REVIEW 2 major objections 3 minor 9 references
Comment on "Physics without determinism: Alternative interpretations of classical physics", Phys. Rev. A, 100:062107, Dec 2019
T0 review · 2 major / 3 minor · reviewed 2026-08-27 · deepseek-v4-flash
Pith's one-line read This comment argues that a finite information quantity's definition is incomplete, because a mere change of measurement unit multiplies it by a constant and creates correlations among its bits that the definition ignores.
desk verdict A pointed but flawed Comment: the unit-change objection to FIQs is real, yet the arithmetic in Appendix A is wrong and must be fixed. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is the finite information quantity $Q = 0.Q_1Q_2\ldots$, a binary string whose digits are Bernoulli random variables with propensities $q_k$; the vector of $q_k$ is the whole representation. The mechanism that carries the argument is the binary full-adder arithmetic for multiplying by a constant, in which the carry bit $C_k$ couples neighbouring digits of the product. This coupling makes joint propensities such as $p_{12}$ differ from the product $p_1p_2$, exposing the information that a marginal-only representation loses.
What would settle it
The claim would be falsified if one could exhibit a constant $L$ and a FIQ $Q$ with independent bits for which $Q'=LQ$ has independent bits and the marginal propensities of $Q'$ determine all joint propensities. The paper's own calculation already provides the opposite check: for $L=(11)_2=3$ and $0<q_3<1$, it gives $p_{12}=0$ while $p_1p_2>0$, so recomputing $p_{12}$ and comparing it with $p_1p_2$ directly settles the claimed information loss in that instance.
Extended reading notes
Core claim
The comment establishes that a FIQ specified by the vector of marginal propensities $q = [q_1,q_2,\ldots,q_M,\frac12,\frac12,\ldots]$ is not closed under the elementary operation of multiplication by a constant $L$, which is exactly what a change of measurement unit requires. Using binary shift-and-add arithmetic, the authors compute $Q' = LQ$ for an example with $L = (11)_2 = 3$ and show that the joint propensity $p_{12}$ of the events $P_1=1$ and $P_2=1$ in the product is $0$, while $p_1 p_2 > 0$; hence the output bits are not independent. Since the original FIQ definition keeps only the individual $q'_k$, the dependence introduced by the operation is deleted, so the information carried by $Q'$ is not preserved. The conclusion is that the definition of a FIQ is not complete and requires further development, for instance by adding information on dependencies among the bits.
Load-bearing premise
The load-bearing premise is that a FIQ is meant to be used in calculations, so multiplying it by a constant—exactly what changing a measurement unit does—must preserve the information it carries; if the original framework was not intended to support arithmetic operations, the conclusion of incompleteness would not follow.
Editorial extensions
If this is right
- A FIQ that stores only single-bit propensities cannot represent the result of a measurement-unit change, so the original definition must be extended if FIQs are to be used in metrology.
- Any complete FIQ calculus would need to keep track of correlations between bits, at least pairwise, or store a joint distribution over the finite bit strings.
- The specific example $L=3$ shows that the failure is not limited to exotic inputs: it occurs for a routine arithmetic operation on an ordinary FIQ.
- Until the definition is amended, statements about the information content of a FIQ should be read as statements about the marginal propensities only, not about the full joint state of knowledge.
Reading between the lines
- The argument likely extends to FIQ addition: the full-adder's carry bit couples neighbouring sum bits even when the addend bits are independent, so any practical FIQ arithmetic would face the same gap.
- A useful test would be to characterise which multipliers $L$ preserve bit independence; multipliers that act as pure shifts may not create correlations, while multipliers with nontrivial binary expansions do, mapping out exactly where the original definition is safe.
