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Talk:Glissando

True glissandi
What this article calles "true glissandi" should actually be referred to as portamenti. Portamento is defined as a continuous change in pitch. Unfortunately, portamenti are often wrongly called glissandi, which leads to the confusion between the two terms. Among trombonists, they are always refered to as glissandi or "glisses" even though what is played is a portamento. In this article the term "true glissando" should be replaced with portamento and "effective glissando" with just glissando.--Hrothgar137

 * Confusion about the origin of the "portamento" term leads to confusing definitions. I tried to help a bit. Uniseek

I think it's better to say the term glissando is simply a more general term than portamento, rather than to say portamenti are "often wrongly called glissandi." The term glissando has a well established usage in referring to both stepped and continuous glides. It's literally just the Italian word for "gliding." So it isn't "wrong" to refer to a continuous glide as a glissando. A quick look at the musical term dictionaries I have handy confirms that. 172.91.107.147 (talk) 23:56, 21 June 2023 (UTC)

All chromatic tones
all the chromatic tones Maybe this is true on a piano, but on a harp it isn't always. When a harpist slides her finger down the strings, she plays the tones the strings are set to: not all the chromatic tones (theoretically she could but that would mean a ton of quick pedal movements). She plays all the "diatonic" tones to the "key" the harp is in. The tones are not always diatonic in the usual sense because the pedals allow the creation of "keys" with any number of sharps and flats. One commonly used gliss has a B# and an E#: not a real key, but it sounds pretty :) dreamyshade
 * Good that you brought this up - it's something I thought about when I wrote the text but later forgot. It's true: neither pianists or harpists play all the chromatic tones. Have to think of a way of reformulating it. Any ideas? --tbackstr

I had a go and ended up completely rewriting it - hope that's OK. I kept all of the good points hopefully, apologies if I over edited anything. - MB
 * Yes, it's definitely better this way, thanks. --tbackstr

I agree it's a lot better, but what's a "melodic note"?

 * A note that constitutes part of the melody, as opposed to an "incidental note"... we probably need a link to an article on melody here. - MB

I thought of one more thing: a very limited true glissando can be played on the harp. It is a pedal slide, and is sometimes used in jazz music, and accidentally other times :). If you play one of the lower strings and immediately move its corresponding pedal, you can sort of get a slide from the original tone up or down a half-step.  I know it's a stretch, and doesn't need to be in the article, but it's an interesting thought. dreamyshade

How about what guitar players call a "slide"? The finger holding the string to the fretboard slides up or down the neck, shifting so rapidly to the different tones as to resemble a true glissando. Ed Poor

Quoted from the article - "On a harp, the player slide his finger up or down the strings, quickly playing the separate notes. Wind, brass and fretted stringed instrument players can effect an extremely rapid chromatic scale, giving the same effect." - MMGB

A request: portamento
It would be nice if someone could revise the article to indicate the difference (if any) between glissando and portamento. They appear to be similar concepts, but as a non-musician it would be nice if the article explained to me the exact relationship between the two terms. Psychonaut 17:23, 7 Mar 2005 (UTC)

 * I echo this request. I still worry that "true glissando" is a misnomer; portamento seems more appropriate here (especially without any citations present to declare otherise). Otherwise a clear distinction between true glissandi and portamenti seems necessary. --Adzze 03:16, 16 January 2007 (UTC)

I agree with the above. The paragraph labeled "Glissando vs. Portmento" describes the similarities, and an expert would probably be able to recognize the truths in the paragraph. But a novice like me, who came here seeking clarification can't figure out which is which, or what the key distinctions are. —Preceding unsigned comment added by 76.229.119.62 (talk) 21:18, 17 June 2008 (UTC)

The difference is, a glissando is a gradual slide between 2 notes, whereas portamento slides as the note changes. Portamento is more like a slur, but with a little bit of a slide; a glissando is just a slide beginning at one pitch and ending at another with a constant change in pitch the whole time.--Veggieburgerfish (talk) 00:06, 21 September 2008 (UTC)

Does this mean that there is no formal difference between a slide on guitar, and a bend on guitar? The former involves running a finger up or down the fretboard from one note, ending at another, while the latter involves pushing a ringing string out to the side, effectively tightening it in a continuous manner to increases the pitch. Both involve the gradual transition from one note to another. Are they thus both glissando? —Preceding unsigned comment added by 130.225.68.149 (talk) 14:29, 5 September 2010 (UTC)

 * I'm not sure what Veggieburgerfish is getting at, but the narrower usage of "glissando"- "...the filling in of discrete intermediate pitches on instruments like the piano, harp and fretted strings..."- would describe a slide, while "continuous glissando or portamento" covers bends.  Btw, you can sign your name by typing four tildas thus: Sparafucil (talk) 21:28, 5 September 2010 (UTC)

Piano tone bending
From the article: "On some instruments, a bending of the tone or continuous sliding is not possible (e.g., piano, harp)" It is possible, if you're willing to damage your instrument a little (and most avant-garde composers are). Volunteer Sibelius Salesman 19:39, 13 July 2005 (UTC)

Fretted string instrument glissando

 * I removed the reference to fretted unstruments reaching a maximum of three semitones by bending; as any beginning guitarist who has played "Sunshine of Your Love" can tell you, bends of at least four semitones (i.e. two steps) are possible. Deltabeignet 03:10, 23 November 2005 (UTC)

Harmonica
Maybe there should be a reference to glissando in harmonica since it is an essential part of blues harp and most methods of playing harmonica.

Guitar terms further muddying the water?
The technique of dragging your finger down a guitar's fretboard is called "a slide" and results in what this article calls "effective glissando". The cylindrical object you can use as an alternative to fretting is also called "a slide" and, when moved, results in what this article calls "true glissando" (what I would exclusively call portamento). I don't know if including that info in this article would simply increase the already high levels of confusion (given that, as has been pointed out, the "true glissando" usage recommended by this article isn't universally accepted). Boris B 08:42, 2 August 2006 (UTC)

Effective glissando on piano
what is the most painless way to play an effective glissando on a piano? —The preceding unsigned comment was added by 67.169.187.230 (talk) 04:42, 14 March 2007 (UTC).

Use the back of your thumb (The thumbnail). Just press down on the note and slide your hand up or down the keyboard. Make sure to use your thumbnail (or any other fingernail). Any other way will hurt. The Luizer 18:05, 10 May 2007 (UTC)

Confusion
This article seems really quite confused at the moment. I came trying to find out what the term was and found conflicting information. A visit to grove music online has cleared it up, and now I don't see why for example 'piano' should be under the 'portamento' heading when you can't normally do portamento on a piano. I'd suggest a rewrite... Yaxu 19:57, 2 May 2007 (UTC)

 * Agreed. Things like this with multiple conflicting definitions need references to clear up the confusion. — Omegatron 18:53, 9 May 2007 (UTC)

References, condensed definitions and examples, and a proposal to merge
The definition for glissando in the Virginia Tech Multimedia Music Dictionary describes the different techniques and results from each without using the term portamento. The definition for portamento does a better job of distinguishing between the two. The dictionary includes pronunciation, apparently recorded by someone with a discernable accent (Italian?); nevertheless, the pronunciation is correct and helpful (in my opinion, anyway).

Both portamento and glissando describe a slide between two notes or pitches. The slide is called a portamento when every tone between two notes is produced. When the slide is limited to sounding individual notes between the two pitches, it is a glissando.

A human voice is capable of producing a portamento. String instruments such as the violin are capable of producing a portamento when the player slides their finger from one pitch to another while drawing the bow across the string. The piano and harp are string instruments that are limited to glissandi. With the exception of a trombone, wind instruments are only capable of glissandi (and that requires mighty fast fingering).

For the sake of clarity, think of a slide between the notes B natural and C natural (mighty short slide); there are tones between the two notes. Instruments that can sound every tone between—voice, string instruments, etc.—create a portamento; instruments limited to playing the two notes themselves and none of the intervening tones—such as a piano—create a glissando.

I see no reason for there to be separate articles for Portamento and Glissando; in order to be informative, each article has to define both terms. Since I'm a "newbie" to this article, I don't feel comfortable placing the Mergefrom and Mergeto templates on the respective pages, Be bold notwithstanding.

Hopefully this was helpful and clarified the differences rather than further confuse the issue.75.58.45.66 17:19, 28 May 2007 (UTC)

I'm not up to merging either, though it seems right to have the main article here. I had a go at a para. == Glissando vs. Portamento == Sparafucil 04:47, 23 June 2007 (UTC)

 * Actually, judging from the comments later on in this discussion as well as the Portamento article, the portamento is a distinctly vocal technique developed for opera singing, that instruments only use when explicitly attempting to emulate vocal technique. E.g. a trombone glissando is not always a portamento simply because it encounters all intermediate pitches, it must also emulate opera style. I think it belongs in its own article for this reason, since there is an "Opera terms" template at the bottom of it. A merge is probably not a good idea. I do agree with the inclusion of clarifying information in the Glissando article, since the distinction is more applicable to instrumentalists (who, in aggregate, are capable of both techniques) than vocalists (who find glissandos very difficult and unusual). Publicly Visible (talk) 21:00, 7 September 2009 (UTC)
 * I just wanted to add an example of what I think is a glissando on piano. Glissando is used repeatedly throughout the song Finally by CeCe Peniston. The first occurrence is around the 0:30 mark. Universal Basic Outcome (talk) 22:11, 2 January 2023 (UTC)

Origin of the term "portamento" and its definition
To make a distinction between "glissando" and "portamento" it simply isn't enough just to go and look the words up in a dictionary, because the two terms are highly disputed even amongst the authors of dictionaries.

I find it useful to go back to the origin of the word "portamento". It was formerly applied only to singing and indicates "the carrying of the voice" from one tone to an other which was meant as a special form of legato-technique.

When a singer changes from one tone to an other (change of frequencies) without stopping the flow of the breath he or she has no choice but to slide through all the frequencies between the first and the second tone. Singers try normally to make this slide inaudible and thus give the impression of two tones being linked very closely (legato).

This is no problem as long as they don't change the register of their voice. But if they have to, then the whole thing gets much more complex and they run the risk of losing sound quality as well as volume (I am sorry of my description being not more detailed but singing is such a complex function of the human body that it can certainly not be fully described in an article like this.).

The solution of this problem is the "carrying of the voice" ("portamento") which basically means that the progress of changing between two tones is slowed down to give the singer more control of all the parameters she or he has to change together with the change of frequency. If the "portamento" is done correctly you will hear at the end of a tone a short slide to the frequency of the next one (mostly upwards, but also downwards). The portamento will be applied before the next syllable is to be pronounced and normally also reaches the target tone before the pronunciation of this syllable (because that is an other thing to help maintaining sound quality and volume).

