TED2010
Benoit Mandelbrot: Fractals and the art of roughness
Benuā Mandelbrots: Fraktāļi un raupjuma māksla
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Matemātikas leģenda Benuā Mandelbrots TED2010 turpina savu 1984. gada TED konferencē aizsākto tēmu -- ārkārtīgo raupjuma sarežģītību un to, kā fraktāļu matemātika spēj atrast kārtību struktūrās, kas šķiet neiedomājami sarežģītas.
Benoit Mandelbrot - Mathematician
Benoit Mandelbrot's work led the world to a deeper understanding of fractals, a broad and powerful tool in the study of roughness, both in nature and in humanity's works. Full bio
Benoit Mandelbrot's work led the world to a deeper understanding of fractals, a broad and powerful tool in the study of roughness, both in nature and in humanity's works. Full bio
Double-click the English transcript below to play the video.
00:15
Thank you very much.
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Liels jums paldies!
00:17
Please excuse me for sitting; I'm very old.
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Lūdzu, atvainojiet, ka sēžu; esmu ļoti vecs.
00:20
(Laughter)
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(Smiekli)
00:22
Well, the topic I'm going to discuss
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Tēma, par ko es stāstīšu,
00:24
is one which is, in a certain sense, very peculiar
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savā ziņā ir ļoti īpatnēja,
00:27
because it's very old.
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jo tā ir ļoti sena.
00:29
Roughness is part of human life
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Raupjums ir daļa no cilvēku dzīves
00:32
forever and forever,
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mūžīgi mūžos.
00:34
and ancient authors have written about it.
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Un seni autori par to ir rakstījuši.
00:37
It was very much uncontrollable,
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Tas bija ļoti nekontrolējams.
00:39
and in a certain sense,
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Un savā ziņā
00:41
it seemed to be the extreme of complexity,
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tas šķita esam sarežģītības galējība,
00:44
just a mess, a mess and a mess.
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tikai juceklis, juceklis un vēlreiz juceklis.
00:46
There are many different kinds of mess.
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Ir dažādu veidu jucekļi.
00:48
Now, in fact,
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Patiesībā,
00:50
by a complete fluke,
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pavisam nejauši
00:52
I got involved many years ago
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daudzus gadus atpakaļ es iesaistījos
00:55
in a study of this form of complexity,
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pētījumā par šo sarežģītības veidu.
00:58
and to my utter amazement,
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Es biju ļoti izbrīnīts,
01:00
I found traces --
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kad atradu pazīmes --
01:02
very strong traces, I must say --
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jāsaka, ļoti spēcīgas pazīmes --
01:04
of order in that roughness.
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kārtībai šajā raupjumā.
01:07
And so today, I would like to present to you
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Un tāpēc šodien es vēlos jums parādīt
01:09
a few examples
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dažus piemērus,
01:11
of what this represents.
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kas to ilustrēs.
01:13
I prefer the word roughness
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Es labāk lietoju vārdu "raupjums",
01:15
to the word irregularity
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nevis "neregularitāte",
01:17
because irregularity --
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jo "neregularitāte" --
01:19
to someone who had Latin
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man, kurš mācījies latīņu valodu,
01:21
in my long-past youth --
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manā sen aizgājušajā jaunībā --
01:23
means the contrary of regularity.
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nozīmē "pretstats regularitātei".
01:25
But it is not so.
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Bet tas tā nav.
01:27
Regularity is the contrary of roughness
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Regularitāte ir raupjuma pretstats,
01:30
because the basic aspect of the world
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jo pasaule savā būtībā
01:32
is very rough.
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ir ļoti raupja.
01:34
So let me show you a few objects.
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Ļaujiet jums parādīt pāris lietas.
01:37
Some of them are artificial.
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Dažas no tām ir mākslīgas.
01:39
Others of them are very real, in a certain sense.
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Dažas no tām ir savā ziņā ļoti dabīgas.
01:42
Now this is the real. It's a cauliflower.
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Šī ir dabīgā. Tas ir ziedkāposts.
01:45
Now why do I show a cauliflower,
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Kāpēc es rādu ziedkāpostu,
01:48
a very ordinary and ancient vegetable?
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ļoti ikdienišķu un senu dārzeni?
01:51
Because old and ancient as it may be,
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Tāpēc, ka, lai arī cik sens tas nebūtu,
01:54
it's very complicated and it's very simple,
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tas ir ļoti sarežģīts un ļoti vienkāršs
01:57
both at the same time.
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vienlaikus.
01:59
If you try to weigh it -- of course it's very easy to weigh it,
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Ja jūs mēģināsiet to nosvērt, tas, protams, būs ļoti vienkārši.
02:02
and when you eat it, the weight matters --
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Un, kad jūs to ēdat, svarīgais ir svars.
02:05
but suppose you try to
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Bet iedomājieties, ka vēlaties
02:08
measure its surface.
