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Multiverse

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This article is about physical cosmology. For religious ideas of a multiverse, see Multiverse (religion).

For other uses, see Multiverse (disambiguation).

Hypothetical group of multiple universes

Part of a series on

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The multiverse,[1] also known as a maniverse, megaverse, metaverse, omniverse, or meta-universe, is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, and the physical laws and constants that describe them.[2][3][4][5] The different universes within the multiverse are called "parallel universes", "other universes", "alternate universes", or "alterverses".[6][7][8]

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Contents

1 History of the concept

2 Brief explanation

3 Search for evidence

4 Proponents and skeptics

5 Arguments against multiverse theories

6 Classification schemes

6.1 Max Tegmark's four levels

6.1.1 Level I: An extension of our Universe

6.1.2 Level II: Universes with different physical constants

6.1.3 Level III: Many-worlds interpretation of quantum mechanics

6.1.4 Level IV: Ultimate ensemble

6.2 Brian Greene's nine types

6.3 Cyclic theories

7 M-theory

8 Black-hole cosmology

9 Anthropic principle

10 Occam's razor

11 Modal realism

12 See also

13 References

14 Further reading

15 External links

History of the concept[edit]

In Dublin in 1952, Erwin Schrödinger gave a lecture in which he jocularly warned his audience that what he was about to say might "seem lunatic". He said that when his equations seemed to describe several different histories, these were "not alternatives, but all really happen simultaneously".[9]

The American philosopher and psychologist William James used the term "multiverse" in 1895, but in a different context.[10] The term was first used in fiction and in its current physics context by Michael Moorcock in his 1963 SF Adventures novella The Sundered Worlds.

Brief explanation[edit]

Multiple universes have been hypothesized in cosmology, physics, astronomy, religion, philosophy, transpersonal psychology, Music and all kinds of literature, particularly in science fiction, Comic books and fantasy. In these contexts, parallel universes are also called "alternate universes", "quantum universes", "interpenetrating dimensions", "parallel universes", "parallel dimensions", "parallel worlds", "parallel realities", "quantum realities", "alternate realities", "alternate timelines", "alternate dimensions" and "dimensional planes".

The physics community has debated the various multiverse theories over time. Prominent physicists are divided about whether any other universes exist outside of our own.

Some physicists say the multiverse is not a legitimate topic of scientific inquiry.[11] Concerns have been raised about whether attempts to exempt the multiverse from experimental verification could erode public confidence in science and ultimately damage the study of fundamental physics.[12] Some have argued that the multiverse is a philosophical notion rather than a scientific hypothesis because it cannot be empirically falsified. The ability to disprove a theory by means of scientific experiment has always been part of the accepted scientific method.[13] Paul Steinhardt has famously argued that no experiment can rule out a theory if the theory provides for all possible outcomes.[14]

In 2007, Nobel laureate Steven Weinberg suggested that if the multiverse existed, "the hope of finding a rational explanation for the precise values of quark masses and other constants of the standard model that we observe in our Big Bang is doomed, for their values would be an accident of the particular part of the multiverse in which we live."[15]

Search for evidence[edit]

Around 2010, scientists such as Stephen M. Feeney analyzed Wilkinson Microwave Anisotropy Probe (WMAP) data and claimed to find evidence suggesting that our universe collided with other (parallel) universes in the distant past.[16][17][18] However, a more thorough analysis of data from the WMAP and from the Planck satellite, which has a resolution 3 times higher than WMAP, did not reveal any statistically significant evidence of such a bubble universe collision.[19][20] In addition, there was no evidence of any gravitational pull of other universes on ours.[21][22]

Proponents and skeptics[edit]

Proponents of one or more of the multiverse hypotheses include Hugh Everett,[23] Don Page,[24] Brian Greene,[25][26] Max Tegmark,[27] Alan Guth,[28] Andrei Linde,[29] Michio Kaku,[30] David Deutsch,[31] Leonard Susskind,[32] Alexander Vilenkin,[33] Yasunori Nomura,[34] Raj Pathria,[35] Laura Mersini-Houghton,[36][37] Neil deGrasse Tyson,[38] Sean Carroll[39]and Stephen Hawking.[40]

Scientists who are generally skeptical of the multiverse hypothesis include: David Gross,[41] Paul Steinhardt,[42][43] Anna Ijjas,[43] Abraham Loeb,[43] David Spergel,[44] Neil Turok,[45] Viatcheslav Mukhanov,[46] Michael S. Turner,[47] Roger Penrose,[48] George Ellis,[49][50] Joe Silk,[51]
Carlo Rovelli,[52] Adam Frank,[53] Marcelo Gleiser,[53] Jim Baggott[54] and Paul Davies.[55]

Arguments against multiverse theories[edit]

In his 2003 New York Times opinion piece, "A Brief History of the Multiverse", author and cosmologist Paul Davies offered a variety of arguments that multiverse theories are non-scientific:[56]

For a start, how is the existence of the other universes to be tested? To be sure, all cosmologists accept that there are some regions of the universe that lie beyond the reach of our telescopes, but somewhere on the slippery slope between that and the idea that there is an infinite number of universes, credibility reaches a limit. As one slips down that slope, more and more must be accepted on faith, and less and less is open to scientific verification. Extreme multiverse explanations are therefore reminiscent of theological discussions. Indeed, invoking an infinity of unseen universes to explain the unusual features of the one we do see is just as ad hoc as invoking an unseen Creator. The multiverse theory may be dressed up in scientific language, but in essence it requires the same leap of faith.

— Paul Davies, The New York Times, "A Brief History of the Multiverse"

George Ellis, writing in August 2011, provided a criticism of the multiverse, and pointed out that it is not a traditional scientific theory. He accepts that the multiverse is thought to exist far beyond the cosmological horizon. He emphasized that it is theorized to be so far away that it is unlikely any evidence will ever be found. Ellis also explained that some theorists do not believe the lack of empirical testability falsifiability is a major concern, but he is opposed to that line of thinking: <link href="mw-data:TemplateStyles:r886047036" rel="mw-deduplicated-inline-style"/>

Many physicists who talk about the multiverse, especially advocates of the string landscape, do not care much about parallel universes per se. For them, objections to the multiverse as a concept are unimportant. Their theories live or die based on internal consistency and, one hopes, eventual laboratory testing.

Ellis says that scientists have proposed the idea of the multiverse as a way of explaining the nature of existence. He points out that it ultimately leaves those questions unresolved because it is a metaphysical issue that cannot be resolved by empirical science. He argues that observational testing is at the core of science and should not be abandoned:[57] <link href="mw-data:TemplateStyles:r886047036" rel="mw-deduplicated-inline-style"/>

As skeptical as I am, I think the contemplation of the multiverse is an excellent opportunity to reflect on the nature of science and on the ultimate nature of existence: why we are here.... In looking at this concept, we need an open mind, though not too open. It is a delicate path to tread. Parallel universes may or may not exist; the case is unproved. We are going to have to live with that uncertainty. Nothing is wrong with scientifically based philosophical speculation, which is what multiverse proposals are. But we should name it for what it is.

— George Ellis, Scientific American, "Does the Multiverse Really Exist?"

Classification schemes[edit]

Max Tegmark and Brian Greene have devised classification schemes for the various theoretical types of multiverses and universes that they might comprise.

Max Tegmark's four levels[edit]

Cosmologist Max Tegmark has provided a taxonomy of universes beyond the familiar observable universe. The four levels of Tegmark's classification are arranged such that subsequent levels can be understood to encompass and expand upon previous levels. They are briefly described below.[58][59]

Level I: An extension of our Universe[edit]

A prediction of chaotic inflation is the existence of an infinite ergodic universe, which, being infinite, must contain Hubble volumes realizing all initial conditions.

Accordingly, an infinite universe will contain an infinite number of Hubble volumes, all having the same physical laws and physical constants. In regard to configurations such as the distribution of matter, almost all will differ from our Hubble volume. However, because there are infinitely many, far beyond the cosmological horizon, there will eventually be Hubble volumes with similar, and even identical, configurations. Tegmark estimates that an identical volume to ours should be about 1010115 meters away from us.[27]

Given infinite space, there would, in fact, be an infinite number of Hubble volumes identical to ours in the universe.[60] This follows directly from the cosmological principle, wherein it is assumed that our Hubble volume is not special or unique.

Level II: Universes with different physical constants[edit]

Bubble universes – every disk represents a bubble universe. Our universe is represented by one of the disks.
Universe 1 to Universe 6 represent bubble universes. Five of them have different physical constants than our universe has.

In the chaotic inflation theory, which is a variant of the cosmic inflation theory, the multiverse or space as a whole is stretching and will continue doing so forever,[61] but some regions of space stop stretching and form distinct bubbles (like gas pockets in a loaf of rising bread). Such bubbles are embryonic level I multiverses.

