A Consciousness is A Dedekind Cut

[ ↓ toc ] Published: 2026-01-16 Updated: 2025-07-26 By: Aditya Athalye

Aiming for last place at the 2025 Berggruen Prize Open Essay Contest, on the theme of consciousness, intelligence, and the nature of mind in an age of advancing artificial systems.

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Contents That which peers, is. That which forefends itself, is. That which slices thinner, is. That which ponders, posits, plays, is. That which senses, is. That which quarrels, is. That which wills, is. That which data inhabits, is. Accountants are our exemplary archetype All databases record state of entities Everything is Process The identity of an entity is the complete life it lives A fact can be true or false What happens when fact and fact collide? Finally, the Two Questions that put the ‘bi’ in the ‘bitemporal’ When did it actually happen? When did we officially record it? No temporal database can contain Reality itself Reality transpires in Dedekind cuts Facts contain observations. Observations are not Reality. Materialised "Reality" depends on who’s asking. The Ones at The Very Edge, are. Epilogue

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Peering into the fishy fisheye lens. "Lomo Walk Mumbai", 2011. (CC BY-SA 4.0, Aditya Athalye.)

That which peers, is.

Forty Three attoseconds. That is how finely we can clock time. Half a proton. That is how finely we can slice distance. 300 trillion digits. That is the current-best precision of Pi. One sense helps us characterize the behaviour of Electrons and other sub-atoms. The other helps us observe ripples in Gravity created by cosmic grains of sand collapsing into themselves eons away in space and time. And with those 3×1014 digits of Pi we could shoot an arrow straight into any literal grain of sand flying anywhere through the known Universe.

High energy physicists, Xenobot creators, meditation masters, number theorists, world-class snipers, the clinically insane, top forensic accountants, psychonauts, superb free divers, toddlers, birthing mothers and other such fringe dwellers access atypical Reality through atypical perception. Like, if I insist to a (Mathematical) Topologist that a straw and a doughnut are not the same "shape", I should fully expect them to look at me funny.

Even so, the sum total of all this variegated human experience—atypical and typical—has transpired through the ages, in an envelope of air and dirt about six feet over and six feet underfoot, on an average, having collectively thought every possible type of thought over and over again. A social being so little that a Large Language Model calculated from reams and reams of textualised approximations of the being’s fecund imagination, motile thought, and churning culture, can emit streams of text that it finds shockingly new and familiar at the same time.

We remain creatures peering ever deeper into spacetime, yet ever fettered by its four dimensions, Ultimate Reality ever moving just beyond our sight.

That which forefends itself, is.

A collection of Top Reasons to stop reading. The rest of the essay falls out of this set of priors—and certainly others which I am unaware of—and dwells on them variously. The Top Reasons:

• As a mere Average Joe programmer—not even a computer scientist—I arrived here because I’ve been trying to model Reality as a Bi-Temporal Database. Studying that sub-subject of Database systems forces a person to ponder the very nature of Time and of Reality itself.
• The Baader-Meinhof phenomenon all but guaranteed that a stray banner ad on Reddit caught my reality-addled brain. That and the fact that I have no free will, only free time and poor impulse control… A fancy essay contest, you say? A slim, slim chance at taking home (up to) USD 50,000? All they need is (up to) ten thousand words of (English) essaying about Consciouness. No problem, ése. After all, as of the banner addling, I had just finished an eleven thousand word essay on temporal data systems. Even my brain knows that ten is less than eleven (on all our number lines).
• A Being is a system. A system’s "will" is "free" within narrow bounds outside of its control or choosing, and gated by sensitivity of measurement within its bounds. Having such limits is not a reductionist model, but rather an expansionist one.
• I subscribe to the TAME model and am "against mind-blindness", as Michael Levin explains. Thermostats also have experiences. All experience is rooted in measurement and sensing, including the experiences of the expert Buddhist meditator, as they work their way through the eight stages of dhyāna until the ultimate (eighth) state of "neither perception, nor non-perception"; a psychological event horizon.
• Tall claims about Large Language Models irk me. No these models will not become "Artificial General Intelligence" (whatever that even means, like "emergent" means whatever it means). Dynamic, mutable, other-sensing, self-modifying systems and cultures will incorporate LLMs as search and discovery engines if they prove to be net-useful, all things considered (such as energy budgets). A single human being is, in fact, such a system and (sub)culture. And human use of LLM technology is subject to what I like to call The Geordi LaForge Paradox. Lt. Cdr. Geordi La Forge, of the USS Enterprise, is the Gen AI-using Engineer Archetype. He uses the Ship’s LLM all the time, not infrequently to solve novel one-off problems (sometimes under life-and-death pressure). However, he is such a successful user only because he can spot incredibly subtle errors and compensate/augment with his own elite training combined with years and years of hands-on field experience. Essentially, he has hard-earned specialist tacit knowledge, which is entirely absent from any static data corpus, no matter how detailed the corpus is.
• In the course of writing this essay, I discovered affinity for pluralism as well as panpsychism. Except for "woo". I absolutely abhor woo, for it is the end of understanding. Understanding requires incessant (re)search (subjective-objective). Peddlers of woo thrive on providing TRUE answers and knowing the ultimate TRUTH, and alas TRUTH-capitalization is defining the zeitgeist even as I type.
• We ought to gladly let "Consciousness" be the Elephant in the room amid we, its blind examiners (who are we and in what ways are we blind?).

