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What Is “Fundamental”
October 28, 2017 to January 22, 2018
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Wandering Towards a Goal
How can mindless mathematical laws give rise to aims and intention?
December 2, 2016 to March 3, 2017
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Trick or Truth: The Mysterious Connection Between Physics and Mathematics
Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation
Media Partner: Scientific American


How Should Humanity Steer the Future?
January 9, 2014 - August 31, 2014
Contest Partners: Jaan Tallinn, The Peter and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific American

It From Bit or Bit From It
March 25 - June 28, 2013
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Questioning the Foundations
Which of Our Basic Physical Assumptions Are Wrong?
May 24 - August 31, 2012
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Is Reality Digital or Analog?
November 2010 - February 2011
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Anthony DiCarlo: on 1/29/16 at 17:41pm UTC, wrote Sara, I simply love the way that you deduce that "life itself" is the key...

Steven Sax: on 5/26/15 at 23:46pm UTC, wrote Hi Sara, (Thanks for your very fascinating questions that you posted on...

Steven Sax: on 4/23/15 at 4:16am UTC, wrote Hi Sara, Thank you for your kind remarks on my essay and for the very...

Sara Walker: on 4/22/15 at 6:02am UTC, wrote Hi Luca, Interesting stuff. To answer your question - time irreversible...

Sara Walker: on 4/22/15 at 6:00am UTC, wrote Dear Alma, Thanks very much for the kind feedback. I am glad you enjoyed...

Sara Walker: on 4/22/15 at 5:58am UTC, wrote Dear Lloyd, Thank for the kind comments. My feeling has been that some...

Sara Walker: on 4/22/15 at 5:56am UTC, wrote Dear Harry, I should be happy if you pointed me to any references on the...

Sara Walker: on 4/22/15 at 5:54am UTC, wrote Thank you :)


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A bench-top experiment could test the notion that gravity breaks delicate quantum superpositions.

Watching the Observers
Accounting for quantum fuzziness could help us measure space and time—and the cosmos—more accurately.

December 13, 2017

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: The Descent of Math by Sara Imari Walker [refresh]
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Author Sara Imari Walker wrote on Mar. 13, 2015 @ 21:07 GMT
Essay Abstract

A perplexing problem in understanding physical reality is why the universe seems comprehensible and correspondingly why there should exist physical systems capable of comprehending it. In this essay I explore the possibility that rather than being an odd coincidence arising due to our strange position as passive (and even more strangely, conscious) observers in the cosmos, these two problems might be intimately related and potentially explainable in terms of fundamental physics – that is, if we are willing to make the concession that information can physically influence the world. My premise begins by distinguishing physically possible states of the world, defined as everything permissible by the laws of physics, from physically accessible states of the world, defined as those that are achievable from a given initial state. For universes where the laws of physics are such that the number of accessible states is less than all that is possible, I argue that the most probable states among all possible states are those that include physical systems which contain information encodings – such as mathematics, language and art – because these are the most highly connected states in the state space of everything that is possible. Such physical systems include life and - of particular interest for the discussion of the place of math in physical reality - humans. Within this framework, the descent of math is a natural outcome of the evolution of the universe, which will tend toward states that are increasingly connected to other possible states of the universe, a process greatly facilitated if some physical systems know the rules of the game. I therefore conclude that our ability to use mathematics to describe, and more importantly manipulate, the natural world may not be an anomaly or trick, but instead a natural part of the structure of reality.

Author Bio

Sara Imari Walker is a theoretical physicist and astrobiologist and Assistant Professor in the Beyond Center for Fundamental Concepts in Science and the School of Earth and Space Exploration at Arizona State University. She received her PhD in Physics from Dartmouth College and has held postdoctoral appointments in the Center for Chemical Evolution at the Georgia Institute of Technology and as a NASA Postdoctoral Program Fellow.

Download Essay PDF File

John C Hodge wrote on Mar. 13, 2015 @ 21:53 GMT
Perhaps, ``the Assent of math''?

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adel sadeq wrote on Mar. 14, 2015 @ 02:50 GMT
Hi Sara,

You seem to be talking like a philosopher. Sorry for being blunt, but I don't see any physics, however it is fine as a fun work.

Maybe if you look at my essay and see if there is any fundamental relationship between physics and math.


Thanks and good luck.

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Author Sara Imari Walker replied on Mar. 14, 2015 @ 06:20 GMT
Blunt is fine. Philosophy is important to the conceptual foundations of physics, especially in areas where we aren't sure the best way to ask a question. I will take a look at your essay.

