Number memory

How many numbers do we store in our memory ? Did this decrease since we started to use electronic telephones (where we can store numbers and then forget them forever) ?

The other day, I left my cellphone in my office, and then had to call a number which should be familiar to me - and I discovered I did not remember it! That caused me a lot of frustration: I have the preconception that I am good at remembering numbers.

I thus decided to compile a simple list of numbers i know by heart.
You can fill a similar list on your own if you wish, and if I collect enough stats in comments below I will post some analysis.

Telephone numbers:
- local (6 to 8 digits): about 40
- off district (9 to 11 digits): about 10
- mobile numbers (10 digits): 2!

Social security, ID cards, Driving license (7 to 9 digits): 5
Credit card: none!
Lufthansa Senator card (15 digits): 1 - plus 5 digits for the pin!
ATM pin (4-5 digits): 2
Computer passwords (8 to 12 digits): 11

Mathematical and Physical constants:
- 3 to 6 digits: about 30
- 7 to 9 digits: 2 (pi=3.1415926 and sqrt(2)=1.4142135)
- more than 9 digits: 1 (that's e=2.71828182845)
- perfect squares (1 to 5 digits): about 100

Zip codes (CAP in Italy) (5 digits): about 10

Other miscellaneous (2 to 4 digits): O(100)

My list is certainly incomplete but cannot be grossly wrong. I can thus claim I allocate in my brain the less than formidable number of 2 kilobytes of memory to store numbers! Give it a 500% uncertainty to be on the safe side: definitely less than 10 kb!

That number is so tiny that I am staring at it in disbelief. Why, I do work with numbers day in and day out! How many times have I seen sqrt(3) displayed on my pocket calculator, to not feel embarassed now by not being able to remember the meager first 4 digits of it ? It's such a shame I am considering to avoid posting this.

On the other hand, our brain is definitely more adjusted to remembering things that benefit from our automatic processes of logical association: not numbers, but poetry, sentences, music. And only my Italian vocabulary probably occupies more than 300 kbytes of memory. Maybe 100 kbytes for the English vocabulary. Add some 200 kbytes for all the poems I know by heart (quite a few - you'd be surprised). Add maybe 50 kbytes for chess openings variations. Add 50 kbytes of Physics formulae (and this is probably an overestimate!). Add maybe 1Mbyte for piano pieces I can play by heart, and 200 kbytes for lyrics to go with those that I sing along.

Still, I'm unimpressed. My knowledge does not stop at vocabularies and poetry, but the small part of it which can easily be reduced to a sheer byte count is really ridiculous... Less than 10 megabytes ??? Come on! I have 100 trillion neuron synapses...

One often reads statements about how tiny is the portion of our brain we are able to use. I think that while it is true that by exercise and sheer will we can expand our byte-accountable memory by one or two orders of magnitude, most of our brain is used to store memories in
a sort of fuzzy logic - images, concepts, but not bit-by-bit maps of the original information our brain attempted to store. Our survival as men never depended on such precision...

Will it always be like that ? Probably: we now live constantly attached to our laptops, cellphones, tablet PCs, iPODs. Less and less of our bit-by-bit memory is needed. Actually, fewer and fewer people are taught to compute square roots, and divisions or multiplications are already beyond the skill of many. I remember a short story by Isaac Asimov (yes, always Asimov - I cherish him) dealing with a far future when nobody, but one man, can compute with paper and pencil, and he saves humanity with his powerful gift...

A partly-sucked mint to the first reader that suggests the title of that story.

Comments

[little miss demosthenes]

lol @ big oh notation and book teaser.

don’t worry doc, what you posted is pretty normal, and there shouldn't be any shame because you're not alone. like ben herbster once said, "the greatest waste in the world is the difference between what we are and what we could become." *a lot* of brain power is trashed. it isn't until we actually put things we commit to memory or use on a daily basis into categories, like you did, do we truly see how much we overrate ourselves.

then again, some people utilize their crunching capabilities, some don't - or simply can't. my great-aunt was rumored to play chess, watch soap operas, blabber on the phone, read the newspaper, and eat breakfast simultaneously every day. i never really believed that, but i guess it's definitely possible.

and, i had a chat with an old friend of mine that moved away when we were both in 7th grade. though we're both kind of good at math, we're strong in different areas. he continues to amaze me with his mental crunching abilities, whereas he says i'm more of the hilbert-girl -- conceptual to the core.

keep in mind too that a lot of things we could memorize, but we sort of ignore. if we were alert to every single action through the day, that would be another matter, eh?

cheers
-demie

[aalu paneer]

you forgot to recall that you also (and hopefully do) remember the family birth dates and anniversary dates!

