Is there a mathematical formula relating time and memory?

January 31, 2006 6:51 AM

Is there a mathematical formula relating time and memory?

I have been working for a while on the correlation between different kind of memory with different kind of mass media. Eventually, I looked for basic definitions relating time to memory in physics or mathematics... and couldn't find anything.

Time seems to be the only variable considered anywhere (with many kinds of time, each with its definition), whereas memory seems to be used as a given, not needing any mathematical definition.

I know the pitfalls of using common sense when it comes to science, but it's all I have for now; and here is the conundrum:
If you try to define time, ultimately it's "the measure of a difference".
Now, let's try memory: "the measure of a difference"????

No. That can't be. Memory and time are not the same thing. So I am wrong. Great. Somebody knows why. Please.

posted by bru to science & nature (16 comments total)

Geoffry Sonnabend, in his seminal work "Obliscence: Theories of Forgetting and the Problem of Matter," did some really interesting work in this area.

(It is not believed that Mr. Sonnabend bears any relation to Ileana Sonnabend, founder of the Sonnabend Gallery where Vito Acconci once sat under a ramp, notoriously.

(I <3 mjt.)
posted by TonyRobots at 7:38 AM on January 31, 2006

Sorry, typos:
...Ileana Sonnabend, founder of the Sonnabend Gallery...
posted by TonyRobots at 7:42 AM on January 31, 2006

Yes, you can get a qualatative measure of nostalgias per second (n/s) with the formula
t = 1/m * p
Where p is Proust's Constant, approx 2.14323

Ha ha, just kidding.

What do you mean by "memory" do you mean physical and chemical changes in the brain, or the subjective experience of those changes?

The former is an effect of physics on a physical object, an effect of time, really. The later is a subjective phenomenon.
posted by Capn at 8:15 AM on January 31, 2006

Wait a sec -- how can "the former" (aka "time") be "...an effect of time, really?" Time is its own effect? That's actually kind of heavy.

As for distinguishing memory as being a subjective phenomenon -- some have argued that time is a subjective phenomenon as well.
posted by TonyRobots at 8:30 AM on January 31, 2006

I'm not following what you mean by "time" and "memory" in reference to your question? Time as in long-term memories as opposed to short-term? Are you referring to retaining information after exposure to a data source? Scientifically speaking memory is the recording of information in a brain's neurons. But if you talk about a collective memory then that is something much different.
posted by JJ86 at 8:34 AM on January 31, 2006

What? Sorry, your post is really confusing and the answers so far aren't any clearer.

Perhaps you can start with information theory. Does that have anything to do with what you're asking about?
posted by Khalad at 8:41 AM on January 31, 2006

If you sit down and memorize a random fact, you will tend to forget it in 2 or 3 days. If you remind yourself of the fact just before you forget it, you can extend that by a little bit more. If you do this about 10 times in a row you should retain it for a decade or two, if you have a good memory..
posted by parallax7d at 8:51 AM on January 31, 2006

Well you can parse your way through this, I believe it may have what you are looking for: Modeling Hippocampal and Neocortical Contributions to Recognition
Memory: A Complementary-Learning-Systems Approach

posted by ozomatli at 8:58 AM on January 31, 2006

In signal processing, "Memory" is defined as needing to know values of x(t) at times other than the particular t you're looking at.

I'm not sure if it's what you're looking for though, as you need to know the entire transfer function; but perhaps you can find some works with signal degradation...
posted by arrhn at 9:10 AM on January 31, 2006

Paul Ricoeur's Memory, History, Forgetting has a pretty good discussion about the temporal nature of memory that stems from Aristotle through the big names in philosophy and what-not. I think you'll find there is a whole lot of uncertainty about the nature of memory that kind of precludes the creation of a mathematical formula.
posted by jmgorman at 9:40 AM on January 31, 2006

Thank you all.
I will read later all the links, although I am somewhat familiar with Shannon and I have to clarify my question: I don't mean it in terms of human memory but in a fundamental way (a fossile is a memory of an animal or a plant, with or wihtout human beings to read it). That's why I am looking for the possibility of a mathematical formula.

