Max Tegmark, Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139
I advocate an extreme “shut-up-and-calculate” approach to physics, where our external physical reality is assumed to be purely mathematical. This brief essay motivates this “it’s all just equations” assumption and discusses its implications.
What is the meaning of life, the universe and everything? In the sci-ﬁ spoof The Hitchhiker’s Guide to the Galaxy, the answer was found to be 42; the hardest part turned out to be ﬁnding the real question. Indeed, although our inquisitive ancestors undoubtedly asked such big questions, their search for a “theory of everything” evolved as their knowledge grew. As the ancient Greeks replaced myth-based explanations with mechanistic models of the solar system, their emphasis shifted from asking “why” to asking “how”.
Since then, the scope of our questioning has dwindled in some areas and mushroomed in others. Some questions were abandoned as naive or misguided, such as explaining the sizes of planetary orbits from ﬁrst principles, which was popular during the Renaissance. The same may happen to currently trendy pursuits like predicting the amount of dark energy in the cosmos, if it turns out that the amount in our neighbourhood is a historical accident. Yet our ability to answer other questions has surpassed earlier generations’ wildest expectations: Newton would have been amazed to know that we would one
day measure the age of our universe to an accuracy of 1 per cent, and comprehend the microworld well enough to make an iPhone.
Mathematics has played a striking role in these successes. The idea that our universe is in some sense mathematical goes back at least to the Pythagoreans of ancient Greece, and has spawned centuries of discussion among physicists and philosophers. In the 17th century, Galileo famously stated that the universe is a “grand book” written in the language of mathematics. More recently, the physics Nobel laureate Eugene Wigner argued in the 1960s that “the unreasonable effectiveness of mathematics in the natural sciences” demanded an explanation.
Here, I will push this idea to its extreme and argue that our universe is not just described by mathematics — it is mathematics. While this hypothesis might sound rather abstract and far-fetched, it makes startling predictions about the structure of the universe that could be testable by observations. It should also be useful in narrowing down what an ultimate theory of everything can look like.
Tiešām, tā ir vienkārša patiesība: visi universa procesi ‘rēķina’ tos pašus vienādojumus, kurus mēs uzrakstām un risinām. Tikai – citā, reālo fizikālo procesu valodā. Mēs taču arī varam risināt svārsta vienādojumus, to darbinot. Bet bieži mums vieglāk un ērtāk ir šos pašus procesus risināt ‘virtuālajā vidē’ – mūsu izdomātu simbolu vidē, bet tā, lai šajā vidē procesi ‘notiktu’ adekvāti, iespējami tuvu tai ārējās pasaules realitātei. Tad mēs skaļi priecājamies un sakām, ka mums ir ‘laba teorija’, kas precīzi apraksta ārējās pasaules notikumus.
Tegmarka ‘teorija’, ka ‘Universs ir matemātika’ izskatās pēc metafiziskas ieceres kaut kur ieraudzīt universālo, visaptverošo, vienīgo pareizo Dieva matemātiku, kas eksistē ārpus fizikālās realitātes kaut kādā Platona pasaulē. Protams, ka ‘nesaprotamā matemātikas efektivitāte’ skaidrojama vienkārši: daži mūsu modeļi ir tuvu realitātei. Bet, kā zinām, vairākums – nav.
“Stephen Hawking once asked, “What is it that breathes fire into the equations and makes a universe for them to describe?” In the case of the mathematical cosmos, there is no fire-breathing required, since the point is not that a mathematical structure describes a universe, but that it is a universe.” Yon
Precīzi. Nekāda ‘uguns iededzināšana’ nav vajadzīga – dabas fizikālie procesi vienkārši notiek. Likumus un matemātiku to aprakstam esam izdomājuši mēs.