https://www.youtube.com/watch?v=w-I6XTVZXww
:roll:
That is mathematical dadaism. He makes up off the wall rules as he goes and uses irrelevant sums. He also uses the fallacious principle of an infinite series stopping. What is disturbing about this is that the video has 11,001 likes and only 618 dislikes. Now I understand why so many used car salesman types get elected to office. This is unbelievable. Please comment on that video and tear it to shreds. Thank you.
"mathematical charlatan"
The lulz were plentiful.
I don't understand much of math, but can you apply the principle he's using with infinite series?
Edit: just read the comments, seems many people are also calling this one out. Do you per chance know of any other of these's guys videos that are also flawed?
It's not a very good video. Those kinds of vid do often put things in a rather sensational manner, but in this case they've stepped too far into the realm of the inaccurate and the misleading in order to be more exciting.
It's worth noting that the guy is a physicist, not a mathematician, and so it's possible he doesn't fully understand the material. When he says "the sum really is -1/12", what he really means is that assigning it a value of -1/12 gives us physical predictions which are actually correct, which is indeed interesting.
But he shouldn't just call it a "sum" without any explanation. What he's doing is not really a sum, it's just like a sum in some ways.
If you add up the first term (1), and then the first two terms (1 + 2 = 3), and then the first three terms (1 + 2 + 3 = 6), and so on, you get a sequence of numbers which just get bigger and bigger. Therefore the sum does not exist. This is in contrast with a series like 1/2 + 1/4 + 1/8 + ... , where adding up the successive numbers gets you closer and closer to 1, and we say the sum is 1.
Note that summing is therefore a way of assigning a number, which we call "the sum", to some strings of numbers.
Now, what the guy is really talking about is a different way of assigning a number to the string of numbers "1, 2, 3, ... ". In this sense the "sum" is just a function from strings to numbers, which doesn't pose us any troubles. We are free to define arbitrary functions. For example, I can define a function F, which sends "1, 2, 3, ... " to 100, "1/2, 1/4, 1/8, ... " to pi, and every other infinite sequence to -1. Of course, this F is completely arbitrary and useless, and has no correspondence to "summing". But there are other functions which will share some properties of classical summing. One important property we should require is that, for any string which does have a classical sum, like "1/2, 1/4, 1/8, ... ", the function will send it to the correct number (in this case, 1). Another property might be that, if the function assigns the number A to "a1, a2, a3, ... ", and the number B to "b1, b2, b3, ... ", then it will assign the number A + B to "a1 + b1, a2 + b2, a3 + b3, ... ". There are a bunch of functions with these properties, which also assign values to strings like "1, 2, 3, ... " - and the value turns out to be -1/12. We then might call such a function a "summation method", but that's just a name. The important point is that these functions turn out to be well-defined, interesting, and even physically useful.
So you're saying he's just over-simplifying things to the point of total inaccuracy? Not necessarily making up non-existent postulates and stuff?
Xei, that's interesting, but don't you think he is talking nonsense when he uses the rationale that the two possibilities for where it "stops" are 0 and 1 so we take the average of the two? An infinite series does not stop. Some have finite sums, but they do not "stop." The sum of all natural numbers is not even finite. As for getting the average of 0 and 1, this is math, not a divorce settlement. Does his idea there have any touch with reality whatsoever? You agree that the sum of all natural numbers is infinite, but you are saying that assigning a value to it can be useful? I have a lot to learn about physics, but no matter how useful it may be to assign a value, I would say the guy is straight up wrong about the sum of all natural numbers. Also, what do the sums involving negative integers have to do with anything? No natural numbers are negative.
I just discovered him last night, but apparently he is pretty popular on YouTube. I would be willing to bet that he has lots of other flawed videos, but I haven't watched any.Quote:
Originally Posted by Zoth
It's nonsense if, by the word "sum", you mean the usual idea which everybody understands. For that concept, the rationale is incorrect. The sum has no value.
The thing is that, like many words in the English language, such as "rest", or "temple", sometimes mathematical words refer to several distinct ideas, which may be somewhat related or completely unrelated. The problem with the video is that, in order to seem more impressive, it neglects to mention that it does not mean the usual definition of "sum"; it refers to an analogous, but different, and in several cases contradictory, concept.
The video is therefore totally misleading and uninformative, though not technically wrong. If you were to watch it again, but every time he makes the sound "sum" replace it with "pseudosum" or even "funky string function", it would make a lot more sense. It would, however, be a lot less impressive.
I'm not a physicist and can't say exactly why funky string function is useful, but it probably has something to do with quantum field theory, where you have to combine an infinite bunch of things together to get a result. When you do this, you get quantitative predictions about the universe which turn out to be correct.
Okay, that explains a lot. They switched up the meanings of words. How educational of them. People who play games like that make me feel like doing this: :bslap:
I know how you feel, immigrants make me feel the same way.Quote:
Originally Posted by Universal Mind
:awesomed:
http://www.youtube.com/watch?v=bcYppAs6ZdIQuote:
Originally Posted by GavinGill
Lol...the guy who writes Slate articles on Astronomy posted this last week. Let's just say he "got ripped a new one" and had to post a retraction. Now it seems his retraction is not adequate enough and may need to be retracted....
There is a huge flaw in the very first problem he does. You can't just say, "I don't know the answer so I will take the average." That isn't math. It is definitely possible to get multiple answers in math, but you don't just take the averages of the possible answer.
Some people have faces that, when I look at them, make me want to violently pummel them, but not kill them because they piss me off. Both of these guys possess such faces, although I must admit it has nothing to do with the content of this video or any of the channel owner's other videos.
Yes, I realize that I have contributed nothing to this thread, but I feel strongly enough that I was compelled to post. UM, let me join you in :bslap: