41 - Richard Sorabji on Time and Eternity in Aristotle

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Peter talks to Sir Richard Sorabji about Aristotle's physics, focusing on the definition of time and the eternity of the universe.



Further Reading

• R. Sorabji, Matter, Space, and Motion (London: 1988).

• R. Sorabji, Time, Creation, and the Continuum (London: 1983).

Prof Sorabji's website with a list of his publications


Jon on 14 July 2011

Thanks, and Golden Mountain Question

Hello -

Thank you so much for this podcast series. It has come at exactly the right moment for me. I only discovered the history of philosophy recently (as part of a mid-life crisis). I have read several overviews and was looking for something more detailed. This podcast is perfect.

I have a question about the Richard Sorabji episode on Aristotle's view of Time and Eternity.

Would it be possible to expand on what Richard' said about monkeys writing Shakespeare or a golden mountain existing given infinite time. He said "that looks completely implausible and so it is mistaken", but didn't say why. This came up in a conversation I was having recently so I'd really like to know the philosophical argument for it being false.

I understand why it isn't certain given modern physics (because we only have 10^100 years until the heat death of the universe ;-) ...but if Aristotle believed that all matter was contained in a fixed area, was constantly being rearranged and would continue to do so for an infinite amount of time, and if there is nothing in principle to prevent golden mountains from existing, why wouldn't it be certain to happen eventually? In fact why wouldn't there be an infinite number of golden mountains?


- Jon

In reply to by Jon

Peter Adamson on 15 July 2011

Infinite monkeys

Hi Jon,

Glad you are enjoying the podcasts! To be honest I wondered that when I was doing the interview with Richard, too. I think one might need to ask a mathematician and not a philosopher (or at least, not this philosopher). I know a mathematician and I'll ask him. But one thought might be this: if there are N possibilities, that doesn't mean that given an N number of trials, every possibility will be realized. For example if you roll a six-sided dice, you won't necessarily get each of the six numbers. Indeed, in theory there is nothing to prevent rolling a six-sided dice, say, 100 million times, without ever getting the number 4 to come up. That would be astronomically unlikely, but not impossible. 

Now in the infinity case our intuitions tend to fail because infinity is so tricky. But it seems like it is just the same kind of case: there are an infinity of possible situations and an infinity of times when situations can obtain. Thus we have N possible outcomes and N trials or opportunities. As with the dice case it does not follow that every one of the N outcomes will arise.

Does that help?


In reply to by Peter Adamson

Jon on 15 July 2011

Re: infinite monkeys


It helps a bit, but I'm still not sure. The more outcomes there are, the closer the probability comes to 100%. I understand that if there are a vast but finite number of outcomes the probability never quite reaches 100%, but it's infinity which throws me. It sounds like over an infinite period of time the probability that the monkeys will write the entire works of Shakespeare (many times over) is infinitely close to 100%. At that point the difference between that number and 100% doesn't seem meaningful.

Thanks again

- Jon

In reply to by Jon

Michael P on 16 July 2011

Re: Infinite monkeys

I think that there are many examples where you might have never-ceasing motion, and yet this doesn't mean that every possible arrangement will eventually occur.  

For example, consider a pendulum, that moves forever (say in zero gravity or whatever).  As long as the string is taut at the beginning, it will always remain taut.  So the weight will always remain at a fixed distance from the pivot.  Although it is possible is for the string to bend and the weight touch the pivot (a possible arrangement), this will never occur.  

A simpler example: the motion of a planet, which always remains in its orbit, forever (not really, but whatever).  And I think that it's more general: usually when we describe motion by a mathematical equation, the object's location is very restricted, although it might in theory move forever.  (Ignoring examples of chaos theory.)

In reply to by Michael P

Peter Adamson on 16 July 2011

Even more infinite monkeys

Thanks, that's helpful: so the point is that if there are constraints, it doesn't matter how long you keep trying, you will never get certain outcomes. The planet example is of course Aristotle's picture: he thinks that the heavens rotate eternally and for a variety of reasons nothing can stop them from doing this. So for him the "probability" of the heavens suddenly stopping is zero and you can wait as long as you want, it will never occur.

I think there's still a lingering question along the lines put by Jon: if you have an outcome which _does_ have a positive probability, so that it is not constrained not to happen, then intuitively, the more trials you run the more likely it is that this outcome will occur at some point. (So compare flipping a coin once to flipping it 100 times: the probability of getting heads after one trial is .5, the probability after 100 times is close to 1.) Jon's reasoning, I take it, is that anything with a positive probability should therefore occur given an infinite amount of trials (times where things can happen). So even something very improbable, like monkeys banging out Shakespeare, will have a probability of 1 or approaching 1 over an infinite number of trials/amount of time.

