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For context, Im using kalshi and they have perpetuals for cryptos like btc and eth and I was wondering, why cant I just leverage “safe” crypto?. I know I can get liquidated but lets say a crypto like eth shouldnt be THAT swingy. Why arent many people saying this is a viable strategy? (Also I have almost no knowledge on trading, investing, and crypto. So take this lightheartedly.) submitted by /u/Busy_Presentation463 [link] [Kommentare]

ben.eth i want to send him some roses. I just love how he scammed all of us. If you have a location it would be great submitted by /u/Taking-up-space- [link] [Kommentare]

Stanford Encyclopedia of Philosophy Browse Table of Contents What's New Random Entry Chronological Archives About Editorial Information About the SEP Editorial Board How to Cite the SEP Special Characters Advanced Tools Contact Support SEP Support the SEP PDFs for SEP Friends Make a Donation SEPIA for Libraries Entry Contents Bibliography Academic Tools Friends PDF Preview Author and Citation Info Back to Top Computation in Physical SystemsFirst published Wed Jul 21, 2010; substantive revision Wed Aug 20, 2025 In our ordinary discourse, we distinguish between physical systems that perform computations, such as computers and calculators, and physical systems that don’t, such as rocks. Among computing devices, we distinguish between more and less powerful ones. These distinctions affect our behavior: if a device is computationally more powerful than another, we pay more money for it. What grounds these distinctions? What is the principled difference, if there is one, between a rock and a calculator, or between a calculator and a computer? Answering these questions is more difficult than it may seem. In addition to our ordinary discourse, computation is central to many sciences. Computer scientists design, build, and program computers. But again, what counts as a computer? If a salesperson sold you an ordinary rock as a computer, you should probably get your money back. Again, what does the rock lack that a genuine computer has? How powerful a computer can you build? Can you build a machine that computes anything you wish? Although it is often said that modern computers can compute anything (i.e., any function defined over a denumerable domain, such as the natural numbers or strings of letters from a finite alphabet), this is incorrect. Ordinary computers can compute only a tiny subset of all functions. Is it physically possible to do better? Which functions are physically computable? These questions are bound up with the foundations of physics. Computation is also central to the mind sciences, and perhaps other areas of biology. According to the computational theory of cognition, cognition is a kind of computation: the behavior of cognitive systems is causally explained by the computations they perform. In order to test a computational theory of something, we need to know what counts as a computation in a physical system. Once again, the nature of physical computation lies at the foundation of empirical science. 1. Abstract Computation and Concrete Computation 2. Accounts of Concrete Computation 2.1 The Simple Mapping Account 2.2 Restricted Mapping Accounts 2.3 The Semantic Account 2.4 The Syntactic Account 2.5 The Mechanistic Account 3. Is Every Physical System Computational? 3.1 Varieties of Pancomputationalism 3.2 Unlimited Pancomputationalism 3.3 Limited Pancomputationalism 3.4 The Universe as a Computing System 4. Physical Computability 4.1 The Physical Church-Turing Thesis: Bold 4.2 The Physical Church-Turing Thesis: Modest 4.3 Hypercomputation Bibliography Academic Tools Other Internet Resources Related Entries 1. Abstract Computation and Concrete Computation Computation may be studied mathematically by formally defining computational objects, such as algorithms and Turing machines, and proving theorems about their properties. The mathematical theory of computation is a well-established branch of mathematics. It deals with computation in the abstract, without worrying much about physical implementation. By contrast, most uses of computation in science and ordinary practice deal with concrete computation: computation in concrete physical systems such as computers and brains. Concrete computation is closely related to abstract computation: we speak of physical systems as running an algorithm or as implementing a Turing machine, for example. But the relationship between concrete computation and abstract computation is not part of the mathematical theory of computation per se and requires further investigation (cf. Curtis-Trudel 2022 for an argument that abstract and concrete computation cannot be given a unified account). Questions about concrete computation are the main subject of this entry. Nevertheless, it is important to bear in mind some basic mathematical results. An important notion of computation is that of digital computation, which Alan Turing, Kurt Gödel, Alonzo Church, Emil Post, and Stephen Kleene formalized in the 1930s. Their work investigated the foundations of mathematics. One crucial question was whether first order logic is decidable — whether there is an algorithm that determines whether any given first order logical formula is a theorem. Both Turing (1936–7) and Church (1936) proved that the answer is negative: there is no such algorithm. To show this, they offered precise characterizations of the informal notion of algorithmically computable function (over a denumerable domain). Turing did so in terms of so-called Turing machines (TMs) — devices that manipulate discrete symbols written on a tape in accordance with finitely many instructions. Other logicians did the same thing — they formalized the notion of algorithmically computable function — in terms of other notions, such as general recursive functions and λ-definable functions. To their surprise, all such notions turned out to be extensionally equivalent, that is, any function computable within any of these formalisms is computable within any of the others. This is evidence