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Q: Why 2 + 2 = 4 always ? ( Answered,   16 Comments ) Question
 Subject: Why 2 + 2 = 4 always ? Category: Science > Physics Asked by: kamal3r-ga List Price: \$2.00 Posted: 15 Apr 2004 01:25 PDT Expires: 15 May 2004 01:25 PDT Question ID: 330537
 ```In a world governed by the uncertainty principle of Quantum Mehanics, Why should 2 + 2 always = 4 in Mathematics?``` Subject: Re: Why 2 + 2 = 4 always ? Answered By: siliconsamurai-ga on 15 Apr 2004 05:54 PDT
 ```Hi, thank you for your question. I hope you like this brief answer to what is actually an incredibly complex question. The simple answer is that, in everyday mathematics, in number base systems higher than ?4,? 2 + 2 = 4 because it is defined as such. Based on the definitions of the number ?2?, the number ?4?, and the mathematical operation of addition, the answer is always the same. It is at the basis of all number theory and other branches of mathematics. Simply put, if you take a pile of objects that we designate as consisting of ?2? objects, and place it with another identical pile, the count of the resulting pile of objects is equal to what we label as the number ?4.? Of course, there are other number systems and other ways of doing math where that definition is not used, but they don?t generally produce very useful results for everyday applications. You can find a longer explanation at: http://www.mathmojo.com/interestinglessons/why%20do2plus2equal4/why%20do2plus2equal4.html, but it says generally the same thing. It may surprise you to learn that an entire book, Principia Mathematica, (the one by Whitehead and Russell, 1910-1913, not the one by Sir Isaac Newton in 1687) devotes several hundred pages to deriving an explanation of just why 2 + 2 = 4 (actually, as I recall, it was 1 + 1 = 2). I don?t recommend that you pick up a copy of this 2,000-page, three-volume set, since it consists almost entirely of equations. You can find some excellent discussions about the nature of mathematical proofs and in particular some 3,000 logic and set theory proofs at: http://us.metamath.org/mpegif/mmset.html In particular, you can find links to a 122-level ?proof? of why 2 + 2 = 4 at: http://us.metamath.org/mpegif/mmset.html#trivia A complete proof, such as the one presented in Principia Mathematica, involves 1,789 sub-theorems consisting of 19,731 individual steps. As some others have already commented, the question about quantum mechanics only applies to extremely small events at and below the atomic level. The mathematics involved in solving questions in quantum mechanics seldom even involves addition. In the simplest sense, as I once heard an old friend, John Van Vleck, Nobel Laureate Physics, 1977, say, you should always think of any question involving quantum mechanics as being a question of probabilities. In that sense, in quantum mechanics 2 + 2 never = 4 with any certainty. You will find a more extensive, but still reasonably accessible, introduction to quantum mechanics and mathematics at: http://www.math.rutgers.edu/~oldstein/quote.html One thing to keep in mind is that when you start getting into the details of advanced physics then you must switch languages. The reason things don?t seem to make sense at the atomic and sub-atomic levels is that non-physicists are forced to discuss things in English or some other language, which leads to what appear to be contradictions. In reality, you can only discuss such things in mathematics, which is why you will find most scientists very reluctant to talk about their work with non-scientists. Think about it this way. You would never use chemistry notation to show someone how to bake a cake. In the same way, you simply can?t explain most advanced physics concepts in English or any spoken language; the best you can do is