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 Poll

  • Question: Math thread, Y or N?
  • Yes
  • No
  • Yes

 Topic: Could we get a Math section?

 (Read 41134 times)
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  • Could we get a Math section?
     Reply #120 - February 22, 2015, 12:16 AM
    No, they aren't logically equivalent. Look at s1 reformulated, it implies that X dies of melanoma almost every hour. You can only die once.

    S2 doesn't have this problem.

    In terms of daily language use they are basically equivalent,but not logically. This was posed to me by a mathematician, took me some time to realise the above.
    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #121 - February 22, 2015, 12:24 AM
    Ah, yes! Sorry, I am slow at times. The reason I never read it was I didn't consider it iteratively (ie S1 -> S1 -> ... -> S1 on a hourly cyclic process). Though I guess I did this because the human brain isn't really programmed to accept the absurdity element and corrects for it (single death terminating the cycle). You are right though from a logical perspective it is incomplete without this termination made explicit!
    One only acquires wisdom when one sets the heart and mind open to new ideas.

    Chat: http://client01.chat.mibbit.com/#ex-muslims
  • Could we get a Math section?
     Reply #122 - February 22, 2015, 12:26 AM
    Yeah lol, it caught me by surprise too. Pure mathematicians tend to spot this stuff easily because they always deal in precise language. The general populace normally doesn't.

    I only got it after reformulating S1. I think the termination aspect is pretty obvious once we consider it in the context of one X.  "Dies" would denote  the termination.
    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #123 - February 22, 2015, 12:33 AM
    Yes, I think I've gone rusty now. Pure maths was my thing but it's been two years now since I touched that stuff. Really do miss it! I don't feel I'm naturally gifted at it either so I need a little practice to get my head back in that mode of thought which other science just doesn't give you. Well at least I get to relive it on this forum thanks to you Qtian! Smiley
    One only acquires wisdom when one sets the heart and mind open to new ideas.

    Chat: http://client01.chat.mibbit.com/#ex-muslims
  • Could we get a Math section?
     Reply #124 - February 22, 2015, 12:37 AM
    I'm no pure mathematician either  grin12

    I rarely do math for the sake of math, I do it because of what real world results I can derive. Either that, or because formal logic is fun.

    I don't do much mathematics these days, too far removed from it.
    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #125 - February 22, 2015, 12:42 AM
    Well you're borderline genius in my books! I enjoy having these sorts of conversations that I don't usually get to have. And I think you'd be good with any type of maths or philosophy, you've definitely got the talent!
    One only acquires wisdom when one sets the heart and mind open to new ideas.

    Chat: http://client01.chat.mibbit.com/#ex-muslims
  • Could we get a Math section?
     Reply #126 - February 22, 2015, 12:45 AM
    BTW, is your area of study mathematical physics? 
    Or just some other combination of math and physics?
    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #127 - February 22, 2015, 12:52 AM
    It was a combination of Maths and Physics, did this until Masters. Unfortunately the best opportunity after that involved straying from the pure and into the applied - now I do quantum mechanical simulations of iron, mainly.

    The problem is ideas are never strung well in these sorts of degrees, I have actually shifted more to your idea the other day as presented that reading the logic and philosophy alongside means you can understand things better. Definitely gives you a level of rigour that you don't get just reading the maths alone. I used to ponder over the proofs in the notes but there were so many that analysing them in depth was nigh on impossible sometimes. They were quite deep in terms of their result. Thing is the side effect is hardly anyone is ready to do proper research after as they don't really know the way to think properly to produce new proof and arguments! It is all very philosophical when done correctly.
    One only acquires wisdom when one sets the heart and mind open to new ideas.

    Chat: http://client01.chat.mibbit.com/#ex-muslims
  • Could we get a Math section?
     Reply #128 - February 22, 2015, 12:59 AM
    I get what you mean. Does your PhD involve teaching classes? That would be fun.

    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #129 - February 22, 2015, 11:00 AM
    I want to teach classes, in fact I wanted to teach these people some maths and LaTeX because they don't know the basics generally, but I haven't really had a chance! Not got round to it yet because I've got an overload of work to do, especially because I don't just research in my hometown but also 140 miles away.
    One only acquires wisdom when one sets the heart and mind open to new ideas.

    Chat: http://client01.chat.mibbit.com/#ex-muslims
  • Could we get a Math section?
     Reply #130 - February 22, 2015, 11:13 AM
    $\mathbb {LaTex}$ is very useful, I'm used to the stack exchange format which uses MathJax to render it.

    I learnt it by myself. Initially, I felt lost but it is quite rewarding being able to type equations at your own discretion.




