The physics toolkit

W.D.Clinger said:
Evidence?

Tony seldom agrees with people who possess real technical ability, so we can't just take his word for it.

No competent scientist would ever use the MacQueen-Szamboti data to argue that no jolts occurred during the collapse. Even Tony appears to have acknowledged that the data presented in his paper do not support that argument.

Despite its obvious nonsense, that paper has not been retracted, repudiated, or withdrawn by its authors.
Click to expand...

That's the ludicrous part of arguing with Tony. Not only does he pretend to have reached conclusions that based on his own data are incorrect, he claims to have a superior grasp of the core concepts when has demonstrated he does not.
 
DGM said:
You didn't really answer my question. Is CD really a requirement for MIHOP? I really don't think so, LIHOP on the other hand definitely excludes it.
Click to expand...

If the plane strikes had anything to do with the buildings actually coming down then maybe your point would be well taken, but there is no chance they did. The wings never made it to the central cores and volumetrically the fuselage could have flown clear through the building and still not have caused a structural concern. They were nothing but a causal ruse.
 
Tony Szamboti said:
If the plane strikes had anything to do with the buildings actually coming down then maybe your point would be well taken, but there is no chance they did. The wings never made it to the central cores and volumetrically the fuselage could have flown clear through the building and still not have caused a structural concern. They were nothing but a causal ruse.
Click to expand...
OK, Thanks.
 
W.D.Clinger said:
Evidence?

Tony seldom agrees with people who possess real technical ability, so we can't just take his word for it.

No competent scientist would ever use the MacQueen-Szamboti data to argue that no jolts occurred during the collapse. Even Tony appears to have acknowledged that the data presented in his paper do not support that argument.

Despite its obvious nonsense, that paper has not been retracted, repudiated, or withdrawn by its authors.
Click to expand...

There is no deceleration in the fall of WTC 1 and you have to know it.

Even if you accept that the feeble little blips in femr2's graphs are some sort of miniscule deceleration they are nowhere near enough to cause building collapse.

You should really be trying to figure out just what could have taken those buildings down if there was no deceleration. The fact that you aren't is puzzling and sort of says you are not interested in what actually happened.
 
Tony Szamboti said:
If the plane strikes had anything to do with the buildings actually coming down then maybe your point would be well taken, but there is no chance they did. The wings never made it to the central cores and volumetrically the fuselage could have flown clear through the building and still not have caused a structural concern. They were nothing but a causal ruse.
Click to expand...


That's about the most detailed analysis I've ever seen from a truther.

Tony has slipped into Christophera land......
 
AZCat said:
Gravity.

It's always been gravity, deceleration or no deceleration.
Click to expand...

Really, so I guess you have some sort of different phenomena to explain why the buildings could stand to begin with.

You really are quite amazingly talented when it comes to not providing technical detail in your responses.

The reality is that a deceleration is necessary to provide an amplified load since the building structure below was designed to handle several times the load above it.
 
Tony Szamboti said:
Even if you accept that the feeble little blips in femr2's graphs are some sort of miniscule deceleration they are nowhere near enough to cause building collapse.
Click to expand...
It's this kind of thing that results in me responding to you Tony.

What ? Cause building collapse ? That's what I was trying to get you to see by saying *wrong end of the chain*.

The low magnitude points of deceleration (which are definitely there) don't cause anything at all. They are the result of some collision events which produce jolts at the NW corner.

Now then...

There are NO large magnitude jolts traceable at the NW corner. No-one is arguing that point in the slightest. They are not there.

Everyone OK with that, yes ?

Observation shows that the perimeter sheets do not collide, but overlap as they descend, so no ginourmous jolts are expected from perimeter-perimeter collisions.

That leaves core and OOS regions.

The ROOSD study shows visually confirmable detail which indicates that the internal *debris avalance* consisting essentially of pancaking floors descended far in advance of the trailing level of perimeter destruction, which consisted primarily of *peeling* (caused by the debris funnel descending behind the *crush fronts* pressing outwards upon the perimeter).

As the floor descents preceed the outwardly visible destruction, there's no reason to think there should be any OOS-OOS floor collisions that are traceable at the NW corner.

The core destruction is not well described imo, but it's feasible that the upper 50/60 floors of the core could have been dismembered by the descending debris. CC's are surprisingly skinny up there.

