Space, Time, Relativity and the I

Placing Physics on a Biological Base.

by

Frank W. Andres

© Copyright, Frank W. Andres, 2023.

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Introduction

Time, Space, Relativity. We have really gone through all of this before – way back in the 1970s. We thought we had left these topics behind – for good. However, we have read books recently which still address relativity as if it were a topic which should be addressed. In these books very often the criticisms we made way back when – are actually mentioned – but then ignored. Well, what happened way back when was: Einstein wrote a book on relativity designed especially for high school students. It was a masterly work, wherein all the basic ideas were set out plainly in just a few pages. All of the defects in the theory were laid out plainly for all to see. So we wrote our book – and well, now 50 years later, as we say, this topic seems to repeatedly raise its ugly head! But this time instead of explanations in a few pages – the same hypotheses are back with 20 to 30 pages of mathematics attached to each topic! – deduced from the same original ideas! All of this mathematics is really just an obfuscation – a fog – that lies on top to simply overwhelm the reader as it creeps in – ‘on little cat’s feet’ – to reference a famous poet.

So, as we have said: We have gone through all of this before – back in the 1970s. The fact is: Space and time, of course – are not ‘out there’ –somewhere in the black of the cosmos! They are tools that our mind uses to describe, examine, and measure objects in the world external to us – and describe, examine, and measure their movements. And really, no ideas have emerged to convince us otherwise. Well, fifty years later we are older and a bit wiser – so let us revisit those ideas – but now we shall consider all of these ideas – in the light of the I.

In our past minibooks, we have placed all of the social sciences on a biological base. Now, it is clear: it is physic’s turn – it is physics time – to be placed on a biological base. Well, we shall make a start here. We shall be more thorough in our next minibook which will be concerned with: Quantum Mechanics. Yes, after all these years – the I seems to be the answer physics has been looking for. In this minbook, we shall begin to show how the fact that there is a hydrogen ion in your brain – that is, ‘looking out’ – is able to shed light – over all of this!

Space, Time, and Energy

The social sciences can be made more powerful by placing them all on a biological base – and we have made considerable progress in doing this in previous minibooks. If all disciplines have the same methodology, and are all grounded in a biological perpective – they can talk to each other. What isn’t apparent immediately is that if these changes in the social sciences are made, not only are the social sciences compatible with each other, they are compatible with all the physical, chemical, and biological sciences, as well. This allows all the sciences to talk to and work with each other. We are truly striving towards one Science – which will include: Everything.

What is also not apparent is: Chemistry and physics need to be placed on a biological base as well. The benefits of doing this with physics

will become apparent in this and the next minibook.

In this minibook, we shall look at the concepts of space and time – the four dimensions – and our investigation will lead easily to an unexpected discovery: the fifth dimension! We really – have gone through all of this before!

Philosophers and physicists are different in their comprehension of space and time – right off the bat. Philosophers think that space and time are tools in our minds, utilized by the mind to deal with matter outside us. Physicists think that space and time are ‘out there’ – somewhere – that the four dimensions are external to us – they are necessary to understand the external world, but they were not created by our minds – more exactly: they were not created by Consciousness – they are just kind of woven into the fabric – of the universe.

So the first question we shall ask in this minibook is: exactly what are the five dimensions? A physicist does not really seriously consider an answer to this question. He or she would simply asssert that these things are obvious to anyone. Well, clearly, they are not! Addressing this question is simply indispensable if a physicist is serious about finding a theory of everything – about finding that one theory that can explain everything!

So what is a dimension? Well, a philosopher would say: A dimension is a tool – that the I utilizes to examine, describe, and measure objects and the movement of objects in the external world. When one uses such a tool, he or she takes something that she or he knows and compares it with something he or she doesn’t know. How does this work? Well, here we go: Let us put our knowledge to work!

So, what is space? That is easy, you say: Space is ‘out there’ – somewhere – all material objects reside in it – it must be like nothing.

Well, as we have said, a philosopher would say: Space is a tool – it is a comparison – made by our minds – between something we know – and something we don’t know. Yes, indeed, we do such a thing in order that we might be able to examine, describe, and measure objects that are external to our bodies. Space measures the extension of matter – it does not exist without matter. If there is no matter, there is no space – the usual understanding of space is that it is the absence of matter. However, if there were no matter, we would not have an idea of ‘no matter’ – thus there would be no space. It is why the concept of ‘zero’ was long in coming – ‘zero’ always has a context – zero what? – ‘zero’ is always related to something – there is nothing on the hill over there – what? – well, there are no cows. Oh. Space is always related to something.