My response to that was that if there are an infinite number of possible outcomes, which there are in the case of something like the monkeys on the typewriters (unless we set a limit to the length of what they're writing, or something), then the probabilistic reasoning won't work. Let's say that each outcome has an equal probability: then it will be positive, but infinitely small. So again, it's just like doing something like rolling a 6-sided die 6 times: you have N equally possible outcomes and N trials, and this certainly doesn't guarantee that each possible outcome will occur. 

In reply to by Peter Adamson

Michael P on 16 July 2011

Those darn monkeys

Peter's suggestion that with infinite possible events, individual events can have infinitesimal probabilities, which don't necessarily sum to 1, is surely right.  In fact, standard probability theory has to deal with this thing all the time.  Usually we avoid the language of infinitesimals in mathematics, but we could rephrase it without infinitesimals in this case and put it on solid ground.  But instead, I want to discuss a different approach, that doesn't require Peter's suggestion.

The thing is, the probability of having the works of Shakespeare is NOT a constant, like 0.5.  Rather, it depends on the current situation.  It's higher when a lucky monkey has managed to type a couple words correctly, and lower after the typing the next word, "gbbbfsbs".  With a variable probability, the chance of getting Shakespeare does not necessarily have to approach 100%.  Specifically:

Let p(n) be the probability of obtaining the goal during time n.  Let q(n)=1-p(n).  Then the probability of never obtaining Shakespeare is the infinite product, q(1)q(2)q(3)...q(n)..., so the probability of getting Shakespeare is 1 minus that.  If p(n) is any constant, say p(n)=0.01, then q(n) is a constant 0.99, so the infinite product q(1)q(2)q(3)...q(n)... will approach 0, so the probability of getting Shakespeare will approach 1, which is 100%, as we expect.  

But if p(n) is not constant, q(1)q(2)q(3)...q(n)... might approach something other than 1.  For example, if it approaches 1/2, then the probability of getting Shakespeare would approach (1 - 1/2) = 1/2, which is only 50%.  To give you a concrete example demonstrating this, let p(n) = 1/(n+1)^2.  Then

q(n) = 1 - 1/(n+1)^2

     =  n(n+2) / (n+1)^2

     = [(n+2)/(n+1)] / [(n+1)/n ]

     = [1 + 1/(n+1)] / [1 + 1/n], 

so the product q(1)q(2)q(3)...q(n) = [1 + 1/(n+1)] / [1 + 1/1] = (1/2) [1 + 1/(n+1)], which approaches 1/2 as n goes to infinity.  

(By the way, there's nothing special about "1/2"; I could have set it up to approach any constant between 0 and 1.  It's more general than that; the only real requirements are that the product q(1)q(2)q(3)...q(n) must be between 0 and 1 and always be decreasing.)

Finally: Jon seemed to have another question: what does it _mean_ to say that a probability of something approaches 100% as time goes to infinity: does it mean it is guaranteed to happen "eventually, after an infinite amount of time", or does the probability go to 100% with some mysteriously improbable but real chance that it might never happen? Here, math doesn't help.  When you look at the formal definition we use for a "limit", the whole point is to sidestep that sort of issue, while still being able to do whatever calculations we want to do and have it be correct (no matter how the issue is decided).

In reply to by Michael P

Peter Adamson on 16 July 2011

Monkey puzzles

Thanks Mike, that's brilliant. Just to take this back to Aristotle for a second, I find it interesting that he seems to have not only the (apparently false) intuition that everything possible will happen given an infinite time, but also the countervaling intuition that randomness _doesn't_ give you apparently ordered results. Hence his refutation of Empedocles which, to oversimplify, is just to say that a chance process will never give you a result that looks overall well-ordered.

In reply to by Peter Adamson

Jon on 18 July 2011

infintely confused

Hi Mike-

Thanks for the detailed answer

I'm not a mathematician, but I think I understood your infinite products and the reason something which wasn't a constant wouldn't necessarily tend towards 1, but I'm not sure I understand why the probability of typing the works of Shakespeare in a given time is not a constant.

