If all you’re concerned with is the answer of =2, then not only do you not understand math, you’re almost certainly not performing it correctly. I cannot fathom how you guys can be in here demanding math but not understand the significance of notation. This is unbelievable.
Even your counter example underscored your aversion to context. 2+2=4. But 4 doesn’t necessarily equal 2+2. 4 could easily equal 1+3. It’s all about the CONTEXT. This isn’t some insignificant distinction, it’s the entire reason for notation in the first place. All you have to do is TALK the equation out loud and you can see why this is true.
Question: Two plus two equals? Answer: Four.
Question: Four equals? Answer: Any number of things, only ONE of which is “two plus two.”
I promise you, the contextual difference in the statements is EVERY BIT AS IMPORTANT as the conclusion. You can’t just ignore context just because the math FITS.
I have no idea why you’d disagree with this other than the fact that I’M the one saying it.
How can you guys demand to see math but not understand this basic a principle in math? I’m being serious when I ask that. I can’t even process the nerve of demanding to see complex maths if this simple bit is beyond their ability to comprehend. I simply cannot fathom such a demand coming from a person who can’t contextualize ANY DIFFERENCE between 1+1 and 1-(-1) JUST BECAUSE the answer is 2 in both cases. You can say the differences are irrelevant, but you can’t say they are saying the SAME THING. No wonder you’re unable to argue against my points without linking to other people arguing against points which have nothing to do with what I’M saying.
I had no idea things had gotten this out of hand. I’ve deliberately avoided making any “outlandish” claims for 7 or 8 pages now, and it’s still the same group of people disagreeing with every single thing I say, no matter how basic it is. If you’re to the point where you’re going to disagree with BASIC MATH just because I’m the one saying it, then you are clearly making this personal. Quit making this personal and debate points responsibly. You might even learn a thing or two in the process, man.
OOO! OOO! I can answer that one (bolding mine). Everyone talking to you thinks that that little “=” sign means is the same thing as. When you write “2+2=4” they read “2+2 *is the same thing as *4”. In particular, everyone you are talking to thinks the following statement is one of the foundations of mathematics:
[QUOTE=Euclid (approximately)]
if a = b, and b = c, then a = c.
[/QUOTE]
So, they all think that this statement:
is gibberish. 2+2=4. 4=1+3. 2+2=1+3. Always and forever.
2+2 = 4 which is the same as 1+3 which is the same as 0+4 which is the same as 6+(-2) and so forth.
Mathematically, they’re all exactly equivalent.
If we’re talking about 2 cows + 2 cows = 4 cows, this is the same as grouping them as 1 cow + 3 cows = 4 cows. It’s not “a different way to get to the same answer” the same way as if you’re using different independent dating methods running on completely different timing mechanisms to verify the age of a space rock or something. You’re just rearranging an equation and claiming it means something different even though it’s just another way to represent the same thing. There are four friggin cows.
You don’t get new information by simply rearranging what you know.
4=4, which can be represented in infinitely many ways. So what?
Because you were claiming that a-(-b) is somehow different from a+b. It’s not.
Because you don’t understand basic math principles.
Because you don’t understand complex maths.
Because they are different representations of the same thing. Again, do you think A+A=14 is different from 10+10=20?
They aren’t the same thing in terms of how they’re written. But in terms of what they actually mean and represent in our physical reality, they are exactly the same thing.
A first year engineering student math problem? Seriously, this is your test? I haven’t done hex in ages as I don’t do programming, but sure.
Deliberately misleading question. Assuming the … means “repeating”, which is usually the case, then the values would be equal, considering that there are no definable numbers which exist in-between the two defined values. There are ways to deliberately complicate the matter, but nothing particularly honest.
So sure, I agree. Due to the fact of their being no values in between those specified. So the values would have to be equal. And since all we’re dealing with is values, then they can be represented in a number of ways. This question is almost as silly as asking me if 3/3 = 1. It’s different representations of the same VALUE. If you can’t define a value in between two given values, then those values are representing the same thing. However, this is only dealing with the endpoints of the values. Any mathematical computation where you arriving at .999 repeating is almost ALWAYS done in a manner which is dissimilar to arriving at 1, so the actual contextual difference in the questions could be very different.