So the idea of ‘space’ is used to describe the ‘extension’ of matter. Well, let us be moe specific about this – in this way we can quickly bring mathematics into the discussion of these things.

Well, we utilize ‘space’ in the following way: As we say, a dimension is a tool that an I utilizes to examine, describe, and measure objects external to it. A dimension is a comparison – yes, that is right – surprise! It is always a tool, an idea that exists in one’s mind – that compares something that we know – know for sure – with something that we do not know very well. We use a dimension to gain a better idea of what that object external to us – might really be like – and in this way we obtain information that we might use to manipulate that object and change the world around us – to build a better world in which we may live – and survive.

So the dimension of Space is: We take an extension of known length – a ruler – and measure an object (say, a rock) of unknown extension – we use the ruler in three directions – René Descartes came up with all of this. First, using the ruler, we measure straight across, horizonatal to our sight – second, straight up and down, perpendicular to the first direction – and then, third, the direction perpendicular to both one and two – in each of these directions we utilize the ruler to describe the rock. We have marked the ruler with inches and feet, units universally recognized and we have compared these markings with the extension of the rock in each direction. These comparisons give the recipient an idea about the rock. An examination of the rock, a scientific discussion concerning the rock, may now be based – on these three comparisons.

However, we may be more general about all of this – about what ‘extension’ may actually refer to.

In mathematics the effort to unify the disparate fields of mathematics into One has centered around one focus: the concept of symmetry. For example, in the field of geometry, any rotation is a symmetry of a round table. Study of symmetrics has led mathematics to the notion of a group. So groups: In mathematics, there are groups of rotations; there are braid groups – and so, so much more. In physics there are groups which have been used to classify elementary particles and they helped predict the existence of quarks.

So symmetry: Let us relate this to the ideas of space and time. Space as we have said, is related to the ‘extension’ of an object. An object is symmetrical if it maintains its shape and movement – even when we apply change to it. An object which maintains this constancy is deemed to be ‘symmetrical’. As we have said, a ruler can be helpful in discerning such symmetry. Space leads to the discernment of extension in objects, then to similarity among the extensions of various objects – to the grouping of these objects on the basis of such similarities – then to definitions attached to objects which can be grouped in a book – so we can be looking for certain objects that we might be interested in investigating.

So what is time? Continuing on with this line of thought: Well, we have found that Space measures the extension of matter – so Time measures the movement of matter. Again: ‘Time’ is a comparison between something we know with somethng we don’t know. If there is no matter, there is no time. How do we use time? We take a movement we know – like the movement of the earth – which a clock duplicates – and we compare that movement with the movement of matter (like a girl running) which we do not know. The earth moves so many miles during the same duration that the girl moves so many feet – a clock divides the circumference of the earth into distances – called: hours, minutes, and seconds – each equivalent to a certain number of miles – this comparison gives the recipient another idea about objects external to our bodies along with an object’s composition, visual appearnace, chemical reactivity – and scientific discussions may come from this description, examination, and measurement of objects external to us.

To measure the movment of particles, something faster than the movement of the earth is required – mainly to save time – we must remember that the rotation of the earth may always be used for this comparison!: so, the speed of light is a constant, known speed with which we can compare other particle movements. However, as we say: One must take care to make certain in the use of dimensions – that the universal rulers and earths and light used for measurement must remain constant – that they do not vary in any way from a normal expectancy. For example, if for some reason a scientist might think that light always travels the same speed regardless of the motion, the speed, that a perceiver may be transporting his or herself – which would be nonsense – then light would necessarily have to be moving at billions of speeds all at once. Even if this were possible – which obviously it isn’t – then light would no longer serve as an instrument with which one might desicrbe the movment of other particles. One would have to go back to that one certain movement we know is constant – the movement of the earth – even if such calculations might be more laborious and time-consuming. As we say: The speed of the earth – does not change. Therefore, it may always serve as an instrument for measuring time. You see: when one gets caught up in a flurry of extensive mathematical discursions – one might inadvertantly forget what he or she is actually talking about!

