Here's an uncomfortable question. Can you accurately judge somebody's intelligence based on their beliefs? Now the polite answer is no, of course not. But my own experiences make me think otherwise. Specifically when people defend plainly inaccurate beliefs, it can reveal a few things. The amount of research they've done, their intellectual integrity, or perhaps their ability to think critically. Ultimately I believe we can make these inferences for one reason. Truth is discoverable. Anybody with a sincerely open mind, the tools for research, and the capacity to critically think can discover true knowledge about the world. Though it doesn't necessarily mean of course they will. Now throughout this article I'll be referencing intellectual integrity so allow me to define upfront what I mean. I'm talking about a genuine commitment to acknowledge the truth wherever it leads. Even if it means rejecting previously held beliefs. It means having a humble, open, and self-critical mind. Without intellectual integrity it doesn't really matter how much research you've done nor how smart you are. If your beliefs aren't guided by the pursuit of truth, your conclusions are likely to be arbitrary and false. So before everybody assumes I'm just an elitist snob, let me clarify a couple of things. First, I believe that most inaccurate conclusions are simply due to a lack of research or intellectual integrity. Not necessarily a lack of mental capacity. One primary reason for this lack of research is the catastrophic error of intellectual dismissal, which is something I've talked a little bit about in the past.  There are a hundred reasons why somebody might hold wrong beliefs not related to their intelligence or intellectual integrity. If I was raised in a sheltered environment where all the textbooks and people around me claim that the moon was made of cheese, believing so wouldn't mean I was stupid. Let's take an easy case. When I was a child, I believed in Santa Claus. Everybody around me told me the same fanciful story, which I believed to be true. No problem. As I got older, my critical reasoning got a little sharper and I eventually rejected this belief. But imagine in the 21st century with access to the internet if I currently believed that Santa Claus was real. Now, I think it would be reasonable to assume one of three things. Number one, I'm not interested in the truth. Or number two, I haven't done enough research. And or number three, I do not have the capacity for critical reasoning. It becomes reasonable to make inferences about somebody's intellectual integrity or intelligence only if they refuse to change their beliefs when presented with superior arguments. Practically everybody experiences this change as they grow out of childhood. If an adult believes everything identically as he believed in childhood, we can probably make some reasonable assumptions about his mind. This might sound obvious when talking about Santa Claus, so let's take a more difficult case, economics. You might have heard of Paul Krugman. He's an economist and writer and he won a Nobel Prize in economics. He's also a vocal proponent of raising the minimum wage. I won't make the case here, but suffice to say, raising the minimum wage is bad economic policy. The information is freely available for anybody with an open mind to discover and the case is overwhelming. So what then can we conclude about Paul Krugman? I'd say two things, one more controversial than the other. I don't think Paul Krugman is stupid, and I don't think he's unfamiliar with sound economic arguments. I do think, quite confidently, that he is not intellectually integritous. He is a shill in support of progressive ideology, regardless of that ideology's accuracy. But here's the provocative part. To the extent that Paul Krugman is intellectually integritous and has researched the minimum wage, his conclusions must come from a lack of intelligence. I don't see another option, given the fact that the minimum wage is clearly bad economic policy. I realize that sounds terrible, but enough resources exist for anybody with an open mind and an internet connection with enough time to understand why the minimum wage harms the economy.  I just think he values ideology more than accuracy. If I'm correct, then it implies the following. People who are capable, open-minded, and do enough research will often arrive at the same conclusions. The truth. Again, this also correlates with my own personal experiences. Of course, it may simply reflect my own bias, but those individuals whom I perceive sincerely as pursuing the truth almost always hold very similar core beliefs as I do, whether philosophic or political. But this shouldn't shock anybody if indeed objective truth is discoverable, if people arrive at their conclusions for a reason. Of course, I don't mean to imply that all intelligent truth seekers agree on everything. That's not even close to being true. The gray areas where objective truth is unclear greatly outnumber the black and white areas. What is the ontological status of universals, for example? Well, extremely intelligent people can disagree with each other on this question and for good reason. But in my own limited experience, nearly all the disciplines I've studied have basic fundamental truths which can be discovered. In economics, the problem with the minimum wage is clear. In philosophy, the problems with thinking that we can know no objective truth are clear and discoverable to everybody, even in something like a physical discipline like the martial arts. There are core principles which can be rationally understood by those who are open to discovery. Consider Ptolemy as a final example.  He developed the Ptolemaic model of astronomy, a theory about the movement of heavenly bodies. The predictions of his theory were incredibly accurate and they meshed with the earlier works of Aristotle, and they were consistent with a dominant strain of metaphysical thought at his time. If you were a smart, integritous young man, you could check Ptolemy's predictions and measurements, and you would find, without using modern tools of course, that his predictions were accurate. The problem is, as reasonable as useful as those ideas were, they were wrong. His theory relied on the Earth being the center of the universe, which apparently it isn't. Everybody who believed so was wrong.  It simply means that enough evidence accumulated to challenge his model and that evidence was coherently explained by a superior theory of heliocentricism. Ah, but what about the dogmatist who insists on the Ptolemaic model, regardless of the superior arguments? He's the one I want to focus on. I think we can conclude one of three things. That individual is ultimately not concerned for the truth, or he hasn't done enough research, or he outright lacks the capacity to critically analyze. Given our limited intellectual status humans, our best theories in astronomy are likely wrong. But that's no problem. Inaccuracies can be corrected over time. Once a superior theory is discovered, we can each critically analyze it and determine whether our old beliefs should be discarded or not. Now to be honest, I'm still working out the implications of these thoughts. I don't know the ratio between the disingenuous, the uninformed, and the inept. The kind and youthful part of me wants to give everybody the benefit of the doubt. The harsh pessimist in me isn't so charitable. Regardless, this I can say for sure. Intelligence is not determined by the accuracy of your conclusions. What matters is the ability to adjust your beliefs in relation to the best arguments. And when somebody dogmatically insists on inaccurate beliefs, I think they reveal more about themselves than they intend. Thanks for watching.


Statistics and Excel Uniform Distribution Dice Example. Got data? Let's get stuck into it with statistics and Excel. Actually, we'll be looking at one note here, but we'll be talking about Excel. You're not required to, but if you have access to one note, we're in the icon left-hand side, one note presentation, 1510 Uniform Distribution Dice tab. We've also been uploading transcripts to one note so that you can go into the view tab, immersive reader tool, change the language if you so choose, being able to either read or listen to the transcripts in multiple different languages using the timestamps to tie in to the video presentations. First, a word from our sponsor.  Like our CPA six pack shirts, a must have for any pool or beach time, mixing money with muscle, always sure to attract attention. Yeah, even if you're not a CPA, you need this shirt so you can like pull in that iconic CPA six pack stomach muscle vibe man.  Yeah, as a CPA, I actually and unusually don't have tremendous abs. However, I was blessed with a whole lot of belly hair. Yeah, allowing me to sculpt the hair into a nice CPA six pack like shape, which is highly attractive. Yeah, maybe the shirt will help you generate some belly hair too. And if it does, make sure to let me know. Maybe I'll try wearing it on my head. And yes, I know six pack isn't spelled right, but three letters is more efficient than four. So I trimmed it down a bit. Okay. It's an improvement. If you would like a commercial free experience, consider subscribing to our website at accountinginstruction.com or accountinginstruction.thinkific.com. One note desktop version here in prior presentations, we've thought about how we can represent and describe different data sets, both mathematically using calculations such as the average, the mean, the median, the core tiles and so on and pictorially using box and whiskers as well as histograms. The histograms often being what we visualize when we're thinking about the distribution of the data and then using terms to describe the distribution of the data in the histogram, such as skewed to the right skewed to the left and so on. What we would like to think about now is the families of curves and formulas that we can put together that can often characterize certain data sets. And if we can do that, if we can represent a data set with some kind of curve, some kind of formula, it gives us more predictive power over that data set. So that's kind of the goal that we would like to have if we can say, hey, this data set looks like it can be characterized at least approximately with some kind of line or some kind of curve that we have a formula for. That would be a useful tool to have. Now the first one that we're going to look at, the first family of curves will be the uniform distributions. It's going to be the easiest one because it's basically a straight line. So when we said uniform distributions, you might have imagined that we're going to kind of distribute out uniforms for the accounting instruction statistics course and you're going to get a uniform or something. No, we're talking about uniform distribution as a family of a curve, basically representing data. All right, so we're going to be thinking about dice rolls here to get an idea of what this will look like.  