Different bubbles may experience different spontaneous symmetry breaking, which results in different properties, such as different physical constants.[60]

Level II also includes John Archibald Wheeler's oscillatory universe theory and Lee Smolin's fecund universes theory.

Level III: Many-worlds interpretation of quantum mechanics[edit]

Hugh Everett III's many-worlds interpretation (MWI) is one of several mainstream interpretations of quantum mechanics.

In brief, one aspect of quantum mechanics is that certain observations cannot be predicted absolutely. Instead, there is a range of possible observations, each with a different probability. According to the MWI, each of these possible observations corresponds to a different universe. Suppose a six-sided die is thrown and that the result of the throw corresponds to a quantum mechanics observable. All six possible ways the die can fall correspond to six different universes.

Tegmark argues that a Level III multiverse does not contain more possibilities in the Hubble volume than a Level I or Level II multiverse. In effect, all the different "worlds" created by "splits" in a Level III multiverse with the same physical constants can be found in some Hubble volume in a Level I multiverse. Tegmark writes that, "The only difference between Level I and Level III is where your doppelgängers reside. In Level I they live elsewhere in good old three-dimensional space. In Level III they live on another quantum branch in infinite-dimensional Hilbert space."

Similarly, all Level II bubble universes with different physical constants can, in effect, be found as "worlds" created by "splits" at the moment of spontaneous symmetry breaking in a Level III multiverse.[60] According to Yasunori Nomura,[34] Raphael Bousso, and Leonard Susskind,[32] this is because global spacetime appearing in the (eternally) inflating multiverse is a redundant concept. This implies that the multiverses of Levels I, II, and III are, in fact, the same thing. This hypothesis is referred to as "Multiverse = Quantum Many Worlds". According to Yasunori Nomura, this quantum multiverse is static, and time is a simple illusion.[62]

Related to the many-worlds idea are Richard Feynman's multiple histories interpretation and H. Dieter Zeh's many-minds interpretation.

Level IV: Ultimate ensemble[edit]

The ultimate mathematical universe hypothesis is Tegmark's own hypothesis.[63]

This level considers all universes to be equally real which can be described by different mathematical structures.

Tegmark writes: <link href="mw-data:TemplateStyles:r886047036" rel="mw-deduplicated-inline-style"/>

Abstract mathematics is so general that any Theory Of Everything (TOE) which is definable in purely formal terms (independent of vague human terminology) is also a mathematical structure. For instance, a TOE involving a set of different types of entities (denoted by words, say) and relations between them (denoted by additional words) is nothing but what mathematicians call a set-theoretical model, and one can generally find a formal system that it is a model of.

He argues that this "implies that any conceivable parallel universe theory can be described at Level IV" and "subsumes all other ensembles, therefore brings closure to the hierarchy of multiverses, and there cannot be, say, a Level V."[27]

Jürgen Schmidhuber, however, says that the set of mathematical structures is not even well-defined and that it admits only universe representations describable by constructive mathematics—that is, computer programs.

Schmidhuber explicitly includes universe representations describable by non-halting programs whose output bits converge after finite time, although the convergence time itself may not be predictable by a halting program, due to the undecidability of the halting problem.[64][65][66] He also explicitly discusses the more restricted ensemble of quickly computable universes.[67]

Brian Greene's nine types[edit]

The American theoretical physicist and string theorist Brian Greene discussed nine types of multiverses:[68]

Quilted

The quilted multiverse works only in an infinite universe. With an infinite amount of space, every possible event will occur an infinite number of times. However, the speed of light prevents us from being aware of these other identical areas.

Inflationary

The inflationary multiverse is composed of various pockets in which inflation fields collapse and form new universes.

Brane

The brane multiverse version postulates that our entire universe exists on a membrane (brane) which floats in a higher dimension or "bulk". In this bulk, there are other membranes with their own universes. These universes can interact with one another, and when they collide, the violence and energy produced is more than enough to give rise to a big bang. The branes float or drift near each other in the bulk, and every few trillion years, attracted by gravity or some other force we do not understand, collide and bang into each other. This repeated contact gives rise to multiple or "cyclic" big bangs. This particular hypothesis falls under the string theory umbrella as it requires extra spatial dimensions.

Cyclic

The cyclic multiverse has multiple branes that have collided, causing Big Bangs. The universes bounce back and pass through time until they are pulled back together and again collide, destroying the old contents and creating them anew.

Landscape

The landscape multiverse relies on string theory's Calabi–Yau spaces. Quantum fluctuations drop the shapes to a lower energy level, creating a pocket with a set of laws different from that of the surrounding space.

Quantum

The quantum multiverse creates a new universe when a diversion in events occurs, as in the many-worlds interpretation of quantum mechanics.

Holographic

The holographic multiverse is derived from the theory that the surface area of a space can encode the contents of the volume of the region.

Simulated

The simulated multiverse exists on complex computer systems that simulate entire universes.

Ultimate

The ultimate multiverse contains every mathematically possible universe under different laws of physics.

Cyclic theories[edit]

Main article: Cyclic model

In several theories, there is a series of infinite, self-sustaining cycles (for example, an eternity of Big Bangs, Big Crunches, and/or Big Freezes).

M-theory[edit]

See also: Introduction to M-theory, M-theory, Brane cosmology, and String theory landscape

A multiverse of a somewhat different kind has been envisaged within string theory and its higher-dimensional extension, M-theory.[69]

These theories require the presence of 10 or 11 spacetime dimensions respectively. The extra 6 or 7 dimensions may either be compactified on a very small scale, or our universe may simply be localized on a dynamical (3+1)-dimensional object, a D3-brane. This opens up the possibility that there are other branes which could support other universes.[70][71]

Black-hole cosmology[edit]

Main article: Black-hole cosmology

Black-hole cosmology is a cosmological model in which the observable universe is the interior of a black hole existing as one of possibly many universes inside a larger universe.[citation needed] This includes the theory of white holes, which are on the opposite side of space-time.

Anthropic principle[edit]

Main article: Anthropic principle

The concept of other universes has been proposed to explain how our own universe appears to be fine-tuned for conscious life as we experience it.

If there were a large (possibly infinite) number of universes, each with possibly different physical laws (or different fundamental physical constants), then some of these universes (even if very few) would have the combination of laws and fundamental parameters that are suitable for the development of matter, astronomical structures, elemental diversity, stars, and planets that can exist long enough for life to emerge and evolve.

The weak anthropic principle could then be applied to conclude that we (as conscious beings) would only exist in one of those few universes that happened to be finely tuned, permitting the existence of life with developed consciousness. Thus, while the probability might be extremely small that any particular universe would have the requisite conditions for life (as we understand life), those conditions do not require intelligent design as an explanation for the conditions in the Universe that promote our existence in it.

An early form of this reasoning is evident in Arthur Schopenhauer's 1844 work "Von der Nichtigkeit und dem Leiden des Lebens", where he argues that our world must be the worst of all possible worlds, because if it were significantly worse in any respect it could not continue to exist.[72]

Occam's razor[edit]

Proponents and critics disagree about how to apply Occam's razor. Critics argue that to postulate an almost infinite number of unobservable universes, just to explain our own universe, is contrary to Occam's razor.[73] However, proponents argue that in terms of Kolmogorov complexity the proposed multiverse is simpler than a single idiosyncratic universe.[60]

For example, multiverse proponent Max Tegmark argues: <link href="mw-data:TemplateStyles:r886047036" rel="mw-deduplicated-inline-style"/>

[A]n entire ensemble is often much simpler than one of its members. This principle can be stated more formally using the notion of algorithmic information content. The algorithmic information content in a number is, roughly speaking, the length of the shortest computer program that will produce that number as output. For example, consider the set of all integers. Which is simpler, the whole set or just one number? Naively, you might think that a single number is simpler, but the entire set can be generated by quite a trivial computer program, whereas a single number can be hugely long. Therefore, the whole set is actually simpler... (Similarly), the higher-level multiverses are simpler. Going from our universe to the Level I multiverse eliminates the need to specify initial conditions, upgrading to Level II eliminates the need to specify physical constants, and the Level IV multiverse eliminates the need to specify anything at all... A common feature of all four multiverse levels is that the simplest and arguably most elegant theory involves parallel universes by default. To deny the existence of those universes, one needs to complicate the theory by adding experimentally unsupported processes and ad hoc postulates: finite space, wave function collapse and ontological asymmetry. Our judgment therefore comes down to which we find more wasteful and inelegant: many worlds or many words. Perhaps we will gradually get used to the weird ways of our cosmos and find its strangeness to be part of its charm.[60][74]

— Max Tegmark

Modal realism[edit]

Possible worlds are a way of explaining probability and hypothetical statements. Some philosophers, such as David Lewis, believe that all possible worlds exist and that they are just as real as the world we live in (a position known as modal realism).[75]

See also[edit]

A Universe from Nothing

Beyond black holes

Cosmogony

Hugh Everett III

The Fabric of Reality

Impossible world

Laura Mersini-Houghton

Copenhagen interpretation

Many-worlds interpretation

Holographic principle

Modal realism

Multiverse (religion)

Nature timeline

Parallel universes in fiction

Roger Penrose

Philosophy of physics

Philosophy of space and time

Reductionism

Martin Rees, Astronomer Royal

Simulated reality

Ultimate fate of the universe

Hindu Cosmology

References[edit]

^ Laszlo, Ervin (2003).
The Cennectivity Hypothesis: Fountations of an Integral Science of Quantum, Cosmos, Life, and Consciousness, p.108. State University of New York Press, Albany.
ISBN 0791457850

^ "Planck reveals an almost perfect Universe".