that their quest for a precise definition of “algorithm” or “algorithmically computable function” had been successful. The resulting view — that TMs and other equivalent formalisms capture the informal notion of algorithm for computing functions over a denumerable domain — is now known as the Church-Turing thesis (more on this in Section 4). The study of computable functions, made possible by the work of Turing et al., is part of the mathematical theory of computation. The theoretical significance of Turing et al.’s notion of computation can hardly be overstated. As Gödel pointed out (in a lecture following one by Tarski): Tarski has stressed in his lecture (and I think justly) the great importance of the concept of general recursiveness (or Turing’s computability). It seems to me that this importance is largely due to the fact that with this concept one has for the first time succeeded in giving an absolute definition of an interesting epistemological notion, i.e., one not depending on the formalism chosen. (Gödel 1946, 84) Turing also showed that there are universal TMs — machines that can compute any function computable by any other TM. Universal TMs do this by executing instructions that encode the behavior of the machine they simulate. Assuming the Church-Turing thesis, universal TMs can compute any function computable by algorithm. This result is significant for computer science: you don’t need to build different computers for different functions; one universal computer will suffice to compute any computable function. Modern digital computers are universal in this sense: they can compute any function computable by algorithm for as long as they have time and memory. (Strictly speaking, a universal machine has an unbounded memory, whereas digital computer memories can be extended but not indefinitely, so they are not unbounded.) The above result should not be confused with the common claim that computers can compute anything. This claim is false: another important result of computability theory is that most functions are not computable by TMs (and hence, by digital computers). TMs compute functions defined over denumerable domains, such as strings of letters from a finite alphabet. There are uncountably many such functions. But there are only countably many TMs; you can enumerate TMs by enumerating all lists of TM instructions. Since an uncountable infinity is much larger than a countable one, it follows that TMs (and hence digital computers) can compute only a tiny portion of all functions (over denumerable domains, such as natural numbers or strings of letters). TMs and most modern computers are known as (classical) digital computers, that is, computers that manipulate strings of discrete, unambiguously distinguishable states by performing discrete operations that are sensitive to the position of a state within the string. Digital computers are sometimes contrasted with analog computers, which manipulate variables that can be continuous via operations such as integration and differentiation. Continuous variables are variables that can change their value continuously over time while taking any value within a certain interval. Analog computers are used primarily to solve certain systems of differential equations (Pour-El 1974, Rubel 1993). Classical digital computers may also be contrasted with quantum computers. Quantum computers manipulate quantum states called qudits (usually binary qudits, known as qubits). Unlike the computational states of digital computers, qubits are not unambiguously distinguishable from one another. This entry will focus primarily on classical computation. For more on quantum computation, see the entry on quantum computing. The same objects studied in the mathematical theory of computation — TMs, algorithms, and so on — are typically said to be implemented by concrete physical systems. This poses a problem: how can a concrete, physical system perform a computation when computation is defined by an abstract mathematical formalism? This may be called the problem of computational implementation. The problem of computational implementation may be formulated in a couple of different ways. Platonists interpret the formalisms of computability theory as defining abstract objects. According to platonists, TMs, algorithms, and the like are abstract objects. But how can a concrete physical system implement an abstract object? Non-platonists treat the formalisms of computability theory as abstract computational descriptions. But how can a concrete physical system satisfy an abstract computational description in a way that turns it into a system that performs the computation defined by the computational description? Regardless of how the problem of computational implementation is formulated, solving it requires an account of concrete computation — an account of what it takes for a physical system to implement a given computation. A closely related problem is that of distinguishing between physical systems such as digital computers, which appear to compute, and physical systems such as rocks, which appear not to compute. Unlike computers, ordinary rocks are not sold in computer stores and are usually not considered computers. Why? What do computers have that rocks lack, such that computers compute and rocks don’t? (If indeed they don’t?) In other words, what properties must a physical system have to implement computations? Different answers to these questions give rise to different accounts of concrete computation. Questions on the nature of concrete computation should not be confused with questions about computational modeling. The dynamical evolution of many physical systems may be described by computational models — computer programs that simulate the dynamics of a system. The behavior of rocks — as well as rivers, ecosystems, and planetary systems, among many others — may well be modeled computationally. It doesn’t follow that the modeled systems are computing devices — that they themselves perform computations. Prima facie, only relatively few and quite special systems compute. Explaining what makes them special — or explaining away our feeling that they are special — is the job of an account of concrete computation. 