KoGuan Leo wrote on Mar. 15, 2015 @ 03:39 GMT
Dear Sara,

Yes, I agree with your conclusion stated below: "Our ability to use mathematics to describe, and more importantly manipulate, the natural world may not be an anomaly or “trick”, but instead could be an intimate facet of the structure of physical reality." In my essay TianmingRen in the Cloud, I advanced that the initial state: everything is connected that bit is it, and the final state and all in between: everything is still connected that it is bit. Hope you can comment and rate my essay.

Best of luck,

Leo KoGuan

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Author Sara Imari Walker replied on Mar. 26, 2015 @ 20:20 GMT
Thanks Leo. Will take a look. Best of luck to you as well.

Jonathan Khanlian wrote on Mar. 15, 2015 @ 03:54 GMT
Hi Sara,

Any essay that works in some soccer references is good in my book. I like the analysis of information encoding being essential for life, but I think this may still be possible in a deterministic system.

You talk about information being lost in your node system when there are many-to-one mappings. I intuitively agree, but there could be a way around this. I think if the many-to-one mapping happens below the level at which the universe emerges (or outside the system), this may not be an issue that violates what Leonard Susskind refers to as the Zeroth or Minus 1st law of physics, which is that information is never destroyed. Are you familiar with Wolfram’s causal networks? They are a node based systems where different updating orders still correspond to the same causal networks. Maybe in that sense information outside the system is loss, but information viewed from within the system is not. I don’t think your node model and his node model are trying to explain things at the same scale, but it may still be worth a look…Maybe there are some ideas there that will help you and Paul flesh out your theory some more.

I definitely think information is essential, and I like node models, so I'm interested to see how your work evolves.

Please check out my Digital Physics movie essay if you get the chance.



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Author Sara Imari Walker replied on Mar. 26, 2015 @ 20:28 GMT
Thanks Jon. I will certainly look into the causal network models in more depth. It sounds very related to some of the work I am doing now.

As a clarification on specifically what I mean by "information loss" as a result of many-to-one mappings is that for such cases the past is uncertain as there are multiple possible pasts consistent with the current state. The "information lost" is therefore with regard to your certainty that specific past events happened.

Looking forward to reading your essay.



Jonathan Khanlian replied on Mar. 27, 2015 @ 16:05 GMT
I understand what you are saying about not knowing the past from the current state because there are many previous states that could have lead to the same current state.

I remember being surprised when Leonard Susskind talked about even when you have an OR gate in a computer that outputs a yes, you would think that you don't know if you had a yes/no, yes/yes, or no/yes input after the...

view entire post

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Dipak Kumar Bhunia wrote on Mar. 16, 2015 @ 13:52 GMT
Dear Sara,

Thanks for the essay. But if it advocates merely to establish an anthropic connection between physics and mathematics would definitely be a confusing; as you mentioned, "why does the universe seem comprehensible and why should beings like us be here to comprehend it". Because, we are, whether "passive" or active (is that make any difference?) observers, the intrinsic parts of the universe.

In that same universe (or nature in broader senses), obviously there would be one most important role of "information" indeed. Without information one never could comprehend anything about anything comprehensible. But such information communicates only through any quantized signal. That is any of ours comprehensible to and fro information would be fundamentally quantized too. Therefore, from where no such comprehensible quantized information emerges out to reach to or received by us never could be comprehended. That is, we have always an intrinsic quantized information limit for the nature to comprehend. That limit not necessarily would be in any technological terms but natural as we are fundamentally sum of few quanta. Hence all our perception patterns are appear comfortable to begin with any initial state of casualty from which any such quantized information about the physical system received for its comprehension.

I think, the domain of "conscious" would start beyond that zone of zero quantized information. But being an intrinsic quantized-observer we can only imagine about the patterns of such conscious domain. Never could comprehend that pattern properly.

Otherwise your essay is enjoyable.

Best wishes


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Author Sara Imari Walker replied on Mar. 26, 2015 @ 20:34 GMT
Dear Dipak, Thanks for the comments.

With regard to whether observers are "active" or "passive" - I absolutely think it does make a difference. If observers are active, there is potentially an explanation for their existence as they actually matter to the world of matter - they are physical systems. If they are "passive" I think the existence of observers is much harder to explain, why would they be there in the first place?