To take a shorter example, if there are 4 keys on the keyboard (k=4 eg. A, B, C and D) and the text we are looking for is 3 letters long (t=3 eg. "BAD") then I think the probability of getting it right in exactly t keystrokes is (1/k)^t (in this example, 1/4 * 1/4 * 1/4 = 1/64)

So the probability of failure in any 3 keystrokes is 63/64 and the probability of failure in repeated sets of 3 keystrokes over an extended period of time q(1)q(2)q(3)...q(n) is (63/64)^n ...which will tend towards zero (as you said constants would)

When you said the probability of success was higher after typing a correct word than a gibberish word, I assume you meant that the full text could appear anywhere in a longer series of keystrokes. After a correct word we would be part of the way there and after gibberish we would have to start again. In that case the maths is beyond me, but it sounds like the result would be more likely to appear sooner than in my first example (there are only 128 ways of getting BAD in two sets of three keystrokes (64 x "BAD???" and 64 x "???BAD"), but 256 ways in 6 keystrokes (64 x "BAD???", 64 x "?BAD??", 64 x "??BAD?" and 64 x ???BAD)

Thanks again

And Peter I'm sorry for hijacking your Aristotle comments

- Jon

In reply to by Jon

Michael P on 19 July 2011



Hi, Jon.  Yes, the gibberish word example probably wasn't my smartest move. If you have equal (constant!) probability of hitting each key each second, then the chance of getting Shakespeare will go to 1, regardless of the fact that sometimes there are setbacks.  So let me back off that exact example.
There are other reasons that probability might not be constant.  Maybe the monkeys lose interest in the "a" key gradually, so the probability of hitting "a" gradually decreases.  If it decreases fast enough, then you will get the kind of effect I described in the earlier post.  
Is it fair to modify the infinite monkey scenario in that way?  Actually, I think it's not fair to assume otherwise, that is, to assume that the monkeys will hit each key with a fixed probability, independent of the keys they hit previously.  We are really only interested in monkeys insofar as it is a metaphor for the universe, and why should the universe be like that?  That is, why should the universe be describable as process over a finite set of equally likely states? 
While that is how probability works with coins, dice and cards, it's not true in general.  In particular, when there are infinitely many possibilities (as mentioned already by Peter), then the likelihood of each possibility may well be infinitely small, in which case it isn't even obvious whether "equally likely" can be a sensible notion anymore.  (In fact there is a reasonable analogue, but it's not immediate, and it's not always appropriate.)
Let's start over.  A more general approach is to think of the universe (say, which includes a room of monkeys) as a "random process".  At any time, the universe is in some state, and in the next moment it changes to another state according to a certain probability.  For example, if the monkeys have written "To b" so far, then in the next second the paper could be "To ba", "To bb", "To bc", ..., "To bz", or "To b ", etc., or the monkey might rip out the paper and starts over.  Each new state has a certainly probability of occurring.  The probability of the next letter being "a" changes over time, and depends also on the current state: for example, I'd guess that repeating a letter is more likely than not, and ripping out the paper becomes more probable as time goes on.  I think that this is a better model for the universe than assuming that the one where the letter "a" always appears with the same probability.  
But there's more.  When we have "To b", the probability of "To ba" won't equal to the probability of "To bb", but what may be more interesting is that the probability of getting "Ham sandwich" is zero.  The universe is like this, too: I could move 10cm left or 10cm right, but I can't suddenly reappear in Wichita.  So, in general, from a given state, you can only go to a small set of other states, and there are many states that you cannot get to immediately.  But then it's quite possible that that there could be two states X,Y, such that if you start from state X, you will never (after any number of steps) get to state Y.  For example (maybe too simple): while it might be possible for a moon to be in any location, once it settles into a particular orbit, it will never suddenly jump away from it (assuming ideal circumstances), so it will never end up in a different orbit.  
Apologies, I write too much.

In reply to by Michael P

Felix on 19 July 2011

Michael, interesting


interesting discussion!

Couple of things - you mentioned again "infinitely many possibilities" but I don't think that applies in a finite universe? But that is just nit-picking.

In terms of the monkeys, even if the probability of hitting the 'a' key decreases over time, or if the monkeys might rip the paper out half way through King Lear, my intuition tells me that as long as the probability of each of these is respectively greater than zero, less than one, then in infinite time the Complete Works would still be completed.

Apologies if you think you nailed this with you earlier maths-heavy comment - I confess that I did not fully grasp that. But I would suggest the following:


You said

"The thing is, the probability of having the works of Shakespeare is NOT a constant, like 0.5.  Rather, it depends on the current situation.  It's higher when a lucky monkey has managed to type a couple words correctly, and lower after the typing the next word, "gbbbfsbs"."