And if we were to roll the die a thousand times and what would be the likelihood that any one number, whether that number be a one, two, three up to six, what's the likelihood that we roll how many ones or what's the likelihood to roll a one each time, for example, well, it would be one over six, which would be the 16.66 on and on. So if I rolled it a thousand times, what would be basically the expected value that you would have for any one number? It would be this times 1000, right times 1000. So you would expect there'd be 166.66 and so on of each individual number of one through six, that would be kind of our visualized outcome in our mind. Now note that this visualized outcome is just a model, we're coming up with a model that hopefully provides us some predictive power, but of course is not perfect in real life, which is clearly described to us by the fact that we have an un-whole number here. So it would be impossible for our predictive model to actually become true, because there's no way that we're going to get 0.67 of a one or a two that we roll, right? We can't roll it 0.67 times. But you can see that the model gives us predictive power over what what possible the chances are in the future. So if we take then that data and and I was to graph it or plot it out, if I look at the dice numbers, there's six numbers on the die one through six. And if I rolled the die a thousand times, each one of those numbers we would expect to come up to around 166.67. So our our kind of perfect model that we have in our head, which is too perfect because it doesn't take into effect, I count the randomness because this is basically a sample instead of the entire population of dice rules, which we imagine to be like an infinite number of dice rules. It would look like this. Now, if I was to graph that in a histogram, then we've got the dice one through six, and the expected roll, it would be just a straight line, right? We would expect all of them to be 167 across the board. And obviously, we have now a straight line. And notice that the straight line, you might say that the uniform, that's what the uniform distribution will be. You might say, well, look, there's only one of those, not really a family of curves.  So it'd be 33. So the so it's actually kind of a family of curves, because the straight line is up here. If we roll the 200 times, it would have a straight line at the 33. So these are family of curves, that which are basically straight lines, which are just straight lines, right, which are the uniform distribution that that that we would have, that would be our expected outcome formula for it, f of x equals C, we're going to have the same, the same outcome, because it's uniform. Nice, easy equation for us. Our predictions are nice and easy, although they're not going to be perfect, because in real life, there's going to be the randomness involved. Now, if we were to approximate what actually would happen, if I roll the dice 1000 times, you could do this in Excel, and you could do it by by using the random number generator, which would look like this random between, and then the bottom number would be one top number would be six. My voice cracked. I'm just going to copy it. If we copied that down 1000 times, I don't think I added all 1000. I only went down to here. But if you do this in the Excel worksheet that we will have as well, you would have 1000 numbers that are approximating that are randomly generated as a dice rule would be random in theory, right? One through six. So the likelihood of this one coming out a two was, you know, one out of six, right?  So if we take then that data, we could say let's do it this way, we can say, okay, now we've got the dice one through six, we've got the X, the expected rules were even. This is what we expected to happen. But this is what actually happened. Now this actual data, we're pulling in from from our data set over here by basically counting the numbers that are coming up. And the formula in Excel would look something like this, we're going to say equals count if brackets, we're going to be picking up our entire range, you can see it goes down to 1000 and in Excel. And then we want the criteria. So we want you to count every number in this range, if it has q two, which represents this number one. So if you find this number one in the range, count it. And it says that that happened 182 times. And then we have how many twos happened 170 163 is 164 fours 149 fives and 175 sixes. And we can see that those add up to 1000, which makes sense because we rolled it 1000 times, that's kind of our check figure. The difference then this is what we expected to happen. This is what actually happened. So there's a difference of 15 is pretty close, but not exact. A difference of three, a difference of seven on the positive side, a difference of three, a difference of 18, a difference of eight, and so on. So then if I was to plot this, I can say this is the actual outcome, right? So the expected was a straight line. But the actual outcome is not exactly a straight line. But if I was to try to predict what's going to happen in the future, it's useful for me to be able to use a function of basically just the straight line, right? I'm going to you if I'm going to say what's going to happen in the future. Well, this looks like it can be approximated pretty closely with the straight line. So that's why the straight that's why that's going to give us some predictive power about what will happen in the future. If I wasn't able to do that, if I was to say, hey, look, this doesn't look like it conforms to anything. It's just the numbers are coming up randomly, which could very well happen in different circumstances. Some data sets might not be able to be represented with some kind of line or approximating a formula. And if that's the case, then then it's going to be a lot more complex for us to use past data to project future data into the future. But if we're saying, hey, look, this looks like it approximates some kind of actual curve in this case, a straight line, then we can use the formula to help give us some predictive power of what's going to happen in the future. So notice that this histogram up top, I made with a bar chart, and we could make the make the histogram as well with a histogram in Excel. If we do it with a histogram, the histogram in Excel is going to try to give us a top and bottom number. But you can see there's a there's one, it's one number distance apart. So we so you can use either of those formula those charts to in essence get get the same results. So if you want to check that out in Excel, we'll have that in Excel. Now in Excel, if also, you wanted to run this experience, this experiment multiple times and say, okay, that's pretty close right here to the straight line. What if I did it four times? Uh, then and I can run multiple experiments and say, okay, are all of them going to come out similar similar. So we rolled once again, we did the the random number generator between one through six, as if we rolled the dice 1000 times four times, right. So again, this is what what apparently they used to do for for the in the universities, you know, if you worked in there, they had, you know, people just roll in dice all day. And they're part of the union job and stuff. But now we have the computer doing that, you know, it took a long time, but that but now the dice rollers are out of there. And we just we generate it with a computer now. So then if we if we made our our histograms this way, you could see again, it's approximating a straight line. This is the first results. This is then the second results. It's not exactly the same, of course, because there's randomness in it. But you can see it still kind of approximates the straight line. Here's the third one of 1000 rules. So they're all different. But they all, you know, approximate basically that straight line. And the idea, if you think about the sampling concept, would be that if I was to roll this an infinite amount of times, which would be the entire population, then it would in essence be, you know, a straight line representation, meaning you would expect the outcome to be one over six, right, for each roll times an infinite number of times, right? But because we have a sample of the data, it's not going to it's not going to come out perfect, but we can approximate it with our formula. And so that's the easiest kind of formula to approximate, right? It's a straight line. We can see we can see that now, obviously, if we can do a similar thing with curves, which we'll talk about in future presentations, representing the data with a more complex formula, but still a formula so that we can make predictions with with a with a formula, then that would be great as well. And we'll get into some of those in future presentations.


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All right, let me do a little survey of our audience How do I sound how's everyone doing today? Boys coming through okay, not too Not too grating. I hope Let's see. I think we have all our panelists here. I think people are settling in taking their seats so So while people are settling in I think I'll Go ahead and gavel us to order with my opening remarks Let's see okay. Hello everyone welcome to the inaugural panel discussion at the science circle For the fall 2019 semester and thank you for attending As a preliminary housekeeping matter, I want to remind everyone that the science circle is a grant-funded nonprofit organization It's dedicated to advancing the use of virtual worlds in education Because it's a grant fund it's grant funded We have to be pretty strict about conduct in attire. So Wanted to thank everyone for your understanding about that today or tonight or this morning. Whatever your case might be Our topic is unanswered questions The idea was to assemble speakers in different disciplines And have them speak about open questions in their field and we have with us today Nikolai Neve void William wall scissor G and Rob Knopp Rob I'm very pleased to have Nikolai void with us today to talk about his crazy math Apparently, it's rare that we have the opportunity to discuss academic math. So I'm particularly pleased to have Nikolai with us After Nikolai William scissor G will tell us about astronomy and Finally Rob Knopp will sort of tie our topics together and tell us about questions concerning the Hubble constant And so without further ado, I will I will ask Nikolai void. I think as his SL Tag to tell us a little bit about what he studies and to go ahead and open with his Presentation tell us what he wants to talk about make it away Nikolai Okay So I'm Nikolai Neve addition from In I spent a lot of time So today I will talk about The strange and crazy thing because the answer on the on the question on Can be a is a standard boring discussion of of various conjectures and so on Riemann conjectures