New answers tagged

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As you know humans are only one of the species among myriads of animals. As in the case of other animals, when awake, their senses are opened outwards. I mean, senses are usually used to receive information regarding outside world only. And it is through senses he sees this phenomenal world. Each object he sees or perceives would never make him think of ...


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The status of zero has always been a source of philosophical dispute. There seems to have been an incremental process towards understanding it's importance & usefulness. Modern use seems to have been established by the time of Ptolemy's very influential work on astronomy, 130AD. The earliest notation for zero was in Ancient Egypt,1330BC. The Ancient ...


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"So my question is: what is it that human mind can do which a computer (Universal TM) can not?" For a start, UTMs once set in motion have no inputs so can't perceive anything. You might say, well we'll simply make an extension to Turings 1936 definition of a UTM that allows real-time inputs, but (a) that's not a UTM and (b) allowing real-time inputs opens up ...


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Qeuestion: So my question is: what is it that human mind can do which a computer (Universal TM) can not? Answer: The answer is “to have qualia and consicousness” it its system. Physically, our mind functions from a very complex group of biological circuits made up of carbon-based elements, but these circuits operate solely on physical laws (i.e., no magics ...


3

So my question is: what is it that human mind can do which a computer (Universal TM) can not? INTRODUCTION Let us presume that you set aside the obvious retort: human brains are embodied and have control mechanisms like the endocrine system which regulate behavior based on emotion. Also, let us set aside the difference in performance characteristics ...


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Usually computers hardly have power of imagination. In other words its power of imagination is very low. So it cannot compose beautiful poems, dramas or other similar creations in which very great imagination is required.


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Mathematics is a toolkit of valuable concepts for interpreting data in the world around us. We often say that there is a distinction between “pure” and “applied” maths to delineate the way in which sometimes we are just interested in building up our toolkit and our familiarity with its intricacies, and at other times we are using it to help make statements, ...


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Are you asking if in another universe 2 + 2 = 5 is true but with the same meaning of the concepts behind “2”, “+”, “=” and “5” as for us? It can only be, if successful (correct) rational inference might yield truths which are not necessary truths. But if that’s so, is unanswerable. Are you asking about the application of mathematics? That in another ...


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There is something called Intuitionistic Logic. It's used in lots of AI and was created by the great topologist Brouwer. It considers only Potential Infinity as real. https://plato.stanford.edu/entries/intuitionism/#IntLog The exact nature of logic is viewed by many professional logicians as a fundamental, yet open problem. Considering fundamental logic, ...


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I think you are referring to simple math , like arithmetic. A universe where counting does not exist. You can't count objects. Numbers have no meaning. Space and time have no meaning and there is something else in its place. A place where logic does not exist. I don't have the answer, I am just trying to clarify your question. Why would some ...


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The mathematization of science is a lot stronger a movement than just: "the modern success of the hard sciences". it is actually a reasonable inference from material reductionism. This is because matter appears, at the quantum scale to not really be material, but mathematical. The rationale behind the dominant view of QM, the Copenhagen Interpretation, s "...


1

When studying nature we often study the relationships between various forms of energy. These relationships are the origin of the structures which we use mathematics to describe. This method works quite well but the idea that we are projecting structure onto the universe based upon our current understanding of mathematics is inescapably true. We usually frame ...


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Chalmers does not mean ordinary visual imagination (our faculty to create representations which faintly resemble real visual sense impressions). Instead he means something like forming a concept, though only incompletely. I. e. not grasping all details, all internal relations of a concept – of which some may turn out to be incoherent. Descartes famously ...


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A perfect circle can be imagined and visualized by a mathematician who is a geometer, and its definition can be precisely expressed by him or her mathematically. That mathematical expression can be readily presented graphically as part of the definition and accepted as valid by other mathematicians, even though the graphic representation of it is ...


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Wittgenstein discusses at length the meaning of unproved conjectures, and of the status of their truth value, during his middle period in Philosophical Grammar and Philosophical Remarks, and during the late period in Lectures on the Foundations of Mathematics and Remarks on the Foundations of Mathematics. Although much in his views changes, he basically ...


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Mathematics is the observation of immutable laws and principles. Take a simple observable, immutable reality, such as the conservation of energy. One can express it as an invariant equation such as the following: E(t1) = E(t2) For any two times t1 and t2. For dynamical laws that involve variability and yet for which there are still immutable constraints (...


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To motivate this, consider a sandbox theory: The nature of the shape of the Earth. We might be pretty sure that the Earth is round-ish. That is, if you were to travel along the surface of the Earth trying to keep a constant heading, dealing as you might with oceans and mountains etc., eventually you would come back to where you started. And that you could ...


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Short version: No, this doesn't work. First, note that you haven't stated Godel's theorem correctly - rather, it is: Every consistent computably axiomatizable theory "containing enough arithmetic" is incomplete. "Computably axiomatizable" here basically means that the theory isn't so complicated as to be impossible to describe; for example, taking a ...


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Endless Possibilities You are skeptical of the claim that "everything will occur, given an infinite number of opportunities." Other answers have given a good explanation of when this claim is true and when it is false. However, I would like to assemble the various ideas into a single answer. Probability problems are often formulated in terms of choosing ...


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You are right that infinite trials do not imply that a given state will ever be reached. The independence assumption of letters, coin tosses, and die rolls means that we are sampling with replacement. The probability that a certain sequence will never occur over infinite independent samples, while infinitesimally small, is nonzero. Thus the gambler's fallacy ...


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This isn't a full answer, but I'd like to point out that you've formulated an alternate version of Zeno's Paradox. As the amount of time increases, the probability that some rare event does not occur becomes smaller and smaller but is never exactly zero. This is similar to how Zeno moves ever closer to but never reaches the target destination. Nonetheless, ...


1

One fallacy that is evident in your question but has not been addressed by the other answers is: everything will occur in an infinite timeline And you said something that is an instance of the fallacy: if the Universe is infinite, there must be a planet exactly like ours somewhere Both of these are completely fallacious. Nothing about an infinite ...


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The people who are pointing out that you've stumbled upon the concept of "almost sure event" in probability theory are correct, but this is rather beside the point. The fact is that "almost sure events" (that is, events having probability 1) fail to happen all the time. Any experiment where a fair coin is tossed countably many times and a specific sequence ...


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Here, I think, is a more succinct answer: Let's say we have a dice with 1 trillion sides. Then, the probability of a given outcome on the next roll of the dice is one-in-a-trillion. On the other hand, the probability of getting a given outcome, at least once, given infinite dice rolls approaches 1. Given enough time, monkeys banging randomly at a ...


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You're right about the gambler's fallacy, but you're missing something essential about infinity. Infinity doesn't stop. So, you've got your immortal monkey and his endless reams of typewriter supplies, and a typewriter with 40 keys. He endlessly hammers on the keys perfectly randomly. The probability that he types a "T" on the first try is 1/40. The ...


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"If you made 1,000,000 similar decisions, the probability of that final outcome being reached at any one moment is 1 in a million." That quote represents the root of your misconception. If a coin is tossed 1 million times, the likelihood of any specific sequence of 1 million tosses is 1 in 2^1000000. However, the chances of tossing heads 10 times in a row ...


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It looks like you've hit upon the concept of almost surely in probability theory. Something occurs "almost surely" if it happens with probability 1, but there still exist situations where that thing does not occur. The infinite coin flips problem is a great example - with infinite coin flips, you will almost surely see at least one result of heads, that is, ...


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