But as I've just described the floors descending first, there's very little connecting the core to the NW corner (hat truss, yeah, but soon as the cap separates, nowt), and again, I wouldn't expect to see huge jolts in that scenario. I know you don't agree.

Elements of initiation, I'm not happy about, but am not going to be jumping up and down making claims without getting my hands very dirty first.

Now, Tony, reading between the lines of what I've just written, I've put on the table... a mechanism which strips the floors from the core and perimeter, and forces the perimeter outwards in peeling motion, leaving only the lower portion of the core standing.

And barring said initiation unhappiness :( there's nowt there that intrinsically requires anything except gravity.

I've also described where and why I don't think the observed mechanism of destruction leaves much room for the sort of jolts you're looking for.

I'm also firmly leaving the door open on the initiation side of things.

Stop talking about jolts. It's boring. They are not there.

Apply your time to a detailed description of initiation that supports your position, and absolutely matches observables.
 
Last edited:
Seymour Butz said:
That's about the most detailed analysis I've ever seen from a truther.

Tony has slipped into Christophera land......
Click to expand...

Dangerously close to Jammoniousville. After all saying the planes were a ruse is right next to saying there were no planes.
 
Tony,

Why are you so constantly sloppy. It is not possible to be technically competent if you're sloppy.

Tony Szamboti said:
If you are actually claiming that NIST does not admit that WTC 7 fell at freefall acceleration for 2.25 seconds ...
Click to expand...

That's not what you said. You're sloppy.

That's not what I objected to. You're sloppy.

This was your comment.

Tony Szamboti said:
These methods also showed WTC 7 was undergoing full freefall acceleration during the first 2.25 seconds of its fall, which NIST admitted was true.
Click to expand...

It's sloppy & wrong.

Tony Szamboti said:
... then you aren't worth responding to.
Click to expand...

You're unremitting sloppiness makes conversation with you tedious, Tony.
It's also what makes your analyses so consistently flawed.

Why don't you try again to state what NIST really said accurately?


Tom
 
Tony Szamboti said:
Really, so I guess you have some sort of different phenomena to explain why the buildings could stand to begin with.

You really are quite amazingly talented when it comes to not providing technical detail in your responses.

The reality is that a deceleration is necessary to provide an amplified load since the building structure below was designed to handle several times the load above it.
Click to expand...

The building structure was no longer intact due to collision damage and was further weakened by fire till it failed due to gravity.
 
tfk said:
Tony,

Why are you so constantly sloppy. It is not possible to be technically competent if you're sloppy.



That's not what you said. You're sloppy.

That's not what I objected to. You're sloppy.

This was your comment.



It's sloppy & wrong.



You're unremitting sloppiness makes conversation with you tedious, Tony.
It's also what makes your analyses so consistently flawed.

Why don't you try again to state what NIST really said accurately?


Tom
Click to expand...

Tom,

After this reply there is only one way I will respond to you and your spin, and that is in a televised debate like you challenged me to on Hardfire through its host Ron Wieck about six to eight months ago.

I told Ron I would be glad to debate you as long as you publicly stated who you were. He said you would have to and then I didn't hear any more about it. What happened?
 
Last edited:
tsig said:
The building structure was no longer intact due to collision damage and was further weakened by fire till it failed due to gravity.
Click to expand...

It could not fail purely due to gravity without deceleration and velocity loss, as the load above was insufficient to overcome the reserve strength of the structure below without amplification, which requires deceleration and velocity loss.
 
Tony Szamboti said:
There is no deceleration in the fall of WTC 1 and you have to know it.
Click to expand...
No, Tony, I don't know for certain whether there were decelerations (or jolts, as you call them).

On the other hand, both Chandler's data and the MacQueen-Szamboti data suggest there were decelerations.

Two things I know for certain:
  1. For each of those datasets, there exist infinitely many continuous and differentiable acceleration functions that are consistent with the dataset and imply actual decelerations.
  2. No competent scientist would use either dataset to argue there were no actual decelerations.
For both of those datasets, it is easier to come up with a plausible, continuous, and differentiable acceleration function that implies decelerations than it is to come up with one that doesn't imply decelerations. I will illustrate that point in another post.