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izmērīt tā virsmas laukumu.
02:10
Well, it's very interesting.
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Tas jau ir interesantāk.
02:12
If you cut, with a sharp knife,
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Ja jūs ar asu nazi nogriežat
02:15
one of the florets of a cauliflower
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vienu no ziedkāposta ziediem
02:17
and look at it separately,
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un apskatāt to atsevišķi,
02:19
you think of a whole cauliflower, but smaller.
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jūs redzat veselu ziedkāpostu, tikai mazāku.
02:22
And then you cut again,
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Un tad jūs griežat atkal
02:24
again, again, again, again, again, again, again, again,
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un atkal, un atkal, un atkal, un atkal, un atkal.
02:27
and you still get small cauliflowers.
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Un jums vēl arvien ir mazs ziedkāposts.
02:29
So the experience of humanity
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Tātad cilvēces pieredzē
02:31
has always been that there are some shapes
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vienmēr ir bijušas kontūras,
02:34
which have this peculiar property,
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kurām ir šī īpatnējā īpašība,
02:36
that each part is like the whole,
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ka katra daļa ir kā veselums,
02:39
but smaller.
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tikai mazāka.
02:41
Now, what did humanity do with that?
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Ko cilvēce ar to darīja?
02:44
Very, very little.
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Ļoti, ļoti maz.
02:47
(Laughter)
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(Smiekli)
02:50
So what I did actually is to
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Savukārt es
02:53
study this problem,
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pētīju šo problēmu
02:56
and I found something quite surprising.
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un atklāju ko ļoti pārsteidzošu.
02:59
That one can measure roughness
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Mēs varam izmērīt raupjumu
03:02
by a number, a number,
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un apzīmēt to ar skaitli,
03:05
2.3, 1.2 and sometimes much more.
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piemēram, 2,3, 1,2, un dažreiz daudz vairāk.
03:08
One day, a friend of mine,
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Kādu dienu mans draugs,
03:10
to bug me,
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lai pakaitinātu mani,
03:12
brought a picture and said,
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atnesa bildi un teica:
03:14
"What is the roughness of this curve?"
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"Kāds ir šīs līnijas raupjums?"
03:16
I said, "Well, just short of 1.5."
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Es teicu: "Nu, gandrīz 1,5."
03:19
It was 1.48.
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Tas bija 1,48.
03:21
Now, it didn't take me any time.
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Tas man neaizņēma daudz laika.
03:23
I've been looking at these things for so long.
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Esmu skatījies uz šīm lietām tik ilgi.
03:25
So these numbers are the numbers
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Tātad šie skaitļi ir tas,
03:27
which denote the roughness of these surfaces.
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kas apzīmē virsmas raupjumu.
03:30
I hasten to say that these surfaces
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Piebildīšu, ka šīs virsmas
03:32
are completely artificial.
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ir pilnībā mākslīgas.
03:34
They were done on a computer,
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Tās tika izveidotas ar datoru.
03:36
and the only input is a number,
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Un vienīgais ievadītais lielums ir skaitlis.
03:38
and that number is roughness.
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Un šis skaitlis ir raupjums.
03:41
So on the left,
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Tātad, kreisajā pusē
03:43
I took the roughness copied from many landscapes.
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es paņēmu raupjumu no daudziem dabas skatiem.
03:46
To the right, I took a higher roughness.
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Labajā pusē, es paņēmu lielāku raupjumu.
03:49
So the eye, after a while,
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Pēc kāda laika acs
03:51
can distinguish these two very well.
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spēj šīs abas ļoti labi atšķirt.
03:54
Humanity had to learn about measuring roughness.
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Cilvēcei bija jāiemācās izmērīt raupjumu.
03:56
This is very rough, and this is sort of smooth, and this perfectly smooth.
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Šis ir ļoti raupjš, šis ir samērā raupjš, un šis ir ļoti gluds.
03:59
Very few things are very smooth.
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Tikai nedaudzas lietas ir ļoti gludas.
04:03
So then if you try to ask questions:
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Kas notiek, ja jūs uzdodat jautājumu:
04:06
"What's the surface of a cauliflower?"
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"Kāds ir ziedkāposta virsmas laukums?"
04:08
Well, you measure and measure and measure.
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Jūs mērāt un mērāt, un mērāt.
04:11
Each time you're closer, it gets bigger,
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Katrreiz pietuvinoties tas kļūst arvien lielāks
04:14
down to very, very small distances.
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līdz pat ļoti, ļoti maziem attālumiem.
04:16
What's the length of the coastline
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Kāds ir šī ezera krasta
04:18
of these lakes?
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garums?
04:20
The closer you measure, the longer it is.
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Jo tuvāk jūs mērāt, jo garāks tas ir.
