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They do trade with India but as you say, the one that controls Syria is always on the top between the two of them...
Now why is that? For Far Eastern goods to get to the Mediterranean market, they would have to come over land a long way to get to Antioch for sale.
To get to Alexandria at this point, starting in western/southern Indian docks, they come by sea up the Red Sea, where they can be supplemented by a number of the valuable goods that are produced in southern Arabia, and thence by short overland portage or indeed by the revived Nile-Red Sea canal by barge to the queen city of the Mediterranean world, where they are offered in trade alongside Egyptian goods such as grain, and the craft produce of populous and technically developed Egypt as well.
Now I suppose to some extent I am dialectically answering my own question! While some exotic Eastern goods include Egyptian spices and Indian products, others include Chinese goods such as silks, and they are apparently not being traded by sea to India. A glance at the map shows that if they were, they'd have a long long voyage through chancy seas, past Southeast Asian and Indonesian ports before even a fraction of them could be offered to Ptolemaic traders. In fact in this era what Chinese goods move out of China tend to either be traded pretty locally, to other nations more or less in the Sinosphere on the Pacific, or else go west overland along the "Silk Road." Seen that way, Diodotian wealth is high because they get first crack at it, and are the last major craft/exotic Western goods emporium going east--the silver and other precious metals and jewels that pay for whatever the Chinese will sell only for that after buying a smattering of western goods filter through there as well and presumably some stick to their central Asian fingers. But Diodotia is not really in much of a position to buy all the Chinese exports for their own use; they must serve as middlemen for the Seleucids, who with Antioch can most directly port Chinese goods to the Med and Western goods along with basically money eastward over the shortest land route. I suppose what moves past Diodotian borders makes for the upper river courses of the streams feeding Mesopotamia; not an inconsiderable amount of them branch south to be ultimately sold for use there--Mesopotamian productivity, like Egyptian, could in itself produce substantial surpluses in the primary goods of grain and other foodstuffs, and also support an elaborately developed craft industry that also produces exportable goods. There of course was the capital Seleucia. The rest continue to make their way west, probably assisted by navigable streams (at least navigable on a scale supporting the low-weight, high value goods that filtered so far west overland through Central Asia) thence to Antioch. Also they would be joined by Arabian products brought overland through desert routes carefully monopolized by certain peoples (I believe a northern Arab branch, possibly Aramaic) whom I have mentioned before.
Thus for Alexandria to compete in those goods, the traders must either tap in to the Silk Route somewhere, or encourage an alternate coastwise trade that I suppose hardly exists at this point, at least not to connect Indian ports with Chinese ones all the way, even through intermediaries. I'd have to check on the status of Indochinese and Indonesian trade cultures at this point, but I suspect these did not really develop until many many centuries hence--and even if they did, it is not clear, across such a long convoluted sea route with so many potential middlemen and pirates lying along the way, that it would be strongly competitive in any way with the established northern and shorter overland route. I believe sea travel is generally orders of magnitude better, in terms of tons per mile per unit of human labor to move it, but that may depend very much on details. The Mediterranean is a relatively calm and enclosed body of water; I'm told there is no point in it, or anyway very few and easily avoided regions, where one cannot see some sign of land on a clear day, so navigation is also especially easy there. If winds do not serve, contrary ones and currents are rarely such that rowing will not get one where one needs to go. Not so, obviously, the Atlantic or the Indian ocean! The waters of Indonesia I am not so sure of but anyway I believe the winds there would be stronger and more apt to be surprisingly contrary than on the Med (or Red Sea)--at least there, some kind of landfall wouldn't be too hard to find, but one might well regret it with aggressive native peoples who might prove very hard or impossible to buy off and more than capable of overwhelming even a large and well-defended vessel. From there one is on the home stretch at least to South China, but in this era I think the southern tier of modern China is outside the Empire; one has to push on to the Yellow River ports. This home stretch, however long or short, is again basically open Pacific, a little bit sheltered but still a rough stormy sea.
So multipliers that are valid for the Mediterranean might not be nearly as good for this long haul from the mouth of the Red Sea to Chinese ports.
At this point anyway, even the great scholar Eratosthenes has scarcely even heard the rumor of China, if we can take
this map (a 19th century reproduction, attributed to knowledge circa 194 BCE, or six years after our current TL date) as representative of his work. Note how "Taprobane," nowadays known as Sri Lanka, is on the southeast corner and the coast north and east of it is that of eastern India--basically the mouth of the Ganges meeting up with someplace in Kazakstan around the tip of a mountain range representing the Himalayas is the far east of the world as far as he could guess. Not only is China absent, so is IndoChina and Indonesia as well!