And now to address the marketing headline of this essay…. What does the notion of the Dedekind Cut have to do with Consciousness?

That which slices thinner, is.

Luckily, we do not need nuclear reactor powered datacenter-sized computers to suss out intelligent answers, or Answering Intelligences (same thing), to illuminate the notion of Consciousness. Calculating the digits of Pi by hand can paint us a pretty good picture. But that is too much work (we will have to draw a series of many-sided symmetric polygons). And, frankly, the long division it demands is too much arithmetic for me. As it happens, the square root of Two is not only far easier to locate than Pi, it is also just like Pi; Real and Irrational. The perfect body-double.

What is it; the Square Root of Two? Well, since one times one is one, and Two’s square root must by definition multiply itself up to Two, it must sit somewhere between One and Two. That narrows things down, but we can do better. Cut into it and multiply each book-end of the gap once again. Two’s square root is less than 1.5 (which squares to 2.25), but greater than 1.4 (which squares to 1.96). Sharpen the blade. Slice again. Now it is greater than 1.41 and less than 1.42. Keep sharpening and slicing… greater than 1.41421356237 and less than 1.41421356238… and sharper and sharper and sharper.

The square root of Two, it turns out, is an unending quest of finding Interval within Interval within Interval, until both book-ends of some Ultimate Interval collide into a dimensionless object that is, by golly, also an Infinity due to its very construction. A (Mathematical) Singularity. Ditto Pi, which though equally frustrating, is at least the more useful of the two, seeing as it defines any circle, and circular things help us get around the place.

Dedekind cut at square root of two. (Wikimedia Commons).

This is the Dedekind Cut. A Mathematician’s method to locate any given Real number on an unbroken number line from negative infinity, through zero, to infinity. A pointing finger built from an axiomatically defined absence of whatever One True Real number we seek.

Pi and the square root of two, though utterly Irrational, have objective definitions, because they are Real Numbers and every Real number is uniquely identified by the corresponding Dedekind Cut. Yet, Pi remains incalculable. We can keep narrowing our interval until the heat death of the Universe and still not reach the Dedekind Cut that locates it.

Last but not least, is Pi equal to Pi? Depends who’s counting. The mathematician, the physicist, the geometer, the computer’s floating point arithmetic engine, the enlightened mystic, the romantic poet. Though none may agree with the other on the exact value of Pi, none can deny the reality of Pi itself.

We are but creatures consigned to snake ceaselessly about our spacetime, on paths inscribed by Pi-likes, swallowing our own tail, final destination unknown.

That which ponders, posits, plays, is.

For those throwing up a little at the rabidly anthropocentric preface (not to mention the terrible arithmetical puns), fear not. The promised, most inhuman of objects (most inhumane to programmers), The Bi-Temporal Database will be discussed soon. Since that concerns Reality-modeling, I will lay out my as-of-now averment about Reality and Consciousness on the, ah, Table (yes, Database puns also feature).

Assertions:

• Let this assert Reality: Reality is an unbroken, indivisible, and total continuum including every dimension; spacetime and beyond. i.e Reality is everything everywhere all at once. I love that movie.
• Let this assert Perception: Perception is any abstract, contiguous, discrete, ongoing process that approximates the continuum of Reality along one or more dimensions. i.e. Perception models Reality.
• Let this assert Being: Every Being is a bounded system that generates measurements of a specific Reality Model. i.e. Beings model Perception.
• Let this assert Consciousness: Consciousness is a dimensionless event horizon into which collapse all Reality models. It is simultaneously an infinitesimal and a fundamental motive that makes Reality project into all Perception which in turn projects into all Beings. In the limit case, where all Beings meld into an unbroken continuum of total perception, Consciousness is indistinguishable from Reality; a Platonic totality.

In other words, Reality-Consciousness is a continuum subsuming all dimensions including itself. And perception is a function of the folding of this Reality-Consciousness continuum into itself. Just as the continuum of Dedekind Cuts is indistinguishable from the unbroken, continuous universe of Real Numbers, so is a continuum of infinitesimal Consciousnesses indistinguishable from Reality.

Panpsychism by another name, if you will.

If we accept this world-view, then axiomatically, all Beings at all scales exercise perception through direct and indirect measurement of dimensions available to them—spacetime and whatever is revealed after spacetime breaks down at very small values of time and distance. We already know exactly where this cut occurs. We can’t measure past it, yet.