2. Accounts of Concrete Computation Consider a mathematically defined computational system undergoing a state transition, s1 → s2, and a concrete physical system undergoing a state transition, p1 → p2. What must be the case for p1 → p2 to implement s1 → s2? Different accounts give different answers. 2.1 The Simple Mapping Account One of the earliest and most influential accounts of computation, due to Hilary Putnam (1960/1975a, 365; 1967/1975a, 433–4), was dubbed the “simple mapping account” by Godfrey-Smith (2009). To a first approximation, the account says that anything that is accurately described by a computational description C is a computing system implementing C. More precisely, a physical system S performs computation C just in case (i) there is a mapping from the states ascribed to S by a physical description to the states defined by computational description C, such that (ii) the state transitions between the physical states, such as p1 → p2, mirror the state transitions between the computational states, such as s1 → s2. Clause (ii) requires that for any computational state transition of the form s1 → s2 (specified by the computational description C), if the system is in a physical state that maps onto s1, it then goes into a physical state that maps onto s2. One difficulty with the formulation above is that ordinary physical descriptions, such as systems of differential equations, generally ascribe uncountably many states to physical systems, whereas ordinary computational descriptions, such as TMs tables, ascribe at most countably many states. Thus, there are not enough computational states for the physical states to map onto. One solution to this problem is to reverse the direction of the mapping, requiring a mapping of the computational states onto (a subset of) the physical states. A more common solution — often left implicit — is to select either a subset of the physical states or equivalence classes of the physical states and map those onto the computational states. When this is done, clause (i) is replaced by the following: (i′) there is a mapping from a subset of (or equivalence classes of) the states ascribed to S by a physical description to the states defined by computational description C. The simple mapping account turns out to be very liberal: it attributes many computations to many systems. In the absence of restrictions on which mappings are acceptable, such mappings are relatively easy to come by. As a consequence, some have argued that every physical system of enough complexity implements every computation from a broad class (Putnam 1988, Searle 1992). This thesis, which trivializes the claim that something is a computing system, will be discussed in Section 3.1. Meanwhile, the desire to avoid this trivialization result is one motivation behind other accounts of concrete computation. 2.2 Restricted Mapping Accounts One way to construct accounts of computation that are more restrictive than the simple mapping account is to constrain acceptable mappings. As we’ve seen, according to the simple mapping account, clause (ii) requires that for any computational state transition of the form s1 → s2 (specified by a computational description), if the system is in a physical state that maps onto s1, it then goes into a physical state that maps onto s2. That second part of (ii) is a material conditional. It may be strengthened by turning it into a logically stronger conditional — specifically, a conditional expressing a relation that supports counterfactuals. In a pure counterfactual account, clause (ii) is strengthened simply by requiring that the physical state transitions support certain counterfactuals (Block 1978, Maudlin 1989, Copeland 1996, Rescorla 2014; Campbell and Yang 2021). In other words, a pure counterfactual account requires the mapping between computational and physical descriptions to be such that the counterfactual relations between the physical states be isomorphic to the counterfactual relations between the computational states. These counterfactuals are not satisfied by the material conditional of clause (ii) as it appears in the simple mapping account of computation. Thus, counterfactual accounts are stronger than the simple mapping account. An account of concrete computation in which the physical state transitions support counterfactuals may also be generated by appealing to causal, nomic, or dispositional relations, assuming (as most people do) that causal, nomic, or dispositional relations support counterfactuals. Appealing to causation or dispositions may also have advantages over pure counterfactual accounts in blocking unwanted computational implementations (Klein 2008, 145, makes the case for dispositional versus counterfactual accounts). In a causal account, clause (ii) is strengthened by requiring a causal relation between the physical states: for any computational state transition of the form s1 → s2 (specified by a computational description), if the system is in a physical state that maps onto s1, its physical state causes it to go into a physical state that maps onto s2 (Chrisley 1995, Chalmers 1995, 1996, 2011, Scheutz 1999, 2001). To this causal constraint on acceptable mappings, David Chalmers (1995, 1996, 2011) adds a further restriction (in order to avoid unlimited pancomputationalism, which is discussed in Section 3): a genuine physical implementation of a computational system must divide into separate physical components, each of which maps onto the components specified by the computational formalism. As Godfrey-Smith (2009, 293) notes, this combination of a causal and a localizational constraint goes in the direction of mechanistic explanation (Machamer, Darden, and Craver 2000). Accounts of computation that are explicitly based on mechanistic explanation will be discussed in Section 2.5. For now, the causal account simpliciter requires only that the mappings between physical and computational descriptions be