schematic: Silicon-based life and dust-based life are fiction and not fact. I use them as examples to illustrate an abstract argument. The examples are taken from science-fiction but the abstract argument is rigorous science. The abstract concepts are valid, whether or not the examples are real. The concepts are digital-life and analog-life. The concepts are based on a broad definition of life. For the purposes of this discussion, life is defined as a material system that can acquire, store, process, and use information to organize its activities. In this broad view, the essence of life is information, but information is not synonymous with life. To be alive, a system must not only hold information but process and use it. It is the active use of information, and not the passive storage, that constitutes life.
[FREEMAN DYSON:] One of my favorite books is Great Mambo Chicken and the Transhuman Condition" by Ed Regis. The book is a collection of stories about weird ideas and weird people. The transhuman condition is an idea suggested by Hans Moravec. It is the way you live when your memories and mental processes are down-loaded from your brain into a computer. The wiring system of the computer is a substitute for the axons and synapses of the brain. You can then use the computer as a back-up, to keep your personality going in case your brain gets smashed in a car accident, or in case your brain develops Alzheimer's. After your old brain is gone, you might decide to upload yourself into a new brain, or you might decide to cut your losses and live happily as a transhuman in the computer. The transhumans won't have to worry about keeping warm. They can adjust their temperature to fit their surroundings. If the computer is made of silicon, the transhuman condition is silicon-based life. Silicon-based life is a possible form for life in a cold universe to adopt, whether or not it happens to begin with water-based creatures like us made of flesh and blood.
賈倫·拉尼爾 | 計算機科學家;音樂家;作者，誰擁有未來？
I was trying to besubtle and non-confrontative in my initial post, but I have a sense that I wasa bit too subtle. Why are we confusing our inventions with natural systems? Whyis this confusion being asserted with such force and regularity? What is to begained from it?
To be moreexplicit: "Analog" and "Digital" are two technologies ofrelatively recent invention. They both can be usefully understood throughsimple ideas about state and causality that can probably not be applied to allof nature at all scales. Each technology is made possible because we havelearned to artificially construct material systems in which certain traits arewell enough controlled that they conform to simple models with enoughreliability for practical uses,
Digital computerscan hypothetically be applied to a significantly general class of problems, butin practice are hard to scale. Analog circuits can hypothetically be applied toa significantly general class of problems, but in practice are hard to scale.Aspects of biological systems are usefully modeled by manageably small digitalprograms. An overlapping but different set of biological problems are usefullymodeled by manageably small analog circuits.
Analog systemsshould not be confused with continuous mathematics, and neither should digitalcomputers be confused with discrete mathematics, as Lee Smolin pointed out.
Freeman Dyson isfascinated by whether this or that configuration could be "alive" or"conscious". It's hard to respond to him on a purely technical level,because the terms aren't well enough defined. Taken on a philosophical or poeticlevel, he seems to ignore an obvious question of subjectivity and observation.
A digitalinterpretation of a computer is completely superfluous unless you're a personusing the computer. A Macintosh will do the same thing whether it's modeled asan analog device, a digital device, a quantum phenomenon, or a thermodynamicevent. For something to be digital, in the sense of an information bearingdevice, someone has to appreciate it as bearing its information which somehowends up as subjective experience. I don't think the celebrated"observer" of quantum measurement is nearly as provocative as this"observer" of computers, who is so obvious as to be easily missed.
The mysteries ofphilosophy don't go away because we have the metaphor of the computer ‹ theyonly increase. I don't think these objections need to be part of a scientificdiscussion, but neither should the scientific community be broadcasting the"man is a computer" or "life is a computer" tropes.
查爾斯·西蒙尼 | 軟體工程師，計算機科學家，企業家，慈善家
Letters carved ina rock are definitely digital (not binary, but digital).
Bison carved inthe rock may be called analog, unless it is a part of an alphabet, in whichcase it would be digital too. (pictures of egyptian deities on an inscription:definitely digital, that is why they were called the "enead", thegroup of nine (or eleven?)
The informationcarried in digital form (Hamurabi, etc.) from ancient times was incrediblydurable. digital rocks.
I am not sure iflife is analog or digital. Freeman seems to take it for granted that theuniverse is analog ‹ (with good reasons ; ‹ ). But maybe the issue is:
Are real numbersreal?
(or was this oneof the Y2000 questions already?)
