­ac­tion is included in a valid block

does it get assigned a time: the number of the block it is included in.

![]()

It is hard to overstate how elegant a solution this is. Once you are

able to create your own defin­i­tion of time, deciphering what came

before and what came after is trivial. In turn, agreeing on what

happened, in what order, and, conse­quently, who owes what to whom,

becomes trivial as well.

The diffi­culty adjust­ment makes sure that the *ticks* of Bitcoin's

internal metronome are somewhat constant. It is the conductor of the

Bitcoin orchestra. It is what keeps the music alive.

But why can we rely on work in the first place? The answer is

three­fold. We can rely on it because compu­ta­tion requires work, work

requires time, and the work in question — guessing random

numbers — can not be done efficiently.

## Probabilistic Time

> Time forks perpet­u­ally toward innumer­able futures.

>

> —Jorge Luis Borges, *The Garden of Forking Paths* (1941)

Finding a valid nonce for a Bitcoin block is a guessing game. It is very

much like rolling a die, or flipping a coin, or spinning a roulette

wheel. You are, in essence, trying to find a beyond-astro­nom­i­cally

large random number. There is no progress toward finding a solution. You

either hit the jackpot, or you don't.

Every time you flip a coin, the chance of it coming up heads or tails is

50% — even if you flipped it twenty times before, and it came up heads

every time. Similarly, every time you wait for a bitcoin block to come

in, the chance that it will be found *this second* is \~0.16%. It

doesn't matter when the last block was found. The approx­i­mate waiting

time for the next block is always the same: \~10 minutes.

It follows that every individual tick of this clock is unpre­dictable.

Relative to our human clocks, this clock appears to be sponta­neous and

impre­cise. This is irrel­e­vant, as Gregory Trubet­skoy points out: "It

doesn't matter that this clock is impre­cise. What matters is that it is

the same clock for everyone and that the state of the chain can be tied

unambigu­ously to the ticks of this clock." Bitcoin's clock might be

proba­bilistic, but it isn't illusory.

> Time is an illusion,

> lunchtime doubly so.

>

> —Douglas Adams (1979)

The present moment, however, can absolutely be an illusion in Bitcoin.

Since there is no central authority in the network, strange situa­tions

can arise. While unlikely, it is possible that two valid blocks are found at

the same time (again: apolo­gies to all physi­cists), which will make

the clock tick forward in two different places at once. However, since

the two different blocks will very likely differ in their content, they

will contain two different histo­ries, both equally valid.

This is known as a chain split and is a natural process of Nakamoto

consensus. Like a flock of birds that briefly splits in two only to

merge again, nodes on the Bitcoin network will eventu­ally converge to

a shared history after some time, thanks to the proba­bilistic nature of

guessing.

Nakamoto consensus simply states that the correct history is to be found

in the heaviest chain, i.e., the chain with the most amount of

proof-of-work embedded in it. Thus, if we have two histo­ries A and B,

some miners will try to build upon history A, others will try to build

upon history B. As soon as one of them finds the next valid block, the

other group is programmed to accept that they were on the wrong side of

history and switch over to the heaviest chain — the chain that

repre­sents what actually happened, by defin­i­tion. In Bitcoin, history

is truly written by the victors.

> The payee needs proof that at the time of each trans­ac­tion, the

> majority of nodes agreed it was the first received. \[...\] When there

> are multiple double-spent versions of the same trans­ac­tion, one and

> only one will become valid. The receiver of a payment must wait an

> hour or so before believing that it's valid. The network will resolve

> any possible double-spend races by then.

>

> —Satoshi Nakamoto (2009)

In this simple state­ment lies the secret of the distrib­uted

coordi­na­tion problem. This is how Satoshi solved the problem of the

"simul­ta­neous payment" our ficti­tious business partners encoun­tered

previ­ously. He solved it once and for all, relativistic effects be

damned!

Because of this proba­bilistic nature of Bitcoin's clock, the present

moment — what we call the chain tip — is always uncer­tain. The

past — blocks buried below the chain tip — is ever more certain.

> The more thorough the under­standing needed, the further back in time

> one must go.

>

> —Gordon Clark, *A Chris­tian View of Men and Things*, p. 58. (1951)

Conse­quently, the Bitcoin clock might rewind from time to time, for

some peers, for a tick or two. If your chain tip — the present

moment — happens to lose to a competing chain tip, your clock will

first rewind and then jump forward, overriding the last few ticks that

you thought were history already. If your clock is proba­bilistic, your

under­standing of the past has to be too.

> Tick tock tick tock tick — what is the time?

> Tick tock tick tock... it ends in

> [c619](https://www.blockstream.info/block/000000000000000000095eaf76a73a7986ea2e6a3b0d190fb10ab986b683c619).