^ "Space in Images".

^ "Multiple universes".

^ "Multiple universes principle".

^ "Multiverses: Do Other Universes Exist?".

^ "Split the Universe".

^ "Hidden Portals in Earth's Magnetic Field".

^ "Erwin Schrödinger and the Quantum Revolution by John Gribbin: review".

^ James, William, The Will to Believe, 1895; and earlier in 1895, as cited in OED's new 2003 entry for "multiverse": James, William (October 1895), "Is Life Worth Living?", Internat. JRNL. Ethics, 6: 10, doi:10.1086/205378, <q>Visible nature is all plasticity and indifference, a multiverse, as one might call it, and not a universe.</q><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

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^ "Astronomers Find First Evidence Of Other Universe". technologyreview.com. 13 December 2010. Retrieved 12 October 2013.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

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^ The Many Worlds of Hugh Everett,  Scientific American

^ https://grandinmedia.ca/god-exist-multiverse/

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^ a b c Tegmark, Max (2003). "Parallel Universes". In "Science and Ultimate Reality: From Quantum to Cosmos", Honoring John Wheeler's Th Birthday. J. D. Barrow, P.C.W. Davies, & C.L. Harper Eds. v1. 288 (5): 40–51. arXiv:astro-ph/0302131. Bibcode:2003SciAm.288e..40T. doi:10.1038/scientificamerican0503-40.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=In+%22Science+and+Ultimate+Reality%3A+From+Quantum+to+Cosmos%22%2C+Honoring+John+Wheeler%27s+Th+Birthday.+J.+D.+Barrow%2C+P.C.W.+Davies%2C+%26+C.L.+Harper+Eds.&rft.atitle=Parallel+Universes&rft.volume=288&rft.issue=5&rft.pages=40-51&rft.date=2003&rft_id=info%3Aarxiv%2Fastro-ph%2F0302131&rft_id=info%3Adoi%2F10.1038%2Fscientificamerican0503-40&rft_id=info%3Abibcode%2F2003SciAm.288e..40T&rft.aulast=Tegmark&rft.aufirst=Max&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/> Tegmark, M (May 2003). "Parallel universes. Not just a staple of science fiction, other universes are a direct implication of cosmological observations". Scientific American. Vol. 288. pp. 40–51. arXiv:astro-ph/0302131. Bibcode:2003SciAm.288e..40T. doi:10.1038/scientificamerican0503-40. PMID 12701329.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+American&rft.atitle=Parallel+universes.+Not+just+a+staple+of+science+fiction%2C+other+universes+are+a+direct+implication+of+cosmological+observations&rft.volume=288&rft.pages=40-51&rft.date=2003-05&rft_id=info%3Aarxiv%2Fastro-ph%2F0302131&rft_id=info%3Apmid%2F12701329&rft_id=info%3Adoi%2F10.1038%2Fscientificamerican0503-40&rft_id=info%3Abibcode%2F2003SciAm.288e..40T&rft.aulast=Tegmark&rft.aufirst=M&rft_id=http%3A%2F%2Fcds.cern.ch%2Frecord%2F604580&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ "Alan Guth: Inflationary Cosmology: Is Our Universe Part of a Multiverse?". YouTube. Retrieved 6 October 2014.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Linde, Andrei (27 January 2012). "Inflation in Supergravity and String Theory: Brief History of the Multiverse" (PDF). ctc.cam.ac.uk. Archived (PDF) from the original on 14 July 2014. Retrieved 13 September 2014.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Parallel Worlds: A Journey Through Creation, Higher Dimensions, and the Future of the Cosmos

^ David Deutsch (1997). "The Ends of the Universe". The Fabric of Reality: The Science of Parallel Universes—and Its Implications. London: Penguin Press. <link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>ISBN 0-7139-9061-9.

