Search found 144 matches

by madaco
Tue Jul 18, 2017 6:41 am UTC
Forum: Mathematics
Topic: Help with a recurrence relation, related to partitions, and related to random infinite permutations
Replies: 5
Views: 445

Help with a recurrence relation, related to partitions, and related to random infinite permutations

Hi, I am looking at defining a function a(n) in terms of another function f(n), with a(n) defined as: a(n) = f(n) - ∑ i=1 n-1 ( f(i)*a(n-i) ) I have noticed that for some functions f, the sum of a(n) over positive integers n goes to 1. I have proved this for f(n)=1/(n+1) , as well as for f(n) = c , ...
by madaco
Wed Jul 05, 2017 3:21 pm UTC
Forum: Mathematics
Topic: Looking for practice problems for algebra ?
Replies: 8
Views: 391

Re: Looking for practice problems for algebra ?

Uh,

Which algebra?

Do you mean like, "solve for x" or like, "prove that the degree of x divides the degree of the group", or something else?
by madaco
Mon Jun 19, 2017 6:20 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1852: "Election Map"
Replies: 29
Views: 2047

Re: 1852: "Election Map"

What if, we took some political observer, with some set of positions, and checked how the average positions of each district compared to those of that observer, at 2 (or more) different times, and used that to determine some notion of "relative velocity", and then chose levels of red or bl...
by madaco
Fri Jun 09, 2017 8:24 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1844: "Voting Systems"
Replies: 83
Views: 4508

Re: 1844: "Voting Systems"

One idea which I had, which I assume is entirely impractical, but which I think might be good if it could be implemented in practice, is Assume that each person/voter has a vNM utility for each candidate. Normalize each voter's utility function such that their first choice has a utility of 1, and th...
by madaco
Thu Jun 08, 2017 6:14 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1844: "Voting Systems"
Replies: 83
Views: 4508

Re: 1844: "Voting Systems"

If you cannot (or will not) answer the question, then trying to decide on a voting system is just partisan politics, designed to promote whatever agenda you have at the moment. No, because the reason I will not answer the question is that you've sucked out all of the relevant details and oversimpli...
by madaco
Tue May 30, 2017 5:00 pm UTC
Forum: Mathematics
Topic: What would happen if $-1 bills were minted?
Replies: 20
Views: 1802

Re: What would happen if $-1 bills were minted?

Here is a variation on the idea: Imagine a world where anyone can create a dollar from nothing, but doing so causes a number associated with oneself to become $1 more negative, and this number can be observed by looking at the person, and any dollar created this way indicates what this number was wh...
by madaco
Tue May 23, 2017 6:41 pm UTC
Forum: Mathematics
Topic: Interesting question regarding Fermat nested radicals
Replies: 9
Views: 898

Re: Interesting question regarding Fermat nested radicals

Are you looking to prove that it converges, efficiently calculate approximations to it, or find a closed form expression for it?

I think I've convinced myself that it converges (but I might have made a mistake in my reasoning).
by madaco
Fri May 12, 2017 6:47 am UTC
Forum: Mathematics
Topic: ONAG: "Surreal Numbers" make a field?
Replies: 10
Views: 1978

Re: ONAG: "Surreal Numbers" make a field?

I'm still rather stuck on how the surreals are closed under multiplication, class or no. Does anybody have any advice? Theorem 8. (i) If x and y are numbers, so is xy. The proof is given in On Numbers and Games , by John H. Conway. What part of the proof is the sticking point? When they called the ...
by madaco
Thu May 11, 2017 10:30 pm UTC
Forum: Science
Topic: Why haven't any animals evolved wheels?
Replies: 22
Views: 2047

Re: Why haven't any animals evolved wheels?

How would these wheels generate motion? If you had another spinning wheel, you could use gears, of course, but that doesn't let you get started. It seems easier to combine many small parts that pull or push a little into a larger part that pulls or pushes more, than to take many small parts that cau...
by madaco
Sun May 07, 2017 3:38 pm UTC
Forum: Religious Wars
Topic: Is 1 prime?
Replies: 30
Views: 11502

Re: Is 1 prime?