Far from being reductionist, this model is expansionist. It founts the "we" and the "want" in the sentence "We want our perception to seep into every pore of every aspect of whatever we may find". First we know that there is much that we don’t know. Then we slice into what we know. Eventually we cut through it, fully expecting the next unknown to at last show itself.

Dedekind Cut is to Real Number what Event Horizon is to Singularity what Measurement is to Reality what Perception is to Consciouness. One is not the other. Yet one is inseparable from the other, as pure idea and as visceral spacetime. It is why we find Mathematical Structures in Brains, and Brains in Mathematical Structures. And, in limit cases, as perception becomes finer and denser, one becomes indistinguishable from the other.

Pointing Finger shows Moon, but when perception senses pure gravity, where does one begin and the other end? Picture Neo seeing The Matrix.

That which senses, is.

All sensory experience is thus Reality-Consciousness to the extent that it perceives itself in the form of a reality model. Physical Beings may be stated as systems belonging to the four dimensions of spacetime, that are collectively contained in time by the limiting speed of light, and in space by the observable edge of a singularity. That is, consciousness available to such beings is at the event horizon of the spacetime slice of the platonic totality of Reality-Consciousness.

Subjective experience is a specific Being’s reconstruction of the parts of reality it has access to. A Being’s reality-construct is itself made of Dedekind Cuts, thus infinitely detailed, and so one Being cannot transmit it entirely to the other Being within the limits of spacetime that bind them. Beings therefore must approximate each other’s subjective experience by measuring and reconstructing each other’s Reality models, including models of models; recursive infinities such as "I know you know that I know what you know." This property remains conserved across groups of Beings and groups of groups of Beings, and still bigger still more heterogeneous groups. Consequently, all other-experience, including a concrete Being’s experience of shared experience, is approximate, i.e. subjective.

Concretely, this fundamental subjectivity of experience is why A Person cannot ever truly know what it is to be a Bat. We could get pretty close, but the finer we see, the more abstract Bat-ness will be, and there will come a point where the "what it is to be" of Person-ness and Bat-ness are not only part of the same unbroken spectrum of spacetime-experience, but overlap and merge into each other without prejudice.

That which quarrels, is.

The Reality-Consciousness model explains what happens to the deep meditator, the psychonaut, the marathoner in runner’s high, the writer who’s pen is moving at the speed of thought. Attenuating and modulating the nervous system’s usual signal processing removes chatter that competes with other simultaneous, but weaker phenomena available for sensory measurement (perception). Whereas chemically overloading it weakens some energy barriers allowing weak signals to leak and generate perception where they could not, as well as amplifies some weak signals such that they overflow unmodified energy gradients which normally are forbidding, absent the chemical disruption.

This is good, nay great, news. Well, bad news for charlatans, because the great news means there is no such thing as A Chosen And Oh So Special Arbiter Of Access To "Various Higher Planes" Of Consciousness.

Such a Reality-Consciousness continuum axiomatically pervades all beings at all scales of spacetime because all beings cannot help but sense and respond to it. Mere mortal human beings are, in fact, always experiencing the Reality-Consciouness continuum. Our body-system-as-instrument’s calibration determines the qualia that is our experience.

Which is the sort of thinking that makes me want to quarrel with Nick Bostrom’s "How Long Before Superintelligence?", for setting up a fatally flawed premise from the get go. The paper sets up an arbitrary definition of what a "super" intelligence is supposed to be, and then proceeds to fail a group of people on that criteria by the arbitrary standard of "you can’t have real time conversation" with a scientific community. Well, the "CAP theorem" / Brewer’s theorem says this about distributed data systems… You can’t have a real-time globally-consistent conversation with any sufficiently large network because distributed systems are like that.

Just like "Good, Fast, Cheap", pick any two, Brewer’s theorem says "Consistency, Availability, Partition-Tolerance", pick any two. This real-world result flies counter to Bostrom’s paper, which frames superintelligence as a monolithic centrally-synchronised system.

Well, what if I make a bunch of superintelligences talk to each other? The CAP theorem provides that any such collective will be nerfed according to the paper’s very criterion, because "A superintelligence cannot (by the laws of Physics embodied in Brewster’s theorem) have a real-time conversation with a group of superintelligences".

Change the goalposts changes the goals and the rules of goal-making. Donella Meadows wrote (paraphrasing); An entity that can set a system’s goal has power over the system. We set the thermostat. What sets us?

That which wills, is.

What if "What of Free Will?" is the wrong question to ask in the first place?

We humans can no more will ourselves to fly than a fly can will itself to think about the concept of will—to the best of our knowledge, the fly-system does not contain capacity to probe that. It can only probe the sticky-licky delicious precious. Whereas, we non-flies can will objects into being that make us airborne, as well as probe the fly that is probing the sticky-lick delicious precious.

What if Will is simply the amount of (free) energy we can harness, as a species, to turn thought-stuff into material-stuff (and vice-versa). More generally, what if it is free energy that a Being can harness to direct and control their use of spacetime (because all of spacetime is always available to all beings to the degree they can access it).