^ a b Bousso, R.; Susskind, L. (2012). "Multiverse interpretation of quantum mechanics". Physical Review D. 85 (4): 045007. arXiv:1105.3796. Bibcode:2012PhRvD..85d5007B. doi:10.1103/PhysRevD.85.045007.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Multiverse+interpretation+of+quantum+mechanics&rft.volume=85&rft.issue=4&rft.pages=045007&rft.date=2012&rft_id=info%3Aarxiv%2F1105.3796&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.85.045007&rft_id=info%3Abibcode%2F2012PhRvD..85d5007B&rft.aulast=Bousso&rft.aufirst=R.&rft.au=Susskind%2C+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Vilenkin, Alex (2007). Many Worlds in One: The Search for Other Universes. ISBN <bdi>9780374707149</bdi>.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ a b Nomura, Y. (2011). "Physical theories, eternal inflation, and the quantum universe". Journal of High Energy Physics. 2011 (11): 63. arXiv:1104.2324. Bibcode:2011JHEP...11..063N. doi:10.1007/JHEP11(2011)063.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Journal+of+High+Energy+Physics&rft.atitle=Physical+theories%2C+eternal+inflation%2C+and+the+quantum+universe&rft.volume=2011&rft.issue=11&rft.pages=63&rft.date=2011&rft_id=info%3Aarxiv%2F1104.2324&rft_id=info%3Adoi%2F10.1007%2FJHEP11%282011%29063&rft_id=info%3Abibcode%2F2011JHEP...11..063N&rft.aulast=Nomura&rft.aufirst=Y.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Pathria, R. K. (1972). "The Universe as a Black Hole". Nature. 240 (5379): 298–299. Bibcode:1972Natur.240..298P. doi:10.1038/240298a0.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Catchpole, Heather (24 November 2009). "Weird data suggests something big beyond the edge of the universe". Cosmos. Archived from the original on 14 July 2014. Retrieved 27 July 2014.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Moon, Timur (19 May 2013). "Planck Space Data Yields Evidence of Universes Beyond Our Own". International Business Times. Retrieved 27 July 2014.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Freeman, David (4 March 2014). "Why Revive 'Cosmos?' Neil DeGrasse Tyson Says Just About Everything We Know Has Changed". huffingtonpost.com. Archived from the original on 13 September 2014. Retrieved 12 September 2014.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=huffingtonpost.com&rft.atitle=Why+Revive+%27Cosmos%3F%27+Neil+DeGrasse+Tyson+Says+Just+About+Everything+We+Know+Has+Changed&rft.date=2014-03-04&rft.aulast=Freeman&rft.aufirst=David&rft_id=http%3A%2F%2Fwww.huffingtonpost.com%2F2014%2F03%2F04%2Fneil-degrasse-tyson-cosmos-god-alien-life-multiverses-interview_n_4790408.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Sean Carroll (18 October 2011). "Welcome to the Multiverse". Discover. Retrieved 5 May 2015.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Carr, Bernard (21 June 2007). Universe or Multiverse. p. 19. ISBN <bdi>9780521848411</bdi>. <q>Some physicists would prefer to believe that string theory, or M-theory, will answer these questions and uniquely predict the features of the Universe. Others adopt the view that the initial state of the Universe is prescribed by an outside agency, code-named God, or that there are many universes, with ours being picked out by the anthropic principle. Hawking argued that string theory is unlikely to predict the distinctive features of the Universe. But neither is he is an advocate of God. He therefore opts for the last approach, favoring the type of multiverse which arises naturally within the context of his own work in quantum cosmology.</q><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Davies, Paul (2008). "Many Scientists Hate the Multiverse Idea". The Goldilocks Enigma: Why Is the Universe Just Right for Life?. Houghton Mifflin Harcourt. p. 207. ISBN <bdi>9780547348469</bdi>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Many+Scientists+Hate+the+Multiverse+Idea&rft.btitle=The+Goldilocks+Enigma%3A+Why+Is+the+Universe+Just+Right+for+Life%3F&rft.pages=207&rft.pub=Houghton+Mifflin+Harcourt&rft.date=2008&rft.isbn=9780547348469&rft.aulast=Davies&rft.aufirst=Paul&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DktkvIoOanJsC%26pg%3DPT207&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Steinhardt, Paul (9 March 2014). "Theories of Anything". edge.org. 2014 : WHAT SCIENTIFIC IDEA IS READY FOR RETIREMENT?. Archived from the original on 10 March 2014. Retrieved 9 March 2014.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ a b c Ijjas, Anna; Loeb, Abraham; Steinhardt, Paul (February 2017), "Cosmic Inflation Theory Faces Challenges", Scientific American, 316 (2): 32–39, doi:10.1038/scientificamerican0217-32, PMID 28118351<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+American&rft.atitle=Cosmic+Inflation+Theory+Faces+Challenges&rft.volume=316&rft.issue=2&rft.pages=32-39&rft.date=2017-02&rft_id=info%3Adoi%2F10.1038%2Fscientificamerican0217-32&rft_id=info%3Apmid%2F28118351&rft.aulast=Ijjas&rft.aufirst=Anna&rft.au=Loeb%2C+Abraham&rft.au=Steinhardt%2C+Paul&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ "Is Nature Simple? 2018 Breakthrough Prize Symposium Panel". YouTube. Retrieved 14 January 2018.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Gibbons, G.W.; Turok, Neil (2008). "The Measure Problem in Cosmology". Phys. Rev. D. 77 (6): 063516. arXiv:hep-th/0609095. Bibcode:2008PhRvD..77f3516G. doi:10.1103/PhysRevD.77.063516.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Phys.+Rev.+D&rft.atitle=The+Measure+Problem+in+Cosmology&rft.volume=77&rft.issue=6&rft.pages=063516&rft.date=2008&rft_id=info%3Aarxiv%2Fhep-th%2F0609095&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.77.063516&rft_id=info%3Abibcode%2F2008PhRvD..77f3516G&rft.aulast=Gibbons&rft.aufirst=G.W.&rft.au=Turok%2C+Neil&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Mukhanov, Viatcheslav (2014). "Inflation without Selfreproduction". Fortschritte der Physik. 63 (1): 36–41. arXiv:1409.2335. Bibcode:2015ForPh..63...36M. doi:10.1002/prop.201400074.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Fortschritte+der+Physik&rft.atitle=Inflation+without+Selfreproduction&rft.volume=63&rft.issue=1&rft.pages=36-41&rft.date=2014&rft_id=info%3Aarxiv%2F1409.2335&rft_id=info%3Adoi%2F10.1002%2Fprop.201400074&rft_id=info%3Abibcode%2F2015ForPh..63...36M&rft.aulast=Mukhanov&rft.aufirst=Viatcheslav&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Woit, Peter (9 June 2015). "A Crisis at the (Western) Edge of Physics". Not Even Wrong.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Woit, Peter (14 June 2015). "CMB @ 50". Not Even Wrong.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Ellis, George F. R. (1 August 2011). "Does the Multiverse Really Exist?". Scientific American. Vol. 305 no. 2. New York City: Nature Publishing Group. pp. 38–43. Bibcode:2011SciAm.305a..38E. doi:10.1038/scientificamerican0811-38. ISSN 0036-8733. LCCN 04017574. OCLC 828582568. Retrieved 12 September 2014.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+American&rft.atitle=Does+the+Multiverse+Really+Exist%3F&rft.volume=305&rft.issue=2&rft.pages=38-43&rft.date=2011-08-01&rft_id=info%3Abibcode%2F2011SciAm.305a..38E&rft_id=info%3Aoclcnum%2F828582568&rft_id=info%3Alccn%2F04017574&rft_id=info%3Adoi%2F10.1038%2Fscientificamerican0811-38&rft.issn=0036-8733&rft.aulast=Ellis&rft.aufirst=George+F.+R.&rft_id=http%3A%2F%2Fwww.scientificamerican.com%2Farticle%2Fdoes-the-multiverse-really-exist%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Ellis, George (2012). "The Multiverse: Conjecture, Proof, and Science" (PDF). Slides for a talk at Nicolai Fest Golm 2012. Archived (PDF) from the original on 13 September 2014. Retrieved 12 September 2014.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Ellis, George; Silk, Joe (16 December 2014), "Scientific Method: Defend the Integrity of Physics", Nature, 516 (7531): 321–323, Bibcode:2014Natur.516..321E, doi:10.1038/516321a, PMID 25519115<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature&rft.atitle=Scientific+Method%3A+Defend+the+Integrity+of+Physics&rft.volume=516&rft.issue=7531&rft.pages=321-323&rft.date=2014-12-16&rft_id=info%3Apmid%2F25519115&rft_id=info%3Adoi%2F10.1038%2F516321a&rft_id=info%3Abibcode%2F2014Natur.516..321E&rft.aulast=Ellis&rft.aufirst=George&rft.au=Silk%2C+Joe&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Scoles; Sarah (19 April 2016), "Can Physics Ever Prove the Multiverse is Real", Smithsonian.com<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ a b Frank, Adam; Gleiser, Marcelo (5 June 2015). "A Crisis at the Edge of Physics". The New York Times.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Baggott, Jim (1 August 2013). Farewell to Reality: How Modern Physics Has Betrayed the Search for Scientific Truth. Pegasus. ISBN <bdi>978-1-60598-472-8</bdi>.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Davies, Paul (12 April 2003). "A Brief History of the Multiverse". The New York Times.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Davies, Paul (12 April 2003). "A Brief History of the Multiverse". New York Times. Retrieved 16 August 2011.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Ellis, George F. R. (1 August 2011). "Does the Multiverse Really Exist?". Scientific American. Vol. 305 no. 2. New York City: Nature Publishing Group. pp. 38–43. Bibcode:2011SciAm.305a..38E. doi:10.1038/scientificamerican0811-38. ISSN 0036-8733. LCCN 04017574. OCLC 828582568. Retrieved 16 August 2011.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+American&rft.atitle=Does+the+Multiverse+Really+Exist%3F&rft.volume=305&rft.issue=2&rft.pages=38-43&rft.date=2011-08-01&rft_id=info%3Abibcode%2F2011SciAm.305a..38E&rft_id=info%3Aoclcnum%2F828582568&rft_id=info%3Alccn%2F04017574&rft_id=info%3Adoi%2F10.1038%2Fscientificamerican0811-38&rft.issn=0036-8733&rft.aulast=Ellis&rft.aufirst=George+F.+R.&rft_id=http%3A%2F%2Fwww.scientificamerican.com%2Farticle%2Fdoes-the-multiverse-really-exist%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Tegmark, Max (May 2003). "Parallel Universes". Scientific American. Vol. 288. pp. 40–51. arXiv:astro-ph/0302131. Bibcode:2003SciAm.288e..40T. doi:10.1038/scientificamerican0503-40. PMID 12701329.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+American&rft.atitle=Parallel+Universes&rft.volume=288&rft.pages=40-51&rft.date=2003-05&rft_id=info%3Aarxiv%2Fastro-ph%2F0302131&rft_id=info%3Apmid%2F12701329&rft_id=info%3Adoi%2F10.1038%2Fscientificamerican0503-40&rft_id=info%3Abibcode%2F2003SciAm.288e..40T&rft.aulast=Tegmark&rft.aufirst=Max&rft_id=http%3A%2F%2Fcds.cern.ch%2Frecord%2F604580&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Tegmark, Max (23 January 2003). Parallel Universes (PDF). Retrieved 7 February 2006.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ a b c d e "Parallel universes. Not just a staple of science fiction, other universes are a direct implication of cosmological observations.", Tegmark M., Sci Am. 2003 May;288(5):40–51.