I think the real question is whether the zero ring is a field, and whether 1 belongs with the prime powers. The characteristic of the field of size p^k is p. If 1 is a prime power, then it is p^0 for every p. So, if the field of one element were to exist, shouldn't it have every characteristic or so...
by madaco
Wed May 03, 2017 6:41 am UTC
Forum: Fictional Science
Topic: In scientific's definition, in a fantasy world would a beastman or an elf be considered the same species?
Replies: 24
Views: 2751

Re: In scientific's definition, in a fantasy world would a beastman or an elf be considered the same species?

(But, actually, the concept of Ring Species confuses things, too.) That article says "The textbook examples of ring species, including the circumpolar herring gull complex, the greenish warbler of Asia, and the Ensatina salamanders of America, have all been challenged, so ring species are at b...
by madaco
Mon May 01, 2017 8:29 pm UTC
Forum: Mathematics
Topic: Halting Problem
Replies: 200
Views: 6102

Re: Halting Problem

main(input: file) {  if willHalt(program: file, data: file) {    while true {}   // infinite loop  }}  This program takes an input file, called “file”. Then it calls the “willHalt” program. The “willHalt” program takes two parameters which are both files. One is a program and one is a data fil...
by madaco
Sun Apr 23, 2017 12:59 am UTC
Forum: Science
Topic: Lay question about entropy
Replies: 29
Views: 2511

Re: Lay question about entropy

I think they meant something like (and I'm going to say this very poorly) that even if the "time progressing" function is a bijection, that if some macrostates have more possible microstates than others, that the output of the function will be a microstate of a macrostate with more possibl...
by madaco
Fri Apr 21, 2017 9:43 am UTC
Forum: Science
Topic: Why do humans see themselves as different from animals?
Replies: 34
Views: 2468

Re: Why do humans see themselves as different from animals?

Humans ask why humans see themselves as different from animals. "It is customary to insist that man resembles the other creatures. Yes; and that very resemblance he alone can see. The fish does not trace the fishbone pattern in the fowls of the air, or the elephant and the EMU compare skeletons...
by madaco
Sun Mar 19, 2017 5:11 am UTC
Forum: Computer Science
Topic: A Category of problems
Replies: 1
Views: 1151

Re: A Category of problems

Alright, so apparently ~217 people have viewed this, but none have decided to respond. I am not sure if this is because what I said was uninteresting, or because it was unclear. I don't know which one to hope for. __ A reduction of a problem to the empty problem would be a solution to the problem. I...
by madaco
Fri Mar 17, 2017 4:18 am UTC
Forum: Science
Topic: Free Will
Replies: 161
Views: 6830

Re: Free Will

Err, Wouldn't the standard response to that be that the soul is what we are referring to as "Fred" when we say that "Fred has/doesn't-have 'free will' " ? Then we just examine the soul's mechanism. It's funny how susceptible the soul's decisionmaking process is to the external w...
by madaco
Fri Mar 17, 2017 4:10 am UTC
Forum: Science
Topic: Science-based what-if questions
Replies: 286
Views: 20019

Re: Planet's spin

in 4d space I think there can be 2 axes of rotation which are at independant speeds. Idk how many dimensions you need for 3 axis. I'm guessing 6 spatial dimensions? The idea of an axis of rotation only works in 3D space. That's because if things are moving round in a circle in 2 of the dimensions, ...
by madaco
Thu Mar 16, 2017 9:01 am UTC
Forum: Science
Topic: Free Will
Replies: 161
Views: 6830

Re: Free Will

If this putative soul were "outside" (not part of) the entity, then the soul would be a puppetmaster, and Fred would just be dancing to his soul's strings. Fred himself wouldn't have free will. Err, Wouldn't the standard response to that be that the soul is what we are referring to as &qu...
by madaco
Thu Mar 16, 2017 8:56 am UTC
Forum: Science
Topic: Science-based what-if questions
Replies: 286
Views: 20019

Re: Planet's spin

in 4d space I think there can be 2 axes of rotation which are at independant speeds.