I suppose I should also dredge up the old "Missing Jolt" thread and post my analysis of the MacQueen-Szamboti data there. If you'd prefer I discuss your newer data, then you should make that raw data available. Don't just post four data points to JREF and then pretend you've presented your raw data for inspection.

Tony Szamboti said:
You should really be trying to figure out just what could have taken those buildings down if there was no deceleration. The fact that you aren't is puzzling and sort of says you are not interested in what actually happened.
Click to expand...
Several points for you to ponder:
  • No one has shown there was no deceleration.
  • The available data are consistent with decelerations, and it is moderately difficult to come up with a scientifically plausible acceleration function that is consistent with the data and does not imply a deceleration.
  • Even if we could somehow establish that there was no deceleration of some feature near the roof, that would not imply there were no decelerations of features on the failing substructures.
  • Not all possible mechanisms of collapse require decelerations.
  • I am more interested in what actually happened than in what puzzles someone who continues to defend a preconceived conclusion that contradicts his own raw data.
 
Tony Szamboti said:
Really, so I guess you have some sort of different phenomena to explain why the buildings could stand to begin with.
Click to expand...
If you have some explanation other than gravity you certainly haven't presented sufficient evidence here. Even controlled demolitions rely on gravity. Are you headed off into Judy Woods territory?

You really are quite amazingly talented when it comes to not providing technical detail in your responses.
Click to expand...
What responses would those be? The ones where I performed some elementary calculations that proved your conclusions were incorrect based on the data you provided? Yeah, I didn't provide much detail. Since the math I used was from high school I figured a big bad engineer like you wouldn't need me to walk you through every step.

The reality is that a deceleration is necessary to provide an amplified load since the building structure below was designed to handle several times the load above it.
Click to expand...
This argument again? It's been refuted on several forums (including this one), yet you continue to bring it out like it's still valid.
 
Tony Szamboti said:
Really, so I guess you have some sort of different phenomena to explain why the buildings could stand to begin with.
.
Click to expand...

Steel buildings stand up just fine unless they catch fire and people are unable to fight the fire.
 
Tony Szamboti said:
It could not fail purely due to gravity without deceleration and velocity loss, as the load above was insufficient to overcome the reserve strength of the structure below without amplification, which requires deceleration and velocity loss.
Click to expand...

So we should have expected the building to stand indefinitely in spite of structural damage and fire?
 
AZCat said:
If you have some explanation other than gravity you certainly haven't presented sufficient evidence here. Even controlled demolitions rely on gravity. Are you headed off into Judy Woods territory?
Click to expand...

Not at all. Controlled demolitions rely on gravity after they break enough of it loose to generate enough momentum to cause a significant dynamic load. A dynamic load and its amplification require deceleration which isn't observed in WTC 1. It is obvious that unnatural forces were breaking up the building since no deceleration was observed after the alleged fire instigated initiation.

You keep dancing around this but it is plain as day.
 
tsig said:
So we should have expected the building to stand indefinitely in spite of structural damage and fire?
Click to expand...

The structural damage and fire were not sufficient to cause the collapse initiation let alone a continuation of the collapse.
 
Tony Szamboti said:
Not at all. Controlled demolitions rely on gravity after they break enough of it loose to generate enough momentum to cause a significant dynamic load. A dynamic load and its amplification require deceleration which isn't observed in WTC 1. It is obvious that unnatural forces were breaking up the building since no deceleration was observed after the alleged fire instigated initiation.

You keep dancing around this but it is plain as day.
Click to expand...

Your stupid paper has been exposed. You are a charlatan Tony. A liar and a charlatan.
 
Tony Szamboti said:
The structural damage and fire were not sufficient to cause the collapse initiation.
Click to expand...


I must have missed the earth shattering paper you did that debunked the NIST report.

That must have been quite the achievement without all the structural details avaiable to you.

So how did you do this?

Oh, that's right, I forgot.

You're a liar.
 
funk de fino said:
Your stupid paper has been exposed. You are a charlatan Tony. A liar and a charlatan.
Click to expand...

The premise of the paper is correct and it doesn't matter what kind of comments anonymous freaks want to make about it or me. There should have been a serious deceleration of the upper section of WTC 1 after its initial fall if it had been a natural collapse.
 
Tony Szamboti said:
The premise of the paper is correct and it doesn't matter what kind of comments anonymous freaks want to make about it or me. There should have been a serious deceleration of the upper section of WTC 1 after its initial fall if it had been a natural collapse.
Click to expand...

