Unless I missunderstood you, you are planning to bulb machinery with a GE. It is more likely to get the oracle than this. (I can fail getting the GE three times in a row every day... and I am up!

)
edit: beside you need the GE before the GS... I really think all this is a bad idea. Imo it would need to produce a slow GE (at +3 gpp without polution) as first great people to have any chance, but then it would be way too slow.
ie I think we should oracle MC only if we drop the astro plan.
Okay, it's my fault for not being clear here.
My point about running an Engineer Specialist is that we would do so alongside Scientist Specialists and, ideally, we will NEVER generate a Great Engineer at all, or if we do, it is our 4th Great Person.
Let's look at GPP production without Caste System, because that's the case that I am talking about running an Engineer Specialist for. If we use Caste Sytem, then we'll just run purely Scientist Specialists.
So, if we don't have Pacifism, then, when running 2 Scientists, it takes us:
150 / 6 = 25 turns for our first Great Person
300 / 6 = 50 turns for our second Great Person
450 / 6 = 75 turns for our third Great Person (probably too long, at least certainly not doable in "54 turns")
and too long for our fourth Great Person
If we do have Pacifism, then when running 2 Scientists, assuming that we did not use the Oracle to get Philosophy, it takes us:
150 / 6 = 25 turns for our first Great Person (because we don't have Pacifism yet)
300 / 12 = 25 turns for our second Great Person
450 / 12 = 38 turns for our third Great Person
600 / 12 = 50 turns for our fourth Great Person
750 / 12 = 63 turns for our fifth Great Person
But, what if we could run a 3rd Scientist? Well, we're using Slavery, so we can't. But we can instead run an Engineer or a Merchant Specialist (or 2 Merchant Specialists, or one of each, or possibly, with a lot of whipping, 1 Engineer and 2 Merchants).
Running a 3rd Specialist could speed up our Great People generation significantly when we are running Pacifism. for example:
450 / 18 = 25 turns for our third Great Person
600 / 18 = 34 turns for our fourth Great Person
750 / 18 = 42 turns for our fifth Great Person
Suddenly, the numbers look even better.
Now, LC is advocating spending 54 turns on Great Person generation, which gives us 2 Scientists. Those 2 Scientists will Lightbulb Astronomy, since that's the most efficient tech for our Great Scientists to Lightbulb (as per LC's earlier explanation in this thread about tech bonuses). It makes reasonable sense, too, in that you need about 1.8 to 1.9 Great Scientists to Lightbulb Astronomy, so they are relatively efficiently used.
In his scenario, we would still need to self-tech Optics.
With Pacifism, we get more Great People. We still want 2 Great Scientists for Astronomy.
We will invest a third Great Scientist in Pacifism.
At this point, we are "even" between the two approaches, as long as you are willing to believe that we would research Code of Laws in both cases, otherwise we are still behind by the cost of researching Code of Laws in the Pacifism case.
If we also were to use the Oracle on Metal Casting, we'd be behind by the cost of Machinery, too.
However, I'm suggesting that by using Pacifism (really, it's mdy's idea), we'd get more than those 3 Great People.
Let's say that the 4th Great Person that we get is a Great Scientist. Well, we'll just use him to Lightbulb Optics. The cost is roughly the same as Machinery.
If however, we happen to generate a Great Engineer, while hoping for a Great Scientist, we'll just Lightbulb Machinery instead.
Now, let's say that we will aim to get 5 Great People. 1 for Philosophy, 2 for Astronomy, and 1 for either Optics or Machinery. That leaves us 1 Great Person to figure out what we're going to do with.
We can play around with this 5th Great Person in multiple ways.
One way is to say that we'll get an Academy. An Academy isn't going to be all that great on this map, particularly pre-Bureaucracy, and we might not even want a post-Bureaucracy Academy, since once we learn Civil Service, we'll hopefully be done most or all of our teching.
So, let's say that we'll aim to Lightbulb with this 5th Great Person, but will use it on an Academy if its our 5th Great Scientist in a row. That's reasonably fair, right? I mean, it won't help us ALL that much as a 5th Great Scientist, but everyone loves an Academy, so it won't be the end of the world if we get an Academy.
If we fail to get a Great Engineer by our 4th Great Person, then we're at a point where we should just give up on trying to get a Great Engineer and should start self-teching Machinery.
However, we'd be okay with getting a 5th Great Scientist, but we'd probably be even happier getting a Great Merchant at this point, so that we can Lightbulb most of Civil Service.
Okay, so for one or more of our 2nd, 3rd, and 4th Great People, we can try to get either a Great Scientist or a Great Engineer. To avoid getting 2 Great Engineers, we can only have 1 City running an Engineer Specialist at a time, until said City generates a Great Person, at which point, if it did not get a Great Engineer, another City could add an Engineer Specialist (or the same City could keep trying for a Great Engineer, whichever approach is deemed to be more efficient at the time).