Certainly quantumenergy states are digital in spirit. In a popular column I said that they helpgold to remember that it should shine and water that it is supposed to be aliquid. In an alternative analog world all of these interesting propertieswould be quickly forgotten as the electrons would wind down into the nucleus ina truly analog fashion.
Best wishes toall.
約翰·麥卡錫 |史丹福大學計算機科學教授
Freeman Dysonincludes
For the purposesof this discussion, life is defined as a material system that can acquire,store, process, and use information to organize its activities. In this broadview, the essence of life is information, but information is not synonymouswith life. To be alive, a system must not only hold information but process anduse it. It is the active use of information, and not the passive storage, thatconstitutes life.
1. I want morethan that life merely process information. Our form of life can process arbitrarydigital information. It must be able to represent the same facts about theworld that humans do and be able to make arbitrary computations (acceptinglimitations of speed, storage and time) that humans make.
2. Consider aphysical digital circuit. It is in fact an analog circuit. What makes itworkable for digital purposes is the nonlinear behavior that permits it toapproximate discrete states and make arbitrary computations. Marvin Minsky'sPhD thesis showed that processing information essentially requires only thatthe basic processing element have a negative part in its response curve, i.e.sometimes increasing inputs leads to reducing outputs. This negative part ofthe transfer functions is also what prevents small deviations from destroying theinformation.
3. That the analogsystem can compute some functions digital systems can'd doesn't show that theanalog system can preserve information, correct errors and process itlogically.
4. Does the blackcloud have these information storage and processing capabilities?
斯圖爾特品牌 | 創始人，整個地球目錄;聯合創始人，井;聯合創始人，長期現在基金會，和復興和恢復;作者，整個地球學科
My point on digital is nonprofound. Justthat reading a CD in 30 years will be a chore, like reading an 8 inch floppynow. Rocks and paper stay readily readable ‹ the eyeball platform is fairlyconstant over centuries, and alphabets seem to leave a lineage you can traceback for understanding old forms. Language is mutable though, sometimesevanescent.
馬文·明斯基 | 數學家;計算機科學家;麻省理工學院媒體藝術和科學教授;麻省理工學院人工智慧實驗室聯合創始人;作者，情感機器
Danny Hillis wrote: "I see no reasonto believe that the technical distinction pointed out by Pour-El /Richards arein any way relevant to the actual 'computation' of life."
Or to anything else, so far as I can see.As I recall, that theorem is based on assuming the existence of continuous realvariables. That amounts to first throwing the baby into the bath, and thenappearing to magically take it out again. Along with Feynman, I'm inclined tosuspect, instead, that the universe has a finite information density.
Worse, it is hard to imagine any wayeither to prove this or to prove the contrary. So, it's probably best to justforget it.
Anyway, in regard to Stuart Brand'sremark, surely a CD is just a small soft rock A 650 megabyte hand carved rockwould consume a square kilometer or so. Besides, it is not really analog. It isdigital with a local redundancy of the order of 10**20 in molecular atomplacement. A CD has far less redundancy.
Umm, surely a CD is just a small softrock. Still, a CD can be made with a good deal of redundancy. A 650 megabytehand carved rock would consume a square kilometer or so. Besides, it is notreally analog. It is digital with a local redundancy of the order of 10**20 inmolecular atom placement.
By the way, I don't agree with Dyson'sassessment of Pour-El et al's theorem. The assumptions are based on theexistence of continuous real variables. That amounts to first throwing the babyinto the bath, and then appearing to magically take it out.
I suspect, instead, that the universe hasa finite information density. I also suspect that there's no way to proveeither that or the contrary. So, on second thought, forget it.
丹尼爾·希利斯 | 物理學家，計算機科學家，聯合創始人，應用發明;作者，《石頭上的圖案》
Freeman, I am not sure I understand yourquestion. If you are asking a question about the life-as-we-know-it, surely theanswer is "both" since we know of many examples of the both analogand digital information processing in biology.
Your own book Origins ofLife make this point very eloquently, so I wonder if you are asking iflife-in-principle is analog or digital? Surely the answer to this is"either".
In almost all circumstances digital lifecan simulate analog life to arbitrary precision and visa versa. I see no reasonto believe that the technical distinction pointed out by Pour-El /Richards arein any way relevant to the actual "computation" of life. In thespecial circumstance of extreme cooling, where both noise and signal are fadingtogether, it may well be that only the analog implementation works .
But would this make life analog? I don'tthink so.