04:23
The concept of length of coastline,
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Priekšstats par krasta līnijas garumu,
04:25
which seems to be so natural
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kas šķiet tik dabīga,
04:27
because it's given in many cases,
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jo tā ir bieži norādīta,
04:29
is, in fact, complete fallacy; there's no such thing.
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patiesībā ir pilnīgas muļķības; tas neeksistē.
04:32
You must do it differently.
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Tas jādara citādāk.
04:35
What good is that, to know these things?
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Ko dod šo lietu zināšana?
04:37
Well, surprisingly enough,
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Patiesībā, pārsteidzošā kārtā,
04:39
it's good in many ways.
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tas ir daudzējādā ziņā noderīgi.
04:41
To begin with, artificial landscapes,
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Iesākumam, mākslīgie dabasskati,
04:43
which I invented sort of,
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kurus es savā ziņā izgudroju,
04:45
are used in cinema all the time.
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bieži tiek izmantoti kino.
04:48
We see mountains in the distance.
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Mēs tālumā redzam kalnus.
04:50
They may be mountains, but they may be just formulae, just cranked on.
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Tie varētu būt kalni, bet tie varētu būt arī vienkārši funkciju grafiki.
04:53
Now it's very easy to do.
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Tagad to izdarīt ir ļoti viegli.
04:55
It used to be very time-consuming, but now it's nothing.
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Agrāk tas paņēma ļoti daudz laika, bet tagad tas nav nekas.
04:58
Now look at that. That's a real lung.
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Tagad apskatiet šo. Tās ir īstas plaušas.
05:01
Now a lung is something very strange.
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Plaušas ir kaut kas ļoti dīvains.
05:03
If you take this thing,
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Ja jūs tās paceļat,
05:05
you know very well it weighs very little.
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jūs ļoti labi zināt, ka tās sver ļoti maz.
05:08
The volume of a lung is very small,
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Plaušu tilpums ir ļoti mazs.
05:10
but what about the area of the lung?
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Bet kā ar plaušu virsmas laukumu?
05:13
Anatomists were arguing very much about that.
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Anatomi par šo ļoti daudz strīdējās.
05:16
Some say that a normal male's lung
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Daži saka, ka parastu vīrieša plaušu
05:19
has an area of the inside
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virsmas laukums ir tāds pats
05:21
of a basketball [court].
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kā basketbola [laukumam].
05:23
And the others say, no, five basketball [courts].
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Citi saka: "Nē, pieciem basketbola [laukumiem]."
05:27
Enormous disagreements.
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Milzīgas domstarpības.
05:29
Why so? Because, in fact, the area of the lung
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Kāpēc tā? Tāpēc, ka plaušu virsmas laukuma jēdziens
05:32
is something very ill-defined.
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ir ļoti slikti definēts.
05:35
The bronchi branch, branch, branch
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Bronhi sazarojas, sazarojas, sazarojas,
05:38
and they stop branching,
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un tie pārstāj sazarošanos
05:41
not because of any matter of principle,
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ne kāda īpaša principa dēļ,
05:44
but because of physical considerations:
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bet fizikālu apsvērumu,
05:47
the mucus, which is in the lung.
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plaušu gļotu dēļ.
05:50
So what happens is that in a way
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Tādējādi sanāk, ka
05:52
you have a much bigger lung,
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jums ir krietni lielākas plaušas,
05:54
but it branches and branches
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kuras sazarojas un sazarojas
05:56
down to distances about the same for a whale, for a man
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līdz zaru izmēriem, kas ir aptuveni vienādi valim, cilvēkam
05:59
and for a little rodent.
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un mazam grauzējam.
06:02
Now, what good is it to have that?
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Bet kāds no tā labums?
06:05
Well, surprisingly enough, amazingly enough,
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Pārsteidzošā kārtā
06:07
the anatomists had a very poor idea
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anatomiem vēl pavisam nesen
06:10
of the structure of the lung until very recently.
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bija ļoti vāja izpratne par plaušu uzbūvi.
06:13
And I think that my mathematics,
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Un es domāju, ka mana matemātika,
06:15
surprisingly enough,
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pārsteidzošā kārtā,
06:17
has been of great help
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ir ļoti palīdzējusi
06:19
to the surgeons
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ķirurgiem,
06:21
studying lung illnesses
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pētot plaušu slimības,
06:23
and also kidney illnesses,
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kā arī nieru slimības,
06:25
all these branching systems,
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visas šīs sazarotās sistēmas,
06:27
for which there was no geometry.
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kurām nebija ģeometrijas.
06:30
So I found myself, in other words,
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Citiem vārdiem sakot, es attapos,
06:32
constructing a geometry,
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veidojot ģeometriju lietām,
06:34
a geometry of things which had no geometry.
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kurām nebija ģeometrijas.