something more patient what is it useful like big data and so on or just Crazy and so I prefer to be crazy and so Discuss the point which is very well known to all the Potomac issues at least starting from some level that the main question of mathematics is So it sounds Little bit silly strange and But it is not that silly it is a paradox and then it in politics itself is Is Itself is a paradox and so it works It goes from paradox to paradox. It is something about so this It is easy to just relate in one line Why this song because all the science has some natural objects outside of the science to investigate like so nature or languages or everything you like and Object of mathematics is Them politics itself though, but Let's come to details. So the standard common opinion from the Initial textbooks on politics that Mathematics has objects. So they are numbers and figures It is a very good point and it is actually so but It is extremely developed opinion which came from two thousand years of Euclid elements as a measure textbook and Euclid elements is Not elementary. It is come to him of All known to read or mathematics of This time and it's really We learned But it is not simple They pretty they've helped and complicate point of view but from these two numbers and figures numbers are I got down and eagles are Lended by people Those ideas about space Numbers themselves Really felt like God done, but are they are as we know now as a subject of Syrians paradox to fish tells us that The numbers and it's arithmetic is equivalent logically equivalent to all the That's first point there, but that's second point that you have no way to be sure that arithmetic doesn't contain contradiction so We have no way to be sure that accurately and consistently comes in of our In come for example, we You'll never come to Paradox that is equal to one. So some mathematicians speculate that the main problem of Mathematics is to fight a contradiction Inside but we hope that it is not so but but but I was in after We can only believe Magic doesn't contain addiction in its initial physical structure if we are using and so Equivalent to arithmetic is objective, but it is a kind of objective face. So so it is initial paradox of all the So I will focus on Two stories to illustrate the strange situation with one but in Which is Actually, how strange it is it isn't in common knowledge Common knowledge from mathematicians, but So The story is the story of Zero and position of number system how accidents in mathematics defines realization and so extremely So That you'll be my The position of numbers as we now know 19th century Actually Babylonians civilization was before it it was a Bible So now we know that Babylonian use face x the position of number six System but without zero and they was very good And now we know that they have a geometry astronomy They've held algorithm and for example one of Babylonian Algorithm are working now and is possible now for computer Babylonian algorithm which was analyzed in the 80s in the 70s and so error perfection Babylonian algorithm international Financial tables So then Greeks Greeks who are Owners of Our science as we understand it Who developed Bump button politics a lot in form of geometry Had no position on number six So they wasn't able to calculate fast And then how zero they they Optical how zero they discuss this object but speculated that nothing can't have a name Actually They had two kinds of numbers one of Rational numbers which are for merchants actually and geometrical numbers Represented by intervals They discuss the relation between them and this relation is extremely important and actually It is important The understanding of this patient on some deep level continuous up to now so but The position of numbers history was almost invented by Archiment So he stopped actually in one line Before the discovery of Judicial number system, so he was interested in multiplying our big numbers To do it and so it contained everything the purpose is no number system and There is an opinion of great mathematician The Gauss that it is calamity in history of science was the failure of It is to invent positional attach to what hates Wood science now be Rised if Archie it has had Made it discovery road Gauss in the middle of 19th century Equated that 19th age of science could happen as they did in all of the common air if Archimedes didn't stop one line before Discovery of positional number system There modern system More than ten base How we know it was created in India in six ancient theory Together with mathematical zero as we know it and negative number And it boosted science and engineering astronomy and so on in India but India was offered from Muslim Invasion Which destroyed huge ecosystem of Indian Education and universities, but still Mathematics survived on the very south of India in so-called Malabar Kerala or by just by the name of temple village nilas cool of mathematics and so At those hard times So they developed Analyzes integration Astronomers There's some ancient of infinite Ethics here as in 15th 16th page are you just 100 years before liveness and So it became actually known on the recent because This line survived Just didn't European colonial in fashion colonial wars and so those writings was on Tamil and Palayalam language eaten on Palm leaves well here I have a picture of palm leaf book South India and so the library is this collection of those Endless creeps was lost in fire in fortune and Unfortunately, but The main known Indian mathematician now the Manajan the Mathematically at least he is Relative he come from this school while it is obvious He did exactly this In that way But it is not stated explicitly anywhere So from India This come to Arabs The Numbers system was learned by Arabs. And so there was one more occasion It was brought to Europe occasion Because At the end of 12th century one merchant from pizza He got out that Arabs can count extremely fast and he he sent his Son Harder to Arab school. It was somewhere in Algeria and The other who is now known as Banachi learned Arab language and this art of counting translated the book of Al-Kharezmi on the Hindu art of according to Latin English and then On book and so seen that the art of past countings and spread it in Europe and actually from their Side of Exxon's They boosted the element of Astronomy and so on and so on and so on. You know, it's once more time came to analysis and show Our days, but it was occasion because it happened One hundred years later or Earlier Changes The next story is about numbers and figures numbers are God-done figures are invented as our view as patients there is implicit in patient between numbers and figures is the dimension So Aristotle proved by Well known to us XYZ argument that Our space is three dimensional, but it was Up to 1845 the space could have the tension only one two and and this Yeah, grassman German teacher of classical published a paper Where he presented Multi-dimensional space and the tools to describe with Geometry it was not acknowledged Before his death, but after his death people immediately understood that it is an extremely good thing to input Geometry on the spaces of Allusions of the structure of pieces on the solutions of equations of Algebra differential equations and physics and so on and so on so it is So algebra and physics obtain a geometry as a result, but in 1777 Josh Cantor crashed Aristotle argument So he established one-to-one Correspondence between the point of intervals and point of square and points of cool and just points of Aristotle's intentional space so Aristotle arguments That's the book so The engine appears to be something system is Instance after he discovered here wrote history and that I can't I see it, but I don't believe So the absolute physical space from Aristotle lost dimension it was big trouble and And Sorry wrong slide it was trouble so many people Great people was trying to fight with it with this situation so that the engine and physical space appears to be paradox So the point was that in Cantor's map and the maps based On his arguments, so they're killed by piano They are somehow non-continuous But at that time there was no explicit notion of what means to be continuous so everybody Something is continuous something is not continuous, but there was no founding of continuity And as there is all the of resolving of this paradox the continuity was needed and if that's to the Preparant of the poetry mostly by one career So and finally the problem was so In this line by 29 years old Adition Hector Berthos Young Browler 1910 So it was in fresh tools of as you did typology and homological algebra. He proved the invariance of continuous dimension and As a result we got Good notion what means to be continuous space which is actually Now time base of physics So Latinity and so on and so on but This notion of space it is deep and good mathematical model bear Physics somehow works, but it isn't absolute sense something because for example to be good to every dimension the space should consist of something what We never saw from points and more over Any on any scale any two points could be Which would be able to separate one from another by small neighbors so It works, okay, so on large scale Anton physics and Anton he has a Things also become one I Not absolute thing it is in practical aspects of the trans-communications. So you see that mathematics is paradoxical, and so on this, obviously, examples, historical examples of the PC car, how it tries to understand itself. And so actually all the big problems in mathematics which are hard to explain to the general audience, because it is an interior problems. They are interior problems out in the structure of mathematics, out of some symmetries in mathematics, symmetries in the geometry and numbers and so on and so on and so on. And actually all the known problems, actually as a Poincaré problem, as a driven architecture and so on, they are problems on this car. So I think my time is over now, so okay? Okay, yes. Thank you, Nikolai. That was really fun, and I have to say your slides are quite enjoyable. I'm sorry for my English mistakes, I stress my English isn't good now. Yeah, yeah. Okay. I think you did just fine. Thank you very much. We really appreciate your work to prepare that presentation and to share it with us. Thank you very much. So I'm working not on palm leaves, but on iPads. It is much more easy. Yeah? Yeah, very good, very good. Let's see. Is that better? I just moved my microphone, so hopefully I'm sounding a little bit better now. Don't really see too many questions in the local chat, so let's move right along, since we still have two more speakers. Our next speaker is Syzygy, William Wall, and he's going to update us on astronomy, basically. Nikolai, if you would go ahead and I guess just remove your slide screen. Just take that back in inventory. I was wondering if I could maybe ask a question of Nikolai. Oh