For our 3rd, 4th, and 5th Great Perople, we can try to get either a Great Scientist or a Great Merchant. Again, to avoid getting 2 Great Merchants, we can only ahve 1 City running 1 to 2 Merchant Specialists at a time, until said City generats a Great Person, at which point, if it did not get a Great Merchant, another City could add 1 or 2 Great Merchant Specialists (or the same City could keep trying for a Great Merchant).
So, essentially, we'll play the odds in that we will hope to get mostly Great Scientists, so that we will still be able to "keep trying" to get a different Great Person type for our later Great People, which allows us to run more than 2 Specailists at a time while using Slavery.
Ideally, we will get ONE of a Great Engineer as our 4th Great Person or a Great Merchant as our 5th Great Person, with the rest of the Great People being Great Scientists.
If that scenario doesn't work out, we're still pretty flexible.
The worst case scenario is that we get a Great Engineer and a Great Merchant as our, say, 2nd and 3rd Great People, which means that we can only run Scientist Specialists while trying to get our 4th and 5th Great People. If such a case occurs, we're going to be stuck switching into Caste System.
But, as long as you only try for a Great Engineer in one City at a time and only try for a Great Merchant in one City at a time (which may or may not be the same City), then just about any other case allows us to skip using Caste System altogether, while still generating 5 Great People.
The nicest part about trying for either a Great Scientist or a Great Merchant as our 5th Great Person is that we can maximally get the Great Person in:
750 / 24 = 32 turns for our fifth Great Person
The whole idea is about playing the odds (Russian roulette, if you were) of "pretending to try" to get a non-Great-Scientist while actually hoping that we get mostly or all Great Scientists.
Getting a different Great Person type means that we'll get a Great Person that we can still use for Lightbulbing, but it unfortunately means that we will have to stop running Specialists of the corresponding type (no more Engineer Specialists if we got a Great Engineer, for example).
By not trying for a Great Engineer for our 5th Great Person, we will be able to start manual research on Machinery, without worrying about getting a Great Engineer that we won't be able to use for Lightbulbing. At this point, it means that we likely got 4 Great Scientists, so Optics will be Lightbulbable and our 5th Great Person is mostly going to be used for Civil Service... either to Lightbulb most of it as a Great Merchant or to help research it faster as an Academy.
If we do get a Great Engineer by the time that we get our 4th Great Person, then we'll use him to Lightbulb Machinery and will manually research Optics instead of manually researching Machinery.
The last Great Person can once again be used for an Academy, if it is a Great Scientist, or for Lightbulbing most of Civil Service, if it is a Great Merchant.
In fact, if we want, we can skip going for the 5th Great Person altogether.
Getting those 4 Great Scientists with Pacifism will take just a bit longer than getting 2 Great Scientists without Pacifism. If we are willing to "play the odds," and I don't see why we wouldn't, then we can feasibly speed up one or more of these 4 Great People, to bring the timing much closer between the two scenarios.
If we plan on getting 4 Great People, then we might not run any Merchant Specialists at all, but we'd still be able to leverage a 3rd Specialist by way of an Engineer Specialist, while hoping that we won't get a Great Engineer or that if we do, we'll get him as our 4th Great Person.
If our strategy requires us to try for 3 Great People without Pacifism, then a Pacifism approach is lightyears ahead.
In summary:
If we Oracle Machinery and aim not to run Pacifism, we'll need to manually research:
- Metal Casting = 1053 Flasks
- maybe we'll skip Code of Laws altogether or maybe we'll have to research Polytheism instead of Meditation, but I'll just pretend that we'll skip Code of Laws
- Optics = 1404 Flasks
1053 + 1404 = 2457 Flasks
If we Oracle Metal Casting and aim to run Pacifism, we'll need to manually research:
- Code of Laws = 819 Flasks
- One of Optics or Machinery = 1404 Flasks or 1638 Flasks, but let's assume the worst case of Machinery
819 + 1638 = 2457 Flasks
Look at that! The amount of manual Flasks to research is identical!
Of course, the Pacifism scenario will allow us to pop-rush Courthouses, if we choose to do so.
We're not even talking about running Caste System, so there isn't a cost to switching out of Slavery. There also isn't a cost of running 5 Scientist Specialists at a time instead of other potentially-profitable squares.
However, we are talking about running the occasional 3rd Specialist--a Great Engineer, for the Pacifism case. We would not dare to do so for the Oracle Machinery case, since a Great Engineer would not help us to Lightbulb Astronomy.