威廉·卡爾文 | 理論神經生物學家;華盛頓大學名譽副教授;作者， 全球熱
I am happy to see life defined not only asinfo acquisition and storage but the ability to do something with it, to act inthe real world. Contemplation without action has been so much the model, at thehigh end of the scale, that we forget that consciousness really ought to beformulated as readiness for action, generating and improving plans for the nextmove.
I get involved all the time inneurophysiological cautions to Moravec's uploading, and to some extent the samecautions apply to the basics of life, not just higher intellectual functions.Organisms are always in the process of turning into something else, whetheraging on the individual level or evolving on the species level. Yet they haveto maintain their integrity in much the same way as any other bureaucracy;variations around the fringes are OK but there is a developmental core that hasto remain very conservative.
So robustness is always a consideration:how well does the organism bounce back when perturbed? As we all know, digitalmedia (including DNA) have the ability to avoid degrading copies and, ifmutations occur in a master record, a certain resiliency about fixing it. Idon't hear of analog examples of such fidelity and robustness.
史蒂夫·格蘭德 | 網絡生活研究創始人;作者， 創造：生活與如何創造
The world is divided into two camps: thosethat believe in dichotomies and, er, nobody else...
Perhaps at a theoretical level analogueand digital are two branches of a dichotomy, but at a practical level theynever are (and certainly their etymologies do not make them into antonyms). Forexample, analogue computers represent physical quantities using"continuously varying" voltages. But instantaneous voltage isquantised, with a resolution of 1eV, so in practice this "analogue"signal is really digital (albeit a very close approximation, thanks toAvogadro's Number). Likewise all practical digital signals are analogue, sincethe system takes a finite time to slew between any two states. Maybe this isn'ttrue with quantum flips, but instead perhaps we are stuck with a finite period(of uncertain length) in which the states are superimposed - 0 and 1simultaneously. A digital system has to make a deliberate decision on how totreat this finite transition ‹ in practice we usually use hysteresis (e.g. aSchmitt Trigger in electronics) to define that the intermediate state is simplythe old state until it passes some (presumably quantised) threshold.Fundamentally it's a mess ‹ analogue and digital are not distinct andcomplementary, and they're more in the eye of the beholder/receiver thananything else.
When it comes to life, we see theanalogue/digital distinction disappear completely, to be replaced by thespectrum of forms of encoding it really is. Take a nerve signal: at atheoretical level we can treat an action potential as a differentiated square wave,i.e. a spike of infinitesimal width and infinite height ‹ the ultimate indigital. But in practice the cell membrane takes a finite time to transitbetween polarised and depolarised states and so forms a smooth (if sharp) curve‹ this is an analogue change (discrete at the quantum level). But then again,there are only two significant states, polarised and depolarised, sowe're back to a digital system. And yet what really matters is the choice ofencoding scheme, which for the majority of neurons seems to be frequencymodulation, and so the true signal is analogue and can varycontinuously. Mind you, two spike peaks can only vary in distance by a wholenumber of molecules, and so this analogue signal is really discrete... Argh!
Much the same mess and mix of mechanismsapplies to DNA too. ACTG may be digital, but genes are also encoded by thefolding structure of DNA, RNA and the relevant enzymes, so although theresultant protein's amino acid sequence is defined digitally, the particularphysical form it takes on (proteins can often fold up in many different ways,with different properties) depends on much less clear-cut factors.
The idea of digital might seemlike a neat trick to us humans, who've only just discovered it. But naturesimply isn't impressed either way.
Perhaps a more important distinction isnot between analogue and digital in the sense of "real number" versus"integer", but between "analogue" in its original sense asanexplicit representation of another physical process, and"symbolic" (conventionally in its most elegant form of binarynumbers), where the shape of the signal bears no similarity to the physicalprocess it is emulating. But my feeling is that this distinction only reallyapplies to mathematical models and computer simulations, which are pretendingto be something else. Life just is, so the concept of a"representation" doesn't apply (outside of the question of whetherand how brains make mental models of the world), and it's pointless askingwhether the information is explicit or symbolic.
So "is life digital oranalogue?" is surely therefore a non question, since the word"is" implies that it's a practical question, not a theoretical one?" Could life be digital or analogue" is a theoreticalquestion (although it's a practical one for people like me, who work inArtificial Life). But the answer here is surely: it doesn't care. Whenever anetwork of cause and effect is capable of sustaining itself, it will. Perhapsit now boils down to how discrete such information flows need to be in order tobe self-sustaining, and my hunch here is that highly discretised signals (likeACTG) are an advantage but not a necessity.