Now ITTL he might know a bit more and there might be some fragment of Burma or even Cambodia, maybe with a chain of exotic spice islands lying off to their east, in his final edition of Geography and possible maps. He might even skew the salient southward in line with far-ranging Hellenic expeditions taking due note of the position of the Sun, though they'd have to stay long or visit frequently to confirm it oscillates back and forth evenly about the zenith and therefore lies in the Torrid Zone. This might encourage him to put in some speculative ágnosto édaphos in the northeast corner. And more aggressive Ptolemaics in Indian ports might have heard tell of far China earlier than Classical Mediterranean origin traders did OTL, giving him something to scrawl in there.
Since it is evident now how and why Antioch might not only equal Alexandria but does in fact surpass it, if not as a city in size than anyway in importance to the Mediterranean markets, I do wish someone had corrected my earlier mistaken assumption Alexandria must be the leading emporium of eastern goods! It is plain now that although by developing demand for Indian and perhaps east African goods it can grow to match the Seleucid port, it cannot supplant it, because Chinese goods will continue to be available only on the Silk Road. Even if Alexandria sends a large and ambitious expedition eastward past Taprobane to scout out the far reaches of east Asia, and this expedition manages to complete its mission by finding Chinese ports, get out of them without being detained, and send at least some remnant all the way back to familiar Indian ports again (a project liable to consume years and essentially swallow up every drachma invested with no immediate return if it can succeed at all) the Ptolemaics still have no likelihood of matching Silk Road deliveries for generations to come. The hazards along the way (offset by other opportunities such as Indonesian spices to be sure, if in fact these are cultivated in marketable form yet--their status is as up in the air as coffee would be), the sheer distance involved, and the possibility that the Chinese will simply refuse to trade with these supplicant sea barbarians if they manage to show up at all all tell against it. At any rate, it is more likely over later generations when and if intermediate markets form allowing sufficient Hellenic projection to guard their ships.
Thus I need to reevaluate my recent enthusiastic notion that Ptolemies can profit by taking Antioch. It was always plain this would be largely a negative accomplishment, at considerable cost, but I did believe that Alexandria would profit by concentrating all Eastern trade in its hands and that overall the volumes reaching Mediterranean markets would remain the same. In fact, Antioch and northern Syria and southeast, perhaps all of Eastern, Anatolia would all suffer, along with the northern desert Semitic trading kingdom, and the Egyptians would little profit nor find any gratitude as they would basically cut off a portion of the existing Eastern trade to no one's benefit. If the Seleucids could not simply punch back west to the Med, finding themselves welcome for doing so by all locals and thus presumably getting their help in the project, they can always shrug and simply pocket the entire Silk Road output themselves in Mesopotamia, losing little by being cut off from Mediterranean products since Mesopotamian and other Seleucid territories and products can probably suffice for their own needs and for trading with Diodotia.
Meanwhile the Diodotians, if not perfectly satisfied to go on trading with Seleucia, can branch north around the Caspian or across it, and create or tap into caravans going to the Black Sea, where the Bosphorian Kingdom or some other Black Sea power can ship the goods on west to Hellenic markets along that sea and through the straits to Greece itself. In suppressing the Seleucid port, they may deal their rival an annoying blow, but the Ptolemaics still will not capture the trade in Chinese goods that will merely be diverted somewhat northward. It cannot come south into Ptolemaic hands without either the Seleucids permitting it to for profit of their own, or the Egyptians leveling up to the point where they can conquer essentially all of Seleucia! It would not strictly be necessary to conquer Iran; perhaps that could be left to the Diodotians to deal with. But the project of attacking the Seleucid link to Mediterranean trade looks far less reasonably likely to bring the Ptolemies any gain they can realize worth the clearly high cost.
Neither power is bound to consider what is wisest or best for world development of course. Both might be too consumed with the chimera of exterminating the other major claimant to Alexander's legacy to consider the balance sheet carefully enough. i've got little enough sympathy for the Seleucids to be sure. But I can better see now what their basis is, and rather hope the Egyptians focus their ambitions elsewhere lest the Ptolemaic dynasty waste its assets on a losing game they might find themselves trapped in by prestige.
. Basically every one that wants to put his own top 5 list, would be more than welcomed.