While the numbers for generating 4 Great People in the Pacifism case might put us slightly behind if we were to only run 2 Scientists at a time, we can leverage the Great Engineer to speed things up and help this scenario to have a competitive pace with the 2-Great-Person approach.
Now, let's take LC's further comment about wanting to use additional Great People for Golden Ages.
Non-Pacifism scenario: we have used 2 Great People, so we, say, will want to generate Great People 3, 4, and 5.
Pacifism scenario: we have used 4 Great People, so we, say, will want to generate Great People 5, 6, and 7. However, I will also provide the numbers for the 8th Great Person, in case we want to use the Pacifism's approach of Lightbulbing or Academying the 5th Great Person and thus would use Great People 6, 7, and 8 for Golden Ages. Let's see how the numbers stack up.
2 Specialists case:
Non-Pacifism Scenario's Great People:
450 / 6 = 75 turns for our third Great Person
600 / 6 = 100 turns for our fourth Great Person
750 / 6 = 125 turns for our fifth Great Person
Pacifism Scenario's Great People:
750 / 12 = 63 turns for our fifth Great Person
900 / 12 = 75 turns for our sixth Great Person
1050 / 12 = 88 turns for our seventh Great Person
1200 / 12 = 100 turns for our eighth Great Person (in case we want to use our fifth Great Person for an Academy or for Lightbulbing)
3 Specialists case:
Non-Pacifism Scenario's Great People:
450 / 9 = 50 turns for our third Great Person
600 / 9 = 67 turns for our fourth Great Person
750 / 9 = 84 turns for our fifth Great Person
Pacifism Scenario's Great People:
750 / 18 = 42 turns for our fifth Great Person
900 / 18 = 50 turns for our sixth Great Person
1050 / 18 = 59 turns for our seventh Great Person
1200 / 18 = 67 turns for our eighth Great Person (in case we want to use our fifth Great Person for an Academy or for Lightbulbing)
4 Specialists case:
Non-Pacifism Scenario's Great People:
450 / 12 = 38 turns for our third Great Person
600 / 12 = 50 turns for our fourth Great Person
750 / 12 = 63 turns for our fifth Great Person
Pacifism Scenario's Great People:
750 / 24 = 32 turns for our fifth Great Person
900 / 24 = 38 turns for our sixth Great Person
1050 / 24 = 44 turns for our seventh Great Person
1200 / 24 = 50 turns for our eighth Great Person (in case we want to use our fifth Great Person for an Academy or for Lightbulbing)
5 Specialists case:
Non-Pacifism Scenario's Great People:
450 / 15 = 30 turns for our third Great Person
600 / 15 = 40 turns for our fourth Great Person
750 / 15 = 50 turns for our fifth Great Person
Pacifism Scenario's Great People:
750 / 30 = 25 turns for our fifth Great Person
900 / 30 = 30 turns for our sixth Great Person
1050 / 30 = 35 turns for our seventh Great Person
1200 / 30 = 40 turns for our eighth Great Person (in case we want to use our fifth Great Person for an Academy or for Lightbulbing)
So, the 4-Great-Person Pacifism Scenario comes ahead in terms of the total number of techs and the ability to get future Golden Ages. The arrival of the pre-Astronomy Great People isn't that far behind the 2-Great-Person approach and may be close to equal if we run a 3rd Specialist by way of an Engineer Specialist.
The Pacifism Scenario also has the option of giving us a 5th Great Person for either Lightbulbing or an Academy, but the 2-Great-Person approach would take too long to generate the 3rd Great Person to help out... so, when comparing them head-to-head, we look at using only 4 Great People, but the Pacifism approach gives us the flexibility of using that 5th Great Person to get ahead in terms of Lightbulbing (or in terms of having an Academy), while STILL being able to get the 6th, 7th, and 8th Great People for 2 Golden Ages faster than the non-Pacifism approach.
Now, mdy has proposed an aggressive, third alternative, which is to Oracle Machinery and Lightbulb Philosophy. The issue with that approach is that we almost certainly will want to run Caste System for a while, giving up on Slavery, since we cannot afford to run an Engineer Specialist.
I'm simply offering an alternative that allows us to stay in Slavery the whole time and compete pretty closely in time with the 2-Great-Scientist non-Pacifism approach. If we were to decide to switch into Caste System for a short period of time with my scenario, then we'd definitely kick the pants off of the non-Pacifism approach in terms of our Astronomy timing, although at the cost of not being able to use Slavery for a while and temporarily losing some production due to hiring Scientist Specialists instead of working squares with citizens. That's kind of why I suggested an approach that still allows us to maintain about the same amount of production by playing the odds of Great People generation--so that we wouldn't fall behind production-wise.