Er, maybe all I've done here is rephrasethe question. Does that make me a philosopher?
斯圖爾特品牌 | 創始人，整個地球目錄;聯合創始人，井;聯合創始人，長期現在基金會，和復興和恢復;作者，整個地球學科
When you compare digital storage of data(eg. a CD) with analog storage (eg. letters carved in rock), analog is provingto be far more durable over time. Mathematically it's not a profounddifference, but practically it is.
尼古拉斯·漢弗萊 | 倫敦經濟學院心理學名譽教授;人文學院哲學客座教授;劍橋達爾文學院高級會員;作者， 靈魂塵埃
If information in DNA — in genes — isdigital, while information in culture — in memes — is analog, the answer has tobe that life was digital, and will be analog.
賈倫·拉尼爾 | 計算機科學家;音樂家;作者，誰擁有未來？
It seems to me that there's anepistemological difference between analog and digital systems. A digital systemmust adhere to an idea of what constitutes a bit, and an on and off state for abit. This idea, which might be thought of as a "standard" for a givenfundamental digital platform, is a way of interpreting digital informationcontent in a fundamentally analog system. A digital system can only be definedor perceived through the use of this kind of extra layer of specification, orwhat might be called in another context an extra layer of"subjectivity". A digital interpretation's very essence is that itignores a lot of information in the system; It is made artificially not only finitebut small, and therefore more easy to understand and predict for many purposes.Any digital system can be made to "die" by putting it in extremeconditions where either the bits dissipate or the difference between the on andoff states is no longer present in a useful way.
Therefore, I think a better question toask is, "What digital interpretations of living systems might prove to beuseful?" There might be multiple useful ways in which the human brain canbe thought of as a digital system. Each of these might have a different idea ofthe material instantiation of a bit and the states of a bit. For the samereasons that there is no perfectly reliable digital computer in the real world,there will be no perfectly applicable mapping of a digital interpretation ontoa natural system such as a brain. But we should expect useful digitalinterpretations (indeed there is already a thriving community of computationalneuroscientists), and I hope we will not be burdened by an a priori bias aboutwhether a single mapping or many should be emphasized in the future. Thepossibility of such a bias is why it's worth pointing out the epistemologicalissue. (Also note that temporal and phase-sensitive phenomena in natural livingsystems can be particularly hard to interpret with sufficient resolutiondigitally — so it might take a while before we have powerful enough computersto usefully map onto some behaviors of analog brains.)
約旦波拉克 | 布蘭迪斯大學計算機科學教授兼主席
Freeman's material definition eliminatesthe idea that software could be alive, and places no constraints on thedirection of the process. I prefer the lower level thermodynamic definition: aprocess far from equilibrium which dissipates energy and creates a localreversal of entropy. All the other elements of life-as-we-know it, likeinformation and replication would fall right out, were we were to reallyunderstand self-organization.
As a computer scientist, whether life isanalog or digital seems to me to be the wrong question. It is a similarquestion as whether a chair must be made out of wood or plastic."Chairness" is in the organization which enables a platform of acertain height to support a certain weight. Similarly "life" is ameasurement of the organization in a system. The yes or no answer to the"is it alive?", is like the yes or no answer to the question to"is it hot?"
So it doesnt matter whether a system ismade from silicon, carbon, chips, polymers, potentiometers, relays and motors,legos, or tinkertoys or even pure software. What matters is where thebiologically complex organization will come from.
I think both (analog) complex dynamicalsystems and (digital) software engineering have been failures at evenrecognizing the scope of the problem of biological complexity. All themathematical models of complex systems theory focus on quite low dimensionalsystems, like cellular automata, and mostly on convergence phenomena or prettygraphics. And AI-type programs like symbolic manipulation systems as well astrained neural networks, always reduce to small bits of organization: businesslogic plus a relational database — or a polynomial with lots of parameters toset.
There seems to be a fundamental limit toorganization which is buildable by human teams. In fact, a dirty secret of thesoftware engineering field is that 2 or 3 good programmers can build anything,and tools and fancy methodologies havent changed the equation. Hundreds ofother people are necessary just to keep businesses going and to tweak the codeto market. Big computer programs are just "suites" of separate 1million line programs, requiring a human brain in the middle to select andapply different functions usually via a menu system.
The amount of organization in a singleautonomous biological cell dramatically exceeds the amount of organization of amodern computer program. The real question is how do we get self-organizationof systems going to the point they achieve biological complexity, not whetherthey are digital or analog in nature.