[Tommaso Dorigo]

Hi Aalu,

good catch!
... but the total stays at a lame 10k even with those in... :(

Hi Demie,
computing. That's another matter IMO. As every strong chessplayer knows, to win a good game you have to memorize lots of games, AND to use your CPU to the utmost to compute more variations in more depth than your opponent. Surely, if you had a PC with a 3GHz CPU and a RAM of 10 kb you would be seriously considering using it as a bookend.
I tend to believe our brains has both a huge potential CPU and a great deal of available memory, as you do. How to best use both, that's the problem... Not just memorizing, but practicing intensive computing. That is the reasoning, I think, behind the commonplace that chessplayers are intelligent. Chess, in a sense, develops your CPU and keeps it in good shape, as admittedly many other human occupations do.
T.

[Amanda]

I used to know almost all my friend's phone numbers by heart, but quit doing that once I got a cell phone and started using the "Add Contact" feature. Now I barely know any of them.

I know:
-80 digits of Pi (yes, I typed that number correctly)
-8 digits of e (for some reason, e's never interested me enough to memorize)
-One of my library card accounts
-Student number
-SS Number

It's kind of a shame that I don't know more, really.
--Amanda

[Chris Lee]

Tommaso, Dont feel that bad, I started to try and think of all the numbers that I can remember and its about a 3rd... if not less of what you put up there.

Of course I have never been good at remembering numbers but before cell phones as you said, I used to be proud of the fact that I never used to even own a telephone book with friends and family numbers and could recite 90% of them without thinking twice. Now days its not the case.

Birthdays I excuse myself from as I believe I am one of those people who will never remember them, Though I must say I can remember friends from junior schools birthdays, but never their Telephone numbers to phone them.

The only plus side I believe is that there is a whole lot of other information stored with those numbers we do remember. Last 10 to 20 times you phoned, What you said, How long you spoke. When you last typed in that computer password, how many times you forgot CAPS lock on when typing it, how much money you have in the bank from when you last used your bank card (or how much you owe the bank usually in my case).

Compound that with other data like how your coffee smelt and tasted when you logged into to your PC this morning and where the keys are located on the keyboard (even if some people cant seem to remember that), etc

What I dont understand is why with all that information stored away, I can never remember where I left my car keys 5 mins ago?

[Jason Freeman]

This is an interesting discussion! One of my favorite books, although it is a bit technical, is "Wider than the Sky: The Phenomenal Gift of Consciousness" by Gerald Edelman (Nobel Prize winner).

I have one response to your comment: "Surely, if you had a PC with a 3GHz CPU and a RAM of 10 kb you would be seriously considering using it as a bookend." Keeping the computer analogy going (although it is an imperfect one for the brain) isn't it possible that our software is so far superior to PC software that 10 KB of RAM is sufficient? I have always thought of myself as having a so-so memory (especially short term!) but outstanding association skills. Thus, information can fly through the system in ways that MS Windows has never imagined!

Pattern recognition, etc., explains why I can cross a street more easily than a robot. I don't actually input and process the speed, distance, and size of every car or other obstacle. My brain processes the situation and relates it to similar ones.

I think this makes my conclusion that remembering passwords and phone numbers is better done by computers, which is why I am such a frequent user of the "Forgot your PIN" link on multiple websites!

Thanks for the interesting conversation starter! -Jason

[Doug Abe]

I think your story is "The Feeling of Power," 1958, in which Asimov's future has a technician dabbling in numerical computation without a machine. This incidentally leads to the idea of the memorable Manned missile, as a cost-saving alternative to computer-guided weaponry.
I remembered this story and have described it to many of my calculator-fixated students, but your entry prompted me to look up it's title...

