# Sensory and Physical Worlds

Animals have different sensory capabilities compared to us humans. Cats, 例如, can hear up to 60kHz, while the highest note we have ever heard was about 20kHz. 似乎, we could hear that high a note only in our childhood. 所以, if we are trying to pull a fast one on a cat with the best hifi multi-channel, Dolby-whatever recording of a mouse, we will fail pathetically. It won&#8217;t be fooled because it lives in a different sensory world, while sharing the same physical world as ours. There is a humongous difference between the sensory and physical worlds.

# Why did Federer Lose?

I am a Federer fan. His inevitable decline has been a source of grief for me. When it comes to shot selection, imagination and pure magical talent, there isn’t another tennis player who could ever hold a candle to him. Why did he have to go and lose in the second round of Wimbledon? It damn near broke my heart.

A few months ago, I listened to a series of interesting lectures on the effects of aging on our perception and sensory processes. One thing new that I learned there was that we all have a sixth sense, in addition to sight, hearing, touch, taste and smell. It is the kinesthetic, muscle feedback, which is the sense that allows you to apply just the right amount of pressure, 例如, when braking your car, or holding a baby. You may lose this sense when you get angry and break the glass you are holding, if we are to believe Hollywood movies. In certain games, this sense can make an enormous difference. I had a friend who was a pool shark. He once told me that at the top of his game, he could feel the tiny nicks and scratches on the cue ball through the cue stick in his hand. When I knew him, he was well past his prime, but he could still call shots like bank off the point of the side pocket, and double kiss into the corner pocket. And make them. So I believe him and Eddie Felson (The Hustler) when he says the cue stick, when he holds it, has nerves. I bet Federer could feel the seams of the tennis ball and the amount of spin he was putting on them through the strings and the grip of his racket.

Age blunts the sharpness of all of your senses. The most obvious is your sight. In your forties, you have to hold your smart phone farther and farther away from your face to read the tiny screen. 在一些点, your hand is not long enough and you end up using reading glasses — reluctantly at first, but more readily as the years roll by and the images get blurrier. Apparently you lose your sensitivity to high pitched sound as well. So teenagers can download ringtones that their parents and teachers are deaf to. But the first sense to go is the muscle feedback, which begins to decline in your teens. 这, 显然, is the reason why the Olympic gymnasts are all teenagers. By the time they are in their twenties, this sense of theirs is already too weak to keep them competitive at that level. I guess it is this sense that has deserted Roger Federer as well.

Frederer’s brand of tennis with its finesse and artistry demanded more of this sense. His opponents tend to hit flatter and harder. I read somewhere that they use stiffer rackets for this purpose, and can hold Federer behind the baseline. The champion stubbornly refuses to switch to this style and this kind of rackets. May be he is getting a bit too old. Reminds me of Bjorn Borg, when he attempted a mini come-back with his wooden racket.

# 什么是太空?

 图: 插图的感觉输入大脑的代表性的过程. 气味是化学成分和浓度水平我们的鼻子的感官的表示. 声音是由一个振动物体所产生的空气压力波的映射. 在望, 我们表示是空间, 并可能时间. 然而, 我们不知道它是什么的代表性.

Visual perception is the basis of our sense of reality. All other senses provide corroborating or complementing perceptions to the visual reality.

[This post has borrowed quite a bit from my book.]

# 轻旅行时间效应和宇宙学特点

This unpublished article is a sequel to my earlier paper (also posted here as “为无线电源和伽玛射线暴管腔围油栏?“). This blog version contains the abstract, introduction and conclusions. The full version of the article is available as a PDF file.

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Abstract

Light travel time effects (LTT) are an optical manifestation of the finite speed of light. They can also be considered perceptual constraints to the cognitive picture of space and time. Based on this interpretation of LTT effects, we recently presented a new hypothetical model for the temporal and spatial variation of the spectrum of Gamma Ray Bursts (GRB) and radio sources. In this article, we take the analysis further and show that LTT effects can provide a good framework to describe such cosmological features as the redshift observation of an expanding universe, and the cosmic microwave background radiation. The unification of these seemingly distinct phenomena at vastly different length and time scales, along with its conceptual simplicity, can be regarded as indicators of the curious usefulness of this framework, if not its validity.