So the idea of a portamento is to give two tones in legato the maximum beauty (as it is understood in belcanto-style).

If one tries to apply this idea to other instruments than the human voice, it would mean:

1. Hold a tone as long as possible

2. Shortly before the change to the next tone use the tones in between whilst maintaining sound quality and volume

3. "Touch down" on the target tone before the beat by marking it a little bit on the beat

If a portamento effect is wanted on the piano it would be best to play a marked apoggiatura consisting of the tone you are about to leave before the target tone rather than to break your fingers in an attempt to make a glissando.

"Glissando" means to glide from one tone to an other by using all the available tones in between. The kind of glissando you are able to produce is determined by the limitations of your instrument. The reason the term is often mixed up with the "portamento" is that one uses indeed a little "glissando" when executing a portamento but only as a part of a much more complex procedure. The term "glissando" sets the focus on the movement between two tones and there are many ways of executing a "glissando" including the possibility that the tones at the beginning and the end are of no musical importance at all, which is absolutely against the idea of the portamento. Of course singers can produce a "glissando" too. --Uniseek 11:46, 10 August 2007 (UTC)

Harp arpeggio
I am very confused by what the article says about harp glissandos involving an arpeggio. What confuses me is the notes given: B, C♭, D, E♯, F, G♯, A♭. Aren't B and C♭ the same note? What about E♯ and F, and G♯ and A♭? Someone the Person 23:18, 14 August 2007 (UTC)

Technically, no. Although they do sound the same, and in the western civilization's system of mean temperment, (e.g. how we tune our instruments) the notes have the same wavelength, the notes B and Cb are given because it is more correct to write this way. In musical notation in the written work, it is preferred that when giving a list of pitches, as above, that it is written diatonically, or in order. Otherwise, the list would look like this: B B D F F Ab Ab. These notes make up the B°7 chord, and an arpeggio is a broken up chord. The notes are different because a Cb is just that, a C lowered 1/2 of a step. It just happens to be the same note because of our tuning. In this instance, we have to think about the note Cb in relation to c, from whence the tone is derived. The person is just following conventional musical theory rules when writing notes out for printing. I will agree however that the section needs clean-up, I'll see waht I can do. Thenextstephensondheim1 20:29, 18 August 2007 (UTC)
 * This is a harp-specific spelling convention, different to most other instruments. There are 7 strings per octave, all of which can be raised or lowered by pedals, allowing the diminished seventh chord B-D-F-Ab to be played without skipping over any strings. Sparafucil 07:45, 20 September 2007 (UTC)

Additional citations
What, how, why, and where does this article need additional citations? Hyacinth (talk) 02:39, 3 April 2010 (UTC)
 * Apart from the one claim marked a needing a source, the entire section "'Continuous glissando' or portamento" lacks citations. This is also a major offender in the self-contradiction problem (see next section).—Jerome Kohl (talk) 03:52, 3 April 2010 (UTC)
 * Why does the "'Continuous glissando' or portamento" section need citations, or what in it does? Citations may simply help describe a contradiction, not eliminate it, though I guess that would take it out of our hands and put it in those of the sources cited. Hyacinth (talk) 09:16, 3 April 2010 (UTC)

Tag removed. Hyacinth (talk) 02:46, 18 January 2012 (UTC)

Contradict
How does this article appear to contradict itself and how should it be cleaned up? Hyacinth (talk) 02:40, 3 April 2010 (UTC)
 * For once, this was a banner that I placed myself, so I have a fairly good idea why it is there. First, the article says that glissando and portamento cannot be distinguished, then it goes on at some length trying to make this difference clear. The corresponding article on Portamento does not help a lot, either.—Jerome Kohl (talk) 03:49, 3 April 2010 (UTC)
 * It seems to me standard usage is contradictory and it isnt the job of (yet another) encyclopedia to fix things. The addition to the lede of "...performed or considered as continuous" was problematic, so I've tried again. Sparafucil (talk) 21:51, 5 September 2010 (UTC)
 * I think your change to the lede is a distinct improvement. It is very true that "standard usage" is contradictory, but that wasn't what I meant when I said this article contradicts itself. It is of course perfectly legitimate to explain that there are contradictions in usage, but it is quite another thing to say in one paragraph that chalk and cheese cannot be distinguished, and then follow it up with a paragraph explaining how the distinction should be made.
 * FWIW, I have been trying to track down the history of this terminology and, much to my surprise, have discovered that neither "portamento" nor "glissando" have an entry in the first edition of Grove (1878–1899). The earliest citation for "glissando" in the OED is from 1873, and refers exclusively to piano technique. Three years later, Stainer and Barrett's Dictionary of Musical Terms already presents the two possibilities of a rapid series of discrete pitches (piano) and continuous glide (violin), though admittedly their description of the violin technique is vague ("a rapid slur"). "Portamento", on the other hand, is found in English as early as 1771 (in Charles Burney's Present State Music France & Italy), though he does not define it. When exactly the term "portamento" started to be applied to a piano half-staccato is not so clear. The OED's earliest citation for this sense is from 1938, but Heinrich Schenker already discusses the term in the first volume of his Kontrapunkt (1910) as if it were already long in common use in German, at least.—Jerome Kohl (talk) 22:19, 5 September 2010 (UTC)
 * You mean interchangable use of portamento and portato?  I suppose some of this should (hint..) be making its way into the namespace... Sparafucil (talk) 20:12, 7 September 2010 (UTC)
 * That may be what is meant, but I am neither a pianist nor an historian of piano technique. I don't understand what you mean by a "namespace".—Jerome Kohl (talk) 20:44, 7 September 2010 (UTC)
 * I meant the article proper, though experienced WP readers probably know to check the talk pages for these nuggets.  I just put portato in the see also section of portamento; maybe that's good enough for now... Sparafucil (talk) 04:07, 18 January 2012 (UTC)

Trem arm on guitar
Some work as described here, by moving the bridge; but others, like the Bigby and similar, operate by moving a roller to which the strings are attached. Wschart (talk) 13:53, 14 December 2013 (UTC)

New paragraph, and clarification of "a mess"
After reading the whole article, I wrote the second paragraph, trying to provide a scientific foundation for the rest of the article. In the edit description, I too-concisely referred to the article as "a mess", which really needs clarification.

I'm only an amateur, although my father was Nicholas Bessaraboff (whose first name is frequently misspelled according to French usage, even in the award intended to honor him!!). I'd welcome editing to provide more rigorous wording, if such is needed.

Regarding "mess", the article seems to implicitly reveal a lack of education in musical acoustics and specific topics in physics. I've been an amateur recorder player for country dancing, even being paid a few times for half of a very few Playford balls in NYC, some decades ago. However, mostly as an independent scholar, have taught myself musical acoustics, and studied (among others) Juan G. Roederer's book on psychophysics, and the late Arthur Benade's _Horns, Strings, and Harmony_, if I recall his title correctly. Having a foot in both camps, I have profound respect for musicians, and sympathize with their struggles to pull together their own points of view in the article and Talk page.

A related topic is the mess regarding vibrato (FM!) vs. tremolo (AM!). (I wonder about pipe organ tremulants -- a bit of both, likely much more loudness than frequency variation, at a guess.)

Best regards, Nikevich 18:42, 1 March 2015 (UTC) (Signed in, for a change; perhaps login status should always be clear when starting an edit)

 * Welcome to Wikipedia. It is a strange and wondrous place, with many an unexpected quirk. While I generally agree with your assessment of this article and welcome your additions, one of the fundamental requirements on Wikipedia is that reliable sources be used to verify all but the most self-evident claims. I have tagged your additions accordingly, but I do not want you to think this is meant in any way as hostile to your intent. If you do not have any suitable sources immediately to hand, then other editors may be able to supply them. You mention Roederer and Benade (and you do recall his title correctly), which no doubt will supply some of the needed material.
 * There is also the fact that the term "glissando" is first and foremost a musical term, and only comes under the scrutiny of acousticians because of its use by bumbling, unscientific-minded musicians. Nevertheless, both views should be represented, and it is always amusing to watch scientists trying to make tidy sense of the terminological mess we musicians leave lying about.
 * The matter of vibrato vs tremolo is really a side issue for this article, but you should be aware that these terms are not cut-and-dried so far as musicians are concerned (for acousticians, this may be an entirely different matter). For example, on the violin and similar bowed string instruments, there are two distinct effects, both of which are referred to as "tremolo". One is a rapid alternation between two notes more than a whole tone apart (like a wide trill, and sometimes called "fingered tremolo"), the other is a reiteration on one note made by rapidly reversing the direction of the bow (sometimes called "bowed tremolo"). Vibrato, similarly, is produced on different instruments in different ways, and in the case of vocal vibrato there are differing opinion about whether it is primarily the frequency or the amplitude that is modulated (both are necessarily involved, for reasons of physiology of the vocal tract).—Jerome Kohl (talk) 21:46, 1 March 2015 (UTC)

Slide vs. glissando?
The word "slide" occurs about 4 times in this article, but none of these is a link to slide (music), and no explanation is given about their difference. I think that would be helpful. User:Haraldmmueller 16:39, 16 March 2023 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Glissando


text:
Original proof of Gödel's completeness theorem

The proof of Gödel's completeness theorem given by Kurt Gödel in his doctoral dissertation of 1929 (and a shorter version of the proof, published as an article in 1930, titled "The completeness of the axioms of the functional calculus of logic" (in German)) is not easy to read today; it uses concepts and formalisms that are no longer used and terminology that is often obscure. The version given below attempts to represent all the steps in the proof and all the important ideas faithfully, while restating the proof in the modern language of mathematical logic. This outline should not be considered a rigorous proof of the theorem.

Assumptions
We work with first-order predicate calculus. Our languages allow constant, function and relation symbols. Structures consist of (non-empty) domains and interpretations of the relevant symbols as constant members, functions or relations over that domain.

We assume classical logic (as opposed to intuitionistic logic for example).

We fix some axiomatization (i.e. a syntax-based, machine-manageable proof system) of the predicate calculus: logical axioms and rules of inference. Any of the several well-known equivalent axiomatizations will do. Gödel's original proof assumed the Hilbert-Ackermann proof system.

We assume without proof all the basic well-known results about our formalism that we need, such as the normal form theorem or the soundness theorem.

We axiomatize predicate calculus without equality (sometimes confusingly called without identity), i.e. there are no special axioms expressing the properties of (object) equality as a special relation symbol. After the basic form of the theorem has been proved, it will be easy to extend it to the case of predicate calculus with equality.

Statement of the theorem and its proof
In the following, we state two equivalent forms of the theorem, and show their equivalence.