An ant can lift a multiple of its body weight "normally", presumably with nearly no will at play. A person can will themselves to deadlift half a tonne of mass, but at great cost to the physical integrity of the self. To lift heavier, people, like Ants, need to team up… form collectives that will together. A collective is a collective being, possessing intelligence that is "super" to the constituent unit.

How about other stuff / beings?

Is a virus a being? Is a subducting continental plate a being? Is a star a being? Sharks are older than the rings of Saturn, that are older than trees. Why should the whole species not be deemed a continued Consciousness, four hundred million years and counting? And what is Time even? What is Intelligence? And if it is so smart, why does it need Sleep? What is Life? What is Death? What about Morality, and Ethics, and Justice, and Truth?

"Yes", say interrogators of Physics, Mathematics, Chemistry, Biology, Philosophy, Speculative Fiction, Lawmaking and other such departments of Poetry.

Is an Electron a being? Probably. We have never directly observed an electron. We know of the existence of the entity known as an Electron based on a specific statistical phenomenon within the subatomic soup it inhabits. An Electron is a statistical quantity. Likewise, other subatomic particles and quanta.

Is a Black Hole a being? Probably. We have never directly observed any Singularity. In the Intergalactic Soup, it is an inferred entity; the theorised Absence Of Reality As We Know It. We can perceive its halo of Hawking Radiation, we can feel the gravity waves from its cataclysmic formation eons past. We know it became. We know it is. Yet we cannot look inside. All perception ends at the singularity. Does Consciousness exist at the other side? What is the "other side" of a Singularity even? One can only imagine.

At the very extreme, all constants are facts that remain true from the beginning of time to its end. The limiting speed of light is valid only in this universe, to the best of our current knowledge.

And the implications of that fact vex the Temporal Database Engineer.

That which data inhabits, is.

"What is it to be conscious?" is a hazardous question not unlike pointing at the moon and telling a story about the moon. I can only sketch a story about what it is, heavily influenced by life as a bit-pusher. Mere as my tribe may be, intractable questions about Reality and Time vex us too. Except we traffic not in the Great Truths, but in grimy data.

For one, Time, the strange bedfellow of the Reality-Consciouness continuum is absolutely irksome to us, because it shows up as an insoluble sequencing problem. The limiting speed of light is literally our problem. Various words like Concurrency, Simultaneity, Byzantine Generals, Vector Clocks and the impossibility of totally ordered events are abstract concepts that best the best of us. If you feel queasy, rest assured, I do too, and it’s my job to deal with it.

For another, consciousness is joined at the hip with reality-models; be they the ten thousand year old oral tradition of Australian Aboriginal tribes (ref: longnow.org), or fleeting tiktok trends.

Fads swept the youth of the Sprawl at the speed of light; entire subcultures could rise overnight, thrive for a dozen weeks, and then vanish utterly.

— William Gibson, Neuromancer

Having to model "reality" forces (at least some of) us to confront questions of existence, meaning, meaning of meaning, being-ness, self-awareness and so forth. Especially people making databases, having thoughts about Data and Reality.

All great programmers are artists. And while all good artists copy, great artists steal (thanks, Austin Kleon).

Accountants are our exemplary archetype

The cashier at Temporal Convenience Store K9, just handed us our bill. Oi; where is that 10% discount applicable to our bulk purchase of provisions as loyal customers (it’s going to be a long trip)?!

Now we think that, but we ask politely, because we know there are many civil ways to sort this snafu without shoplifting or violence. Two universally accepted remedies are:

• The cashier has direct authority to fix it, and they may gladly oblige.
• The cashier’s hands are sadly tied. For ERP reasons, accounts alone has authority to issue refunds for bills over a certain value. But we asked nicely so the cashier kindly nods us to accounts, in the backroom.

Odds are that the store people will fix it by issuing two new transactions.

• One transaction to cancel the last bill and reverse the related charge to our spacecard.
• Another transaction issuing the corrected bill, including the discounted amount, with a fresh charge made to our spacecard.

Meanwhile, Temporal Convenience Store K9’s various ledgers have received corresponding debits and credits too, of course. But enough. A programmer, though Poor, is no Fool. One does not simply trespass The Field of Accountants. There be dragons.

So… Back to the DB.

One way or another, the store’s accounting database must tell these facts:

• At TxTime-7543, Cashier-Adric at Store-K9 ISSUED bill ID-13579 having value 100 spacecoin, and charged it to SpaceCard-1337.

• At TxTime-7587, Cashier-Adric at Store-K9 REVERSED bill ID-13579 having value 100 spacecoin, and refunded it to SpaceCard-1337.

• Maaaybe a note about why it was reversed.

• At TxTime-7715, Accounts-Nyssa at Store-K9 ISSUED bill ID-13579-v2 for 90 spacecoin, with a total value of 100 spacecoin minus 10 spacecoin going to discount, and charged 90 spacecoin to SpaceCard-1337.