^ "First Second of the Big Bang". How The Universe Works 3. 2014. Discovery Science.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Nomura, Yasunori; Johnson, Matthew C.; Mortlock, Daniel J.; Peiris, Hiranya V. (2012). "Static quantum multiverse". Physical Review D. 86 (8): 083505. arXiv:1205.5550. Bibcode:2012PhRvD..86h3505N. doi:10.1103/PhysRevD.86.083505.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+D&rft.atitle=Static+quantum+multiverse&rft.volume=86&rft.issue=8&rft.pages=083505&rft.date=2012&rft_id=info%3Aarxiv%2F1205.5550&rft_id=info%3Adoi%2F10.1103%2FPhysRevD.86.083505&rft_id=info%3Abibcode%2F2012PhRvD..86h3505N&rft.aulast=Nomura&rft.aufirst=Yasunori&rft.au=Johnson%2C+Matthew+C.&rft.au=Mortlock%2C+Daniel+J.&rft.au=Peiris%2C+Hiranya+V.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Tegmark, Max (2014). Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. Knopf Doubleday Publishing Group. ISBN <bdi>9780307599803</bdi>.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ J. Schmidhuber (1997): A Computer Scientist's View of Life, the Universe, and Everything. Lecture Notes in Computer Science, pp. 201–208, Springer: IDSIA – Dalle Molle Institute for Artificial Intelligence

^ Schmidhuber, Juergen (2000). "Algorithmic Theories of Everything". Sections In: Hierarchies of Generalized Kolmogorov Complexities and Nonenumerable Universal Measures Computable in the Limit. International Journal of Foundations of Computer Science ():587-612 (2002). Section 6 In: The Speed Prior: A New Simplicity Measure Yielding Near-Optimal Computable Predictions. In J. Kivinen and R. H. Sloan, Editors, Proceedings of the 15th Annual Conference on Computational Learning Theory(COLT 2002), Sydney, Australia, Lecture Notes in Artificial Intelligence, Pages 216-228. Springer, 2002. 13 (4): 1–5. arXiv:quant-ph/0011122. Bibcode:2000quant.ph.11122S.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Sections+In%3A+Hierarchies+of+Generalized+Kolmogorov+Complexities+and+Nonenumerable+Universal+Measures+Computable+in+the+Limit.+International+Journal+of+Foundations+of+Computer+Science+%28%29%3A587-612+%282002%29.+Section+6+In%3A+The+Speed+Prior%3A+A+New+Simplicity+Measure+Yielding+Near-Optimal+Computable+Predictions.+In+J.+Kivinen+and+R.+H.+Sloan%2C+Editors%2C+Proceedings+of+the+15th+Annual+Conference+on+Computational+Learning+Theory%28COLT+2002%29%2C+Sydney%2C+Australia%2C+Lecture+Notes+in+Artificial+Intelligence%2C+Pages+216-228.+Springer%2C+2002&rft.atitle=Algorithmic+Theories+of+Everything&rft.volume=13&rft.issue=4&rft.pages=1-5&rft.date=2000&rft_id=info%3Aarxiv%2Fquant-ph%2F0011122&rft_id=info%3Abibcode%2F2000quant.ph.11122S&rft.aulast=Schmidhuber&rft.aufirst=Juergen&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ J. Schmidhuber (2002): Hierarchies of generalized Kolmogorov complexities and nonenumerable universal measures computable in the limit. International Journal of Foundations of Computer Science 13(4):587–612 IDSIA – Dalle Molle Institute for Artificial Intelligence

^ J. Schmidhuber (2002): The Speed Prior: A New Simplicity Measure Yielding Near-Optimal Computable Predictions. Proc. 15th Annual Conference on Computational Learning Theory (COLT 2002), Sydney, Australia, Lecture Notes in Artificial Intelligence, pp. 216–228. Springer: IDSIA – Dalle Molle Institute for Artificial Intelligence

^ In The Hidden Reality: Parallel Universes and the Deep Laws of the Cosmos, 2011

^ Weinberg, Steven (2005). "Living in the Multiverse". arXiv:hep-th/0511037v1.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Richard J Szabo, An introduction to string theory and D-brane dynamics (2004)

^ Maurizio Gasperini, Elements of String Cosmology (2007)

^ Arthur Schopenhauer, "Die Welt als Wille und Vorstellung," supplement to the 4th book "Von der Nichtigkeit und dem Leiden des Lebens". see also R.B. Haldane and J. Kemp's translation "On the Vanity and Suffering of Life" pp 395-6

^ Trinh, Xuan Thuan (2006).  Staune, Jean (ed.). Science & the Search for Meaning: Perspectives from International Scientists. West Conshohocken, PA: Templeton Foundation. p. 186. ISBN <bdi>978-1-59947-102-0</bdi>.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ "Parallel universes. Not just a staple of science fiction, other universes are a direct implication of cosmological observations". Scientific American. Vol. 288 no. 5. May 2003. pp. 40–51. arXiv:astro-ph/0302131. Bibcode:2003SciAm.288e..40T. doi:10.1038/scientificamerican0503-40. PMID 12701329.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Scientific+American&rft.atitle=Parallel+universes.+Not+just+a+staple+of+science+fiction%2C+other+universes+are+a+direct+implication+of+cosmological+observations&rft.volume=288&rft.issue=5&rft.pages=40-51&rft.date=2003-05&rft_id=info%3Aarxiv%2Fastro-ph%2F0302131&rft_id=info%3Apmid%2F12701329&rft_id=info%3Adoi%2F10.1038%2Fscientificamerican0503-40&rft_id=info%3Abibcode%2F2003SciAm.288e..40T&rft_id=http%3A%2F%2Fcds.cern.ch%2Frecord%2F604580&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

^ Lewis, David (1986). On the Plurality of Worlds. Basil Blackwell. ISBN <bdi>978-0-631-22426-6</bdi>.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

Further reading[edit]

Carr, Bernard. Universe or Multiverse? (2007 ed.). Cambridge University Press.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

Deutsch, David (1985). "Quantum theory, the Church–Turing principle and the universal quantum computer" (PDF). Proceedings of the Royal Society of London A. 400 (1818): 97–117. Bibcode:1985RSPSA.400...97D. CiteSeerX 10.1.1.41.2382. doi:10.1098/rspa.1985.0070.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+Royal+Society+of+London+A&rft.atitle=Quantum+theory%2C+the+Church%E2%80%93Turing+principle+and+the+universal+quantum+computer&rft.volume=400&rft.issue=1818&rft.pages=97-117&rft.date=1985&rft_id=%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.41.2382&rft_id=info%3Adoi%2F10.1098%2Frspa.1985.0070&rft_id=info%3Abibcode%2F1985RSPSA.400...97D&rft.aulast=Deutsch&rft.aufirst=David&rft_id=http%3A%2F%2Fwww.cs.berkeley.edu%2F~christos%2Fclassics%2FDeutsch_quantum_theory.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

Ellis, George F.R.; William R. Stoeger; Stoeger, W. R. (2004). "Multiverses and physical cosmology". Monthly Notices of the Royal Astronomical Society. 347 (3): 921–936. arXiv:astro-ph/0305292. Bibcode:2004MNRAS.347..921E. doi:10.1111/j.1365-2966.2004.07261.x.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Monthly+Notices+of+the+Royal+Astronomical+Society&rft.atitle=Multiverses+and+physical+cosmology&rft.volume=347&rft.issue=3&rft.pages=921-936&rft.date=2004&rft_id=info%3Aarxiv%2Fastro-ph%2F0305292&rft_id=info%3Adoi%2F10.1111%2Fj.1365-2966.2004.07261.x&rft_id=info%3Abibcode%2F2004MNRAS.347..921E&rft.aulast=Ellis&rft.aufirst=George+F.R.&rft.au=William+R.+Stoeger&rft.au=Stoeger%2C+W.+R.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AMultiverse"><link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

Manly, Steven (2011). Visions of the Multiverse (1st ed.). Pompton Plains, New Jersey: New Page Books. ISBN <bdi>9781601631299</bdi>.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

Surya-Siddhanta: A Text Book of Hindu Astronomy by Ebenezer Burgess, ed. Phanindralal Gangooly (1989/1997) with a 45-page commentary by P. C. Sengupta (1935).

Melmond (2019). I Know the Multiverse Is Real. All Poetry.<link href="mw-data:TemplateStyles:r886058088" rel="mw-deduplicated-inline-style"/>

External links[edit]

Look up multiverse in Wiktionary, the free dictionary.

Wikiquote has quotations related to: Multiverse

Wikimedia Commons has media related to Multiverse.

Interview with Tufts cosmologist Alex Vilenkin on his new book, "Many Worlds in One: The Search for Other Universes" on the podcast and public radio interview program ThoughtCast.

Joseph Pine II about Multiverse, Presentation at Mobile Monday Amsterdam, 2008

Multiverse – Radio-discussion on BBC Four with Melvyn Bragg

What Is The Multiverse? A layman's explanation

Why There Might be Many More Universes Besides Our Own, by Phillip Ball, March 21, 2016, bbc.com.