Later, we prove the theorem. This is done in the following steps:

 * 1) Reducing the theorem to sentences (formulas with no free variables) in prenex form, i.e. with all quantifiers ($∀$ and $∃$) at the beginning. Furthermore, we reduce it to formulas whose first quantifier is $∀$. This is possible because for every sentence, there is an equivalent one in prenex form whose first quantifier is $∀$.
 * 2) Reducing the theorem to sentences of the form $∀x_{1} ∀x_{2} ... ∀x_{k} ∃y_{1} ∃y_{2} ... ∃y_{m} φ(x_{1} ... x_{k}, y_{1} ... y_{m})$. While we cannot do this by simply rearranging the quantifiers, we show that it is yet enough to prove the theorem for sentences of that form.
 * 3) Finally we prove the theorem for sentences of that form.
 * 4) * This is done by first noting that a sentence such as $B = ∀ x_{1} ∀ x_{2} ...∀ x_{k} ∃ y_{1} ∃ y_{2} ...∃ y_{m} φ( x_{1} ... x_{k}, y_{1} ... y_{m} )$ is either refutable (its negation is always true) or satisfiable, i.e. there is some model in which it holds (it might even be always true, i.e. a tautology); this model is simply assigning truth values to the subpropositions from which B is built. The reason for that is the completeness of propositional logic, with the existential quantifiers playing no role.
 * 5) * We extend this result to more and more complex and lengthy sentences, Dn (n = 1,2...), built out from B, so that either any of them is refutable and therefore so is φ, or all of them are not refutable and therefore each holds in some model.
 * 6) * We finally use the models in which the Dn hold (in case all are not refutable) in order to build a model in which φ holds.

Theorem 1. Every valid formula (true in all structures) is provable.
This is the most basic form of the completeness theorem. We immediately restate it in a form more convenient for our purposes: When we say "all structures", it is important to specify that the structures involved are classical (Tarskian) interpretations I, where I =  (U is a non-empty (possibly infinite) set of objects, whereas F is a set of functions from expressions of the interpreted symbolism into U). [By contrast, so-called "free logics" allow possibly empty sets for U. For more regarding free logics, see the work of Karel Lambert.]

Theorem 2. Every formula φ is either refutable or satisfiable in some structure.
"φ is refutable" means by definition "¬φ is provable".

Equivalence of both theorems
If Theorem 1 holds, and φ is not satisfiable in any structure, then ¬φ is valid in all structures and therefore provable, thus φ is refutable and Theorem 2 holds. If on the other hand Theorem 2 holds and φ is valid in all structures, then ¬φ is not satisfiable in any structure and therefore refutable; then ¬¬φ is provable and then so is φ, thus Theorem 1 holds.

Proof of theorem 2: first step
We approach the proof of Theorem 2 by successively restricting the class of all formulas φ for which we need to prove "φ is either refutable or satisfiable". At the beginning we need to prove this for all possible formulas φ in our language. However, suppose that for every formula φ there is some formula ψ taken from a more restricted class of formulas C, such that "ψ is either refutable or satisfiable" → "φ is either refutable or satisfiable". Then, once this claim (expressed in the previous sentence) is proved, it will suffice to prove "φ is either refutable or satisfiable" only for φ's belonging to the class C. If φ is provably equivalent to ψ (i.e., (φ ≡ ψ) is provable), then it is indeed the case that "ψ is either refutable or satisfiable" → "φ is either refutable or satisfiable" (the soundness theorem is needed to show this).

There are standard techniques for rewriting an arbitrary formula into one that does not use function or constant symbols, at the cost of introducing additional quantifiers; we will therefore assume that all formulas are free of such symbols. Gödel's paper uses a version of first-order predicate calculus that has no function or constant symbols to begin with.

Next we consider a generic formula φ (which no longer uses function or constant symbols) and apply the prenex form theorem to find a formula ψ in normal form such that φ ≡ ψ (ψ being in normal form means that all the quantifiers in ψ, if there are any, are found at the very beginning of ψ). It follows now that we need only prove Theorem 2 for formulas φ in normal form.

Next, we eliminate all free variables from φ by quantifying them existentially: if, say, x1...xn are free in φ, we form $$\psi = \exists x_1 \cdots \exists x_n \varphi$$. If ψ is satisfiable in a structure M, then certainly so is φ and if ψ is refutable, then $$\neg \psi = \forall x_1 \cdots \forall x_n \neg \varphi$$ is provable, and then so is ¬φ, thus φ is refutable. We see that we can restrict φ to be a sentence, that is, a formula with no free variables.

Finally, we would like, for reasons of technical convenience, that the prefix of φ (that is, the string of quantifiers at the beginning of φ, which is in normal form) begin with a universal quantifier and end with an existential quantifier. To achieve this for a generic φ (subject to restrictions we have already proved), we take some one-place relation symbol F unused in φ, and two new variables y and z.. If φ = (P)Φ, where (P) stands for the prefix of φ and Φ for the matrix (the remaining, quantifier-free part of φ) we form $$\psi = \forall y (P) \exists z ( \Phi \wedge [ F(y) \vee \neg F(z) ] )$$. Since $$\forall y \exists z ( F(y) \vee \neg F(z) )$$ is clearly provable, it is easy to see that $$\varphi=\psi$$ is provable.

Reducing the theorem to formulas of degree 1
Our generic formula φ now is a sentence, in normal form, and its prefix starts with a universal quantifier and ends with an existential quantifier. Let us call the class of all such formulas R. We are faced with proving that every formula in R is either refutable or satisfiable. Given our formula φ, we group strings of quantifiers of one kind together in blocks:

 * $$\varphi = (\forall x_1 \cdots \forall x_{k_1})(\exists x_{k_1+1} \cdots \exists x_{k_2}) \cdots (\forall x_{k_{n-2}+1} \cdots \forall x_{k_{n-1}})(\exists x_{k_{n-1}+1} \cdots \exists x_{k_n}) (\Phi)$$

We define the degree of $$\varphi$$ to be the number of universal quantifier blocks, separated by existential quantifier blocks as shown above, in the prefix of $$\varphi$$. The following lemma, which Gödel adapted from Skolem's proof of the Löwenheim–Skolem theorem, lets us sharply reduce the complexity of the generic formula $$\varphi$$ we need to prove the theorem for:

Lemma. Let k ≥ 1. If every formula in R of degree k is either refutable or satisfiable, then so is every formula in R of degree k + 1.

 * Comment: Take a formula φ of degree k + 1 of the form $$\varphi = (\forall x)(\exists y)(\forall u)(\exist v) (P) \psi$$, where $$(P)\psi$$ is the remainder of $$\varphi$$ (it is thus of degree k − 1). φ states that for every x there is a y such that... (something). It would have been nice to have a predicate Q'  so that for every x, Q′(x,y) would be true if and only if y is the required one to make (something) true. Then we could have written a formula of degree k, which is equivalent to φ, namely $$(\forall x')(\forall x)(\forall y)(\forall u)(\exist v)(\exist y') (P) Q'(x',y') \wedge (Q'(x,y) \rightarrow \psi)$$. This formula is indeed equivalent to φ because it states that for every x, if there is a y that satisfies Q'(x,y), then (something) holds, and furthermore, we know that there is such a y, because for every x', there is a y' that satisfies Q'(x',y'). Therefore φ follows from this formula. It is also easy to show that if the formula is false, then so is φ. Unfortunately, in general there is no such predicate Q'. However, this idea can be understood as a basis for the following proof of the Lemma.

Proof. Let φ be a formula of degree k + 1; then we can write it as

 * $$\varphi = (\forall x)(\exists y)(\forall u)(\exist v) (P) \psi$$

where (P) is the remainder of the prefix of $$\varphi$$ (it is thus of degree k – 1) and $$\psi$$ is the quantifier-free matrix of $$\varphi$$. x, y, u and v denote here tuples of variables rather than single variables; e.g. $$(\forall x)$$ really stands for $$\forall x_1 \forall x_2 \cdots \forall x_n$$ where $$x_1 \ldots x_n$$ are some distinct variables.

Let now x' and y' be tuples of previously unused variables of the same length as x and y respectively, and let Q be a previously unused relation symbol that takes as many arguments as the sum of lengths of x and y; we consider the formula

 * $$\Phi = (\forall x')(\exists y') Q(x',y') \wedge (\forall x)(\forall y)( Q(x,y) \rightarrow (\forall u)(\exist v)(P)\psi )$$

Clearly, $$\Phi \rightarrow \varphi$$ is provable.

Now since the string of quantifiers $$(\forall u)(\exists v)(P)$$ does not contain variables from x or y, the following equivalence is easily provable with the help of whatever formalism we're using:

 * $$( Q(x,y) \rightarrow (\forall u )(\exists v)(P) \psi) \equiv (\forall u)(\exists v)(P) ( Q(x,y) \rightarrow \psi )$$

And since these two formulas are equivalent, if we replace the first with the second inside Φ, we obtain the formula Φ' such that Φ≡Φ':

 * $$\Phi' = (\forall x')(\exist y') Q(x',y') \wedge (\forall x)(\forall y) (\forall u)(\exists v)(P) ( Q(x,y) \rightarrow \psi )$$

Now Φ' has the form $$(S)\rho \wedge (S')\rho'$$, where (S) and (S') are some quantifier strings, ρ and ρ' are quantifier-free, and, furthermore, no variable of (S) occurs in ρ' and no variable of (S') occurs in ρ. Under such conditions every formula of the form $$(T)(\rho \wedge \rho')$$, where (T) is a string of quantifiers containing all quantifiers in (S) and (S') interleaved among themselves in any fashion, but maintaining the relative order inside (S) and (S'), will be equivalent to the original formula Φ'(this is yet another basic result in first-order predicate calculus that we rely on). To wit, we form Ψ as follows:
 * $$\Psi = (\forall x')(\forall x)(\forall y) (\forall u)(\exists y')(\exists v)(P)Q(x',y') \wedge (Q(x,y) \rightarrow \psi )$$

and we have $$\Phi' \equiv \Psi$$.

Now $$\Psi$$ is a formula of degree k and therefore by assumption either refutable or satisfiable. If $$\Psi$$ is satisfiable in a structure M, then, considering $$\Psi \equiv \Phi' \equiv \Phi \wedge \Phi \rightarrow \varphi$$, we see that $$\varphi$$ is satisfiable as well. If $$\Psi$$ is refutable, then so is $$\Phi$$, which is equivalent to it; thus $$\neg \Phi$$ is provable. Now we can replace all occurrences of Q inside the provable formula $$\neg \Phi$$ by some other formula dependent on the same variables, and we will still get a provable formula. (This is yet another basic result of first-order predicate calculus. Depending on the particular formalism adopted for the calculus, it may be seen as a simple application of a "functional substitution" rule of inference, as in Gödel's paper, or it may be proved by considering the formal proof of $$\neg \Phi$$, replacing in it all occurrences of Q by some other formula with the same free variables, and noting that all logical axioms in the formal proof remain logical axioms after the substitution, and all rules of inference still apply in the same way.)

