WI: Algebra, Zero, Infinity, Invented ~2000 BCE

Algebra was invented (in my opinion) strangely late. Only in the last five hundred years has it really existed, but isn't it a relatively simple concept? A number being represented by another symbol to show it has a value to be determined.

This is difficult in Greco-Roman numerals, or any numeral system where letters and numbers are the same, but Babylonians did have separate symbols for numbers.

Of course this is unlikely and difficult but what I am asking is not how to get there but the consequences of such. Assuming that the concepts of zero and infinity are also known, what could have happened had algebra been developed in the Bronze Age?
 
The ancient greeks were amazing as it is. This would seriously lessen the handicap they had so who knows how much more might they have discovered - and than used it for some idocy like the steam puppets.
 
The ancient greeks were amazing as it is. This would seriously lessen the handicap they had so who knows how much more might they have discovered - and than used it for some idocy like the steam puppets.
Would algebra, zero, infinity, necessarily lead to steam power any earlier?


Oh! What it may lead to is far earlier calculus though, which might have some very interesting consequences that I really couldn't talk about myself.
 
I know many concepts predate the invention of modern algebra, that's what gave me the idea for the thread, and Al-Khwarizmi's isn't considered modern algebra in the sense we think of it afaik.

When mathematicians talk about "modern algebra", they're usually referring to abstract algebra with an axiomatic approach (i.e. first specifying the laws of algebra and then using them to solve probems). The algebra used by Al-Khwarizmi etc. is just fine for solving equations and most high-school-level problems. Certainly there have been important developments in algebra in the past 500 years but the idea of "A numberbeing represented by another symbol to show it has a value to be determined." goes back at least to the ancient Greeks.
 
Would algebra, zero, infinity, necessarily lead to steam power any earlier?


Oh! What it may lead to is far earlier calculus though, which might have some very interesting consequences that I really couldn't talk about myself.

No, they had steam power. But they used it to power an automatic puppet show. So whatever they invented thanks to getting rid of their handicap they would probably use it for something stupid.
 
That wasn't a puppet show or anything, just a little spinning piece of metal, and also wasn't ancient, but in the Common Era...

2000 BCE is waaaaay before that, and algebra doesn't even necessarily imply earlier steam.

From the vicky article: "...passes out through the bent tubes towards the lid, and causes the ball to revolve, as in the case of the dancing figures." Also could look up the passage in Greens Alexander to Actium where I read it abouth a month ago, but im too tired.

Also please read my post before commenting on them. I brought up the steam engine as an example how greeks could invent incredible things for their time and use it for something idiotic. My actual statement was that they would likely do something similarly stupid with whatever great discovery they made thanks to better maths. Not that I linked the two any more closely than this.

Also as it was proposed that it could be Babylon that makes this discovery this knowledge would become available to the greeks latest in the hellenistic period. They made incredible discoveries on this field OTL with serious handicaps like no Zero etc. With getting rid of some of those I expect them to do even better.
 
From the vicky article: "...passes out through the bent tubes towards the lid, and causes the ball to revolve, as in the case of the dancing figures." Also could look up the passage in Greens Alexander to Actium where I read it abouth a month ago, but im too tired.

Also please read my post before commenting on them. I brought up the steam engine as an example how greeks could invent incredible things for their time and use it for something idiotic. My actual statement was that they would likely do something similarly stupid with whatever great discovery they made thanks to better maths. Not that I linked the two any more closely than this.

Also as it was proposed that it could be Babylon that makes this discovery this knowledge would become available to the greeks latest in the hellenistic period. They made incredible discoveries on this field OTL with serious handicaps like no Zero etc. With getting rid of some of those I expect them to do even better.
Ah I misread your initial posts then, I didn't mean any disrespect.
 
That is utter nonsense. You can't do advanced math without zero and infinity, and algebra is a fundamental unifier of mathematics.

You can do advanced math without infinity provided you're willing to wrap your head around infinite sequences of finite numbers. Really much of 18th and 19th century analysis was mathematicians trying to show that you could do calculus without infinity. Infinity was seen as a philosophically suspect concept, and was avoided by Western mathematicians, up until the time of Cantor in the 1890s.
 
Oh! What it may lead to is far earlier calculus though, which might have some very interesting consequences that I really couldn't talk about myself.

Maybe...

I think that the main issue is that calculus IOTL wasn't invented in vacuum but rather by Newton and Liebnitz needing a mathematical terminology to describe and relate their theories of physics. Those theories in turn are things that, whilst impressive scientific achievements, occurred in a social context vastly different from that of ancient Greece. For one thing, Christianity meant that religious authority was largely taken out of local control, meaning that it would be harder for anyone to get Socrates'd (though of course still not impossible) as long as they kept quiet and freethinkers could build on one another more than earlier. Gallileo, for example, was able despite his persecution to formulate half of Newton's First Law as a lasting idea later expanded on by the Englishman. I just don't think that the Greek world is interconnected enough to allow ideas to spread in the same way at least until Alexander's time, and even then land infrastructure and especially naval technology were both not as conducive to rapid transfer of ideas as in the 17th century. Thus, calculus or concepts associated with calculus might well have emerged earlier--I could picture either Herakleitos or the Pythagoreans developing differential calculus much earlier--but I think this knowledge would either be lost in the burning of Alexandria's library or beforehand or simply be considered a novelty until the Scientific Revolution. Integral calculus might see some of the same patterns happen--Aristotle after all did create many ideas now associated with integral calculus to disprove Zeno's Paradoxes--but would likewise be considered a curiosity. Certainly, I'd think, nobody would realize the fundamental theorems much earlier than IOTL.

Now, it's certainly possible that someone does--I'd say that a Greek philosopher in the Roman period could demonstrate the utility of calculus for Roman engineering projects--but I'd say that this is rather unlikely. Certainly not ASB, but it would require all the right factors to fall into place.
 
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