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regex = re.compile('^tocsection-')
content_lis = soup.find_all('li', attrs={'class': regex})
print(content_lis)[
1 History of the concept
,
2 Brief explanation
,
3 Search for evidence
,
4 Proponents and skeptics
,
5 Arguments against multiverse theories
,
6 Classification schemes

6.1 Max Tegmark's four levels

6.1.1 Level I: An extension of our Universe

6.1.2 Level II: Universes with different physical constants

6.1.3 Level III: Many-worlds interpretation of quantum mechanics

6.1.4 Level IV: Ultimate ensemble

6.2 Brian Greene's nine types

6.3 Cyclic theories

,
6.1 Max Tegmark's four levels

6.1.1 Level I: An extension of our Universe

6.1.2 Level II: Universes with different physical constants

6.1.3 Level III: Many-worlds interpretation of quantum mechanics

6.1.4 Level IV: Ultimate ensemble

,
6.1.1 Level I: An extension of our Universe
,
6.1.2 Level II: Universes with different physical constants
,
6.1.3 Level III: Many-worlds interpretation of quantum mechanics
,
6.1.4 Level IV: Ultimate ensemble
,
6.2 Brian Greene's nine types
,
6.3 Cyclic theories
,
7 M-theory
,
8 Black-hole cosmology
,
9 Anthropic principle
,
10 Occam's razor
,
11 Modal realism
,
12 See also
,
13 References
,
14 Further reading
,
15 External links
]
content = []
for li in content_lis:
    content.append(li.getText().split('\n')[0])
print(content)['1 History of the concept', '2 Brief explanation', '3 Search for evidence', '4 Proponents and skeptics', '5 Arguments against multiverse theories', '6 Classification schemes', "6.1 Max Tegmark's four levels", '6.1.1 Level I: An extension of our Universe', '6.1.2 Level II: Universes with different physical constants', '6.1.3 Level III: Many-worlds interpretation of quantum mechanics', '6.1.4 Level IV: Ultimate ensemble', "6.2 Brian Greene's nine types", '6.3 Cyclic theories', '7 M-theory', '8 Black-hole cosmology', '9 Anthropic principle', "10 Occam's razor", '11 Modal realism', '12 See also', '13 References', '14 Further reading', '15 External links']
see_also_section = soup.find('div', attrs={'class': 'div-col columns column-width'})
see_also_soup =  see_also_section.find_all('li')
print(see_also_soup)[
A Universe from Nothing
,
Beyond black holes
,
Cosmogony
,
Hugh Everett III
,
The Fabric of Reality
,
Impossible world
,
Laura Mersini-Houghton
,
Copenhagen interpretation
,
Many-worlds interpretation
,
Holographic principle
,
Modal realism
,
Multiverse (religion)
,
Nature timeline
,
Parallel universes in fiction
,
Roger Penrose
,
Philosophy of physics
,
Philosophy of space and time
,
Reductionism
,
Martin Rees, Astronomer Royal
,
Simulated reality
,
Ultimate fate of the universe
,
Hindu Cosmology
]
see_also = []
for li in see_also_soup:
    a_tag = li.find('a', href=True, attrs={'title':True, 'class':False}) # find a tags that have a title and a class
    href = a_tag['href'] # get the href attribute
    text = a_tag.getText() # get the text
    see_also.append([href, text]) # append to array
print(see_also)_____no_output_____with open('content.txt', 'w') as f:
    for i in content:
        f.write(i+"\n")_____no_output_____with open('see_also.csv', 'w') as f:
    for i in see_also:
        f.write(",".join(i)+"\n")_____no_output_____


# Notebook from maxoboe/QUOQAS
Path: StackOverflow/Generate Database.ipynb

# Use sqlite file for output
import sqlite3
import pandas
con = sqlite3.connect('SO_quality.db')
cur = con.cursor()_____no_output_____cur.execute("drop table if exists data;")
cur.execute(
"create table data( \
    id int, \
    ViewCount int, \
    AnswerCount int, \
    Score int, \
    ViewRatio float, \
    AnswerRatio float, \
    Category varchar \
);")
from xml.dom import minidom
categories =['earthscience', 'physics', 'chemistry', 'astronomy', 'biology']
for category in categories:
    xmldoc = minidom.parse(category + '.stackexchange.com/Posts.xml')
    postlist = xmldoc.getElementsByTagName('row')
    to_db = []
    for post in postlist:
        if int(post.attributes['PostTypeId'].value) is not 1:
            continue
        post_id = int(post.attributes['Id'].value)
        ViewCount = int(post.attributes['ViewCount'].value)
        AnswerCount = int(post.attributes['AnswerCount'].value)
        Score = int(post.attributes['Score'].value)
        ViewRatio = float(Score) / ViewCount
        AnswerRatio = float(Score) / AnswerCount if AnswerCount > 0 else None
        to_db.append((post_id, ViewCount, AnswerCount, Score, ViewRatio, AnswerRatio, category))
    cur.executemany("insert into data (id, ViewCount, AnswerCount, Score, ViewRatio, AnswerRatio, Category ) \
                 VALUES (?, ?, ?, ?, ?, ?, ?);", to_db)_____no_output_____import numpy
ViewRatioTable_NonNegScores = pandas.read_sql('select ViewRatio from data where Score >= 0 AND ViewCount > 100', con)
AnswerRatioTable_NonNegScores = pandas.read_sql('select AnswerRatio from data where Score >= 0 AND AnswerRatio is NOT NULL', con)
Avg_ViewRatioTable_NonNegScores = numpy.average(ViewRatioTable_NonNegScores.values)
Avg_AnswerRatioTable_NonNegScores = numpy.average(AnswerRatioTable_NonNegScores.values)
cur.execute("DROP TABLE IF EXISTS good_bad;")
cur.execute("CREATE TABLE good_bad \
            AS SELECT *, AnswerRatio IS NOT NULL AND AnswerRatio > " + str(Avg_AnswerRatioTable_NonNegScores ) + " as answer_good, \
            AnswerRatio IS NOT NULL AND Score IS 0 as answer_bad, \
            ViewCount > 100 AND ViewRatio > " + str(Avg_ViewRatioTable_NonNegScores / 2) + " as view_good, \
            ViewCount > 100 AND Score IS 0 as view_bad from data;")
print(pandas.read_sql('select answer_good, answer_bad, view_good, view_bad, count(*) from good_bad \
                        GROUP BY answer_good, answer_bad, view_good, view_bad', con))
con.commit()
con.close()   answer_good  answer_bad  view_good  view_bad  count(*)
0            0           0          0         0     68608
1            0           0          0         1      1964
2            0           0          1         0     28390
3            0           1          0         0     13001
4            0           1          0         1     16827
5            1           0          0         0     13116
6            1           0          1         0     27233
# Make new database for training and testing
con = sqlite3.connect('SO.db')
cur = con.cursor()
cur.execute("DROP TABLE IF EXISTS data;")
cur.execute(
"create table data( \
    id int, \
    ViewCount int, \
    AnswerCount int, \
    Score int, \
    ViewRatio float, \
    AnswerRatio float, \
    Category varchar, \
    Body varchar, \
    Title varchar, \
    view_good int, \
    view_bad int, \
    answer_good int, \
    answer_bad int \
);")
from xml.dom import minidom
categories =['earthscience', 'physics', 'chemistry', 'astronomy', 'biology']
for category in categories:
    xmldoc = minidom.parse(category + '.stackexchange.com/Posts.xml')
    postlist = xmldoc.getElementsByTagName('row')
    to_db = []
    for post in postlist:
        if int(post.attributes['PostTypeId'].value) is not 1:
            continue
        post_id = int(post.attributes['Id'].value)
        ViewCount = int(post.attributes['ViewCount'].value)
        AnswerCount = int(post.attributes['AnswerCount'].value)
        Score = int(post.attributes['Score'].value)
        ViewRatio = float(Score) / ViewCount
        AnswerRatio = float(Score) / AnswerCount if AnswerCount > 0 else None
        body = post.attributes['Body'].value.lower()
        title = post.attributes['Title'].value.lower()
        answer_good = AnswerCount > 0 and AnswerRatio > Avg_AnswerRatioTable_NonNegScores
        answer_bad = AnswerCount > 0 and Score is 0
        view_good = ViewCount > 100 and ViewRatio > Avg_ViewRatioTable_NonNegScores / 2
        view_bad = ViewCount > 100 and Score is 0
        to_db.append((post_id, ViewCount, AnswerCount, Score, ViewRatio, AnswerRatio, category, body, title,
                     int(answer_good), int(answer_bad), int(view_good), int(view_bad)))
    cur.executemany("insert into data (id, ViewCount, AnswerCount, Score, ViewRatio, AnswerRatio, Category, \
                    Body, Title, view_good, view_bad, answer_good, answer_bad) \
                 VALUES (?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?);", to_db)
# Attach the quality database and read out all the things, including the good and the bad
# So that thing includes the metrics of data quality. It's a thing. Maybe include that generation part here as well?
# Okay great gonna do that
# Then I make a new database, just SO.db, that has the quality metrics and all of the text
print(pandas.read_sql('select * from data limit 5', con))
con.commit()
con.close()   id  ViewCount  AnswerCount  Score  ViewRatio  AnswerRatio      Category  \
0   1        436            2     21   0.048165         10.5  earthscience
1   2        120            1     14   0.116667         14.0  earthscience
2   3         91            1      9   0.098901          9.0  earthscience
3   4         92            1      8   0.086957          8.0  earthscience
4   5        123            1      8   0.065041          8.0  earthscience

                                                Body  \
0
the atmosphere is a highly dynamical system...
1
in-situ measurements in deep convective sys...
2
remote sounding of the atmosphere is a well...
3
the <a href="https://en.wikipedia.org/wiki/...
4
so we know that surface air temperatures ar...

