Maybe someone like Pliny (not exactly him but someone similar) could discover four field crop rotation and then we've got massive increases in yields.
But four field crop rotation never caught on in the Mediterranean; the climate isn't suited for it.
Everyone assumes that an explosion of industry means that factories powered by coal (and thus the asthma and coal) are the only way to go, which is just false. Already in their heyday IOTL the Romans were making good use of water-power in some areas, but never really managed to properly combine that with their aqueduct civil engineering projects to make phenominal watermill plants. Windmills, too, could be more common-- besides water-pumping duties, IOTL later windmills also became power sources for sawmills, pulp and papermills, and many other early industrial businesses.
Well, there's Arles. And water mills were common enough to be mentioned in price edicts in the 4th century...
Banking, too, was needed to foster ambitious entrepeneurs who would be willing to front the money for all these endeavors. The Industrial Revolution was caused by and developed much more than just machines.
Basically if steel gets accidentally invented early, I would think technology would progress pretty quick.
Hrmm. How long did China have steel before its industrial revolution?
Some info on Roman banking, for the curious:
"Roman banking may have been largely monetized, but it also displays a distinct lack of sophistication in the use of money in comparison with Italy after the commercial revolution of the 13th century. In Medieval Italy it was possible to make payments by transfer between different banks, and both cheques and negotiable paper came into existence. Perhaps even more important was the bill of exchange, which which proved vital in the development of commercial exchange in Europe in the 13th century. "
So far, so good. But what about Rome?
"In the roman world, outside of Egypt, there are no traces of affiliation between banks in different places.... this means that, indefault of any clearing system, banks could not be used to transfer funds from one place to another. Perhaps even more important... there were no bills of exchange and no negotiable paper. Furthermore, cheques.... are unknown outside of Egypt."
Furthermore, "Even in Egypt cheques relied upon trust of the payee (there was no relevent legislation[1]) and there is no evidence that cheques could be endorsed so as to become negotiable. The vulnerability of banks, in which interest bearing deposits could be withdrawn on demand and partnerships were dissolved by the death or wish of one party, cannot have been conducive to the devleopment of complex procedures, or to the full use of such services as were offered."
"In the Roman world the possibility of moving funds without the physical transer of coin was confined to the elite, who could rely on friends with widespread interests, or to those who, like governors under the Republic, could make private use of the system for the transfer of tax revenues through publicani. Under the Principate there appears to be no evidence of private individuals taking advantage of the government's mechanism for the transfer of revenues or through the publicani."
The existence of the societas publicanorum
did not - to alarge extent - depend on the individuals involved; a
representative could act 'for the company;' ownership was fungible,
traded in the form of shares andd separated from the control of the
company."
"We also learn that the shares were traded. In his second speech
against Verres (1,55,143), Ccero implies the transferability of shares, when he quotes an exceptional restriction: Qui de L. Marcio M. Perperna censoribus redemerit... socium non admittito neve partem dato neve redimito, i.e. anyone who had been leasing under the censors L. Marcius and M. Perperna was not admitted to the current lease, neither as a partner, nor as a shareholder, nor should he be allowed to buy any shares later. His quote and the context of the case reveal that shares were often traded between participes after the contract had been assigned to a societas publicanorum.
What makes the partes look even more like modern shares - and is
additional evidence partes were not just loans with variable interest rate, as proposed by Duff45 - is the mention of variable "stock prices." In P. Vat 12,29 Cicero speaks of partes illo tempore carissimae, of 'shares that had a very high price at that time.' He implies that the value of the shares depends upon the success of the enterprise and was as such subject to fluctuations, just like today's stock market. In fact, the "stock-market jargon" in this and
similar quotes have led some scholars to believe that a "stock-market
life" existed in Rome [2].46'