#### Introduction

The finite speed of light plays an important part in how we perceive distance and speed. This fact should hardly come as a surprise because we do know that things are not as we see them. The sun that we see, 例如, is already eight minutes old by the time we see it. This delay is trivial; 如果我们想知道现在是怎么回事太阳, 所有我们需要做的就是等待八分钟. We, nonetheless, have to “正确” for this distortion in our perception due to the finite speed of light before we can trust what we see.

Exploring the second option, we assume an underlying reality that gives rise to our perceived picture. We further model this underlying reality as obeying classical mechanics, and work out our perceived picture through the apparatus of perception. 换句话说, we do not attribute the manifestations of the finite speed of light to the properties of the underlying reality. 相反，, we work out our perceived picture that this model predicts and verify whether the properties we do observe can originate from this perceptual constraint.

Note that we are not implying that the manifestations of perception are mere delusions. They are not; they are indeed part of our sensed reality because reality is an end result of perception. This insight may be behind Goethe’s famous statement, “错觉是光的真理。”

We applied this line of thinking to a physics problem recently. We looked at the spectral evolution of a GRB and found it to be remarkably similar to that in a sonic boom. Using this fact, we presented a model for GRB as our perception of a “luminal” boom, with the understanding that it is our perceived picture of reality that obeys Lorentz invariance and our model for the underlying reality (causing the perceived picture) may violate relativistic physics. The striking agreement between the model and the observed features, 然而，, extended beyond GRBs to symmetric radio sources, which can also be regarded as perceptual effects of hypothetical luminal booms.

In this article, we look at other implications of the model. We start with the similarities between the light travel time (LTT) effects and the coordinate transformation in Special Relativity (SR). These similarities are hardly surprising because SR is derived partly based on LTT effects. We then propose an interpretation of SR as a formalization of LTT effects and study a few observed cosmological phenomena in the light of this interpretation.

#### Similarities between Light Travel Time Effects and SR

Special relativity seeks a linear coordinate transformation between coordinate systems in motion with respect to each other. We can trace the origin of linearity to a hidden assumption on the nature of space and time built into SR, as stated by Einstein: “In the first place it is clear that the equations must be linear on account of the properties of homogeneity which we attribute to space and time.” Because of this assumption of linearity, the original derivation of the transformation equations ignores the asymmetry between approaching and receding objects. Both approaching and receding objects can be described by two coordinate systems that are always receding from each other. 例如, if a system $K$ is moving with respect to another system $k$ along the positive X axis of $k$, then an object at rest in $K$ at a positive $x$ is receding while another object at a negative $x$ is approaching an observer at the origin of $k$.

The coordinate transformation in Einstein’s original paper is derived, in part, a manifestation of the light travel time (LTT) effects and the consequence of imposing the constancy of light speed in all inertial frames. This is most obvious in the first thought experiment, where observers moving with a rod find their clocks not synchronized due to the difference in light travel times along the length of the rod. 然而, in the current interpretation of SR, the coordinate transformation is considered a basic property of space and time.

One difficulty that arises from this interpretation of SR is that the definition of the relative velocity between the two inertial frames becomes ambiguous. If it is the velocity of the moving frame as measured by the observer, then the observed superluminal motion in radio jets starting from the core region becomes a violation of SR. If it is a velocity that we have to deduce by considering LT effects, then we have to employ the extra ad-hoc assumption that superluminality is forbidden. These difficulties suggest that it may be better to disentangle the light travel time effects from the rest of SR.

In this section, we will consider space and time as a part of the cognitive model created by the brain, and argue that special relativity applies to the cognitive model. The absolute reality (of which the SR-like space-time is our perception) does not have to obey the restrictions of SR. 特别是, objects are not restricted to subluminal speeds, but they may appear to us as though they are restricted to subluminal speeds in our perception of space and time. If we disentangle LTT effects from the rest of SR, we can understand a wide array of phenomena, as we shall see in this article.

Unlike SR, considerations based on LTT effects result in intrinsically different set of transformation laws for objects approaching an observer and those receding from him. More generally, the transformation depends on the angle between the velocity of the object and the observer’s line of sight. Since the transformation equations based on LTT effects treat approaching and receding objects asymmetrically, they provide a natural solution to the twin paradox, 例如.

#### Conclusions

Because space and time are a part of a reality created out of light inputs to our eyes, some of their properties are manifestations of LTT effects, especially on our perception of motion. The absolute, physical reality presumably generating the light inputs does not have to obey the properties we ascribe to our perceived space and time.