yeah, sure, please go ahead. Yeah, absolutely. Yeah, let's see. Anyway, yeah, I was struck by the way you can apparently map a single dimension, a line into say two spaces, like a cube, or map it into a three space. As I understand it, different kinds of infinities, like one kind of infinity is the number of rational numbers, and another kind of irrational numbers. It seems to me that that's sort of similar to the type of mapping you're talking about, or maybe I'm completely wrong. I'm just wondering if you could comment on that. Sure, sure. Can't approve that point on the interval, on the geometric interval, is continuous. And so it is the same continuous in space by establishing just one-to-one respondents. So then it was a pretty complicated political argument. And so this made more clear by piano, more geometrical by piano. And even this map, but it is still complicated, this map is approximated by the continuous map, but finally the map is discontinuous in all the points. But it is right, yes, they have the same number of points. Thanks for that. Yeah, I enjoyed your slides too. So thanks for coming here, everybody, and hello to everyone. I'm, I thank the organizers for inviting me. That's Shantel, Jess, and I guess that's Matthew too. So I was asked to come up with a research question to attack in detail. And like Nikolai, I figured I would do something a little more general, because it's a good question. What is astronomy? And one way to look at that question is to come up with, provide a list of the research questions, the many research questions there are in astronomy. I'm doing basically the whole universe. Here's a picture of the universe. This is a nearby cluster of, not that nearby, L370, and it's lensing a distant cluster of galaxies. It's a cluster of galaxies, lensing a distant cluster of galaxies. And you can see the strange shapes of these galaxies in the background that are being lensed. One point I'm making here is that astronomical sources are great laboratories for testing our ideas. So I'm basically going to be doing the entire universe in 20 minutes, which, yes, it's overly ambitious, maybe even insane. It could be useful in some way, you tell me. Even though I won't be answering any of the questions that I'll be putting forward, the idea is to provide a glimpse of the sweeping this of the astronomical research, which I think will be interesting in itself. And we can always discuss these questions later on, maybe at some future date. Okay, here it is. So any field of scientific inquiry is vast, and compiling a list of key questions. Determining which questions are key is very difficult and requires hindsight, really. You can only tell after the fact which ones truly were important. And I would say that's even more so for astronomy than for other fields, because it literally studies the entire universe. So astronomy involves physics, chemistry, geology, and biology. These are vast fields in themselves. But astronomy overlaps and even pushes back the frontiers in those fields. Astronomy involves every subfield of physics, and I've listed the number of them here. Classical physics, relativity, atomic physics, nuclear physics, thermodynamics, and electromagnetism, condensed matter physics, and so on. So in addition to these subfields of physics, there are real subfields of astrochemistry, astrogeology, and astrobiology, which have their own journals. Astrobiology, too, which I found a little bit surprising, because there are no living specimens from outside the Earth. And there are actual books on astrobiology now. There's an astrobiology journal. Astrogeology Journal, this is a U.S. Geological Survey Geological Map of Mars. And here's the Hubble Ultra-Diet Field, which answers questions about, helps us answer questions about cosmology, as well as the galaxy of evolution. So what I'm saying here is it is a daunting task to be certain, but it'll help us better understand a field if we attempt to find the key questions. And the boundaries of the field, what is the field and what is not the field, what separates those two, if such a separation is fine, which can help set priorities for future research and inspire future research. It promotes thinking outside the box, which is a bad idea for a cat, but it's a great idea for scientists. It is a great learning experience to do this. So a good place to start, of course, is the Internet. And Wikipedia has this article on the list of unsolved problems in astronomy. This article has, well, it's far from complete. And there's a lot of stuff missing, but I'll try to fill in at least some of it. There's no way you're going to fill in all of it in 20 minutes. Planetary astronomy questions are questions of planets beyond Neptune, or are there planets beyond Neptune? There are dwarf planets beyond Neptune, and there are elongated orbits seem to have some kind of rotation, which is good. There are questions about Saturn's rotation and magnetosphere, and these questions like them apply to Jupiter. Well, then there's stellar astronomy. Good place to start, of course, is the Sun. It has a magnetic field, which affects its sunspots, and seems to be a diagnostic of its overall activity. When there's a sunspot minimum, called the Monder Minimum, the Sun was unusually cold, and so was the Earth. So why did this Monder Minimum occur? Did the Sun recover from the Monder Minimum? Then there's the Sun's corona. I realize I'm going quickly through here, not addressing every question, but we can always come back to this later if there are questions. It's so much hotter than the Sun's surface. And why is that? Well, the answer might be in the next section. The next question. Magnetic reconnection of the Sun's magnetic field, you can think of them as rubber bands threading the Sun. There's a lot of energy in these rubber bands, and when they're stretched, they're actually in the Sun by the rotation of the Sun. They will break, and they'll reform new rubber bands that fly off into the Solar System, and these rubber bands are carrying charged particles with them. So you get solar flares and coronal mass ejections. But they seem to be happening faster. These reconnection events are faster than depicted by standard models. Why is it happening so fast? This one problem with this Wikipedia article is they have almost no questions about star formation, and that is a very important question in astronomy, the details of star formation. One question they have here, and I'll come back to star formation a little bit later, is about the stellar initial mass function. This is when the stars form, they have a distribution of masses, what determines that. What is the exact mechanism by which you have a core collapse supernova, and that's represented by this diagram here? How does that exactly work? I don't know why this is in the stellar astronomy section, but maybe because stars are the reasons for a fast radio burst. These are transient radio pulses that are very strong. They seem to come from very tiny regions compared to the size of even a planet, and they have been detected in the galaxy. There's a gigaparsec away. The first repetition, these fast radio bursts apparently do repeat. The first repetition was detected by this telescope here. A series of troughs. It's an impressive telescope. It's 80 meters by 100 meters, and it's made on a shoestring budget because it has no mechanical moving parts. Very large radio telescope. Called CHIME, Canadian H1 mapping experiment in the interior of British Columbia, Canada. I've been to see this telescope because I used to be a graduate student at the laboratory. It is impressive. That was the first to detect this repetition of a fast radio burst, which may help us understand fast radio bursts better. Then there are questions about cosmic rays. They interact with the cosmic background radiation, so they shouldn't be able to travel very far, with some exceptions, which aren't understood. And then there's Tabby's star, which some have heard about. Supposedly aliens built structures around it that caused fluctuations in its brightness because it was one star. 2018, there's a paper published found that it was actually the fluctuations are not quite as strong, suggesting it's probably just dust. So I like the caption here, which you can't really read. It says it's not aliens, it's never aliens. And next, another incomplete list about galactic astronomy. You see here, let's see, this is a galaxy. And as we go out in distance along this graph here, you see this, and there's velocity this way. We can look at the rotation of this galaxy. And the rotation follows this curve. Beyond a certain distance, it should be falling off, but it's not falling off. Why isn't it falling off? You'd expect it to be going down like this. One reason is probably something called dark matter that's responsible for it, although there are other explanation, modified Newtonian gravity, which actually works very well on it. Just called Mond for short. Now stars, as they age, they become more metallic, which means they produce more elements that are heavier than helium. So you'd expect an age-metallicity relationship in our galaxy. There seems to be a somewhat universal relationship, depending on where you look. It's not completely universal. I don't know. They didn't ask any questions about spiral density waves in this article. That would be interesting because we have, of course, galaxies like this one, M51, with the spiral arms. Spiral arm pattern. Spiral arm pattern is how stable is it? How long will it live? Maybe it's galaxies shift from one spiral pattern to another, and then there are other spiral, and there are other instabilities in the plane, such as spars, which are not totally understood either, and how they affect star formation. And here's a picture you've seen before. Rob has given us a talk on the first image of a black hole by the Event Horizon Telescope. One of our telescopes in Mexico was involved with that, the Large Millimeter-Rape Telescope Alpha Fonzo Sorrano. The right thing about black holes is they help us understand general relativity and also the interface between general relativity and quantum mechanics, which is why Stephen Hawking was so interested in black holes. So many questions about internal structure, if such exists. They produce thermal radiation. Do they produce the Hawking radiation at the level you'd expect? Then they would evaporate what happens to the information inside them because quantum mechanics doesn't allow for loss of information. And then there's a question about how supermassive black holes form. Had to have very massive black holes merging, and we know that black holes merge because of the LIGO experiment. Gravitational radiation from the mergers.  