    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #131 - February 22, 2015, 11:19 AM
    Hehe I tend to typeset in LaTeX using MikTeX on Windows when I'm writing documents - Word becomes obsolete (but then sometimes it is easier to just use the latter). Did my final year thesis in LaTeX, had to self teach it which was difficult (the topic was to do an exposé on Julia and Mandelbrot sets which was extremely difficult in itself!) By the way I corrected the love post on the other thread loooool, now it is a lot more rigorous Tongue
    One only acquires wisdom when one sets the heart and mind open to new ideas.

    Chat: http://client01.chat.mibbit.com/#ex-muslims
  • Could we get a Math section?
     Reply #132 - February 22, 2015, 11:26 AM
    Quote
    By the way I corrected the love post on the other thread


    Let's just pretend that the above never happened  lipsrsealed

    Regarding your thesis, damn. That must have been quite difficult to do on LaTex.
    I would've just given up and written it by hand lol.

    I remember once I was working on a deadline like 40 minutes before it was due in, I was just about to finish but I realised there was no way that I had enough time to draw a graph on the computer, so I had to do it by hand. Another problem, I had no camera on my phone so I couldn't take a picture of the fucking graph lol.


    I had to draw a variant of one of these for an Economics module:


    So, I mindlessly ran around campus at the crack of dawn, until I found a kind soul who took a picture and sent it to me.

    I definitely cut that deadline close.


    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #133 - February 22, 2015, 11:52 AM
    Looool indeed let's pretend it didn't happen (though it is now corrected in Modus Ponens form Cheesy)

    Deadlines are the most frustrating thing ever, but I guess do get people to do their work. I don't like deadlines and nor the way mark schemes work in general. As for the graph, it is very pretty! It looks familiar from a very distant past... I am glad it got done, I've had my fair share of close calls where deadlines come! Happy someone went out of their way to help you out!
    One only acquires wisdom when one sets the heart and mind open to new ideas.

    Chat: http://client01.chat.mibbit.com/#ex-muslims
  • Could we get a Math section?
     Reply #134 - February 22, 2015, 12:37 PM
    It's known as the Solow-Swan, it basically tries to model steady states of the economy (which could be why you somewhat recognise it?)

    It's part of the neoclassical beast.
    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #135 - February 22, 2015, 12:41 PM
    It looks like some graphs which used to be posted up on the wall in Business Studies class, all those years ago (10 years back) when I took it! I never studied Economics as a part of that class but I believe they were from A level Economics students. The business studies class was not mathematical at all. Needless to say I did not enjoy it at all lol
    One only acquires wisdom when one sets the heart and mind open to new ideas.

    Chat: http://client01.chat.mibbit.com/#ex-muslims
  • Could we get a Math section?
     Reply #136 - February 22, 2015, 12:46 PM
    Hmm, SS isn't touched in A level (too complicated), I guess you could've come across something slightly similar or maybe an extremely stripped down version of it.

    Yeah, business, finance etc... bore me to death. Even large portions of Economics bores me, but I like exploring "heterodox" areas.

    I was thinking about getting into mathematical finance (good money) but I think I would rather kill myself tbh.
    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #137 - February 22, 2015, 12:58 PM
    Yeah it was linear rather than having a non linear function f lol. Definitely was stripped down. It was 10 years back mind you, so I could easily have dreamt the whole situation up. Cheesy

    Yes playing with money (what I call finance) does yield money for yourself in the process but there is a lot of report writing and other tedious aspects. Plus I question the ethics of the system but that's a whole other topic haha. You could go for the modelling side which is more mathematical, I remember doing a module in Mathematical modelling in finance, basically involved solving lots of differential equations (mainly stemming from the Black Scholes equation, even though that is relatively obsolete now). Still closer to real maths than sat down writing extensive reports. In fact any form of modelling now could be the only way to stay closer to the theoretical side - every further applied aspect is frustrating and a huge bore.
    One only acquires wisdom when one sets the heart and mind open to new ideas.

    Chat: http://client01.chat.mibbit.com/#ex-muslims
  • Could we get a Math section?
     Reply #138 - February 22, 2015, 01:03 PM
    Black Scholes is silly, I will not grovel to silliness.


    Just because it's a PDE and it looks cute, it doesn't mean that it's good.
    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #139 - February 22, 2015, 01:07 PM
    Yeah, it IS very pretty (I thought the same myself when studying) but I can't see how well it would model anything beyond a few basic models. It oversimplifies a lot.
    One only acquires wisdom when one sets the heart and mind open to new ideas.

    Chat: http://client01.chat.mibbit.com/#ex-muslims
  • Could we get a Math section?
     Reply #140 - February 22, 2015, 01:08 PM
    Mind you I find the Schrödinger equation a lot more pretty than the BS equation. Appropriate when contracted :p
    One only acquires wisdom when one sets the heart and mind open to new ideas.