Your own paper debunked your claims here. That made it doubly funny. keep repeating your nonsense Tony. No-one is paying any attention to your claims. Even other truthers laugh at them.

You tried to claim Verinage was the same as the WTC. The whole point of the Verinage is what we are saying the WTC did not do, because the WTC tilted. You tried for months to claim no tilt when everyone could see it. You lied about Larry.

Is there anything you will not stoop to? Any barrel you will not scrape.
 
funk de fino said:
Your own paper debunked your claims here. That made it doubly funny. keep repeating your nonsense Tony. No-one is paying any attention to your claims. Even other truthers laugh at them.

You tried to claim Verinage was the same as the WTC. The whole point of the Verinage is what we are saying the WTC did not do, because the WTC tilted. You tried for months to claim no tilt when everyone could see it. You lied about Larry.

Is there anything you will not stoop to? Any barrel you will not scrape.
Click to expand...

There was very little if any tilt of WTC 1's upper section before it started to descend. This has been proven and it has been shown that it could not cause enough misalignment to prevent a jolt in a natural collapse.

Some others here have tried to say the tilt caused separate impacts spread over time, which would keep a large jolt from being observable. However, the separate jolts of the exterior should still be observable. So the tilt does not explain why there is no deceleration of the exterior faces, especially the north face, which was the hinge for the tilt.

You are just blowing smoke Funk and it is apparent that you are the one stooping quite low.
 
Last edited:
AZCat said:
That's the ludicrous part of arguing with Tony. Not only does he pretend to have reached conclusions that based on his own data are incorrect, he claims to have a superior grasp of the core concepts when has demonstrated he does not.
Click to expand...

If you've ever heard the saying... "I reject your reality and substitute it with my own" you kind of have idea of what you're dealing with. Debating somebody like that is like banging your head against a boulder.
 
Tony Szamboti said:
There was very little if any tilt of WTC 1's upper section before it started to descend.
Click to expand...
Roughly 1 degree.

Saying things like *if any* does not do you any favours at all Tony. One might even think you are deliberately making your statement vague to imply ZERO degrees. That would be rather a shameful trick.

This has been proven and it has been shown that it could not cause enough misalignment to prevent a jolt in a natural collapse.
Click to expand...
False. Proven by whom exactly ?
I assume you are referring to MY accurate 3D core model.
Clarify.

Some others here have tried to say the tilt caused separate impacts spread over time
Click to expand...
100% guaranteed to. Impossible to be otherwise. Not that the reality of the situation is that simple. There would be no virtual clean breaks in CCs. Try and get the rigid virtual model out of mind Tony.

which would keep a large jolt from being observable.
Click to expand...
You are talking about jolts again. It's very boring.
You need to move forward and start describing the initiation mechanism, with or without explosives. The description of the initiation behaviour is the same regardless. We can SEE it.

However, the separate jolts of the exterior should still be observable.
Click to expand...
Tony, how many times do I have to remind you that the perimeters overlapped in the real world.

What is impacting what ?

Show me.

So the tilt does not explain why there is no deceleration of the exterior faces, especially the north face, which was the hinge for the tilt.
Click to expand...
False. The North face is the one we can see most clearly. And what we see is overlapping perimeters, not impacting perimeters.

You are just blowing smoke Funk and it is apparent that you are the one stooping quite low.
Click to expand...
Ahem.

I'm not in the habit of being accused of being a *fake* MIHOP'er. I suggest you get your act together Tony.

I have no reason to doubt your technical background, but the discussion recently is showing willful ignorance of the visual evidence we can all simply WATCH.

If your opinion does not match with the visual evidence, it's simply wrong, and I will not feel bad for reminding you of such at every point in time I notice it occuring.

Sort it out.

(Would have been better to have this discussion in private *back home*, but am afraid I don't take kindly to the kind of accusations you've been throwing around.)
 
femr2 said:
...

(Would have been better to have this discussion in private *back home*, but am afraid I don't take kindly to the kind of accusations you've been throwing around.)
Click to expand...


Just curious, why do you say this? Isn't public debate healthy for a theory and generally an accepted part of the scientific method?
 
Hokulele said:
Just curious, why do you say this? Isn't public debate healthy for a theory and generally an accepted part of the scientific method?
Click to expand...

