Jump to content

=FEW=Revolves

Members
  • Content Count

    9
  • Joined

  • Last visited

Community Reputation

1 Neutral

About =FEW=Revolves

  • Rank
    Member
  1. Still, I think I can say the above with confidence. Simply because it's not something the open source community considers as "We can solve it in the next 100 years" but it instead is of the category "Almost certainly impossible". Of course, lacking a proof renders this into speculation.
  2. The quantum computing thing: That's a common misconception. Quantum computers don't simulate all possible 2^n states using n qbits. If that were the case, then every single NP problem could be solved using a simple polynomial time and space algorithm using qbits. If this were actually the case, I could tell you a whole lot more of people would be researching quantum computing, not to mention a whole lot more money would be going into it right now. As it stands, only very few problems are actually known to be quickly solveable by quantum computers which classical computers can not do - in particular, integer factorization. See this comic (very scientific source ayyy lmao - but it truely is a concise description): http://www.smbc-comics.com/comic/the-talk-3
  3. From my perspective I got hit by a short burst (all in the span of a second) - I didn't even see any tracers at all. Not doubting what happened on your screen - just super lag problems ;( The server crashed about 30 mins after you hit me.
  4. It was my pleasure, always love to talk about the history/philosophy of math I can't speak for the physicists - some their statements irk me as well (I've studied math - not physics)
  5. Yes the incompleteness theorem also applies to consitency of proofs using infinity. The theorem holds for mainstream mathematics as well as for the finite sort. IIRC you can prove the consistency of finite systems using an infinite one. Galileo's Paradox: The issue here is that we're fumbling about with what we mean by "size". The defination of size in math actually depends on the kind of object you're looking at, and how you're looking at it. There are several ways we can look at a subset of natural numbers: 1. Just as a set. This is Galileo's approach. 2. The algebraic way of looking at a set of natural numbers. (consider the natural numbers as a semiring - meaning you can add and multiple numbers together to get new ones - and sometimes subtract and divide) 3. The metric space of looking at a set of natural numbers (using the distance function d(n,m) = |n -m| you can tell the distance between any two numbers) (And probably way many more...) If we look at the set of natural numbers {0, 1, 2, 3, 4, 5, 6, 7, ...} using the different approches you'll see what I mean: Approach 1 (Just as a set) Since we see {0, 1, 2, 3, 4, 5, 6, 7, ...} merely as a box holding a bunch of stuff, we can rename it to {cheese, apple, fruit, banana, il-2, t-70, ...} and we wouldn't know the difference. That's why it's also ok to rename {0, 1, 2, 3, 4, 5, 6, 7, ...} to {0, 1, 4, 9, 16, ...}. That's why the two objects are the same. Approach 2 (The numbers are a semiring) Now we see {0, 1, 2, 3, 4, 5, 6, 7, ...} as a set where you can add two numbers (and multiply them) together, and get back a number in the set. For example, 1+2 =3 - we know that 3 is in the set. Note we can't replace the numbers with random words like we did in approach 1, since you can't add words together. We can not replace {0, 1, 2, 3, 4, 5, 6, 7, ...} with {0, 1, 4, 9, 16, ...} since the second object is NOT a semiring. This is because 1 + 4 = 5 - and 5 is not in the second set even though 1 and 4 are. So we see that the first object is strictly bigger than the second. Our defination of size has now changed - you can see it has something to do with addition and multiplication - instead of just renaming all the numbers without regards as to how they add and multiply. Approach 3 (The numbers are a metric space) Taking a metric space approach to the set {0, 1, 2, 3, 4, 5, 6, 7, ...} means we now consider the fact that we can tell the distance between two numbers. We can for example, now say that the distance between 3 and 5 is 2. Taking the set {0, 1, 4, 9, 16, ...} you can easily see that the distances are still defined. However, the two objects are NOT the same, because there are no two elements in {0, 1, 4, 9, 16, ...} which have the distance 2. But 1 and 3have the distance 2 in {0, 1, 2, 3, 4, 5, 6, 7, ...} . In fact, it's easy to show using this approach to size that {0, 1, 4, 9, 16, ...} is strictly smaller than {0, 1, 2, 3, 4, 5, 6, 7, ...} A bit of a mindfuck though: {0, 1, 2, 3, 4, 5, 6, 7, ...} has the same size as {0, 1, 4, 6, 8, 9, 10, 12 ...} (Remove all the primes) according to this defination of size. This is relatively easy to show. Conclusion: So if you really want to compare the size of two mathematical objects, you have to consider in what framework you're considering them in. Most people consider the natural numbers to be an algebraic structure - i.e. a semiring (even though most ppl don't know the terminology - just the ideas behind it). So when you bamboozle ppl about size using approach 1, you're really just stripping the numbers of what makes the numbers important. What is a 2 if I can't even do 2 + 2? Absolutely worthless. So why should I even bother to consider the 2 without being able to add it with other numbers? This should also apply to when I'm determining the size of a set of natural numbers.