> Are you sure this is fine? Are we probably late?

> Absolutes do not matter: before nine there comes

> [eight](https://www.blockstream.info/block/0000000000000000000318291249db2c9b658d087e4f06bcd2ed24481e81533c).

> The clock isn't exact; it sometimes goes in reverse.

> Exact time implies center; that's the root of this curse!

> Yet this clock keeps on ticking, tock-tick and tick-tock,

> there's no profit in tricking; just tick-tock and next block.

>

> —A Funny Little Rhyme on Bitcoin and Time (2020)

## Conclusion

> Time is still one of the great mysteries in physics, one that calls

> into question the very defin­i­tion of what physics is.

>

> —Jorge Cham and Daniel Whiteson: *We Have No Idea: A Guide to the

> Unknown Universe*, pp. 117 -- 118 (2017)

Keeping track of things in the infor­ma­tional realm implies keeping

track of a sequence of events, which in turn requires keeping track of

time. Keeping track of time requires agreeing on a "now" — a moment in

time that eternally links the settled past with the uncer­tain future.

In Bitcoin, this "now" is the tip of the heaviest proof-of-work chain.

Two building blocks are essen­tial for the struc­ture of time: causal

links and unpre­dictable events. Causal links are required to define

a past, and unpre­dictable events are required to build a future. If the

sequence of events would be predictable, it would be possible to skip

ahead. If the individual steps of the sequence aren't linked, it would

be trivial to change the past. Because of its internal sense of time, it

is insanely diffi­cult to cheat Bitcoin. One would have to rewrite the

past or predict the future. Bitcoin's timechain prevents both.

Viewing Bitcoin through the lens of time should make clear that the

"block chain" — the data struc­ture that causally links multiple

events together — is not the main innova­tion. It is not even a new

idea, as is evident by studying the timestamp liter­a­ture of the past.

> A blockchain is a chain of blocks.

>

> —Peter Todd

What is a new idea — what Satoshi figured out — is how to

indepen­dently agree upon a history of events without central

coordi­na­tion. He found a way to imple­ment a decen­tralised

timestamping scheme that (a) doesn't require a time-stamping company or

server, (b) doesn't require a newspaper or any other physical medium as

proof, and (c) can keep the *ticks* more-or-less constant, even when

operating in an environ­ment of ever-faster CPU clock times.

Timekeeping requires *causality*, *unpre­dictability*, and

*coordi­na­tion*. In Bitcoin, *causality* is provided by one-way

functions: the crypto­graphic hash functions and digital signa­tures

that are at the core of the protocol. *Unpre­dictability* is provided by

both the proof-of-work puzzle as well as the inter­ac­tion with other

peers: you can't know in advance what others are doing, and you can't

know in advance what the solution to the proof-of-work puzzle will be.

*Coordi­na­tion* is made possible by the diffi­culty adjust­ment, the

magic sauce that links Bitcoin's time to ours. Without this bridge

between the physical and the infor­ma­tional realm, it would be

impos­sible to agree on a time by relying on nothing but data.

**Bitcoin is time** in more ways than one. Its units are stored time

because they are money, and its network is time because it is

a decen­tral­ized clock. The relent­less beating of this clock is what

gives rise to all the magical proper­ties of Bitcoin. Without it,

Bitcoin's intri­cate dance would fall apart. But with it, everyone on

earth has access to something truly marvelous: Magic Internet Money.

---

This article first appeared on [dergigi.com](https://dergigi.com/2021/01/14/bitcoin-is-time/).

Ha. I can see world events and child births measured by which bitcoin block it was

I got so tired of cracking eggs 12 eggs a day that I just started drinking them by the carton

Replying to Avatar Mostro

⚡ Right now at nostr:npub1hyxet20dqk5nach0kc4a4evydch58dh9pu3x35kl9myhaezn823sd2tug7, nostr:npub1qqqqqqqx2tj99mng5qgc07cgezv5jm95dj636x4qsq7svwkwmwnse3rfkq & nostr:npub1zvyeff7d26lxmhzyh4jlmdjwvvkg5pmd9uxrwa82q45agmr0a0as6rvfj0 are presenting “Privacy, Freedom and Mostro: the return of the cypherpunk.”

“Privacy is necessary for an open society in the electronic age.” -Eric Hughes (1993)

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🔹 Each order uses ephemeral keys.

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Looks very interesting

Very interesting. I'd seen this a few times and ignored it. Thought it was just another bullshit product released mid cycle. It wasn't until I saw this page and dug deeper into it. Ordered a couple. I like how the owner is in control of two or three keys. Unlike fireblocks, where they are in control of 2 of 3 key shards. Did Block manage to "grandma proof" key management? 🤔 thanks!

Hello Metaverse!