In this particular case, we replace Q(x',y') in $$\neg \Phi$$ with the formula $$(\forall u)(\exists v)(P)\psi(x,y\mid x',y')$$. Here (x,y | x',y') means that instead of ψ we are writing a different formula, in which x and y are replaced with x' and y'. Q(x,y) is simply replaced by $$(\forall u)(\exists v)(P)\psi$$.

$$\neg \Phi$$ then becomes

 * $$\neg ( (\forall x')(\exists y') (\forall u)(\exists v)(P)\psi(x,y\mid x',y') \wedge (\forall x)(\forall y) ( (\forall u)(\exists v)(P)\psi \rightarrow (\forall u)(\exists v)(P) \psi ) )$$

and this formula is provable; since the part under negation and after the $$\wedge$$ sign is obviously provable, and the part under negation and before the $$\wedge$$ sign is obviously φ, just with x and y replaced by x' and y', we see that $$\neg \varphi$$ is provable, and φ is refutable. We have proved that φ is either satisfiable or refutable, and this concludes the proof of the Lemma.

Notice that we could not have used $$(\forall u)(\exists v)(P)\psi(x,y\mid x',y')$$ instead of Q(x',y') from the beginning, because $$\Psi$$ would not have been a well-formed formula in that case. This is why we cannot naively use the argument appearing at the comment that precedes the proof.

Proving the theorem for formulas of degree 1
As shown by the Lemma above, we only need to prove our theorem for formulas φ in R of degree 1. φ cannot be of degree 0, since formulas in R have no free variables and don't use constant symbols. So the formula φ has the general form:

 * $$ (\forall x_1\ldots x_k)(\exists y_1\ldots y_m) \varphi(x_1\ldots x_k, y_1\ldots y_m).$$

Now we define an ordering of the k-tuples of natural numbers as follows: $$ (x_1\ldots x_k) < (y_1\ldots y_k) $$ should hold if either $$ \Sigma_k (x_1\ldots x_k) < \Sigma_k (y_1\ldots y_k) $$, or $$ \Sigma_k (x_1\ldots x_k) = \Sigma_k (y_1\ldots y_k) $$, and $$ (x_1\ldots x_k) $$ precedes $$ (y_1...y_k) $$ in lexicographic order. [Here $$ \Sigma_k (x_1\ldots x_k) $$ denotes the sum of the terms of the tuple.] Denote the nth tuple in this order by $$ (a^n_1\ldots a^n_k) $$.

Set the formula $$ B_n $$ as $$ \varphi(z_{a^n_1}\ldots z_{a^n_k}, z_{(n-1)m+2}, z_{(n-1)m+3}\ldots z_{nm+1}) $$. Then put $$D_n$$ as
 * $$ (\exists z_1\ldots z_{nm+1}) (B_1 \wedge B_2 \wedge \cdots \wedge B_n).$$

Lemma: For every n, $$ \varphi \rightarrow D_n$$.

Proof: By induction on n; we have $$ D_n \Leftarrow D_{n-1} \wedge (\forall z_1\ldots z_{(n-1)m+1})(\exists z_{(n-1)m+2}\ldots z_{nm+1}) B_n \Leftarrow D_{n-1} \wedge (\forall z_{a^n_1}\ldots z_{a^n_k})(\exists y_1\ldots y_m) \varphi(z_{a^n_1}\ldots z_{a^n_k}, y_1\ldots y_m) $$, where the latter implication holds by variable substitution, since the ordering of the tuples is such that $$(\forall k)(a^n_1 \ldots a^n_k) < (n-1)m + 2$$. But the last formula is equivalent to $$ D_{n-1} \wedge $$φ.

For the base case, $$ D_1 \equiv (\exists z_1\ldots z_{m+1}) \varphi(z_{a^1_1}\ldots z_{a^1_k}, z_2, z_3\ldots z_{m+1}) \equiv (\exists z_1\ldots z_{m+1}) \varphi(z_1\ldots z_1, z_2, z_3\ldots z_{m+1}) $$ is obviously a corollary of φ as well. So the Lemma is proven.

Now if $$ D_n $$ is refutable for some n, it follows that φ is refutable. On the other hand, suppose that $$ D_n $$ is not refutable for any n. Then for each n there is some way of assigning truth values to the distinct subpropositions $$E_h$$ (ordered by their first appearance in $$D_n$$; "distinct" here means either distinct predicates, or distinct bound variables) in $$ B_k $$, such that $$ D_n $$ will be true when each proposition is evaluated in this fashion. This follows from the completeness of the underlying propositional logic.

We will now show that there is such an assignment of truth values to $$E_h$$, so that all $$D_n$$ will be true: The $$E_h$$ appear in the same order in every $$ D_n $$; we will inductively define a general assignment to them by a sort of "majority vote": Since there are infinitely many assignments (one for each $$ D_n $$) affecting $$E_1$$, either infinitely many make $$E_1$$ true, or infinitely many make it false and only finitely many make it true. In the former case, we choose $$E_1$$ to be true in general; in the latter we take it to be false in general. Then from the infinitely many n for which $$E_1$$ through $$E_{h-1}$$ are assigned the same truth value as in the general assignment, we pick a general assignment to $$E_h$$ in the same fashion.

This general assignment must lead to every one of the $$B_k$$ and $$D_k$$ being true, since if one of the $$B_k$$ were false under the general assignment, $$D_n$$ would also be false for every n > k. But this contradicts the fact that for the finite collection of general $$E_h$$ assignments appearing in $$D_k$$, there are infinitely many n where the assignment making $$D_n$$ true matches the general assignment.

From this general assignment, which makes all of the $$D_k$$ true, we construct an interpretation of the language's predicates that makes φ true. The universe of the model will be the natural numbers. Each i-ary predicate $$\Psi$$ should be true of the naturals $$(u_1\ldots u_i)$$ precisely when the proposition $$\Psi(z_{u_1}\ldots z_{u_i})$$ is either true in the general assignment, or not assigned by it (because it never appears in any of the $$D_k$$).

In this model, each of the formulas $$ (\exists y_1\ldots y_m) \varphi(a^n_1\ldots a^n_k, y_1...y_m) $$ is true by construction. But this implies that φ itself is true in the model, since the $$a^n$$ range over all possible k-tuples of natural numbers. So φ is satisfiable, and we are done.

Intuitive explanation
We may write each Bi as Φ(x1...xk,y1...ym) for some xs, which we may call "first arguments" and ys that we may call "last arguments".

Take B1 for example. Its "last arguments" are z2,z3...zm+1, and for every possible combination of k of these variables there is some j so that they appear as "first arguments" in Bj. Thus for large enough n1, Dn 1 has the property that the "last arguments" of B1 appear, in every possible combinations of k of them, as "first arguments" in other Bjs within Dn. For every Bi there is a Dn i with the corresponding property.

Therefore in a model that satisfies all the Dns, there are objects corresponding to z1, z2... and each combination of k of these appear as "first arguments" in some Bj, meaning that for every k of these objects zp 1 ...zp k there are zq 1 ...zq m, which makes Φ(zp 1 ...zp k ,zq 1 ...zq m ) satisfied. By taking a submodel with only these z1, z2... objects, we have a model satisfying φ.

Extension to first-order predicate calculus with equality
Gödel reduced a formula containing instances of the equality predicate to ones without it in an extended language. His method involves replacing a formula φ containing some instances of equality with the formula

 * $$ (\forall x) Eq(x, x) \wedge (\forall x,y,z) [Eq(x, y) \rightarrow (Eq(x, z) \rightarrow Eq(y, z))] $$ $$ \wedge (\forall x,y,z) [Eq(x, y) \rightarrow (Eq(z, x) \rightarrow Eq(z, y))] $$
 * $$ \wedge $$
 * $$ (\forall x_1\ldots x_k, y_1\ldots x_k) [(Eq(x_1, y_1) \wedge \cdots \wedge Eq(x_k, y_k)) \rightarrow (A(x_1\ldots x_k) \equiv A(y_1\ldots y_k))] $$
 * $$ \wedge \cdots \wedge $$
 * $$ (\forall x_1\ldots x_m, y_1\ldots x_m) [(Eq(x_1, y_1) \wedge \cdots \wedge Eq(x_m, y_m)) \rightarrow (Z(x_1\ldots x_m) \equiv Z(y_1\ldots y_m))] $$
 * $$ \wedge $$
 * $$ \varphi'.$$

Here $$A \ldots Z$$ denote the predicates appearing in φ (with $$k \ldots  m$$ their respective arities), and φ' is the formula φ with all occurrences of equality replaced with the new predicate Eq. If this new formula is refutable, the original φ was as well; the same is true of satisfiability, since we may take a quotient of satisfying model of the new formula by the equivalence relation representing Eq. This quotient is well-defined with respect to the other predicates, and therefore will satisfy the original formula φ.

Extension to countable sets of formulas
Gödel also considered the case where there are a countably infinite collection of formulas. Using the same reductions as above, he was able to consider only those cases where each formula is of degree 1 and contains no uses of equality. For a countable collection of formulas $$ \varphi^i $$ of degree 1, we may define $$ B^i_k $$ as above; then define $$ D_k $$ to be the closure of $$ B^1_1\ldots B^1_k, \ldots, B^k_1\ldots B^k_k $$. The remainder of the proof then went through as before.

Extension to arbitrary sets of formulas
When there is an uncountably infinite collection of formulas, the Axiom of Choice (or at least some weak form of it) is needed. Using the full AC, one can well-order the formulas, and prove the uncountable case with the same argument as the countable one, except with transfinite induction. Other approaches can be used to prove that the completeness theorem in this case is equivalent to the Boolean prime ideal theorem, a weak form of AC.


text:
Grits

Grits are a type of porridge made from coarsely ground dried maize or hominy, the latter being maize that has been treated with an alkali in a process called nixtamalization, with the pericarp (ovary wall) removed. Grits are cooked in warm salted water or milk. They are often served with flavorings as a breakfast dish. Grits can be savory or sweet, with savory seasonings being more common. Grits are similar to other thick maize-based porridges from around the world, such as polenta and mieliepap. The dish originated in the Southern United States but is now available nationwide. Grits are often part of a dinner entrée shrimp and grits, served primarily in the Southern United States.

The word "grits" is derived from the Old English word grytt, meaning "coarse meal". In the Charleston, South Carolina area, cooked hominy grits were primarily referred to as "hominy" until the 1980s.