We call this a temporal data system because it incorporates the passage of time.

• No information is ever modified in-place or deleted.
• New information is always appended.
• To grok the latest state of the accounts, one must read the sequence of all facts recorded in the database.
• Reading a fact updates a separate, current view of the accounts… our "as of now" understanding of the world.
• The "current view" can be rebuilt from scratch, up to any point in time, whether it is "as of now", or "as of last week", or "as of next quarter" (which will be useful only if we add synthetic projected-future events into the database).

So… What to think about in order to design a general-purpose temporal data system that does this for us?

All databases record state of entities

People, things, processes etc. State is the discrete value of some attribute of an entity at a specific point in time.

• Values are timeless and context free (17).
• Attributes provide context ('age'), which we use to suggest and interpret the meaning of a value (= age 17).
• Entities are real or imaginary objects ( Adric) having attributes (age).

Thus, the State of Adric can be stated as: Adric’s age is 17 as of now.

In a current database—which is just a fancy way of saying database—the as of now is implicit. So is the concept of "age is an attribute of the entity Adric". We just call it Schema, in the abstract.

entity	age
Adric	17

Let’s re-state our traditional table as Entity-Attribute-Value (EAV) triplets. Let’s also add a column for time (as we often do) to answer questions like "when was Adric’s age last updated in our database?".

entity	attribute	value	time
Adric	age	17	as-of-date-time

From this kernel shall spring forth our world, wrought of facts and time itself. But first, one must acknowledge that…

All the world’s a stage, And all the men and women merely players; They have their exits and their entrances, And one man in his time plays many parts, His acts being seven ages.

— William Shakespeare, As You Like It, Act-II, Scene-VII, Lines 139-143

As my theater gentlefriends like to say…

Everything is Process

We understand the world in terms of processes. All of Reality is a live process which we want to participate in—control, influence, react, adapt. Ergo, all information is part of some process. Yes, even universal constants like c and PI, which we can confidently assume to be constant only in our observable universe. Because even these came to be after the moment of the big bang, and will remain only until the eventual heat death of the universe (assuming our universe is ever-expanding, and not a bouncing singularity).

It follows that, to understand the world, we must observe and respond to data; information about various attributes of various meaningful aspects of reality, as we perceive it. Said another way, we understand the world by observing and modifying the state of entities over time—the past, the now, and the later. A person’s address, a valve’s current position, the remaining free volume of a container, the trajectory of a comet, one’s fast-emptying savings account.

entity	attribute	value	time
Adric	age	17	as-of-date-time
Adric	address	Foo	as-of-date-time
Adric	bitemporal belief	1	as-of-date-time

The more sophisticated a being is, the more context about entities and entity-relationships it is able to keep alive and/or use simultaneously.

The identity of an entity is the complete life it lives

Never-ending process is the beating heart, the whistling wind, the pulsing quasar, the furious procreation, the tectonic Subduction, the whispered good-bye, the thermodynamic survival instinct of all things. Process is the why of being. One could even say that an entity without id can have no identity.

This is why, to properly identify an entity, we must egolessly maintain an up-to-date mental-model about it. For that, we must continually observe, record, and aggregate a succession of states of the entity in question.

Consequently, knowledge of entity-attributes alone is not sufficient (Adric has age, address, belief). Knowledge of attribute-values is required too (age is x, address is y, belief is z). And without a sense of time, we simply cannot complete the picture.

To make it concrete:

• Every person’s life revolves around their address and we can guess different things about them based on how their address changes.

• You know which Adric is being spoken about because you know

• Adric’s age was 17 last year. Adric’s age is 18 as of now. Adric’s age will be 319 on <specific date>.

• Adric’s address was Foo last year. Adric’s address is Baz as of now. Adric’s address will be Bar after December 2025.

• Adric’s belief in bitemporality was 1% last year. Adric’s belief in bitemporality is 99% as of now.

• Adric’s temporal innocence level was 99% last year. Adric’s temporal innocence level is 1% as of now.

• A reader of this set of facts can confidently determine: As-of-now, Adric is an eighteen year old entity that lives at ‘Baz’, believes strongly in bitemporality, and has nearly no temporal innocence.

E	A	V	as-of-time
Adric	{:age [:time :years]}	17	date-last-year
Adric	{:age [:time :years]}	18	date-now
Adric	{:age [:time :years]}	319	date-future
Adric	{:address [:text :string]}	Foo	date-last-year
Adric	{:address [:text :string]}	Baz	date-now
Adric	{:address [:text :string]}	Bar	date-future
Adric	{:belief [:bitemporality :%]}	1	date-last-year
Adric	{:belief [:bitemporality :%]}	99	date-now
Adric	{:innocence [:temporal :%]}	99	date-last-year
Adric	{:innocence [:temporal :%]}	1	date-now

KEY: E(ntity), A(ttribute), V(alue)

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Having gained this factual understanding, a dear reader may be tempted to further theorise; Adric lost his temporal innocence and eventually ended up living at ‘Bar’, where he always is these days. Of course, to prove such an allegation, the dear reader would have to piece together many more facts about Adric, and show causation, not mere correlation.