06:37
And a surprising aspect of it
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Un pārsteidzoši ir tas,
06:39
is that very often, the rules of this geometry
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ka ļoti bieži šīs ģeometrijas likumi
06:42
are extremely short.
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ir ļoti īsi.
06:44
You have formulas that long.
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Jums ir tik garas formulas.
06:46
And you crank it several times.
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Un jūs tās pielietojas vairākas reizes.
06:48
Sometimes repeatedly: again, again, again,
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Reizēm atkārtoti atkal un atkal, un atkal.
06:50
the same repetition.
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Tie paši atkārtojumi.
06:52
And at the end, you get things like that.
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Un beigās jūs iegūstat kaut ko šādu.
06:54
This cloud is completely,
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Šis mākonis ir pilnībā,
06:56
100 percent artificial.
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100% mākslīgs.
06:59
Well, 99.9.
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Nu, 99,9%.
07:01
And the only part which is natural
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Vienīgā dabīgā daļa ir
07:03
is a number, the roughness of the cloud,
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skaitlis, mākoņa raupjums,
07:05
which is taken from nature.
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kas ir paņemts no dabas.
07:07
Something so complicated like a cloud,
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Kaut ko tik sarežģītu kā mākonis,
07:09
so unstable, so varying,
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tik nenoturīgu, tik mainīgu,
07:11
should have a simple rule behind it.
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vajadzētu varēt aprakstīt ar vienkāršu likumu.
07:14
Now this simple rule
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Šis vienkāršais likums
07:17
is not an explanation of clouds.
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nav mākoņu skaidrojums.
07:20
The seer of clouds had to
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Mākoņu vērotājam
07:22
take account of it.
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tas jāņem vērā.
07:24
I don't know how much advanced
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Es nezinu, cik attīstītas
07:27
these pictures are. They're old.
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šīs bildes ir. Tās ir vecas.
07:29
I was very much involved in it,
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Es šeit biju aktīvi iesaistīts,
07:31
but then turned my attention to other phenomena.
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bet tad pievērsos citām parādībām.
07:34
Now, here is another thing
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Šeit ir cita lieta,
07:36
which is rather interesting.
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kas ir diezgan interesanta.
07:39
One of the shattering events
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Viens no graujošākajiem notikumiem
07:41
in the history of mathematics,
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matemātikas vēsturē,
07:43
which is not appreciated by many people,
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ko daudzi nenovērtē,
07:46
occurred about 130 years ago,
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notika pirms 130 gadiem,
07:48
145 years ago.
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pirms 145 gadiem.
07:50
Mathematicians began to create
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Matemātiķi sāka veidot
07:52
shapes that didn't exist.
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kontūras, kas neeksistēja.
07:54
Mathematicians got into self-praise
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Matemātiķi sāka sevi slavēt
07:57
to an extent which was absolutely amazing,
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tādā apjomā, kas bija vienkārši pārsteidzošs,
07:59
that man can invent things
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ka cilvēks spēj izgudrot lietas,
08:01
that nature did not know.
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ko daba nepazina.
08:03
In particular, it could invent
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Precīzāk, cilvēks spēja izgudrot tādas lietas
08:05
things like a curve which fills the plane.
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kā līniju, kas aizpilda plakni.
08:08
A curve's a curve, a plane's a plane,
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Līnija ir līnija un plakne ir plakne,
08:10
and the two won't mix.
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un tie neiet kopā.
08:12
Well, they do mix.
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Patiesībā tie iet kopā.
08:14
A man named Peano
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Vīrs vārdā Peano
08:16
did define such curves,
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definēja šādas līnijas,
08:18
and it became an object of extraordinary interest.
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un tās kļuva par ārkārtīgas intereses objektu.
08:21
It was very important, but mostly interesting
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Tas bija ļoti nozīmīgi, bet galvenokārt interesanti,
08:24
because a kind of break,
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jo parādījās tāda kā plaisa,
08:26
a separation between
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dalījums starp matemātiku,
08:28
the mathematics coming from reality, on the one hand,
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kas nākusi no reālās pasaules,
08:31
and new mathematics coming from pure man's mind.
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un jauno matemātiku, kas nākusi no tīrā cilvēka saprāta.
08:34
Well, I was very sorry to point out
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Nu, es ar nožēlu norādīju,
08:37
that the pure man's mind
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ka tīrais cilvēka saprāts
08:39
has, in fact,
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ir, patiesībā,
08:41
seen at long last
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beidzot pamanījis to,
08:43
what had been seen for a long time.
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kas bija redzams jau sen.
08:45
And so here I introduce something,
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Un šeit es jūs iepazīstinu
08:47
the set of rivers of a plane-filling curve.
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ar plakni piepildošu upju kopu.
08:50
And well,
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Un, patiesībā,
08:52
it's a story unto itself.
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tas ir stāsts pats par sevi.