I have no problem with public debate. I get no pleasure from such negative discussion or forcing any public embarrassment however. Tony has provided me with useful information both in the past and present, but it would be better if he did not say silly things (such as implying zero degree tilt), or make ridiculous accusations. Such discussion has nothing to do with the scientific method.
 
the Chandler-MacQueen-Szamboti fallacy

In separate papers, David Chandler and MacQueen/Szamboti have argued that
David Chandler said:
The roof line of the North Tower of the World Trade Center is shown to have been in constant downward acceleration until it disappeared.
Click to expand...
As I will demonstrate in this post, that argument is fallacious. As I will show below, plausible interpretations of the raw data presented by Chandler and by MacQueen/Szamboti involve brief upward accelerations.

At its core, the Chandler-MacQueen-Szamboti argument is built upon naive misapplication of the Shannon-Nyquist sampling theoremWP. That theorem asserts that it is possible to reconstruct a signal from regularly spaced samples provided

  1. There are infinitely many samples.
  2. The signal is band-limited.
  3. The sampling rate exceeds the signal's Nyquist rateWP.
Whenever Chandler or MacQueen/Szamboti claim that no decelerations are seen in their data, they are implicitly appealing to this fundamental sampling theorem. That argument is fallacious because

  1. There are only finitely many samples in their data.
  2. The signal is not known to be band-limited.
  3. The sampling rate is lower than the Nyquist rateWP expected for the signal.
Point 1 (finitely many samples) isn't so bad: It just means we'll get an imperfect estimate of the original signal instead of a perfect reconstruction.

Points 2 and 3 are fatal to the Chandler-MacQueen-Szamboti argument. Because the signal is not known to be band-limited, and the sampling rate is too low for a signal that contains jolts as brief as the ones that Chandler, MacQueen, and Szamboti are attempting to rule out, there are infinitely many reconstructions of the signal from their sampled position data. The more plausible reconstructions contain the decelerations that Chandler, MacQueen, and Szamboti have been denying.

Before I demonstrate that fact using three specific reconstructions that match Chandler's data, let's take a moment to consider how such a fundamental mistake could have been made by a teacher of high school science, a professor of religious studies, and a mechanical engineer. The sampling theorem is important for electrical engineering, and a required topic in undergraduate EE curricula. It is less important for mechanical engineering, and I do not know whether it is even a required topic for ME or physics majors. It is not a required topic in most undergraduate math curricula, although it would be covered in some elective courses.

It is therefore quite possible that Chandler, MacQueen, and Szamboti never encountered the fundamental theorem of sampling during their formal education, or have simply forgotten its details. That may excuse their ignorance of the theorem on which their "argument" rests, but it does not excuse their arrogance and arguments from false authority. Building your argument upon mathematics you don't understand seldom ends well.

To illustrate the range of signals that will fit sampled position data, I will use Chandler's raw data as reported on pages 6 and 7 of

David Chandler. Destruction of the World Trade Center North Tower and Fundamental Physics (Interpreted for a less technical audience).
http://journalof911studies.com/volume/2010/ChandlerDownwardAccelerationOfWTC1.pdf

These data were obtained using the Tracker program, which Tony Szamboti used to obtain the four new data points he has made public. Chandler's data measure the height (in meters) of the North Tower's roof at intervals of 1/5 second. To facilitate comparison with the MacQueen/Szamboti data, I converted Chandler's heights to distance fallen, but left the data in meters. (The MacQueen/Szamboti data are in feet.) I set the time origin to the (approximate) beginning of the collapse.

Here is a graph of Chandler's data, on which I have overlain three different reconstructions of the signal:

chandlerY.jpg


All three reconstructions match Chandler's data and each other so well that you can't see the tiny differences between them in that graph. The differences will become more visible when we differentiate the reconstructed signals (to obtain their instantaneous velocities), and will become obvious when we differentiate a second time (to obtain their instantaneous accelerations). Had Chandler, MacQueen, and Szamboti understood that tiny differences in a position signal often correspond to large differences in acceleration, they might have been more careful when drawing conclusions from their sampled data.