The dear reader may happily play temporal sleuth. However, the temporal database and temporal data engineer are not here to judge. Our role is simply to record the facts as presented, without ego, without prejudice, with integrity, so that the temporal data sleuth may use it productively to figure out what happened, when, and why.

For there is more to facts than meets the eye.

"I’m not in the judgment business, Mr. Orr. I’m after facts. And the events of the mind, believe me, to me are facts. When you see another man’s dream as he dreams it recorded in black and white on the electroencephalograph, as I’ve done ten thousand times, you don’t speak of dreams as ‘unreal.’ They exist; they are events; they leave a mark behind them."

— Dr. William Haber

The Lathe of Heaven, Ursula K. Le Guin.

A fact can be true or false

The temporal sleuth knows that one must resolve the reality of a fact by asserting whether it is true or false.

Our facts table can be expressed as something like the table below. Aspiring temporal data engineers will do well to avoid speculating why a fact might have been asserted true or false. Our ilk must simply realise that we can assert facts this way; <statement of fact> is <true/false?> as of <time>.

Each state of the Adric entity can thus be re-written as an assertion of a fact.

• "Adric’s age is 17" is a true fact as of date-last-year.
• "Adric’s age is 17" is a false fact as of date-now.

E	A	V	assert	as-of-time
Adric	{:age [:time :years]}	17	true	date-last-year
Adric	{:age [:time :years]}	17	false	date-now

KEY: E(ntity), A(ttribute), V(alue)

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With just this information, the temporal sleuth can infer that Adric’s age definitely changed at least once sometime between date-last-year and date-now. But how many times, and to what value, is anybody’s guess. For that, we need more temporal observations. Which thickens the plot. For now, we might receive conflicting observations.

What happens when fact and fact collide?

You Won’t Believe This One Trick Accountants Use To Deal With Changing Facts. They never delete old entries from their ledgers, they simply make new "correcting entries" (We established this in our motivating example.).

Earlier, we were told to record that the Adric entity’s age is 17 as of date-last-year. Presently, we are told to make a note that Adric is NOT 17 any more. We have no idea about Adric’s birth date creation date, by the way. We just make a note of assertions of facts about Adric’s age, as we are told.

E	A	V	assert	as-of-time
Adric	{:age [:time :years]}	17	true	date-last-year
Adric	{:age [:time :years]}	17	false	date-now

KEY: E(ntity), A(ttribute), V(alue)

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At this point, if anyone asks for Adric’s age "as of now", the only truth we can tell is "we don’t know". Think about this for a moment. How should we interrogate this temporal data store, to make sense of the information it contains? It’s subtle. Hopefully all the thinky thoughting to come will build a clearer intuition. But we are out of time right now…

Sixty seconds later, we are interrupted and told that Adric is in fact 18, and oh by the way, he was already 18 as of date-now. And does it bother us that we wrote the earlier thing down already? No it doesn’t. We just assert the new fact.

And just like that…

Now if anyone asks for Adric’s age "as of now", we can truthfully answer 18. Because now our table looks like…

E	A	V	assert	as-of-time
Adric	{:age [:time :years]}	17	true	date-last-year
Adric	{:age [:time :years]}	17	false	date-now
Adric	{:age [:time :years]}	18	true	date-now

KEY: E(ntity), A(ttribute), V(alue)

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Similarly, we make note of other facts about Adric as of various dates on the timeline. But let’s add one more key detail… the time at which we made note of the information.

Finally, the Two Questions that put the ‘bi’ in the ‘bitemporal’

Events always occur before they can be recorded. It’s just how nature works. Therefore, we can only ever make a note of a fact, after the fact. And so it comes to pass, that any self-respecting temporal sleuth naturally begins their temporal interrogation with two questions:

When did it actually happen?

Only a fact-sender may lay claim to the time an event occurred. And this timestamp must always travel with the fact. Whether the claimed timestamp is acceptable or not is between the fact-sender and the temporal sleuth. The temporal data store and engineer just make sure it is written down exactly as given.

When did we officially record it?

Only the temporal data store—not even the temporal data engineer—may lay claim to when this happened. For the temporal data engineer is just a fallible puny human who can screw up in so many ways. Making typos. Misreading the clock. Lazily avoiding recording facts until the auditor comes a-calling. Or even forgetting the fact entirely, upon discovery of which fact, the temporal sleuth gets called in to piece together what might have happened.

So, let’s update our temporal data table with the "transaction" time, at which the data store guarantees that it has immutably inscribed a fact.