One word concerning the speed of light at this juncture:

There is no empirical reason that nothing can move faster than the speed of light. And what is happening in the real world is what is of concern to us here – and not what might be deduced from some mathematical equation. Scientists have actually made decisions concerning the ‘spin’ of a particle – which we shall talk about in our next minibook: a particle cannot possibly rotate like a top, they say – it does seem to revolve somehow and this revolution should exist for the observed magnetism to be there. However, it is impossible for a particle to rotate like a top – because, well, if it were a photon – it would be traveling at the speed of light already and a rotation would necessitate some part of that particle – what in the heck would that part be? – to rotate faster than the speed of light!

So!!?? I think scientists have just found an instance in the universe where the speed of an object is moving faster than the speed of light. This to us seems to carry more weight than the origin of this myth: which was the result of a ‘thought’, ‘gedanken‘, experiment that Einstein somehow conducted.

Still: Again there must be symmetry in the concept of time. The interaction among certain objects must exhibit a certain constancy, similarity – over time – first one moves, for example, then the next,- and we notice the sequence of occurrences again and again – for symmetry to exist in this.

In this it must be recognized that the idea of ‘change’ is like the ideas of space and time – all of these are mental things – ideas. Ideas are products of two things always working together – a Consciousness – is always working with an allied memory. There is not space, time, or change ‘out there’ – only the present with its memory of past presents – past Nows. (Please see the section on Nows – below.)

So what is the fifth dimension? Look around the room you are in. Immanuel Kant said that the dimensions exhaust, describe everything in the room around you. He said the dimensions are space and time – but he missed one: What in the room around you is not described by the four dimensions?

Light! Well, the light from the lamps in a room, the light from the sun. Light is energy. Energy is the fifth dimension.

Which brings to mind Einstein’s equation: E = mc^2 – m incorporates the three dimesnions of space, c is the speed of light, used in the fourth dimension of time – E incorporates the comparison of a uniform, known quantity of energy against which an unknown amount of energy can be compared and measured. Notice that in this equation, the equals sign is not an equals sign: As that would mean that the term on the left side of the equals sign is a subset of the terms on the right side of the equals sign – which an autonomous dimesnion cannot be: Thus, this equals sign is actually a transformation sign – think nuclear explosion! Notice that one reason a formula like this is so simple is that the terms include a lot of complexity and comparfison with other things to begin with.

All right, so, what if there are more than five dimensions – what would they be like? Well, as we already entertained in the previous books we have written: dimensions are used to describe essential aspects of matter – extension, movement, and of energy – associated with objects in the external world. Other dimensions might describe things like: Smell, taste, sound, beauty – when physicists talk about strings of energy folded up and hiding seven or eight dimensions – well, this mght look neat mathematically – but conceptually things are more messy – with time and space you have rulers, and clocks. With other dimesions: You will have things like roses and honey Mathematics and dimensions are not of the gods – We are animals. We have to go through certain steps – to arrive at a Truth! First, we must know what reality is. Then we can use mathematics and dimensions to describe that reality. You cannot start with mathematics and expect to generate the real world – a priori – unless you are interested in how the left side of the brain works. The left side of the brain possesses interconnections and structures that mimick regular patterns found in the external world – because neurons are made of the same stuff. Still – some of what is found in that hemisphere is relevant to a discussion of the external world around one – and most isn’t. It is better to start with the real world – make generalizations, and hypotheses – which the right side of the brain is super at doing. People are either left or right hemispheric dominant in their brains – they are not both. Then using mathematics one can develop models which can test these right hemispheric hypotheses in an empirical way. Both sides of the brain must work together.

See how physics – quickly becomes biological.

Relativity

Now that we know what the five dimensions are – we can look at the concept of relativity. Of course, the topic of relativity is associated in our minds with Albert Einstein. Actually the first scholar to look at relativity was Bishop George Berkeley. He was plenty exhaustive in his examination of it – yet he did not come up with the shocking, incomprehensible conclusions that Einstein did. Now that we know what the five dimensions are, we can see where Einstein has made mistakes with his conception of relativity. A lot of confusion enters his thought here as he mixes two attributes of the speed of light: Speed of light as a physical phenomenon; and speed of light as a tool which we can use – to measure movement of objects external to us.