Idk how many dimensions you need for 3 axis. I'm guessing 6 spatial dimensions?
by madaco
Wed Mar 15, 2017 12:54 am UTC
Forum: Computer Science
Topic: A Category of problems
Replies: 1
Views: 1151

A Category of problems

I'm not sure if this goes here or in the fleeting thoughts section, or maybe even in the math subforum, but this is my best guess. As always, I expect that this is either not useful, or is already known about, or a more useful version is already known, but I don't know where to find it. I'm not sure...
by madaco
Thu Mar 09, 2017 4:43 pm UTC
Forum: Science
Topic: Free Will
Replies: 161
Views: 6830

Re: Free Will

So, is it just me not understanding, or does many worlds seem rather like modal realism?
by madaco
Wed Mar 08, 2017 7:02 am UTC
Forum: Science
Topic: What is the Biggest Non-Repeating Molecule?
Replies: 39
Views: 5048

Re: What is the Biggest Non-Repeating Molecule?

[Edit: I am writing this in order] To try to get at the idea of "repeating" which is [edit: maybe] meant, I get the impression that they don't want the molecule to be a chain of "blocks" where each "block" is from some structured family. (By a "block" I mean s...
by madaco
Fri Jan 06, 2017 11:10 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1782: "Team Chat"
Replies: 84
Views: 7595

Re: 1782: "Team Chat"

That'd mean limiting the total feature set to whatever you included in your federated standard. There's no incentive to do that, and no compelling incentive for a user to prefer your service on the basis of your choice to do so. Then, of course, your universal standard is still only as universal as...
by madaco
Fri Jan 06, 2017 8:17 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1782: "Team Chat"
Replies: 84
Views: 7595

Re: 1782: "Team Chat"

Aren't Skype and Slack proprietary though? This seems to be acting like switching to them is progress in some way, but I don't see what would be better about skype or slack? Is it the voice chat, or sub-topics or something? They have a bunch of nice features that IRC doesn't provide out of the box....
by madaco
Fri Jan 06, 2017 6:54 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1779: "2017"
Replies: 71
Views: 6972

Re: 1779: "2017"

Oh! See these "frozen peaches" and "wet knees", As we all drink down those sweet <outgroup> tears. What truths can be found from barbs such as these? No comedy will calm these restless fears! _____ But the important thing is I've found a way to feel superior to both of them.
by madaco
Fri Jan 06, 2017 5:27 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1782: "Team Chat"
Replies: 84
Views: 7595

Re: 1782: "Team Chat"

Aren't Skype and Slack proprietary though?

This seems to be acting like switching to them is progress in some way, but I don't see what would be better about skype or slack?

Is it the voice chat, or sub-topics or something?
by madaco
Fri Dec 09, 2016 11:15 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1770: "UI Change"
Replies: 56
Views: 7372

Re: 1770: "UI Change"

Or he does and doesn't care, because the actual point of the comic is to be smug toward people who don't like UI changes. Yes, curse that smug Randall, reminding us all that we're growing old while he stays young and beautiful forever thanks to his Elven heritage You're very bad at understanding th...
by madaco
Wed Nov 30, 2016 11:44 pm UTC
Forum: Mathematics
Topic: Misunderstanding basic math concepts, help please?
Replies: 338
Views: 39414

Re: Misunderstanding basic math concepts, help please?

When people are saying that nonwellfounded sets don't exist, they mean that they don't exist in ZFC, right? I don't think Aczel's anti-foundation axiom has been shown to cause a contradiction or anything like that. I'm somewhat fond of mathematical platonism, and I personally find non-well-founded s...
by madaco
Tue Nov 22, 2016 10:45 pm UTC
Forum: Science
Topic: Quantum Mechanics over Finite Fields?
Replies: 3
Views: 1553

Re: Quantum Mechanics over Finite Fields?

I know there are some books on this. Or at least, I know there are one book on this. And this is a thing: https://en.wikipedia.org/wiki/P-adic_quantum_mechanics Oh! Thank you! I had briefly looked at that page, but didn't read it in depth, and didn't notice it had a section on finite fields. I've n...
by madaco
Tue Nov 22, 2016 8:46 am UTC
Forum: Science
Topic: Quantum Mechanics over Finite Fields?
Replies: 3
Views: 1553

Quantum Mechanics over Finite Fields?