[Quantoken]

As for memory for numbers, no one I know is better than me. My favorite is PI, at some point I memorized 10000 digits. And for more than 10 years I still remember no less than 600 digits. And I believe I can keep 200-300 digits for the rest of my life.

My favorite way of generating a computer password, used to be to pick a nominal number N, and then count a few digits starting from the N-th decimal places of PI, certainly skipping a few, and I get a password I could never forget and no one could ever guessed. But I have since abandoned PI and picked another number for this purpose.

Quantoken
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502483021019385211055596446229489549303819644288...gosh I forget. I guess I am getting older :-)

[Tommaso Dorigo]

Hi Jason,

I will take a look at the book you mention, I am typically intrigued by books on that sort of argument. And I've recently read too many books on mountaineering, want to switch topics. As for the software question, I think you can do a lot with a good software, but you cannot extract blood from a stone: information is a constant, you cannot materialize it from nothing. More interesting is asking oneself where do we exactly store our bits, and if - by using the brain as a whole, we can store more than a number of the order of our synapses count. In principle, the position of the synapses relative to each other requires tons more information to be specified with accuracy, and thus can also hold a similar
amount of information to a software able to decode it.

Hi Doug,

thanks for the title. IOU a sucked mint :) the story is the one you mention indeed. A nice one.

Hi Quantoken,

Wow, congratulations... So you're one of those weird few who can do that. I've known
stories of people able to remember many digits of pi.
10000 digits, 10 kbytes. Anyhow, not very far from my estimate of the max amount of bit-by-bit memory we use to store numbers. Certainly that varies from one person to the next, but it is interesting to know there is a physiological order of magnitude of how much we can store. I think much of that has to do with the time needed to write down those bits. It takes a lot of time to memorize each byte compared to the access time of a computer.... Maybe this is the limiting factor, in the end.

Cheers to all!
Tommaso

[Quantoken]

Sorry, I typed one too many 0's. I memorized 1000 digits of PI, not 10000 digits. I spent one whole day to do it at the age of 10, for fun. The main limiting factor is I could not find data source of more digits of PI. I wrote a BASIC program, using a Tylor Series that I discovered to compute those digits on an Apple II. It's be almost 10 years since last time I attempted to write down the digits of PI, so looks like I could only get the first 200- digits correct now.

I heard the world record is one million digits, which I do not believe. It takes too much time to even read the number through, and many pages of paper to write it down, too.

Quantoken

[jimbo92107]

Tommaso,

I don't understand why you express neural memory in kilobytes, since neural and digital memories have so little in common. One can pinpoint the exact location of 3.14 stored in RAM or on a hard disk, but where can you "find" it among a tangle of neurons?

The problem is that for each person 3.14 is stored/recollected in an individual way, depending on which neurons were originally stimulated with that value, and to which associated neurons that value was connected. And do we even "store" the number at all, or would it be more accurate to say that we store a jumble of emotionally linked neural impressions, some of which may include an image of the first time you saw pi written on a chalkboard?

In any case, it doesn't surprise me that people actively recall fewer and fewer wrote numerical values. What would be the point? It's like the names of your neighbors in a big apartment complex--why remember them, if they're just going to move away within a couple years? Why invest the emotional energy required to remember their names, much less their phone numbers, which change even more often?

Remembering numbers may also have something to do with the way we recognize patterns, like faces. Mathmatical savant Daniel Tammet described his own experience remembering numbers. He said that each number had its own shape, size, texture and evoked a unique emotional reaction. That sounds more than a bit like the way we recognize faces.

Humans have not needed to memorize numbers for more than a few thousand years, but we are capable of great feats of internal evolution. Maybe we can teach ourselves what Daniel Tammet learned by virtue of his pathology--to regard each number as a thing with its own personality. Then interactions between numbers becomes interactions between personalities, and we can predict the outcomes as we would write a dialog among acquaintences.

[Karen]

Hi Tommaso

What a flurry of responses your posting generated! Just an interesting tidbit to add to the flurry - I think it was Tony Buzan (he of mind map fame) who suggested that to get an idea of the number of possible interconnections between neurons that we have in our brains is a 1 followed by 10 km of typed zeros.

Quite a thoiught!

Cheers