08:54
So it was in 1875 to 1925,
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Tas bija no 1875. līdz 1925. gadam,
08:57
an extraordinary period
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ārkārtīgi neparasts laiks,
08:59
in which mathematics prepared itself to break out from the world.
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kurā matemātika gatavojās izrauties no pasaules.
09:02
And the objects which were used
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Un objekti, kuri tika izmantoti
09:04
as examples, when I was
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kā piemēri, kad es biju
09:06
a child and a student, as examples
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bērns un skolnieks,
09:08
of the break between mathematics
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kas parāda plaisu starp matemātiku
09:11
and visible reality --
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un redzamo pasauli --
09:13
those objects,
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šos objektus
09:15
I turned them completely around.
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es apgriezu kājām gaisā.
09:17
I used them for describing
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Es tos izmantoju, lai aprakstītu
09:19
some of the aspects of the complexity of nature.
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dažus dabas sarežģītības aspektus.
09:22
Well, a man named Hausdorff in 1919
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Vīrs vārdā Hausdorfs 1919. gadā
09:25
introduced a number which was just a mathematical joke,
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ieviesa skaitli, kas bija vienkārši matemātisks joks.
09:28
and I found that this number
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Un es atklāju, ka šis skaitlis
09:30
was a good measurement of roughness.
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bija labs raupjuma mērs.
09:32
When I first told it to my friends in mathematics
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Kad es to pirmo reizi pateicu saviem draugiem matemātiķiem,
09:34
they said, "Don't be silly. It's just something [silly]."
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viņi teica: "Neesi vientiesis! Tas vienkārši ir kaut kas [muļķīgs]."
09:37
Well actually, I was not silly.
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Patiesībā, es nebiju vientiesis.
09:40
The great painter Hokusai knew it very well.
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Lieliskais gleznotājs Hokusai to zināja ļoti labi.
09:43
The things on the ground are algae.
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Tās lietas uz zemes ir aļģes.
09:45
He did not know the mathematics; it didn't yet exist.
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Viņš nezināja šo matemātiku; tā vēl nepastāvēja.
09:48
And he was Japanese who had no contact with the West.
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Un viņš bija japānis, kuram nebija nekādu sakaru ar Rietumiem.
09:51
But painting for a long time had a fractal side.
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Bet glezniecībā ilgu laiku bija fraktāļu aspekts.
09:54
I could speak of that for a long time.
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Es varētu ilgi par to runāt.
09:56
The Eiffel Tower has a fractal aspect.
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Eifeļa tornim ir fraktāļu aspekts.
09:59
I read the book that Mr. Eiffel wrote about his tower,
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Un es izlasīju grāmatu, ko Eifeļa kungs uzrakstīja par savu torni.
10:02
and indeed it was astonishing how much he understood.
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Un tas bija patiešām pārsteidzoši, cik daudz viņš saprata.
10:05
This is a mess, mess, mess, Brownian loop.
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Tas ir juceklis, juceklis, juceklis, Brauna kustības shēma.
10:08
One day I decided --
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Kādu dienu, savas karjeras pusceļā,
10:10
halfway through my career,
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es sapratu, ka
10:12
I was held by so many things in my work --
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manā darbā mani turēja tik daudz lietu,
10:15
I decided to test myself.
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tāpēc nolēmu sevi pārbaudīt.
10:18
Could I just look at something
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Vai es varētu vienkārši apskatīties uz kaut ko,
10:20
which everybody had been looking at for a long time
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ko visi bija vērojuši jau ilgu laiku,
10:23
and find something dramatically new?
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un atrast ko dramatiski jaunu?
10:26
Well, so I looked at these
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Nu, es apskatījos šīs lietas,
10:29
things called Brownian motion -- just goes around.
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ko sauc par Brauna kustību -- vienkārši nejauša kustība.
10:32
I played with it for a while,
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Es paspēlējos ar to kādu laiku
10:34
and I made it return to the origin.
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un liku atgriezties sākumpunktā.
10:37
Then I was telling my assistant,
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Tad es teicu savam palīgam:
10:39
"I don't see anything. Can you paint it?"
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"Es neko neredzu. Vai vari to uzzīmēt?"
10:41
So he painted it, which means
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Viņš to uzzīmēja, kas nozīmē,
10:43
he put inside everything. He said:
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ka viņš visu aizpildīja. Viņš teica:
10:45
"Well, this thing came out ..." And I said, "Stop! Stop! Stop!
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"Nu, sanāca šis..." Un es teicu: "Stāt, stāt, stāt!
10:48
I see; it's an island."
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Es redzu, tā ir sala."
10:51
And amazing.
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Un -- pārsteidzoši --
10:53
So Brownian motion, which happens to have
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šī Brauna kustība, kurai gadījuma pēc
10:55
a roughness number of two, goes around.
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raupjuma skaitlis ir 2, iet apkārt,
10:58
I measured it, 1.33.