But if we take the base probability as being that at the start when zero correct characters have been typed, call it p0(n), any subsequent values of p(n) will be equal to or higher than p0(n).

Then applying that thought to your following paragraph:

"If p(n) is any constant, say p(n)=0.01, then q(n) is a constant 0.99, so the infinite product q(1)q(2)q(3)...q(n)... will approach 0, so the probability of getting Shakespeare will approach 1"

p0(n) is not constant, but it is better than constant since it can only vary in a manner which increases the probability of attaining the goal.

Changing tack slightly, I wonder how the idea of certain states that are unobtainable once an intermediate state has been reached (rather thanunobtainable a priori) relates to the Second Law of thermodynamics - Entropy always increases.

E.g even in an infinte period of time all the matter in the universe will not coalesce into the smallest possible region of space having once left that configuration at the big bang.

Presumably the 2nd law is just a statement of probability which does not hold when infinite time is available?



In reply to by Felix

Michael P on 19 July 2011

less confusion?


Hi.  I think that the confusion may have started when I wrote "obtaining the goal during time n".  And maybe some other stuff I wrote.  Anyway, our confusion about the math is due to different ways of setting up the problem.
The way I set it up, it makes sense if we are saying that during each time period, there is a certain fixed chance of writing Shakespeare.  For example, maybe the time period is 1 day, and at the end of each day we clean the monkey cage and start over.  (Or, instead of a time period, we start over whenever the end of a page is reached - same result, but it seems a bit more natural.)
John's description focuses on probabilities for getting a single letter at a time, and then goes from there.
Felix, your "p(n)" is the probability of obtaining Shakespeare (for the first time?) at time n, when we are observing what has happened since the experiment has begun.  
Although we are all using the letters "p" and/or "q", we have defined them differently for each of us.  That's why they behave differently.

In reply to by Michael P

Jon on 19 July 2011

Got It

Hi -

Thanks Michael - I have it now :-)

If a series of events are truly random, unconstrained and unconnected (eg. we are looking at a random selection of letters) then over an extended period of time the probability that a particular sequence has occured will tend towards 1.

But if a series of events is non-random, interconnected in some way or regulated by natural forces (as almost all macroscopic events will be) then the probability of a particular sequence will trend to something less than 1. I'm happy with that.

Thanks again

- Jon

In reply to by Jon

Michael P on 19 July 2011

Re: Got it

Good!  Although "will trend to" should be "may trend to"; it depends on how the numbers work out.


In reply to by Peter Adamson

Feli on 16 July 2011

"(unless we set a limit to

"(unless we set a limit to the length of what they're writing, or something)"

Since the number of words in the works of Shakespeare (or the number or atoms in a golden mountain) is not infinite each of these events should come to pass eventually if you agree that they have a positive probability; which seems to mean - if you have not used the fact that X can never happen as one of your starting assumptions.

I still agree with Jon but I was surprised by the excellent arguments against the intuitive position.


In reply to by Jon

MMC on 13 April 2012

mathematics doesn't apply

There problem with 100 monkeys is typical of the seeking of understanding thru a model with no reality.

First of all there is the matter of the word processors, and their creation and maintenance.

There is the matter of feeding the monkeys.

Monkeys could not and would not sustain their typing for any period of time.

Etc. Simply, they would never succeed.

In reply to by MMC

Peter Adamson on 13 April 2012


I agree, thinking about infinity in physical contexts is slippery. We could change the example to make it a bit easier to implement (e.g. replace the monkeys on typewriters with computers randomly producing strings of characters) but it is easy to forget, when constructing a thought experiment, that infinite sets cannot actually be physically implemented and that will apply to any such scenario. The question is what that means -- it seems to me that one can ask, "ok, this isn't physically possible, but ignore that -- what would happen if it were to occur?" We're being asked to focus on the mathematical or probability issue and ignore the implementation issue. There's a deeper question here about the role of thought experiments in philosophy, and in particular, impossible thought experiments.

Aristotle himself insisted that infinity is not physically realizable, which is one reason he insists that the cosmos cannot be infinitely large. But he doesn't think that eternal time counts as a physical realization of infinity, since the infinite moments/motions are not all present simultaneously. As we'll be seeing in episodes on late antiquity this position did not go unchallenged.

Henry Audubon … on 28 September 2011

A comment about space and necessity.