So it would take longer than the age of the universe for them to merge. But there must be some mechanism by which they're able to do so because such supermassive black holes exist in the centers of galaxies, including the one in this picture here. Then there are questions on cosmology, and Rob's going to handle one of those. Having to do with the distribution of dark matter and dark energy in the universe. You can see the diagram here. Most of the energy density in the universe is dark energy with some dark matter. And just a tiny amount of the kind of matter that we know about that we can detect called baryonic matter. And this diagram represents the expansion of the universe. There's this early inflation. This is time going up. And this represents the size of the universe inside. Acceleration here is here. So there are basic questions like what is dark matter? It's some kind of particle. Or maybe there is instead of some extension to gravity, like Mond. Then there's questions about the Hubble constant, which Rob will handle. And further questions about the acceleration. What causes acceleration? Presumably dark energy or maybe it's something else. And the fate of the universe. What is the fate of the universe? The latest evidence suggests that we will be undergoing a big rip where everything is torn apart as the universe accelerates faster and faster. Although I don't think this is completely ruled out where the universe undergoes a big crunch. And then who knows, maybe another big bang and it starts again. Could be a cyclical unit. And as I said before, star formation is a very interesting question. It's a very, very star as that we see at night. How did they form? There are many details that we don't understand. Stars form from the interstellar medium and specifically from molecular clouds. The interstellar medium is ionized gas, atomic gas, and molecular gas. And it's almost entirely hydrogen. I'm talking about clouds of molecular hydrogen. Here's a molecular cloud, a giant molecular cloud. The stars form a giant molecular cloud. And we see some stars here. The reason we can see them, this is an image in the infrared. Look through much of the dust. So there are many questions about how the initial conditions, the physical conditions in these molecular clouds, how do they determine the final stellar properties? Do we have an isolated star forming? Not usually. You usually get stellar clusters. And that produces a certain initial mass function. Why that particular initial mass function? Environment. And stars tend to destroy the molecular clouds in which they form. And then there are questions about the stability of giant molecular clouds. Now I have a diagram here, and I'm going to show up a blow-up of this diagram. This is a beautiful diagram. This is the plane of our galaxy. And it's seen in a tracer of molecular hydrogen, carbon monoxide, rotationally. I can talk about that shortly. But papers in the 1970s by Zuckerman et al. have strongly asserted that these clouds have to be turbulently supported. Because if they're not, if they're undergoing large-scale collapse, we would see a star formation much higher than we do see. And we'd also see a spectral signature of collapse. Now there's been recent work by Enrique Vazquez and company at Morelia, UNAM, which is the Autonomous National University in Mexico. They run numerical simulations of the evolution of molecular clouds. And they say that there's enough evidence from observational evidence, as well as from their simulations.  Why don't you have an unusually high star formation rate? Because the stars, as said here, disrupt the clouds that they form in. So that stops the star formation from continuing. Also, you don't expect to see a very simple spectral signature of collapse, because you have collapse occurring at different scales, different hierarchies within the clouds. So let's look at this a bit better. So here's our galaxy. This is the plane of our galaxy from longitude 10 degrees to 50 degrees. The center of our galaxy would be way over here. This is an image of our galactic plane as well. But this is an infrared, so you see hot dust and some stars. And you see some blow-ups of these regions. Here, showing you the structure. This map is beautiful, done with a monobium of 45 meters. You can see all kinds of filamentary structure and clumps. These maps are beautiful and fascinating. Down here, in this particular GMC, the giant molecular cloud, M17 Southwest, you can see filamentary structure on a smaller scale. Now, Enrique and I want to observe with the LMT, the GMC like this one, to see if the filaments behave in the same way as his models. And we might be able to do that with the LMT next year. Hoping that we can do that, because we'll see how well his models work. And of course, another thing that's left out, exoplanets and extraterrestrial life. That's an absolutely fascinating area. I find it fascinating, I think almost everyone finds this fascinating. Questions about exoplanets, how do they form? How do the rotations interact with their orbits? Questions for our own solar system as well. How common are exomoons? They must be very common, but they might be very difficult to detect. And I love this poster. Potentially habitable exoplanets. These exoplanets are real. The images are not real. These are just artist's conceptions, because we don't have actual images of them, but I still like the poster. Then, of course, you get to extraterrestrial life. If you have exoplanets, you might have extraterrestrial life. But can we find unambiguous biosignatures in the spectra of these exoplanet atmospheres? The key word there is unambiguous. Is it possible to find unambiguous signatures? Well, here's an example of a planet spectrum. This is actually just the Earth, what it would look like if we were an exoplanet. I don't think the signal to noise would be so high, but you can see certain lines, oxygen, water vapor lines. And how do they do that? Well, I come over to this diagram. You see if the Earth is in the plane of the exoplanet's orbit, you'll see the planet passing in front of the star. This is called a transit or primary eclipse. And when that happens, you see the light here will dip down. As it passes in front. But if it has an atmosphere, it'll dip down lower. And if it dips down lower, the amount it dips down, that extra dipping varies with wavelength. That variation in that dipping is what you would get in this spectrum here. And if you get oxygen, supposedly it's a great biosignature. But I read, and believe it or not, I checked an astrobiology journal from 2018 saying that this oxygen could actually be produced by photodissociation or photolysis of other molecules like HT2O or CO2 if the star has particularly strong ultraviolet emission. So these oxygen is not necessarily an unambiguous biosignature, fortunately. Anyway, what kinds of stars are likely to have life-bearing exoplanets? Different spectral types means basically different temperatures. And there are questions about, okay. So if you're feeling confused and overwhelmed and you're normal, this is the whole universe in about 20 minutes. This was an incomplete somewhat disorganized survey, but I'm hoping it can phase a sense of the breadth of astronomy. And that the many active subfields of research will push back the boundaries not only of astronomy, but other fields, maybe even biology. There are the references. I've made a PDF version of this talk available to Shantel, so you can get that from her if you're interested. My apologies for going so fast. I wanted to have time for discussion at the end. So feel free to ask me questions. A lot of applause. I thought that was really enjoyable. Thank you. Let me see. Let's see. I'm scrolling back up through our comments. I, since you did leave us a little bit of time, I wanted to touch base on a couple of things. One of your slides mentioned the big rip. I'm not really familiar with that. Can you expand upon that a little bit? And then I have one other question too. Sure, let me see if I can get back there. Yeah, okay. So big rip. The idea is that as the universe expands and the acceleration would supposedly become so intense that the molecules and atoms themselves would be torn apart. Oh, I see. So that's sort of a prospect that the acceleration of the expansion just keeps accelerating until everything just gets ripped apart, sort of. Is that fair to say? Something like that, yeah. I don't understand all the mechanisms of it. I don't know how it would have to be like an acceleration down to very small scales as well so that it would affect. Yes, fascinating. And then one other thing I wanted to mention is the LIGO telescope that detected the gravitational waves. I think that's right. Is it LIGO? So I heard something recently that made me a little bit curious. I was sort of under the impression that the detection of the gravitational waves was kind of a one-off experiment where we set it up and we detected the gravitational waves and then that was the end of it. But I heard something recently that there are sort of ongoing observations of gravitational waves. So now that we have the LIGO telescope set up, is it kind of a working operational telescope that kind of allows us to monitor gravitational waves or what's going on with that? Yeah, it's a full-time observatory and it's not exactly done with. They have had a number of detections. I don't know the rate, maybe Rob knows the rate, but it's something like a couple of per month of some kind of gravitational collapse. I think they've even had a merger of black hole with a neutron star. So yeah, it's ongoing. It's an ongoing observatory and it's not the only one. There are two of them. One in Louisiana, one in Washington. And so they both, they both detect things. Oh, a neutron star and neutron star merger two. Fascinating. So I just love that. That's great. It's gratifying to know that, you know, it's still generating a lot of good science. Yes, it's important because I mean, we're not using electromagnetic spectrum. We're not even using, you know, the usual particles. You're not even trying to have a neutrino observatory, which would be interesting in itself. But it's not using particles or not conventional particles. Anyways, it's fluctuations in space time. Yeah, it's trippy. Okay. Well, thanks very much. I think we should move along. We have a lot of interesting comments in a local chat. Which I would love to get to sometime. I mean, if we had time at the end, maybe we can get through some of... You had some interesting comments too about turbulence and so on, right? Oh, yes, I did. But actually, I think you sort of addressed those as you continued talking. But, well, okay. Anyway, so I'm kind of scrolling back through the chat here. So I guess we should move on and maybe we can come back to these if we have time at the end. Sorry about that, everyone. But I do want to get to Rob's presentation on the Hubble constant, which I assume is going to combine maths with astronomy, sort of tying our topics together. So Rob, why don't you pick up from here? All right. So I guess I'm sort of a conformist because Chantel asked us to talk about a big