                                               Title  view_good  view_bad  \
0                                is climate chaotic?          1         0
1  have there been any attempts to measure profil...          1         0
2  what methods exist for remote profiling of oce...          1         0
3  are there any quantities defined analogically ...          1         0
4  does el niño increase the amount of heat that ...          1         0

   answer_good  answer_bad
0            1           0
1            1           0
2            0           0
3            0           0
4            1           0
con = sqlite3.connect('SO.db')
cur = con.cursor()_____no_output_____con = sqlite3.connect('SO.db')
cur = con.cursor()
count_by_category = []
for row in cur.execute('SELECT count(*), answer_good, answer_bad from data group by answer_good, answer_bad'):
    count_by_category.append(row[0])
    print(row)
print(count_by_category)
total_count = sum(count_by_category)
print('Percent good: ' + str(count_by_category[2] / total_count))
print('Percent bad: ' + str(count_by_category[1] / total_count))
print('Percent unmarked: ' + str(count_by_category[0] / total_count))
# Print percentage where answergood is 1, answerbad is 0
# Print percentage where answergood is 0, answerbad is 1
# Print percentage where answergood is 0, answerbad is 0
# Does all_submissions already remove duplicates? Seems too high...(94725, 0, 0)
(18791, 0, 1)
(55623, 1, 0)
[94725, 18791, 55623]
Percent good: 0.3288596952802133
Percent bad: 0.11109797267336333
Percent unmarked: 0.5600423320464234
con = sqlite3.connect('SO.db')
cur = con.cursor()
count_by_category = []
for row in cur.execute('SELECT count(*), view_good, view_bad from data group by view_good, view_bad'):
    count_by_category.append(row[0])
total_count = sum(count_by_category)
print('Percent good: ' + str(count_by_category[2] / total_count))
print('Percent bad: ' + str(count_by_category[1] / total_count))
print('Percent unmarked: ' + str(count_by_category[0] / total_count))Percent good: 0.23855527110837832
Percent bad: 0.1763519945133884
Percent unmarked: 0.5850927343782333


# Notebook from krajai/testt
Path: Qonto/Qonto_Get_statement_barline.ipynb

_____no_output_____# Qonto - Get statement barline
_____no_output_____**Tags:** #qonto #bank #statement #plotly #barline #naas_drivers #finance #snippet_____no_output_____**Author:** [Florent Ravenel](https://www.linkedin.com/in/florent-ravenel/)_____no_output_____## Input_____no_output_____### Import library_____no_output_____

from naas_drivers import qonto_____no_output_____

### Get your Qonto credentials
How to get your credentials ?_____no_output_____

QONTO_USER_ID = 'YOUR_USER_ID'
QONTO_SECRET_KEY = 'YOUR_SECRET_KEY'_____no_output_____

### Parameters_____no_output_____

# Date to start extraction, format: "AAAA-MM-JJ", example: "2021-01-01"
date_from = None
# Date to end extraction, format: "AAAA-MM-JJ", example: "2021-01-01", default = now
date_to = None
# Title of the graph, default = "Evolution du {date_from} au {date_to}"
title = f"💵 Qonto - Suivi des encaissements / Décaissements
"
# Name of line displayed in legend
line_name = "Solde"
# Line color
line_color = "#1ea1f1"
# Name of cash in bar displayed in legend
cashin_name = "Encaissements"
# Cash in bar color
cashin_color = "#47dd82"
# Name of cash out bar displayed in legend
cashout_name = "Décaissements"
# Cash out bar color
cashout_color = "#ea484f"_____no_output_____

## Model_____no_output_____### Create barline chart_____no_output_____

barline = qonto.connect(QONTO_USER_ID, QONTO_SECRET_KEY).statements.barline(date_from=date_from,
                                                                            date_to=date_to,
                                                                            title=title,
                                                                            line_name=line_name,
                                                                            line_color=line_color,
                                                                            cashin_name=cashin_name,
                                                                            cashin_color=cashin_color,
                                                                            cashout_name=cashout_name,
                                                                            cashout_color=cashout_color)_____no_output_____

## Output_____no_output_____### Display chart_____no_output_____

barline_____no_output_____


# Notebook from lareaulab/SingleCell_paper
Path: data_processing/make_read_counts/get_star_counts.ipynb

<code>
import numpy as np
import pandas as pd
import subprocess as sp
import os_____no_output_____star_dir = '/mnt/lareaulab/cfbuenabadn/RNASeq/Mouse/ChenRNASeq/STAR_pipeline/'
samples = os.listdir(star_dir)
rcounts_tab = pd.DataFrame()

for sample in samples:
    star_tab = pd.read_csv(star_dir + sample + '/star_output/ReadsPerGene.out.tab',
                           names = ['no_specific', 'first_strand', 'reverse_strand'],
                           sep='\t', index_col=0, skiprows=4)

    rcounts_tab[sample] = star_tab.no_specific

rcounts_tab.index = [x.split('.')[0] for x in rcounts_tab.index]

_____no_output_____rcounts_tab.to_csv('chen.star.counts.tab', sep='\t', header=True, index=True)_____no_output_____
</code>


# Notebook from BIPN62/Materials
Path: Discussion/Midterm Review Materials.ipynb

# Midterm Review Materials _____no_output_____## 1. For Loop Example: printing pyramid pattern

Use the for loop to print the following pattern (hint: use the `*` operator to create string with repeated character):

1

2 2

3 3 3

4 4 4 4

5 5 5 5 5 _____no_output_____

#Let's first think about how to generate one of the line from the pattern
#example:

print('3 '*3)
print('4 '*4)3 3 3
4 4 4 4
#solution:

for i in range(1,6):
    repeating_unit=str(i)+' '
    line=repeating_unit*i
    print(line)1
2 2
3 3 3
4 4 4 4
5 5 5 5 5

## 2. For Loop Example: max() function

In this example, we will write a user-defined max() function that returns the maximum value(s) from an integer list.

The logic of this function is that we first assign the first value in the list to the maximum. Then while iterating over the list, if the next value is greater than or equal to the previous value, we reassign the next value to the maximum._____no_output_____

def max(int_list):
    '''this function returns the maximum value(s) from an integer list.'''

    #assign the first value in the list to maximum
    maximum = int_list[0]
    for i in int_list:
        #compare the next value to the previous one
        #then reassign the next value to maximum if it is greater than or equal to the previous value
        if i >= maximum:
            maximum = i
    return maximum_____no_output_____max([1,3,45,2,15,6])_____no_output_____

## 3. GCcontent() Function and Error Raising_____no_output_____

def GCcontent(DNA):

    '''This function returns the GC content of an input DNA string.
    The input DNA string should only contain A,T,C,G.'''

    #pre-check whether the input DNA string contains any illegal characters
    #try to include characters other than A,T,C and G in your Sequence variable
    #to see what happens to the output of the following codes
    allowed_char='ATCG'
    if not all(char in allowed_char for char in DNA):
        #print('Input contains illegal character(s). The input DNA string should only contain A,T,C,G.')
        #raising error stops the code at this step and the for loop below will no longer be executed.
        raise ValueError('Input contains illegal character(s). The input DNA string should only contain A,T,C,G.')

    #Exercise: Add another code block to check whether in the input is a string variable
    #and raise a TypeError('Input has to be a string variable') if it isn't

    #use a for loop the iterate through the input DNA string and count the number of base C and G
    counter=0
    for i in DNA:
        if i=='C' or i=='G':
            counter=counter+1

    #calculate the GC content of the input DNA string
    return(counter/len(DNA))

GCcontent('ACTGACGTAATTGC')_____no_output_____###For the input pre-checking block, the full version of the code is below:
#we first generate a list of boolean variables
#try to include characters other than A,T,C and G in your Sequence variable
#to see what happens to the output of the following codes

Sequence='dATGA'
allowed_char='ATCG'
bool_list=[]
for char in Sequence:
    check_char = char in allowed_char
    #print out messages to better understand how this for loop works
    if check_char == True:
        print(char +' is one of '+ allowed_char)
    else:
        print(char +' is not one of '+ allowed_char)
    bool_list.append(check_char)

print(bool_list)_____no_output_____#The list comprehension equivalent of the for loop above is:

print([char in allowed_char for char in Sequence])_____no_output_____#If at least one of the item within the bool_list is False, then that means there is at least one charater within the
#DNA sequence is not A,T,C or G.We could use the count() function to count the number of False in the bool_list

Count_False=bool_list.count(False)
print(Count_False)
if Count_False >= 1:
    print('Input contains illegal character(s). The input DNA string should only contain A,T,C,G.')_____no_output_____#The all() function takes a list of boolean variables as the input and returns True only if all of the items
#within the input list are True

all_char_legal=all(bool_list)
print(all_char_legal)
if not all_char_legal:
    print ('Input contains illegal character(s). The input DNA string should only contain A,T,C,G.')_____no_output_____

## 4. While Loop Example: Fibonacci Sequence Generator

Fibonacci Sequence: starts with 1, 1. Then from the third number, every number would be the sum of the previous two numbers.