  6. Thanks for your welcome to the weird corner of the forums One more thing: David Hilbert (the guy behind the math behind quantum mechanics) had the same idea as you do (regading it being possible to use only finite objects in math and to get the same theories). Quote from wikipedia (article on Finitism I linked earlier): "Another position was endorsed by David Hilbert: finite mathematical objects are concrete objects, infinite mathematical objects are ideal objects, and accepting ideal mathematical objects does not cause a problem regarding finite mathematical objects. More formally, Hilbert believed that it is possible to show that any theorem about finite mathematical objects that can be obtained using ideal infinite objects can be also obtained without them. Therefore allowing infinite mathematical objects would not cause a problem regarding finite objects." However, there is some bad news: "This led to Hilbert's program of proving consistency of set theory using finitistic means as this would imply that adding ideal mathematical objects is conservative over the finitistic part. Hilbert's views are also associated with formalist philosophy of mathematics. Hilbert's goal of proving the consistency of set theory or even arithmetic through finitistic means turned out to be an impossible task due to Kurt Gödel's incompleteness theorems. However, by Harvey Friedman's grand conjecture most mathematical results should be provable using finitistic means." Basically: It is mathemetically proven (100% certain - no room for error here), that you can't determine whether all proofs using infinite objects can be done using merely finite objects. Finding a proof for or against that claim is impossible. But so far all the practical theorems that deal with finite objects (none artificial ones) can be proven using only finite objects. BTW I feel like the paradoxes using infinity aren't actually paradoxes. For example, Zeno's arrow paradox involving the tortoise which basically says that you can't travel across an infinite number of points in a finite amount of time. Since when going from 0 to 1, you first have to reach 1/2, but to do that you have to reach 1/4, but to do that... That's not really a paradox because there are an infinite amount of timepoints in a finite amount of time (1 second, 0.5 seconds, 0.25 seconds, etc.) - the two infinites effecitvely cancel each other out, since you're using one infinity to go some distance. (There is a more precise mathemetical way to formulate this idea - but it's really hard to formulate without some hand waving) As to whether infinites really exist in the real world - well I think that's up to the philosophers.
  7. Well even in the field of mathematics you have finists : https://en.wikipedia.org/wiki/Finitism - and some others who reject certain infinite sets (by rejecting the axiom of choice) while allowing the more simple ones. But let me pull an analogy out of the left field here: Consider the history of the negative numbers. https://en.wikipedia.org/wiki/Negative_number#History The jist of it is, negative numbers were considired wrong and unnatural up to the 18th century (A quote from wikipedia: " In A.D. 1759, Francis Maseres, an English mathematician, wrote that negative numbers "darken the very whole doctrines of the equations and make dark of the things which are in their nature excessively obvious and simple". He came to the conclusion that negative numbers were nonsensical.[29]"). Slowly but surely a lot of scientists and mathmeticians began to use them in their models/theories - and 2 centuries later negative numbers are considired so natural, that you can teach them to a 5th grader and they won't object. The point here is: Negative numbers are useful for describing the world - as are infinite objects. What does it really matter if the object actually exists (have you ever seen a negative number, except on paper?), if using those constructs lets you describe the world? Just as another example, quantum mechanics is based on functional theory (the study of infinite dimensional vector spaces equipped with norms). Without the deep understanding of infinity developed by Hilbert (and later development of quantum mechanics) you likely wouldn't be using a personal computer today (small semiconductors - an essential part of PCs - are based on quantum phenomena). None of those phenomena were "practically" known before functional theory came around. BTW infinity in the analytical sense ("The sequence converges to 0 as n goes to infinity") is very similair to what you're getting at with arbitrarily large numbers.
  8. Of course. For example, modern statistics wouldn't work without a good understanding of infinity (most of the theorems in statisitics are currently formulated in measure theory - which very commonly deals with infinite objects). The (weak/strong) law of large numbers is proven using a specially chosen infinite sequence. This allows science to use Monte Carlo experiments knowing that they are mathematically sound - as well as to make qualtitive arguments about the results from Monte Carlo experiments. The whole branch of statistical mechanics wouldn't be around without a solid understanding of infinities. Various applications stem from that - deep learning, understanding of financial systems, weather forecasting, etc.
  9. Brief description: Sun glare is only rendered if right eye has direct line of sight to sun. Detailed description, conditions: Happened on the 5th mission of Ten Days Of Autumn If right eye can't see sun because it's blocked by cockpit, then the left eye will have no sun glare. If left eye can't see sun, but right eye can - then both eyes get sunglare. Additional assets (videos, screenshots, logs): https://imgur.com/a/Z4x34 Your PC config data (OS, drivers, specific software): HTC Vive (always on reprojection and asynchernous reprojection), Windows 10, GTX 1080 w/ 385.28 drivers
×
×
  • Create New...