summarize, simplify, and generalize ? the language simply won?t support detailed explanations without resulting in apparent paradoxes or contradictions. I hope you consider this an adequate answer for the price. Google search term: why does 2+2=4 ://www.google.com/search?sourceid=navclient&ie=UTF-8&oe=UTF-8&q=why+does+2%2B2%3D4 principia mathematica 2+2=4 ://www.google.com/search?sourceid=navclient&ie=UTF-8&oe=UTF-8&q=principia+mathematica+2%2B2%3D4 quantum mechanics math ://www.google.com/search?sourceid=navclient&ie=UTF-8&oe=UTF-8&q=quantum+mechanics+math principia mathematica whitehead ://www.google.com/search?sourceid=navclient&ie=UTF-8&oe=UTF-8&q=principia+mathematica+whitehead``` Subject: Re: Why 2 + 2 = 4 always ? From: till-ga on 15 Apr 2004 01:40 PDT
 ```Quantum mechanic as a principle only applies to physical processes in the sub-atomar region, not for macroscopic phenomena. till-ga```
 Subject: Re: Why 2 + 2 = 4 always ? From: poe-ga on 15 Apr 2004 02:54 PDT
 ```It doesn't. In base 3, 2 + 2 = 11.```
 Subject: Re: Why 2 + 2 = 4 always ? From: fj-ga on 15 Apr 2004 03:35 PDT
 `Question ID: 44464 asked: How much is 4 + 4?...`
 Subject: Re: Why 2 + 2 = 4 always ? From: probonopublico-ga on 15 Apr 2004 03:41 PDT
 ```Aw, C'mon, Poe You are pulling our legs ... How can the addition of two even numbers make an odd one? What have you been drinking?```
 Subject: Re: Why 2 + 2 = 4 always ? From: iang-ga on 15 Apr 2004 04:54 PDT
 ```In base 3, 11 isn't an odd number - it's divisible by 2. Mine's a pint! Ian G.```
 Subject: Re: Why 2 + 2 = 4 always ? From: probonopublico-ga on 15 Apr 2004 07:02 PDT
 ```So, there, Poe & Ian G I was right! I was, of course, relying on Principia Mathematica by Whitehead and Russell (1910-1913) for my observation and it's nice to know that Siliconsamurai is also on our same wavelength. I've never come across Siliconsamurai before but he/she is certainly one to watch.```
 Subject: Re: Why 2 + 2 = 4 always ? From: fj-ga on 15 Apr 2004 07:16 PDT
 ```> "You would never use chemistry notation to show someone how to bake a cake" But nethertheless, some people still try!: +++++++++++++++++++++++++++++++++++++++++++++++ Chocolate Chip Cookies: Ingredients: 1. 532.35 cm3 gluten 2. 4.9 cm3 NaHCO3 3. 4.9 cm3 refined halite 4. 236.6 cm3 partially hydrogenated tallow triglyceride 5. 177.45 cm3 crystalline C12H22O11 6. 177.45 cm3 unrefined C12H22O11 7. 4.9 cm3 methyl ether of protocatechuic aldehyde 8. Two calcium carbonate-encapsulated avian albumen-coated protein 9. 473.2 cm3 theobroma cacao 10. 236.6 cm3 de-encapsulated legume meats (sieve size #10) To a 2-L jacketed round reactor vessel (reactor #1) with an overall heat transfer coefficient of about 100 Btu/F-ft2-hr, add ingredients one, two and three with constant agitation. In a second 2-L reactor vessel with a radial flow impeller operating at 100 rpm, add ingredients four, five, six, and seven until the mixture is homogenous. To reactor #2, add ingredient eight, followed by three equal volumes of the homogenous mixture in reactor #1. Additionally, add ingredient nine and ten slowly, with constant agitation. Care must be taken at this point in the reaction to control any temperature rise that may be the result of an exothermic reaction. Using a screw extrude attached to a #4 nodulizer, place the mixture piece-meal on a 316SS sheet (300 x 600 mm). Heat in a 460K oven for a period of time that is in agreement with Frank & Johnston's first order rate expression (see JACOS, 21, 55), or until golden brown. Once the reaction is complete, place the sheet on a 25C heat-transfer table, allowing the product to come to equilibrium```
 Subject: Re: Why 2 + 2 = 4 always ? From: probonopublico-ga on 15 Apr 2004 07:32 PDT