約瑟夫·特勞布 | 哥倫比亞大學計算機科學教授;合著者，複雜性和信息
The Pour-El and Richards result is for aworst case setting. It's been shown that there's no difficulty "on theaverage".
This is not unusual. For example, problemstypically suffer the "curse of dimensionality" in the worst case. Ifone settles for a stochastic assurance (Monte Carlo, for example) the curse isvanquished. The bad result is just an artifact of insisting on certainty.
We now know a considerable amount aboutthe biological basis of number representation — surely Stanislas Dehaene willweigh in here!
What we have learned from studies ofanimals, human infants and adults, and patients with brain damage, is that allsuch creatures have, minimally, an analog magnitude system for computing thenumber of objects or events. this system, mediated by a mechanism that caneither count or time, is approximate, falls under the constraints ofWeber-Fechner law, and thus can do small or large numbers approximately. Someof us (e.g., me, Sue Carey, Liz Spelke) believe that this system is joined byanother that can do small numbers (< 4) precisely.
The emergence, in human history, of alarge precise number system was contingent upon the acquisition of language.Thus, no other animal and no child lacking language will acquire a largeprecise number system, one capable of true digital quantification. However,relevant to the digital-analog issue, it looks like much if not most of thenatural world makes decisions in an analog fashion.
克利福德·皮多弗 | 作者，數學書，物理書，和醫學書三部曲
As a generalbackground to Edge readers, if they feel that only flesh and bloodcan support consciousness, then life would be very difficult in the Final Dayswhen the universe expands and cools and does not contain water nor much energy.But to my way of thinking, there's no reason to exclude the possibility ofnon-organic sentient beings in the final diffuse universe. I call these beingsOmega creatures. If our thoughts and consciousnesses do not depend on theactual substances in our brains but rather on the structures, patterns, andrelationships between parts, then Omega beings could think. If you could make acopy of your brain with the same essential structure but using differentmaterials, the copy would think it was you.
More specifically addressing FreemanDyson's essay, Freeman writes "If we are partly analog, the downloading ofa human consciousness into a digital computer may involve a certain loss of ourfiner feelings and qualities." I would enjoy hearing him expand on thissubject. For example, if I were to digitize an analog LP record at very highresolution, would I really have to lose any of its "finer qualities?"Perhaps the *playback mechanism* for the LP record affects it sounds, but itseems to me I have captured all of the LP record's qualities, and someday,given a good playback mechanism, it would sound just as beautiful. Perhaps weshould even say that a digital capture of an LP record, even today, isindistinguishable in any "meaningful way" from the LP record in termsof the music's "finer qualities," our perception of the music, andthe feelings the music evokes.
I would also enjoy hearing Freeman expandon his sentence, "If the system could live forever, the temperature wouldultimately become much lower than the energy-gap, and the states above the gapwould become inaccessible.... It would be... dead." However, if the amountof energy in the universe asymptotically approaches zero, it will never reachzero. Is it possible that the universe will never reach a condition in whichALL the states of of the components of the living system become unreachable? Isit possible that there will be at least some of the states madepossible via the vacuum fluctuations, where the overall universe's energy isarbitrarily close to zero but locally there may be variations allowingtransient existence — not so different than what we all have now, transientexistences. Even if this state would correspond to a person in a coma who isnot fully conscious, we would still call this person "alive." Andwith life, there is always a hope, even if very slim, of resurrection andrescue from beings in parallel universes or from other dimensions.
弗裡曼·戴森 | 物理學家，高等研究所;作者，《擾亂宇宙》;模式的製作者
Thanks to all nineteen of you whoresponded, some of you twice, with thoughtful objections and disagreements. AsI said in my opening statement, it is much more fun to be contradicted than tobe ignored. I learned a lot from your contradictions.
The following two statements are myattempt to condense a rich assortment of opinions into two sentences. (1) Anyreal computer operating in the real world is partly digital and partly analog,and any living organism is an even more inextricable mixture of digital andanalog components. (2) The concepts of digital and analog were invented todescribe idealized models of human-designed machines, and are far too narrow toencompass the subtleties of living creatures. In other words, when I askedwhether life is analog or digital, (1) the answer is ``both'', and (2) I askedthe wrong question. There seems to be a consensus among the respondents forboth these statements. Beyond that, each of you had interesting things to sayabout details. I comment now on only three of your comments. Sorry it wouldtake too long to give equal time to all of you.