We showed that LTT effects are qualitatively identical to those of SR, noting that SR only considers frames of reference receding from each other. This similarity is not surprising because the coordinate transformation in SR is derived based partly on LTT effects, and partly on the assumption that light travels at the same speed with respect to all inertial frames. In treating it as a manifestation of LTT, we did not address the primary motivation of SR, which is a covariant formulation of Maxwell’s equations. It may be possible to disentangle the covariance of electrodynamics from the coordinate transformation, although it is not attempted in this article.

Unlike SR, LTT effects are asymmetric. This asymmetry provides a resolution to the twin paradox and an interpretation of the assumed causality violations associated with superluminality. 此外, the perception of superluminality is modulated by LTT effects, and explains $gamma$ ray bursts and symmetric jets. As we showed in the article, perception of superluminal motion also holds an explanation for cosmological phenomena like the expansion of the universe and cosmic microwave background radiation. LTT effects should be considered as a fundamental constraint in our perception, and consequently in physics, rather than as a convenient explanation for isolated phenomena.

Given that our perception is filtered through LTT effects, we have to deconvolute them from our perceived reality in order to understand the nature of the absolute, physical reality. This deconvolution, 然而，, results in multiple solutions. 因此，, 绝对, physical reality is beyond our grasp, and any assumed properties of the absolute reality can only be validated through how well the resultant perceived reality agrees with our observations. In this article, we assumed that the underlying reality obeys our intuitively obvious classical mechanics and asked the question how such a reality would be perceived when filtered through light travel time effects. We demonstrated that this particular treatment could explain certain astrophysical and cosmological phenomena that we observe.

The coordinate transformation in SR can be viewed as a redefinition of space and time (或, more generally, 现实) in order to accommodate the distortions in our perception of motion due to light travel time effects. One may be tempted to argue that SR applies to the “实” 空间和时间, not our perception. This line of argument begs the question, what is real? Reality is only a cognitive model created in our brain starting from our sensory inputs, visual inputs being the most significant. Space itself is a part of this cognitive model. The properties of space are a mapping of the constraints of our perception.

The choice of accepting our perception as a true image of reality and redefining space and time as described in special relativity indeed amounts to a philosophical choice. The alternative presented in the article is inspired by the view in modern neuroscience that reality is a cognitive model in the brain based on our sensory inputs. Adopting this alternative reduces us to guessing the nature of the absolute reality and comparing its predicted projection to our real perception. It may simplify and elucidate some theories in physics and explain some puzzling phenomena in our universe. 然而, this option is yet another philosophical stance against the unknowable absolute reality.

# 为无线电源和伽玛射线暴管腔围油栏?

This article was published in the International Journal of Modern Physics D (IJMP–ð) 在 2007. It soon became the 最多访问文章 由杂志 一月 2008.

This blog version contains the abstract, introduction and conclusions. The full version of the article is available as a PDF file.

Journal Reference: IJMP-D全. 16, 别. 6 (2007) PP. 983–1000.

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Abstract

The softening of the GRB afterglow bears remarkable similarities to the frequency evolution in a sonic boom. At the front end of the sonic boom cone, the frequency is infinite, much like a Gamma Ray Burst (GRB). Inside the cone, the frequency rapidly decreases to infrasonic ranges and the sound source appears at two places at the same time, mimicking the double-lobed radio sources. Although a “luminal” boom violates the Lorentz invariance and is therefore forbidden, it is tempting to work out the details and compare them with existing data. This temptation is further enhanced by the observed superluminality in the celestial objects associated with radio sources and some GRBs. In this article, we calculate the temporal and spatial variation of observed frequencies from a hypothetical luminal boom and show remarkable similarity between our calculations and current observations.

#### Introduction

A sonic boom is created when an object emitting sound passes through the medium faster than the speed of sound in that medium. As the object traverses the medium, the sound it emits creates a conical wavefront, 如图 1. The sound frequency at this wavefront is infinite because of the Doppler shift. The frequency behind the conical wavefront drops dramatically and soon reaches the infrasonic range. This frequency evolution is remarkably similar to afterglow evolution of a gamma ray burst (GRB).

