arXiv:0709.4024v1 [physics.pop-ph] 25 Sep 2007

Sh ut up and calculate

∗

Max T egmark

Dept. of Physics, Massachuse tts Institute of T e chnolo gy, Cambridge, MA 02139

I advocate an ex treme “shut-up-and-calculate” approac h to p hysic s, where our external physical

realit y is assumed to b e p urely mathematical . This brief essa y motiv ates th is “it’s all just equations”

assumption and discusses its implications.

What is the meaning of life, the universe and every-

thing? In the sci-ﬁ spo o f The H itchhiker’ s Guide to the

Galaxy , the answer w as found to b e 42; the ha rdest part

turned out to b e ﬁnding the r eal question. Indeed, al-

though our inquisitiv e ancestors undoubtedly asked such

big questions, their sea rch for a “theor y of everything”

evolv ed a s their knowledge gre w . As the ancien t Greeks

replaced myth-based explanations with mechanistic mo d-

els of the so lar s y stem, their emphasis shifted from asking

“why” to a sking “how”.

Since then, the sco p e of o ur questioning has dwindled

in some a reas and mushro omed in others. Some ques-

tions were abandoned as naive or misguided, such as ex-

plaining the sizes of planetar y orbits from ﬁrst pr inciples,

which was popular during the Rena is sance. The same

may happ en to currently trendy pursuits lik e predict-

ing the amoun t of dark ener gy in the cosmos, if it turns

out that the a mount in our neig hbourho o d is a histo r ical

accident. Y et our abilit y to a nswer other questions has

surpassed earlier generations’ wildest exp ectations: New-

ton would hav e b een a mazed to know that we would one

day measure the age of o ur universe to an a ccuracy o f 1

per cent , and comprehend the micr ow orld well enough to

make an iP hone.

Mathematics has play ed a s triking r ole in these suc-

cesses. The idea that our universe is in so me s e ns e math-

ematical go es bac k at le a st to the Pythagorea ns of a n-

cient Gree c e , a nd has s pawned centuries o f discussion

among physicists and philoso phers. In the 17 th cent ury ,

Galileo fa mo usly stated that the universe is a “g rand

bo o k” written in the langua ge of mathematics. More

recently , the physics Nob el la ureate Eugene Wigner ar-

gued in the 196 0 s that “the unre a sonable eﬀectiveness of

mathematics in the natural sc ience s ” demanded an ex-

planation.

Here, I will push this idea to its extreme a nd a rgue that

our universe is not just describ ed by mathematics — it is

mathematics. While this h yp othesis might sound r ather

abstract and far-fetched, it makes startling predictions

ab out the s tructure of the universe that could b e testable

b y observ ations. It should also be useful in narrowing

down what an ultimate theo r y of everything can lo o k

like.

∗

This is the “director’s cut” version of the September 15 2007 Ne w

Scientist co v er story . The “full strength” version is the muc h longer

article [1], whic h includes refer ences.

The foundation of my a rgument is the a s sumption that

there exists a n external ph ysical reality indepe ndent of us

h umans. T his is not to o controv ersial: I would guess that

the ma jority of physicists fav our this lo ng -standing idea ,

though it is still debated. Metaphysical solipsists reject

it ﬂat out, a nd s uppor ters of the so-ca lled Cop enhagen

in terpre ta tion o f quantum mechanics may reject it on the

grounds that there is no reality without observ ation (New

Scien tist, 23 June, p 30). Assuming an external reality

exists, physics theories aim to describ e ho w it works. O ur

most successful theo r ies, such as general relativit y and

quantum mechanics, describ e o nly par ts of this rea lity:

gravit y , for instance, or the behaviour of subatomic parti-

cles. In contrast, the holy g r ail of theoretical physics is a

theory o f everything — a co mplete descr iption o f r eality .

My p ersona l quest for this theory b egins with a n ex-

treme argument ab out what it is a llowed to lo ok like. If

we as s ume that r eality exists independently o f hu mans,

then for a description to be complete, it must also b e

well-deﬁned according to non-hum an entities — aliens or

supe r computers, sa y — that lack a ny understanding of

h uman concepts. Put diﬀerently , such a description must

be expressible in a form that is devoid of any human

baggag e like “particle”, “o bserv ation” or other English

words.

In cont ra st, all ph ysics theories that I hav e bee n

taught hav e tw o compo nent s: mathematical equations,

and words that ex plain how the eq uations are connected

to what we obser ve and in tuitiv ely understand. When

we deriv e the consequences o f a theory , we introduce new

concepts — protons, molecules, star s — b ecause they a re

conv enient . It is impo rtant to remember, how ever, that

it is we humans w ho create these co ncepts; in principle,

everything c o uld be c a lculated without this bagg age. F or

example, a suﬃcient ly p ow erful sup erco mputer could cal-

culate how the state o f the univ erse evolv es ov er time

without in terpre ting what is happ ening in human terms.

All of this r aises the question: is it p ossible to ﬁnd a

description of externa l realit y that inv olves no baggage?

If so, s uch a descr iption of ob jects in this exter nal re-

ality and the relations b etw een them would hav e to be

completely abstract, forcing any words or symbo ls to b e

mere labels with no preconceived meanings whatso ever.

Instead, the o nly prop erties o f these entities would be

those embo died by the rela tio ns b etw een them.

This is where mathematics comes in. T o a mo dern lo-

gician, a mathematical structure is precisely this: a set of

abstract en tities with relations b etw een them. T ak e the

in teger s, for instance, or ge o metric ob jects like the do-