- From a metrology perspective, the missing dependency information parallels the role of correlations in ordinary uncertainty propagation, so an FIQ alternative would inherit the need to track correlation structure rather than only marginal summaries.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This comment paper criticizes the definition of finite information quantities (FIQs) introduced by Del Santo and Gisin in Phys. Rev. A 100:062107 (2019). A FIQ represents the available information about a physical quantity via the marginal propensities q_k of its binary digits Q_k. The authors argue that if one changes the measurement unit, the numerical value of the quantity is multiplied by a constant, and they claim that such a multiplication, e.g., P = 3Q for a specific Q, produces output bits P_k that are not mutually independent even when the original bits are independent. Since the FIQ definition stores only the individual propensities, the resulting joint distribution is not captured, and the authors conclude that the FIQ definition is incomplete. The demonstration is carried out in Appendix A using a shift-and-add multiplier.
Significance. If the argument were correct, the comment would identify a genuine limitation of FIQs as a practical alternative to probability distributions: rescaling a FIQ would not preserve information, undermining the usefulness of the framework in metrological applications. The paper is self-contained, uses no fitted parameters, and does not rely on the authors' prior work. The conceptual point, that marginal propensities do not determine joint distributions of derived quantities, is a meaningful and potentially important critique, provided the supporting arithmetic is correct. However, the central numerical demonstration in Appendix A is mathematically flawed, and the normative premise that a FIQ must support multiplication by a constant is asserted rather than justified. The overall conclusion is plausible but requires a corrected derivation and a clearer statement of its assumptions.
major comments (2)
- [Appendix A, Eqs. (A1)-(A3)] The calculation of P = 3Q is incorrect. The full-adder recursion in (A1)-(A2) treats the carry-in bit C_{k+1} as independent of the current input bits Q_k and R_k. In the shift-and-add multiplication, however, R_k = Q_{k-1}, and C_{k+1} is a function of Q_k through R_{k+1} = Q_k and the subsequent bits, so C_{k+1} is correlated with Q_k. For the example q = [0,0,q3,1/2,...], the exact distribution of Q is (Q3 + U)/8, where U is uniform on [0,1) and independent of the Bernoulli bit Q3, hence P = 3(Q3 + U)/8. A direct computation gives p1 = (2/3)q3, p2 = 1/3, and p3 = 1/3 + q3/3, which contradicts Eq. (A3) (for q3=1, e.g., p1=3/4 in (A3) versus 2/3 exact). The non-independence conclusion p12 = 0 ≠ p1p2 does survive, since p1p2 = 2q3/9 > 0 for q3 > 0, but the demonstration as written must be replaced with a correct derivation.
- [Section 2, first paragraph] The conclusion that the FIQ definition is 'not complete' depends on the normative requirement that a FIQ must be closed under multiplication by a constant and that this operation must preserve all information. The statement 'it is mandatory that calculations with them be possible and, hopefully, simple' is an assertion, not a consequence of the definition given in Ref. [5]. If the original FIQ framework is intended only as a coarse summary of the state of knowledge, rather than as a full probability distribution, then the loss of joint information under rescaling is not a defect of the definition. The authors should either justify this requirement explicitly as a necessary condition for a complete information-carrying quantity, or present their conclusion as conditional on this criterion.
minor comments (3)
- [Table II caption] The caption states 'Q = 0.0Q2Q3...' but the table's first operand is written as '0.00Q3...'; the notation should be made consistent to avoid confusion about the bit alignment.
- [Section 2, paragraph 4] The phrase 'deletes some of the original information' presumes that the marginal propensities are the only information contained in the FIQ. Consider rephrasing to 'the marginal propensities do not determine the joint distribution of the resulting bits' to be more precise about what information is lost.
- [Appendix A, p12 argument] The proof that p12 = 0 is only sketched in the sentence 'the case {Q3=1, C3=1} always generates P2=0'; a more explicit derivation would help, especially since the surrounding recursion is being corrected.
