# Introducing Pip

* A joint author for Dick-Ken’s blog *

Charles Dickens was born 200 years ago last Tuesday. He is considered one of the greatest novelists of all time. Most of his novels were written in serial installments in monthly magazines. Often he would finish one chapter without having decided where the next was going. We wonder if Dickens would have been equally comfortable writing on blogs. It is apparently a myth that he was paid by the word, but on blogs one is generally not paid at all.

Today we, Dick and Ken, are honored to invite one of his most beloved characters, Pip from *Great Expectations*, to join the staff of our blog.

In the novel, Pip is short for Philip Pirrip, an orphan who becomes a gentleman with a hidden benefactor. On this blog, Pip is short for Dick and Ken in a post that is jointly authored in concept. Previously we’ve indicated this by saying “Dick and Ken” in a post’s second paragraph, but the WordPress software uses a single author name “by X” at the top. Hence we created a separate joint account for Pip. Posts that are mainly by one of us, even though the other may contribute a paragraph or even section, will keep our separate names.

We expected Pip to arrive in time for Dickens’ birthday, but his account was unaccountably blocking invitation e-mails until yesterday. He was almost pipped, so to speak, by another Pip from the same era—the ship-boy Pip from Herman Melville’s *Moby-Dick*. Indeed *Moby-Dick* could be another joint association for the staff, since it was the favorite novel of Ken’s father. Another case of independent discovery? However, Dickens’ Pip avoided the fate of Wally Pipp by finally showing up on our site. Here is Pip, as acted by Oscar Kennedy for a BBC TV production in December:

## Why Pip?

As computer scientists and information theorists, we are accustomed to thinking of the *bit* as the fundamental unit of our field. A bit means 1 or 0, on or off, up or down, yes or no, left or right, this way or that way. We’ve wondered whether *something* or *nothing* is the same kind of dichotomy, and we’re beginning to think not. John Wheeler famously declared that the fundament of science was “it from bit,” but we suspect “chip from pip” has a role.

A **pip** is a mark or dot indicating a unit of value. The word is used for the spots on dice and dominoes, and repeated glyphs on playing cards that are not face cards.

Is a pip possibly more than a unary counter? Put another way, can there be more information on the nine-of-clubs in the center than the four bits 1001? It depends on what the absence of a pip signifies. A pip is like a 1, but its absence is not 0—it’s really nothing. A zero is not nothing, it’s nothing with a place. This is what we see in John Horton Conway’s use of rather than for zero.

Our question can be viewed as: is an elementary particle a bit or a pip? It seems like a pip, but in physics it equates to a bit. How does this happen? Insofar as the concept of degrees of freedom applies, this has to do with coordinates for judging placement, the locale of presence or absence. Thus we venture:

A

bitis a designated place where a pip may or might not be observed. Apipis a bit whose placement was uncertain. (?)

Well we really don’t know. Sometimes we will use Pip to ask questions in a childlike manner, mindful that others may have reached definite answers already. Dickens’ Pip was always uncertain of his place in society. We may feel the same about fundamental questions, but we have great expectations of learning as we do.

## Open Problems

Can you answer Pip’s question about particles?

Note this comment by our recent (and next) guest poster Aram Harrow. How, then, do qubits relate to bits and pips?

If you are a currency trader you would know pip

Your next post would be: David Copperfield.

It’s wonderful to see the GLL/FTQC debate extending itself even to literary references like Pip/Dickens. Along this (infinitely extensible) literary-theoretic axis, Charles Bennett and I have independently conceived — and posted at The Quantum Pontiffs — essays on Jorge Luis Borges’ celebrated short story

Averroes’s Search, a story that we both have read (each in our own way) as an extended meditation upon the clash between (1) the subtle physics of quantum localization and entanglement (2) the subtle Wittgensteinian ‘aspect blindness’ that the 20th century’s too-sparse mathematical toolset imposes upon our appreciation of this physics.If there is a path forward, surely that path will blend broad humor and broader mathematics with a desire to discover and a passion to apply those discoveries … and surely these four traits — humor, math, discovery, and applications — have been admirably characteristic of GLL discussions in general, and of this particular GLL/FTQC debate in particular.