So first there is special relativity: This has to do with the speed of light and clocks. As far as space is concerned: Einstein swears that a block becomes shorter as it approaches the speed of light. There is – no physical reason for this. There is no reason a block should become shorter as its speed propels it outwards into space close to the speed of light. This supposedly all occurs as a result of distortions in human perception. The reflection of light off the front edge of the block and then off the rear – ultimately reaching the eyeball at different times – does all the damage. The speed of light supposedly is always traveling the same speed for all observers regardless of their motion or position – so what one see – is Truth! Light cannot lie! All of which defies common sense. However, physicists swear that we must leave intuition and commopn sense behind. This is high powered physics – we should become innured to impossible things!

So .first!: Light is the phenomenon our eyes use to discern and describe objects extenal to us. Second, the speed of light is used as part of the three dimensions to describe the extension of matter. So when Einstein says that objects moving away from us at the speed of light become shorter – what he is saying is: The images of objects normally are not distorted as they move away from us at normal speeds becaue light travels so fast that it could travel around the earth seven times in one second. Therefore, in our experience, perception of things on earth is pretty much instantaneous. There is no noticeable difference between the perception of light reflected from the front and rear of a block as it moves away from us. However, as a block approaches the speed of light, light reflected from the front edge of the block would take longer to each our eyes than light reflected from the rear because there is a longer distance to travel involved! So of course, the block would appear shorter. We can actually calculate what the difference in time would be for the leading-edge light to reach our eyes versus the rear-reflected light, using Einstein’s formula for relativity. But there is a c in the equation – and light is always the same speed regardless of the relative motion of the perceiver – therefore, the block must actually be becoming shorter.

` No! No one is questioning the speed of light here – even if it is – a bunch of nonsense! As we say: It is highly unlikely that light is traveling many speeds at once. Even if there were True: What we are concerned about here is the distance light must travel during a a certain duration of time – with a certain image in tack. The block is moving heck a fast – so by the time a photon of light reflects off the front of the block which is moving outward into the sky and that photon reaches the rear of the block where another photon is now being reflected – the block has moved a long distance – the light reflected from the front of the block and the light reflected from the rear, each with different images embedded in it – are attached to different moments in time and so the block appears to become shorter to the perceiver. If a person were lying on top of the block as it moved at a speed close to the speed of light – and that person were able to survive to testify as to the integrity of the block – he or she would swear upon a Bible that the block is still the same block – its dimensions have not changed! When it comes to blocks moving near the speed of light – symmetry is still there – the predictable is still happening!

Space describes, examines, measures the extension of matter. The dimensions of blocks are not altered by the speed of the blocks – therefore space is not affected by the speed that matter is moving.

Time: When clocks move away from us at speeds close to the speed of light – the light travels a longer distance each instance before it reaches the eye with its image in tack – time seems to be moving slower. Again – well, there are two mistakes here: first the image of clock is moving over longer distances during each second of its moving away from the perceiver – thus the clock seems to moving slower – thus time is slowing down, Again, No! No one is questioning the speed of light here – it is the length of duration between emittance of photons of light – each with its own image attached – that we are talking about here. There is an increased distance between emitter and perceiver every second – thus photons are arriving later and later. This is a perception thing – not a time thing.

And then there is the obvious thing: Clocks have nothing to do with time – per se! A clock has to be doing certain things before all that mechanism has anything to do with time. The hands of the clock are moving around – as we have said: They must be, need to be, duplicating the motion of the earth – exactly – before that clock has anything to do with time! If a clock is perceived to be moving slower over time – well, the earth – is still moving at the same speed. The deviate motion of the clock has not seemed to have impacted the motion of the earth. Time is the comparison between something which is constant – which we know for sure – compared to something whose movement we do not know – namely a a person running – and this has nothing to do with clocks – per se.

So all of this special relativity stuff of Einstein immediately collapses to the Truths Bishop Berkeley talked about years before.

As far as general relativity: Well, this is about gravity. There did not seem to be any gravity particle at the time that Einstein lived – so Einstein asked: How about this idea? What if space and time are ‘out there’ somewhere – and gravity bends it – or it bends and creates gravity – or something? It is a bit confusing as to what Einstein actually said about all of this. Nevertheless – space and time are not ‘out there’ – they are in one’s mind – they are comparisons our mind makes to help describe, examine and measure objects, matter extenal to us. They have nothing to do with gravity. In fact, we now have found that gravity is actually found in only two places – in the nuclei of hydrogen atoms buried deep in tiny Black Holes – and in helium which is created by the fusion of two hydrogen atoms – which results in there being two Black Holes revolvng around each other. So there is now no reason for a space- time continuum ‘out there’ to exist – in order for there to be an explantion as to the origins of gravity. Which is all very fortunate: A space-time continuum couldn’t actually exist anyway.