I’m really not here to take math tests though. I live the subject every day and don’t need additional quizzing on irrelevant trick questions.
Of course not. Why are you even asking this? What could I possibly have said in the last 12 pages to indicate as much?
Hell no. Once again, why you POSSIBLY be asking me this as I’ve indicated nothing remotely similar? Truth be told, I’m a lifelong atheist but I’ve trended more toward agnosticism in the last half of my life. Religion is the scourge of the Earth. But i can’t see how that possibly matters in the slightest one way or the other. Even if I WAS a proponent of ID, you should still be arguing against what I’m saying, not what I represent.
Please tell me you haven’t been arguing against THESE positions this entire time? I’m trying very hard not to come to that conclusion, but it would actually make sense of your flagrant disregard for what i’m ACTUALLY saying and your insistence on arguing against points I’m not making in the slightest. In the interest of advancement, stop trying to categorize my beliefs and deal with what I’m actually saying. I tend to be very deliberate with words, hence why I write so much. I’m not delusional and I’m not religious in the slightest, I just approach science from a contextual perspective instead of purely a mathematical one. I’m a full time scientist and a full time philosopher. I’m ambidextrous like that.
I apologize, Marley. I realize this guy has barged into your forum spouting a lot of nonsense, but now that what he says makes sense and people are still bashing him, it really got to me.
I can’t say I see it, and making sense is not the same thing as being correct. Anyway if you want to argue that his posts made sense, make the actual argument.
“If you’re disagreeing that 1-(-1) covers an entirely separate and infinitely larger set of numbers than 1+1, then you simply don’t understand how math works”
is wrong plain and simple. He’s misrepresenting the expressions now as a range when he initially presented them to express the same value. It’s incorrect.
No, that wasn’t my “test,” technically. I was a top contender in the USAMO and participate heavily on math.stackexchange, and so if you want, I could push you on a great deal of higher-level mathematics to figure out just exactly how much you’re familiar with (but I suspect you’d be unwilling to agree to such a stress-test).
Anyway, the reason I asked you the base question is because you seemed to believe that a+b was somehow different from a-(-b) even though they are both representations of the exact same thing. However, you agree that 10+10=20 in base 10 is the same as A+A=14 in base 16, which is another scenario of two representations of the same thing: 110^1 + 010^0 + 110^1 + 010^0 = 210^1 + 010^0 versus 1016^0 + 10^10^0 = 116^1 + 4*16^0. So why do you draw the line there?
Moving on a bit:
Negative and positive numbers are both abstract representations. If you hold two apples, but eat one, and I ask you how many you now hold, you now hold 2-1 = 1 apples. Here, subtraction of a positive number is a useful way to express what is happening. We could say you have 2+(-1) = 1 apples, but it’s weird to say “You gained a negative apple” in that context even though it is a valid statement.
However, what if we were talking about money? If you have 100 dollars and go into debt 200 dollars, and I ask you what your net worth is, you’d say 100-200 = -100 dollars, which actually means something in that context. It would also make sense to express it as 100+(-200) = -100, too. You could say you’re 100 dollars in the hole, or that you took on a 200 dollar debt, etc. It’s all contextual.
In all these scenarios, it doesn’t matter how you frame it. We’re ultimately solving for results, and so it doesn’t really matter how we choose to split things up or what notations we use as long as we’re consistent and we can explain things in a way that makes meaningful sense. Results are what matter, as they are the measurements we use to benchmark whether or not our explanations work and are consistent.
So to say a-(-b) is somehow fundamentally different than a+b is wrong. They’re exactly the same, just like 10+10=20 and A+A=14 are the same. You’re just expressing the same idea in two different ways. Which representation you use depends on the situation/context that is the most useful and sensible. But in the end, you’re just trying to figure out the most useful way to get the result. Just because one representation is more useful than another doesn’t mean the physical reality is different. If I call a pencil a “pencil” but a Japanese person calls it an “enpitsu,” we’re still talking about the same thing.
Wasn’t a misleading question. That question was a minor primer, since a lot of Theory-of-Everything types tend to wildly misunderstand how infinity works and take issue with things like .999… = 1.