outstanding question. And so I'm talking about just one question. So I won't be giving you a huge history, but I still will give you a history of this question, the question of the Hubble constant. This is the Hubble constant. The tension in the Hubble constant is what I'm identifying as the biggest question in cosmology specifically. And as you just heard from Mike's talk, astronomy is way more than just cosmology. So I would hesitate for the same reason Mike did to say what is the biggest question in astronomy because, you know, find six astronomers and you'll get eight answers to the question. So even in cosmology, people would disagree about what the biggest question is and then you'll have to see, what do you mean by biggest? Is it the biggest as in the most cosmic, the most fundamental? Is it the biggest as in the thing people worry about the most? I don't know. But in any event, this question is a big one because it's sort of an outstanding sore point in cosmology right now. It's a place where stuff on our data doesn't seem to line up quite right and we don't know what's going on. So the Hubble constant, what is the Hubble constant? The Hubble constant is the current expansion rate of the universe. It's a parameter in our cosmology and it's a number, it's a way of saying what is the current expansion rate of the universe. And one way of talking about it is that if you compare the distance of a galaxy to the speed it's moving away from us, well if things farther away are moving faster, that's an expansion, that's what an explosion would be like, although that's not really what the expansion of the universe is. And we observe, and this is from a paper from 2001 which is one of the classic papers on the Hubble constant, that galaxies at greater distances are moving away from us faster and it's a line, the relationship is a line and the Hubble constant is just the proportionality or the constant of proportionality between the two. So the value of 72 kilometers per second for megaparsec says, and I'm going to say this, not one megaparsec, but a galaxy that is 10 megaparsecs away, well I would multiply it by this constant and I would get 720 kilometers per second. So that'll show up right about here on the plot. So something that's 10 megaparsecs away will be moving at 720 kilometers per second away from us. Now that's just due to the expansion of the universe. Galaxies also thrash around each other as they're in clusters and they orbit and things like that as well and that's motion on top of this expansion. But as a whole, galaxies are all moving away from us, they're all getting farther away from us and the Hubble constant tells us the expansion rate. Now it's the Hubble constant, it means today's expansion rate because of the dynamics of dark energy and dark matter and all of that stuff, the expansion rate has changed over the history of the universe. So when you say the Hubble parameter, you're referring to however long since the Big Bang you want to talk about, but the Hubble constant means today's expansion rate. So, and there's various ways to measure today's expansion rate of the universe and you get plots like this one when you do that. Well, so the Hubble constant is so called the Hubble constant because Edwin Hubble is the first one who gave us a value for it. Back in 1929, he published a paper where he had looked at and notice he called them extragalactic nebulae because this was around the same time within 10 years of us figuring out that galaxies were other galaxies and not nebulae in our own galaxies. So the name extragalactic nebula is sort of vestigial from that. He measured Doppler shifts and got speeds and he measured distances from brightnesses of a kind of variable star and made this plot and saw this relationship and notice he got a Hubble constant of 500 that's a whole lot bigger than the one that we have today and the reason for that is that he was looking at one kind of variable star and thought he was looking at a different kind of variable star and so all of the galaxies were actually much farther away than his estimates based on the fact that he was looking at a different type of star from the one he thought he was looking at. Well, all right, so that's 1929 and today we have a different value. The Hubble constant sort of has a long insorted history. So you start back around 1929 there about, you have these early measurements that around 100, you actually have George Lemaitre published a very early one even before Hubble with the idea of the expanding universe and you can see that the estimates of the Hubble constant sort of came down as people measured it towards what is probably much closer to the real value and the sort of interesting things in here you could talk about with the sociology of science as well as just the science itself but somewhere around 1970 we settled on the idea that the Hubble constant in these units had a value somewhere between 50 and 100 and then for about two or three decades it stayed that way and it was sort of interesting that there were two main folks working on measuring the Hubble constant. One was Sandage and Taman and the other was Devokalers and Devokalers. So Sandage always came up with values around 50 and Devokalers always came up with values around 100 and both of them published error bars that were much smaller than the distance between them and astronomers who were not in either camp sort of threw our hands up and said well we'll call it 75 plus or minus 25 because we don't know who's right. Now I would say probably a lot of astronomers sort of believed in their heart that Sandage was right turns out that neither one of them was right they were bracketing what is probably the real value but there was this long period of time and so including when I was in grad school so I went to grad school in 1990 that's actually off the edge of this plot but even still in the early 1990s in fact through basically all of the 1990s the Hubble constant was still uncertain between 50 and 100 we didn't know it to a factor of two so there was a gigantic uncertainty and what the actual expansion rate of our universe was which is the most fundamental parameter in all of cosmology or at least the most basic parameter if not the most fundamental parameter so you know I was working on stuff that wasn't cosmology back in grad school and so I just sort of said okay it's 75 plus or minus 25 we don't really know what it is and in fact it's a little bit like there was this other thing that happened when I was in grad school the Soviet Union went away well I remember in the 80s being in high school the Soviet Union would be forever right I never expected the Soviet Union to go away in my lifetime never mind when I was so young I also expected in grad school that we would not know the value of the Hubble constant for a long time I figured that it's going to be uncertain for a real long time well so this is the thing I want you to remember is that for a very long time we had settled on about what the Hubble constant was close to the modern value but it was uncertain to a factor of two so we just knew that we didn't know it very well but all right the way of measuring the Hubble constant that all these folks did it was by looking at stuff where you knew how bright it was so some kind of variable star or a supernova or something like that and measuring its redshift to see how fast it's moving look at how bright it is to figure out how far away it is there is a whole completely independent different way you could measure the Hubble constant that depends on looking at the cosmic microwave background so this is you and as you look further out into the universe one important thing to realize is that you're also looking back in time it takes time for light to travel so if you're looking at something that is 500 light years away that would be a star in our own galaxy it took 500 years for the light to reach you so if you're looking at something that's billions of light years away you are looking at it as it was billions of years ago we can look back far enough that we are looking so far back in time about 13.7 billion years in time that the universe was all plasma it was all hot and it was all dense and it was one big soup of plasma dark matter mixed in with protons and electrons and some other stuff bouncing around with photons so light all bouncing around and it was opaque and bouncing around and and as the universe expanded and went through a transition from opaque to transparent so if you imagine looking through sort of very thin light towards the surface of a light bulb or the surface of the sun or something like that you can kind of see CC until you get to the opaque surface and then you can't see beyond that and that's what we see we call it the cosmic microwave background when we look just the right distance away that we're looking just the right amount of time in past we see the universe when it was opaque and we see this uniform glow everywhere across the sky and this was a big deal back in the 60s when this was discovered because this was a prediction of the big bang model and then we discovered it and said hey this is really what made people think that the big bang model was a good model to describe our universe measurement since then here's a measurement from 1990 of the spectrum of it what's important about this is the squares are the data points and the error bars on the squares are smaller than the squares the line is a theoretical fit to a pure thermal spectrum something that's glowing just because it's hot the universe when you look at it as a whole looking back when it was all plasma is an extremely perfect black body what's more the temperature is the same you look at one direction in the other direction every direction you look the temperature of the the cosmic microwave background which has to do with how long ago in various different directions was the universe that dense it's consistent to better than one percent so we have this uniform glow everywhere but if you look carefully enough it's not perfectly uniform there are in fact little fluctuations so the fluctuations here are like one part in 40 000 something like that are about where the fluctuations are on top of it there's actually a bigger variation that has to do with the Doppler shift and the motion of the our galaxy through the universe or our sun through the galaxy but leaving that aside there are a few little fluctuations in the cosmic microwave but not a few they're locked they're all over the sky but they're really really tiny one part in 40 000 but they're real and they're there and it turns out by analyzing these fluctuations you can learn all kinds of things all sorts of things about our universe various parameters of our cosmology you can test things like is our basic cosmology model working other things like what's the mass density of the universe how does that compare to the overall density of the universe there's lots of information