Gamma Ray Bursts are very brief, but intense flashes of $\gamma$ rays in the sky, lasting from a few milliseconds to several minutes, and are currently believed to emanate from cataclysmic stellar collapses. The short flashes (the prompt emissions) are followed by an afterglow of progressively softer energies. 因此，, the initial $\gamma$ rays are promptly replaced by X-rays, light and even radio frequency waves. This softening of the spectrum has been known for quite some time, and was first described using a hypernova (fireball) model. In this model, a relativistically expanding fireball produces the $\gamma$ emission, and the spectrum softens as the fireball cools down. The model calculates the energy released in the $\gamma$ region as $10^ {53}$$10^ {54}$ ergs in a few seconds. This energy output is similar to about 1000 times the total energy released by the sun over its entire lifetime.

More recently, an inverse decay of the peak energy with varying time constant has been used to empirically fit the observed time evolution of the peak energy using a collapsar model. According to this model, GRBs are produced when the energy of highly relativistic flows in stellar collapses are dissipated, with the resulting radiation jets angled properly with respect to our line of sight. The collapsar model estimates a lower energy output because the energy release is not isotropic, but concentrated along the jets. 然而, the rate of the collapsar events has to be corrected for the fraction of the solid angle within which the radiation jets can appear as GRBs. GRBs are observed roughly at the rate of once a day. 因此，, the expected rate of the cataclysmic events powering the GRBs is of the order of $10^4$$10^6$ per day. Because of this inverse relationship between the rate and the estimated energy output, the total energy released per observed GRB remains the same.

If we think of a GRB as an effect similar to the sonic boom in supersonic motion, the assumed cataclysmic energy requirement becomes superfluous. Another feature of our perception of supersonic object is that we hear the sound source at two different location as the same time, 如图 2. This curious effect takes place because the sound waves emitted at two different points in the trajectory of the supersonic object reach the observer at the same instant in time. The end result of this effect is the perception of a symmetrically receding pair of sound sources, 哪, in the luminal world, is a good description of symmetric radio sources (Double Radio source Associated with Galactic Nucleus or DRAGN).

Radio Sources are typically symmetric and seem associated with galactic cores, currently considered manifestations of space-time singularities or neutron stars. Different classes of such objects associated with Active Galactic Nuclei (AGN) were found in the last fifty years. 图 3 shows the radio galaxy Cygnus A, an example of such a radio source and one of the brightest radio objects. Many of its features are common to most extragalactic radio sources: the symmetric double lobes, an indication of a core, 喉喂食叶和热点的出现. 一些研究人员报告了更详细的运动学特性, 如热点的叶适当运动.

This article explores the similarities between a hypothetical “luminal” boom and these two astrophysical phenomena, although such a luminal boom is forbidden by the Lorentz invariance. Treating GRB as a manifestation of a hypothetical luminal boom results in a model that unifies these two phenomena and makes detailed predictions of their kinematics.

#### Conclusions

In this article, we looked at the spatio-temporal evolution of a supersonic object (both in its position and the sound frequency we hear). We showed that it closely resembles GRBs and DRAGNs if we were to extend the calculations to light, although a luminal boom would necessitate superluminal motion and is therefore forbidden.

This difficulty notwithstanding, we presented a unified model for Gamma Ray Bursts and jet like radio sources based on bulk superluminal motion. We showed that a single superluminal object flying across our field of vision would appear to us as the symmetric separation of two objects from a fixed core. Using this fact as the model for symmetric jets and GRBs, we explained their kinematic features quantitatively. 特别是, we showed that the angle of separation of the hotspots was parabolic in time, and the redshifts of the two hotspots were almost identical to each other. Even the fact that the spectra of the hotspots are in the radio frequency region is explained by assuming hyperluminal motion and the consequent redshift of the black body radiation of a typical star. The time evolution of the black body radiation of a superluminal object is completely consistent with the softening of the spectra observed in GRBs and radio sources. 此外, our model explains why there is significant blue shift at the core regions of radio sources, why radio sources seem to be associated with optical galaxies and why GRBs appear at random points with no advance indication of their impending appearance.

Although it does not address the energetics issues (the origin of superluminality), our model presents an intriguing option based on how we would perceive hypothetical superluminal motion. We presented a set of predictions and compared them to existing data from DRAGNs and GRBs. The features such as the blueness of the core, symmetry of the lobes, the transient $\gamma$ and X-Ray bursts, the measured evolution of the spectra along the jet all find natural and simple explanations in this model as perceptual effects. Encouraged by this initial success, we may accept our model based on luminal boom as a working model for these astrophysical phenomena.

