Yes: the ancients were right on to the subject of infinite series and the essence of Calculus. Archimedes' "Method of Exhaustion" is a prime example.

Most of the Greeks e.g. Zeno, Plato, Pythagoras etc were about 500 BC or thereabouts, but weren't the Chinese and India at it earlier?
This infinity business is similar to Achilles and the tortoise, where in theory he can never catch it because he will always be a tiny bit away from it, the series continues ad infinitum. Oh look another way of saying for infinity!

I think Sumer that was the first urban civilization in the historical region of southern Mesopotamia, modern-day southern Iraq in 4500 – c. 2004 BC.
https://en.wikipedia.org/wiki/Sumer
They still use base 60 in maths.
And even we reading clocks and in navigation.
Why 60?
Count your knuckles and bones on your fingers:)

I wonder if calculus works in a parallel universe.
Most likely but 11 dimensions?
Mind gobbling!
I have to ask Mad Max and Laura about this...
https://twitter.com/tegmark
https://vimeo.com/75833771

BTW Mad Max is now 50 years old:)
http://news.mit.edu/2017/king-carl-xvi-gustaf-sweden-visits-mit-0508

Max Tegmark, a professor of physics at MIT who was born in Stockholm, moderated the discussions, gave an introduction in Swedish to the delegation, and provided a few remarks of his own about artificial intelligence.
“We don’t want to make any mistakes,” Tegmark said. “We want to get it right.” Tegmark’s concerns stem from the idea, he added, that “We want to be proactive, not reactive,” about the impact of technology on society.

This infinity business is similar to Achilles and the tortoise, where in theory he can never catch it because he will always be a tiny bit away from it, the series continues ad infinitum. Oh look another way of saying for infinity!

Zeno's paradox... the intellectual leap the ancient Greeks don't seem to have universally made is that an infinite series can have a finite sum... ie:



Archimedes was getting there, but the Romans... er... intervened. Also Aristotle although a philosopher understood it. They were very close to calculus, but lacked the algebraic framework and notation to support it.

Side note: One of the niftiest and most counterintuitive results of this is that the "Harmonic Series"...



... diverges to infinity. It doesn't seem possible because after a few terms it grows so slowly and this rate falls off so fast.... it takes 144 iterations to get to 6, but to get to 10 takes 12,367, and to 100 takes over 10⁴³! Yet the proof is there in the article (Comparison Test proof) and quite easily understandable.

Edit: one of the integral equations shown has ∞ as both the upper range of the integral and the result, showing its use in mathematics.

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The fact that the measuring technique or tool employed is insufficient to detect the passing through the time point "midnight" does not mean that the time point "midnight" does not exist.
In your example the resolution of your tool and technique is far too course - two micro seconds is a very long time...

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Bob Smith
Member of Seti PIPPS (Pluto is a Planet Protest Society)
Somewhere in the (un)known Universe?

The best time resolution measurable would be Planck Time, about 5.4 x 10^-44s. There would be a theoretical "exact" midnight but it couldn't of course be measured. Time is likely quantized along with space and has a slight irreducible granularity.

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The best time resolution measurable would be Planck Time, about 5.4 x 10^-44s. There would be a theoretical "exact" midnight but it couldn't of course be measured. Time is likely quantized along with space and has a slight irreducible granularity.

Yes. And of course. Every object in space has it's own time.
What's now for me it's not now for you.
Mind gobbling.

Or is it?
Arranging a meeting always requires two pieces of information.
Time and place.

Now that some silly geese have made a mess here how about trying to out smart Stephen Hawkings then, Black holes could be portals to a PARALLEL UNIVERSE.

Quite frankly I'm glad that scientists have an optimistic view of things to achieve wonders other than those here who have a constant pessimistic outlook which gets us nowhere.

Yes you know that I'm talking about you.

Cheers.

Incredible how a thread can degenerate.......

It's also unbelievable how some others here have also degenerated with age Sten (unlike us), they were fairly bright once upon a time, but sadly senility seems to have overtaken them. ;-)

Cheers.

Now that some silly geese have made a mess here how about trying to out smart Stephen Hawkings then, Black holes could be portals to a PARALLEL UNIVERSE.
Quite frankly I'm glad that scientists have an optimistic view of things to achieve wonders other than those here who have a constant pessimistic outlook which gets us nowhere.
Yes you know that I'm talking about you.
Cheers.

Hawkings said: "Things can get out of a black hole, both from the outside and possibly through another universe."
Not a parallel universe that was coined by Hugh Everett III.
There is a huge difference between the two concepts.
There is also one third or more concept but that is off topic.

It can't get anymore off topic than it is already Janne. ;-)

Cheers.

It can't get anymore off topic than it is already Janne. ;-)
Cheers.

When it comes to universes nothing is off topic.
Ask Mad Max. LOL:)