Half-Life Fallout: Why Math is Awesome - Half-Life Fallout

http://www.wimp.com/biginfinity/

I think mathematics is under-represented this day and age. Science has taken a step back and gave way to new-age pseudoscience and I truly believe critical thinking is an ability more and more parents choose not to give their children.
Admittedly, I have a degree in mathematics and computer science so I'm totally biased, but I think the video above is absolutely fascinating and is a good example of how, even though there are a lot of really abstract subjects in math, it can be explained quite simply and open up a small window of curiosity. It also showcases how extremely clever ideas can prove in a simple way something that looks impossible to prove. The subject this movie is about is not that complicated but with huge implications on the entire scientific world.

It's not a long video at less than 10 minutes, give it a try.

Maybe you're hanging around the wrong kind of people (in real life, on the internet, and what you encounter in the media).

I doubt there is a significantly larger group of people who believe in hogwash pseudo-science than there was before. In fact, I'd rather surmise that people are more and more educated in true science and knowledge than ever before. Setting aside "the good old days".

I suck at math (in the sense that I have trouble with differential calculus, not that I can't deal with percentages & fractions), but I do love me some science vulgarisation! So thanks. Yay!

I suggest you go to TED.com often to see all kinds of cool lectures on various topics (some of them, truth be told, plain obnoxiously up their own arse)

Though the video was interesting, I wasn't overly impressed or even convinced by some of the nararrator's explanations. Sure, I've heard it all before in school, but just because someone says something is one way and that everyone agrees with them, it doesn't necessarily mean that it's convincing or even true. Sometimes I feel that mathematicians purposely try to lock themselves into solving irrational puzzles in a "logical" way without thinking of the implications w.r.t. the real world around them, or even common sense. That's not to say that I'm talking about irrational numbers, but that I'm talking about things that defy common logical sense.

For example, even the basis of the video, the explanation that the infinity composed of all the even numbers is equally as great as the infinity composed of all of the (whole) numbers, is by simple common sense, untrue. Regardless of how many people agree with the fact that (imo, conjecture that) if you can make a set of items which has an "equal" number of matching items as another set, they are equal in size.

1, 2, 3, 4, 5, 6, 7, 8...
2, 4, 6, 8...

It doesn't matter that you could "match" 2 with 1, 4 with 2, 6 with 3, and 8 with 4, the set is still intrinsically missing 1, 3, 5, and 7. You can go on forever, and the further you go, the more numbers there will be that are intrinsically missing from the even set, that are still included in the set of whole numbers. For every extra even number that you generate as a double of any whole number (all the way to infinity), you will always miss the odd number in between, which is intrinsically included in the set of whole numbers. It's the same exact logic he used to describe that Joe Shmoe's set of irrational numbers can never include all of the irrational numbers because he could simply find a decimal that isn't in the list. Well I can find a number that's not in the list of even numbers (e.g. 3), which IS in the list of whole numbers. By common logical sense, the list of all even numbers to infinity AND 3 is a larger set than the list of all the even numbers to infinity, and always will be, no matter how the math works out in the equations on paper.

Yeah, whatever, it's not a rigorous "mathematical" proof that haughty PhDs will jizz over, but it's grounded in common sense. I'm sure someone will try to write up some proof or show me some peer-reviewed paper showing otherwise, but I'll defer to my own judgement on this one. Not that it matters in the slightest because it has no basis in reality, which is why I think many people become so bored with math. If kids were taught at a younger age how the math they learn applies to the physical world, I think they would be more interested.

Just my opinion. Maybe I'm just as naive as Cantor's rivals, but there's probably a good reason that Cantor ended up as a loony toon in his later years and his contemporaries (likely) didn't.

Vert- your common sense isn't wrong, it's just your definition of infinity that's different from what is used ever since Cantor changed the world of math. You said the list of all evens and 3 is bigger than the list of all evens. Well, so what? That's true but uninteresting and there's nothing that can be learnt from that. There's only one strength of infinity that you are talking about. There's a finite list of numbers and then there's an infinite list. The rationals and the real numbers? Equally infinite. That's why Cantor came and said this- I'll define infinity slightly differently so I can study it better. I'll try to explain why Cantor's explanation can be intuitive-
I create a hotel in which there is room for all natural numbers (0, 1, 2, 3 and so on). When I finish building it, sadly all the odd numbers say they can't come stay. So, we only get the even numbers. However, it's no problem for the hotel's profits because we can still put a guest in every room. So, it's the same infinity, isn't it? That's why the infinities are similiar, said to be equally powerful.
More interestingly, if I take all rational numbers as guests, my hotel won't be overcrowded even though intuitively it very damn well should be, as you explained! I think that's interesting.
Even more - Cantor showed that when you take all real numbers, you cannot house them in the same hotel. Actually, you can't build any hotel with any number of rooms that can house the real numbers. That's interesting because you'd have thought the rational numbers and the irrational to be quite similiar- numbers that aren't whole. However, Cantor showed that not only are they not the same, the irrational numbers have a much stronger infinity. That's completely unintuitive.