 ```Wow, fj, I bet Pinkfreud (who knows a good recipe when she sees one) will try this one, for sure. Incidentally, I really do like the idea of 2 + 2 = 11. Being an accountant, I can think of some great applications.```
 Subject: Re: Why 2 + 2 = 4 always ? From: sasquatch77-ga on 15 Apr 2004 07:44 PDT
 ```2 subatomic particles plus 2 subatomic doesn't equal 4 subatomic particles. You're right about that, and many believe that that uncertainty extends to everything on the macrosopic level (via a sort've butterfly effect) . . . but 2 + 2 still equals 4 every time because mathematics is not a physical thing which can be measured. It is a concept (like a language) which we use for measuring things. You can't go visit the number 2, or hold "2" in your hand. But if you have a couple pairs of cookies in your hand, you can apply the concept of 2 and 2 and then use the concept of mathematics to deduce 2 + 2 = 4. So, the entire process of arriving at the number 4 is free from the influence of quantum uncertainty (OK, so maybe quantum indeterminacy in some microtubule in your brain could cause a glitch in your thinking process, but that doesn't affect the concept of math, just your understanding of it in that precise moment)```
 Subject: Re: Why 2 + 2 = 4 always ? From: sublime1-ga on 15 Apr 2004 08:15 PDT
 ```kamal3r... I don't know about 2 + 2, but here's an interesting proof that 1 = 0. Of course it's not true, but it should offer you some food for thought: Given a = b multiply both sides by a: a^2 = ab subtract b^2 from both sides: a^2-b^2 = ab-b^2 factor: (a+b)(a-b) = b(a-b) divide both sides by (a-b): (a+b)(a-b)/(a-b) = b(a-b)/(a-b) a+b = b substitute b for a, since a = b 2b = b divide by b: 2 = 1 subtract 1 from each side: 1 = 0 I notice this question is being asked on income tax deadline day, so maybe this will be of some help to you in preparing your returns... : )```
 Subject: Re: Why 2 + 2 = 4 always ? From: bastian-ga on 15 Apr 2004 09:37 PDT
 ```I think what it comes down to at it's simplest, is 2+2=4 because we defined it to, just like we defined the word hot to be hot. We made up the number 2 and we made up the number 4, the idea of it and the shape of the symbol for it and presto. I say "resilono" means 100. Why does it mean 100? Because I said so.```
 Subject: Re: Why 2 + 2 = 4 always ? From: probonopublico-ga on 15 Apr 2004 09:55 PDT
 ```I have just searched for 'resilono' and NOTHING! Sorry, Bastian, but your marketing of this word leaves something to be desired. I DO like it though. Well done!```
 Subject: Re: Why 2 + 2 = 4 always ? From: bastian-ga on 15 Apr 2004 10:22 PDT
 ```As for the 1=0 proof, you cant divide both sides by a-b because a=b and so a-b = 0 and you cant divide by 0.```
 Subject: Re: Why 2 + 2 = 4 always ? fj-ga From: siliconsamurai-ga on 15 Apr 2004 13:30 PDT
 ```WONDERFUL!!! Although I'm not taking the time to assess that recipe, it looks pretty good but I'm not sure about the thermodynamics - I would probably go with 425 or 400 degrees. Actually I got pretty good grades in chemistry at Harvard (AHH, the old Mallinckrodt building, does anyone know if it's still there?) but I learned to bake mostly around Radcliff, at least from The French Cheff (Julia) who I worked with at WGBH back in the 60's. (NOTE, Julia Child lived nearby in Cambridge back then and was often seen around some "Cliffie" dorms.) Me, I lived on a boat out in Winthrop.```
 Subject: Re: Why 2 + 2 = 4 always ? From: hedgie-ga on 19 Apr 2004 11:10 PDT
 ```My vote for the best answers goes to poe. He answered the question, correctly, with proper explanation. Other may have added some wisdom and folklor .. which however may obscure the basic mathematical fact, that validity of an aquation depends on the base system.```
 Subject: Re: Why 2 + 2 = 4 always ? From: probonopublico-ga on 19 Apr 2004 11:16 PDT
 ```An aquation, Hedgie? Surely you mean aquestrian ... Something to do with horses.``` 