The Now

‘What is,’ said the philospher Parmenides, not quite a million days ago, ‘is uncreated and indestructible, alone, complete, immovable and without end.’ What is – is – of course, totally incomprehensible. Of course what Parmenides was talking about was: Consciousness. When we talk about space, time and relatviity, we are addressing the most important questions a physicist can ask. A physicist is roaming far from his field. Into the field of philosophy – wherein there are experts – more suitably trained – with dispositions more in tune with the temperament of such discussions.

As we have said, in the first draft of this minibook: We were attempting to place physics upon a biological base. The problem is: During the past 100 years, physicists have opted to build the future of physics using only the tools of mathematics – and little else. Therefore, we shall accept their wisdom of approach – and turn our attention to this mathematics that they have so much faith in – well, we shall consider all of this in detail in our next minibook – which will address the topic of: Quantum Mechanics.

The thing is: It is apparent after some thought – that it is mathematics itself that needs to be placed upon a biological base – then everything seems to fall in place – especially when one is talking about the unification of all the fields of mathematics. But this is part of a discussion to come.

Here, we are attempting to gain a perspective that will instantly help a discipline – that is, physics – that is caught in a quagmire of ideas, such as: Relativity, quantum mechanics, space, and time – Yes, as we have said: Indeed, this effort has been like physicists attempting to be philosophers. Yet this effort has evolved to be more like physicits attempting to be mathematicians. Which is all right even necessary – as long as it is accepted that mathematics is only one discipline among many – that all the disciplines are necessary to address problems nowadays. We need a Science of Everything. Otherwise one is left on an island of isolation – stranded in an ocean of ideas that are unable to progress.

As we say: Of course what Parmedides was talking about is the I. He was talking about the ‘Now,’ He, without realizing it – was talking about the phenomenon – of Consciousness.

We know that from the Intellectual Autobiography of the Viennese philosopher Rudolf Carnap, that there was the following conversation between Carnap and Einstein on time:

Once Einstein said that the problem of the Now worried him seriously. He explained that the experience of the Now means something special for man, something essentially different from the past and the future, but that this important difference does not and cannot occur within physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation.

And well he should be concerned! Because – of course, the ‘Now’ that Einstein was referring to was related to the one crucial thing – that as we have said – that physics has indeed left out of its equations: Consciousness!

Where there is movement, there is energy. Where there is energy there is Consciousness. Where there is Consciousness – there is time! Consciousness is Now!

‘Now’ – is the beginning – it is an empirical instance in – it is the cosmic declaration of – Time!

For some reason some physicists actually believe that because physics can be reduced to a theory of everything – which in their dreams will be some sort of definitive equation – a succinct declaration Truth of All things!

– when such mathematical equations are possible – ones that can stand for all things for all time – then time itself will seem to become frozen – perhaps even will be kind of sloughed away. In the physicist’s dreams: We won’t need time at all.

There is one problem wth this:

The Now.

The Now is Consciousness. The Now – is a moment in time – which can never be erased – without erasing the I – that is attempting to utilize mathematics in the first place.

A Now is a moment in time. Yet a Now is fragile.

A Now is unable to stand alone. Consciousness has never stood for that. It has always had memory by its side. One isolated Now cannot be sustained, accepted, continued. There must be past Nows in a memory nearby – for a present Now to be meaningful. There must be past Nows – for an I too move – to move a body – to move a world! Consciousness will simply not – accept – lack of meaning. Consciousness simply cannot exist without past experience – or DNA which provides instinctual information, a sort of canned memory that comes with the console..

In addition, once there is memory, there is one other thing: There is now the possibility of: Projection! – into the future – the anticipation of future Nows.

Can’t you see how all of this is in the brain. There is no Now – ‘out there’ – somewhere!