Circularity Check
No circularity: the comment applies standard arithmetic to the target FIQ definition and does not derive its conclusion from its own inputs.
full rationale
The paper is a self-contained critique of the FIQ definition in Del Santo and Gisin. It takes that definition as the object of analysis, not as a premise it re-derives. The central demonstration is that multiplying a FIQ by a constant (a unit change) produces output bits that are not independent, so the propensity vector alone is incomplete. This conclusion is obtained by explicit binary-arithmetic calculations in Appendix A, not by fitting parameters, not by renaming an empirical pattern, and not by invoking the authors' own prior results. The citations to metrology guides and to mathematical literature on independent binary digits are contextual support, not load-bearing self-citations. The only normative element is the requirement that a practical alternative to probability distributions support simple calculations such as multiplication by a constant; that requirement is stated as an external adequacy condition, not as a consequence of the FIQ definition. Therefore no step of the derivation reduces by construction to its own inputs, and the non-independence claim, even if its arithmetic were later corrected, is not a formal restatement of the FIQ definition. The correct circularity score is 0.
Assumptions & free parameters
assumptions (3)
- domain assumption A FIQ is intended as a practical alternative to probability distributions for expressing measurement results.
- domain assumption A complete specification of a state of knowledge must preserve all information under a change of measurement unit.
- standard math Standard binary addition and carry arithmetic are valid.
Cite this review
Pith. "Pith review of Comment on "Physics without determinism: Alternative interpretations of classical physics", Phys. Rev. A, 100:062107, Dec 2019." pith.science (2026). https://pith.science/paper/UAFTDR24
@misc{pith2026200911709,
author = {Pith},
title = {Pith review of: Comment on "Physics without determinism: Alternative interpretations of classical physics", Phys. Rev. A, 100:062107, Dec 2019},
year = {2026},
howpublished = {\url{https://pith.science/paper/UAFTDR24}},
note = {Machine review of arXiv:2009.11709}
}
read the original abstract
The paper "Physics without determinism: Alternative interpretations of classical physics" [Phys. Rev. A, 100:062107, Dec 2019] defines finite information quantities (FIQ). A FIQ expresses the available information about the value of a physical quantity. We show that a change in the measurement unit does not preserve the information carried by a FIQ, and therefore that the definition provided in the paper is not complete.
Reference graph
Works this paper leans on
-
[5]
BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Supplement 2 to the ‘Guide to the Expression of Uncertainty in Measurement’ – Extension t o any number of output quantities, JCGM 102:2011 . BIPM, 2011
work page 2011
-
[1]
0 0 Q3 . . . + 0 . 0 Q3 Q4 . . . = 0 . P1 P2 P3 . . . TABLE II. Multiplication table, P = LQ where Q = 0.0Q2Q3 . . .and L = (11)2 = (3)10. L = (11) 2 = (3) 10, then p1 = 1 2 q2 3 + 1 4 q3, p2 = q3 − q2 3 + 1 4 , p3 = 1 2 , . . . (A3) The propensity of occurrence of specific digit couples can al so be computed. For example, denoting as p12 the propensity of...
-
[2]
International Vocabulary of Metrol- ogy, JCGM 200:2012
BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. International Vocabulary of Metrol- ogy, JCGM 200:2012 . BIPM, 2012
work page 2012
-
[3]
BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Guide to the Expression of Uncer- tainty in Measurement, JCGM 100:2008, GUM 1995 with minor co rrections. BIPM, 2008
work page 2008
-
[4]
BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Supplement 1 to the ‘Guide to the Expression of Uncertainty in Measurement’ – Propagation of distributions using a Monte Carlo method, JCGM 101:2008 . BIPM, 2008
work page 2008
-
[6]
Physics without dete rminism: Alternative interpretations of classical physics
Flavio Del Santo and Nicolas Gisin. Physics without dete rminism: Alternative interpretations of classical physics. Phys. Rev. A , 100:062107, Dec 2019
work page 2019
- [7]
-
[8]
N. V. Pratsevityi and G. M. Torbin. Superfractality of th e set of numbers having no frequency of n-adic digits, and fractal probability distributions. J. Ukr. Math. , 47:1113–1118, 1995
work page 1995
Show all 9 references
-
[9]
Albeverio, Ya
S. Albeverio, Ya. Goncharenko, M. Pratsiovytyi, and G. T orbin. Convolutions of distributions of random variables with independent binary digits. Random Oper. Stochastic Eq. , 15(1):89–104, 2007. 5
2007
Reviewed August 27, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.