you can get from this and one of those pieces of information you can get is the Hubble constant now this sounds a little paradoxical because we are looking 13.7 billion years in the past and getting today's value of the Hubble constant from it so how does that work well basically because what we're doing is we're taking our standard model of cosmology and applying it to this cosmic microwave background image and to get the right picture what value of today's expansion do we need and so that's a way that you can get the Hubble constant just one of the parameters of cosmology by looking at the cosmic microwave background so it's a different way of measuring the Hubble constant from looking at bright stars or looking at supernova and doing and looking what I'm going to call the current way the local universe or the recent way of looking at the Hubble constant where we're looking no more back in time than say a billion years which while sounds like a long time to you compared to 13.7 billion years for the whole universe that's not really all that long so if we look at nearby quote unquote nearby galaxies up to say you know a billion light years away something like that that's the first way I told you about measuring the Hubble constant if you look at the cosmic microwave background you're looking back in time of 13.7 billion years you get a different way of measuring the Hubble constant so as recently as night as 2004 just a few years ago these measurements were still pretty much consistent with each other so when I say the distance ladder that's a technical term but it has to do with looking at stars and supernova and things like that in nearby galaxies this was our best estimate 73 plus or minus 2.4 you can see that the error bar has gone down since that 2001 paper from the cosmic microwave background we had a more precise value it was 69.6 plus or minus 0.7 the error bars don't exactly overlap but they're very close and so they were not different by more than 2 sigma and that's not something you'd get excited about there was a several percent chance that randomly we would get values different by that much so we considered this basic consistency at least it was a minor inconsistency but not real so we saw you know we had an idea that we knew the value of the Hubble constant probably to about one percent because we had this measurement that's good to one percent and it's consistent with this measurement that's good to about three percent and at least they were they were almost consistent and they you know to the 90 percent level they were consistent sort of thing so great we felt good about that that was the last time we felt good about the Hubble constant because over the next few years this happened so what are you looking at here well on the horizontal axis is year of publication it only goes back to 2000 and here is the Hubble constant with values between 60 and 80 now here's the thing I want you to notice about this remember on an earlier slide we had values that all the way from zero up to like 600 and between 1970 and 2000 it was uncertain between 50 and 100 so all the differences on that you know that would have been going from here up to off the top of my slide so the differences we're talking about here are much smaller than the differences we used to be talking about before this is that 2001 measurement that gave us 73 plus or minus eight so that was our best measurement Cephyids is a kind of variable star so that's one way of measuring it TRGB stands for tip of the red giant branch it's another way of looking at stars to try and get an estimate for the Hubble constant that's been used more recently and then CMB stands for cosmic microwave background and our early CMB values of the Hubble constant which came from the WMAP satellite were 100% consistent absolutely consistent with the values that we had before and when you get to 2004 you know you're here in 2004 they're still barely overlapping right after that we started getting lower error bar measurements of the cosmic microwave background the Planck satellite started returning lower error bar measurements and what's more we were getting better and better measurements with these Cepheid variable stars and the two diverged basically they were consistent up to here but then as the error bars shrank they didn't come together and so now these two measurements are discrepant with each other at a statistically significant level so we have two different ways of measuring the Hubble constant one of them gives us here something like 68 or 67 kilometers per second per megaparsec the other one gives us a value of like 72 or 73 kilometers per parsec or kilometers per second for megaparsec now those are so close together that if you went back in time and told me in grad school we were uncertain about that I would say what are you complaining about you have it way better than we have it but the error bars are also extremely small and so the precision of these estimates are such that even though they're really close compared to what we would have thought in the 1990s they are not consistent with each other there's this big difference between those two and then here's this third measurement that that some people started using recently the tip of the red giant branch and you notice it nicely comes in between so oh dear so what's going on here there are other ways of measuring the Hubble constant and by and large most of the ways I mean some of them have big old error bars so they're they're preliminary and we don't yet know what they're going to tell us but another there are other ways of measuring it many of them most of them where you look in the local universe give a value more consistent with this value and inconsistent with the cosmic microwave background so we have this problem that we have different ways of measuring the Hubble constant the most fundamental parameter of our universe and they're different and so that tells us something is wrong something somewhere is wrong you see headlines about this all the time usually the headlines include words like new physics or throw out our model of cosmology or things like that which are a little hyperbolic in my view this is a real outstanding problem but that doesn't necessarily mean we have to throw out all our model of cosmology so when I say our model of cosmology what do we need well really it's on a couple different levels our fundamental model the big picture idea is just the big bang and the big bang is just this idea that the universe a long time ago was in a very hot and dense state and it has expanded and cooled off to today where we have stars and galaxies that's the hugest overview of the big bang the big bang is an interesting name for the theory because it's named after a moment that honest pictures include as a question mark because we don't actually understand and in fact we know that we don't understand because we know we don't have physics that works to even estimate what happened at quote unquote the moment of bang if there was such a thing so really we can only start estimating a short time after that our tiny fraction of a second after it but then we can do calculations a lot of calculations that are consistent with a lot of different data from this tiny fraction of a second to today so the big bang as the idea that the universe was hot and dense it started with a rapid expansion rate it was hot and dense and then as it has expanded it's gotten lower density and cooled off that's the basic picture of the big bang and that's in no danger whatsoever however the big bang is a big gigantic umbrella and within the big bang there's a lot of more detailed models and in fact we have a standard more detailed model that we call lambda CDM and so if you read news articles sometimes it will refer to lambda CDM what's important to realize is that lambda CDM is not synonymous with the big bang the big bang is a car lambda CDM is a Volkswagen bug it's just one way you can do the big bang it's our standard model because you start with the big bang but then there's all kinds of various parameters that aren't set there lambda CDM chooses what a bunch of those parameters are and those choices seem to fit the data really well and it has this name well that there's two pieces to the name the first one is lambda lambda was what Einstein originally called his cosmological constant what it really means is that this mysterious dark energy the stuff that we don't know what it is but the it's making the universe's expansion accelerate it's really bizarre well in the lambda CDM model it's vacuum energy what does that mean that means get a region of space take out everything that you can take out take out all the atoms take out all of the fundamental particles take out all of the photons until you can't take anything else out it's there's still some residual energy density that would be vacuum energy and so if that residual energy density is not zero but it's really small well that would that would cause the universe's expansion to accelerate and that's what dark energy would be that's our default model now there's lots many other possibilities for what dark energy is if dark energy is a cosmological constant we will not have a big rip dark energy has to be different from vacuum energy to get a big rip and so obviously we're thinking about other kinds of dark energy the other half of this is CDM the other big mystery oh wait I thought the big mystery was the Hubble tension well okay two of the big mysteries are what is dark energy and what is dark matter CDM is this particular kind of dark matter called cold dark matter and cold doesn't mean what you think it means it doesn't mean that you can put ice cream in it keep it cold if you you know the air in your stove when you heat it up to 350 Fahrenheit is cold in that none of the air molecules are moving close to the speed of light so when a cosmologist refers to something as cold they just mean the particles are not moving close to the speed of light so the surface of the sun is cold in that way of talking about it so cold dark matter just means the dark matter particles are big enough they're still tiny fundamental particles but they're big enough that with the energies they have they are not moving close to the speed of light so detailed models of the growth of structure match cold dark matter very well and so we believe cold dark matter is the right kind of dark matter and lamb to CDM together matches a whole bunch of stuff very well but there is this problem that if lamb to CDM is right then the measurements of the Hubble constant from the cosmic microwave background and the local measurements of the Hubble constant should be consistent with each other and they're not and so this is what we say when we say our standard model is in trouble it means that lamb to CDM is in trouble maybe and I'll explain the maybe a little bit on the next slide it doesn't mean the big bang is in trouble it just means either dark