Origin
The dish originated with the Native American Muscogee tribe using maize. American colonists learned to make the dish from the Native Americans, and it quickly became an American staple.

At that time, maize or hominy for grits was ground on a stone mill. The ground material was passed through screens, the finer sifted material used as grit meal, and the coarser as grits.

Three-quarters of the grits sold in the U.S. are bought in the South, in an area stretching from Lower Texas to Washington, D.C., that is sometimes called the "grits belt". The state of Georgia declared grits to be its official prepared food in 2002. A similar bill was introduced in South Carolina to name it the official state food, but it did not advance. Nevertheless, South Carolina still has an entire chapter of legislation dealing exclusively with corn meal and grits. State law in South Carolina requires grits and rice meal to be enriched, similar to the requirement for flour.

Grits may be either yellow or white, depending on the color of the maize used. The most common version in supermarkets is "quick" grits, which are made from non-hominy maize and have the germ and hull removed. Whole kernel grits are sometimes called "speckled".

Preparation
Grits are prepared by mixing water or milk and the dry grits and stirring them over heat, if one uses cornmeal, the food is called mush. Whole grain grits require much longer to become soft than "quick grits".

Dishes
Grits are eaten with a wide variety of foods, such as eggs and bacon, fried catfish, shrimp, salmon croquettes, or country ham.

Shrimp and grits is a traditional dish in the coastal communities in the South Carolina Lowcountry and Georgia's Lower Coastal Plain.

Solidified cooked grits can be sliced and fried in vegetable oil, butter, or bacon grease to make fried grits, or they can first be breaded in beaten egg and bread crumbs.

title: Grits


text:
General Electric

General Electric Company (GE) was an American multinational conglomerate founded in 1892, incorporated in the state of New York and headquartered in Boston. The company had several divisions, including aerospace, energy, healthcare, and finance.

In 2020, GE ranked among the Fortune 500 as the 33rd largest firm in the United States by gross revenue. In 2023, the company was ranked 64th in the Forbes Global 2000. In 2011, GE ranked among the Fortune 20 as the 14th most profitable company, but later very severely underperformed the market (by about 75%) as its profitability collapsed. Two employees of GE—Irving Langmuir (1932) and Ivar Giaever (1973)—have been awarded the Nobel Prize.

Following the Great Recession of the late 2000s, General Electric began selling off various divisions and assets, including its appliances and financial capital divisions, under Jeff Immelt's leadership as CEO. John Flannery, Immelt's replacement in 2017, further divested General Electric's assets in locomotives and lighting in order to focus the company more on aviation. After restrictions on air travel during the COVID-19 pandemic caused General Electric's revenue to fall significantly in 2020, GE's final CEO Larry Culp announced in November 2021 that General Electric was to be broken up into three separate, public companies—GE Aerospace, GE HealthCare, and GE Vernova—by 2024. The new companies are respectively focused on aerospace, healthcare, and energy. GE HealthCare's spin-off was finalized on January 4, 2023. This was followed by the spin-off of GE's portfolio of energy businesses on April 2, 2024, into GE Vernova. Following these transactions, General Electric Company changed its trading name to GE Aerospace, pivoted to aviation, and ceased to exist as a conglomerate.

Formation
During 1889, Thomas Edison (1847–1931) had business interests in many electricity-related companies, including Edison Lamp Company, a lamp manufacturer in East Newark, New Jersey; Edison Machine Works, a manufacturer of dynamos and large electric motors in Schenectady, New York; Bergmann & Company, a manufacturer of electric lighting fixtures, sockets, and other electric lighting devices; and Edison Electric Light Company, the patent-holding company and financial arm for Edison's lighting experiments, backed by J. P. Morgan (1837–1913) and the Vanderbilt family.

In 1889, Drexel, Morgan & Co.—a company founded by J.P. Morgan and Anthony J. Drexel—financed Edison's research and helped merge several of Edison's separate companies under one corporation, forming Edison General Electric Company, which was incorporated in New York on April 24, 1889. The new company acquired Sprague Electric Railway & Motor Company in the same year. The consolidation did not involve all of the companies established by Edison; notably, the Edison Illuminating Company, which would later become Consolidated Edison, was not part of the merger.

In 1880, Gerald Waldo Hart formed the American Electric Company of New Britain, Connecticut, which merged a few years later with Thomson-Houston Electric Company, led by Charles Coffin. In 1887, Hart left to become superintendent of the Edison Electric Company. General Electric was formed through the 1892 merger of Edison General Electric Company and Thomson-Houston Electric Company with the support of Drexel, Morgan & Co. The original plants of both companies continue to operate under the GE banner to this day.

The General Electric business was incorporated in New York, with the Schenectady plant used as headquarters for many years thereafter. Around the same time, General Electric's Canadian counterpart, Canadian General Electric, was formed.

In 1893, General Electric bought the business of Rudolf Eickemeyer in Yonkers, New York, along with all of its patents and designs. Eickemeyer's firm had developed transformers for use in the transmission of electrical power.

Public company
In 1896, General Electric was one of the original 12 companies listed on the newly formed Dow Jones Industrial Average, where it remained a part of the index for 122 years, though not continuously.

In 1911, General Electric absorbed the National Electric Lamp Association (NELA) into its lighting business. GE established its lighting division headquarters at Nela Park in East Cleveland, Ohio. The lighting division has since remained in the same location.

RCA and NBC
Owen D. Young, through GE, founded the Radio Corporation of America (RCA) in 1919 after purchasing the Marconi Wireless Telegraph Company of America. He aimed to expand international radio communications. GE used RCA as its retail arm for radio sales. In 1926, RCA co-founded the National Broadcasting Company (NBC), which built two radio broadcasting networks. In 1930, General Electric was charged with antitrust violations and was ordered to divest itself of RCA.

Television
In 1927, Ernst Alexanderson of GE made the first demonstration of television broadcast reception at his General Electric Realty Plot home at 1132 Adams Road in Schenectady, New York. On January 13, 1928, he made what was said to be the first broadcast to the public in the United States on GE's W2XAD: the pictures were picked up on 1.5 square inches (9.7 square centimeters) screens in the homes of four GE executives. The sound was broadcast on GE's WGY (AM).

Experimental television station W2XAD evolved into the station WRGB, which, along with WGY and WGFM (now WRVE), was owned and operated by General Electric until 1983. In 1965, the company expanded into cable with the launch of a franchise, which was awarded to a non-exclusive franchise in Schenectady through subsidiary General Electric Cablevision Corporation. On February 15, 1965, General Electric expanded its holdings in order to acquire more television stations to meet the maximum limit of the FCC, and more cable holdings through subsidiaries General Electric Broadcasting Company and General Electric Cablevision Corporation.

The company also owned television stations such as KOA-TV (now KCNC-TV) in Denver and WSIX-TV (later WNGE-TV, now WKRN) in Nashville, but like WRGB, General Electric sold off most of its broadcasting holdings, but held on to the Denver television station until in 1986, when General Electric bought out RCA and made it into an owned-and-operated station by NBC. It even stayed on until 1995 when it was transferred to a joint venture between CBS and Group W in a swap deal, alongside KUTV in Salt Lake City for longtime CBS O&O in Philadelphia, WCAU-TV.

Former General Electric-owned stations
Stations are arranged in alphabetical order by state and city of license.
 * (**) Indicates a station that was built and signed on by General Electric.

Power generation
Led by Sanford Alexander Moss, GE moved into the new field of aircraft turbo superchargers. This technology also led to the development of industrial gas turbine engines used for power production. GE introduced the first set of superchargers during World War I and continued to develop them during the interwar period. Superchargers became indispensable in the years immediately before World War II. GE supplied 300,000 turbo superchargers for use in fighter and bomber engines. This work led the U.S. Army Air Corps to select GE to develop the nation's first jet engine during the war. This experience, in turn, made GE a natural selection to develop the Whittle W.1 jet engine that was demonstrated in the United States in 1941. GE was ranked ninth among United States corporations in the value of wartime production contracts. However, their early work with Whittle's designs was later handed to Allison Engine Company. GE Aviation then emerged as one of the world's largest engine manufacturers, bypassing the British company Rolls-Royce plc.

Some consumers boycotted GE light bulbs, refrigerators, and other products during the 1980s and 1990s. The purpose of the boycott was to protest against GE's role in nuclear weapons production.

In 2002, GE acquired the wind power assets of Enron during its bankruptcy proceedings. Enron Wind was the only surviving U.S. manufacturer of large wind turbines at the time, and GE increased engineering and supplies for the Wind Division and doubled the annual sales to $1.2 billion in 2003. It acquired ScanWind in 2009.

In 2018, GE Power garnered press attention when a model 7HA gas turbine in Texas was shut down for two months due to the break of a turbine blade. This model uses similar blade technology to GE's newest and most efficient model, the 9HA. After the break, GE developed new protective coatings and heat treatment methods. Gas turbines represent a significant portion of GE Power's revenue, and also represent a significant portion of the power generation fleet of several utility companies in the United States. Chubu Electric of Japan and Électricité de France also had units that were impacted. Initially, GE did not realize the turbine blade issue of the 9FB unit would impact the new HA units.

Computing
GE was one of the eight major computer companies of the 1960s along with IBM, Burroughs, NCR, Control Data Corporation, Honeywell, RCA, and UNIVAC. GE had a line of general purpose and special purpose computers, including the GE 200, GE 400, and GE 600 series general-purpose computers, the GE/PAC 4000 series real-time process control computers, and the DATANET-30 and Datanet 355 message switching computers (DATANET-30 and 355 were also used as front end processors for GE mainframe computers). A Datanet 500 computer was designed but never sold.

In 1956 Homer Oldfield had been promoted to General Manager of GE's Computer Department. He facilitated the invention and construction of the Bank of America ERMA system, the first computerized system designed to read magnetized numbers on checks. But he was fired from GE in 1958 by Ralph J. Cordiner for overstepping his bounds and successfully gaining the ERMA contract. Cordiner was strongly against GE entering the computer business because he did not see the potential in it. In 1962, GE started developing its GECOS (later renamed GCOS) operating system, originally for batch processing, but later extended to time-sharing and transaction processing. Versions of GCOS are still in use today. From 1964 to 1969, GE and Bell Laboratories (which soon dropped out) joined with MIT to develop the Multics operating system on the GE 645 mainframe computer. The project took longer than expected and was not a major commercial success, but it demonstrated concepts such as single-level storage, dynamic linking, hierarchical file system, and ring-oriented security. Active development of Multics continued until 1985.