Lawrence B Crowell wrote on Mar. 16, 2015 @ 22:37 GMT

Nice essay. I have pondered something similar to this. The idea that N_A = N_P is similar to Gel Mann’s totalitarian principle, “Anything that is not absolutely impossible is mandatory.” This ergodic principle is in some ways a frequentist interpretation of probability. A phenomenological perspective is more Bayesian, which says that probabilities are assigned only on the...

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Author Sara Imari Walker replied on Mar. 26, 2015 @ 20:38 GMT
Dear Lawrence, These are some interesting point. I do think of this much like a cosmology of observers, so I am happy to see you made that connection!

To clarify your last paragraph - do you mean "obs" to represent the number of states with observers, or the number of observable states?

Chidi Idika wrote on Mar. 17, 2015 @ 01:36 GMT
Hi Sara,

I very much appreciate your essay because it is not often that one comes across a physicist trying boldly to connect with biology at a theoretical level.

You say: “biological systems [may be] uniquely defined as a class of physical systems where information plays a causal role.”

In fact in my essay I adopt a particular quantity to define man/life as my "initial condition"; something no more than what mathematics calls the number bases (Peano’s “constant”) and which analogously physics calls the “quantum” of observables. Initial condition is what I define to be “the observer” state (the "natural unit").

And to illustrate man as such, I adopt the quantity threshold potential of the action potential; it signifying say man’s sensory threshold. And dare I say here I have found in my calculations that this quantity actually does make clear quantitative and qualitative connections with accepted physical constants such as Boltzmann entropy constant.

This is bearing in mind that any initial condition must be itself a state either of complete or null information (or indeed both?). This will mean that we are talking here of a state space as a Godel’s “formal system” (Peano’s “successor function” or “constant”). So a proof is any connection between systems (your "nodes").

For me, ultimately, initial condition is either a “completeness” or “incompleteness” of proof (essentially both i.e. really an “un-decidable” of Godel’s and “uncertainty” of Heisenberg’s). And information is simply negative entropy.

I find it exhilarating that you have thought along this line at all and I hope you will find the time to read and comment on my argument.



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Author Sara Imari Walker replied on Mar. 26, 2015 @ 20:47 GMT
Hello Chidi, Thanks for the thoughtful comments. I haven't had the chance to read your essay yet, but will try to do so. It does indeed sound related.

One important distinction I might make is that one of my motivations is that I would very much like to see a formalism that removes dependence on the initial condition. If you really think you can get "anywhere from anywhere" the initial condition is arbitrary. This is a particularly important point because under this case, if you start with an arbitrary initial condition, you are likely to eventually end up in states that contain life because they make the most states accessible (there may however be bottlenecks, so this I suppose could also be consistent with "life is rare" hypotheses). So there is very little dependence of the observed complexity on the initial condition under this formalism.

Chidi Idika replied on Mar. 27, 2015 @ 13:52 GMT
Dear Sara,

Question is: what exactly should we understand by "initial condition"? If we take initial condition to mean simply threshold as in "sensory threshold" or "quantum of observables" or even mathematically "number bases" or indeed Einstein's "inertial frame" then every initial condition is also unique.

I see initial condition as generalizing the intuitive notion "observer", or vice versa. Thus initial condition imply also a unique "path", more precisely a completeness; picture a geodesic or a spherical coordinate system or a phase space (indeed in thermodynamics an "isolated system").

This formalism brings us straight to an Everett sort "many worlds" but which I personally interpret in the sense of qualia i.e. observer specific reality. And it is my concept of quantum gravity.

I crave your indulgence to find the time to read and comment frankly on my basic axioms/formalism.

All the best,


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Martin Seltsam wrote on Mar. 29, 2015 @ 23:17 GMT
Dear Sara,

WOW! I think this essay is my personal favorite/winner! The ideas are really interesting and actually reminded me of a book I read a year ago: "The Beginning of Infinity" by David Deutsch. The reach of explanations and transformative powers of understanding agents are explored in this book and its conclusions share some similarities with you key points. Your view that states containing information encoding are more probable/accessible certainly align nicely with the thoughts of Deutsch and I am very inclined to agree with your perspective.

As you touch upon the question of which physical states are realized, I thought I dare to point to my little opera "Map = Territory" where I try to address similar issues (what it really means for states to be physically realized) and ponder the possibility of an actual merger of the description and the described in fundamental physics.

I would be honoured by your feedback.