matter isn't strictly CDM or dark energy isn't vacuum energy or both and the differences may not even need to be all that big to explain the discrepancy in the Hubble constant it just does mean though that it can't be exactly this and of course Sisi G has said a couple times now or the observations that are in error and so resolving the tension that's my number one why do we have this tension the observations are in error because of course we've been down this road many times before I say unidentified systematic Sisi G also mentioned or the error bars are underestimated the hope the history of the Hubble constant is a history of people underestimating their error bars I think we do a lot better job about it now than people did back in the 70s and 80s but it's conceivable that we still are not estimating our error bars right well the statistical error bars I'd be surprised if those weren't estimated right but it could be there's additional systematic errors what that means is for example looking at Cepheid variable stars Cepheid variable stars are massive stars tend to be found in regions of galaxies that have lots of dust have we corrected for the dust correctly well we think so but maybe we have it for example so it could be that there are systematic errors that we are not correcting for that would shift the estimate of the Hubble constant if we did correct them for it could be in both methods one or both methods it could be that we have a systematic errors with our nearby measurements it could be systematic errors in the plank measurements I don't know and if I had to bet I would bet that this is what it's going to turn out to be that we will discover some small systematics and the measurements will become consistent with each other that would be my bet but of course that's just a bet I don't have a real scientific reason for believing that so we need to consider the other possibilities and one is lambda cdm isn't quite right version one dark energy is more complicated than vacuum energy and of course if it's a kind of dark energy that we call phantom dark energy that would lead to a big rip and so that's kind of awesome we kind of want that because everything being torn apart and a huge gigantic explosion that rips apart even atoms and molecules who wouldn't want that right right anyway so it's possible that dark energy is not just vacuum energy now the thing is is the people who have tried to model this and explain the differences it's kind of challenging actually to do it without making dark energy especially contrived but okay that's one possibility another is dark matter isn't strictly cold and once again it's the same thing people who've tried to model it haven't been able to explain it with very sort of the simplest ways of modifying dark matter but you know this is a possibility there are other possibilities people think about and it might be that we actually live in a slightly special region of space and that's sort of heresy because the fundamental assumption of cosmology the cosmological principle is that we are nowhere special that we're not in a special place in the universe but we're in a typical place in the universe well what if it turns out that there's fluctuations in the overall density and we happen to be in a low density region that could explain some of the differences and obviously something else I haven't mentioned there's other things people are thinking about I haven't mentioned and um something yeah maybe gravity general relativity is a little bit off is another possibility but it's also possible it's something that nobody's thought of yet will explain the discrepancy so we have right now the most basic parameter of our universe is the current expansion rate it's parameterized by the Hubble constant and we have two ways of measuring it by looking at two different epics in the universe way back when and now and we get two values that are different by several percent but the uncertainties are much smaller than that so we know something is wrong and so this is a giant outstanding question in cosmology right now that lots of people are working on one way or the other lots of people are thinking about and the implications of the answer to this question will resonate throughout all of cosmology maybe if it turns out it's systematic error is not so much if it turns out it's not systematic errors then that's going to affect what we think about dark energy dark matter maybe gravity how the universe expanded all that sort of thing I would not say though that this discrepancy threatens the notion of the big bang at all so when you read our in the newspapers about our whole our model of the universe has to be thrown out they're not talking about the big bang they're talking about lamb to cdm so I will stop there and leave us some time in case anyone has any questions okay great Rob that was fantastic really loved your slides really liked the use of color here on this last slide to highlight the different bullet points that's very nice so I don't know that I may have any questions if anyone if any of our panelists have questions feel free to speak up in voice and if our students have questions feel free to post them in nearby chat and we'll try to address them all right lots of applause Arianne has a question if I'm an astronomer from Mars what do I think about the future of the earth well I guess if I'm an astronomer from Mars I'm jealous because earth has such a thick atmosphere and is so warm on the other hand if I'm an astronomer from Mars I probably really like thin atmosphere and cold so I think the earth is a nightmare world like we think Venus is yeah I mean that's sort of an interesting question because would an astronomer from Mars think differently about global warming and climate change climate change than the people here on earth do and of course you know on earth you listen to the people who actually do the science on climate change and we know pretty well that we're in a lot of trouble it's sort of the the world rulers are finding various ways to drag their feet on even admitting that it's real so what would an astronomer from Mars think yeah I think maybe they'd think damn I'm glad I don't live there they're going to be in trouble in a hundred years yeah that's an interesting question and it reminds me of a cartoon that was it might have been a far-sight cartoon where you see a bunch of Martians maybe they're astronomer Martians they're looking at the earth and and all these mushroom clouds are are are enveloping the surface of the earth and some large uh conflagration they're saying great fireworks show all right actually I have a I want to go back and ask Sean Pierre a question um I I think I might have remembered history wrong I had this idea that the Hindu mathematicians did not have zero and it was the Arabs who introduced zero am I wrong about that yeah I thought that too is uh is it Nikolai yeah yeah I'm here I'm just I was following him asking this question uh no mathematical zero it is extremely interesting object so that that zero was mathematically understood as a number equal to uh natural numbers beside one property you can divide by by zero they uh it was first produced by uh Indian mathematicians uh in the sea by uh Indian astronomer actually and uh then uh it was a big story about it so it was also impressive ancient uh also for Indian so the intention that it is some kind uh naming of nothing so it is uh output of typically Indian yoga and uh put in 500 years after it there was a discussions uh in intensive discussions in Indian permitting I think how to uh make possible to divide by zero so it's you know mathematical zero is really uh Indian invention and it was recommended to carry that so Indian's contribution to mathematics was nothing nothing and other things it is very impossible it is a naming of nothing the name for nothing which uh make nothing equal to something yes it is it's kind of cool though that in some sense their culture and their religion sort of maybe conditioned them or it made them open to the concept of nothingness and that and that it required a name and that perhaps the west and western cultures um were less open to that because their culture didn't really have a philosophical or or cultural basis to really appreciate the importance of nothing yeah sure sure sure you are completely right and actually one of the origin of mathematics not on the counting not on the numbers but uh theological disputes and so uh the disputes about the naming of gods and uh actually there was a dispute about naming of nothing and so on and so on and so on they and uh actually uh if you look at uh mathematical in your house there is ashes either in internet so uh who learned from whom then uh any runes goes through uh these ideologies and it is actually uh logical disputes uh is pretty pretty relative to this question and the uh provides a great input in the kind of mathematical word is learning now um yeah you know I didn't expect to land at this place but uh after this discussion but maybe we should all take another look at the Bhagavad Gita oh yes and so to uh Indian uh the previous brand of Indian philosophy yeah I'll watch it for example extremely interesting so kind of yoga of uh is only yes yes indeed yeah I find it interesting um that India um I find that like there's a um the idea of giving nothing to mathematics is is somewhat um contradictory on the surface and you see these surface contradictions that seem to be um inherent in certain philosophy like or certain ways of thinking like meditation part of an Indian culture is meditation and in order to clear your mind you're supposed to allow yourself to think of things during meditation and conscious of what you're thinking of and then you let them go doing that repeatedly breathing correctly yes that's right it's quieting the monkey mind in your head exactly so that's they embrace contradictions in their culture and so they would see the value of nothing yes sure sure actually uh I'm spending sometimes sometimes uh in the south of India where all this development of Indian mathematics was gone and so they up to now have absolutely unique tradition of teaching mathematics so in homes in in small colleges near temples and they they are using some pedagogical x which is unknown to us and so they really can simple people really can count and so have some interesting view and understanding of mathematics is turn off your mind relax and float downstream it is not dying okay on that uh off off key note uh i'm regret we really should wrap it up here we're at our time limit i think i want to thank our panelists who were fantastic today and for our students for their enjoyable commentary and to Chan and Jess for organizing today's talk and here i will gavel our panel discussion to a close thanks everyone thank you everybody yeah thanks thanks thanks to everyone for coming thanks to the organizers thanks to my other panel panel members and to Matthew