It has to be emphasized that perceptual effects can masquerade as apparent violations of traditional physics. An example of such an effect is the apparent superluminal motion, which was explained and anticipated within the context of the special theory of relativity even before it was actually observed. Although the observation of superluminal motion was the starting point behind the work presented in this article, it is by no means an indication of the validity of our model. The similarity between a sonic boom and a hypothetical luminal boom in spatio-temporal and spectral evolution is presented here as a curious, albeit probably unsound, foundation for our model.

One can, 然而，, argue that the special theory of relativity (SR) does not deal with superluminality and, 因此, superluminal motion and luminal booms are not inconsistent with SR. As evidenced by the opening statements of Einstein’s original paper, the primary motivation for SR is a covariant formulation of Maxwell’s equations, which requires a coordinate transformation derived based partly on light travel time (LTT) effects, and partly on the assumption that light travels at the same speed with respect to all inertial frames. Despite this dependence on LTT, the LTT effects are currently assumed to apply on a space-time that obeys SR. SR is a redefinition of space and time (或, more generally, 现实) in order to accommodate its two basic postulates. It may be that there is a deeper structure to space-time, of which SR is only our perception, filtered through the LTT effects. By treating them as an optical illusion to be applied on a space-time that obeys SR, we may be double counting them. We may avoid the double counting by disentangling the covariance of Maxwell’s equations from the coordinate transformations part of SR. Treating the LTT effects separately (without attributing their consequences to the basic nature of space and time), we can accommodate superluminality and obtain elegant explanations of the astrophysical phenomena described in this article. Our unified explanation for GRBs and symmetric radio sources, 因此, has implications as far reaching as our basic understanding of the nature of space and time.

# 虚幻宇宙 — Seeing Light in Science and Spirituality

The same delay in seeing has a lesser known manifestation in the way we perceive moving objects. It distorts our perception such that something coming towards us would look as though it is coming in faster. Strange as it may sound, this effect has been observed in astrophysical studies. Some of the heavenly bodies do look as though they are moving several times the speed of light, while their “实” speed is probably a lot lower.

#### Light in Physics

Einstein chose the first route. In his groundbreaking paper over a hundred years ago, he introduced the special theory of relativity, in which he attributed the manifestations of the finite speed of light to the fundamental properties of space and time. One core idea in special relativity (SR) is that the notion of simultaneity needs to be redefined because it takes some time for light from an event at a distant place to reach us, and we become aware of the event. The concept of “现在” doesn’t make much sense, as we saw, when we speak of an event happening in the sun, 例如. 同时性是相对的.

Einstein defined simultaneity using the instants in time we detect the event. 检测, 他将其定义, involves a round-trip travel of light similar to Radar detection. We send out light, and look at the reflection. If the reflected light from two events reaches us at the same instant, they are simultaneous.
Another way of defining simultaneity is using sensing — we can call two events simultaneous if the light from them reaches us at the same instant. 换句话说, we can use the light generated by the objects under observation rather than sending light to them and looking at the reflection.

The other possibility has an advantage when it comes to describing objects in motion because it corresponds better with how we measure them. We don’t use Radar to see the stars in motion; 我们仅仅感测的光 (或其他辐射) 他们来了. But this choice of using a sensory paradigm, rather than Radar-like detection, to describe the universe results in a slightly uglier mathematical picture.

For symmetric objects, if we assume (因为我们经常做的) 该波开始的旅程大致在同一时刻, we end up with a picture of two “实” 对称的叶片或多或少的方式看到它们.

But there is different possibility that the waves originated from the same object (这是在运动) 在两个时间不同的时刻, 在同一时刻到达望远镜. This possibility explains some spectral and temporal properties of such symmetric radio sources, which is what I mathematically described in a recent physics article. 现在, which of these two pictures should we take as real? 两个对称的物体，因为我们看到他们或一个物体以这样的方式移动，就好像给我们的印象? Does it really matter which one is “实”? Does “实” 意味着在这方面的任何?

The philosophical stance in implied in special relativity answers this question unequivocally. There is an unambiguous physical reality from which we get the two symmetric radio sources, although it takes a bit of mathematical work to get to it. 数学排除了移动以这样的方式单一对象的可能性，以模拟的两个对象. 从本质, 我们看到的是什么就在那里.