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es to izmēru, 1,33,
11:00
Again, again, again.
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atkal un atkal, un atkal.
11:02
Long measurements, big Brownian motions,
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Ilgi mērījumi, plaša Brauna kustība,
11:04
1.33.
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1,33.
11:06
Mathematical problem: how to prove it?
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Matemātiska problēma -- kā to pierādīt?
11:09
It took my friends 20 years.
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Tas aizņēma maniem draugiem 20 gadus.
11:12
Three of them were having incomplete proofs.
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Trim no viņiem bija nepilnīgi pierādījumi.
11:15
They got together, and together they had the proof.
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Viņi sanāca kopā, un kopā viņiem sanāca pierādījums.
11:19
So they got the big [Fields] medal in mathematics,
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Un viņi saņēma lielo [Fīldsa] medaļu matemātikā,
11:22
one of the three medals that people have received
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vienu no trim medaļām, ko cilvēki ir saņēmuši par to,
11:24
for proving things which I've seen
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ka pierādījuši lietas, ko esmu redzējis,
11:27
without being able to prove them.
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bet neesmu spējis pierādīt.
11:30
Now everybody asks me at one point or another,
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Tagad katrs kādā brīdī man prasa:
11:33
"How did it all start?
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"Kā tas viss sākās?
11:35
What got you in that strange business?"
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Kas Jūs ievilka šajā dīvainajā nodarbē?
11:38
What got you to be,
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Kas lika Jums kļūt
11:40
at the same time, a mechanical engineer,
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vienlaikus par inženieri-mehāniķi,
11:42
a geographer
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ģeogrāfu,
11:44
and a mathematician and so on, a physicist?
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matemātiķi, fiziķi un tā tālāk?"
11:46
Well actually I started, oddly enough,
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Nu, patiesībā, es sāku, neparastā kārtā,
11:49
studying stock market prices.
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pētot akciju tirgus cenas.
11:51
And so here
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Un tā šeit
11:53
I had this theory,
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man radās šī teorija,
11:56
and I wrote books about it --
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un es par to sarakstīju grāmatas
11:58
financial prices increments.
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Finanšu cenu svārstības.
12:00
To the left you see data over a long period.
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Kreisajā pusē jūs redzat datus par ilgu laika periodu.
12:02
To the right, on top,
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Labajā pusē augšā
12:04
you see a theory which is very, very fashionable.
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jūs redzat teoriju, kas ir ļoti, ļoti populāra.
12:07
It was very easy, and you can write many books very fast about it.
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Tā bija ļoti vienkārša un jūs par to varat uzrakstīt daudzas grāmatas ļoti ātri.
12:10
(Laughter)
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(Smiekli)
12:12
There are thousands of books on that.
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Par to ir tūkstošiem grāmatu.
12:15
Now compare that with real price increments.
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Tagad salīdziniet to ar patiesajām cenu svārstībām.
12:18
Where are real price increments?
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Kur ir patiesās cenu svārstības?
12:20
Well, these other lines
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Dažas no šīm pārējām līnijām
12:22
include some real price increments
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ir patiesās cenu svārstības,
12:24
and some forgery which I did.
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dažas -- mani viltojumi.
12:26
So the idea there was
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Ideja šeit bija tāda,
12:28
that one must be able to -- how do you say? --
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ka ir jāspēj -- kā to saka? --
12:30
model price variation.
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modelēt cenu svārstības.
12:33
And it went really well 50 years ago.
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Un pirms 50 gadiem tas izdevās ļoti labi.
12:36
For 50 years, people were sort of pooh-poohing me
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50 gadus cilvēki tā kā nievāja mani,
12:39
because they could do it much, much easier.
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jo viņi to varēja izdarīt krietni vienkāršāk.
12:41
But I tell you, at this point, people listened to me.
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Bet es jums teikšu, ka šobrīd cilvēki manī klausās!
12:44
(Laughter)
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(Smiekli)
12:46
These two curves are averages:
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Šīs divas līknes ir vidējie.
12:48
Standard & Poor, the blue one;
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Standard & Poor's ir zilā līnija.
12:50
and the red one is Standard & Poor's
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Sarkanā ir Standard & Poor's,
12:52
from which the five biggest discontinuities
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no kura ir izņemti ārā
12:55
are taken out.
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pieci lielākie vienas dienas lēcieni.
12:57
Now discontinuities are a nuisance,
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Lēcieni ir traucēklis.
12:59
so in many studies of prices,
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Tāpēc daudzos cenu pētījumos
13:02
one puts them aside.
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tās noliek malā.
13:04
"Well, acts of God.
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"Nu, Dieva darbi."
13:06
And you have the little nonsense which is left.
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Un jums pāri paliek tā nelielā bezjēdzība.