Let us say with Charles Dicken’s great character Oliver Twist:

“Please, sirs, we want some more!”🙂To answer this question you need to start thinking in terms of groups and not in terms numbers. Groups are abstract entities in themselves and have structure independent of their representations. For instance, if you think in terms of the standard model, the observation of certain particles provides considerable amout of information of a much deeper structure.

The question is delving into the notions of what a field is in quantum field theory. The field can exist and still be in a ground state where there are zero real particles present. The field however is still exchanging virtual particles, and those exchanges will follow whatever rules there are as dictacted by the group structure of the field itself.

When talking about fundamental particles, if we say there is some fundamental entity (like a string), we should be thinking along the lines that there are some total energy that can be distributed across some number of those entities, those entities can be in different modes, and that there are some number of configurations that those entities can be in (entropy).

However, what is an interesting result, which tells us a lot about our universe already, is that there are constraints on entropy related to the notions of surface area and volume. This result implies that their is structure present that provides a bound on the configurations and modes of whatever fundamental entity we might think of. This bounding is determined by the fundamental field of that fundamental entity (and if we think in terms of string theory, the reason physicists are still interested in the theory is that it for certain types of black holes, it can provide the upper bound on the configurations within a give volume/surface).

The answer then depends on what one thinks a bit is. Is the bit a represenation of a fundamental entity that is recording the state of that entity, or is it more abstract? If that entity can have an infinite number of modes, than it wouldn’t be a good candidate for a our notion of bit. However, if a bit is merely a fundamental unit of measure for some configuration space, a measure of information/entropy, then a bit is merely the smallest meaningful quantity we can talk about, and is more analgous to our notion of a unit vector. So saying a particle is a bit would be like correlating a real foot with the unit of measure called a foot.

So what is being measured? Well it turns out that what we are talking about when we are talking about quantum information is not the particles, but the states of those particles as represented by quantum numbers. A good understanding of this can be had by examining the hydrogen model and how fundametal quantum numbers are used in that model.

Thanks very much for this thoughtful contribution. Regarding your fourth paragraph with the “interesting result”, I had in mind the proof of the black-hole entropy theorem when saying a particle was being equated to a bit. It seemed better to link the Bekenstein-bound section of Wikipedia’s article on the holographic principle, however.

Thanks for the kind words, this is a great topic to think about.

Hal, systems engineers commonly work with concrete quantum systems that embody your general philosophical points.

As a computational example, let us consider the Hamiltonian dynamics of a cluster of (say) nuclear magnetic moments (or equivalently qubits) that interact by dipolar couplings. Considered as a Hamiltonian matrix of dimension , space appears as a parameter nowhere in the Hamiltonian matrix. After all, perhaps the nuclei/qubits are arrayed on a lattice of dimensions, or on a sphere, or on an arbitrary shape of arbitrary dimension. Thus the geometry and dimension of “space” are associated to the Hamiltonian as a whole, and it is perfectly feasible for to specify Hamiltonians for which no notion of “space” is present at all.

So how is it (computationally speaking) that notions of “space” emerge from a specified spin/qubit dynamics? In practice, for systems engineers, the macroscopic descriptors associated with “space” arise naturally — if they arise at all — from microscopic descriptors of “dust” (the nonspatial Hamiltonian matrix elements) via the transport equations that generically arise within Onsager/Green-Kubo (etc.) relations.

Thus the dynamical reduction — viewed as a well-posed mathematical recipe having immense practical utility — has been much-studied for many decades and is reasonably well-understood in many respects.

Broadly speaking (for systems engineers at least), many of the philosophical problems that traditionally are associated to “space” can be pragmatically dissolved by regarding “space” as a parameter appearing solely in transport equations that inherently are approximations, and whose physical reality need not be regarded as absolute (or even fundamental).