Yes! Of course time – is an I thing. It is a mental thing. This ultimately is because Change – is a mental thing. A noticeable difference – between two Nows – Wherein which process, the I is utilzing memory. Yes, what there is: Is a hydrogen ion in our brain which drags the cosmos into our lives. All science, all thinking must begin – with the I. Each of the sciences must be placed upon a biological base – each must be viewed from the perspective, the knowledge possessed – by the I – in one’s brain. But you counter, that I is not bioloigcal – it is cosmic. Indeed it is, my son and daughter. And that makes Life Cosmic entities – nevertheless as long as Is are attached to a brain, well, as long as an I is in charge of a living entity – it is a biological entitiy – until death occurs to that larger biological entity of which it is a part.

THE END

Notes

The Greater Cosmos and the I

It has always puzzled us how scientists can assert that the universe is ‘flat’ – and then one never hears about that phenomenon ever again. Isn’t that fact sort of important? We mean: If there was a Big Bang – well, if that happened: There must have been an explosion – and explosions usually result in a sphere of firey hell – not a flat whisp of a cosmic hair piece. Well, physicists say: there was expansion, contraction, untold numbers of variations in the creation of the cosmos that could have resulted in a flat universe that is like a sheet of paper.

We don’t think so. We don’t have minds of physicists – we have experience with ten other disciplines – other things come to our minds – a flat universe may be an important piece of information which can help one conjecture as to the creation of the universe itelf.

So the physicist myth of creation is: Well, there was nothing. And well, Boom – there was everything! So there!

Well, there is something physicists call: The cosmic vacuum. Wherein: Anything is possible! And from which, in which, anything – may emerge.

Let us put on another hat right now of say: well, a sociologist – well, someone without any preconceived ideas about cosmic things. So the universe is flat – eh? Well, what if the universe was not the result of an explosion – of which there seems to be little evidence except that galaxies are moving outward from one spot – well, so, no explosion. What if what happened is: there was a cosmic flare – like a flare emitted routinely from the sun. As below – so it is above. The same processes seem to occur at various levels in the universe. A flare would be more like a sheet of paper than like an explosion.

Yeh, but there is no sun!? So we must be saying that there was something there before the universe was created – which was immense and the universe is just an incidental propulsion from this immense thing’s surface. Why haven’t we seen such an immense thing? Well, it may be an immense Black Hole. There seem to be Black Holes at the center – at the creation of everything in the universe – including hydrogen ions which were the first things that were created by this immense thing.

So if this were True – then the whole question of multiverses – remains – a question. An immense Cosmos that predated our cosmos would mean the following:

All the laws we are aware of – came from the same immense origin – which presumably has created all the universes within our reach that we might ever be aware of.

Somehow this immense entity has created a world exactly right for us to live. Or more likely a bunch of hydrogen ions took what was given to them on earth – and created Life which was consistent with what they were given.

By the way, they made all of Life – out of sugar! How have scientists missed this?

All of the cosmos was created by one immense Consciousness. One immense Consciousness did not give of itself – annihilate itself and break into a countless number of Is. One immense Black Hole created a baby cosmos comprised of one hundred galaxies with Black Holes at the center which probably had something to do with the galaxies’ creation – and every particle then created which were hydrogen atoms – possessed tiny Black Holes, too.

Thus the flair emitted from the greater cosmos – was full of Black Holes, Consciousness, and gravity,

Well, as we have speculated before in other minibooks: If this flair is flat – and if hydrogen ions created Life – then these talented, Consciousness embued particles must have done things like this before somewhere else – either above or below the present flair – or as part of the immense cosmos.

So my son and daughter – there is the counterpart to a God. We are not – alone!

Bibliography

Arianrhod, Robyn, Einstein’s Heroes – Imagining the World through the Language of Mathematics (New York: Oxford University Press, 2005), 323 pp.

Barrow, John D., New Theories of Everything (New York: Oxford University Press, 2007), 260 pp.

Feynman, Richard, et. al., The Feynman Lectures on Physics, Vol. II (Reading, Massachusetts: Addison – Wesley Publishing Co., 1964), 263 pp.

Mlodinow, Leonard, The Drunkard’s Walk – Randomness Rules Our Lives

(New York: Pantheon Books, 2008), 252 pp.

Orlin, Ben, Change is the Only Constant – The Wisdom of Calculus in a Madcap World (New York: Black Dog & Leventhal Publishers, 2019), 319 pp.