Consider the following.

The Greeks are credited with advancing geometry by large amounts, but consider if one could go back in time and teach Algebra to the ancient Greeks. How would that knowledge hurt their development of geometry and how would it have helped further the advancement of algebra.

How would our world be different today?

Just now, Eric Smith said:

Consider the following.

The Greeks are credited with advancing geometry by large amounts, but consider if one could go back in time and teach Algebra to the ancient Greeks. How would that knowledge hurt their development of geometry and how would it have helped further the advancement of algebra.

How would our world be different today?

Perhaps you would like to explain what is behind this question ?

The ancient Chinese development fell bewteen the two stools of algebra and geometry so you have a case in point if you study that for an answer.

Have you read Johnny Ball's book wonders beyond numbers ?

You will find an unbiased introduction there.

1 hour ago, Eric Smith said:

The Greeks are credited with advancing geometry by large amounts, but consider if one could go back in time and teach Algebra to the ancient Greeks. How would that knowledge hurt their development of geometry and how would it have helped further the advancement of algebra.

Wouldn't they let themselves be conquered by the Romans?

8 hours ago, Eric Smith said:

How would our world be different today?

You mean, if we could go back in time and change the past how would that affect the future?

How could we know? You have just changed the past.

What Newton have done if I could go back in time and teach him Einstein's discoveries?

Not sure why you have put this in hard maths.

Just now, pinball1970 said:

What Newton have done if I could go back in time and teach him Einstein's discoveries?

Interestingly there is a book by a german professor of Physics, the late Harald Fritzsch, on this very subject.

Edited August 3Aug 3 by studiot

42 minutes ago, studiot said:

Interestingly there is a book by a german professor of Physics, the late Harald Fritzsch, on this very subject.

+1

You recommend? How strong is it on tensor calculus? I found Newton easier than Einstein!

Just now, pinball1970 said:

You recommend? How strong is it on tensor calculus? I found Newton easier than Einstein!

It's a popsci book, but being german, it is accurate, so yes I would recommend it.

Here is the flysheet. the book is for reading not studying. It is a good read.

And note Fritzch had an earlier book too, along with many other properly scientific publications.

However it is not about tensor calculus.

If you are interested in that I would recommend Visual Geometry and Forms By Needham. It's much more up to date than MTW.

But this is a digression if you really want to explore books on these subjects, we should do it in another thread.

Markus had a thread like that when he was (self) studying the stuff.

3 minutes ago, studiot said:

But this is a digression if you really want to explore books on these subjects, we should do it in another thread.

Understood and thanks for the refs, I will check those out too.

Edited August 3Aug 3 by pinball1970
Missed a word out

16 hours ago, Eric Smith said:

Consider the following.

The Greeks are credited with advancing geometry by large amounts, but consider if one could go back in time and teach Algebra to the ancient Greeks. How would that knowledge hurt their development of geometry and how would it have helped further the advancement of algebra.

How would our world be different today?

We'd have different people accredited with advancing geometry, other than that, not a lot...

If thing's are understandable by a human, then eventually a human will understand it...

On 8/3/2025 at 12:08 AM, pinball1970 said:

You mean, if we could go back in time and change the past how would that affect the future?

How could we know? You have just changed the past.

What Newton have done if I could go back in time and teach him Einstein's discoveries?

Not sure why you have put this in hard maths.

That's the spirit.

Just now, Eric Smith said:

That's the spirit.

So this is a wind up then.

On 8/2/2025 at 3:32 PM, studiot said:

Perhaps you would like to explain what is behind this question ?

The ancient Chinese development fell bewteen the two stools of algebra and geometry so you have a case in point if you study that for an answer.

Have you read Johnny Ball's book wonders beyond numbers ?

You will find an unbiased introduction there.

I never heard of that book, but I will check it out.

The reason behind my question is because the Geometry shaped our world in many ways, and I can imagine it would suffer if not for their work, but Algebra shaped our world in other ways and if more advanced that too would have a profound impact.

1 hour ago, Eric Smith said:

I never heard of that book, but I will check it out.

The reason behind my question is because the Geometry shaped our world in many ways, and I can imagine it would suffer if not for their work, but Algebra shaped our world in other ways and if more advanced that too would have a profound impact.

I should have thought that if the followers of Euclid could have read about Al-Jabr , which includes completing the square to solve quadratic equations, it might have moved both algebra and geometry on significantly. The Greeks worked on conic sections, after all, so the algebraic expression of a parabola as a quadratic equation would have rung a lot of bells. Coordinate geometry, instead of waiting for Descartes, would have taken off almost 2000 years earlier!