13:09
Acts of God." In this picture,
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Dieva darbi šajā bildē,
13:12
five acts of God are as important as everything else.
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pieci Dieva darbi ir tikpat nozīmīgi kā jebkas cits.
13:15
In other words,
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Citiem vārdiem,
13:17
it is not acts of God that we should put aside.
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tie nav Dieva darbi, ko vajadzētu nolikt malā.
13:19
That is the meat, the problem.
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Tā ir problēmas būtība.
13:22
If you master these, you master price,
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Ja jūs pārvaldāt šos, jūs pārvaldāt cenas.
13:25
and if you don't master these, you can master
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Bet, ja jūs nepārvaldāt šos, jūs varat pārvaldīt
13:27
the little noise as well as you can,
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to mazo troksni, cik labi varat,
13:29
but it's not important.
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bet tas nav svarīgi.
13:31
Well, here are the curves for it.
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Nu, šeit tam ir līknes.
13:33
Now, I get to the final thing, which is the set
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Te es nonāku pie pēdējās lietas, kas ir tā kopa,
13:35
of which my name is attached.
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kurai ir pievienots mans vārds.
13:37
In a way, it's the story of my life.
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Savā ziņā tā ir manas dzīves stāsts.
13:39
My adolescence was spent
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Savus jaunības gadus es pavadīju
13:41
during the German occupation of France.
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Vācijas okupētajā Francijā.
13:43
Since I thought that I might
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Un, tā kā es domāju, ka es varētu
13:46
vanish within a day or a week,
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pazust kuru katru dienu,
13:49
I had very big dreams.
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man bija ļoti lieli sapņi.
13:52
And after the war,
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Un pēc kara
13:54
I saw an uncle again.
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es atkal satiku savu onkuli.
13:56
My uncle was a very prominent mathematician, and he told me,
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Mans onkulis bija ļoti ievērojams matemātiķis, un viņš man teica:
13:58
"Look, there's a problem
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"Skat, te ir problēma,
14:00
which I could not solve 25 years ago,
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kuru nevarēju atrisināt pirms 25 gadiem
14:02
and which nobody can solve.
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un kuru neviens nevar atrisināt.
14:04
This is a construction of a man named [Gaston] Julia
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Tā ir konstrukcija, ko izveidoja vīri vārdā [Gastons] Žiliā
14:06
and [Pierre] Fatou.
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un [Pjērs] Fatū.
14:08
If you could
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Ja tu vari
14:10
find something new, anything,
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atrast ko jaunu, jebko,
14:12
you will get your career made."
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tu būsi izveidojis sev karjeru."
14:14
Very simple.
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Ļoti vienkārši.
14:16
So I looked,
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Tā nu es skatījos
14:18
and like the thousands of people that had tried before,
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un, tāpat kā daudzi citi, kuri bija mēģinājuši pirms manis,
14:20
I found nothing.
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neko neatradu.
14:23
But then the computer came,
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Bet tad parādījās dators.
14:25
and I decided to apply the computer,
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Un es nolēmu pielietot datoru
14:27
not to new problems in mathematics --
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nevis jaunām matemātikas problēmām --
14:30
like this wiggle wiggle, that's a new problem --
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kā tā laivas valstīšanās, tā ir jauna problēma --,
14:32
but to old problems.
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bet vecām problēmām.
14:34
And I went from what's called
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Un tas aizgāja no tā sauktajiem
14:36
real numbers, which are points on a line,
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reālajiem skaitļiem, kas ir skaitļu taisne,
14:38
to imaginary, complex numbers,
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uz imaginārajiem, kompleksajiem skaitļiem,
14:40
which are points on a plane,
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kas ir skaitļu plakne,
14:42
which is what one should do there,
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kas jāizmanto šajā problēmām.
14:44
and this shape came out.
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Un šis ir tas, kas sanāca.
14:46
This shape is of an extraordinary complication.
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Šī kontūra ir ārkārtīgi sarežģīta.
14:49
The equation is hidden there,
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Vienādojums ir paslēpts tur,
14:51
z goes into z squared, plus c.
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z kļūst par z² plus c.
14:54
It's so simple, so dry.
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Tas ir tik vienkārši, tik sausi.
14:56
It's so uninteresting.
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Tas ir tik neinteresanti.
14:58
Now you turn the crank once, twice:
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Tagad jūs pielietojat šo vienreiz, otrreiz,
15:01
twice,
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otrreiz,
15:04
marvels come out.
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sanāk brīnumi.
15:06
I mean this comes out.
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Sanāk šis.
15:08
I don't want to explain these things.
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Es negribu šīs lietas paskaidrot.
15:10
This comes out. This comes out.
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Sanāk šis. Sanāk šis.
15:12
Shapes which are of such complication,
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Kontūras, kas ir tik sarežģītas,
15:14
such harmony and such beauty.
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tik harmoniskas un tik skaistas.