Sorry if this isn't a good place to put this. This thread is about me wondering how much it would make sense to try to do quantum mechanics type calculations except over finite fields instead of the field C . I am under the impression that the Bekenstein Bound (and related things) suggest that the n...
by madaco
Mon Jul 18, 2016 6:41 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1708: "Dehydration"
Replies: 109
Views: 8837

Re: 1708: "Dehydration"

You are evil, and wrong. [Citation Needed] Evil and Wrong are independent sets, the statement was an intersection of the two self-evident examples (harmful manipulative doubt is equivalent with evil, "Actually, this is by far the most common bit of pop hydration advice you will get from friend...
by madaco
Fri Jun 10, 2016 7:17 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1692: "Man Page"
Replies: 51
Views: 7624

Re: 1692: "Man Page"

ahaha its the page on true bugs.
by madaco
Mon May 23, 2016 4:00 pm UTC
Forum: Computer Science
Topic: Fleeting Thoughts (CS Edition)
Replies: 99
Views: 55549

Re: Fleeting Thoughts (CS Edition)

Since then, a machine with, 1920 states has been found which also cannot be shown to never halt under zfc (but which can be shown to never halt under zfc+"zfc is consistent"). Also, wrt the large cardinal thing: As I understand it, ZFC + large cardinal is the thing that they used to show t...
by madaco
Wed Apr 13, 2016 4:25 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1667: "Algorithms"
Replies: 49
Views: 6928

Re: 1667: "Algorithms"

My primary intent was to have an instant riposte whenever some dope says "I can do [this weird thing] in Excel." I boot up Pong and say "You can but that doesn't mean you should." That's obviously something you definitely should have made, then, to prove that there's such things...
by madaco
Wed Mar 16, 2016 12:33 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1357: "Free Speech"
Replies: 1346
Views: 115975

Re: 1357: "Free Speech"

Gmal also said nothing about net negative or positive, just significant. It doesn't seem like it would have a very noticeable effect, either way. Also, the word you're looking for is "effect". I say aeffect because I didn't care to remember which was effect and which was affect. (Pseudo e...
by madaco
Tue Mar 15, 2016 4:58 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1357: "Free Speech"
Replies: 1346
Views: 115975

Re: 1357: "Free Speech"

Do you have any evidence whatsoever that this comic has had a significant impact on the freeze peach "debate"? All it does is point out a simple and uncontroversial truth about what rights actually mean. Well, people do seem to quote/link/etc. It, while interpreting it in perhaps not quit...
by madaco
Fri Mar 11, 2016 6:41 pm UTC
Forum: Mathematics
Topic: does every unit length curve lie inside the semicircle?
Replies: 12
Views: 2535

Re: does every unit length curve lie inside the semicircle?

Here's an idea: If a curve cannot be fit inside the semi-circle, then for a given way of putting it on the semicircle, there is a related curve of the same length which meets the boundary of the semi-circle at the same points (because the semi circle is convex). It seems like either the result would...
by madaco
Mon Feb 29, 2016 4:26 pm UTC
Forum: Computer Science
Topic: Machine Learning Algorithm with Oracle
Replies: 1
Views: 2932

Re: Machine Learning Algorithm with Oracle

Hm, Ok so I don't think I can provide an answer, but I might be able to provide questions that the answers might help someone answer? Is C large or small? Is the goal to minimize the cost, with the requirement that you get a classifier to work, or do you get a reward for each accurate classification...
by madaco
Thu Feb 25, 2016 10:26 pm UTC
Forum: Science
Topic: If spin really did represent particles actual spin...
Replies: 18
Views: 3319

Re: If spin really did represent particles actual spin...

Oh, spin corresponds to/is actual angular momentum?

Thank you. I didn't know that.
by madaco
Wed Feb 17, 2016 2:34 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1643: "Degrees"
Replies: 147
Views: 16252

Re: 1643: "Degrees"

No, the reason the Planck units are what they are is because they make (a particular choice of) conversion factors all equal to 1. Madaco was proposing a system of units that also has that property, but where the scale of all the units is tied to something other than the observed quanta of the univ...

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