Edited August 4Aug 4 by exchemist

1 hour ago, Eric Smith said:

The reason behind my question is because the Geometry shaped our world in many ways

Yes as did algebra, number theory, calculus and many other branches of mathematics.

1 hour ago, studiot said:

So this is a wind up then.

No I don't think so. If he follows the stupid nonsense Ken Wheeler writes he probably believes it.

Just now, pinball1970 said:

Yes as did algebra, number theory, calculus and many other branches of mathematics.

No I don't think so. If he follows the stupid nonsense Ken Wheeler writes he probably believes it.

Let's hope so it could be a good discussion.

But he doesn't seem to be putting much effort into it.

1 hour ago, studiot said:

But he doesn't seem to be putting much effort into it

He is regurgitating a known crank on a serious science website. I think that is the max effort we can expect.

On 8/4/2025 at 1:24 PM, pinball1970 said:

Yes as did algebra, number theory, calculus and many other branches of mathematics.

No I don't think so. If he follows the stupid nonsense Ken Wheeler writes he probably believes it.

Einstein has not been proven, it simply had lots of mounting evidence. If relativity was truely the answer, there would be no need for "special relativity". It's not a theory of everything.

Where Ken Wheeler is concerned, I simply remain open to the possibilities.

On 8/4/2025 at 2:28 PM, studiot said:

Let's hope so it could be a good discussion.

But he doesn't seem to be putting much effort into it.

It's meant to be a thought provoking to inspire some deep thought on the topic. Imagine two different Earths. One had the history we all know, and other had one where the Greeks discovered Algebra early and Geometry was not as advanced. How would the two Earths be different today?

6 minutes ago, Eric Smith said:

Einstein has not been proven, it simply had lots of mounting evidence. If relativity was truely the answer, there would be no need for "special relativity". It's not a theory of everything.

Where Ken Wheeler is concerned, I simply remain open to the possibilities.

Science does not go in for proof, that is lawyers or mathematicians.

Science goes in for the best available 'fit' to known observations and is subject to change at any time due to new and (hopefully) better observations.

9 minutes ago, Eric Smith said:

Einstein has not been proven, it simply had lots of mounting evidence. If relativity was truely the answer, there would be no need for "special relativity". It's not a theory of everything.

Where Ken Wheeler is concerned, I simply remain open to the possibilities.

It's meant to be a thought provoking to inspire some deep thought on the topic. Imagine two different Earths. One had the history we all know, and other had one where the Greeks discovered Algebra early and Geometry was not as advanced. How would the two Earths be different today?

The "special" in special relativity just means it applies to certain simple cases. It came first historically. General relativity came later and is much harder to work with but, as the name indicates, applies far more generally. I suggest a little bit of reading about the subject.

4 minutes ago, studiot said:

Science does not go in for proof, that is lawyers or mathematicians.

Science goes in for the best available 'fit' to known observations and is subject to change at any time due to new and (hopefully) better observations.

Which is exactly why we need to remain open.

1 minute ago, exchemist said:

The "special" in special relativity just means it applies to certain simple cases. It came first historically. General relativity came later and is much harder to work with but, as the name indicates, applies far more generally. I suggest a little bit of reading about the subject.

I was not aware that it came first. I shall read up on that.

3 minutes ago, Eric Smith said:

Which is exactly why we need to remain open.

Exactly.

Unfortuneately scientists are human and sometimes succumb to social or popular pressure about imprecise terms.

Scientific proof is such an example.

2 hours ago, Eric Smith said:

I was not aware that it came first.

That much was obvious. And yet you decided to pontificate on the topic, as you have on a few others. You might ponder on the issue of credibility.

On 8/2/2025 at 9:26 PM, Eric Smith said:

The Greeks are credited with advancing geometry by large amounts, but consider if one could go back in time and teach Algebra to the ancient Greeks.

That would be difficult, because Algegra is an Islamic word..

1 hour ago, Sensei said:

That would be difficult, because Algegra is an Islamic word..

It comes from an Arabic word (is Islamic a language? Is algebra a tenet of the religion?) and what does that have to do with anything about teaching them the math?

19 hours ago, Eric Smith said:

I was not aware that it came first. I shall read up on that.

Leonard Susskind has done a decent series called the "Theoretical minimum," lots of other books on this subject and Taylor and Wheeler, "Space-time physics," is often recommended on physics sites.

That Wheeler is John Archibald Wheeler the eminent physicist, just to be clear.