Lee Smolin gave the longest and mostsubstantial response. He describes a third possible form of informationprocessing which is neither analog (because it is based on discrete rather thancontinuous components) nor digital (because it cannot be simulated by a digitalcomputer algorithm). His information storage is based on the topologicalstructure of finite graphs in three-dimensional space. This illustrates thegeneral statement that the categories of analog and digital are too narrow tocover the range of possible machines and organisms. It is possible thatSmolin's topological information processing may actually exist, both in livingcells and in the fine-structure of space-time.
Steve Grand reformulates my question in aninteresting way. He asks whether the signals carrying information are similaror dissimilar to the objects that they represent. If the signals are similar wemay call them analog, and if they are dissimilar we may call them digital. Whenthe question is put in this way, it becomes clear that living creatures areusually neither analog nor digital, because life does not usually representanything. Life is not a symbol for something else. Life just is. On the otherhand, brains do represent external objects, and the question whether a brainuses analog or digital symbols is meaningful.
Two respondents, Joseph Traub and JohnBaez, criticize my mention of the Pour-El-Richards theorem on technicalgrounds. The theorem says that an analog computer is more powerful than anydigital computer for performing certain abstractly defined tasks. Traub andBaez correctly point out that the theorem only applies to an ideal mathematicaluniverse and not to the physical universe that we inhabit. I never said thatthe theorem applies directly to the real world. I only said that it makes thesuperiority of analog devices in a cold universe less surprising. I challengeany mathematicians among you to find out whether some version of the theoremmight hold under conditions closer to the real world. John Baez has alreadyanswered this question in the negative for one particular set of assumptions.
In conclusion, I thank you all for raisinga lot of new questions which I hope we will continue to think about. Sciencethrives on mysteries, and the nature of life remains as mysterious as ever. Ihope and believe we will never run out of good questions.
菲利普·安德森 |諾貝爾獎得主;物理學家
I have the impression that the best answerto any question in the form "is X Y or Z?" is almost always"neither!" (As, for instance, was Bohr or Einstein right?") Tofocus strictly on life as an information process is to miss the point, widely.This is a mistake I myself was guilty of in my two decades old papers on theorigin of life, buying too naively into the "RNA world" and the ideathat self-replicating information was the essence of life.
In his most recent book,"Investigations", Stuart Kauffman defines a living organism as"an agent which can act on its own behalf". Perhaps this is toorestrictive, perhaps one should add replication and say "and itsdescendants' behalf", but the crucial word here is "act". Theinformation-handling capacity — sensing the gradient of nutrient for a motilebacterium, finding the direction from which the sunlight is coming — is merelya facilitation of the basic requirement, which is to go out and find a sourceof energy and to convert that energy into work. Work here is defined in itsthermodynamic sense as energy without entropy, energy which can be used todrive the system as far out of equilibrium as may be necessary to achieve thebasic goal of survival and reproduction.
To put this in Freeman's terms, somethingwill have to maintain, the black cloud or the silicon chip against, at the veryleast, the depredations of other black clouds or silicon chips wanting the sameenergy source, and Stu and I would argue that it would be this maintenanceobject which is actually alive. The information which the cloud containsrepresents a large departure from thermal equilibrium and to maintain and useit, or to replicate it accurately, work will be necessary, and the schemesdescribed do not tell me where the work is coming from.
(The above is the result of severaldiscussions with Stu about the material of his book, inspired on my part to agreat extent by Hopfield's beautiful discussions of the thermodynamics ofbiological proofreading of a couple of decades ago.)
There are of course other problems withthe view of life as pure information — where do the qualia go, does the blackcloud still see red? Does it experience depression or beauty? Isn't almost allperception an active process? and most thinking a social one, in the end — canone think without language?
喬治·戴森 | 科學史學家;作者，圖靈大教堂;機器中的達爾文
When I heard thatFreeman's Edge question was "Is life analog or digital?" Iwas intrigued, because, as Freeman so eloquently argued in *Origins of Life*(1986) the answer is "both".
Assuming Freeman's model wherebylife-as-we-know-it originated as the result of a digital parasite incorporatedinto the analog metabolism of its original host, the time-without-end questionis whether we can now slowly exterminate (or at least permanently archive) theparasite without killing the host. Seems to me the answer is yes.