Wikipedia's definition is as good as many others: Time is currently one of the few fundamental quantities (quantities which cannot be defined via other quantities because there is nothing more fundamental known at present).
I certainly don't have the means nor the intention to go against any scientific knowledge, but I don't get this "fundamental" part.

I am no mathematician, but I can imagine something going like that:

For anything called A, there is a state called A1 at time T1. At time T2, A is in a different state A2 (this state includes all possible internal, spatial and external differences):
# If there is no time, there can't be any difference, right? So: A1= A2. No difference = no memory.
# If there is time, but there is no memory, there is no reference so:
A1 = whatever and A2 = whatever; nobody cares; nobody can care.
Note that it seems that there is now way to differentiate "memory with no time" and "time with no memory", because both = no memory.

Apparently, if there is no memory, there is no time. The end. So memory is more fundamental than time, or equally fudamental. So memory should be defined at least as codependent with time.

And obviously, I am wrong, right?
posted by bru at 9:47 AM on January 31, 2006

Typos. Sorry.
posted by bru at 10:02 AM on January 31, 2006

There is more than one type of "Time" and I think you are conflating two of them: Subjective Time and Mathematical Time. The latter can be treated just like an extra dimension, with dT handled in the same way as dX.

The former involves observers (us) somehow "moving" through time with the local present corresponding to a specified state of the universe. Its arguable what causes this phenomenon of subjective time but it may all be psychological - that is, as you say, memory, or rather the direction of anti-entropic flow (with our brain becoming more organized as it accumulates information about the surrounding universe) is what gives us this sense of motion. If nothing ever changed, there would be no change in our minds, there would be no "sense" of Time.

So, we cant characterize the flow of time but something we can characterize is different states and their organization. So it seems to me that the question you are asking is a question about thermodynamics more than anything else: The transition of a collection of objects from state A to state B can be characterized and also carries implicit information about its past state:

E.g If I see a nicely arranged set of billiard balls on the table, I can assume that at some past point somebody put them up there even though I have no memory of the event. The arrangement itself contains implicit information about its past.
posted by vacapinta at 10:27 AM on January 31, 2006

bru: So what you're saying is that the only reason we know time is passing is because we can think back to five seconds and remember that things were different. That's your point, right?

Well, you're completely right. What you've stumbled upon is that there is no empirical way to tell the difference between these two situations:

(a) We are living in one universe, moving through normal time.
(b) There is no real time, only an infinity of static universes, each one internally consistent and simultaneously in existence. We 'move' through the universes, thinking we're experiencing time, but in reality it's an illusion.

Now, this is indeed an interesting philosophical discussion. But you're trying to figure it out in terms of scientific formulae, and things that we can measure. That just makes no sense, because, by definition, we can't measure the differences between those two situations. Whether we're in scenario (a) or scenario (b), it makes no difference to what perceive.

Even more simply, I would argue that there is no difference between 'memory' and 'time' in the senses that you're using those words. Perhaps you could argue there's a philosophical difference, but there's no measurable, real-world difference.

You're actually using two words to talk about the same thing, and then noticing that you can't have one without the other, and that they must be equally fundamental. Yes, that's true, but it's not exactly an amazing discovery.

In conclusion, here is your formula:

Time = Memory
posted by chrismear at 10:38 AM on January 31, 2006

If there is time, but there is no memory, there is no reference so:
A1 = whatever and A2 = whatever; nobody cares; nobody can care.

"Caring" isn't necessary to differentiate between time and "memory". I can imagine a universe where there is no motion, but time still progresses.

An interesting avenue you might explore is automata, mathematically-defined "universes" with rules and a notion of time. By virtue of having sequences of states automata have time, but there isn't necessarily any "memory" involved. They can repeat states, or get locked into a static state that doesn't change. Information can be lost from one state to the next.

You need to figure out what it is you mean by memory before you continue this line of thought, really. Being very precise about your terms will make these ideas a lot less ambiguous and handwavy.
posted by Khalad at 11:00 AM on January 31, 2006

Apparently, if there is no memory, there is no time. The end. So memory is more fundamental than time, or equally fundamental. So memory should be defined at least as codependant with time.

And obviously, I am wrong, right?

Did time exist before humans? Time is independent to memory.
posted by ozomatli at 11:06 AM on January 31, 2006