I have a comment about the discussion at the end of the episode regarding empty space and the distinction between ability and opportunity. Richard seems to argue that space beyond the stars might have the ability to receive matter, but not the opportunity to do so, since the stars are confined to circular motion. But if space is an eternal thing, then, by Aristotle's conception of necessity, the fact that space beyond the stars is eternally without matter implies that it is necessarily without matter, and thus that it lacks the ability to receive matter. 

In reply to by Henry Audubon …

Peter Adamson on 1 October 2011

Space outside the cosmos

Dear Henry,

Yes, that's a nice point. Remember though that according to Aristotle there is no "space" (or in his terms place, empty or otherwise) outside the cosmos -- there is absolutely nothing outside, not even emptiness. And Richard was trying to explain what he takes to be a reason Aristotle thinks that, namely that a place is something that can be occupied. Hence:

1. A place is where a body can be

2. There is never a body outside the cosmos [because of nature of heavenly motion]

3. What never happens is impossible

4. It is impossible for a body to be outside the cosmos [from 2 and 3]

5. There is no place outside the cosmos

If I'm right that this is what Richard was getting at, the argument he was ascribing to Aristotle actually presupposes the principle you mention, in point 3.

Thanks for the comment!


Felix on 30 November 2011

Golden Mountains

Warning: Not much philosophy here :-)

I feel that Richard dismissed the possibility of a golden mountain out of hand without any basis.

It seems to me that in a universe infinite in time and very large in volume, populated with biological beings like humans, magpies and ants the eventuality that one being, or group of beings, will place enough gold in a single location to be termed a mountain is exceedingly easy to imagine.

Just to prove to every body else on your planet that you are the biggest poo-bah or whatever!

However ...  I may now have to alter my view, since wikipedia tells me that 'only' 165,000 tonnes of gold have been mined by humans and that this represents a cube of approx 20 metres on a side (I checked the maths and it is correct despite initial scepticism).

Therefore if we wanted to contruct a gold mountain of, say, 600m^2 base and 300m in height we would need the gold from 4240 earths!  (700 million tonnes)

Therefore it seems unlikely that they would be enough gold in a single solar system to make a gold mountain.

But wait! The BBC tells us that the asteroid Eros is thought to contain "20,000 million tonnes of aluminium along with similar amounts of gold, platinum and other rarer metals". http://news.bbc.co.uk/1/hi/sci/tech/401227.stm

So all that is required is for one enterprising sentient being to capture a large asteroid and seperate it in to its various constituents in large piles and the golden mountain would be a reality! (28 times over)







In reply to by Felix

Peter Adamson on 30 November 2011

Golden mountain

Hi Felix,

Sounds like a worthy project for a government grant application.


Denziloe on 14 October 2013


I agree with those below who say that rejecting a golden mountain ever occurring essentially "because it's weird" is hardly philosophically satisfying. Yes it's weird, but any visceral objections you raise are being based on your experience of finite periods of time, and thus of little import when discussing eternity.

Though I think there are many valid objections which could have been raised. For instance, it'd be perfectly possible (though tragic) for me not to marry. In that case, waiting for eternity won't do any good. It's an event that's not going to happen - unless you resort to saying that "I" will also recur. But by "I" I'm referring to the version which exists right now. Denying my ability to refer to the current point in time, distinguished from other points in time, would seem to land you in some very serious philosophical trouble. Indeed in Aristotle's case it's central to his very concept of time.

The argument about whether there could be no space beyond the celestial sphere was also rather questionable. I suspect it was entirely semantic; what does having the "ability" to receive an object mean if, as is the case in Aristotle's physics, the event can never come to be? I don't think it refers to anything. It's just a different way of phrasing the exact same state of affairs. There'd be no tangible difference. I think this is a case of talking past one other; writing off Aristotle as "wrong" rather than just discussing something differently was rather irksome.

Most irksome though was writing off the typewriting monkeys thing as some kind of erroneous piece of pop culture. I actually have a degree in mathematics and am something of an aficionado for infinity, but in fact you only need fairly elementary (and well established) probability to settle this one. If you have a single monkey who presses a random keyboard key once every second, it will indeed eventually produce the works of Shakespeare at some finite point in time. Of course, this is just an analogy - monkeys won't press perfectly random keys every second, plus they eventually die - but if you really want to rephrase it in terms of something realistic (like quantum fluctuations), you can. If these trivialities of the analogy are what caused it to be so casually dismissed, that's rather disappointing. But I don't know because no reason was given.

