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enLots of science today (meteorology, cosmology) is based on computer simulation
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Lots of science today (meteorology, cosmology) is based on computer simulation or modeling for those phenomena that are difficult to observe directly. If a computer simulation gives me a result consistent with what we can see (star distribution for two galaxies that collide) can we infer that the underlying process is the same in the simulation and in physical world? The simulation is just numbers (or symbols) input as data about the system(s) modeled. Are numbers the underlying "stuff" of objects, too, rather than atomic particles, etc.? </div>
Wed, 26 Sep 2018 15:27:04 +0000Anonymous27517 at http://www.askphilosophers.orgIf I investigate the Goldbach conjecture by testing individual even integers to
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If I investigate the Goldbach conjecture by testing individual even integers to verify that they accord with it, do I have more reason to believe that the conjecture is true the more integers I verify? Or am I in just the same epistemic position regarding the conjecture whether I've verified one integer or a billion? </div>
Sun, 29 Oct 2017 09:39:02 +0000Anonymous26974 at http://www.askphilosophers.orgIn mathematics, it is commonly accepted that it is impossible to divide any
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In mathematics, it is commonly accepted that it is impossible to divide any number by zero. But I don't see why this necessarily has to be the case. For example, it used to be thought of impossible to take the square root of a negative number, until imaginary numbers were invented. If one could create another set of numbers to account for the square root of negatives, then what is stopping anyone from creating another set of numbers to account for division by zero. </div>
Thu, 31 Aug 2017 16:11:42 +0000Anonymous26829 at http://www.askphilosophers.orgConsider the mathematical number Pi. It is a number that extends numerically
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Consider the mathematical number Pi. It is a number that extends numerically into infinity, it has no end and has no repeating pattern to its digits. Currently we have computers that can calculate Pi out to many thousands of digits but at a certain point we reach a limit. Beyond that limit those numbers are unknown and essentially do not exist until they are observed.
With that in mind, my question is this, if we could create a more powerful computer that could continue to calculate Pi beyond the current limit, and we started at exactly the same time to compute Pi out beyond the current limit on two identical computers, would we observe the computers generating the same numbers in sequence. If this is the case would that not infer that reality is deterministic in that unobserved and unknown numbers only become “real” upon being observed and that if identical numbers are generated those numbers have been, somehow, predetermined. Alternatively, if our reality was non-deterministic would that not mean that the two computers would generate potentially different numbers at each iteration as it moved forward into unobserved infinity inferring that unobserved reality is not set and therefore we live in a reality defined by free will?
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Wed, 28 Jun 2017 18:57:47 +0000Anonymous26686 at http://www.askphilosophers.orgIf there is a category "Empty Set" it has to have the property "emptiness". It
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If there is a category "Empty Set" it has to have the property "emptiness". It must have this property that separates it from every other set. Thus it is not propertyless - contradiction? </div>
Fri, 16 Jun 2017 11:48:03 +0000Anonymous26652 at http://www.askphilosophers.orgIs it strange that you can't divide by zero?
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Is it strange that you can't divide by zero? </div>
Sun, 21 May 2017 23:16:50 +0000Anonymous26594 at http://www.askphilosophers.orgso What is more real? The number two or my two feet?
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so What is more real? The number two or my two feet? </div>
Tue, 28 Feb 2017 02:26:28 +0000Anonymous26318 at http://www.askphilosophers.orgRepresentation of reality by irrational numbers.
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Representation of reality by irrational numbers.
In the world there are an infinite number of space/time positions represented by irrational numbers. I should think that all these positions are real, even though they cannot be precisely described mathematically. Does this mean that mathematics cannot fully describe reality? What are the philosophical implications of this?
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Wed, 07 Dec 2016 10:39:48 +0000Anonymous26085 at http://www.askphilosophers.orgIt seems to me that there are two kinds of numbers: the kind that the concept of
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It seems to me that there are two kinds of numbers: the kind that the concept of which we can grasp by imagining a case that instantiates the concept, and the kind that we cannot imagine. For example, we can grasp the concept of 1 by imagining one object. The same goes for 2, 3, 0.5 or 0, and pretty much all the most common numbers. But there is this second kind that we cannot imagine. For example, i (square root of -1) or '532,740,029'. It seems to me that nobody can really imagine what 532,740,029 objects or i object(you see, I don't even know whether I should put 'object' or 'objects' here or not because I don't know whether i is single or plural; I don't know what i is) are like. So, Q1) if I cannot imagine a case that instantiates concepts like '532,740,029', do I really know the concept, and if so, how do I know the concept? Q2) is there a fundamental difference between numbers whose instances I can imagine and those I cannot? (I lead towards there is no difference, but I don't know how to account for this at least seemingly existent difference with regards to human imagination) </div>
Fri, 11 Nov 2016 18:48:19 +0000Anonymous26033 at http://www.askphilosophers.orgI have been intrigued by the theory expounded by the MIT physicist Max Tegmark
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I have been intrigued by the theory expounded by the MIT physicist Max Tegmark that the universe is composed entirely of mathematical structure and logical pattern, and that all perceived and measured reality is that which has emerged quite naturally from the mathematics. That theory simplifies the question of why mathematics is such a powerful and necessary tool in the sciences. The theory is platonist in essence, reducing all of existence to pure mathematical forms that, perhaps, lie even beyond the realm of spacetime. Mathematics, in fact, may be eternal in that sense.
The Tegmarkian scheme contains some compelling arguments. One is that atomic and subatomic particles have only mathematical properties (mass, spin, wavelength, etc). Any proton, for example, is quite interchangeable with any other. And, of course, these mathematical particles are the building blocks of the universe, so it follows that the universe is composed of mathematical structures. Another is that the vastness of the universe is not so vast if composed of math, which can outpace any physical greatness with ease, even when all specie of multiple multiplying universes are in the mix. Tegmark's theory coexists happily and cozily with Hugh Everett's famous many-worlds hypothesis.
Dr. Tegmark, by the way, explains our conscious-being status as being the result of the evolution of "self-aware mathematical structures".
I have taken a liking to Max Tegmark. His ideas somehow make a lot of sense to me, and I find his theory actually liberating and satisfying. However, it just about makes the case that reality itself is illusory (which in my heart I'm quite okay with).
Anyway, given the power of his theory, and it's potential utility, I am surprised it has not been a more visible subject of inquiry and reflection among philosophers. I would be delighted to know the place that such theory has in the philosophy of existence, the philosophy of mathematics, the theory of knowledge, or the philosophy of science. Is Tegmark's theory an active and common subject of debate? (I think it should be.) </div>
Sat, 24 Sep 2016 04:09:58 +0000Anonymous25880 at http://www.askphilosophers.org