15:17
This comes out
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Sanāk šis
15:19
repeatedly, again, again, again.
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atkal un atkal, un atkal.
15:21
And that was one of my major discoveries,
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Un viens no maniem lielajiem atklājumiem bija,
15:23
to find that these islands were the same
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ka šīs salas ir tādas pašas,
15:25
as the whole big thing, more or less.
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kā lielā sala, vairāk vai mazāk.
15:27
And then you get these
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Un tad jūs viskaut kur dabūjat šīs
15:29
extraordinary baroque decorations all over the place.
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neparastās baroka dekorācijas.
15:32
All that from this little formula,
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Tas viss no šīs mazās formulas,
15:35
which has whatever, five symbols in it.
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kurā ir nieka pieci simboli.
15:38
And then this one.
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Un tad vēl šis.
15:40
The color was added for two reasons.
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Krāsa tika pievienota divu iemeslu dēļ.
15:42
First of all, because these shapes
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Pirmkārt, tāpēc, ka šīs kontūras
15:44
are so complicated
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ir tik sarežģītas,
15:47
that one couldn't make any sense of the numbers.
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ka tās nevar saprast, pētot skaitļus.
15:50
And if you plot them, you must choose some system.
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Un, ja jūs tos atzīmējat, jums jāizvēlas kāda sistēma.
15:53
And so my principle has been
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Un mans princips ir bijis
15:55
to always present the shapes
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vienmēr rādīt šīs kontūras
15:58
with different colorings
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dažādos krāsojumos,
16:00
because some colorings emphasize that,
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jo daži krāsojumi uzsver šo,
16:02
and others it is that or that.
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citi -- kaut ko citu.
16:04
It's so complicated.
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Tas ir tik sarežģīti.
16:06
(Laughter)
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(Smiekli)
16:08
In 1990, I was in Cambridge, U.K.
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1990. gadā es biju Kembridžā, Lielbritānijā,
16:10
to receive a prize from the university,
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lai saņemtu universitātes apbalvojumu.
16:13
and three days later,
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Un trīs dienas vēlāk
16:15
a pilot was flying over the landscape and found this thing.
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kāds pilots lidoja pāri laukam un atrada šo.
16:18
So where did this come from?
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No kurienes tas uzradies?
16:20
Obviously, from extraterrestrials.
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Acīmredzami, no citplanētiešiem.
16:22
(Laughter)
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(Smiekli)
16:25
Well, so the newspaper in Cambridge
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Nu, laikraksts Kembridžā
16:27
published an article about that "discovery"
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publicēja ziņu par šo atklājumu
16:29
and received the next day
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un nākamajā dienā saņēma
16:31
5,000 letters from people saying,
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5 000 vēstules no cilvēkiem, kas teica:
16:33
"But that's simply a Mandelbrot set very big."
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"Bet tas taču vienkārši ir ļoti liels Mandelbrota kopas attēlojums."
16:37
Well, let me finish.
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Labi, ļaujiet man pabeigt.
16:39
This shape here just came
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Šī kontūra radās
16:41
out of an exercise in pure mathematics.
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no uzdevuma tīrajā matemātikā.
16:43
Bottomless wonders spring from simple rules,
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Nebeidzami brīnumi nāk no vienkāršiem likumiem,
16:46
which are repeated without end.
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kas tiek bezgalīgi atkārtoti.
16:49
Thank you very much.
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Liels jums paldies!
16:51
(Applause)
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(Aplausi)
ABOUT THE SPEAKER
Benoit Mandelbrot - MathematicianBenoit Mandelbrot's work led the world to a deeper understanding of fractals, a broad and powerful tool in the study of roughness, both in nature and in humanity's works.
Why you should listen
Studying complex dynamics in the 1970s, Benoit Mandelbrot had a key insight about a particular set of mathematical objects: that these self-similar structures with infinitely repeating complexities were not just curiosities, as they'd been considered since the turn of the century, but were in fact a key to explaining non-smooth objects and complex data sets -- which make up, let's face it, quite a lot of the world. Mandelbrot coined the term "fractal" to describe these objects, and set about sharing his insight with the world.
The Mandelbrot set (expressed as z² + c) was named in Mandelbrot's honor by Adrien Douady and John H. Hubbard. Its boundary can be magnified infinitely and yet remain magnificently complicated, and its elegant shape made it a poster child for the popular understanding of fractals. Led by Mandelbrot's enthusiastic work, fractal math has brought new insight to the study of pretty much everything, from the behavior of stocks to the distribution of stars in the universe.
Benoit Mandelbrot appeared at the first TED in 1984, and returned in 2010 to give an overview of the study of fractals and the paradigm-flipping insights they've brought to many fields. He died in October 2010 at age 85. Read more about his life on NYBooks.com >>
Benoit Mandelbrot | Speaker | TED.com