Thread: units of time, units of 1

A big debate has been raging about the "point" of time, what is it "that".


Time was introduced historically in the mathematical system of dividing space. Space was "over" time, it was "divided" by time. That's how our equations of time first manifest, as "velocity". And now think what what better metaphor for time as change other than "velocity"?

Um, in case any of you are wondering why I posted this here, it is because this is a "history of mathematics" question. I thought it wise to first consult those who should know their own history.



I read something recently that suggested time played no use to the topography of space. Time and space, and this is my point, is the cornerstone of mathematics. It should be the job of mathematicians to finely craft that cornerstone. Yet, the question here, is how "time" was first used in mathematics relevant to your own study of mathematics? I guess, did time surface when the idea mathematically of "1" surfaced, as a way of explaining the topology of space?

Time isn't of great importance to mathematics, it doesn't get any special treatment that i'm aware of. Time as a concept is used to assign an ordering or duration to events that occur in the physical world, thus it's a physics concept. Much of physics involves mathematics so at some point someone realised that you can formalise this notion mathematically by treating time in the same way you would treat any other coordinate.

By "point" of time are you referring to the nature of time at an instant as in a single point of time, or are you are referring to the purpose of time?

I suspect you are referring to the latter -- the purpose of time. It seems an odd way of looking at the world, things don't have to have a purpose in order to exist. Unless of course you phrase it in the context of doubting the existence of time, and that humans have just invented it to help them describe the universe... in which case you should really think a little deeper and try to consider a world without time -- because then you would see that it would not resemble the world we live in!

Originally Posted by theQuestIsNotOver

Time was introduced historically in the mathematical system of dividing space.

Surely time mesurement and calculation was introduced as a way of dividing up days and years (or, errm... time). The earliest timekeepers that we know of were the Egyptians and Mesopotamians(1). They needed accurate calendar calculations to know when the rivers would flood, which was vital knowledge for agriculture. With the rise of organized labor and cities and it became important to be able to divide the day into working hours, shifts, rest periods, etc.

(1) Which is why there are 60 seconds in a minute, 60 minutes in an hour, etc.

Yes, dividing. Like the calendar. Yes. Ultimately dividing up space on it's smallest level when it comes to employing mathematics to space-time theories.

I guess that's the answer then, namely calculations using calendars. I thought there may have been an official time in the history of mathematics when "time" first became the focus of mathematical calculation. But really that's how mathematics started really, with the calculation of time, hours, days, and so on. Calendars.

Originally Posted by theQuestIsNotOver

Time was introduced historically in the mathematical system of dividing space.

I don't necessarily dispute that, but it does differ from what has been written by others who have looked into the matter more than I have. The following is a quote from the book "The Natural Philosophy of Time" by G.J.Whitrow: "The peculiarly close relation between time and counting has been emphasized both by philosophers of time and philosophers of mathematics. For example, Aristotle in endeavouring to distinguish between time and motion, came very close to reducing time to number. On the other hand, L.E.J Brouwer in developing his celebrated 'intuitionist' theory of mathematics in the first two decades of the present century (20th century) based his construction of the natural numbers on the conceptual multiplicity of intervals of time, which he regarded as the primary intuition of the human intellect. Brouwer's doctrine derives from Kant who argued that "arithmetic produces its concepts of number through successive addition of units of time". What Brouwer seemed to have in mind is that the order which we see in 1,2,3,4...... arises because we see 2 as later than 1 and 3 as later than 2 .. and so on.

Originally Posted by theQuestIsNotOver

But really that's how mathematics started really, with the calculation of time, hours, days, and so on. Calendars.

I remember reading an old article from Time (no pun) about ancient calculators. It was a primitive form of arithmetic on stones to count quantity of objects, like sheep in herds, rather than time itself. But the counting of physical objects and measuring time are both so basic, it's hard to reason if one was even developed before the other.

Mathematics concerning time was probably more about "counting" it, and then as we better understood the cycle of seasons and such, noticing how change came in continuous loops, we divided it into subunits, making the calendar system. And we combined time and distance (space), into an equation to calculate velocity, which is change over distance. And then time and velocity itself, to calculate acceleration (change of distance over time) using square units of time... which is just like the space-time idea.

So then, historically regarding the idea of mathematics and time, first it is the dividing of space using numbers, then "time" enters the division of space according to an intuitive component we have of recognising "changes" in space that appear to act independently of our own volition, hence the most basic form of measuring the changes in the gross appearances of space around us, night and day, and thus the employment of calendars. That seems to be what happened. I wonder though if there is a more fundamental truth to it all, not making the suggestion that there is of course.

Is any part of mathematics "intuitive" though? Historically. What presented itself to the earliest mathematicians for them to "need" to include time in their formulation of equations?

The calendar? In who's name as a likely intuitive source? What greatness.....

And how do we appreciate this source? Ok, subliminally, of course. Intuitively.

So, what comes first, "faith" (in going with the flow, intuitively, being God-like), or dividing "space"?

By our own education, what should come first?

Now what if I said God divided everything up? What still comes first? (what came first, God or dividing, as a sentence wrote).

Ineed, how mathematical is this? It's what happened before or after the idea of time that which became known to mathematics.

Chance. It's mathematical chance in its purest form. The ability to start something new.

Mod says: I cannot convince myself this thread is going anywhere useful, at least not in terms of mathematics as it is usually understood. Correct me if I am wrong, otherwise I propose a lock-down. Opinions?

I guess this is 1 time to end it.

Ok. It got a bit wordy. Division of space and calendars is the clear answer. Thanks all.