In reply to by Denziloe

Adrian Woolfson on 27 February 2014

Infinite Monkeys

Forgive me for dipping in here around 2 years late. But in one sense Aristotle's argument for the non-existence of time in absence of an observer to acknowledge and record its instantaneous moments may be relevant to the issue discussed extensively above. For like the lethal mosquito bite, in a world of immune victims, in the absence of an aesthetic to acknowledge a Shakespeare-like text, the constructions of the infinite monkeys would be meaningless. In other words there needs to be a semantic dimension as well.

In reply to by Adrian Woolfson

Peter Adamson on 27 February 2014

Infinite monkeys redux

On the internet it's never too late!

I like your point, though I think one could get around it to focus on the question here which is about inevitability, rather than meaning. So one could ask e.g. would the infinite monkeys produce a sequence of letters and spaces that is identical to an edition of Shakespeare, leaving aside the question of whether the text they produce "is" an edition of Shakespeare if it wasproduced randomly.


In reply to by Peter Adamson

Adrian Woolfson on 8 March 2014

Implications of closed time

A quick question. How would our perspective on this issue change if time were closed, ie circular?

In reply to by Adrian Woolfson

Peter Adamson on 8 March 2014

closed time

Well, I think the obvious point to make here would be that if time is closed in the sense that the same thing happens again, then you are no longer dealing with infinite time in the relevant sense -- rather you have finite time which repeats. So you don't get into this infinite monkey issue at all, I guess.

I would never have thought that this passing remark by Sorabji would be the one thing that provokes the most comment in the whole podcast series! But I don't think anything else has sparked such debate. Interesting.

Harry Roberts on 8 July 2014

A scientist's perspective

Again, another late comment; however I have only just come across these podcasts and enjoying them immensely.

There are several things which have struck me so far this series, but this episode in particular.

As someone with a scientific background and little philosophy I often find myself thinking about topics discussed in the podcasts with a different perspective.

First of all there are many theories presented by historical philosophers, including the great Plato and Aristotle that are wrong. (This is not a criticism but an observation). So why do we study these ideas/philosophers and ascribe to them great intelligence, when given the progress of another several millennia of human civilisation? Is it the case that being a great thinker is something which is not absolute but relative to the time in which you live, i.e all that is required is that you are exceptional among your society? To give another example, would an ancient Roman citizen who treated his slaves with dignity be considered a great reformer/humanitarian, although if he were alive today he would be considered to be the opposite? i.e if Plato and Aristotle were alive today, would they be professors of philosophy at top universities? I doubt it, as human society has become more educated (I hope) the threshold for being considered a great thinker would have increased compared to Athens 4000BC. Therefore I can understand why we study them as a matter of historical interest, because these characters were exceptional for their time. However I question why we study their ideas when A) we know some of them to be wrong and B) their great ideas are only 'great' relative to their time, we derive no benefit from studying ethics from the kind Roman slave owner.

As for this specific episode. A couple of points where my way of thinking deviated from Professor Sorabji's. (some of these have already been discussed above - I just want to record my own thoughts)

First of all, the infinite monkeys & golden mountain.

My understanding is that if a monkey was given a typewriter and an infinite amount of time, s/he would write the complete works of Shakespeare not just once but an infinite amount of times. I cannot understand why the professor dismissed the idea of a golden mountain, it seems fairly obvious to me that a infinitely large universe (which as I understand, our universe is not) would hold an infinite number of golden mountains, of every possible size and shape, including some which themselves were infinitely large. (The difficulties of tangling with the concepts of infinity!!!) But we can abandon though experiments to do with infinity, and instead consider that a computer program which generated a string of random letters would eventually generate a string of letters which exactly matched with the works of Shakespeare within a finite amount of time. A similar computer program which, instead of generating a string of letters, started randomly listing some of the elements of the periodic table (i.e. helium, aluminium, cobalt, gold, helium, iron... etc etc) would at some point produce an uninterrupted series of 'gold' 100,000,000 times, again within a finite amount of time. The time it would take for the computer to do this would be as a function of how quickly the computer could work.

Secondly, the lethality of mosquitos

I don't like the example of using the lethality of mosquitoes to provide an analogy for time and whether it is countable without any conscious body to measure it. To definite the attribute of lethality, I would say it is an action done to an object with the potential to cause a change their state of living to a state of non-living. It relies on several things, one of which as mentioned, is the ability for the subject to stop living as a result of the bite. Therefore I think it is quite a complicated attribute to have, and I think is steps into the world of semantics. When you describe something as lethal, are you obliged to mention what it is lethal towards? i.e a mosquito is lethal to humans but not to a rock. Or is something describable as lethal if it has any potential to kill anything regardless? i.e if a pebble is lethal to an ant, then a pebble is lethal.