Why does all this matter? Well, all of this led up to showing that there unanswerable questions in math, and therefor in the all scientific branches. Unified theory of physics? Perhaps impossible. That's big.

Thanks for the video Breserk.

I'm graduating soon with a bachelor's in Engineering with a minor in Mathematics. I must say math is fantastic. It's a great way to represent many things. It's also a universal language. Math is everywhere in our daily life. Hence the strong collaboration with physics. I think these days many people do not like math. Strictly because they don't understand it or they were never taught properly. The same thing happened to me throughout grade school. I always had miserable, terrible teachers for mathematics. Then when I hit college I started out a bit rough but ended up getting the hang of it. Like I have said it's a language. When somebody starts learning a language they're not going to start out speaking it fluently. You start slow and build strong. Everything in math builds up more and more over time. I've went from having trouble with simple algebra to doing differential equations, linear algebra, three-dimensional vector calculus, calculus based probability and statistics and Euclidean geometry.

At this point I now can look at a complex equation, understand it and visualize it in my head. I also can relate it to real-world analysis. It's quite fascinating. Math is looked down upon by many young students due to poor teaching of the basics. If someone were taught properly from the beginning it would be easier for them as they continue on. I also thing that all of the symbols and whatnot in more complex mathematics seem to scare people meanwhile they're there to help. Refer to my picture below.



I'm actually quite proud of myself that I have gotten this far. Most people really don't. Also considering I was terrible at math in high school it comes as a big shock.

I suck at maths... All these numbers scare me

City 17, on 19 August 2012 - 04:18 AM, said:

How many numbers do you see in the picture posted above? Yeah. I think you mean counting

I'm not a huge fan of maths, but I think it's very important and useful in many real world appliances (well, a must really).

This might be a tautology but I think people who take the advanced courses in math that actually show you proofs to very important equations and not the basic ones which just teach you how to solve an equation are the people who will end up loving math. Seeing how everything falls together perfectly in place and how a clever little thought can open up an entire new field in math which is absolutely critical for researching even basic physics problems is beautiful. This is missing from nearly all math lessons both in high school and in college, since most lessons only dwell on the "practical" side of math - this is an equation. This is how you solve it. That's boring! Show me how the first person thought about how to solve it! That's fascinating!

So, if you go to college and you have a choice about which math lesson to choose just try, for one semester, to study the more in-depth course. Most people who hate math and got into those courses end up loving it.

I will watch the infinity video again later to properly wrap my head around it. But for the moment just want to say great topic!

In the last 2 months I have been revisiting and teaching myself a lot of maths (not the most advanced kind but still). And it's absolutely beautiful the way everything fits together. Not only does it give you ways to reason out problems but often it allows you to put down on paper and break down the way your own brain's internal logic works when solving problems- a logic that we often take for granted. I agree with you regarding the proofs, too often we are taught the proofs at the beginning of a chapter but then as we go on solving problems we end up forgetting the proofs (meaning) and simply remembering it's conclusion (e.g. a formula). Now that I am teaching maths to myself rather than as part of a course syllabus; it has given me more freedom to keep revisiting and appreciating those fundamental connections- rather than memorizing a formula.

Humbug, on 19 August 2012 - 04:13 AM, said:

You're right. I find myself relating math to explaining real world "problems". Then people tell me "humm I never looked at it like that". It's like a form of critical problem solving for just about anything. In terms of proofs however I think it depends on the person and the major. Math majors enjoy doing proofs and all of that. Engineers mostly want formulas in order to get answers and to proceed from there. Proofs are interesting but it seems to be a waste of time for engineering majors. It's useful for math majors because they eventually use those proofs to build upon other things.

I've found that when I'm busy with a practical problem the math and theory behind it becomes a lot more interesting and one understands it better.

I like math, it's difficult, but it's almost always right.
It's nice to see it work in practice, like surveying. Or in theory like in structural calculation.

Is this thread bugging out for anyone else or is it just me? HLF be broken.

Artifacts like that happen sometimes, I blame your web browser (I blame all web browsers).
Scroll up away and back down to fix it.