GE got into computer manufacturing because, in the 1950s, they were the largest user of computers outside the United States federal government, aside from being the first business in the world to own a computer. Its major appliance manufacturing plant "Appliance Park" was the first non-governmental site to host one. However, in 1970, GE sold its computer division to Honeywell, exiting the computer manufacturing industry, though it retained its timesharing operations for some years afterward. GE was a major provider of computer time-sharing services through General Electric Information Services (GEIS, now GXS), offering online computing services that included GEnie.

In 2000, when United Technologies Corp. planned to buy Honeywell, GE made a counter-offer that was approved by Honeywell. On July 3, 2001, the European Union issued a statement that "prohibit the proposed acquisition by General Electric Co. of Honeywell Inc.". The reasons given were it "would create or strengthen dominant positions on several markets and that the remedies proposed by GE were insufficient to resolve the competition concerns resulting from the proposed acquisition of Honeywell".

On June 27, 2014, GE partnered with collaborative design company Quirky to announce its connected LED bulb called Link. The Link bulb is designed to communicate with smartphones and tablets using a mobile app called Wink.

Acquisitions and divestments
In December 1985, GE reacquired the RCA Corporation, primarily to gain ownership of the NBC television network for $6.28 billion; this merger surpassed the Capital Cities/ABC merger that happened earlier that year as the largest non-oil merger in world business history. The remainder of RCA was sold to various companies, including Bertelsmann which absorbed RCA Records and Thomson SA, which licensed the manufacture of RCA branded electronics, traced its roots to Thomson-Houston, one of the original components of GE. Also in 1986, Kidder, Peabody & Co., a U.S.-based securities firm, was sold to GE and following heavy losses was sold to PaineWebber in 1994.

In 1997, Genpact was founded as a unit of General Electric in Gurgaon. The company was founded as GE Capital International Services (GECIS). In the beginning, GECIS created processes for outsourcing back-office activities for GE Capital such as processing car loans and credit card transactions. It was an experimental concept at the time and the beginning of the business process outsourcing (BPO) industry. GE sold 60% stake in Genpact to General Atlantic and Oak Hill Capital Partners in 2005 and hived off Genpact into an independent business. GE is still a major client to Genpact today for services in customer service, finance, information technology, and analytics.

In 2001, GE acquired Spanish-language broadcaster Telemundo and incorporated it into NBC.

In 2002, Francisco Partners and Norwest Venture Partners acquired a division of GE called GE Information Systems (GEIS). The new company, named GXS, is based in Gaithersburg, Maryland. GXS is a provider of business-to-business e-commerce solutions. GE maintains a minority stake in GXS. Also in 2002, GE Wind Energy was formed when GE bought the wind turbine manufacturing assets of Enron Wind after the Enron scandals.

In 2004, GE bought 80% of Vivendi Universal Entertainment, the parent of Universal Pictures from Vivendi. Vivendi bought 20% of NBC, forming the company NBCUniversal. GE then owned 80% of NBCUniversal and Vivendi owned 20%. In 2004, GE completed the spin-off of most of its mortgage and life insurance assets into an independent company, Genworth Financial, based in Richmond, Virginia.

In May 2007, GE acquired Smiths Aerospace for $4.8 billion. Also in 2007, GE Oil & Gas acquired Vetco Gray for $1.9 billion, followed by the acquisition of Hydril Pressure & Control in 2008 for $1.1 billion.

GE Plastics was sold in 2008 to SABIC (Saudi Arabia Basic Industries Corporation). In May 2008, GE announced it was exploring options for divesting the bulk of its consumer and industrial business.

On December 3, 2009, it was announced that NBCUniversal would become a joint venture between GE and cable television operator Comcast. Comcast would hold a controlling interest in the company, while GE would retain a 49% stake and would buy out shares owned by Vivendi.

Vivendi would sell its 20% stake in NBCUniversal to GE for US$5.8 billion. Vivendi would sell 7.66% of NBCUniversal to GE for US$2 billion if the GE/Comcast deal was not completed by September 2010 and then sell the remaining 12.34% stake of NBCUniversal to GE for US$3.8 billion when the deal was completed or to the public via an IPO if the deal was not completed.

On March 1, 2010, GE announced plans to sell its 20.85% stake in Turkey-based Garanti Bank. In August 2010, GE Healthcare signed a strategic partnership to bring cardiovascular Computed Tomography (CT) technology from start-up Arineta Ltd. of Israel to the hospital market. In October 2010, GE acquired gas engines manufacturer Dresser Industries in a $3 billion deal and also bought a $1.6 billion portfolio of retail credit cards from Citigroup Inc. On October 14, 2010, GE announced the acquisition of data migration & SCADA simulation specialists Opal Software. In December 2010, for the second time that year (after the Dresser acquisition), GE bought the oil sector company Wellstream, an oil pipe maker, for 800 million pounds ($1.3 billion).

In March 2011, GE announced that it had completed the acquisition of privately held Lineage Power Holdings from The Gores Group. In April 2011, GE announced it had completed its purchase of John Wood plc's Well Support Division for $2.8 billion.

In 2011, GE Capital sold its $2 billion Mexican assets to Santander for $162 million and exited the business in Mexico. Santander additionally assumed the portfolio debts of GE Capital in the country. Following this, GE Capital focused on its core business and shed its non-core assets.

In June 2012, CEO and President of GE Jeff Immelt said that the company would invest ₹3 billion to accelerate its businesses in Karnataka. In October 2012, GE acquired $7 billion worth of bank deposits from MetLife Inc.

On March 19, 2013, Comcast bought GE's shares in NBCU for $16.7 billion, ending the company's longtime stake in television and film media.

In April 2013, GE acquired oilfield pump maker Lufkin Industries for $2.98 billion.

In April 2014, it was announced that GE was in talks to acquire the global power division of French engineering group Alstom for a figure of around $13 billion. A rival joint bid was submitted in June 2014 by Siemens and Mitsubishi Heavy Industries (MHI) with Siemens seeking to acquire Alstom's gas turbine business for €3.9 billion, and MHI proposing a joint venture in steam turbines, plus a €3.1 billion cash investment. In June 2014, a formal offer from GE worth $17 billion was agreed by the Alstom board. Part of the transaction involved the French government taking a 20% stake in Alstom to help secure France's energy and transport interests and French jobs. A rival offer from Siemens Mitsubishi Heavy Industries was rejected. The acquisition was expected to be completed in 2015. In October 2014, GE announced it was considering the sale of its Polish banking business Bank BPH.

Later in 2014, General Electric announced plans to open its global operations center in Cincinnati, Ohio. The Global Operations Center opened in October 2016 as home to GE's multifunctional shared services organization. It supports the company's finance/accounting, human resources, information technology, supply chain, legal and commercial operations, and is one of GE's four multifunctional shared services centers worldwide in Pudong, China; Budapest, Hungary; and Monterrey, Mexico.

In April 2015, GE announced its intention to sell off its property portfolio, worth $26.5 billion, to Wells Fargo and The Blackstone Group. It was announced in April 2015 that GE would sell most of its finance unit and return around $90 billion to shareholders as the firm looked to trim down on its holdings and rid itself of its image of a "hybrid" company, working in both banking and manufacturing. In August 2015, GE Capital agreed to sell its Healthcare Financial Services business to Capital One for US$9 billion. The transaction involved US$8.5 billion of loans made to a wide array of sectors, including senior housing, hospitals, medical offices, outpatient services, pharmaceuticals, and medical devices. Also in August 2015, GE Capital agreed to sell GE Capital Bank's on-line deposit platform to Goldman Sachs. Terms of the transaction were not disclosed, but the sale included US$8 billion of on-line deposits and another US$8 billion of brokered certificates of deposit. The sale was part of GE's strategic plan to exit the U.S. banking sector and to free itself from tightening banking regulations. GE also aimed to shed its status as a "systematically important financial institution".

In September 2015, GE Capital agreed to sell its transportation finance unit to Canada's Bank of Montreal. The unit sold had US$8.7 billion (CA$11.5 billion) of assets, 600 employees, and 15 offices in the U.S. and Canada. The exact terms of the sale were not disclosed, but the final price would be based on the value of the assets at closing, plus a premium according to the parties. In October 2015, activist investor Nelson Peltz's fund Trian bought a $2.5 billion stake in the company.

In January 2016, Haier acquired GE's appliance division for $5.4 billion. In October 2016, GE Renewable Energy agreed to pay €1.5 billion to Doughty Hanson & Co for LM Wind Power during 2017.

At the end of October 2016, it was announced that GE was under negotiations for a deal valued at about $30 billion to combine GE Oil & Gas with Baker Hughes. The transaction would create a publicly traded entity controlled by GE. It was announced that GE Oil & Gas would sell off its water treatment business, GE Water & Process Technologies, as part of its divestment agreement with Baker Hughes. The deal was cleared by the EU in May 2017, and by the United States Department of Justice in June 2017. The merger agreement was approved by shareholders at the end of June 2017. On July 3, 2017, the transaction was completed, and Baker Hughes became a GE company and was renamed Baker Hughes, a GE Company (BHGE). In November 2018, GE reduced its stake in Baker Hughes to 50.4%. On October 18, 2019, GE reduced its stake to 36.8% and the company was renamed back to Baker Hughes.

In May 2017, GE had signed $15 billion of business deals with Saudi Arabia. Saudi Arabia is one of GE's largest customers. In September 2017, GE announced the sale of its Industrial Solutions Business to ABB. The deal closed on June 30, 2018.

Fraud allegations and notice of possible SEC civil action
On August 15, 2019, Harry Markopolos, a financial fraud investigator known for his discovery of a Ponzi Scheme run by Bernard Madoff, accused General Electric of being a "bigger fraud than Enron," alleging $38 billion in accounting fraud. GE denied wrongdoing.

On October 6, 2020, General Electric reported it received a Wells notice from the Securities and Exchange Commission stating the SEC may take civil action for possible violations of securities laws.

Insufficient reserves for long-term care policies
It is alleged that GE is "hiding" (i.e. under-reserved) $29 billion in losses related to its long-term care business.

According to an August 2019 Fitch Ratings report, there are concerns that GE has not set aside enough money to cover its long-term care liabilities.

In 2018, a lawsuit (the Bezio case) was filed in New York state court on behalf of participants in GE's 401(k) plan and shareowners alleging violations of Section 11 of the Securities Act of 1933 based on alleged misstatements and omissions related to insurance reserves and performance of GE's business segments.

The Kansas Insurance Department (KID) is requiring General Electric to make $14.5 billion of capital contributions for its insurance contracts during the 7-year period ending in 2024.