Finally in thinking about whether time is countable/exists without consciousness.

I think that 'Time' will exist whether someone is around to count it or not. When the world was formed, there were no conscious beings alive on it. Over time, life began, and complex organisms evolved. Without time this would not have happened. Also now that we are conscious beings, we can study the pre-historic world and (estimate) measurements of time from before life on our planet. Therefore the time before life is measurable, even if no one was around to measure it at that moment. Thus time exists whether a conscious being measures it or not.

I think thats about it. Much longer than I intended this to be, but I got carried away! Thank you for this series of podcasts, I'm really enjoying them.

In reply to by Harry Roberts

Peter Adamson on 12 July 2014

Wrong but interesting

Hi there - glad you are enjoying the podcasts! I just saw Richard Sorabji over the past few days, it's a shame I didn't see this first or I could have asked him about these issues again. But have a look at "Mike P"s comment above which I think is a pretty definitive judgment on the infinite monkeys issue. (The poster is a math professor friend of mine so he knows what he is talking about.)

Just to touch on your first most general question, as to why we study false ideas like ancient cosmological theories: I think that there are two obvious reasons. Namely that (a) the history of the way we see things now grows out of these false ideas; if we want to know how science arrived at better answers we need to know which other options were rejected and why. And (b) the false ideas are intimiately connected with other important philosophical topics in these historical figures, for instance you can't understand Aristotle's views on god and human nature without knowing something about his physics. (Of course then one could ask who cares about his views on god and human nature but that's another issue.) I myself think there may be other reasons to explore these topics though, for instance the opportunity to immerse ourselves in a completely different worldview, which is useful in all kinds of ways e.g. by drawing attention to assumptions we didn't even know we were making. But even from the point of view of the modern day scientist (never mind philosopher) I think there are plenty of reasons why studying the history of science is a valuable enterprise.

In reply to by Peter Adamson

mmc11 on 13 July 2014

Past errors

Another reason to study errors of the past is that current science is most probably fantasizing about many of its accepted truths. Einstein and others have many flaws known, along with some things accepted as true. Just because a vigorous thinker comes up with a theory doesn't make it true, and current thinkers, though they will never admit it, are highly likely to be proven as wrong as the ancients.

In reply to by mmc11

Adrian Woolfson on 1 September 2014

Monkeys, monkeys and more monkeys...

Quick question:

1. Can anyone here devise an experiment (and not just a thought experiment) that is able to falsify the notion that time might be circular?

2. Have we agreed that we as a group have now achieved closure on the infinite monkeys and golden mountain issue? I'm not entirely certain that we have a definitive answer that we can comfortably assert is the case? Did Richard express a view?

I think that I agree with the idea that if the monkeys themselves are just a metaphor, then the mathematical search space comprising every possible combination of strings of letters parsed into volumes with sentence and paragraph structures with identity to the complete works of Shakespeare must have a finite (and really very large) size, and consequently the probability of deriving the historically correct versions can be precisely computed. Given infinite time, one imagines that eventually they would all be 'discovered'. Nevertheless I argue that the process of recovering them from the sea of 'junk' in which they are embedded i.e. the 'selective' element of the problem, outweighs and even trivialises the 'generative' part of the problem.

We should not forget that the most efficient engine for searching this particular space of mathematical possibility was of course Shakespeare himself. Had he been alive today, he might also have recovered some of the other volumes lying out there in the Borgesian space of possible Shakespeare plays, some of which might be considerably better than the historical ones.

In reply to by Harry Roberts

RK on 9 July 2021

Infinitely large gold mountain

Harry Roberts wrote:

it seems fairly obvious to me that a infinitely large universe (which as I understand, our universe is not) would hold an infinite number of golden mountains, of every possible size and shape, including some which themselves were infinitely large.

An infinitely large golden mountain is clearly physically impossible, because if you make a lump of gold (or any kind of matter) big enough, eventually its mass will be big enough that it will turn itself into a black hole. Even before that, the mass would be great enough to turn into some sort of degenerate matter.