such that the causal relations between the physical states are isomorphic to the relations between state transitions specified by the computational description. In this sense, according to the causal account, concrete computation is the causal structure of a physical process. In a dispositional account, clause (ii) is strengthened by requiring a dispositional relation between the physical states: for any computational state transition of the form s1 → s2 (specified by a computational description), if the system is in a physical state that maps onto s1, the system manifests a disposition whose manifestation is the transition from the physical state that maps onto s1 to a physical state that maps onto s2 (Klein 2008). In other words, the dispositional account requires the mapping between computational and physical descriptions to be such that the dispositional relations between the physical states be isomorphic to the relations between state transitions specified by the computational description. Thus, according to the dispositional account, concrete computation is the dispositional structure of a physical process. Other restricted mapping accounts may restrict clause (ii) by requiring that the physical state transitions mapping onto computational state transitions be lawful (Stabler 1987), that mappings between physical and computational transitions minimize the length of the shortest program that can return a computational description given a physical description (Millhouse 2019), or that physical states that map onto computational states be predictive of the computational transitions (Horsman et al. 2014; 2018; cf. Fletcher 2018). The difference between the simple mapping account and restrictive mapping accounts may be seen by examining a simple example. Consider a rock under the sun, early in the morning. During any time interval, the rock’s temperature rises. The rock goes from temperature T to temperature T+1, to T+2, to T+3. Now consider a two-state automaton that alternates between its two states (call them 0 and 1) on each computational step, which will be loosely called a ‘NOT gate with feedback’ hereafter for simplicity. At first, suppose the NOT gate receives ‘0’ as an input; it then returns a ‘1’. After the ‘1’ is fed back to the NOT gate, the gate returns a ‘0’ again, and so on. The NOT gate goes back and forth between outputting a ‘0’ and outputting a ‘1’. Now map physical states T and T+2 onto ‘0’; then map T+1 and T+3 onto ‘1’. According to the simple mapping account, the rock implements a NOT gate with feedback undergoing the computation represented by ‘0101’. By contast, according to the counterfactual account, the rock’s putative computational implementation is spurious, because the physical state transitions do not support counterfactuals. If the rock were put in state T, it may or may not transition into T+1 depending on whether it is morning or evening and other extraneous factors. Since the rock’s physical state transitions that map onto the NOT gate’s computational state transitions do not support counterfactuals, the rock does not implement the NOT gate with feedback according to the counterfactual account. According to the causal and dispositional accounts too, this putative computational implementation is spurious, because the physical state transitions are not due to causal or dispositional properties of the rock and its states. T does not cause T+1, nor does the rock have a disposition to go into T+1 when it is in T. Rather, the rock changes its state due to the action of the sun. Since the rock’s physical state transitions that map onto the NOT gate’s computational state transitions are not grounded in either the causal or dispositional properties of the rock and its states, the rock does not implement the NOT gate with feedback according to the causal and dispositional accounts. Importantly, under the above family of restrictive mapping accounts, there are mappings between any physical system and at least some computational descriptions. Thus, according to these accounts, everything performs at least some computations (cf. Section 3.2). This still strikes some as overly inclusive. In computer science and cognitive science, there seems to be a distinction between systems that compute and systems that do not. To account for this distinction, Anderson and Piccinini (2024) propose a “robust mapping account” based on three precise mapping restrictions that are independently motivated by physical information theory. First, if a physical system P is to implement a computational system defined by computational description C, it must possess physical states that map onto all computational states defined by C — more precisely, there must be physical states belonging to subsystems of P that map onto each value of each variable defined by C. Second, if p1 and p2 are physical states that map onto computational states s1 and s2, respectively, then the physical state transition p1 → p2 must map onto the computational state transition s1 → s2. Finally, and most significantly, for any computational state s defined by C, each physical state that maps onto s must be equally informative about the computational trajectory of the system as is s. In other words, it should not be possible to infer either more or less about the computational evolution of the system by knowing which particular physical state the system is in than one could infer by knowing the computational state onto which that physical state maps. This robustness condition generalizes on a faithfulness requirement proposed by Ladyman et al. (2007). In our example of the rock under the sun, knowing the temperature of the rock allows one to infer whether it is transitioning into the first occurrence of ‘1’, the first occurrence of ‘0’, the second occurrence of ‘1’, and so forth, which is a lot more than what can be inferred by knowing that the input was ‘0’ or ‘1’. Thus, a rock does not implement a NOT gate with feedback by laying under the sun. By similar reasoning, Anderson and Piccinini (2024) argue that many mappings that count as computational implementations under other restricted mapping accounts are not robust enough for physical systems to bear the physical signature of any computation. To bear the physical signature of a computation, they argue, a physical system must satisfy the three conditions they propose. 