So if you don’t mind, let’s go one step further: Do you think Zeno’s Paradox is a real paradox?
Well, probably more factually incorrect is that Anthem is saying that we can’t see electrons and can only see the nucleus. That is patently false and I explained why in the post. Energy (in the form of light) comes in, hits electrons, those electrons get excited and move up in energy levels. Then when the come back down they release energy - a specific energy which results in specific color. Everything takes place in the electron cloud and not the nucleus. That’s why I wince whenever I feel the urge to rebut because it’s just not getting through.
Most frustrating is Anthem taking analogies literally. Arguing an analogy of someone walking down the street 2 different ways with ass-logic of the sound of that person’s footsteps hitting the ground is emotionally painful.
Well, sure. Just like everything we touch involves electrons. Those of us who have had any actual education knew what you were saying!
It reminds me of Sherlock Holmes knowing which way a bicycle had gone because the rear tire tracks cut over the front tire tracks. It sounds convincing…but doesn’t actually work!
There’s no hope for the OP but maybe I can sway you yet.
The big one. 1+1 vs 1-(-1). I guess the simplest analogy I can break it down is that 1-(-1) is a double negative. If I told you that I can’t get no satisfaction vs me telling you that I can get satisfaction, do I take different logical paths in getting to the same conclusion? My interpretation is that if it’s impossible to get no satisfaction, that only leaves getting satisfaction in the realm of possible. Anthem’s is that a person gets so little satisfaction that it inverts itself into some kind of sadistic satisfaction.
I’m kidding, partially but that’s basically what the “goes into the negative that it inverts on itself back to the positive” interpretation is implying. It’s just wrong.
The best explanation would be to posit yourself on the number line. Facing towards the positive and moving 1 unit up is +1. Facing towards the negative and moving back 1 is -(-1) and results in +1.
2) The 99% argument. Anthem says in a tangent that we can’t see the electrons and can only see the nucleus because of the electron cloud. The electron cloud is only a statistical representation of the possible locations of where electrons could be. It’s not a physical cloud of electrons. On top of all that, electrons are the only thing we can see. We see atoms by having light reflect off it, but the reflection process is a bit more complex than just the atoms acting like a mirror. Light comes in, hits the electrons. The electrons absorb the energy, jump into a higher energy state, and then drops back down. In that drop down, energy is released and that’s the reflected light. that’s why when white light hits an object, it reflects a specific color. That color is set based on what energy level the electrons settle down to. So really, at least as far as seeing electrons goes, I know that Anthem is wrong.
+/- position vs +/- charge. Anthem interchanges +/- when referring to +/- direction and charge. Positive/negative position is an arbitrary statement. Me going 200 miles north will get me to philly but that’s 200 miles south to someone in NYC. However, an electron is negative to both me and the New Yorker. That’s why when Anthem says something like
it’s a nothing statement.
in/out
I think I’ve figured out what Anthem says by in/out based on his latest retort. He’s claiming that from any point radiating outwards, that is the 4th spatial dimension. Imagine a light bulb and the light rays eminating from the center. All of those lines represents the “out” axis. Well that’s a novel idea except it lacks understanding. 3-dimensions doesn’t just fit into x-y-z. X-y-z is merely a system humans have concocted to describe where things are, and it’s not the only system. There are other systems.
Cylindrical describes things with 2 distances and an angle. Say that there’s a spider hanging from your ceiling and you want to describe the position of that spider. You can say (starting from a corner of the room) 2 feet forward, 2 feet right, and 2 feet up - 3 distances - an x-y-z coordinate. You can also say: take a tape measure and extend it 2 feet along a wall. Then raise the tape measure 2 feet. Then spin out the tape measure 45 degrees. The result would be that tape measure hitting the spider and you gave 2 distances and an angle.
You could also describe it using spherical coordinates. That would be taking a tape measure. Extending it 2 feet. Rotate it 45 degrees clockwise with it flush on the ground. Then angle it upwards 45 degrees. This is giving 2 angles and a distance. In all 3 systems you end up describing where the spider is, and in all 3 systems you require 3 pieces of information. That would be the 3 dimensions we live in.