GE reported the total liability related to its insurance contracts increased significantly from 2016 to 2019:
 * December 31, 2016 $26.1 billion
 * December 31, 2017 $38.6 billion
 * December 31, 2018 $35.6 billion
 * December 31, 2019 $39.6 billion

In 2018, GE announced that the issuance of the new standard by the Financial Accounting Standards Board (FASB) regarding Financial Services – Insurance (Topic 944) would materially affect its financial statements. Mr. Markopolos estimated there would be a $US 10.5 billion charge when the new accounting standard is adopted in the first quarter of 2021.

Anticipated $8 billion loss upon disposition of Baker Hughes
In 2017, GE acquired a 62.5% interest in Baker Hughes (BHGE) when it combined its oil & gas business with Baker Hughes Incorporated. In 2018, GE reduced its interest to 50.4%, resulting in the realization of a $2.1 billion loss. GE is planning to divest its remaining interest and has warned that the divestment will result in an additional loss of $8.4 billion (assuming a BHGE share price of $23.57 per share). In response to the fraud allegations, GE noted the amount of the loss would be $7.4 billion if the divestment occurred on July 26, 2019. Mr. Markopolos noted that BHGE is an asset available for sale and therefore mark-to-market accounting is required.

Markopolos noted GE's current ratio was only 0.67. He expressed concerns that GE may file for bankruptcy if there is a recession.

Final years and three-way split (2018–2024)
In 2018, the GE Pension Plan reported losses of US$3.3 billion on plan assets.

In 2018, General Electric changed the discount rate used to calculate the actuarial liabilities of its pension plans. The rate was increased from 3.64% to 4.34%. Consequently, the reported liability for the underfunded pension plans decreased by $7 billion year-over-year, from $34.2 billion in 2017 to $27.2 billion in 2018.

In October 2018, General Electric announced it would "freeze pensions" for about 20,000 salaried U.S. employees. The employees will be moved to a defined contribution retirement plan in 2021.

On March 30, 2020, General Electric factory workers protested to convert jet engine factories to make ventilators during the COVID-19 crisis.

In June 2020, GE made an agreement to sell its Lighting business to Savant Systems, Inc. Financial details of the transaction were not disclosed.

In November 2020, General Electric warned it would be cutting jobs waiting for a recovery due to the COVID-19 pandemic.

On November 9, 2021, the company announced it would divide itself into three public companies. On July 18, 2022, GE unveiled the brand names of the companies it had devised through its planned separation: GE Aerospace, GE HealthCare, and GE Vernova. The new companies are respectively focused on aerospace, healthcare, and energy (renewable energy, power, and digital). The first spin-off of GE HealthCare was finalized on January 4, 2023; GE continues to hold 10.24% of shares and intends to sell the remaining over time. This was followed by the spin-off of GE's portfolio of energy businesses, which became GE Vernova on April 2, 2024. Following these transactions, GE became an aviation-focused company; GE Aerospace is the legal successor of the original GE. The company's legal name is still General Electric Company.

Dividends
General Electric was a longtime "dividend aristocrat" (a company with a long history of maintaining dividend payments to shareholders). Until 2017, the company had never cut dividends for 119 years before a 50% dividend reduction from 24 cents per share to 12 cents per share. In 2018, GE further reduced its quarterly dividend from 12 cents to 1 cent per share.

Stock
As a publicly traded company on the New York Stock Exchange, GE stock was one of the 30 components of the Dow Jones Industrial Average from 1907 to 2018, the longest continuous presence of any company on the index, and during this time the only company which was part of the original Dow Jones Industrial Index created in 1896. In August 2000, the company had a market capitalization of $601 billion, and was the most valuable company in the world. On June 26, 2018, the stock was removed from the index and replaced with Walgreens Boots Alliance. In the years leading to its removal, GE was the worst performing stock in the Dow, falling more than 55 percent year on year and more than 25 percent year to date. The company continued to lose value after being removed from the index.

General Electric Co. announced on July 30, 2021 (the completion of) a reverse stock split of GE common stock at a ratio of 1-for-8 and trading on a split-adjusted basis with a new ISIN number (US3696043013) starting on August 2, 2021.

Corporate affairs

In 1959, General Electric was accused of promoting the largest illegal cartel in the United States since the adoption of the Sherman Antitrust Act of 1890 in order to maintain artificially high prices. In total, 29 companies and 45 executives would be convicted. Subsequent parliamentary inquiries revealed that "white-collar crime" was by far the most costly form of crime for the United States' finances.

GE is a multinational conglomerate headquartered in Boston, Massachusetts. However its main offices are located at 30 Rockefeller Plaza at Rockefeller Center in New York City, known now as the Comcast Building. It was formerly known as the GE Building for the prominent GE logo on the roof; NBC's headquarters and main studios are also located in the building. Through its RCA subsidiary, it has been associated with the center since its construction in the 1930s. GE moved its corporate headquarters from the GE Building on Lexington Avenue to Fairfield, Connecticut in 1974. In 2016, GE announced a move to the South Boston Waterfront neighborhood of Boston, Massachusetts, partly as a result of an incentive package provide by state and city governments. The first group of workers arrived in the summer of 2016, and the full move will be completed by 2018. Due to poor financial performance and corporate downsizing, GE sold the land it planned to build its new headquarters building on, instead choosing to occupy neighboring leased buildings.

GE's tax return is the largest return filed in the United States; the 2005 return was approximately 24,000 pages when printed out, and 237 megabytes when submitted electronically. As of 2011, the company spent more on U.S. lobbying than any other company.

In 2005, GE launched its "Ecomagination" initiative in an attempt to position itself as a "green" company. GE is one of the biggest players in the wind power industry and is developing environment-friendly products such as hybrid locomotives, desalination and water reuse solutions, and photovoltaic cells. The company "plans to build the largest solar-panel-making factory in the U.S." and has set goals for its subsidiaries to lower their greenhouse gas emissions.

On May 21, 2007, GE announced it would sell its GE Plastics division to petrochemicals manufacturer SABIC for net proceeds of $11.6 billion. The transaction took place on August 31, 2007, and the company name changed to SABIC Innovative Plastics, with Brian Gladden as CEO.

In July 2010, GE agreed to pay $23.4 million to settle an SEC complaint without admitting or denying the allegations that two of its subsidiaries bribed Iraqi government officials to win contracts under the U.N. oil-for-food program between 2002 and 2003.

In February 2017, GE announced that the company intends to close the gender gap by promising to hire and place 20,000 women in technical roles by 2020. The company is also seeking to have a 50:50 male-to-female gender representation in all entry-level technical programs.

In October 2017, GE announced they would be closing research and development centers in Shanghai, Munich and Rio de Janeiro. The company spent $5 billion on R&D in the last year.

On February 25, 2019, GE sold its diesel locomotive business to Wabtec.

CEO
, John L. Flannery was replaced by H. Lawrence "Larry" Culp Jr. as chairman and CEO, in a unanimous vote of the GE Board of Directors.
 * Charles A. Coffin (1913–1922)
 * Owen D. Young (1922–1939, 1942–1945)
 * Philip D. Reed (1940–1942, 1945–1958)
 * Ralph J. Cordiner (1958–1963)
 * Gerald L. Phillippe (1963–1972)
 * Fred J. Borch (1967–1972)
 * Reginald H. Jones (1972–1981)
 * Jack Welch (1981–2001)
 * Jeff Immelt (2001–2017)
 * John L. Flannery (2017–2018)
 * H. Lawrence Culp Jr. (2018–2024)

Corporate recognition and rankings
In 2011, Fortune ranked GE the sixth-largest firm in the U.S., and the 14th-most profitable. Other rankings for 2011–2012 include the following:
 * # 18 company for leaders (Fortune)
 * # 82 green company (Newsweek)
 * # 91 most admired company (Fortune)
 * # 19 most innovative company (Fast Company).

In 2012, GE's brand was valued at $28.8 billion. CEO Jeff Immelt had a set of changes in the presentation of the brand commissioned in 2004, after he took the reins as chairman, to unify the diversified businesses of GE.

Tom Geismar later stated that looking back at the logos of the 1910s, 1920s, and 1930s, one can clearly judge that they are old-fashioned. Chermayeff & Geismar, along with colleagues Bill Brown and Ivan Chermaev, created the modern 1980 logo. They, in turn, argued that even now the old logos look out of date, earlier they were good. The changes included a new corporate color palette, small modifications to the GE logo, a new customized font (GE Inspira) and a new slogan, "Imagination at work", composed by David Lucas, to replace the slogan "We Bring Good Things to Life" used since 1979. The standard requires many headlines to be lowercased and adds visual "white space" to documents and advertising. The changes were designed by Wolff Olins and are used on GE's marketing, literature, and website. In 2014, a second typeface family was introduced: GE Sans and Serif by Bold Monday, created under art direction by Wolff Olins.

, GE had appeared on the Fortune 500 list for 22 years and held the 11th rank. GE was removed from the Dow Jones Industrial Average on June 28, 2018, after the value had dropped below 1% of the index's weight.

Businesses
GE's primary business divisions are:
 * GE Additive
 * GE Aerospace
 * GE Capital
 * GE Digital
 * GE Healthcare
 * GE Power
 * GE Renewable Energy
 * GE Research

Through these businesses, GE participates in markets that include the generation, transmission and distribution of electricity (e.g. nuclear, gas and solar), industrial automation, medical imaging equipment, motors, aircraft jet engines, and aviation services. Through GE Commercial Finance, GE Consumer Finance, GE Equipment Services, and GE Insurance, it offers a range of financial services. It has a presence in over 100 countries.

General Imaging manufacturers GE digital cameras.

Even though the first wave of conglomerates (such as ITT Corporation, Ling-Temco-Vought, Tenneco, etc.) fell by the wayside by the mid-1980s, in the late 1990s, another wave (consisting of Westinghouse, Tyco, and others) tried and failed to emulate GE's success.

GE is planning to set up a silicon carbide chip packaging R&D center in coalition with SUNY Polytechnic Institute in Utica, New York. The project will create 470 jobs with the potential to grow to 820 jobs within 10 years.

On September 14, 2015, GE announced the creation of a new unit: GE Digital, which will bring together its software and IT capabilities. The new business unit will be headed by Bill Ruh, who joined GE in 2011 from Cisco Systems and has since worked on GE's software efforts.

Morgan Stanley sold a stake in GE HealthCare Technologies for $1.1 billion as part of a deal to swap General Electric Co. debt for GE HealthCare stock.

Former divisions
GE Industrial was a division providing appliances, lighting, and industrial products; factory automation systems; plastics, silicones, and quartz products; security and sensors technology; and equipment financing, management, and operating services. As of 2007, it had 70,000 employees, generating $17.7 billion in revenue. After some major realignments in late 2007, GE Industrial was organized in two main sub businesses:
 * GE Consumer & Industrial
 * Appliances
 * Electrical Distribution
 * Lighting
 * GE Enterprise Solutions
 * Digital Energy
 * GE Fanuc Intelligent Platforms
 * Security
 * Sensing & Inspection Technologies

The former GE Plastics division was sold in August 2007 and is now SABIC Innovative Plastics.

