Search found 90 matches

by radams
Wed Jun 14, 2017 6:39 am UTC
Forum: Mathematics
Topic: What would happen if $-1 bills were minted?
Replies: 20
Views: 5832

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

Something like that exists here in Norway [...]A giro: I buy something from you, you write a giro and give it to me. I hand in the giro to my bank, and the money moves from my bank to yours. What if you don't hand the giro to the bank? Jose I'd assume it'd result in either a lawsuit, or in the loss...
by radams
Tue Jun 13, 2017 9:53 pm UTC
Forum: Mathematics
Topic: What would happen if $-1 bills were minted?
Replies: 20
Views: 5832

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

Something like that exists here in Norway and in a few other European countries. They are called giros, and they work like reverse cheques. A cheque: I buy something from you, write out a cheque and give it to you. You take the cheque to your bank, and the money moves from my bank to yours. A giro: ...
by radams
Fri May 26, 2017 4:56 am UTC
Forum: Mathematics
Topic: Confused: how does ZFC allow surreal numbers?
Replies: 4
Views: 2602

Re: Confused: how does ZFC allow surreal numbers?

The usual move is to work in ZFC plus the axiom "There exists a Grothendieck universe". https://en.wikipedia.org/wiki/Grothendieck_universe Then let U be a Grothendieck universe, and replace 'set' with 'element of U', and 'class' with 'set'. Incidentally, Wiles' proof of Fermat's Last Theo...
by radams
Tue Apr 11, 2017 3:08 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1822: "Existential Bug Report"
Replies: 35
Views: 7303

Re: 1822: "Existential Bug Report"

Some synchronicity here between Randall and Zach:

http://www.smbc-comics.com/comic/efficient-sorting
by radams
Wed Aug 10, 2016 8:11 am UTC
Forum: Computer Science
Topic: Precise description of how to encode inputs to a UTM
Replies: 3
Views: 6009

Re: Precise description of how to encode inputs to a UTM

Turing's original 1936 paper gives explicitly both the encoding scheme, and the full list of 4-tuples for the universal machine (Turing called this the table of the machine).

http://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf

Encoding function is on pages 239-241.
by radams
Thu Aug 04, 2016 8:24 pm UTC
Forum: Mathematics
Topic: The liar paradox as a basis for kantian metaphysics
Replies: 11
Views: 3332

Re: The liar paradox as a basis for kantian metaphysics

Type theory prevents every kind of circularity.


That was the hope with type theory, but it turned out not to be so simple. https://en.wikipedia.org/wiki/System_U#Girard.27s_paradox
by radams
Wed Jun 01, 2016 12:10 pm UTC
Forum: Mathematics
Topic: V=L → ω_1=ω_1^CK ?
Replies: 2
Views: 2029

Re: V=L → ω_1=ω_1^CK ?

No. [;\omega_1^{CK};] is the limit of a countable sequence of countable ordinals, so it is countable (given the Axiom of Choice, which is implied by V=L). [;\omega_1^{CK};] is the first ordinal without a recursive bijection to the natural numbers. But "constructible" in the axiom of constr...
by radams
Fri Nov 20, 2015 8:58 am UTC
Forum: Science
Topic: Why is work independent of time?
Replies: 7
Views: 2569

Re: Why is work independent of time?

Moving a box on a frictionless plane to another point takes zero work. All the work done in your scenarios is spent giving kinetic energy to the box. In the 1-second scenario, the box has a lot more velocity when it reaches D than in the 1-year scenario.
by radams
Wed Aug 05, 2015 2:08 pm UTC
Forum: Computer Science
Topic: the halting problem
Replies: 16
Views: 7170

Re: the halting problem

Change your definition of x to this. x takes just one input, and: x(p) internally uses h and works this way: -if program p halts with input p, loop forever -if program p does not halt with input p, return 1 Now x(x) halts if and only if x(x) does not halt. There is an important point here: this is t...
by radams
Tue Apr 14, 2015 9:05 am UTC
Forum: Mathematics
Topic: Simple probability question - cards
Replies: 7
Views: 1827

Re: Simple probability question - cards

You need to multiply by another y-choose-x, because the x aces can occur anywhere among the y cards.

