279. Quadrivial Pursuits: the Oxford Calculators

Posted on 4 June 2017

Bradwardine and other thinkers based at Oxford make breakthroughs in physics by applying mathematics to motion.

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Comments

Quadrupedant on 5 June 2017

Cube roots

Hi Peter,

I think there is a vocal typo at 17:50, you say 3^(1/3) to 2^(1/3) (3 to the third and 2 to the third, i.e. the cube roots) but you mean 3^3 to 2^3.

Peter Adamson on 5 June 2017

Cubes

Oh yes, you're right: in my script it is right but I misspoke when recording it (I like the idea of a "vocal typo").

Let me also heartily congratulate you on your James Brown icon and email address. Make it Funky (Parts 3 and 4)!

Erik Holkers on 29 April 2024

dusting of high school math ?

I listen to each podcast at least 3 times (I need that) but in this podcast I heard you say 3 to the 3rd to 2 to the 3rd (yes, I heard it 3 times).
So i think you were right all 3 times, it means 3 times 3 times 3 to 2 times 2 times 2. No vocal typo. No correction needed.
To the third doesn't mean to a power of one third (1/3), that would have been a cube root, like 27 tot the 1/3 equals 3 , going the other way round.
Or did you rerecord that ?

Anyway, I get the idea that it needed some big step to start applying algebra into physics for the first time, but what I don't get is that if they already did so in astronomy (for a long time) , why would it take so much to extend it to velocity ?

Peter Adamson on 29 April 2024

Correcting the record

Oh good! I'm glad it isn't wrong after all (I didn't re-record it).

That's a good question about why it took so long. I'm not really the right person to answer this, but for the sake of argument: pne factor may be that the branch of mathematics used in astronomy was "spherics" and not arithmetic. Also, astronomy allows for exact measurement with pre-modern resources (just observe the changing position of the planets), whereas measuring the speed of a projectile is really difficult - I mean, it's not like they had speed guns. Even when the Oxford Calculators started using mathematics to model sublunary motions the values they used are totally fictional, like, "say that Socrates is moving 2 units of space in 3 units of time," that kind of thing. Part of Galileo's achievement was to figure out clever ways to measure freefall by slowing it down, using inclined planes, which is far from obvious.

Andrew on 17 October 2024

Velocity Sophism

Wouldn't at one point Plato be as fast as Socrates, meaning that the sophistical sentence is true? I mean, if they both start at the same time, then Plato's velocity has to overtake Socrate's at some point, which means there has to be a point inbetween being slower than Socrates and faster than Socrates where Plato is the same speed as Socrates? Even if it is just for an instantaneous moment. Or do they mean something else by velocity than what we mean by it?

The section I am referring to starts roughly at 9:55 where the example for spatial motion is given for the sophism.

Peter Adamson on 19 October 2024

Velocity sophism

So this is the one about the sentence "Socrates and Plato will begin to move equally fast." As I say, when Plato catches up with Socrates then at that point their "speed" (meaning here, distance covered in a certain amount of time, not velocity) is the same. But I think their idea is that you can't say they "begin" to move at the same speed since it is only an instant where the time and distance are equal. If you "begin to do X" you must be doing X for an extended period of time.