Elevator SummaryWithin simulation-centric computational frameworks, it suffices for many practical purposes to regard “space” as a non-fundamental notion that is associated not with “it from bit”, but rather with the well-understood thermodynamical principle “pips from flow”, that is, “pips” of low entropy density that arise generically from transport relations that are spatially separatory yet inherently approximate.Ooops … in the above, is the number of dipolar (pairwise) nuclear spin (qubit) couplings, which in turn determine a Hamiltonian matrix of dimension .

The point of the example is that, for generic quantum mechanical systems, the parametric descriptors that conventionally are associated to “space” (considered as a geometric object) generically are not present in the microscopic quantum descriptors, but rather are generated pragmatically, creatively, and emergently (yet naturally) during the mundane process — yet how can any inherently creative process be entirely mundane? — of constructing transport relations that are coarse-grained and therefore (necessarily) approximate.

John,

Thanks for the excellent discussion. I find that approaching these sorts of problems philosophically is necessary since our human language is much more forgiving than more formal languages. In any case, when one resorts to human language it does begin to highlight possible contradictions. Sometimes this is due to the use of certain words being mapped to multiple definitions related to different contexts. So for instance, if I see the word Hamiltonian, my mind has now been trained to think of total energy, and when I think of total energy I think of mass, and when I think of mass I think of space.

Within the realm of quantum mechanics, I see Hamiltonian and I think mass spectrum. Now within pure quantum mechanics we can ignore any notion of gravity and thus ignore questions of space, however, we have to keep in mind that this is an artificiality that we maintain for convenience of computation and not something that reflects reality. For that reason, in my mind, any discussion of energy in a real context does imply a discussion of some physical space.

That being said, my immediate thought is to equate any discussion of tranport phenomenon to flux, and since flux has to be defined across some surface or volume it shouldn’t be surprising that space has to arise naturally as a precursor to any discussion of flux. With that in mind, base on the comment I think that pips and particles are more related than bits and particles. Some of this is simply because I can’t help think of the statement “A pip is a mark or dot indicating a unit of value” and not begin to equate that to marks left on photographic paper in some sort of experiment involving particles travelling through slits.

With that in mind, an absense of pips quickly becomes an absence of particles, however I go back to my earlier comment on the nature of fields. One has to stop and ask if an absence of particles means an absense of fields, or rather, how do I know the field is there if I can’t observe the particle? (aka, if a tree falls in the woods…)

In any case, my mind thinks at this point that any notion of bit must be tied to our concept of measurement, and what is being measured when we talk about entropy is some property of the field related to the particles in question.

Dick and Ken, you may already know this, but if not, let me point out that the notion of a pip seems virtually identical to the occupation number in quantum field theory. This is simply the number of particles in a particluar mode. While in general the occupation can be any non-negative integer, for fermions it is restricted to either 0 or 1.

There isn’t really any conceptual difference between something versus nothing (i.e. the vacuum state versus a single excitation of a specific mode) and the two orthogonal states of a bit or qubit (which amount to an excitation of either of two modes). Both are simply a set of two orthogonal states, and physically both are subject to the same laws governing dynamics. These aren’t really two different things, but rather two faces of the same thing.

With this in mind, it should be clear that information theory applies in exactly the same way to both cases.

I should also mention that you can for fairly natural bases out of orthogonal states composed of an indeterminant number of particles. An example of this are so-called coherent states, which are essentially what is produced by a laser.

At this time I am ready to do my breakfast, once having my breakfast

coming over again to read other news.

I really like the analogy of pip to the character by the same name in Charles Dickens’ novel. Indeed, both are vying for some validation of their existence. Well done, this was a remarkable read.

I have something (e.g., better lower bounds) for proving that NP is not P, but many computer science journals’ responses were nothing (rejecting my submissions without any proof). So, something and nothing are really not 1 and 0.

Can you (pip) send me the name of the computer science who agrees to check my proof (about 3 pp..)?