With deep respect and best wishes for your success,


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Author Sara Imari Walker replied on Apr. 22, 2015 @ 05:49 GMT
Dear Martin, Thanks very much for the enthusiastic response to my essay! You are right to spot the connection to David Deutsch's thinking - I am very inspired by his work, particularly some of the recent work on constructor theory. Interested to read your essay.



Member Rick Searle wrote on Mar. 30, 2015 @ 01:46 GMT
Hi Sara,

I really loved your essay. It should be doing much better in this contest.

I am really looking forward to your upcoming work with Paul Davies.

Will this be a paper? A book?

Please take the time to check out my own essay, tell me what you think, and give me your vote.

All the best,

Rick Searle

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Author Sara Imari Walker replied on Apr. 22, 2015 @ 05:52 GMT
Dear Rick, Thank you. I am glad you enjoyed it! Right now I am working on a few papers related to the topics presented - a book perhaps, but down the road.



James Lee Hoover wrote on Mar. 30, 2015 @ 04:29 GMT

This is an impressive essay that states truths usually not mentioned about the problems with "initial states" in physics studies.

You mention "a pattern in how the world works" reminds me of an example I use in quantum biology of the European robin. A British physicist works with an molecular genetics professor to determine how the robin navigates South to Africa (a pattern regarding how the robin's world works) . They present strong evidence of the connection of the macro and quantum worlds to produce a avian chemical compass. A combination of mind, math, and physics connect to make this possible.

Like you I believe the "ability to use math to describe, and more importantly manipulate, the natural world" uncovers physical reality.


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Author Sara Imari Walker replied on Apr. 22, 2015 @ 05:53 GMT
Thanks Jim. This is a great example.

Sujatha Jagannathan wrote on Apr. 1, 2015 @ 11:29 GMT
Great art in your writing.


- Sincerely,

Miss. Sujatha Jagannathan

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Author Sara Imari Walker replied on Apr. 22, 2015 @ 05:54 GMT
Thank you :)

Harry Hamlin Ricker III wrote on Apr. 2, 2015 @ 13:45 GMT
Dear Sara, I hate to burst your thesis, but my friend Ken Garst was talking about you thesis 20 years ago and developed the mathematics to justify the evolution of biological systems. So the idea is not really new. The other comment I have is that the argument is not as profound as the one developed by Ken Garst. Finally, I don't see the connection to the essay topic.

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LLOYD TAMARAPREYE OKOKO replied on Apr. 5, 2015 @ 17:45 GMT
Dear Sara,

I admire your essay;most especially,your inclination to thrive in the use of philosophy as a via-media for unravelling the conceptual foundations of physics and mathematics.

Your conclusion,which sees the coefficiency between maths and physics as far from being an anomaly but a natural part of the structure of reality converges with my assertions on the subject matter.

I hope you can read;make comments and rate my essay.

Keep on flourishing,

Lloyd Tamarapreye Okoko.

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Author Sara Imari Walker replied on Apr. 22, 2015 @ 05:56 GMT
Dear Harry, I should be happy if you pointed me to any references on the work by Garst. It is always nice to make new connections to others work.



Author Sara Imari Walker replied on Apr. 22, 2015 @ 05:58 GMT
Dear Lloyd, Thank for the kind comments. My feeling has been that some areas of physics cannot adequately be addressed without first delving into some philosophy. It is great fun. Will look for your essay.



Ted Erikson wrote on Apr. 9, 2015 @ 14:29 GMT
FYI:My Essay 2408 error corrections @

Chicago Section AAPT

Spring Meeting 2015 - Glenbrook South High School

April 11, 2015


Registration and Continental Breakfast


Welcome and Introductions - John Lewis - Host

9:00 -9:15

Dimensionless Dualities

Ted Erikson - R/E UnLtd. -

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Joe Fisher wrote on Apr. 10, 2015 @ 14:50 GMT
Dear Sara,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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James Lee Hoover wrote on Apr. 14, 2015 @ 02:46 GMT

Time grows short, so I am revisiting essays I’ve read to assure I’ve rated them. I find that I rated yours on 3/30, rating it as one I could immediately relate to. I hope you get a chance to look at mine:


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Alma Ionescu wrote on Apr. 18, 2015 @ 15:20 GMT
Dear Sara,

It's not every day that I get to read a completely original idea and one that is so ambitiously attempting to answer the same question that gave birth to the weak anthropic principle which you mentioning as a motivation to your approach. I enjoyed the thought that the connection density within a system is increasing the probability that the system will end up in that specific state or nearby. I hope you do receive the right support for your work and will continue to develop the approach you sketched here. I rated your essay accordingly and I hope this can help your research being completed, at least in the tiniest way. Should you have the time, please do take a look at my essay and let me know what you think.