The ramifications of the two different philosophical stances described above are tremendous. Since modern physics seems to embrace a non-phenomenalistic view of space and time, 它发现自己不符合哲学的一个分支，. 哲学和物理学之间的鸿沟已经发展到这种程度，诺贝尔得奖物理学家, 史蒂芬温伯格, 想知道 (在他的书 “终极理论之梦”) 为什么从哲学到物理学的贡献一直这么小得惊人. 这也提示哲学家做出类似声明, “无论是“本体的现实导致惊人的现实’ 还是“本体的现实是独立于我们的感知它’ 还是“我们感觉到现实的本体,’ 问题仍然是本体现实的概念，是一个完全冗余的概念，科学的分析。”

We have to come to terms with the fact that when it comes to seeing the universe, 有没有这样的事，作为一个错觉, 这也许正是歌德指出，当他说, “错觉是光的真理。”

In my view, the two options are not inherently distinct. The philosophical stance of SR can be thought of as coming from a deep understanding that space is merely a phenomenal construct. If the sense modality introduces distortions in the phenomenal picture, we may argue that one sensible way of handling it is to redefine the properties of the phenomenal reality.

#### Role of Light in Our Reality

This philosophical grand-standing may sound presumptuous and the veiled self-admonition of physicists understandably unwelcome; but I am holding a trump card. Based on this philosophical stance, I have come up with a radically new model for two astrophysical phenomena, and published it in an article titled, “为无线电源和伽玛射线暴管腔围油栏?” in the well-known International Journal of Modern Physics D in June 2007. This article, which soon became one of the top accessed articles of the journal by Jan 2008, is a direct application of the view that the finite speed of light distorts the way we perceive motion. Because of these distortions, the way we see things is a far cry from the way they are.

We may be tempted to think that we can escape such perceptual constraints by using technological extensions to our senses such as radio telescopes, electron microscopes or spectroscopic speed measurements. 毕竟, these instruments do not have “感悟” per se and should be immune to the human weaknesses we suffer from. But these soulless instruments also measure our universe using information carriers limited to the speed of light. We, 因此, cannot escape the basic constraints of our perception even when we use modern instruments. 换句话说, the Hubble telescope may see a billion light years farther than our naked eyes, but what it sees is still a billion years older than what our eyes see.

Our reality, whether technologically enhanced or built upon direct sensory inputs, is the end result of our perceptual process. To the extent that our long range perception is based on light (and is therefore limited to its speed), we get only a distorted picture of the universe.

#### Light in Philosophy and Spirituality

Once we appreciate the special place accorded to light in modern science, we have to ask ourselves how different our universe would have been in the absence of light. 当然, light is only a label we attach to a sensory experience. 因此，, to be more accurate, we have to ask a different question: if we did not have any senses that responded to what we call light, would that affect the form of the universe?

The immediate answer from any normal (就是说, non-philosophical) person is that it is obvious. If everybody is blind, everybody is blind. But the existence of the universe is independent of whether we can see it or not. Is it though? What does it mean to say the universe exists if we cannot sense it? Ah… the age-old conundrum of the falling tree in a deserted forest. Remember, the universe is a cognitive construct or a mental representation of the light input to our eyes. It is not “out there,” but in the neurons of our brain, as everything else is. In the absence of light in our eyes, there is no input to be represented, ergo no universe.

If we had sensed the universe using modalities that operated at other speeds (echolocation, 例如), it is those speeds that would have figured in the fundamental properties of space and time. This is the inescapable conclusion from phenomenalism.

The parallels between the noumenal-phenomenal distinction in phenomenalism and the Brahman-Maya distinction in Advaita are hard to ignore. This time-tested wisdom on the nature of reality from the repertoire of spirituality is now reinvented in modern neuroscience, 它把现实，由大脑产生一种认知表征. 大脑使用感觉输入, 内存, 意识, 甚至语言成分在炮制我们的​​现实感. 这种观点的现实, 然而，, 是物理的东西是没有来的条款. 但是在某种程度上，它的舞台 (空间和时间) 是现实的一部分, 物理学是不能幸免的哲学.

Recognizing and making use of the interconnections among the different domains of human endeavour may be the catalyst for the next breakthrough in our collective wisdom that we have been waiting for.