特倫斯·塞諾夫斯基 | 計算神經科學家;弗朗西斯·克裡克薩爾克研究所教授;霍華德·休斯醫學研究所研究員;合著者（與帕特裡夏丘奇蘭），計算大腦
Freeman Dyson raises several intriguingquestions about life and computation. These questions are closely related totwo different styles of error correction, which is needed to preserveinformation and prevent catastrophic failure.
Digital computer memories use errorcorrection coding schemes, such as block codes, to achieve extremely low errorrates; this allows logical calculations to be carried out to great depth. Cellsuse an error correction scheme to achieve DNA replication error rates of lessthan one base error in 100 million. Modern error correcting codes incommunication are within a few percent of the Shannon limit.
Vertebrate brains depend on statistical redundancyfor reliable operation, which has the advantage of robustness to errors anddamage, but the logical depth of computation is limited. However, brains arenot general purpose computing devices, but special purpose systems withadaptive abilities.
Redundancy is a better strategy when thesignal to noise ratio becomes extremely low and the power available for codingand decoding becomes scarce. Although it might be possible to build a generalpurpose computer with this strategy, a special purpose system, along the linesof brains, might be best adapted to the conditions that Dyson has explored.
李·斯莫林 | 物理學家，周長研究所;作者，愛因斯坦未完成的革命
I am troubled by two assumptions thatFreeman and others seem to be making. First that there are only two choices forhow information can be coded, digital and analogue. Second, that nature isanalogue, apart from some quantum phenomena. Both seem to be false, and thisleads to a possible resolution of Freeman's quandary.
Consider the problem of classifying theembeddings of arbitrarily complicated graphs in three dimensional space, up totopology. The problem is topological and combinatorial, no continuous variablesare involved, but it is not known if there exists an algorithm which can solveit in finite time. It is plausible that the problem is unsolvable. There areother topological and combinatorial problems that are known to be noncomputable, for example classifying four manifolds or classifying finite groupsin general. If the classification problem cannot be solved then the informationcoded in the embedding of a graph is not digital because there is no algorithmwhich can in a finite time reduce the topology of an arbitrarily complicatedgraph to a representation in terms of a finite string of ones and zeros. But nocontinuous quantities are involved as all that is relevant is the topology ofthe embedding.
Furthermore, even if the problem is solvablein principle, it is likely that the time required to classify a graph will growextremely fast as the complexity of the graph is increased. Thus, even amoderately complicated graph may be knotted in a way that no digital computercould classify in a physically relevant amount of time. So it is certainly thecase that the information contained in such topological problems is not digitalfor all practical purposes.
Is this relevant for nature and forFreeman's query? Most likely yes.
One of the basic results of quantumgravity is that at the Planck scale the quantum states of geometry are coded interms of combinatorics and topology. In fact the quantum states of a largeclass of quantum theories of gravity are in one to one correspondence with theembedding classes of certain graphs, called spin networks. If there is nofinite procedure for classifying the embeddings of graphs in three space up totopology then there will be no digital representation of the information codedin quantum geometry, in spite of the complete absence of continuous variables.Even if the problem is solvable in principle, it is still almost certainly thecase that no digital computer built from a subsystem of the universe will beable to classify the possible quantum states of the geometry of the universe ina number of time steps fewer than the age of the universe in Planck units.
Two other results of quantum gravity, theBekenstein bound and the holographic principle, require that only finitedimensional state spaces are required to code the quantum information that canbe extracted from any region of the world with a finite area boundary. So itseems likely that continuous variables play no role in nature, but at the sametime, this does not mean nature is digital in the ordinary sense. The problemis that these finite dimensional state spaces have bases which aredistinguished by solving the problem of classifying embeddings of graphs. Sowhile the holographic principle says that no observer in the universe canaccess more than a finite amount of information, that information may be storedin a way that cannot be represented digitally by any computer that could bebuilt inside the universe.
Now, coming to life, one can wonderwhether cells may make use of combinatorially coded information that is notefficiently coded digitally. Possibilities for such codings are not hard tofind. For example, the topologist Louis Kauffman has hypothesized thatinformation about turning genes on and off may be partially coded in theknotting of DNA molecules. To support this hypothesis he points to theexistence of enzymes which change the topology of the folding of the DNAmolecules.