To ease table-reading life of our fellow our puny humans, we also rearrange the time columns a bit. Now, we can manually read records as follows:

• At Transaction Time t02, the table recorded the following fact:

• As of dt-now, Adric’s :age being 17 stands REDACTED.

• At Transaction Time t03, the table recorded the following fact:

• As of dt-now, Adric’s :age being 18 stands ASSERTED.

tx-time	as-of-time	E	A	V	assert
t01	dt-last-yr	Adric	{:age [:time :years]}	17	true
t02	dt-now	Adric	{:age [:time :years]}	17	false
t03	dt-now	Adric	{:age [:time :years]}	18	true
t04	dt-future	Adric	{:age [:time :years]}	319	true
t05	dt-last-yr	Adric	{:address [:text :string]}	Foo	true
t06	dt-now	Adric	{:address [:text :string]}	Bar	false
t07	dt-now	Adric	{:address [:text :string]}	Baz	true
t08	dt-future	Adric	{:address [:text :string]}	Bar	true
t09	dt-last-yr	Adric	{:belief [:bitemporality :%]}	1	true
t10	dt-now	Adric	{:belief [:bitemporality :%]}	99	true
t11	dt-future	Adric	{:belief [:bitemporality :%]}	0	false
t12	dt-last-yr	Adric	{:innocence [:temporal :%]}	99	true
t13	dt-now	Adric	{:innocence [:temporal :%]}	1	true
t14	dt-future	Adric	{:innocence [:temporal :%]}	33	false

KEY: E(ntity), A(ttribute), V(alue)

---

This brings us to the absurdity of time travel… For things to get better, they have to get weird first.

"Why do you think your mother didn’t notice that reality had changed since last night?" [Dr. Haber]

"Well, she didn’t dream it. I mean, the dream really did change reality. It made a different reality, retroactively, which she’d been part of all along. Being in it, she had no memory of any other. I did, I remembered both, because I was… there… at the moment of the change. This is the only way I can explain it, I know it doesn’t make sense. But I have got to have some explanation or else face the fact that I’m insane." [Mr. Orr]

The Lathe of Heaven, Ursula K. Le Guin.

Actual Time Travel is different each time, because the very act of it interacts with and perturbs Reality. Not being higher dimensional beings, we have evolved to get by, by perceiving very little of very little. To us, convenient fictions are good enough Reality.

No temporal database can contain Reality itself

"The Song" is a convenient fiction.

We love to loop a favourite hit single. Yet…

• A record is not "The Song". All recordings are lossy because all acts of measurement are lossy. That’s just physics.
• A replay is not "The Song". Every replay is the same information yet it is new, because Reality is ever-moving, ever-changing. (Ignoring for a moment the fact that every replay degrades the storage medium—vinyl, compact disk, copper plate, SSD—causing further information loss.)
• Nor are live performances "The Song". Each rendition is different.

Similarly, temporal databases can only mimic Time Travel.

• The experience of Reality can only ever be captured as finite, discrete observations (samples and measurements).
• Therefore, a temporal recording or database can only ever contain approximate observations of Reality.
• Each time we retrieve the observations, we cannot help but reinterpret them because we ourselves have changed in the interval.

We can only ever sing songs about what we believed happened.

Reality transpires in Dedekind cuts

"This Instant" is a convenient fiction.

Every observation of reality exists somewhere inside of an interval, because our means of measurement can only ever approximate the moment of occurrence of an event. The idea of the Dedekind Cut frames this neatly.

A Dedekind cut is a partition of the rationals Q into two subsets A and B such that

1. A is nonempty.
2. A not= Q (equivalently, B is nonempty).
3. If x,y BelongsTo Q, x < y, and y BelongsTo A, then

x
BelongsTo A

. (A is "closed downwards".)

1. If x BelongsTo A, then there exists a y BelongsTo A such that y > x. (A does not contain a greatest element.)

By omitting the first two requirements, we formally obtain the extended real number line.

Remember "Dedekind cut at square root of two."? (Wikimedia Commons).

Why split such philosophical hairs? Why?

Because, we must record temporal facts with proper temporal resolution. For example, an infinitesimal such as a Femtosecond (10-15s) can be…

• Just Right… for that "Femto Laser" Cataract removal or LASIK surgery.
• Waaay over the top… for orchestral arrangements where sub-millisecond (< 10-3s) coordination is more than enough.
• Or too coarse(!)… for Quantum dynamics studies, where incredible things happen in attoseconds (10-18s).

More subtly, because all Temporal Data Processing queries are Interval queries, served by collating facts that happened starting Time X to Time Y.

For example, "Calculate the state of the world as-of some Instant."

To serve this query, we must collate all facts starting from the earliest available ones, right up to whatever as-of time Instant. It could be as-of <some past moment>, or as-of some projected future, or…. as-of this very instant, a.k.a. a now query.

The now query is a special-case as-of query, because now is an expanding query window… ever-increasing "wall-clock time". It means our computer’s temporal resolution, which the temporal database relies on, must suit that of incoming facts. My cheap wristwatch will botch your Formula One lap times.