On May 4, 2008, it was announced that GE would auction off its appliances business for an expected sale of $5–8 billion. However, this plan fell through as a result of the recession.

The former GE Appliances and Lighting segment was dissolved in 2014 when GE's appliance division was attempted to be sold to Electrolux for $5.4 billion, but eventually sold it to Haier in June 2016 due to antitrust filing against Electrolux. GE Lighting (consumer lighting) and the newly created Current, powered by GE, which deals in commercial LED, solar, EV, and energy storage, became stand-alone businesses within the company, until the sale of the latter to American Industrial Partners in April 2019.

The former GE Transportation division merged with Wabtec on February 25, 2019, leaving GE with a 24.9% holding in Wabtec.

On July 1, 2020, GE Lighting was acquired by Savant Systems and remains headquartered at Nela Park in East Cleveland, Ohio.

Carbon footprint
General Electric Company reported Total CO2e emissions (direct + indirect) for the twelve months ending 31 December 2020 at 2,080 Kt (-310 /-13% y-o-y). There has been a consistent declining trend in reported emissions since 2016.

Pollution
Some of GE's activities have given rise to large-scale air and water pollution. Based on data from 2000, Researchers at the Political Economy Research Institute listed the corporation as the fourth-largest corporate producer of air pollution in the United States (behind only E. I. Du Pont de Nemours & Co., United States Steel Corp., and ConocoPhillips), with more than 4.4 million pounds per year (2,000 tons) of toxic chemicals released into the air. GE has also been implicated in the creation of toxic waste. According to United States Environmental Protection Agency (EPA) documents, only the United States Government, Honeywell, and Chevron Corporation are responsible for producing more Superfund toxic waste sites.

In 1983, New York State Attorney General Robert Abrams filed suit in the United States District Court for the Northern District of New York to compel GE to pay for the clean-up of what was claimed to be more than 100,000 tons of chemicals dumped from their plant in Waterford, New York, which polluted nearby groundwater and the Hudson River. In 1999, the company agreed to pay a $250 million settlement in connection with claims it polluted the Housatonic River (at Pittsfield, Massachusetts) and other sites with polychlorinated biphenyls (PCBs) and other hazardous substances.

In 2003, acting on concerns that the plan proposed by GE did not "provide for adequate protection of public health and the environment," EPA issued an administrative order for the company to "address cleanup at the GE site" in Rome, Georgia, also contaminated with PCBs.

The nuclear reactors involved in the 2011 crisis at Fukushima I in Japan were GE designs, and the architectural designs were done by Ebasco, formerly owned by GE. Concerns over the design and safety of these reactors were raised as early as 1972, but tsunami danger was not discussed at that time. , the same model nuclear reactors designed by GE are operating in the US; however, as of May 31, 2019, the controversial Pilgrim Nuclear Generating Station, in Plymouth, Massachusetts, has been shut down and is in the process of decommission.

Pollution of the Hudson River
GE heavily contaminated the Hudson River with PCBs between 1947 and 1977. This pollution caused a range of harmful effects to wildlife and people who eat fish from the river. In 1983 EPA declared a 200-mile (320 km) stretch of the river, from Hudson Falls to New York City, to be a Superfund site requiring cleanup. This Superfund site is considered to be one of the largest in the nation. In addition to receiving extensive fines, GE is continuing its sediment removal operations, pursuant to the Superfund orders, in the 21st century.

Pollution of the Housatonic River
From c. 1932 until 1977, GE polluted the Housatonic River with PCB discharges from its plant at Pittsfield, Massachusetts. EPA designated the Pittsfield plant and several miles of the Housatonic to be a Superfund site in 1997, and ordered GE to remediate the site. Aroclor 1254 and Aroclor 1260, products manufactured by Monsanto, were the principal contaminants that were discharged into the river. The highest concentrations of PCBs in the Housatonic River are found in Woods Pond in Lenox, Massachusetts, just south of Pittsfield, where they have been measured up to 110 mg/kg in the sediment. About 50% of all the PCBs currently in the river are estimated to be retained in the sediment behind Woods Pond dam. This is estimated to be about 11,000 lb of PCBs. Formerly filled oxbows are also polluted. Waterfowl and fish who live in and around the river contain significant levels of PCBs and can present health risks if consumed. In 2020 GE completed remediation and restoration of its 10 manufacturing plant areas within the city of Pittsfield. plans for cleanup of the river south of the city are not finalized.

Environmental initiatives
The environmental work and research of GE can be seen as early as 1968 with the experimental Delta electric car built by the GE Research and Development Center led by Bruce Laumeister. The electric car led to the production shortly after of the cutting-edge technology of the first commercially produced all-electric Elec-Trak garden tractor, which was manufactured from around 1969 until 1975.

On June 6, 2011, GE announced that it had licensed solar thermal technology from California-based eSolar for use in power plants that use both solar and natural gas.

On May 26, 2011, GE unveiled its EV Solar Carport, a carport that incorporates solar panels on its roof, with electric vehicle charging stations under its cover.

In May 2005, GE announced the launch of a program called "Ecomagination", intended, in the words of CEO Jeff Immelt, "to develop tomorrow's solutions such as solar energy, hybrid locomotives, fuel cells, lower-emission aircraft engines, lighter and stronger durable materials, efficient lighting, and water purification technology". The announcement prompted an op-ed piece in The New York Times to observe that, "while General Electric's increased emphasis on clean technology will probably result in improved products and benefit its bottom line, Mr. Immelt's credibility as a spokesman on national environmental policy is fatally flawed because of his company's intransigence in cleaning up its own toxic legacy."

GE has said that it will invest $1.4 billion in clean technology research and development in 2008 as part of its Ecomagination initiative. As of October 2008, the scheme had resulted in 70 green products being brought to market, ranging from halogen lamps to biogas engines. In 2007, GE raised the annual revenue target for its Ecomagination initiative from $20 billion in 2010 to $25 billion following positive market response to its new product lines. In 2010, GE continued to raise its investment by adding $10 billion into Ecomagination over the next five years.

GE Energy's renewable energy business has expanded greatly to keep up with growing U.S. and global demand for clean energy. Since entering the renewable energy industry in 2002, GE has invested more than $850 million in renewable energy commercialization. In August 2008, it acquired Kelman Ltd, a Northern Ireland-based company specializing in advanced monitoring and diagnostics technologies for transformers used in renewable energy generation and announced an expansion of its business in Northern Ireland in May 2010. In 2009, GE's renewable energy initiatives, which include solar power, wind power and GE Jenbacher gas engines using renewable and non-renewable methane-based gases, employ more than 4,900 people globally and have created more than 10,000 supporting jobs.

GE Energy and Orion New Zealand (Orion) have announced the implementation of the first phase of a GE network management system to help improve power reliability for customers. GE's ENMAC Distribution Management System is the foundation of Orion's initiative. The system of smart grid technologies will significantly improve the network company's ability to manage big network emergencies and help it restore power faster when outages occur.

In June 2018, GE Volunteers, an internal group of GE employees, along with the Malaysian Nature Society, transplanted more than 270 plants from the Taman Tugu forest reserve so that they may be replanted in a forest trail that is under construction.

Educational initiatives
GE Healthcare is collaborating with the Wayne State University School of Medicine and the Medical University of South Carolina to offer an integrated radiology curriculum during their respective MD Programs led by investigators of the Advanced Diagnostic Ultrasound in Microgravity study. GE has donated over one million dollars of Logiq E Ultrasound equipment to these two institutions.

Marketing initiatives
Between September 2011 and April 2013, GE ran a content marketing campaign dedicated to telling the stories of "innovators—people who are reshaping the world through act or invention." The initiative included 30 3-minute films from leading documentary film directors (Albert Maysles, Jessica Yu, Leslie Iwerks, Steve James, Alex Gibney, Lixin Fan, Gary Hustwit and others), and a user-generated competition that received over 600 submissions, out of which 20 finalists were chosen.

Short Films, Big Ideas was launched at the 2011 Toronto International Film Festival in partnership with cinelan. Stories included breakthroughs in Slingshot (water vapor distillation system), cancer research, energy production, pain management, and food access. Each of the 30 films received world premiere screenings at a major international film festival, including the Sundance Film Festival and the Tribeca Film Festival. The winning amateur director film, The Cyborg Foundation, was awarded a US$100000 prize at the 2013 Sundance Film Festival. According to GE, the campaign garnered more than 1.5 billion total media impressions, 14 million online views, and was seen in 156 countries.

In January 2017, GE signed an estimated $7 million deal with the Boston Celtics to have its corporate logo put on the NBA team's jersey.

Charity
On March 3, 2022, GE published an international memo pledging to donate $4.5 million to Ukraine amid Russian invasion. According to the memo, $4 million will be used for medical equipment, $400,000 for emergency cash for refugees, and $100,000 will go to Airlink, an NGO that helps communities in crisis.

Political affiliation
In the 1950s, GE sponsored Ronald Reagan's TV career and launched him on the lecture circuit. GE has also designed social programs, supported civil rights organizations, and funded minority education programs.

Notable appearances in media
In the early 1950s, Kurt Vonnegut was a writer for GE. A number of his novels and stories (notably Cat's Cradle and Player Piano) refer to the fictional city of Ilium, which appears to be loosely based on Schenectady, New York. The Ilium Works is the setting for the short story "Deer in the Works".

In 1981, GE won a Clio award for its 30 Soft White Light Bulbs commercial, We Bring Good Things to Life. The slogan "We Bring Good Things to Life" was created by Phil Dusenberry at the ad agency BBDO.

GE was the primary focus of a 1991 short subject Academy Award-winning documentary, Deadly Deception: General Electric, Nuclear Weapons, and Our Environment, that juxtaposed GE's "We Bring Good Things To Life" commercials with the true stories of workers and neighbors whose lives have been affected by the company's activities involving nuclear weapons.

GE was frequently mentioned and parodied in the NBC comedy sitcom 30 Rock from 2006 to 2013. Former General Electric CEO Jack Welch even cameoed as himself, appearing in the season four episode "Future Husband". The episode is a satirical reference to the real-world acquisition of NBC Universal from General Electric by Comcast in November 2009.

In 2013, GE received a National Jefferson Award for Outstanding Service by a Major Corporation.

Branding
The General Electric logo has a blue circle with a white outline. It has four white lines which "suggest the blades of a midcentury tabletop fan." In the center of the circle is the letters "GE." Its design has changed little throughout the company's history. The logo is officially known as the Monogram but is also known by some as "the meatball."

title: General Electric