The difference between combinatorial anddigital coding of information is that when information is coded digitally allthe possible states of the memory are equally accessible. When information iscoded combinatorially, say in the knotting of some graphs, this is not thecase, the time required to store or retrieve information depends very stronglyon the state in which the information is coded. But a cell is not a generalpurpose computer, and there is no need that all possible configurations of themolecules where information is stored be equally accessible. What is requiredis only access to those states that are relevant for the functioning of thecell, and then only at the time they are needed. (Similarly the protein foldingproblem does not have to have a solution for arbitrary amino acid sequences,only for the much smaller subset that are relevant biologically.) So I dowonder whether the digital metaphor may be blinding us to ways in whichinformation could be stored in biological systems using the combinatorics andtopology of molecules.
This seems relevant for Freeman's worry,for if information can be stored in the topology of a system, then the systemcan be cooled or expanded arbitrarily without degrading the information. At thevery least, if the universe has non-trivial topology, on either the large orsmall scale, there are possibilities for storage of combinatorial informationwhere the discreteness of the states are maintained for arbitrarily lowenergies. At worst life will be able to survive by coding itself into thequantum geometry of space itself.
約翰·貝茲 |數學物理學家，.C河濱
Freeman Dyson mentioned a theorem due toPour-El and Richards, and reads it as saying that "analog computers aremore powerful than digital computers". I've worked a bit on this stuff anddisagree with this assessment. As usual, the devil is in the details.
Pour-El and Richards' result goes roughlylike this. They consider the "wave equation", but let me talk aboutMaxwell's equations in a vacuum, since that would work too, and it soundsnicer. They show there are solutions with the following property: at time zero,the electric and magnetic fields are computable functions, but at some latertime, there is one point in space at which the electric or magnetic field isnot computable. The trick is to set up a lot of waves coming in, which allcrash together at a single point at some moment.
As for "computable": herethey're using a more or less standard definition of "computable"functions of several real variables, taking real values. The idea behind thisdefinition is that you can write a computer program that can compute f(x) toany given accuracy if you specify x to sufficiently high accuracy.
Pour-El and Richards' result isinteresting, but notice the catch: to use this setup in a practical device,you'd have to be able to measure the electric or magnetic field at asingle point in spacetime. In practice we never do this: we measuresmeared-outaverages of the electric and magnetic fields, in a mannerlimited by the size of our probe.
In fact, it's crucial to Pour-El andRichard's argument that they are working with solutions where the electric andmagnetic field are continuous and have continuous first derivatives.Mathematicians know that these details can make or break an argument. Ifinstead we work with solutions that merely have finite energy (a weaker condition),their argument no longer works, because finite-energy solutions need not have awell-defined value at a single point in spacetime: only smeared averages arewell-defined!
And in fact, one can show that in thecontext of finite-energy solutions, if the electric and magnetic fields arecomputable at time zero, they will remain computable for all time. I believethis is more relevant to physics than the theorem Pour-El and Richards proved.
Of course, in this other theorem, we needa slightly different definition of "computable", since we're dealingwith solutions where only the smeared-out averages of fields make sense, nottheir values at specific points. But I came up with this definition when I wasan undergrad at a school near where Dyson hangs out. At the time I wasinterested in Schrodinger's equation rather than Maxwell's equation or the waveequation, and I proved that time evolution for Schrodinger's equation takescomputable wavefunctions to computable wavefunctions. But later I realized thatthe same techniques work for these other equations. So these days I doubt thatrealistic analog computers can compute nonrecursive functions.
凱文·凱利 | 資深特立獨行者，有線;作者，失控、技術需要什麼和必然
The discussion so far has made me wonderif my computer is digital. I inspected my iMac to see if I could tell. There'sa lot of stuff in there. The monitor part is definitely analog ‹ all thoserasters and light waves and pixels. There's a power supply which I know is notdigital but analog. There's the CD, which Minsky assures me is a soft analogrock. I see hardware ‹ it is analog, yes? And circuits boards. I have not triedmeasuring them, but I suspect a lot of the electrical currents running throughthe printed wires in this device would have analog curves. Eventually we get tothe CPUs. How much of what goes on in these little chips actually resemblesdigital processes? I have no idea, but my suspicions are high at this point.Even if all the activity in the chip was digital (and I doubt it), it's only asmall part of the life of this machine.
Ah, but it is the most essential part, ifnot the ONLY essential part one would say. Maybe. Reducing the activity of theentire computer to the abstraction of its CPU as a way to measure itsdigitalness seems almost tautological; it's like reducing life to its genes.
If only a part of my computer is digital,and maybe not as much as I first thought, then is this a perspective, as Jaronsuggests, that can change depending on how one looks at it? Is thedigital/analog question like particles and waves?