The reconstruction labelled "degree 0" corresponds to a (piecewise constant) step acceleration that is neither continuous nor differentiable at the sampled times. The reconstructions labelled "degree 2" and "degree 10" correspond to piecewise polynomial accelerations of the form

a(t) = g - c [(h/2)2 - (t - m)2]n
where g is the acceleration of gravity, h is the width of each interval, m is the midpoint of an interval, n=1 or n=5 is one half of the polynomial's degree, and c is the interval-specific constant that matches the acceleration to Chandler's data. These piecewise polynomial accelerations are continuous, and are differentiable even at the endpoints if n>1. In addition, the downward acceleration is limited to 1g; without that limit, noise in the data would lead to brief downward accelerations of greater than 1g, which is physically impossible. Using the raw data and the information in this paragraph, it is a (mildly tedious) exercise in freshman calculus to reproduce every graph in this post.

Differentiation of the three reconstructed position signals is equivalent to integration of the accelerations described above. Both processes yield the following instantaneous velocities:

chandlerV.jpg


The reconstructions of degree 2 and 10 imply actual decelerations near 0.5, 1.1, 1.9, 2.7, and 3.1 seconds. The reconstruction of degree 0 does not involve actual decelerations, but comes close to a deceleration at those five times, and comes very close at 0.5 and 3.1 seconds. Here is a graph of the accelerations that (when integrated) yield the velocity and position signals shown in the previous graphs:

chandlerA.jpg


Before t=0, the roof was basically stationary, with some small shaking. The stepwise acceleration is approximately zero for t<0, and that is the most plausible reconstruction at that time. At or around t=0, something gave way and the roof entered free fall (9.8 meters per second squared) for 200+ milliseconds. That free fall ended sometime between 200 and 400 milliseconds; from the sampled position data, it is impossible to say whether the free fall ended with resistance that kept the acceleration between 0g and 1g (as illustrated by the step function) or with a series of much larger and briefer jolts (as illustrated by the curves for degree 2 and 10).

Consider, however, the interval from 3.0 to 3.2 seconds. The area under the acceleration curve within that integral cannot be changed without damaging the fit to Chandler's data. It is very unlikely that the acceleration that actually occurred during that interval corresponds to a large step whose sides just happen to match up perfectly with the endpoints of that interval. It is far more plausible that the acceleration during that interval is more accurately modelled by the curves for degree 2 and 10. Both of those curves imply actual decelerations during that interval, as do most other plausible reconstructions for that interval.

Similarly, most plausible reconstructions for the signal near 0.5, 1.1, 1.9, and 2.7 seconds involve actual decelerations.

By now it should be obvious that no competent scientist would ever attempt to argue that Chandler's data are inconsistent with decelerations.

What about the MacQueen/Chandler data? Here are the accelerations calculated from the raw data contained within the current (7th?!!!) version of their "Missing Jolt" paper:

szambotiA.jpg


Even the stepwise (degree 0) model of acceleration implies actual decelerations near 0.5, 1.75, and 3.1 seconds. It's pretty hard to come up with a continuous acceleration function that fits the MacQueen/Szamboti data but does not involve decelerations.

For the corresponding velocity and position functions reconstructed from the (current) MacQueen/Szamboti data, see:
http://www.cesura17.net/~will/Ephemera/Sept11/Szamboti/szambotiV.jpg
http://www.cesura17.net/~will/Ephemera/Sept11/Szamboti/szambotiY.jpg

Comparing the accelerations reconstructed from Chandler's data to the accelerations reconstructed from the MacQueen/Szamboti data, some similarities are obvious but the differences are obvious also. Some of those differences may be attributable to the use of Tracker versus hand tracking, but another important difference is that Chandler and MacQueen/Szamboti tracked the descent of different roof features. Not every feature on the roof descended at exactly the same rate at every time.

From that, it follows that we should be cautious about drawing conclusions from any one set of sampled data; another set of data might not support our conclusions. In particular, we should be wary of arguments that use roof data to draw conclusions about the zone of impact. The upper section was not perfectly rigid, so accelerations reconstructed from roof data are likely to be less severe than the jolts occurring several floors below.

To summarize:
  • The Chandler-MacQueen-Szamboti fallacy is built upon failure to understand the fundamental theorem of sampling.
  • Most plausible reconstructions of the raw data published by Chandler and by MacQueen/Szamboti involve actual decelerations.
  • No competent scientist would argue that the sampled data rule out decelerations.
 
You must log in or register to reply here.

Back
Top Bottom