Thinking about the gravitational properties of a large mass of gold makes me wonder if a gold mountain might even be impossible on Earth. Gold has a density of about 19 grams per cubic centimeter. By contrast, typical rocks have densities between 1.5 and 3.5 g/cm^3. To some degree, spots on Earth's crust rise and fall depending on their density, and I wonder if a gold mountain would be massive enough  - with its extremely high density - that it would sink and not stay a mountain. (I suppose this might still mean that a gold mountain, perhaps artificially created, could exist temporarily until it subsided.)

Jose Mena on 11 September 2014

circular definition of time

Professor Adamson,

I had a question about the argument set forward that Aristotle has a circular definition of time. It seems to me that this difficulty can be resolved by considering his understanding of motion relative to the distinction between act and potency.

Professor Sorabji seems to suggest that the concepts "before" and "after" import some notion of time themselves. You talk about the "left side" and "right side" of the room, and walking across it. You, Prof. Adamson, I think hint at the right solution - talking about priority of motion, which is then dismissed. Left and right indeed do not do work to build in temporality into the motion, but act and potency do.

Let us consider you standing on the left side of the room. You are in act on the left side of the room, and in potency relative to the right side of the room. Change is more or less the reduction of potency to act. There is therefore a metaphysical directedness already built in here in the Aristotelian division of being. Potency tends toward act, in some way. So when you take a step toward the right side of the room, you actualize that potentiality; and these are the metaphysical before and after with respect to which we can measure the time.

Does this seem to work to resolve the problem?

Jose Mena

Penelope Vlass… on 17 October 2014


Exceptional podcast! Thank you Peter. Your guest was a pleasure to listen to, very clear in his thought.

Anthony Danalis on 4 December 2018

Eternal monkeys

First, let me start by saying that I love your podcast and I'm very glad to have discovered it. Thanks for dedicating the time needed to undertake such an effort.

I see in the comments below that the subject of eternal monkeys typing the works of Shakespeare has been discussed thoroughly. I would like to add that there is actually a theorem on that, and it is quite nicely explained in the following wikipedia entry: https://en.wikipedia.org/wiki/Infinite_monkey_theorem

Following the same logic we can see that if the atoms of the universe moved about randomly, and organized into groups randomly (just as the different keystrokes of the hypothetical monkeys are random, and the random letters group into words randomly), then indeed the universe would eventually produce mountains of gold. As a matter of fact, it would eventually produce any shape made of any substance, including ... golden giraffes!



In reply to by Anthony Danalis

Peter Adamson on 5 December 2018

Golden giraffes

Many thanks for that, and also for the kind words about the podcast! As for the golden giraffes all I can say is that this is not the first time I find myself living in the wrong possible world.

Kubelick on 11 September 2021

Monkey business

A. I find giraffes are INFINITELY better suited for thought experiments than monkeys.

And b: it is just a thought, being neither a mathematician nor philosopher by trade, how much of a dogma we can make of thoughts of interpretations of copies of interpretations etc. I found your reply, peter, to the question, why immerse oneself in detailed study of a subject one knows to be false, quite fascinating. And considering that an universe of thinkers have added, amended. Revised, embellished and whatnot say Aristotle's works, one inevitably examines or bares witness to collective thought and its ebbs and flows. Rather much larger tha just a scroll of say Aristotle's musings.


P. S. Okay, yes, i suppose it has been done: dogmas founded on wishywashy copies of inaccurate traslations of translations. 

Cliff Balkam on 19 May 2023

Time and Memory

Sorry to be so tardy responding to this excellent discussion, but I started with the podcasts with the medievals, then the Eastern Romans, then have gone back to 001 and have been working my way forward. Ah, time...

So I was surprised to hear no mention of memory in the context of a discussion of time. Clearly, there is no time, there is only change and memory. Time is an imagined or putative measure from a remembered past actual to an present actual, which is itself evanescent. As change proceeds, those who remember fall away, and we must rely, in the nominal present, on the evidence of past actuals, in the form of documents, natural records like dead trees, fossils, and geological strata, and the organization of these records in print, which amounts to spans of remote past to recent past. Time, like form, matter, essence, sense data, and most of the philosopher's armamentarium are fictions that seem to occupy or point to a perspective outside of change; they are the triumph of epistemology over ontology. When you consider how "nature likes to hide, it is easier to "know yourself."" 

In reply to by Cliff Balkam

Peter Adamson on 19 May 2023

Time and memory

The ancient philosopher for that insight is not Aristotle (though he did write a treatise on memory), but Augustine: his discussions of time, especially in the Confessions, heavily involve memory. I talk about this in one of the podcasts on him.

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