For example: 1,1,2,3,5,8,13,...

The fibonacci(upper_limit) function prints out a fibonacci sequence whose last number is no greater than the upper_limit input
_____no_output_____

def fibonacci(upper_limit):
    n_1=1
    n_2=1
    print(n_1)
    print(n_2)
    #define n first before the while loop with a placeholder value
    n=0
    while n<=upper_limit:
        n=n_1+n_2
        #solve the problem of printing out one extra value after the n exceeds the upper_limit
        #and breaks from the while loop
        if n<=upper_limit:
            print(n)
        #update n_1 and n_2 per iteration
        n_1=n_2
        n_2=n_____no_output_____fibonacci(500)1
1
2
3
5
8
13
21
34
55
89
144
233
377

## 5. OOP Example: Car() Class_____no_output_____

###Create a car() class

class car():

    #attributes
    color = 'Black' #color of the car
    year = 2020 #year of the car
    mpg = 20 #milage of the car
    speed = 80 #current speed of the car
    is_stopped = False

    #methods
    def accelerate(self):
        self.speed=self.speed+20
        #exercise: similar to the brake() method below, try to add a max_speed attribute with your desired
        #value and reset the speed of the car class to the max_speed
        #if the speed after running the accelerate() method is above the max_speed
        print("the speed of the car now is "+str(car.speed))

    def brake(self):
        self.speed=self.speed-50
        if self.speed<0:
            print('speed can not be negative.')
            self.speed = 0
        print("the speed of the car now is "+str(car.speed))

    def stop(self):
        self.is_stopped= True
        self.speed = 0
        print('The car has stopped')
    def start(self):
        if self.is_stopped == False:
            raise ValueError('can only start the car when it is stopped')
        else:
            self.is_stopped = False
            self.speed = 20
            print('The car has started')_____no_output_____#creating an instance of the car() class

my_car=car()

#get my_car attributes
print(my_car.mpg)
print(my_car.color)

#call my_car methods
my_car.stop()
my_car.start()
print(my_car.speed)
print(my_car.is_stopped)20
Black
The car has stopped
The car has started
20
False
###Use __init__ keyword to specify instance-specific attributes of a object

class car():

    #initialize instance-specific attributes
    def __init__(self,color,year,mpg,speed):
        self.color = color
        self.year = year
        self.mpg = mpg
        self.speed = speed
        #here I am creating a is_stopped attribute that
        #checks whether the speed attribute is 0.
        #Note that since this is_stopped attribute
        #depends on the value of self.speed and
        #self.speed is only defined within the def __init__() block,
        #you can not define is_stopped outside of the
        #def __init__() block like is_stopped = speed == 0
        self.is_stopped = self.speed == 0

    #methods
    def accelerate(self):
        self.speed=self.speed+20
        print("the speed of the car now is "+str(car.speed))

    def brake(self):
        self.speed=self.speed-50
        print("the speed of the car now is "+str(car.speed))
    def stop(self):
        self.is_stopped= True
        self.speed = 0
        print('The car has stopped')
    def start(self):
        if car.is_stopped == False:
            raise ValueError('can only start the car when it is stopped')
        else:
            self.is_stopped = False
            self.speed = 20
            print('The car has started')_____no_output_____#creating an instance of the car() class with instance-specific attributes

my_car_3 = car('white',2018,25,80)
print(my_car_3.is_stopped)False

## 6. Numpy Example: how to slice array and perform methods with different axis values _____no_output_____

import numpy as np
#creating a 10*8 array with random integer values from 0 to 9
my_matrix = np.random.randint(0,10,size=(10,8))
print(my_matrix)[[1 6 0 7 7 5 9 4]
 [0 8 5 3 7 2 7 3]
 [0 7 4 0 2 3 2 8]
 [8 8 5 8 4 9 3 5]
 [7 8 5 1 0 8 5 5]
 [1 5 3 7 8 1 2 7]
 [2 9 0 9 8 2 8 0]
 [9 7 2 0 3 5 5 3]
 [1 7 2 7 6 7 3 2]
 [5 4 4 5 8 8 2 1]]

The syntax for slicing np array is `array[row_number,column_number]`._____no_output_____

#silcing out a single value with row number 0 and column number 0
#i.e. the value at the top left corner
my_matrix[0,0]_____no_output_____

Remember that when slicing multiple values from a list or string, we used the syntax `list[start_pos:end_pos]`. We could also apply this to slicing out multiple values from the np array._____no_output_____

#silcing out a single value with row number 0 to 3 and column number 0 to 3
#i.e. the 3*3 array on the top left corner
my_matrix[0:3,0:3]_____no_output_____

To slice out row(s), leave the column_number as blank to include all column numbers and indicate the row(s) you would like to slice out for the row_number._____no_output_____

#slicing out the first row of the array
my_matrix[0,]_____no_output_____

To slice out columns(s), you could not leave the row_number as blank to include all row numbers. Instead, use `:` for the row_number without specifing start_pos and end_pos to include all row numbers. Then indicate the row(s) you would like to slice out for the row_number._____no_output_____

#slicing out the last column of the array
my_matrix[:,-1]_____no_output_____

When performing method on arrays, set `axis=0` to perform the method on each column and `axis=1` to perform the method on each row. _____no_output_____

#calculating the average value for each column in the array
np.mean(my_matrix,axis = 1)_____no_output_____#calculating the average value for each row in the array
np.mean(my_matrix,axis = 0)_____no_output_____

## 7. pyplot example: ploting data on different graphs using `subplots()` or plot data on the same graph_____no_output_____In this example, we will going to plot the line graph for the first four columns in the my_matrix array from the previous examples in two ways: ploting them on different graphs using `subplots()` or plot them on the same graph_____no_output_____

import matplotlib.pyplot as plt_____no_output_____fig, ax = plt.subplots(2,2,figsize=(15,5))
#I added fig.tight_layout() line to prevent the titles overlapping with the x-axes of the subplots
fig.tight_layout()
ax[0,0].plot(my_matrix[:,0])
ax[0,1].plot(my_matrix[:,1])
ax[1,0].plot(my_matrix[:,2])
ax[1,1].plot(my_matrix[:,3])
#add titles to each subplot
ax[0,0].set_title("column 1")
ax[0,1].set_title("column 2")
ax[1,0].set_title("column 3")
ax[1,1].set_title("column 4")
plt.show()_____no_output_____plt.plot(my_matrix[:,0])
plt.plot(my_matrix[:,1])
plt.plot(my_matrix[:,2])
plt.plot(my_matrix[:,3])
#add legends to the graph
plt.legend(["column 1","column 2","column 3","column 4"])
#add title to the graph
plt.title("4 columns in one graph")
plt.show()_____no_output_____

useful pyplot methods:

plt:

`xlabel()` and `ylabel()` to set titles for x- and y-axis

`legend()` to add legends when plotting multiple groups of data on the same graph

`title()` to add title for the graph

subplots:

`set_xlabel()` and `set_ylabel()` to set titles for x- and y-axis for each subplot

`set_title()` to add title to each subplot_____no_output_____## 8. Panda Example: working with variant calling tsv file_____no_output_____

#read in the example.tsv file
import pandas as pd
variants_df = pd.read_csv('example.tsv',sep='\t')
variants_df.head()_____no_output_____#set the #ID column to be the index
variants_df = variants_df.set_index('#ID')
variants_df.head()_____no_output_____#slice out column(s)
variants_df['POS']
variants_df[['POS','REF','ALT']]_____no_output_____#slice out row(s)
variants_df.loc['RE-7740_Br']_____no_output_____#filtering the dataframe with column-specific criteria
#e.g. we would like to filter out the data with the ANNO column value as
#'exonic:nonsynonymous_SNV'
exonic_variants_df = variants_df[variants_df['ANNO'] =='exonic:nonsynonymous_SNV']
exonic_variants_df.head()_____no_output_____