So you get [imath](32 C x) (384 C (y-x)) (y C x) / (416 C y)[/imath]. That expression doesn't seem to simplify.
by radams
Mon Mar 17, 2014 11:28 pm UTC
Forum: Mathematics
Topic: Circularity in Formal Languages?
Replies: 51
Views: 12730

Re: Circularity in Formal Languages?

I think you can get all of zfc using just three variable symbols, actually, instead of needing countably many - I forget where that's from, though; I'll try and look up a source later if you're interested. This was first proved in Tarski and Givant "A Formalisation of Set Theory without Variab...
by radams
Mon Jan 06, 2014 4:48 am UTC
Forum: Mathematics
Topic: Some questions about "truth" in formal logic
Replies: 14
Views: 4999

Re: Some questions about "truth" in formal logic

It's a well-formed sentence. Let's abbreviate "There is no number which encodes a proof of X" by "~PX". ~PF = There is no number which encodes a proof of contradiction = "PA is consistent" ~P(~PF) = There is no number which encodes a proof of ~PF = "PA cannot prove...
by radams
Wed Dec 25, 2013 9:20 pm UTC
Forum: Mathematics
Topic: Is it possible to prove that something is unprovable?
Replies: 24
Views: 6667

Re: Is it possible to prove that something is unprovable?

The strengthened finite Ramsey theorem is usually given as the first example of a number-theoretically interesting sentence that has been shown to be undecidable in PA. It states: "For any positive integers n, k, m we can find N with the following property: if we color each of the n-element sub...
by radams
Wed Mar 13, 2013 12:53 am UTC
Forum: Science
Topic: How space programs benefit us here on Earth
Replies: 36
Views: 5534

Re: How space programs benefit us here on Earth

I'll make a list of the obvious ones from the top of my head. These directly involve space exploration: GPS Mapping with satellites Satellite photography Satellite TV International phone calls (still carried via satellite to many areas of the world) Military reconnaissance via satellite Weather sate...
by radams
Wed Jan 23, 2013 11:12 pm UTC
Forum: School
Topic: Major Selection
Replies: 4
Views: 7078

Re: Major Selection

True, your chances of becoming an astronaut are extremely low, but I think it's worth trying. Attempting to become an astronaut will leave you with a much better CV, contacts and insight into several job fields than just keeping your head down and finishing your major. Finance or academia are not ne...
by radams
Wed Jan 23, 2013 10:53 pm UTC
Forum: Mathematics
Topic: ISO giant tech tree of math
Replies: 14
Views: 3127

Re: ISO giant tech tree of math

The others are right: every branch of maths has applications in every other branch of maths. However, this might be close to what you were looking for. There is a lot of formalised mathematics done now with proof assistants - computer programs that write proofs in a formal language, such that the fi...
by radams
Mon Jan 14, 2013 4:10 am UTC
Forum: School
Topic: Major Selection
Replies: 4
Views: 7078

Re: Major Selection

If you want to be an astronaut, systems engineering is definitely the better choice. NASA needs a lot of software engineers, but they stay on Earth and that doesn't look like changing soon. Looking at this page: http://astronauts.nasa.gov/content/broch00.htm NASA say that an astronaut needs a "...
by radams
Wed Nov 21, 2012 12:15 am UTC
Forum: Mathematics
Topic: Fermat's Last Theorem
Replies: 76
Views: 13146

Re: Fermat's Last Theorem

Where does your proof fail when n=2?
by radams
Mon Nov 19, 2012 10:17 pm UTC
Forum: Mathematics
Topic: What did Euclid call this form of reasoning?
Replies: 2
Views: 1688

Re: What did Euclid call this form of reasoning?

Euclid used this all the time. Every theorem in the Elements was stated twice: first as a general statement "In isosceles triangles, the angles at the base are equal to one another", then as a specific statement using letters from the accompanying diagram. "Let ABC be an isosceles tri...
by radams
Thu Nov 15, 2012 11:47 pm UTC
Forum: Serious Business
Topic: Is it possible to have a rational debate on global warming?
Replies: 1714
Views: 296865

Re: Is it possible to have a rational debate on global warmi

This from a freshman physics course at UT Knoxville . Radiation Nuclei and electrons are charged particles. When charged particles accelerate, they emit electromagnetic radiation and loose energy. Vibrating particles are always accelerating since their velocity is always changing. They therefore al...
by radams
Fri Nov 09, 2012 1:20 am UTC
Forum: Gaming
Topic: Games you can't remember the title of.
Replies: 1910
Views: 492247

Re: Games you can't remember the title of.