2.3 The Semantic Account In our everyday life, we usually employ computations to process meaningful symbols, in order to extract information from them. The semantic account of computation turns this practice into a metaphysical doctrine: computation is the processing of representations — or at least, the processing of appropriate representations in appropriate ways. Opinions as to which representational manipulations constitute computations vary a great deal (Fodor 1975, Cummins 1983, Pylyshyn 1984, Churchland and Sejnowski 1992, Shagrir 2006, 2022, Sprevak 2010). What all versions of the semantic account have in common is that, in a slogan, there is “no computation without representation” (Fodor 1981, 180). The semantic account may be seen as imposing a further restriction on acceptable mappings. In addition to the restriction(s) imposed by restricted mapping accounts, the semantic account imposes a semantic restriction. Only physical states that qualify as representations may be mapped onto computational descriptions, thereby qualifying as computational states. If a state is not representational, it is not computational either. The semantic account is popular in philosophy of mind, because it appears to fit some of its specific needs better than other accounts. Since minds and digital computers are generally assumed to manipulate (the right kind of) representations, they turn out to compute. Since most other systems are generally assumed not to manipulate (the relevant kind of) representations, they do not compute. Thus, the semantic account appears to accommodate some common intuitions about what does and does not count as a computing system. It keeps minds and computers in while leaving most everything else out, thereby vindicating the computational theory of cognition as a strong and nontrivial theory. The semantic account raises three important questions: how representations are to be individuated, what counts as a representation of the relevant kind, and what gives representations their semantic content. On the individuation of computational states, the main debate divides internalists from externalists. According to externalists, computational vehicles are symbols individuated by their wide cognitive contents — paradigmatically, the things that the symbols stand for (Burge 1986, Shapiro 1997, Shagrir 2001). In contrast, most internalists maintain that computational vehicles are symbols individuated by narrow cognitive contents (Segal 1991). Narrow contents are, roughly speaking, semantic contents defined in terms of intrinsic properties of the system. Cognitive contents, in turn, are contents ascribed to a system by a cognitive psychological theory. For instance, the cognitive contents of the visual system are visual contents, whereas the cognitive contents of the auditory system are auditory contents. To illustrate the dispute, consider two physically identical cognitive systems A and B. Among the symbols processed by A is symbol S. A produces instances of S whenever A is in front of bodies of water, when A is thinking of water, and when A is forming plans to interact with water. In short, symbol S appears to stand for water. Every time A processes S, system B processes symbol S′, which is physically identical to S. But system B lives in an environment different from A’s environment. Whenever A is surrounded by water, B is surrounded by twater. Twater is a substance superficially indistinguishable from water but in fact physically different from it. Thus, symbol S′ appears to stand for twater (cf. Putnam 1975b). So, we are assuming that A and B live in relevantly different environments, such that S appears to stand for water while S′ appears to stand for twater. We are also assuming that A is processing S in the same way that B is processing S′. There is no intrinsic physical difference between A and B. According to externalists, when A is processing S and B is processing S′ they are in computational states of different types. According to internalists, A and B are in computational states of the same type. In other words, externalists maintain that computational states are individuated in part by their reference, which is determined at least in part independently of the intrinsic physical properties of cognitive systems. By contrast, internalists maintain that computational states are individuated in a way that supervenes solely on the intrinsic physical properties of cognitive systems. So far, externalists and internalists agree on one thing: computational states are individuated by cognitive contents. This assumption can be resisted without abandoning the semantic account of computation. According to Egan (1999, 2025), computational vehicles are not individuated by cognitive contents of any kind, whether wide or narrow. Rather, they are individuated by their mathematical contents — that is, mathematical functions and objects ascribed as semantic contents to the computational vehicles by a computational theory of the system. Since mathematical contents are the same across physical duplicates, Egan maintains that her mathematical contents are a kind of narrow content — she is a kind of internalist. Let us now turn to what counts as a representation. This debate is less clearly delineated. According to some authors, only structures that have a language-like combinatorial syntax, which supports a compositional semantics, count as computational vehicles, and only manipulations that respect the semantic properties of such structures count as computations (Fodor 1975, Pylyshyn 1984). This suggestion flies in the face of computability theory, which imposes no such requirement on what counts as a computational vehicle. Other authors are more inclusive on what representational manipulations count as computations, but