The Tao of It and Bit by Cristinel Stoica

Cristi,

What a truly excellent essay! I will be very surprised and disappointed if you are not a winner. I may later argue a point or two but I simply want to congratulate you on a job well done.

With respect to Smolin's treatment of laws versus Wheeler's treatment, I think Smolin says it best that "If everything that is real is real in a moment, then the distinction between laws and states must be a relative one."

You've stated, "If one believes that there are things that are not included in the mathematical model of the universe, one should describe these things." That is sort of a 'trick question'. If something can be described in words, one can make a mathematical model of some sort. I agree with Smolin that "There are aspects of the real universe that will never be representable in mathematics."

Your Yin-Yang diagram is probably the best way the it/bit question can be answered!

A job well done.

Best,

Edwin Eugene Klingman

Cristi,

What if you have axiom zero and axiom infinity? Wouldn't the tension "require" all "possible," ie. consistent, intermediate stages and this is where "laws" emerge?

The "mother" and the "father" of all possibles.

So energy tries radiating out to infinity, before flatlining to black, while structure tries collapsing to a point, but reaching a parabolic boil that shoots it out across the cosmos.

Is zero the point, or the flatline? Or both?

Is it the void?

Cristi,

One further observation of relations;

Absolute, extant, infinite.

Order, complexity, chaos.

Past, present, future.

Cristi,

Well done! This is a beautifully written piece, with whose premises and conclusions I mostly agree.*

There are only two points with which I would take issue:

1. "If we think that the physical solutions have reality, it becomes natural to admit that they have to behave well at infinity (otherwise they can't have physical reality)."

I can't see that this follows "naturally." What it means for physically real phenomena that have an effect, is that they are not in turn affected by physical conditions. If infinity is a physical condition, then well behaved solutions -- representing physical conditions -- drive the phenomena, and not the other way around; infinity can't be physically fundamental. This is what forced the conclusion in my previous essay that "the source of all information is a point at infinity." That is, only a topological model C* satisfies the bound of a physically real spacetime, by compactifying the complex plane into a sphere with one simple pole at infinity. Hawking back in the '80s explained imaginary time in terms of this 1-point, 2-dimension compactification by noting that one cannot go "north of the North Pole." In this same context, Wheeler reminds us that "the boundary of a boundary is zero." In other words, a walk of time over the unbounded manifold of C* (the simplest Riemann sphere) makes all information locally available as a finite set of infinite things. It's the finite set that's physically well behaved, not the mathematical solution at infinity.

2. "Zero is an axiom."

What does that mean? You seem to say that the Liar's paradox (Russell) is an "axiom." You call that logically consistent -- it isn't. We couldn't even do arithmetic unless zero is a number (with the accompanying axioms of succession and induction). If zero is an axiom, it isn't a number. For a set of axioms to be logically consistent, we cannot simply assume that everything follows from a single axiom. If it did, all numbers would be zero. The binary predicate ("is a member of") fundamentally implies a second set.

Tom

*(My previous essay "The Perfect First Question" was also based on Wheeler's 20 questions variation, and my upcoming essay expanding on that theme has a lot in common with yours.)

Hi Cristi,

Sure, I understand that your " ... position is the 'global consistency principle'." My own sentiments (and proofs) are with Einstein: "All physics is local." By making global consistency primary, you de facto subscribe to the physical reality of nonphysical measurement qualities as a boundary condition. Bell's theorem does the same, in fact. Global consistency, like nonlocality, can only be demonstrated with nonconstructive arguments, i.e., by assuming in the first place what is to be proved.

What I mean by the liar's paradox connection, is that in saying "axiom zero is false," you imply that the axiom is true only if it is false. This is not logically consistent with the meaning of an axiom, which is always true. Only in the binary predicate ("bit" in Wheeler's physical terms) can we create true mathematical statements from a set of axioms.

Best,

Tom

Our posts crossed. I do understand that your possibility space is the space of all possible universes. However, to propose an "axiom zero" as a possibility and then to show that it is an impossibility makes axiom zero a member of the set of all possible universes. Thus, the liar's paradox. If you really mean to say that all universes are equally likely, then I agree.

Tom

(duplicated to place in correct thread. Will try to get duplicate post deleted.)

And you know what? -- it furthers occurs to me that each of those equally likely universes, by your reasoning, allows axiomatically that "zero is a number, and the successor of zero is a number." Very interesting!

Tom

Cristi,

"So, global consistency indeed is primary, because it constrains local solutions, but both global and local consistency have to be true."

Okay, then, we agree in principle! (Now let's talk the additional degrees of freedom needed to make that work.)

Best,

Tom

Cristi,

Pardon me if I seem to have confused the two, but if nothing exists, then wouldn't there be no laws and no need for laws to govern it? In other words, no Platonic realm of math, as it emerges with what it defines. So then Axiom Zero and Zero as Axiom would effectively be the same, where physics and math are one.

Now from that, "the principle of explosion" allows all propositions that fulfill "the principle of logical consistency."

The second principle is math, but what engenders the first principle, if not the potential of infinite possibility?

"But from p and ¬p, any proposition q follows."

...-4, -3, -2, -1, 0, 1, 2, 3,4....

I think, first, I would have to have is education.Because if we have to talk about insult to intelligence, his essay is the best example.Judge yourself with assertions as false logic and experimentally, such as:"Information is not reality. Information has nothing to do with reality."

Why, according to you the information it has nothing to do with reality. Then, the computer I'm using now and that uses algorithms full of information, not real. Eureka: I'm not real, as the information that has nothing to do at all with reality, then the whole information flow of my neurons are pure junk.A little common sense, sir

What actually exists in your computer is material structure and flows of electrons in the structure, along well-defined and purposefully arranged paths. The flow of these electrons interacting with the designed structure causes switches to open and close changing the paths. You can overlay patterns of ones and zeros on these and you can even believe these patterns are "real" and call them "information", but that is merely your belief, and it is what this essay contest is about! I do not find it insulting for Cristi to question this.

It is not about belief, dear Edwin Eugene. The information is real in the sense that there is outside the observer, even if not Perform observation.Information is, for example, number of particles. The universe is in itself, full of information, for the simple reason, that everything can be measured, counted, etc. are numbers, and the numbers are pure information.Therefore,So, for example, the Bekenstein bound is an upper limit on the entropy S, or information I, That can be contained Within a Given finite region of space Which has a finite amount of energy.

[math]I\leq\frac{2\pi RE}{\hbar c\ln2}

[/math]

The vacuum energy density is a pure numerical value, and independent, its value, the observation process, since the expansion of the universe itself, is conditioned to this numerical value.

I do not believe, observe, make theories to explain the observed phenomena, using an informational process of creating algorithms (equations) that give some outputs, and it then taste numerical information outputs of these equations, or algorithms, with the reality of the phenomenon observed physical, measured.All this is information, not subjective beliefs.If I make a theory, with which using an algorithm or routine (equations, etc.), get the measured value of pure number density of vacuum (0.6931 ...), that is objective and real, and it is information. Everything else is to juggle metalinguistic, which are fine for philologists, but does not help the physicists.

regards