Fun fact: The now query returns a Current Database.

Facts contain observations. Observations are not Reality.

"Facts" are a convenient fiction.

To fact-find, we must observe. Observation requires measurement. Measurements are inherently lossy. Consequently, no collection of facts, no matter how fine-grained can ever capture Reality as it actually happened.

Besides, facts depend on who’s observing. Having experienced the world a bit, we have doubtless realised that, routinely…

• The same party told us "use this fact", at different times, with no regard to whatever happened in-between.
• OR, it’s possible that the same party sent us two different facts at the same time, but they were recorded in the table at different times. Maybe the temporal database recorded one fact, but before it could record the other fact, it got waylaid by a VACUUM emergency. It happens.
• OOOORRRR, it is possible that two different parties with different vantage points of a shared reality sent their observations independently, without being aware that other party even exists. Our temporal database just says "okay then", and records both claims of facts about observed reality.

As we established in the Adric scenario, multiple facts for the same E-A-V triple, can claim to have occurred at the same time (Adric is NOT 17 as-of-now, and Adric IS 18 as-of-now).

Consequently, though our bitemporal database notes down distinct facts at different times, we cannot presume that the sequence of recording follows Reality.

In other words…

Facts are mutually independent parallel claims that assert or redact some aspect of concurrent real-world events.

In fact, facts are always so. Variables are mutually dependent or independent; correlated or uncorrelated, because variables subsume Real identities, all of which live in the contiguous fabric of the same shared Universe.

What the Fact?!

Materialised "Reality" depends on who’s asking.

"Reality" is a convenient fiction.

We simulate alternate reality all the time. Worrying about the future. Worrying about what someone must be thinking about us just now. Questioning past life choices and wondering "what if". Much like financial analysts, weather modelers, chess pros, special ops teams running scenarios and doing retrospectives. Except those other people get paid to imagine worst case scenarios.

1. If each fact lives on its own conceptual timeline, then we must necessarily reconstruct reality by threading a point of view through a sequence of recorded facts.
2. Only the temporal sleuth—not the temporal database, nor engineer—get to choose which timeline or timelines (sequence(s) of facts) ought to construct a prospective Reality.
3. Only the temporal sleuth gets to choose the as-of point in time wherefrom to do so—now, past, future; separately or simultaneously. And gets paid to imagine alternate realities.

And so it goes… A few thousand lines of SQL queries reify these abstract (but very real) engineering ideas. Pray to your gods / atoms that you are spared these.

This sub-section’s title is also a pun on Lt. Cdr. Data, because Data is not his vessel alone. Data contains data, and the je ne sait quois that makes him sentient to us.

I’m not sorry. I have already confessed up-front to being a programmer and nerd. You read so far, so who’s fault is it now?

The Ones at The Very Edge, are.

Extremes are worth studying because beyond any extreme there exists the unknown, and the unknown contains infinite capacity for surprise. This is why there are people who will cross hell and high water to find the very edge and stay there.

“I want to stay as close to the edge as I can without going over. Out on the edge you see all kinds of things you can’t see from the center.”

— Kurt Vonnegut

To interrogate the nature of consciousness we ought to delve deeper into the blade edges of singularities; whether within subatomic particles, whether out there, between the accretion disk and the unknowable, or whether in the liminal spaces between living and dying, life and non-life, biologic and non-biologic, matter and antimatter, dimension and dimension.

Today, humanity contains capacity to manipulate and mutate its environment in three physical material dimensions, from pushing around individual atoms, up to planet-scale terraforming, and perceives some things of some of the others; spacetime and gravity. (A news headline that I did not expect to read in my lifetime: "CERN gears up to ship antimatter across Europe." Please, can we skip the Eugenics Wars and get to our Star Trek future already?)

Axiomatically, all new truths are at the edge of our perception as a species… or any society, for that matter, that is contemplating the nature of nature. To such a society, the purpose of Consciousness ought not to be a thing wanting to be named or found or understood, but to be a process; the wide-open forever-quest for ever-greater ever-deeper ever-wider understanding of ourselves as one with the universe. Gladly let Consciousness be the Elephant in the room amid we, its blind examiners.

Here are some of my favourite extremophile humans and composite human-machine systems, at the as-of-now cutting edge of the Reality-Consciouness continuum.

The people at the Levin Labs, and their collaborators elsewhere.

Technological Approach to Mind Everywhere (TAME)’s "Against Mind Blindness" position appeals to me because its proponents refuse to reduce consciousness into a checklist, and instead by explaining how to think about consciousness as a continuum. Consciousness is self-referential. It includes a capacity to self-interrogate. Consciousness is self-mutating. It mixes the self-referential signal into the firehose of all other signals, and then let the body figure out how to mutate itself in-place. It is other-referential. And it is mutual-shared-reality-referential.

Where does Consciousness exist in TAME?

It, lik