Warm regards,


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Author Sara Imari Walker replied on Apr. 22, 2015 @ 06:00 GMT
Dear Alma, Thanks very much for the kind feedback. I am glad you enjoyed the essay.


Luca Valeri wrote on Apr. 21, 2015 @ 01:03 GMT

I liked your essay and I think that is your main ideas can be connected to what I try to show in my essay, although it s not so explicit in my essay.

I argue, that the increasing of entropy means, that the number of potential information ie. the number of possible states knowing the macro state increases. This makes that in a multilevel system, also the number of possible substructures increases, which can be read as an increasing of actual information. In that sense I belief, that the increasing of entropy supports the increase of complex structures up to life.

In quantum mechanics, the interaction is in that way, that it supports the entanglement (connectivity) between the structures (particles). The unitary dynamic of an isolated system is only possible under a very specific environment.

In biological evolution then there is a shift from reacting from outside information the imagination of acting. And from perception of outside structures to the perceptions of inside structures (imagination of structures), meaning awareness.

I hope you get the chance to read my essay and comment on it.

How are time reversible dynamics connected to your special kind of dynamic. Do you have to replace the known law of nature?

Best regards


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Author Sara Imari Walker replied on Apr. 22, 2015 @ 06:02 GMT
Hi Luca, Interesting stuff. To answer your question - time irreversible dynamics emerge due to information loss, so it is similar to time-irreversibility due to coarse-graining. But ultimately here this is also still consistent with microscopically reversible physical laws. So, the dynamics are irreversible even though the laws of physics might be time-reversible. Hope this clarifies.



Steven P Sax wrote on Apr. 23, 2015 @ 04:16 GMT
Hi Sara,

Thank you for your kind remarks on my essay and for the very interesting question that you posed. That's a very fascinating distinction you made regarding self reference manifesting at an instant of time as opposed to being distributed through time, especially considering the effect of self reference on causality. I'm going to address it in a different comment, but for now I wanted to comment and rate your very excellent essay.

Your points are clearly presented in a stimulating and compelling manner and touch on many foundational topics, including the influence of information on physical systems, ergodicity, the second law of thermodynamics, and the state dependent nature of biological evolution. I like how you addressed the deeper anthropic argument of why the universe seems comprehensible and why beings like us are here to comprehend it, and how you addressed it by analyzing the path dependent nature of biological systems. And I see the insightful connection of formulating it this way to information systems and to computation, and thus the connections you made with my essay. This is a brilliant perspective, one that should inspire a lot of fruitful research. Your conclusion that the most commonly visited states are those that are most highly connected agrees with models of information network systems, and I like how you developed this idea to distinguish physical systems that contain information encodings such as mathematics, art, and language. This is a very refreshing contribution that approaches the forum topic thoroughly and goes further by relating other fields as well. I gave it the highest rating.

Best regards, and thanks again for seeking out my essay.

Steve Sax

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Steven P Sax replied on May. 26, 2015 @ 23:46 GMT
Hi Sara,

(Thanks for your very fascinating questions that you posted on my page, which as mentioned just above I'm addressing in a separate comment here).

That's an excellent distinction regarding requiring the self-reference to be manifest at a given instant versus allowing it to dynamically distribute through time. Since a system can be analysed from the perspective of other...

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Anthony DiCarlo wrote on Jan. 29, 2016 @ 17:41 GMT

I simply love the way that you deduce that "life itself" is the key to unlock information unification. Recall that I posted "Unification of Life and Information" ie.,
o_rev7.pdf. This was my attempt as a physicist to express what you imply biologically!

This may imply that ALL living things that "measure" physical information to appropriate physical knowledge should be the focus of our studies that correlates everything back to the physics/chemistry/etc., constituting all life's physical, information makeup (ie., all the measurables) that living things make (whether in a conscious or unconscious state). This living model for the entirety of ALL MEASURES of the universe could then be crunched to deduce things like making physical DNA measures that predict autoimmunity that is coded within. This implies that each individuals DNA sequencing would provide a key (like a projection operator) that unlocks the information contained within the "living model." With shape dynamics, we answer why a kidney is shaped as such... a heart with independent chambers... and of course a brain that contemplates all of this!

Again, your essay was a most pleasant read!


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