Game: Some type of dungeon crawler with the main character being a comical wizard in a purple (or blue) robe Approximate timeframe: 1990-1995 (I believe there was a demo of it on an old PC gamer disc with the Cocoanut Monkey and Isle of the Dead. Concept: It was a top-down view at an angle, you mov...
by radams
Tue Oct 23, 2012 11:15 am UTC
Forum: General
Topic: Amusing science misconceptions
Replies: 161
Views: 26167

Re: Amusing science misconceptions

Javascript is an imperative language.

Oh, and also: Computer Science is a science.
by radams
Mon Oct 15, 2012 9:50 pm UTC
Forum: Books
Topic: Evil point of view
Replies: 16
Views: 28635

Re: Evil point of view

The Wasp Factory

You might also like Grendel by John Gardner - the tale of Beowulf from the monster's point of view.
by radams
Wed Oct 10, 2012 11:14 am UTC
Forum: Mathematics
Topic: On pi being unkowable
Replies: 15
Views: 3523

Re: On pi being unkowable

Surprisingly, we don't have any written proof of this result from Ancient Greek times. Euclid proved that A/d^2 is constant (Theorem 2 in Book XII of the Elements), but not that C/d is constant. Archimedes, starting from the assumption that C/d is constant, proved that it must lie between 22/7 and 2...
by radams
Mon Oct 01, 2012 12:51 pm UTC
Forum: Computer Science
Topic: Why do our robots suck?
Replies: 157
Views: 91956

Re: Why do our robots suck?

It's also emerging that a fair bit of processing happens inside the neurons themselves. A neuron is much more complex than a transistor.
by radams
Wed Sep 12, 2012 9:36 pm UTC
Forum: Mathematics
Topic: I can't find an error in this proof
Replies: 5
Views: 1789

Re: I can't find an error in this proof

The error comes on page 4, where the author says "Matching the (n-1), (n-2), … zero-th order terms in c in equations (7) and (12) ...". The fact that the sums of (7) and (12) are equal does not imply that their individual terms must be equal. For us to conclude that, we would need to know ...
by radams
Wed Aug 22, 2012 8:55 pm UTC
Forum: Books
Topic: Socialist literature
Replies: 40
Views: 39697

Re: Socialist literature

Businesses were owned collectively by their employees and management was elected That sounds plausible. Though noone is preventing people from forming a collectively-owned businesses in a free market economy. There is even a modern name for that - "Bottom-up project management" (OK, not t...
by radams
Wed May 02, 2012 4:59 pm UTC
Forum: Individual XKCD Comic Threads
Topic: 1050: "Forgot Algebra"
Replies: 360
Views: 78630

Re: 1050: "Forgot Algebra"

Dear 14-year-old me, Here is a practical application of math. In a few years, when girls find out you can add up the costs of their purchases and calculate sales tax in your head on the fly, they will want to take you clothes shopping with them. This will be a very good thing. Yours, 33-year-old you.
by radams
Wed Mar 07, 2012 12:48 pm UTC
Forum: Mathematics
Topic: Getting my undergrad in math. How about you?
Replies: 51
Views: 7678

Re: Getting my undergrad in math. How about you?

Age: 33
Education: BA in Mathematics with Philosophy, PhD in Mathematics
What am I doing: Lecturer in Computer Science
by radams
Sat Feb 04, 2012 1:03 am UTC
Forum: Mathematics
Topic: Rude Math Jokes?
Replies: 11
Views: 8264

Re: Rude Math Jokes?

Complex analysts do it continuously.

Real analysts do it almost everywhere.

Algebraists do it in a group, in a ring, in a field.
by radams
Wed Jan 25, 2012 4:46 pm UTC
Forum: Mathematics
Topic: SAS (side angle side) postulate
Replies: 8
Views: 4594

Re: SAS (side angle side) postulate

Antara Mukherjee has studied "taxicab geometry". Take the distance between points (a,b) and (c,d) to be (c-a)+(d-b) - the shortest route from one to the other by a taxicab on a city grid that can only move horizontally or vertically. You get a system that satisfies all five of Euclid's pos...
by radams
Mon Jan 23, 2012 5:17 pm UTC
Forum: Science
Topic: 3D TV, shouldn't it be easy?
Replies: 14
Views: 3800

Re: 3D TV, shouldn't it be easy?

The Nintendo 3DS proves it's possible to have a 3D image without glasses or crossing your eyes. The disadvantages I can see are: first, it only works from a limited range of angles, which would make it harder for a family to all watch TV together. Second, a lot of people report headaches or motion s...
by radams
Thu Jan 19, 2012 10:41 am UTC
Forum: Serious Business
Topic: Should UK citizens face charges for US crimes?
Replies: 39
Views: 8022

Re: Should UK citizens face charges for US crimes?

You're right; I apologise. I missed that one sub-clause somehow, but it makes all the difference. However, extradition in either direction requires an arrest warrant or order of arrest, which is much easier to obtain in the UK than the US. In the US, an arrest warrant requires probable cause. In the...
by radams
Wed Jan 18, 2012 12:26 pm UTC
Forum: Serious Business
Topic: Should UK citizens face charges for US crimes?
Replies: 39
Views: 8022

Re: Should UK citizens face charges for US crimes?

The extradition treaty says a citizen of either country may be extradited provided the allegation is an offence under both country's laws punishable by at least one year's imprisonment, or consists of aiding and abetting such an offence. Presumably, linking to a torrent website counts as aiding and ...
by radams
Sun Jan 08, 2012 11:00 am UTC
Forum: Mathematics
Topic: "Therefore" versus "implies"
Replies: 12
Views: 3872

Re: "Therefore" versus "implies"

Strictly speaking, "A implies B" means the same as "If A then B". It doesn't by itself entail that either A or B is true; only that it's not the case that A is true and B is false. "A therefore B" means you are asserting A to be true, then asserting B to be true, and no...
by radams
Fri Jan 06, 2012 8:00 pm UTC
Forum: Mathematics
Topic: Abacus- Please explain
Replies: 6
Views: 3444

Re: Abacus- Please explain

Normally, each bead on the rightmost wire represents 1, each bead on the wire to its left represents 10, each bead on the wire to its left represents 100, and so on. So, if you slid all ten beads up on all ten wires, that would represent the number 11,111,111,110. That's the largest number that the ...
by radams
Fri Jan 06, 2012 2:51 pm UTC
Forum: Mathematics
Topic: Current Research in Mathematics
Replies: 6
Views: 4318

Re: Current Research in Mathematics

Yes, real analysis is still a very active field. Some fields are more active than others, but there is no field where we are even close to saying "most of the research has already been done". The amount of mathematics research being done in the modern age is astonishing. Have a play around...
by radams
Fri Jan 06, 2012 1:44 pm UTC
Forum: Mathematics
Topic: foundation of mathematics
Replies: 15
Views: 2089

Re: foundation of mathematics

The closest thing to what you were looking for is Nicolas Bourbaki's Elements of Mathematics. Nicolas Bourbaki was the codename for a group of mathematicians who met in Paris from 1934 to 1983 and attempted to produce a series of books containing all of essential mathematics, with the best possible ...
by radams
Thu Jan 05, 2012 5:39 pm UTC
Forum: School
Topic: Motivating people to read/write and improving schools
Replies: 3
Views: 2076

Re: Motivating people to read/write and improving schools

I'm afraid what you're describing already exists. They're called addventures. The biggest community of addventure writers is probably here: http://www.infinite-story.com/ You've come up with a few innovations - namely tags, the voting system, and the teacher view - but you'll be competing with a lot...
by radams
Thu Dec 01, 2011 12:52 am UTC
Forum: General
Topic: When to call the cops?
Replies: 12
Views: 2408

Re: When to call the cops?

Get a voice recorder and record it next time, then bring that to the cops. Nothing illegal - you're just recording in your own home - and your landlords need never know. The cops will be able to give you far better advice than we can on whether they should get involved, what you can do to keeps your...

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