    Chat: http://client01.chat.mibbit.com/#ex-muslims
  • Could we get a Math section?
     Reply #141 - February 22, 2015, 01:12 PM
    Yeah, its main assumptions don't hold (IIRC).

    The standard cop out would be: "It's just a model!" (Which to be fair, is true)

    Either way, let's stop talking about finance, my eyes are beginning to bleed.
    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #142 - February 22, 2015, 01:19 PM
    Risk-free interest rate. Riiiiight!

    Yeah lol sorry let's stop. Tongue Fractals are beautiful! I fell in love during my project with them. Their properties are amazing too! Some of the results are so difficult to follow - I had to read a book "Introduction to Dynamical Systems" by Michael Brin and Garrett Stuck in the process and it is a very heavy read. The results posed use concepts from all over the place, spanning from stereographic projections in complex space to the utilisation of Möbius transformations to find critical points. Needless to say I got totally lost 3 pages into it. Hardest project I've ever encountered!
    One only acquires wisdom when one sets the heart and mind open to new ideas.

    Chat: http://client01.chat.mibbit.com/#ex-muslims
  • Could we get a Math section?
     Reply #143 - February 22, 2015, 01:19 PM
    Quote from: PhysMath on February 22, 2015, 01:08 PM
    the BS equation. Appropriate when contracted :p


    Very much so.
    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #144 - February 22, 2015, 07:44 PM
    Quote from: PhysMath on February 22, 2015, 01:08 PM
    Mind you I find the Schrödinger equation a lot more pretty than the BS equation. Appropriate when contracted :p

    BS as in Black Scholes?
  • Could we get a Math section?
     Reply #145 - February 22, 2015, 07:59 PM
    Yep, as aforementioned. PhysMath was also poking fun at Black Scholes by calling it bullshit.
    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #146 - February 23, 2015, 12:10 AM
    Is it faster to count to the infinite going one by one or two by two?

    I think that questions of this sort mistreat infinity, by thinking of it as a number rather than a concept.  It's like comparing ∞  and ∞/2. At every step of the "counting", you still have an ∞ distance to go, so neither is faster.

    Nonetheless, here is a good answer from MSE:


    Quote
    YES and NO.

    Galileo made the "discovery", the so-called Galileo's paradox, that if you start with the succession of natural numbers:

        1,2,3,...

    and you map it into the succession of even numbers :

        2,4,6,...

    you may map (i.e.associate) every number into its double (today, we call it one-to-one mapping).

    So, you have the same "number" of numbers and of even numbers.

    Modern set theory (from Cantor on) solved the paradox extending the "counting" process to infinite sets, but proving that the euclidean common notion that "The whole is greater than the part" [see Euclid, The Elements, trans T.L.Heath, Dover, Common notions 5] will not hold for an infinite set.

    According to modern set theory, the two above sets can be put in one-to-one correspondence, so they have the same cardinal number, and their "type" of infinity is called denumerable (a set is called denumerable exactly when it can be put in one-to-one correspondence with the set of natural numbers).

    But, again by a result of Cantor, not all infinite sets can be put in one-to-one correspondence: there are infinite sets "more infinite" than another. A set of "a larger kind" of infinity is the set of real numbers; it is not denumerable, in the meaning defined above.

    As for counting "faster": of course, if you count two by two, after a while you will be way "ahead" of your friend that is counting by one. The only problem is that you will not "end" before him, because there is no final goal to be reached!

    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #147 - February 23, 2015, 12:14 AM
    Quote from: PhysMath on February 22, 2015, 01:19 PM
    Risk-free interest rate. Riiiiight!


    Quote
    In theory, the risk-free rate is the minimum return an investor expects for any investment because he or she will not accept additional risk unless the potential rate of return is greater than the risk-free rate.

    In practice, however, the risk-free rate does not exist because even the safest investments carry a very small amount of risk. Thus, the interest rate on a three-month U.S. Treasury bill is often used as the risk-free rate.


    Surprisingly interesting, considering that the topic at hand (finance) is a natural sedative.
    My mind runs, I can never catch it even if I get a head start.
  • Could we get a Math section?
     Reply #148 - February 23, 2015, 12:37 AM
    Is that due to a model they use (doubt it's Black Scholes but perhaps a variation of it) or because they feel it is beneficial for the risk-free rate to exist for some other unrelated reason?
    One only acquires wisdom when one sets the heart and mind open to new ideas.

    Chat: http://client01.chat.mibbit.com/#ex-muslims
  • Could we get a Math section?
     Reply #149 - February 23, 2015, 12:40 AM
    It's basically a proxy for the risk free return, because T-Bills have a (virtually) zero risk of default. It's essentially the closest approximation to risk free that can be actually found, rather than theorised about.
    My mind runs, I can never catch it even if I get a head start.
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