Now what Anthem is trying to do is take the distance in spherical and glue it onto the x-y-z system and claiming it as the 4th dimension, which doesn’t fly.
Another way of thinking about it is with resultants. If you’re trying to cross a quad, you could take the sidewalk around. 20 feet to the right and then 20 feet forward. or you can just go off the sidewalk straight to the other corner. However, have you really walked in a different dimension or did you just combine the right movement and forward movement into one single diagonal movement (moving right and left simultaneously but really not introducing a 3rd dimension. that would require you walking up/down).
There’s a million different ways to shoot down the in/out explanation and it’s pretty much just me summarizing a bunch of fundamental math and physics principles.
Now I didn’t memorize them for the sake of it, but I did learn them. These aren’t shortcuts to reality but just plainly describing reality. I’m not saying I’m smarter than the people who haven’t but at the same time I am far better trained.
To really cut through the foggy BS, maybe I should summarize the way discourse has gone in this thread because often in trying to debunk the trees, we miss the error of the forest. Again, I’m not trying to disprove Anthem for the sake of disproving him. We don’t live in the dark ages. It would be EPIC if he actually did have a theory or even the semblances of a theory but he doesn’t and you can clearly see that by realizing that he
A)Can’t define his theory.
B)Can’t justify his theory.
C)Can’t defend his theory.
definition: Our physical theory inverts itself at the asteroid belt (later amended to outer space).
us: Can you be more specific to the point/line/plane of inversion?
Anthem: 42 light-minutes from the sun
us: why?
Anthem: it’s the distance from the sun to jupiter
us: it actually isn’t exactly 42, and varies based on tilt, where it is in its orbit, etc
Anthem: well that’s just an approximate average time
us: so the boundary is constantly changing?
Anthem: maybe. yes. yes it is.
us: and what of the non-gaseous objects past the gas giants like pluto?
Anthem: there’s another inversion point past the gas giants
us: but pluto’s orbit actually brings it closer to the sun than neptune for brief periods. and what about comets?
Anthem: ::no response::
us: and what do you mean by an inversion point at outer space?
Anthem: space is so different than here on earth
us: there’s a lot of places different than here on earth. are there inversions there too?
Anthem: not so completely different as outer space and earth. heat, sound, movement are all different
us: that’s mostly a product of the vacuum which we can easily replicate on earth with no effects of this inversion
Anthem: it’s just so different
us: but why can’t we observe it in manmade vacuums? plus there’s people who are in space RIGHT NOW and they haven’t observed it either
Anthem: that’s because we can’t observe it. it exists in a dimension we can’t perceive.
us: if we can’t observe it, how is this a theory? plus didn’t you say it did exist? that gas giants and blah blah blah?
Anthem: it is different. the heat, sound, etc.
us: we just told you that those things can be explained mostly be the lack of an atmosphere.
Anthem: did you say you wanted math? here’s a strawman based on my seemingly lack of understanding of negative numbers. 1-(-1) actually goes to negative infinity and skips its way back to 2.
us: No. that’s not how negative numbers work. here’s an analogy to help you better understand.
Anthem: Ah but what you don’t realize is that when somebody “walks” down a number line you can either watch him walk or hear him walk. If you listen, you can see that I’m still correct.
us: No. You missed the point. Nobody is actually watching someone walk down the number line. It’s only an analogy used to teach you how negative numbers work.
Anthem: That’s the point. Your analogy completely falls apart because you just can’t comprehend the 4th dimension.
us: No. It’s…
So really he’s not providing a theory at all but rather constantly painting himself into a corner and then grasping at straws and strawmen to prolong the conversation.
As a postscript, I have 2 friends from college who actually work at the patent office it’s highly upsetting that Anthem suggests that he is as qualified as they are, much less Einstein himself.
I will stop here and leave any further thoughts of Anthem for the pit.
I was in high school during the last such period, and scored SUCH a hit off my science teacher! I recited the list of the planets, from innermost to outermost, ending “Pluto, Neptune.” He said, “Wrong.” I said, “Wrong,” and proved it. One of the best smart-aleck moments of my misspent youth.
Otherwise… Praise to you for taking the time to make a “devil’s advocate” assessment of our correspondent’s ideas. That was exceptionally charitable of you.